CRYSTALLIZATION BEHAVIOR OF A THERMOTROPIC LIQUID CRYSTAL COPOLYESTER

晶化温度对Li2O2ZnO2Al2O32SiO2微晶玻璃物相组成和热膨胀系数的影响隋普辉,陆雷,武相萍,吴国芳(南京工业大学材料科学与工程学院,江苏南京210009)摘　要:采用D TA、XRD、SEM、热膨胀仪等仪器研究了晶化温度对Li2O2ZnO2Al2O3SiO2微晶玻璃的物相组成以及热膨胀系数的影响。

结果表明:在晶化温度为625℃时,微晶玻璃中析出βⅡ2Li2ZnSiO4晶相,650℃时又析出少量方石英晶相;随着晶化温度上升,方石英相逐渐转化为β2石英固溶体,至750℃时βⅡ2Li2ZnSiO4晶相开始转化为γ02Li2ZnSiO4晶相;当温度高于800℃后,微晶玻璃中主要含有β2石英固溶体和γ02Li2ZnSiO4两种晶相,并且晶粒尺寸变大;不同晶化温度下制得微晶玻璃的热膨胀系数在(72～119)×10-7℃-1(20～500℃)之间,随着晶化温度的升高,试样的热膨胀系数先升高而后下降,然后趋于平稳,在650℃达到最大。

关键词:微晶玻璃;晶化温度;热膨胀系数中图分类号:TQ171 文献标志码:A 文章编号:100023738(2009)0520014204E ffect of Crystallization T emperature on Phase Composition and ThermalExpansion Coeff icient of Li2O2ZnO2Al2O32SiO2G lass2ceramicsSUI Pu2hui,L U Lei,WU Xiang2ping,WU G uo2fang(Nanjing U niversity of Technology,Nanjing210009,China)Abstract:The effect of crystallization temperature on the phase composition and thermal expansion coefficient (TEC)of Li2O2ZnO2Al2O32SiO2(L ZAS)glass2ceramic was studied by means of D TA,XRD,SEM and thermal analyzer methods.The results show that the crystallization ofβⅡ2Li2ZnSiO4occurred after the glass was treated at 625℃,and cristobalite crystallite formed at650℃;thenβ2quartz solid solutions replaced cristobalite crystallite gradually with the temperature increasing.The transformation f romβⅡ2Li2ZnSiO4toγ02Li2ZnSiO4took place at 750℃.The crystallization phases in the glass2ceramics obtained at the temperature higher than800℃were β2quartz solid solutions andγ02Li2ZnSiO4,and the size of crystal particles increased gradually.The thermal expansion coefficient of the glass2ceramics which formed at different crystallization temperatures varied from 72×10-7℃-1to119×10-7℃-1in the temperature range of20-500℃,which increased first and reached to the maxinum at650℃,then decreased and changed to be steady.K ey w ords:glass2ceramic;crystallization temperature;thermal expansion coefficient0　引　言封接玻璃分为结晶型玻璃(微晶玻璃)和非结晶型玻璃两种[1],它具有较强的绝缘性,主要用于电真空器件中的金属部件封装。

Crystallization原文：Crystallization is a technique which chemists use to purify solid compounds. It is one of the fundamental procedures each chemist must master to become proficient in the laboratory. Crystallization is based on the principles of solubility: compounds (solutes) tend to be more soluble in hot liquids (solvents) than they are in cold liquids. If a saturated hot solution is allowed to cool, the solute is no longer soluble in thesolvent and forms crystals of pure compound. Impurities are excluded from thegrowing crystals and the pure solid crystals can be separated from the dissolvedimpurities by filtration.(1).Heat some solvent to boiling. Place the solid to be recrystallizedin an Erlenmeyer flask. (2).Pour a small amount of the hot solvent into the flaskcontaining the solid.(3).Swirl the flask to dissolve the solid.(4).Place the flask on the steam bath to keep the solution warm.(5).If the solid is still not dissolved, add a tiny amount more solvent and swirl again.(6).When the solid is all in solution, set it on the bench top.Do not disturb it!(7).After a while, crystals shouldappear in the flask. (8).You can now place the flaskin an ice bath to finish thecrystallization process.翻译：结晶是一种技术，化学家利用它净化固体化合物。

a rXiv:c ond-ma t/9411013v12Nov1994Concentration and energy fluctuations in a critical polymer mixture M.M¨u ller and N.B.Wilding Institut f¨u r Physik,Johannes Gutenberg Universit¨a t,Staudinger Weg 7,D-55099Mainz,Germany Abstract A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB)polymer mixture.By applying the equal peak-weight criterion to the concentration distribution,the coexistence curve separating the A-rich and B-rich phases is identified as a function of temperature and chemical potential.To locate the critical point of the model,the cumulant intersection method is used.The accuracy of this approach for determining the critical parameters of fluids is assessed.Attention is then focused on the joint distribution function of the critical concentration and energy,which is analysed using a mixed-field finite-size-scaling theory that takes due account of the lack of symme-try between the coexisting phases.The essential Ising character of the binary polymer critical point is confirmed by mapping the critical scaling operator distributions onto in-dependently known forms appropriate to the 3D Ising universality class.In the process,estimates are obtained for the field mixing parameters of the model which are compared both with those yielded by a previous method,and with the predictions of a mean field calculation.PACS numbers 64.70Ja,05.70.Jk1IntroductionThe critical point of binary liquid and binary polymer mixtures,has been a subject of abidinginterest to experimentalists and theorists alike for many years now.It is now well established that the critical point properties of binary liquid mixtures fall into the Ising universality class(the default for systems with short ranged interactions and a scalar order parameter)[1]. Recent experimental studies also suggest that the same is true for polymer mixtures[2]–[11].However,since Ising-like critical behaviour is only apparent when the correlation length farexceeds the polymer radius of gyrationξ≫ R g ,the Ising regime in polymer mixtures is confined(for all but the shortest chain lengths)to a very narrow temperature range nearthe critical point.Outside this range a crossover to mean-field type behaviour is seen.Theextent of the Ising region is predicted to narrow with increasing molecular weight in a manner governed by the Ginsburg criterion[12],disappearing entirely in the limit of infinite molecular weight.Although experimental studies of mixtures with differing molecular weights appear to confirm qualitatively this behaviour[5],there are severe problems in understanding the scaling of the so-called“Ginsburg number”(which marks the centre of the crossover region and is empirically extracted from the experimental data[13])with molecular weight Computer simulation potentially offers an additional source of physical insight into polymer critical behaviour,complementing that available from theory and experiment.Unfortunately, simulations of binary polymer mixtures are considerable more exacting in computational terms than those of simple liquid or magnetic systems.The difficulties stem from the problems of deal-ing with the extended physical structure of polymers.In conventional canonical simulations, this gives rise to extremely slow polymer diffusion rates,manifest in protracted correlation times[14,15].Moreover,the canonical ensemble does not easily permit a satisfactory treat-ment of concentrationfluctuations,which are an essential feature of the near-critical region in polymer mixture.In this latter regard,semi-grand-canonical ensemble(SGCE)Monte Carlo schemes are potentially more attractive than their canonical counterparts.In SGCE schemes one attempts to exchange a polymer of species A for one of species B or vice-versa,thereby permitting the concentration of the two species tofluctuate.Owing,however,to excluded volume restrictions,the acceptance rate for such exchanges is in general prohibitively small, except in the restricted case of symmetric polymer mixtures,where the molecular weights of the two coexisting species are identical(N A=N B).All previous simulation work has therefore focussed on these symmetric systems,mapping the phase diagram as a function of chain length and confirming the Ising character of the critical point[16,17,18].Tentative evidence for a crossover from Ising to meanfield behaviour away from the critical point was also obtained [19].Hitherto however,no simulation studies of asymmetric polymer mixtures(N A=N B) have been reported.Recently one of us has developed a new type of SGCE Monte Carlo method that amelio-rates somewhat the computational difficulties of dealing with asymmetric polymer mixtures [20].The method,which is described briefly in section3.1,permits the study of mixtures of polymer species of molecular weight N A and N B=kN A,with k=2,3,4···.In this paper we shall employ the new method to investigate the critical behaviour of such an asymmet-ric polymer mixture.In particular we shall focus on those aspects of the critical behaviour of asymmetric mixtures that differ from those of symmetric mixtures.These difference are rooted in the so called‘field mixing’phenomenon,which manifests the basic lack of energetic(Ising) symmetry between the coexisting phases of all realisticfluid systems.Although it is expected to have no bearing on the universal properties offluids,field mixing does engender certain non-universal effects in near-criticalfluids.The most celebrated of these is a weak energy-like critical singularity in the coexistence diameter[21,22],the existence of which constitutes afailure for the‘law of rectilinear diameter’.As we shall demonstrate however,field mixing has a far more legible signature in the interplay of the near-critical energy and concentration fluctuations,which are directly accessible to computer simulation.In computer simulation of critical phenomena,finite-size-scaling(FSS)techniques are of great utility in allowing one to extract asymptotic data from simulations offinite size[23].One particularly useful tool in this context is the order parameter distribution function[24,25,26]. Simulation studies of magnetic systems such as the Ising[25]andφ4models[27],demonstrate that the critical point form of the order parameter distribution function constitutes a useful hallmark of a university class.Recently however,FSS techniques have been extended tofluids by incorporatingfield mixing effects[28,29].The resulting mixed-field FSS theory has been successfully deployed in Monte Carlo studies of critical phenomena in the2D Lennard-Jones fluid[29]and the2D asymmetric lattice gas model[30].The present work extends this programme offield mixing studies to3D complexfluids with an investigation of an asymmetric polymer mixture.The principal features of our study are as follows.We begin by studying the order parameter(concentration)distribution as a function of temperature and chemical potential.The measured distribution is used in conjunction with the equal peak weight criterion to obtain the coexistence curve of the model.Owing to the presence offield mixing contributions to the concentration distribution,the equal weight criterion is found to break down near thefluid critical point.Its use to locate the coexistence curve and critical concentration therefore results in errors,the magnitude of which we gauge using scaling arguments.Thefield mixing component of the critical concentration distribution is then isolated and used to obtain estimates for thefield mixing parameters of the model. These estimates are compared with the results of a meanfield calculation.We then turn our attention to thefinite-size-scaling behaviour of the critical scaling op-erator distributions.This approach generalises that of previousfield mixing studies which concentrated largely on thefield mixing contribution to the order parameter distribution func-tion.We show that for certain choices of the non-universal critical parameters—the critical temperature,chemical potential and the twofield mixing parameters—these operator distri-butions can be mapped into close correspondence with independently known universal forms representative of the Ising universality class.This data collapse serves two purposes.Firstly,it acts as a powerful means for accurately determining the critical point andfield mixing param-eters of modelfluid systems.Secondly and more generally,it serves to clarify the sense of the universality linking the critical polymer mixture with the critical Ising magnet.We compare the ease and accuracy with which the critical parameters can be determined from the data collapse of the operator distributions,with that possible from studies of the order parameter distribution alone.It is argued that for criticalfluids the study of the scaling operator distri-butions represent the natural extension of the order parameter distribution analysis developed for models of the Ising symmetry.2BackgroundIn this section we review and extend the mixed-fieldfinite-size-scaling theory,placing it within the context of the present study.The system we consider comprises a mixture of two polymer species which we denote A and B,having lengths N A and N B monomers respectively.The configurational energyΦ(which we express in units of k B T)resides in the intra-and inter molecular pairwise interactions between monomers of the polymer chains:N i<j=1v(|r i−r j|)(2.1)Φ({r})=where N=n A N A+n b N B with n A and n B the number of A and B type polymers respectively. N is therefore the total number of monomers(of either species),which in the present study is maintained strictly constant.The inter-monomer potential v is assigned a square-well formv(r)=−ǫr≤r m(2.2)v(r)=0r>r mwhereǫis the well depth and r m denotes the maximum range of the potential.In accordance with previous studies of symmetric polymer mixtures[16,17],we assignǫ≡ǫAA=ǫBB=−ǫAB>0.The independent model parameters at our disposal are the chemical potential difference per monomer between the two species∆µ=µA−µB,and the well depthǫ(both in units of k B T). These quantities serve to control the observables of interest,namely the energy density u and the monomer concentrationsφA andφB.Since the overall monomer densityφN=φA+φB is fixed,however,it is sufficient to consider only one concentration variableφ,which we take as the concentration of A-type monomers:φ≡φA=L−d n A N A(2.3) The dimensionless energy density is defined as:u=L−dǫ−1Φ({r})(2.4) with d=3in the simulations to be chronicled below.The critical point of the model is located by critical values of the reduced chemical potential difference∆µc and reduced well-depthǫc.Deviations ofǫand∆µfrom their critical values control the sizes of the two relevant scalingfield that characterise the critical behaviour.In the absence of the special symmetry prevailing in the Ising model,onefinds that the relevant scalingfields comprise(asymptotically)linear combinations of the well-depth and chemical potential difference[21]:τ=ǫc−ǫ+s(∆µ−∆µc)h=∆µ−∆µc+r(ǫc−ǫ)(2.5) whereτis the thermal scalingfield and h is the ordering scalingfield.The parameters s and r are system-specific quantities controlling the degree offield mixing.In particular r is identifiable as the limiting critical gradient of the coexistence curve in the space of∆µandǫ. The role of s is somewhat less tangible;it controls the degree to which the chemical potential features in the thermal scalingfield,manifest in the widely observed critical singularity of the coexistence curve diameter offluids[1,22,31].Conjugate to the two relevant scalingfields are scaling operators E and M,which comprise linear combinations of the concentration and energy density[28,29]:M=11−sr[u−rφ](2.6) The operator M(which is conjugate to the orderingfield h)is termed the ordering operator, while E(conjugate to the thermalfield)is termed the energy-like operator.In the special caseof models of the Ising symmetry,(for which s=r=0),M is simply the magnetisation while E is the energy density.Near criticality,and in the limit of large system size L,the probability distributions p L(M) and p L(E)of the operators M and E are expected to be describable byfinite-size-scaling relations having the form[25,29]:p L(M)≃a M−1L d−λM˜p M(a M−1L d−λMδM,a M LλM h,a E LλEτ)(2.7a)p L(E)≃a E−1L d−λE˜p E(a E−1L d−λEδE,a M LλM h,a E LλEτ)(2.7b) whereδM≡M−M c andδE≡E−E c.The functions˜p M and˜p E are predicted to be universal,modulo the choice of boundary conditions and the system-specific scale-factors a M and a E of the two relevantfields,whose scaling indices areλM=d−β/νandλE=1/νrespectively.Precisely at criticality(h=τ=0)equations2.7a and 2.7b implyp L(M)≃a M−1Lβ/ν˜p⋆M(a M−1Lβ/νδM)(2.8a)p L(E)≃a E−1L(1−α)/ν˜p⋆E(a E−1L(1−α)/νδE)(2.8b) where˜p⋆M(x)≡˜p M(x,y=0,z=0)˜p⋆E(x)≡˜p E(x,y=0,z=0)(2.9) are functions describing the universal and statistically scale-invariantfluctuation spectra of the scaling operators,characteristic of the critical point.The claim that the binary polymer critical point belongs to the Ising universality class is expressed in its fullest form by the requirement that the critical distribution of thefluid scaling operators p L(M)and p L(E)match quantitatively their respective counterparts—the magneti-sation and energy distributions—in the canonical ensemble of the critical Ising magnet.As we shall demonstrate,these mappings also permit a straightforward and accurate determination of the values of thefield mixing parameters s and r of the model.An alternative route to obtaining estimates of thefield mixing parameters is via thefield mixing correction to the order parameter(i.e.concentration)distribution p L(φ).At criticality, this distribution takes the form[29,30]:p L(φ)≃a M−1Lβ/ν ˜p⋆M(x)−sa E a M−1L−(1−α−β)/ν∂∂x (˜p⋆M(x)˜ω⋆(x)),is a function characterising the mixing of the critical energy-like operator into the order parameter distribution.Thisfield mixing term is down on the first term by a factor L−(1−α−β)/νand therefore represents a correction to the large L lim-iting behaviour.Given further the symmetries of˜ω(x)and˜p⋆M(x),both of which are even (symmetric)in the scaling variable x[29],thefield mixing correction is the leading antisym-metric contribution to the concentration distribution.Accordingly,it can be isolated frommeasurements of the critical concentration distribution simply by antisymmetrising around φc= φ c.The values of s and r are then obtainable by matching the measured critical func-tion−s∂simply by cutting a B-type polymer into k equal segments.Conversely,a B-type polymer is manufactured by connecting together the ends of k A-type polymers.This latter operation is,of course,subject to condition that the connected ends satisfy the bond restrictions of the BFM.Consequently it represents the limiting factor for the efficiency of the method,since for large values of k and N A,the probability that k polymer ends simultaneously satisfy the bond restrictions becomes prohibitively small.The acceptance rate for SGCE moves is also further reduced by factors necessary to ensure that detailed balance is satisfied.In view of this we have chosen k=3,N A=10for the simulations described below,resulting in an acceptance rate for SGCE moves of approximately14%.In addition to the compositionalfluctuations associated with SGCE moves,it is also nec-essary to relax the polymer configurations at constant composition.This is facilitated by monomer moves which can be either of the local displacement form,or of the reptation(‘slith-ering snake’)variety[2].These moves were employed in conjunction with SGCE moves,in the following ratios:local displacement:reptation:semi-grandcanonical=4:12:1the choice of which was found empirically to relax the configurational and compositional modes of the system on approximately equal time scales.In the course of the simulations,a total offive system sizes were studied having linear extent L=32,40,50,64and80.An overall monomerfilling fraction of8φN=0.5was chosen, representative of a dense polymer melt[15].Here the factor of8constitutes the monomeric volume,each monomer occupying8lattice sites.The cutoffrange of the inter-monomeric√square well potential was set at r m=whereφ∗is a parameter defining the boundary between the two peaks.Well below criticality,the value of∆µcx obtained from the equal weight criterion is in-sensitive to the choice ofφ∗,provided it is taken to lie approximately midway between the peaks and well away from the tails.As criticality is approached however,the tails of the two peaks progressively overlap making it impossible to unambiguously define a peak in the manner expressed by equation3.1.For models of the Ising symmetry,for which the peaks are symmetric about the coexistence concentrationφcx,the correct value of∆µcx can nevertheless be obtained by choosingφ∗= φ in equation3.1.In near-criticalfluids,however,the imposed equal weight rule forces a shift in the chemical potential away from its coexistence value in or-der to compensate for the presence of thefield mixing component.Only in the limit as L→∞(where thefield mixing component dies away),will the critical order parameter distribution be symmetric allowing one to chooseφ∗= φ and still obtain the correct coexistence chemical potential.Thus forfinite-size systems,use of the equal weight criterion is expected to lead to errors in the determination of∆µcx near the critical point.Although this error is much smaller than the uncertainty in the location of the critical point along the coexistence curve (see below),it can lead to significant errors in estimates of the critical concentrationφc.To quantify the error inφc it is necessary to match the magnitude of thefield mixing component of the concentration distribution w(δp L),to the magnitude of the peak weight asymmetry w′(δµ)associated with small departuresδµ=∆µ−∆µcx from coexistence:w(δp L)=w′(δµ)(3.2) Now from equation2.10w(δp L)≈ φNφ∗dφδp L(φ)∼L−(1−α−β)/ν(3.3) whilew′(δµ)≈ φNφ∗dφ∂p L(φ)3 m2 2(3.7)where m2and m4are the second and fourth moments respectively of the order parameter m=φ− φ .To the extent thatfield mixing corrections can be neglected,the critical order parameter distribution function is expected to assume a universal scale invariant form. Accordingly,when plotted as a function ofǫ,the coexistence values of G L for different system sizes are expected to intersect at the critical well depthǫc[26].This method is particularly attractive for locating the critical point influid systems because the even moments of the order parameter distribution are insensitive to the antisymmetric(odd)field mixing contribution. Figure2displays the results of performing this cumulant analysis.A well-defined intersection point occurs for a value G L=0.47,in accord with previously published values for the3D Ising universality class[36].The corresponding estimates for the critical well depth and critical chemical potential areǫc=0.02756(15)∆µc=0.003603(15)It is important in this context,that a distinction be drawn between the errors on the location of the critical point,and the error with which the coexistence curve can be determined.The uncertainty in the position of the critical point along the coexistence curve,as determined from the cumulant intersection method,is in general considerably greater than the uncertainty in the location of the coexistence curve itself.This is because the order parameter distribution function is much more sensitive to small deviations offcoexistence(due tofiniteǫ−ǫcx orfinite ∆µ−∆µcx)than it is for deviations along the coexistence curve,(ǫand∆µtuned together to maintain equal weights).In the present case,wefind that the errors on∆µc andǫc are approximately10times those of the coexistence valuesǫcx and∆µcx near the critical point.The concentration distribution function at the assigned value ofǫc and the corresponding value of∆µcx,(determined according to the equal weight rule withφ∗=<φ>),is shown infigure3for the L=40and L=64system sizes.Also shown in thefigure is the critical magnetisation distribution function of the3D Ising model obtained in a separate study[37]. Clearly the L=40and L=64data differ from one another and from the limiting Ising form.These discrepancies manifest both the pure antisymmetricfield mixing component of the true(finite-size)critical concentration distribution,and small departures from coexistence associated with the inability of the equal weight rule to correctly identify the coexistence chemical potential.To extract the infinite-volume value ofφc from thefinite-size data,it is therefore necessary to extrapolate to the thermodynamic limit.To this end,and in accordance with equation3.6,we have plottedφcx(L),representing thefirst moment of the concentration distribution determined according to equal weight criterion at the assigned value ofǫc,against L(1−α)/ν.This extrapolation(figure4)yields the infinite-volume estimate:φc=0.03813(19)corresponding to a reduced A-monomer densityφc/φN=0.610(3).Thefinite-size shift in the value ofφcx(L)is of order2%.We turn next to the determination of thefield mixing parameters r and s.The value of r represents the limiting critical gradient of the coexistence curve which,to a good approxima-tion,can be simply read offfromfigure1with the result r=−0.97(3).Alternatively(and as detailed in[29])r may be obtained as the gradient of the line tangent to the measured critical energy function(equation2.11)atφ=φc.Carrying out this procedure yields r=−1.04(6).The procedure for extracting the value of thefield mixing parameter s from the concentra-tion distribution is rather more involved,and has been described in detail elsewhere[29,30]. The basic strategy is to choose s such as to satisfy∂δp L(φ)=−swhereδp L(φ)is the measured antisymmetricfield mixing component of the critical concen-tration distribution[30],obtained by antisymmetrising the concentration distribution about φc(L)and subtracting additional corrections associated with small departures from coexistence resulting from the failure of the equal weight rule.Carrying out this procedure for the L=40 and L=64critical concentration distributions yields thefield mixing components shown in figure5.The associated estimate for s is0.06(1).Also shown infigure5(solid line)is the predicted universal form of the3D order parameterfield mixing correction−∂u−rφ1−sr p L(E)=p Lsection2).This discrepancy implies that the system size is still too small to reveal the asymp-totic behaviour Nevertheless the data do afford a test of the approach to the limiting regime, via the FSS behaviour of the variance of the energy distribution.Recalling equation2.14, we anticipate that this variance exhibits the same FSS behaviour as the Ising susceptibility, namely:L d( u2 −u2c)∼Lγ/ν(3.10) By contrast,the variance of the scaling operator E is expected to display the FSS behaviour of the Ising specific heat:L d( E2 −E2c)∼Lα/ν.(3.11) Figure9shows the measured system size dependence of these two quantities at criticality.Also shown is the scaled variance of the ordering operator L d( M2 −M2c)∼Lγ/ν.Straight lines of the form Lγ/νand Lα/ν,(indicative of the FSS behaviour of the Ising susceptibility and specific heat respectively)have also been superimposed on the data.Clearly for large L,the scaling behaviour of the variance of the energy distribution does indeed appear to approach that of the ordering operator distribution.4Meanfield calculationsIn this section we derive approximate formulae for the values of thefield mixing parameters s and r on the basis of a meanfield calculation.Within the well-known Flory-Huggins theory of polymer mixtures,the mean-field equation of state takes the form:∆µ=1N Bln(1−ρ)−2zǫ(2ρ−1)+C(4.1)In this equation,z≈2.7is the effective monomer coordination number,whose value we have obtained from the measured pair correlation function.ρ=φ/φN is the density of A-type monomers and the constant C is the entropy density difference of the pure phases,which is independent of temperature and composition.In what follows we reexpressρby the concen-trationφ.The critical point is defined by the condition:∂∂φ2∆µc=0(4.2) where∆µc=∆µ(φc,ǫc).This relation can be used to determine the critical concentration and critical well-depth,for which onefindsφc1+1/√ǫc=z4N A N BN A+√where the expansion coefficients take the formr ′=−2z (2φc φN b =(1+√3√k )4φ+−φ−(4.6)where φ−and φ+denote the concentration of A monomers in the A-poor phase and A-rich phases respectively.Thus to leading order in ǫ,the phase boundary is given by :∆µcx (ǫ)=∆µc +r ′δǫc +···(4.7)Consequently we can identify the expansion coefficient r ′with the field mixing parameter r (c.f.equation 2.5)that controls the limiting critical gradient of the coexistence curve in the space of ∆µand ǫ.Substituting for ∆µc and ǫc in equation 4.7and setting k =3,we find r =−1.45,in order-of-magnitude agreement with the FSS analysis of the simulation data.In order to calculate the value of the field mixing parameter s ,it is necessary to obtain the concentration and energy densities of the coexisting phases near the critical point.The concentration of A-type monomers in each phase is given byδφ±=φ±−φc =± b −2acδǫ2−φc =−2acδǫ2 z s +z (2ρ−1)2 =−φN φN −1)2+rδφ−2z2−u (φc )=−2za5zb δǫ+···(4.11)Now since (1−rs ) M = δφ −s δu vanishes along the coexistence line,equations 4.9and4.11yield the following estimate for the field mixing parameter s :s = δφ 5zb 1+r cφN 20z √20z √[30].The sign of the product rs differs however from that found at the liquid-vapour critical point.In the present context this product is given byrs10(√NB)2N A N B(4.13)However an analogous treatment of the van der Waalsfluid predicts a positive sign rs,in agreement with that found at the liquid vapour critical point[29,30].5Concluding remarksIn summary we have employed a semi-grand-canonical Monte Carlo algorithm to explore the critical point behaviour of a binary polymer mixture.The near-critical concentration and scal-ing operator distributions have been analysed within the framework of a mixed-fieldfinite-size scaling theory.The scaling operator distributions were found to match independently known universal forms,thereby confirming the essential Ising character of the binary polymer critical point.Interestingly,this universal behaviour sets in on remarkably short length scales,being already evident in systems of linear extent L=32,containing only an average of approximately 100polymers.Regarding the specific computational issues raised by our study,wefind that the concen-tration distribution can be employed in conjunction with the cumulant intersection method and the equal weight rule to obtain a rather accurate estimate for the critical temperature and chemical potential.The accuracy of this estimate is not adversely affected by the anti-symmetric(odd)field mixing contribution to the order parameter distribution,since only even moments of the distribution feature in the cumulant ratio.Unfortunately,the method can lead to significant errors in estimates of the critical concentrationφc,which are sensitive to the magnitude of thefield mixing contribution.The infinite-volume value ofφc must therefore be estimated by extrapolating thefinite-size data to the thermodynamic limit(where thefield mixing component vanishes).Estimates of thefield mixing parameters s and r can also be extracted from thefield mixing component of the order parameter distribution,although in practice wefind that they can be determined more accurately and straightforwardly from the data collapse of the scaling operators onto their universalfixed point forms.In addition to clarifying the universal aspects of the binary polymer critical point,the results of this study also serve more generally to underline the crucial role offield mixing in the behaviour of criticalfluids.This is exhibited most strikingly in the form of the critical energy distribution,which in contrast to models of the Ising symmetry,is doubly peaked with variance controlled by the Ising susceptibility exponent.Clearly therefore close attention must be paid tofield mixing effects if one wishes to perform a comprehensive simulation study of criticalfluids.In this regard,the scaling operator distributions are likely to prove themselves of considerable utility in future simulation studies.These operator distributions represent the natural extension tofluids of the order parameter distribution analysis deployed so successfully in critical phenomena studies of(Ising)magnetic systems.Provided therefore that one works within an ensemble that affords adequate sampling of the near-criticalfluctuations,use of the operator distribution functions should also permit detailed studies offluid critical behaviour. AcknowledgementsThe authors thank K.Binder for helpful discussions.NBW acknowledges thefinancial sup-port of a Max Planck fellowship from the Max Planck Institut f¨u r Polymerforschung,Mainz.。

Novel high performance Al2O3/poly(ether ether ketone)nanocomposites for electronics applicationsR.K.Goyal a,*,A.N.Tiwari b,U.P.Mulik a,Y.S.Negi c,*a Centre for Materials for Electronics Technology(C-MET),Department of Information Technology,Govt.of India,Panchwati,OffPashan Road,Pune411008,Indiab Department of Metallurgical Engineering and Materials Science,Indian Institute of Technology,Bombay,Powai,Mumbai400076,Indiac Polymer Science and Technology Laboratory,Department of Paper Technology,Indian Institute of Technology,Roorkee,Saharanpur Campus,Saharanpur,U.P.247001,IndiaAbstractThis paper deals with the preparation and characterization of nanocomposites of poly(ether ether ketone)(PEEK)containing nano-aluminum oxide(n-Al2O3)filler up to30wt%(12vol%)loading.Nanocomposites showed improved thermal stability,crystallization, and coefficient of thermal expansion(CTE).Thermogravimetric analysis showed enhanced thermal stability and char yield on increasing the n-Al2O3loading in PEEK matrix.The peak crystallization temperature is increased up to13°C for the nanocomposites as compared to pure PEEK.The CTE is decreased to a value very close to the CTE of copper at12vol%Al2O3loading.The CTE values obtained were compared with the theoretical equations in the literature.The X-ray diffraction showed that PEEK crystalline structure is unchanged with addition of n-Al2O3.The distribution of n-Al2O3in the PEEK matrix was studied by transmission electron microscopy and scanning electron microscopy.The results show that the prepared n-Al2O3/PEEK nanocomposites may have potential applications in electronics.Keywords:A.Polymer-matrix composites;PEEK;B.Thermal properties;D.X-ray diffraction;D.Transmission electron microscopy1.IntroductionHigh performance polymer composites such as poly(-ether ether ketone)(PEEK),polyethersulphone(PES), polyphenylenesulphide(PPS)and polyimides reinforced with ceramicfillers result in unique combination of ther-mal,mechanical and electrical properties,which make them useful for various applications.By introducing suit-able reinforcingfillers in polymers,composite properties can be tailored to meet specific design requirements such as low density,high strength,high stiffness,high damping, chemical resistance,thermal shock resistance,high thermal conductivity,low coefficient of thermal expansion(CTE) and good electrical properties such as dielectric constant.It is well documented that PEEK exhibits excellent ther-mal,mechanical,electrical properties,good moisture and chemicals resistance[1].Recently,its properties have been further improved by incorporating micron size particles such as aluminum nitride(AlN)[2,3],aluminum oxide (Al2O3)[4],CaCO3[5],and hydroxiapatite(HA)[6]fillers. In the last one decade,polymer based nanocomposites con-taining nanofillers have been intensively investigated due to filler’s much higher surface area to volume ratio,which results in much higher interface between the nanofillers and the polymer matrix as compared to conventionally used micron sizefillers and polymer matrix.Hence,a very low loading(<5vol%)of nanofillers is required to improve the thermal,mechanical,optical,electrical and magnetic properties in contrast to high loading(>20vol%)of micronsizefillers.In particular the typical micron sizefillers needed for reducing the CTE of polymers are as high as 50vol%[7].As a result of highfiller loading,the main advantages such as ease of processing and light weight of polymers get lost.Therefore,the use of nanofiller in poly-mer composites has attracted the attention of materials sci-entists,technologists,and industrialists for different applications.Nevertheless,the effect of nanofiller on prop-erties of composites depends strongly on its shape,size, aggregates size,surface characteristics and degree of dis-persion.In order to improve properties of polymer nano-composites,a homogeneous dispersion of the nanofillers in the polymer matrix is essential[8–14].There are a several hundred publications on the effect of ceramicfillers on different polymer properties,but there is rare literature on the effect of n-Al2O3filler on PEEK. However,recently Kuo et al.have studied the effect of n-Al2O3and n-SiO2(up to5vol%)on PEEK’s mechanical and thermal properties[15].Moreover,Wang et al.have studied the wear properties of PEEK by incorporating SiC[16],SiO2[17],Si3N4[18],and ZrO2[19]nanofillers up to20wt%.Nevertheless,higher loading offillers is required to decrease the CTE of the polymer to avoid the thermal stresses and to increase the thermal conductivity of polymer to dissipate the heat generated during turning on and turning offthe electronic devices.In view of the above,in present paper a systematic inves-tigation of the effect of electrically insulating and thermally conducting n-Al2O3filler on the PEEK nanocomposites prepared by mixing PEEK and n-Al2O3fillers(up to 30wt%)in alcohol medium using mechanical stirring fol-lowed by hot compression molding was studied.The den-sity,thermal stability,melting and crystallization behavior,CTE,and crystal structure of the nanocompos-ites were characterized by using density,thermogravimetric analysis(TGA),differential scanning calorimetry(DSC), thermomechanical analyzer,ands X-ray diffraction tech-nique,respectively.The dispersion of the n-Al2O3fillers in PEEK matrix was observed by scanning electron micros-copy(SEM)and transmission electron microscopy.2.Experimental2.1.MaterialsThe commercial PEEK,grade5300PF donated by Gharda Chemicals Ltd.Panoli,Gujarat,India under the trade name GATONE TM PEEK was used as matrix.It has a reported inherent viscosity of0.87dl/g measured at a con-centration of0.5g/dl in H2SO4.Thefiller used in the prep-aration of nanocomposites was n-Al2O3of density4.00g/ cm3.It was used as supplied by Aldrich Chemical Company. Figs.1a and b are typical SEM micrographs of PEEK pow-der and n-Al2O3powder,respectively.As received ethanol of Merck grade was used for homogenizing the n-Al2O3 and PEEK mixture.The particle size of the PEEK deter-mined by GALAI CIS-1laser particle size analyzer was ranges from4to49l m.The mean size of the PEEK particle was25l m.The reported average particle size and surface area of n-Al2O3is39nm and43m2/g,respectively.2.2.Nanocomposites preparationNanocomposites of PEEK reinforced with n-Al2O3up to 30wt%loading were prepared using the method described in our previous paper[2].Dried powder of n-Al2O3and PEEK were well premixed through magnetic stirring at high stirring speed using an ethanol as medium and the resultant slurry was dried in an oven at120°C to remove the excess alcohol.The pure PEEK(controlled)and nanocomposite samples were prepared by using a laboratory hot press under a pressure of15MPa at a temperature of350°C. 3.Characterization3.1.DensityThe density of the nanocomposites prepared by taking appropriate amount of PEEK and n-Al2O3was increased due to higher density of n-Al2O3(4.00g/cm3)ascompared Fig.1.SEM micrographs of:(a)PEEK powder,magnification=2·103;(b)n-Al2O3powder,magnification=10·103.1803to pure PEEK(1.30g/cm3).Theoretical density(q th,c)of the nanocomposites was calculated by the rule of mixture with no voids and no loss offillers during processingq th;c¼q m V mþq f V fð1Þwhere q m,q f,V m,and V f is the density of matrix,density of filler,volume fraction of matrix,and volume fraction offil-ler,respectively.Experimental density(q ex,c)of the PEEK nanocompos-ites was determined by Archimedes’s method using:q ex;c¼½W air=ðW airÀW alcoholÞ Áq alcoholð2Þwhere W air and W alcohol is the weight of the sample in air and in alcohol medium,respectively.The q alcohol is the den-sity of the alcohol medium used.3.2.Thermogravimetric analysis(TGA)The thermal stability of the PEEK nanocomposites was determined on a TGA using Mettler-Toledo TGA/SDTA 851e.The samples were heated from room temperature to 1000°C at the heating rate of10°C/min in air or nitrogen atmosphere.The maximum decomposition temperature (T m),was taken as the temperature corresponding to the maximum of the peak obtained by thefirst order derivative curve.The%char yield was determined at temperature of 1000°C in nitrogen atmosphere.3.3.Differential scanning calorimetry(DSC)The melting and non-isothermal crystallization behavior of PEEK nanocomposites was performed on DuPont Instruments910DSC.The samples placed in aluminum pan werefirst heated from30°C to400°C at a heating rate of5°C/min and soaked isothermally at400°C for5min to allow complete melting of the polymer.The samples were then cooled to30°C at a cooling rate of5°C/min.Each sample was subjected to single heating and cooling cycles under a dry nitrogen purge.3.4.X-ray diffraction measurementsXRD pattern of as molded PEEK nanocomposites was recorded on Philips X’Pert PANalytical PW3040/60.Ni-filtered Cu K a radiation(k=1.54A˚)generated at40kV and30mA was used for the angle(2h)ranged from10°to50°.The scan step size and time per step was0.02°and5s,respectively.3.5.Morphological examinationMorphological analysis of the PEEK powder,n-Al2O3 powder and nanocomposites pellets was conducted with a SEM(Quanta200HV,FEI).For SEM study of nanocom-posites,a small piece of the sample was cut from the pellets and mounted in a block of acrylic based polymer resin (DPI-RR cold cure).The obtained sample surfaces were manually ground and polished with successivefiner grades of emery papers followed by cloth(mounted on wheel)pol-ishing to remove scratches developed during emery paper polishing.Thus,obtained samples were called as polished samples in the present study.The same polished samples were also etched for5min in a2%w/v solution of potas-sium permanganate in a mixture of4vol.of orthophos-phoric acid and1vol.of water and were called as etched samples.After polishing and etching,samples were rinsed well in water and dried for examining the polished and etched samples,respectively.The morphology of PEEK and Al2O3powder was determined by suspending powder in an ethanol followed by dispersing on metal stub.Finally the samples were coated with a thin layer of gold using gold sputter coater[Polaron SC7610]to make the sample elec-trically conducting.Dispersability of the n-Al2O3filler in the PEEK matrix was also observed using TEM(Philips CM30)operated at an accelerating voltage of200kV. The ultra-thin section slice($100nm thick)of the nano-composites was cut with ultramicrotome(Leica Ultracut UCT)at room temperature.The slices were mounted on 200-mesh copper grids and dried before the TEM observation.3.6.Thermo mechanical analyzer(TMA)The out-of-plane(through thickness direction)CTE of the nanocomposites were determined using Perkin–Elmer DMA7e in thermo mechanical analyzer mode.The detailed procedure of the CTE measurement was described elsewhere[20].The annealed sample was heated under pressure of50mN from30to250°C at a heating rate of 5°C/min in argon atmosphere.The sample was then cooled to30°C and reheated at5°C/min to250°C.The results were reported for the second run and an average value of CTE was determined over a specific temperature range of30–140°C,i.e.below glass transition temperature (T g)of PEEK.4.Results and discussionPEEK nanocomposites reinforced with varying weight fraction of n-Al2O3were prepared by hot compression molding technique.Resulting compositions were character-ized and discussed in details in this section.Table1showed the properties of the PEEK matrix and Al2O3filler.These Table1Properties of PEEK and Al2O3Material PEEK[1]Al2O3[7] Density(g/cc) 1.30a 4.00b CTE(·10À6/°C)58a 6.6 Young’s modulus(GPa) 3.6385 Shear modulus(GPa) 1.3155Bulk modulus(GPa) 6.2247 Poisson ratio0.400.24a Experimental results.b Suppliers datasheet.1804properties were used to estimate the theoretical density and CTE of the composites.Table2showed the weight%and volume%of the n-Al2O3filler added into the PEEK matrix.From the given weight fraction offiller,volume fraction of thefiller can be determined by using:V f¼W f=½W fþð1ÀW fÞÁq f=q m ð3Þwhere W f is the weight fraction of thefiller.4.1.DensityFig.2shows the density of the n-Al2O3filled PEEK as a function of n-Al2O3content.It can be seen that the nano-composites density increased with n-Al2O3loading in a lin-ear fashion due to the higher density of n-Al2O3(4.00g/ cm3)than that of pure PEEK(1.30g/cm3).The experimen-tal density of the nanocomposites is in good agreement with the theoretical density except at12vol%nano-Al2O3.This might be an indication of the porosity free samples due to good processing conditions.The experimen-tal density of the NC-30nanocomposite is about1.3%les-ser than theoretical density.This may be due to the presence of voids,which is resulted from the n-Al2O3 agglomerates.During hot pressing the infiltration of melt PEEK resin,due to very high viscosity,is difficult through the agglomerates,hence results in voids in thefinal samples.4.2.Thermogravimetric analysis(TGA)Figs.3and4show the percentage of original weight remaining as a function of temperature in nitrogen and air atmosphere,respectively.The temperature of10wt% loss was taken as the degradation temperature(T10)and tabulated in Table3.It can be seen from Table3that pure PEEK has T10in nitrogen atmosphereðT10;N2Þat570°C and in air atmosphere(T10,air)at556°C,which is attrib-uted to the decomposition of the PEEK matrix.Pure n-Al2O3powder does not show(not shown infigure)any abrupt change in weight and only a slight($3–4%) decrease at500°C appears due to the loss of physisorbed water[21].It is observed that as the n-Al2O3loading increases in PEEK the degradation temperature(thermal stability)of nanocomposites is improved significantly.The increase in thermal stability by14°C and28°C was observed for the NC-10nanocomposites in nitrogen and air atmosphere, respectively.However,on further increasing the n-Al2O3 loading to30wt%decreased the T10value to below theTable2Composition of n-Al2O3/PEEK nanocompositesSample code Al2O3in PEEK by:wt%vol% NC-000 NC-1 1.250.41 NC-2 2.50.82 NC-5 5.0 1.67 NC-77.5 2.54 NC-1010 3.46 NC-20207.46 NC-303012.14Fig.3.TG curves of the nanocomposites at the heating rate of10°C/min under nitrogen atmosphere:(a)NC-0,(b)NC-1,(c)NC-2,(d)NC-5,(e) NC-7,(f)NC-10,(g)NC-20,and(h)NC-30.Fig.4.TGA curves of the nanocomposites at the heating rate of10°C/ min under air atmosphere:(a)NC-0,(b)NC-1,(c)NC-2,(d)NC-5,(e) NC-7,(f)NC-10,(g)NC-20,and(h)NC-30.1805580°C.As the n -Al 2O 3content increased the agglomera-tion tendency of n -Al 2O 3fillers increased,and thermal sta-bility decreased but it is still higher than pure PEEK.Therefore,the incorporation of n -Al 2O 3in PEEK matrix improved thermal stability of the nanocomposites in both atmospheres.The increase in thermal stability could be attributed to the interaction between the n -Al 2O 3and PEEK matrix,which hindered the segmental movement of the PEEK [22].Figs.5and 6show the derivative thermogravimetric analysis (DTG)curves of nanocomposites in nitrogen and air atmosphere,respectively.It can be seen from Fig.5that there is 6–10°C increase in maximum decompo-sition temperature (T m1)in nitrogen atmosphere.The increase in T m1did not vary much with increase in volume fraction of n -Al 2O 3.Fig.6shows two decomposition stages of PEEK nanocomposites under air atmosphere in contrast to single decomposition stage under nitrogen atmosphere.The lower maximum decomposition temperature (T m1)is probably occurred from the degradation of the PEEK mol-ecules due to thermal energy,while the higher maximum decomposition temperature (T m2)is expected to be the oxi-dation of the degraded PEEK backbone.As shown in Table 3,there is no significant change in T m1.However,T m2is significantly increased from 644°C for pure PEEK (NC-0)to 695°C for NC-10.This implies that thermo-oxi-dative stability of nanocomposites is improved by about 50°C.Moreover,the final decomposition temperature (T f )in air atmosphere is increased by about 42°C from 694°C for NC-0to 736°C for NC-10.The n -Al 2O 3filler,uniformly dispersed within the PEEK matrix,probably interfere with degradation mechanism hence improved the decomposition temperature.Table 3shows that the char yield of pure PEEK is about 48%,in agreement with a reported value [23].This char yield was increased to 62%for NC-30due to the increase in wt%of n -Al 2O 3,which is thermally very stable at higher temperature.Similar trend of char yield was obtained for micron size Al 2O 3incorporated PEEK composites [4].4.3.Differential scanning calorimetry (DSC)DSC measurements were carried out to determine the thermal properties such as melting temperature (T m ),heat of crystallization (H c ),degree of crystallinity,onset crystal-lization temperature (T on ),and peak crystallization temper-ature (T c )of PEEK nanocomposites.The DSC heating and cooling curves are shown in Figs.7and 8,respectively.Table 3Degradation temperature and char yield of the n -Al 2O 3/PEEK nanocomposites Sample code T d in air atmosphere (°C)T d in N 2,atmosphere (°C)Char yield,%T 10,air a T m,1T m,2T f T 10;N 2b T m,1NC-055659064466457058448NC-158059067074457859249NC-256458264267057259049NC-556758865869257059250NC-757858867873557359053NC-1058458869573658459453NC-2056758869571557559056NC-3058059068871058059062a T 10,air is the degradation temperature at 10wt%loss in air atmosphere.bT 10;N2is the degradation temperature at 10wt%loss in nitrogenatmosphere.Fig.5.DTG curves of the nanocomposites at the heating rate of 10°C/min under nitrogen atmosphere:(a)NC-0,(b)NC-1,(c)NC-2,(d)NC-5,(e)NC-7,(f)NC-10,(g)NC-20,and (h)NC-30.Fig.6.DTG curves of the nanocomposites at the heating rate of 10°C/min under air atmosphere:(a)NC-0,(b)NC-1,(c)NC-2,(d)NC-5,(e)NC-7,(f)NC-10,(g)NC-20,and (h)NC-30.1806From the recorded heating and cooling curves,thermal properties were calculated and tabulated in Table 4.The crystallinity percentage of PEEK (v c )was calculated with a value of the heat of crystallization for the 100%crystal-line PEEK as 130cal/g [2].The crystallinity of PEEK con-stituent in composite was determined by:v c ð%Crystallinity Þ¼D H c Â100=ðD H 0c w Þð4Þwhere D H 0c is the heat of crystallization (130J/g)for 100%crystalline PEEK,and w is the mass fraction of PEEK in the composites.It is seen from the curves (a–h)of Fig.7and Table 4that T m is increased by 1–6°C as the n -Al 2O 3content increased in PEEK.However,above 10wt%the significant increase in T m was not observed.The similar increasing trend in T m was reported recently for AlN (5l m)/PEEK [2]and Al 2O 3(8l m)/PEEK [4]composites.However,a recent study has shown that the addition of nano Al 2O 3and nano SiO 2decreases slightly the T m of PEEK [15].Lorenzo MLD et al.reported that T m of the PET is decreased with the addition of untreated CaCO 3but increased with the addition of treated CaCO 3due to good adhesion between the filler and matrix [24].Pingping et al.have not found sig-nificant change in the T m of CaCO 3/PET composites [25].However,the decrease in T m about 5–6°C of CaCO 3/PEEK composites was observed,irrespective of filler’s sur-face treatment [5].It is well known that the melting point of the polymer crystals is a function of lamellar thickness anddegree of crystal perfection [26].Therefore,the increase in T m ,in present study,may be due to the increased crystal size,and crystal perfection.Priya et al.reported that change in crystal structure/morphology of composite due to the addition of filler affect the T m of the polymer [27].This factor may be ruled out for the present study because the XRD results have shown that there is not any change in PEEK crystal structure.From Fig.8,it was observed that the T on ,T c ,and half time of crystallization (t 1/2)of PEEK was affected by the presence of the n -Al 2O 3,which indicate that nucleation is inhomogeneous.The addition of n -Al 2O 3in PEEK shifts the T c towards higher temperature by 2–12°C depending on the n -Al 2O 3content in PEEK for a given cooling rate in comparison to pure PEEK.This implies that the addition of n -Al 2O 3into PEEK enhanced the rate of PEEK crystalli-zation.A similar enhancement of crystallization was reported for AlN/PEEK [2],CaCO 3/PP [13],SiO 2/PP [26,28,29],clay/PVDF [27],SiO 2/PET [30,31],clay/PET [32],and nanocomposites.However,our results are in con-trast to the recent study of CaCO 3/PEEK [5]and Al 2O 3/PEEK [15]nanocomposites,where decrease in T c was found with the increase of fillers in PEEK matrix.This difference may be attributed to the shape,size,loading,dispersion level,adhesion,and surface morphology of the filler.Never-Fig.7.DSC heating curves of the nanocomposites:(a)NC-0,(b)NC-1,(c)NC-2,(d)NC-5,(e)NC-7,(f)NC-10,(g)NC-20,and (h)NC-30.Fig.8.DSC cooling curves of the nanocomposites:(a)NC-0,(b)NC-1,(c)NC-2,(d)NC-5,(e)NC-7,(f)NC-10,(g)NC-20,and (h)NC-30.1807theless the impurities present on thefiller’s surface may also affect the crystallization behavior of the polymer.The half time(t1/2)of crystallization temperature of PEEK nanocomposites was determined by using the equa-tion[t1/2=(T onÀT c)/rate of cooling].Table4shows that t1/2value of nanocomposite decreases with the increase in n-Al2O3content in PEEK.The t1/2for the pure PEEK is 2.8min,which is decreased to about1.4min for the NC-30nanocomposites.The t1/2for the nanocomposites varies 2.6–1.4min depending on the nanofiller loading.The decrease in t1/2implies that the nucleation effect is increased for PEEK with increase in n-Al2O3.For the same rate of cooling,there is enough time for the molecular chains of PEEK to pack into a closer arrangement. Although the enthalpy of crystallization(D H c)for nano-composites decreased slightly with the increase of n-Al2O3 as compared to the pure PEEK.Moreover,there is not any trend in D H c with n-Al2O3content.The supercooling temperature(D T)of the nanocomposites decreases with increasing n-Al2O3in PEEK,indicating that the crystalliza-tion becomes easier in the nanocomposites due to the nucleating effect of the n-Al2O3.4.4.Crystal structureFig.9shows intensity versus angular position(2h)in the range10–50°of major crystallographic reflection for the PEEK nanocomposites.The pure PEEK and PEEK consti-tute of nanocomposites crystallizes primarily in the form-I [33]with orthorhombic crystal structure which shows dif-fraction peaks(2h)at about18.7°,20.8°,22.9°and28.9°, corresponding to diffraction planes of(110),(111), (200),and(211).In the studied angular range for nano-composites,there are only two weak diffraction peaks of n-Al2O3appearing at about39.41°,and45.815°,corre-sponding to Miller indices(222),and(400).Apparently, apart from those of pure constitutes,no new diffracting peaks were observed in the diffraction pattern of the nano-composites.Moreover,all nanocomposite samples showed the same XRD patterns with varying peak intensity in pro-portion of the constituent’s volume faction.The absence of new diffraction peaks showed that the presence of n-Al2O3 did not change the crystal structure of PEEK.However,in other polymer nanocomposite system a new diffracting peak was observed which implies new morphology of the polymer[27,34].4.5.Morphological examinationFig.1a shows micrographs of pure PEEK powder at 2000·magnification.PEEK powders have irregular parti-cles of rod like shape of length ranging from10to 50l m.In order to determine the morphology of the n-Al2O3filler,it was dispersed in ethanol for15min under ultra sonic bath and observed under the SEM.Thefillers are seen as agglomerates in Fig.1b with sub-micron size of primary particles,which are difficult to be resolved by the SEM.This is due to the fact that n-Al2O3particles have a strong tendency to form agglomerate due to Wander Wall’s forces between particle-particle.However the same can be observed well separated in composites under SEM due to interaction between n-Al2O3and PEEK,which results in well dispersion in PEEK matrix.Figs.10a and b show SEM micrographs for NC-1and NC-10after pol-ishing.Due to the nano size,fillers are not distinctly visible. In order to get distinct boundary between the n-Al2O3filler and the PEEK matrix,NC-1and NC-10nanocomposites were etched in2%w/v solution of potassium permanganate in a mixture of4vol.of orthophosphoric acid and1vol.of water.During etching amorphous PEEK or loosely bounded PEEK surrounding the n-Al2O3fillers were etchedTable4The melting and crystallization data of n-Al2O3/PEEK nanocompositesSample T m(°C)T c(°C)T on(°C)D H c(J/g)a v c t1/2(min)D T(°C) NC-033427028431.8324.46 2.864NC-133526827730.1823.22 2.067NC-233627628827.0420.8 2.460NC-533527228529.1922.45 2.663NC-733827528530.3523.35 2.063NC-1034027328329.5622.74 2.064NC-2033727928928.7322.10 2.056NC-303362832903224.62 1.453a Normalized heat of crystallization of PEEK constituent innanocomposites.Fig.9.X-ray diffraction pattern of the nanocomposites.For clarity,scansof NC-1–NC-30have been displaced upward.1808out,which results in appearance of n -Al 2O 3fillers in PEEK matrix.It could be seen from Figs.10c–f that n -Al 2O 3fill-ers were uniformly distributed throughout the PEEK matrix.However,some n -Al 2O 3agglomerates were also seen in the PEEK matrix.Nevertheless,with increase of n -Al 2O 3content,the inter particle distance decreases which results in formation of Al 2O 3aggregates.As shown in Figs.10c–f,SEM could not provide good contrast between n -Al 2O 3and PEEK matrix.For this reason,NC-1and NC-10nanocomposites were also examined with TEM.Figs.11a and b show TEM images of pure n -Al 2O 3powder.The n -Al 2O 3particles are almost spherical in shape and its size varies between 20and 90nm.Figs.11c and d show TEM images of NC-1and NC-10nanocomposites,respec-tively.The most of the n -Al 2O 3particles remained individ-ual in NC-1nanocomposite.However,as the n -Al 2O 3content increased to 10wt%(NC-10)in PEEK,due to the particle-particle interaction some aggregates of about 100nm size was also observed with individual n -Al 2O 3par-ticles.This shows that shear forces applied during mechan-ical stirring were not capable of breaking and uniformly distributing the n -Al 2O 3in PEEKmatrix.Fig.10.SEM micrographs of:(a)polished NC-1,magnification =6·104;(b)polished NC-10,magnification =6·104;(c)etched NC-1,magnifica-tion =8·104;(d)etched NC-1,magnification =1.6·105;(e)etched NC-10,magnification =8·104;(f)etched NC-10,magnification =1.6·105.18094.6.Coefficient of thermal expansion (CTE)The T g of the PEEK determined by inflection in the curve between dimension change and temperature was found about 153°C.The average out-of-plane CTE below T g for the nanocomposites is shown in Fig.12as a function of volume %of n -Al 2O 3filler.The CTE of the NC-0was 58·10À6/°C and decreased with increasing n -Al 2O 3filler in PEEK matrix.The CTE of the NC-30(12vol%)nanocomposite was about 23·10À6/°C.The reduction in CTE may be attributed to three reasons.First,decrease in volume fraction of the PEEK in the composite results in decreased free volume of PEEK,hence reduced room for PEEK expansion.Second,well dispersion of n -Al 2O 3filler results in good interfacial area between n -Al 2O 3and PEEK.It is well known that in par-ticulate polymer composites,particles are surrounded by two regions;first by tightly bounded polymer or con-strained polymer chain,and second,by loosely bounded polymer chains or unconstrained polymer chain.As the average inter-particle distance decreases with the incorpo-ration of more filler particles,the loosely bound polymergradually gets transformed to the tightly bound polymer.Hence,the volume fraction of loosely bound polymer decreases [3,35].Hence formation of increasedcon-Fig.11.TEM micrographs of:(a)n -Al 2O 3powder as received,magnification =6.6·104;(b)n -Al 2O 3powder as received,magnification =1.15·105;(c)NC-1,magnification =3.8·104;(d)NC-10,magnification =3.8·104.1810。

Flow Induced Crystallization ofPolymersApplication to Injection MouldingChapter 1IntroductionThe final properties of a product, produced from semi-crystalline polymers, are to a great extend determined by the internal structure, which itself is established during processing of that product. For example,flow gradients act as a source for viscoelastic stresses, which can enhance nucleation and crystallization, not only accelerating the process, but also leading to different types of crystalline structures. A complete modeling, providing the means for pre-dicting the final product properties, is stillnot available. This study presents two important parts of that modeling; (i)a flow-induced crystallization model, based on the recoverable strain inthe melt and, (ii) a new experimental technique to determine the specific volume of semi-crystalline polymers, and its relation to cooling rate dependent crystallization kinet-ics. Both are implemented in a computercode for the numerical simulation of the injection moulding process, and validated by comparing the predicted results with well defined exper-iments (partly from literature). Applications are found in predicting internal structures (i) as resulting from the SCORIM process (which is a specific procedure (’push-pull’) to enhance mechanical properties like strength and stiffness), (ii) as present in a moulded strip (as a function of different processing conditions) and, finally, (iii) in their relation withlong-term dimensional stability.Crystallization of polymers is influenced by the thermo-mechanical history during pro-cessing. Dependent on the amount of strain experienced during flow, the number and type of the nuclei formed will be different, and so will be the final crystalline structure. For example,in the injection moulding process, the absence of shear in the center of a product results in a spherulitical structure, while in the highly strained regions atthe cavity walls an oriented structure (in polyolefins often referred toas ’shish-kebabs’)can be present (fig. 1.1). T o clarify the role of the processing conditions on the crystallization process (and, vice versa,therole of the growing crystal structure on processing behavior), a short overview will be presented concerning their mutual interactions.1.1 Crystallization of polymers related to processing: an overview 1.1.1 Molecular configuration, conformation and flowThe molecular configuration of polymer materials determines thematerials ability for order-ing. Three types of molecular structures are generally distinguished: isotactic, all side groups a re present at one side of the backbone of the polymer chain; syndiotactic, with alternating side groups; and atactic, with randomly positioned side groups. Crystallization is possible if the chain is symmetric or has only small side groups, which fit in a regularly packed confor-Fig. 1.1: A cross section of a product. After (44).mation; the polymer chain has to be linear and stereo specific. Therefore, isotactic polymers have the ability to crystallize; syndiotactic polymers might have this ability, depending on the side groups, while atactic polymers can not crystallize. The influence of isotacticity on the crystallization kinetics during quiescent crystallization has been studied by, for example,Janimak (41).Polymer molecules, in general, show a random configuration without any orientation,when in s olutions o r melts. However, t heir s tate (conformation a nd o rientation) c an b e a ltered by flow gradients, i.e. by stirring solutions or shearing melts. According to Keller ( 48)only two stages of orientation exist; the fully random and the fully stretched chain, with no stable intermediate stages. The trans ition from one stage to the other is assumed to be sharp, showing a molecular weight dependent coil-stretch transformation at a critical strain rate and temperature. Thus, with gradually increasing the elongational rate, first only s mall differences in the chain conformation will appear, but once a critical elongational rate has been reached, the chain will switch to the almost fully stretched stage of the conformation(‹˙θ> 1, with‹˙the deformation rate and θ= θ(M w, T , ...) the relaxation time). Moreover, not only has the critical elongational rate to be reached, it must be maintained for a certain time as well (‹˙t > 1, with t the deformation time). The structures observed in solutions or melts, all are the result of a c ombination o f b oth t hese s tages.1.1.2 CrystallizationThe crystallization behavior of polymers is determined by their ability to form ordered struc-tures; the configuration determines the conformation, which is influenced by the processing conditions. Crystallization under quiescent conditions is a phase transformation process,which is caused by a change in the thermodynamic state of the system. This change can be a lowering of the temperature or a change in the hydrostatic pressure. In flow, chain extension can occur as explained in the preceding section. Thermodynamically, chain extension will increase the opportunity of crystal formation by increasing the melting point, while kineti-cally the extended chain is closer to a crystal state than a random chain. By stretching the polymer chains, the rate of crystallization increases. Dependent on the conformation of thepolymer chain, two types of crystals can be formed; the random polymer chain will lead to lamellar, chain folded crystals that finally form spherulites, while the fully extended chain will lead to extended chain crystals, finally resulting in shish-kebab structures (Keller ( 48)).It has been shown, e.g. by Bashir (2) and Mackley (62), that the high end tail of the molecular weight distribution promotes the formation of extended chain crystals. Following Bashir ( 2),these high end tail molecules are stretched out while the rest remains practically unchanged;a stronger elongational rate results in a broader part of the molecular weight distribution to be extended. The elongational rate, therefore, determines the amount of oriented molecules(extended chain crystals) present. These extended chain crystals themselves are inadequate to influence the material properties, given their limited number. However, they serve as nuclei for lamellar crystallization of the not oriented lower molecular bulk, which will show lamel-lar over-growth at a later stage, perpendicular to the central core (Bashir ( 2)). The structure formed is called a shish-kebab. It has been shown by Petermann ( 67) that the number of core crystals, nucleated at a specific temperature, depends on the external strain. The core itself consists of a shish-kebab structure on a finer scale (Keller ( 48)).A certain strain and strain rate have to be present for shear flow to induce (noticeable)crystallization. After a nucleus has been formed, continuous crystallization of polymers is kinetically controlled, the motion involved refers to the transport of molecules from the dis-ordered liquid phase to the ordered solid phase, and to the rotation and rearrangement of the molecules at the surface of the crystal, similar to quiescent crystallization. The crystallization process can thus be subdivided into three stages:Nucleation: Nucleation can have different causes like overall nucleation from a nucleation agent, pressure induced nucleation, strain induced nucleation and cooling. The nuclei formed act as starting points forpolymer crystallization. There is no complete agreement on the physical background of the nucleation process. For example, Terrill et al. ( 81) considered,based on experimental evidence (WAXD and SAXS), the nucleation event during spinning of isotactic polypropylene to be the result of density fluctuations, although a repetition of old discussions on the true interpretation of combined WAXD and SAXS data 1 question these re-sults. Even without considering the basic underlying physics precisely, in case of flow, nuclei can be created by flow-induced o rdering phenomena in the melt, while the nucleation process for a quiescent melt can be described by a Poisson point process (Janeschitz-Kriegl ( 40)). For polymers containing nucleation agents, also clustered point processes have some importance.Growth: The nuclei grow, dependent on the thermo-mechanical history which they experi-ence; if the nuclei are sufficiently strained they will grow into threads, otherwise they stay spherical and will further grow radially. In these, so called spherulites, the lamellae are present like twisted spokes in a sphere, while thread-like nuclei grow mainly perpendicular to the thread(fig.1.2).Perfection: Perfectioning is the process of improvement of the interior crystalline structure of the crystalline regions. This is also referred to as secondary crystallization.Fig. 1.2: A schematic outline of the concept of crystallization. After (48) and (55).1.1.3 ModelingHistorically, crystallization transformations are described by using a phase diagram assuming the transformation to be in a quasi-equilibrium state,leading to a front model. An example of this approach is the description of the growth of the ice layer on the polar see (a Stefan-problem (78)). It has been shown by Berger (5), that the front model is inadequate in describ-ing solidification, if the process is governed by the kinetics of a phase change. For example,the occurrence of completely amorphous layers can never be understood using a front model.A zone model has to be used, were a phase change (crystallization) determines the solidifi-cation behavior. Crystallization in a moving zone takes place when the characteristic time of heat diffusion is less than the characteristic time of crystallization. In the limiting case of very fast crystallization, compared with the process of heat conduction, the zone model shows a transition into the front model.Quiescent crystallization: Describing the growth of the crystalline spherulites in case of quiescent crystallization has been done by representing the spherulites as spheres (Schultz ( 75)).Spherulitical growth is then accounted for by enlarging the sphere radius. However, the crys-tallizing medium is limited by free surfaces or other boundaries that induce truncations of crystalline entities and locally modify the crystallization kinetics. Benard ( 4) formulated a mathematical description for the growth of already existing nuclei and concluded that the ki-netics clearly are the controlling factor in the systems investigated.A more complete model for quiescent crystallization has been described by Janeschitz-Kriegl ( 39), which is based on the Kolmogoroff equation (Kolmogoroff ( 49)), who formulated the crystallization kinetics in terms of time dependent (bulk) nucleation and crystal growth rate. This formulation has b een extended for the influence of confining surfaces and surface nucleation processes by Eder (15; 16). A Poisson point process with special intensity measures for the description of the nucleation process and a deterministic law for crystal growth forms the basis. Using the method proposed by Schneider ( 74), this generalized Kolmogoroff equation can be trans-formed in a set of differential equations (Schneider’s rate equations), which give a complete description of the crystalline structure. These rate equations are coupled with the energy equation by the source term, which takes into account the latent heat when the polymer crys-tallizes (Eder (17)).Flow-induced crystallization: An onset for the description of flow-induced structures has been given by Eder et al. (19), who based their theory on the shear rate as the driving force for crystallization. Their model for flow-induced crystallization resembles their model for quiescent crystallization. It is assumed that the influence of the deformation on crystal-lization, is due to the formation of thread-likenuclei (shish), on which lamellae grow mainly perpendicular (kebabs). This model is described in chapter 3 of this thesis. Jerschow (45)used this model in analyzing the structure distribution found in isotactic polypropylene, after fast short term shear at low degrees of super-cooling. Besides a flow-induced (shi sh-kebab)structure at the surface and a spherulitical structure in the center, in between both layers a fine grained layer has been observed. It has been suggested that this layer consists of thread-like structures perpendicular to the flow direction. A model based on the conformation of the molecules in the melt has been proposed by Bushman ( 8) and Doufas (12), which includes a conformation tensor (the driving force, calculated using a viscoelastic model), an orienta-tion tensor and the degree of crystallinity. No description is available, however, of the final structure (size of structures, etc.). Other models have been proposed by Ito ( 37), based on the strain present in the melt, and by V erhoyen ( 86), based on the Cauchy stress. An iso-kinetic approach is used in models based on the Nakamura equations (Nakamura ( 66)) by Isayev (35)and Guo (29). The (dis)advantages of all these models are discussed in chapter 3.1.1.4 Relation with other material propertiesThe evolution of structure (spherulites and shish-kebabs) will influence the material proper-ties. The most severe effects are observed in the viscosity and the specific volume. Effects in other properties like the thermal conductivity and thermal capacity will not be discussed here.Viscosity: The coupling between the crystal structure and the viscosity of a polymer melt, is not fully clarified yet. For example, in startup flow experiments, it has been observed by Lagasse (52) that a sudden rise in the viscosity correlates with the appearance of crystal s in the sheared melt. Experiments by Vleeshouwers ( 87) showed the same kind of behavior.Initially, the melt still shows an amorphous behavior, since the amount of crystalline material(or the number of crystals) is very low. With increasing amount (or number) the influence on the viscosity will increase. Guo et al. (27) assumed that the melt loses its fluidity upon the occurrence of crystallization, i.e. a step-like change in the viscosity. They do not give a physical explanation although; one could assume that a network occurs in this stage. Another possibility could be, that the crystals form a separate phase in the amorphous melt. The rhe-ology will then be changed like is known from dispersion rheology (see for example Ito ( 36) and V erhoyen (85)).Specific volume: In polymer processing, the specific volume isinfluenced by process-ing characteristics like temperature, pressure and flow history, and it determines shrinkage which expresses itself by dimensional (in)stability. For amorphous polymers, the pressure and temperature history determine the specific volume and (frozen in) molecular orientation determines the anisotropic dimensional instability via (slow) relaxation processes below the glass transition temperature (Meijer (65)). For semi-crystalline polymers, however, the spe-cific volume is also influenced by the crystalline structure. This structure itself is influenced by the pressure and the temperature history, by the configuration of the polymer chains and flow induced ordering phenomena as well. Consequently, for semi-crystalline polymers the specific volume has to be related to pressure, temperature, cooling rate and the crystalline state (Zuidema (94)). For a correct modeling of the injection moulding of semi-crystalline polymers, accurate measurements and modeling of the specific volume have to be achieved not only in relation to the pressure and temperature, but al so to the cooling rate and ordered state of the molecules. This conclusion is subscribed by Fleischmann ( 22), regarding the influence of the processing conditions on the specific volume. The specific volume will be discussed in more detail in chapter 4.1.1.5 ProcessingFor polymer melts it has been observed (V an der V egt ( 83)) that the flow through a capillary die can become blocked by crystal formation, induced by the elongational flow at the con-striction. Bashir (2; 3) and Keller (48) explored these findings somewhat further and observed a macroscopical rheological effect in capillary flow of high molecular weight polyethylenes;a reduced flow resistance coupled with the absence of extrudate distortions when extruding a polymer melt in a specific processing window. Experiments by T as ( 80) showed that, dur-ing film blowing of LDPE films, the viscoelastic stresses at the freeze line determine the majority of the mechanical properties by directing the crystallization. Saiu ( 71) performed an experimental study on the influence of injection moulding conditions on product proper-ties for an isotactic polypropylene. Chiang ( 11) studied shrinkage, warpage and sink marks resulting from the injection moulding process, using semi-crystalline polymers. The effect of crystallization on the mechanical and physical properties has been studied, for isotactic polypropylenes with different molar masses. It has been observed (Guo ( 28)) that increasing the injection speed or the melt injection temperature leads to a decrease in the thickness of the flow-induced layer. The complicated thermo-mechanical history, in all these examples,requires a numericalanalysis. The effect of processing conditions will be discussed in more detail in chapter 5.1.1.6 Mechanical propertiesThe resulting morphology of the product is, together with the molecular composition, the factor determining the mechanical and dimensional properties. Because the solidification be-havior of amorphous polymers is quite well understood, prediction of warpage and shrinkage from ejection up to the complete life cycle of a product can be done (Caspers ( 9), Meijer (65)).This knowledge allows one to reduce shrinkage and warpage by choosing a different polymer(with different relaxation time/molecular weight (distribution)) by adjusting the processing conditions, or by improving the mould design. For semi-crystalline polymers, the different crystalline structures present (spherulites and/or shish-kebabs) have a different influence on secondary crystallization and physical aging. The mechanical properties of semi-crystalline polymers improve with increasing the amount of long polymer chains that function as ’tie-molecules’ between crystals. Also, a preferred molecular orientation in a product enhances the properties in the orientation direction, while perpendicular the properties reduce. An ex-treme example is the fiber spinning process of HPPE (High Performance Polyethylene fibers),where all molecules are aligned along the thread.An attempt to quantify the influence of injection moulding processing conditions on the mechanical properties has been performed by Fleischmann ( 23) who studied the effect of molecular orientation on the tensile behavior of an isotactic polypropylene. The application of packing pressure, the distance from the gate and the orientation of the testing direction relative to the chain orientation, all proved to influence the tensile behavior. Hsiung ( 34)showed that with decreasing the injection speed, the elongation to break, tensile strength and impact strength increase in injection moulded dumbbells. Gahleitner ( 25) investigated the influence of the molecular structure on the crystallinity and mechanical properties for two different polypropylene homopolymers, as influenced by their molar mass and heterogeneous nucleation, and he studied (24) the influence of processing on physical ageing. Additional to the generally observed correlation between mechanical properties and spherulite size, it has been shown that mechanical properties are influenced by the formation of highly ori-ented skin layers through shear induced crystallization. Based on these considerations, we conducted a number of, relatively extreme, experiments at the Borealis laboratory in Linz incooperation with Markus Gahleitner. Rectangular plates were injection moulded using an isotactic polypropylene. Different injection temperatures, mould temperatures and volume fluxes during filling were applied in order to study their influence on the resulting morphol-ogy and the mechanical properties. One of the conclusions was that the strongest effect on skin layer thickness and shrinkage resulted from a change in the melt temperature. Results are discussed in chapter 5. Generally, they are in line with previous examinations at the same polymer. Gahleitner (24) earlier also concluded that an increased melt temperature re-duces shrinkage. Moreover, he found that an increased wall temperature only weakly reduces shrinkage, while an increased volume flux during filling reduces shrinkage. Density near the injection gate was higher than far from the gate, while stiffness was higher in longitudinal compared to the transverse direction. Ageing has shown to follow a log-linear behavior, as was confirmed by Fiebig (21). Jansen (42) found that a variation of holding pressure affects both longitudinal and transverse shrinkage.1.1.2 Thesis’ objective and overviewThe main objective of this thesis is to predict the structure di stribution during injection mould-ing in dependence of polymer parameters and processing conditions of semi-crystalline poly-mers, given its direct relevance to dimensional stability and mechanical properties. Different models that describe (flow-induced) crystallization of semi-crystalline polymers are imple-mented in our software code VIp (Polymer Processing & Product Properties Prediction Pro-gram, Caspers (9)). A new model is proposed, based on the molecular conformation in the melt, i.e. the recoverable strain, as expressed by the highest relaxation time using the sec-ond invariant of the Finger tensor, and it replaces the until now used process parameter, the shear rate. The development and validation of thi s model for flow-induced crystallization is elucidated in chapter 3. Specific volume depends strongly on the crystalline structure and represents, therefore, an interesting material property. In chapter 4 the standard methods used to measure the specific volume are summarized and their deficiencies when used to charac-terize semi-crystalline polymers are discussed. A new experimental setup is proposed, able to measure specific volumes of semi-crystalline polymers dependent on both cooling rate and pressure applied. A model is proposed that relates structure distribution to specific vol-ume. Combining the set of equations that describe crystalline structure development, with the model for specific volume and using our injection moulding simulation software VIp, we are,finally, able to try to study the influence of processing variables, as they influence the struc-ture distribution (chapter 5). The thesis endswith a short discussion and recommendations for future research (chapter6).Hunan University of Arts and Science (118.239.51.229) - 2014/10/11Download。

The behavior of light in photoniccrystalsHave you ever wondered how light interacts with matter? Photonic crystals are fascinating materials that can manipulate the behavior of light in a unique way. In this article, we will explore the physics behind photonic crystals and the potential applications of these materials.What are photonic crystals?A photonic crystal is an artificial material that has a periodic structure on the scale of the wavelength of light. This means that the material has a repeated pattern that can interact with light in a controlled way. The periodic structure of photonic crystals can be created using various techniques, such as lithography, self-assembly, and holography.How do photonic crystals affect light?Photonic crystals can affect light in several ways. One of the most important effects is the photonic bandgap. A photonic bandgap is a range of wavelengths of light that cannot propagate through the photonic crystal. This is similar to the electronic bandgap in semiconductors, which blocks the flow of electrons in certain energy regions.The photonic bandgap arises from the interference of the electromagnetic waves within the periodic structure of the photonic crystal. When the wavelength of light is comparable to the distance between the features of the crystal, the wave experiences constructive and destructive interference, leading to the formation of the bandgap. The size and location of the bandgap can be engineered by adjusting the periodicity and shape of the photonic crystal.Another effect that photonic crystals can have on light is the modification of its dispersion relation. The dispersion relation describes the relationship between the wavelength and the direction of light propagation in a certain material. In photonic crystals, the dispersion relation can be altered by introducing defects or changing thestructure of the crystal. This can lead to the formation of photonic modes that have novel properties, such as slow light or supercollimation.Applications of photonic crystalsThe unique properties of photonic crystals have led to a wide range of applications in science and technology. One of the most promising applications is in the field of optical computing. Photonic crystals can be used as waveguides and resonators to create compact and efficient devices for signal processing and communication.Another application of photonic crystals is in the field of solar energy. The bandgap of photonic crystals can be tuned to match the absorption spectrum of solar cells, leading to higher efficiency and reduced waste heat. Photonic crystals can also be used as anti-reflection coatings to enhance the absorption of light in solar panels.Photonic crystals also have potential applications in the field of sensing. The high sensitivity of photonic crystal sensors to changes in the refractive index or chemical composition of the surrounding environment can be used for the detection of biomolecules, gases, and pollutants.ConclusionIn conclusion, photonic crystals are fascinating materials that can manipulate the behavior of light in a controlled way. The photonic bandgap and modification of the dispersion relation are two of the most important effects that photonic crystals can have on light. The unique properties of photonic crystals have led to a wide range of applications in science and technology, including optical computing, solar energy, and sensing. As research in photonic crystals continues to advance, we can expect to see even more exciting applications in the future.。

Rheological and thermodynamic behaviors of different calcium aluminosilicate melts with the same non-bridgingoxygen contentM.Solvanga,1,Y.Z.Yueb,*,S.L.Jensen c ,D.B.DingwelldaDepartment of Production,Aalborg University,Aalborg,DenmarkbSection of Chemistry,Department of Life Sciences,Aalborg University,Aalborg,DenmarkcRockwool International A/S,Hedehusene,DenmarkdDepartment of Earth and Environmental Sciences,University of Munich,Munich,GermanyReceived 28July 2003;received in revised form 8January 2004AbstractThe relationships between the chemical composition and the derivative rheological and thermodynamic values have been determined for two melt series in the anorthite–wollastonite–gehlenite (An–Wo–Geh)compatibility triangle.The melt series have 0.5and 1non-bridging oxygens per tetrahedrally coordinated cation (NBO/T),respectively.The influences of the ratio Si/(Si +AlCa 1=2)and NBO/T on the fragility and the configurational entropy at T g are evaluated.Linear dependencies of the viscosity,the glass transition temperature and the fragility on the ratio Si/(Si +AlCa 1=2)are found for the two melt series.A crossover in the viscosity–temperature relationship is observed for both series,i.e.an inverse compositional dependence of viscosity in the high and low viscous range.The crossover presumably reflects different responses of the adjustment of melt structure to the substitution of Al 3þ+1/2Ca 2þfor Si 4þin the low versus the high viscous ranges.The crossover shifts to higher temperature with increasing NBO/T.Ó2004Elsevier B.V.All rights reserved.PACS:65.50;83.70.G;64.70.Pf1.IntroductionUnderstanding rheology and thermodynamics of the calcium aluminosilicate melts is important for the glass fiber industry,especially the stone wool industry,be-cause it is beneficial to revealing the relationships between chemical composition,properties,and micro-structure of glass fibers.Studying the dependencies of fiber properties,fiber quality,fiber drawing ability on melt composition are crucial for optimizing fiber prop-erties (e.g.bio-solubility and mechanical strength of fi-bers)and production conditions.The melts for making the stone fibers are multicomponent systems,each chemical component of which has a different effect on the rheological and thermodynamic properties.In this work,the three-component aluminosilicate systems:i.e.the CaO–Al 2O 3–SiO 2(CAS)systems are investigated.The three components make up approximately 80mol%of the stone wool fibers.Previous investigations of the compositional depen-dence of melt properties in the CAS system have been focused primarily on the metaluminous join SiO 2–CaAl 2O 4,for which the amount of non-bridging oxygen per tetrahedrally coordinated cation (NBO/T)is equal to 0.In contrast,this study is aimed at increasing the knowledge about the ‘peralkaline’field by studying the compositional dependence of melt properties along the lines with NBO/T ¼0.5and 1.This will allow us to study the compositional effect on the rheological and thermodynamic properties at a constant degree of poly-merization and to explore the structural changes along and between the lines.The chemical compositions of the investigated melts are chosen within the anorthite–wol-lastonite–gehlenite (CaAl 2Si 2O 8–CaSiO 3–Ca 2Al 2SiO 7)(An–Wo–Geh)compatibility triangle (see Fig.1).So far*Corresponding author.Tel.:+45-96358522;fax:+45-96350558.E-mail address:yy@bio.auc.dk (Y.Z.Yue).1Present address:Materials Research Department,RisøNational Laboratory,Frederiksborgvej 399,DK-4000Roskilde,Denmark.0022-3093/$-see front matter Ó2004Elsevier B.V.All rights reserved.doi:10.1016/j.jnoncrysol.2004.02.009Journal of Non-Crystalline Solids 336(2004)179–188the rheological and thermodynamic aspects of the melts in this triangle have not been systematically studied. Hence,this work will contribute to broadening and deepening the knowledge about structure and properties of high aluminosilicate melts.The rheological and thermodynamic properties of aluminosilicate melts are determined by the arrange-ment of the tetrahedral structural units in the melt, which relates to the chemical bonding situation within a structural unit and between units.Aluminum differs from silicon,since tetrahedrally coordinated aluminum has to be charge-balanced by either two alkali cations or one earth alkaline cation[1].The charge-balancing ca-tions for the Al3þtetrahedra play a large role in the melt structure.The structural role of the alkali or earth alkaline cations depends on the melt composition,i.e. whether or not Al3þis present in the melt[2].The short range ordering in the aluminosilicate network depends on the composition and the charge-balancing or net-work modifying cations.For aluminosilicates it is as-sumed that an energetically favorably case is a random occurrence of the network forming linkages Si–O–Si,Si–O–Al and Al–O–Al.The principle of Al-avoidance[3] postulates that the Al–O–Si linkage is more favorable than the combination of Si–O–Si and Al–O–Al linkages. This postulate means that the short range ordering is not random(not totally disordered).A tendency towards Al-avoidance is inferred based on29Si MAS NMR line widths in aluminosilicate glasses[4].However the pres-ence of a small amount of Si–O–Si in glasses of anorthite compositions observed by triple quantum MAS NMR spectroscopy[5]suggests some Al–O–Al linkages[6].The aim of this work is to study the compositional dependencies of melt viscosity,glass transition temper-ature(T g),heat capacity(C p)as well as the derivative properties such as activation energy for viscousflow (D H g),fragility[7]and configurational entropy at T g (S cðT gÞ).The paper presents the results of systematic viscometric and calorimetric experiments on the melts covered by the An–Wo–Geh compatibility triangle,and discusses the difference in the structural arrangement in the high compared to that in the low viscous range. 2.Theoretical modelsViscosity is one of the melt properties,which has been studied intensively due to its sensitivity to compositional variation[8].At afixed temperature it varies by orders of magnitude as a function of composition.An increase in temperature decreases the viscosity,as the structural rearrangements in the melt become easier[8].The viscosity–temperature relationship has been de-scribed by various theories.Adam and Gibbs[9]found the correlation between the structural relaxation time of a glass forming melt and the configurational entropy (S c).In their analysis the relaxation time increases with 1=TS c.The S c decreases with decreasing temperature until it vanishes at the Kauzmann temperature.The Adam and Gibbs theory explains the temperature dependence of the relaxation in terms of the temperature dependence of the size of the cooperatively rearranging region[9].In this work the Adam–Gibbs equation(AG equa-tion)wasfitted to experimental viscosity data to derive S cðT gÞ.The AG equation is expressed aslog g¼log g1þBTS cðTÞ;ð1Þwhere g1is a pre-exponential constant and B is a con-stant containing a free-energy barrier which must be crossed by the rearranging group.The constant g1for the glass series studied in this work was obtained by fitting the viscosity data(in the range from g¼0:3to 1011Pa s)to Eq.(1),which equals2.88·10À4Pa s[10]. The viscosity range for the validity of Eq.(1)was dis-cussed in[11].S cðTÞcan be calculated from the equationS cðTÞ¼S cðT gÞþZ TT gD C pðTÞTd T;ð2Þwhere the D C pðTÞis the difference in heat capacity be-tween the liquid and the glassy state.For the silicate systems,the heat capacity of the liquid state,C p l,is only slightly temperature dependent and hence,can be approximately regarded as a constant.In this work,the C p value at T g is assigned as the heat capacity of the glassy state,C p g[10],Therefore,the D C pðTÞð¼C p lÀC p gÞcan also be treated as a constant D C p.Both C p l and C p g may be directly determined from the DSC measurement. Eq.(2)can thus be transformed into the formS cðTÞ¼S cðT gÞþD C p lnTT g:ð3Þ180M.Solvang et al./Journal of Non-Crystalline Solids336(2004)179–188Introducing Eq.(3)into Eq.(1)leads to the equationlog g¼log g1þBT S cðT gÞþD C p ln Tg;ð4ÞS cðT gÞcan be obtained byfitting Eq.(4)to the viscosity–temperature data.Two contributions to the S cðTÞhave been involved:a chemical and a topological contribu-tion[12].The chemical contribution is independent of temperature,whereas the relative contribution from the topological arrangement increases with temperature. Finally,at high temperatures,the chemical contribution plays a minor role.The topological arrangement is re-flected by the increase of configurational entropy at T over that at T g,and it will increase more in a relative sense for compositions having a higher D C p.Avramov[13–15]proposed a three-parameter equa-tion that is able to predict the change in viscosity as a function of both temperature and composition.The model describes the kinetics of molecular motion in su-percooled melts[13]and the dependence of the viscosity on the entropy of the melt.According to Avramov,the structural units of the system jump with frequencies depending on the activation energy,which they have to overcome.The dependence of the activation energy on temperature is assumed to obey a power decay law [13–15].From this assumption,he proposed the equation describing the dependence of viscosity on temperature:log g¼log g1þe0T rTa;ð5Þwhere g1is a pre-exponent(in Pa s),i.e.the viscosity of a hypothetical liquid state for T!1,e0is the constantequal to log g Tr Àlog g1,a is a fragility index,and T r is areference temperature.In this work,T g is used as T r. Then,e0¼log g TgÀlog g1.The viscosity of silicate meltat T g is g Tg ¼1012Pa s.log g1and e0may be obtained byfitting the viscosity data to Eq.(5).For the melt series studied in this work,the optimal values of log g1and e0, which lead to bestfitting,are found to be)1.7and13.7,respectively,by using the relation log g Tg ¼log g1þe0¼12.Thus,the Avramov equation(AV equation)canbe rewritten aslog g¼À1:7þ13:7T gTa:ð6ÞThe two parameters,log g1and e0,are not sensitive tothe variation in chemical composition of the CAS sys-tems.However,the sensitivity of these parameters to thevariation in chemical composition has not been testedon other melt systems.The comparisons between the AG,the AV,and the VFT(Vogel–Fulcher–Tammann)equations[16–18]were made in[10]with respect to theirfitting qualities tothe viscosity data for the10CAS melts.Then,it wasfound that the order of thefitting quality isVFT<AG<AV,the average residual errors of whichwere0.116,0.113and0.063,respectively[19].3.ExperimentalTen melts covered by the CaAl2Si2O8–CaSiO3–CaAl2SiO7(anorthite–wollastonite–gehlenite)compati-bility triangle and placed along the two lines with NBO/T¼0.5and1,respectively,were synthesized(Fig.1).The melts were synthesized from analytical chemicalsSiO2,Al2O3and CaCO3in a platinum crucible at1898K for3h in a MoSi2box furnace.Subsequently the meltwas quenched on a metal plate.The chemical compo-sitions were analyzed using an X-rayfluorescence spec-trometer(XRF)(Philips1404).The compositions arelisted in Table1.The low viscosities(<104Pa s)were measured by means of a concentric cylinder viscometer in the tem-perature range from1316to1849K at ambient pressure.The viscometer consists of four parts:a furnace,a vis-cometer head,a spindle and a sample crucible.Thefurnace was a MoSi2box furnace(Deltech Inc.ModelDT-31-RS Mode EE)and the viscometer head was aBrookfield model RTVD with a full range torque of7.2·10À2N m,which both were controlled by aTable1The composition of the10CAS samplesSiO2(mol%)Al2O3(mol%)CaO(mol%)Si4þAl3þCa2þCAS149.48.342.30.460.150.39CAS245.610.543.90.410.190.40CAS341.312.746.10.370.220.41CAS437.314.747.90.330.260.42CAS533.016.450.50.280.280.43CAS649.815.135.10.430.260.30CAS744.117.438.50.380.300.33CAS839.519.940.50.330.330.34CAS934.822.542.70.280.370.35CAS1029.424.745.90.240.400.37The compositions are measured using XRF and given in mol%and the cation fraction.M.Solvang et al./Journal of Non-Crystalline Solids336(2004)179–188181computer.The spindle and the sample crucible were made of Pt80Rh20.The details about both method and equipment are described in[20].The viscometer was calibrated using the National Bureau of Standards (NBS)710standard glass.The high viscosities(107–1012Pa s)were measured using the micropenetration method.The measurements were done in a vertical push-rod dilatometer(B€AHR DIL802V)[21].The Deutsche Glasstechnische Gesell-schaft(DGG)Standard Glass I was used for calibration.A good agreement was achieved between the measured viscosity and standard viscosity values,with the least square R2¼0:996[10].In the intermediate viscous range from104to107Pa s,it was impossible to measure the viscosities,because the strong tendency for the melts to crystallize hindered the measurements.A differential scanning calorimeter(DSC)(Netzsch STA449C)was used to determine T g and C p.The glass samples for the DSC measurements were the ones that had already been measured using the concentric cylin-der viscometer.The samples were drilled out from the viscometer crucible wherein the glass melt was left after finishing the concentric cylinder viscometer measure-ments.The size of the samples for DSC measurements were4·4·1mm.For each composition a baseline was measured with two empty crucibles.Then a standard sapphire sample was measured andfinally the sample was measured in two runs.Thefirst run was made in order to give the sample a defined thermal history,i.e.a given cooling rate that equals to the heating rate.The second run was made for determination of T g and C p. All measurements were done under argon with the heating rate10K/min.The maximum temperature of each measurement was approximately100K above T g. T g and C p were determined from the second DSC up-scan curves.T g was defined as the onset temperature of the glass transition peak on the second DSC upscan curve.4.ResultsThe viscosity–temperature relationships measured by both the micropenetration and the concentric cylinder viscometer methods are shown in Fig.2and also listed in Table2.In Fig.2,a crossover is seen for both melt series with NBO/T¼0.5and1,respectively.The crossover means that all viscosity–temperature curves for each melt series pass through the same viscosity–temperature point.It also means that in the highly viscous range the viscosity increases and in the low viscous range decreases with decreasing Si/ (Si+AlCa1=2)ratio.In other words,the compositional dependence of the viscosity for a constant temperature is opposite in the high compared to the low viscosity range.The crossovers are located at T¼1280K(or 104=T¼7:81)for the line NBO/T¼0.5and at T¼1500K(or104=T¼6:67)for the line NBO/T¼1. The T g values obtained using the DSC are listed in Table3.Fig.3shows the influence of Si/(Si+AlCa1=2) on the two isokom temperatures,T log g¼12and T log g¼0, for the melt series NBO/T¼0.5and1,respectively. T log g¼12is the T g of each melt,since generally T g cor-responds to the viscosity g¼1012Pa s.The inverse slopes shown in Fig.3are just a consequence of the crossover.In classical rate theory,the activation energy may be thought of as a potential energy barrier,which is over-come by atoms when they move from one site to another in the melt[22].Melts with high activation energy show a larger response of viscosity to a temperature change than melts with low activation energy.In this work,the activation energies for viscousflow(D H g)were deter-mined both in the glass transition range and in the high temperature range from1750to1850K(see Table3).D H gðT gÞand D H gðHTÞrefer to the activation energy around T g and in the high temperature range,respec-182M.Solvang et al./Journal of Non-Crystalline Solids336(2004)179–188tively.The activation energies were obtained byfinding the slope of the ln g vs.1=T linear relationship over a narrow temperature range[10].Fig.4shows linear de-pendences of both D H gðT gÞand D H gðHTÞon the Si/ (Si+AlCa1=2)ratio.The inset of Fig.2shows the viscosity–temperature relationships scaled by T g.The fragility index a for each melt was found byfitting Eq.(6)to the log g vs.1=T data (see Table3).Fig.5shows that the fragility increases with decreasing Si/(Si+AlCa1=2)for both lines.In addition,it is found that a increases with increasing mol%CaO for both lines(Fig.6).The AG equation(Eq.(4))was used tofind the configurational entropy at T g ðS cðT gÞÞand the results are listed in Table3and shown in Fig.7,where it is seen that S cðT gÞdecreases with decreasing Si/(Si+AlCa1=2).Table2Viscosity as a function of temperature measured on the10CAS meltsCAS1CAS2CAS3CAS4CAS5T(K)log g(Pa s)T(K)log g(Pa s)T(K)log g(Pa s)T(K)log g(Pa s)T(K)log g(Pa s) 1052.711.441065.811.201091.510.561106.410.261106.510.61 1065.910.701066.811.121105.39.921119.19.751111.810.55 1095.69.531073.910.791116.19.401133.29.121124.69.95 1112.38.851094.39.981124.39.151143.48.761141.39.19 1132.68.141110.79.281133.18.721158.48.161153.18.701130.28.521144.78.341166.78.171316 3.221150.88.101340 2.851365 2.511389 2.211413 1.941437 1.751437 1.691461 1.511461 1.481486 1.311486 1.281510 1.141510 1.1015340.9815340.9315580.8215580.7815580.7315580.6915830.6915830.6815830.5815830.5416070.5616070.5116070.4516070.4016310.4416310.3416310.3316310.2816550.3216550.2916550.2316550.1616790.2216790.1916790.1316790.0517040.1217040.1017040.051704)0.0517280.0217280.021728)0.041728)0.141752)0.071752)0.061752)0.111752)0.221752)0.26 1776)0.151776)0.131776)0.181776)0.301776)0.34 1801)0.231801)0.201801)0.241801)0.371801)0.41 1825)0.311825)0.251825)0.311825)0.441825)0.48 1849)0.391849)0.311849)0.381849)0.501849)0.53CAS6CAS7CAS8CAS9CAS101099.210.301111.210.261107.110.621121.110.421129.410.43 1116.29.791123.49.831140.29.401139.99.721137.210.05 1133.09.151140.09.151150.38.931155.88.911144.49.81 1151.28.471153.98.661160.48.601168.18.581150.59.48 1164.57.981156.98.451169.98.251185.37.911166.28.931169.78.031173.88.591558 1.1215830.9616070.9116070.8016310.9016310.7716310.6616550.7716550.6416550.4916790.6516790.5316790.4217040.5417040.4217040.3017040.13 17280.4417280.3217280.2117280.02 17520.3417520.2317520.111752)0.011752)0.07 17760.2517760.1417760.031776)0.101776)0.16 18010.1618010.051801)0.061801)0.191801)0.24 18250.071825)0.031825)0.141825)0.271825)0.32 1849)0.021849)0.111849)0.221849)0.351849)0.39M.Solvang et al./Journal of Non-Crystalline Solids336(2004)179–1881835.DiscussionThe appearance of the crossover(see Fig.2)and in-verse compositional dependence of D H gðT gÞand D H gðHTÞ(see Fig.4)suggest that the changes in struc-tural arrangement with chemical composition are dif-ferent in the high and low viscosity ranges.The change of viscosity of a silicate melt with temperature is directly associated with that of the frequency of the breaking and bridging of T0–O bonds,where T0stands for tetra-hedrally coordinated cations.With increasing tempera-ture,the breaking of T0–O bonds becomes more frequent,so that the structure units become more mobile and viscosity decreases.According to[23],the changes of viscosity of a melt is also associated with the exchange between different Q n units,where n refers to the number of the oxygens per SiO4or AlO4unit(Q),which are shared with another SiO4or AlO4unit[23].Such ex-change controls viscousflow of melts[23–25].The higher the exchange frequency is,the lower is the vis-cosity of the melt.The exchange frequency depends on the glass composition and hence fragility of a melt.In high temperature region a fragile melt has higher ex-change frequency than a strong one,whereas in low temperature region the former has lower exchange rate than the latter.Consequently,the ratio in the exchange rate between the low and the higher temperature in-creases with substitution of Al3þ+1/2Ca2þfor Si4þ.In the high viscous range,the melt structure is not per-Table3Rheological and thermodynamic quantities of the10CAS meltsT g a(K)D H gðT gÞb(kJ/mol)D H g(HT)b(kJ/mol)a c B d(kJ/mol)S cðT gÞd(J/(mol K)) CAS11043937208 4.18252 6.62CAS21057950170 4.36246 6.52CAS31065991172 4.40254 6.47CAS41075992189 4.61246 6.14CAS510841051175 4.62271 6.84CAS61066881231 3.833027.77CAS71075961219 4.052927.35CAS81082939217 4.252847.09CAS910931002217 4.402907.24CAS1011041036213 4.562847.08a Determined using the DSC,with the heating and cooling rates10K/min.b Estimated in the glass transition region as well as in the high temperature(HT)range1700–1850K.c Found by a least squarefit of the viscosity–temperature data using the Avramov equation[10,13].d Obtained byfitting the Adam–Gibbs equation to the viscosity data[9,10].184M.Solvang et al./Journal of Non-Crystalline Solids336(2004)179–188turbed in the same way as in the low viscous range where the structural units of the glass melt are mobile and, hence,the diffusion is faster.If temperature is scaled by T g,the crossover disappears as shown in the insets of Fig.2,but the curvatures of the log g vs.T g=T plots,that are quantified by the fragility index a,become different among the glasses.Thus the existence of a crossover implies the difference in the fragility between the differ-ent glasses.The dependence of viscosity on the temperature indicates a high and a low temperature structural arrangement in the melts.The diffusivity is dramatically lower in a high viscous range compared to that in a low viscous range.In the high viscous range(g¼108–1012 Pa s),both the charge-balancing ions and the network-modifying cations(Ca2þ)have the tendency to attract the neighboring tetrahedra of glass former.Recently,it has been experimentally confirmed that the Ca2þions contract the channels in the glass network as reported in [26].Therefore,the structural network becomes stronger with increasing substitution of Al3þ+1/2Ca2þfor Si4þbecause of the role of Ca2þions.In other words,the connection of tetrahedra becomes stronger,and hence the formation of larger clusters is favored,if Al3þ+1/ 2Ca2þsubstitutes for Si4þ.As a result,the viscosity in-creases with that substitution in the high viscous range. In this case,the topological and cooperative rearrange-ments of the melt structure are dominant in influencing the change in viscosity.In the high viscous range,the diffusion of the structural units(e.g.tetrahedral groups and Ca2þions)in the melt become more difficult with increasingly substitution of Al3þ+1/2Ca2þfor Si4þbe-cause of the strengthening of structural network by Ca2þ.That is why D H gðT gÞincreases with decreasing Si/ (Si+AlCa1=2)(see Fig.4).The strengthening of the melt structure is also reflected by the increase in T g with increasingly substitution of Al3þ+1/2Ca2þfor Si4þ(see Fig.3and Table3).This is because a high T g value corresponds to the high strength and/or the high degree of polymerization of the melt structure.In the low viscous range,the strength of the chemical bonds,including both the charge-balancing ions and the network-modifying cations lying in the interstice be-tween the Al-tetrahedrons becomes weaker and more unstable.The diffusion process of the structural units become faster and more dominant with substitution of Al3þ+1/2Ca2þfor Si4þand hence leads to a decrease in viscosity for both of the NBO/T lines(see Fig.3).The crossover can also be explained by the recent study on difference in structural relaxation time andM.Solvang et al./Journal of Non-Crystalline Solids336(2004)179–188185calcium mobility for calcium aluminosilicate melts.In [27],it has been found that in the high temperature range the characteristic time of the calcium mobility is the same as the structural relaxation.In contrast,in the low temperature range two kinds of relaxation processes exists.Firstly,a fast process,which corresponds to cal-cium mobility,and secondly,a slow one,which corre-sponds to structural relaxation of the aluminosilicate network.The crossover shifts to higher temperature with increasing NBO/T(see Fig.2).In other words,the temperature range above T g,in which a substitution of Al3þ+1/2Ca2þfor Si4þincreases the viscosity,becomes broader.This suggests that an increase in the concen-tration of Ca2þresults in broadening of the temperature range,in which Ca2þions strengthen the melt structure by attracting the tetrahedra and thus enhancing the grouping of these tetrahedra,i.e.the formation of the clusters.Such structure strengthening is reflected by the fact that the T g values of the melts with NBO/T¼1are higher than those of the melts with NBO/T¼0.5,as shown in Fig.3and Table3.The shift of the crossover also implies that the topological and cooperative rear-rangement of the melt structure in the high viscous range is more predominant and the formation of cluster is more favored for the aluminosilicate melt with more Ca2þcontent than for the melt with less Ca2þcontent, whereas the diffusion of the structural units become more hindered for the former than the latter.The fragility index a shows a linear dependence on both the Si/(Si+AlCa1=2)ratio(see Fig.5)and the CaO content(mol%)(see Fig.6)for both melt series with NBO/T¼0.5and1,respectively.This clearly indicates the sensitivity of fragility to the content of Ca2þin the manner that CaO greatly can increase the fragility of the studied glass melt system.From Fig.5,it can also be seen that the fragility changes more dramatically for melts with NBO/T¼0.5compared to that of melts with NBO/T¼1.In Fig.8,the configurational entropy S cðTÞis com-pared between different melts for a certain value of T=T g. At T=T g¼1:1,S cðTÞslightly increases with increasing Si/(Si+AlCa1=2)ratio,whereas at T=T g¼2,S cðTÞde-creases with increasing Si/(Si+AlCa1=2)ratio.This shows that the dependence of S cðTÞat T=T g¼1:1on the Si/(Si+AlCa1=2)ratio is inverse to that for T=T g¼2.In other words,the compositional dependencies of S cðTÞat T=T g¼1:1and at T=T g¼2are inverse.This indicates a relative change of the ratio between the chemical and topological contributions to the configurational en-tropy.With increasing temperature,the relative chemi-cal contribution to S cðTÞdecreases,while the topological contribution increases(see Eq.(4)).The relative increase in S cðTÞwith increasing temperature is largest for the melt with the lowest Si/(Si+AlCa1=2)ratio(see Fig.8), because it has the highest D C p(see Eq.(4))[10].This is related to the fact that the perturbation of the local structural environment becomes more intense with decreasing the Si/(Si+AlCa1=2)ratio.The increase in concentration of Al3þleads to an increase in degree of disorder of the melt structure.In the low temperature range,the chemical contribution controls the configu-rational entropy,whereas in the high temperature range the topological contribution controls the configurational entropy as also discussed in the work[12,28].Regarding each of the two compositional joins (NBO/T¼0.5and1)as part of a mixing series,a neg-ative deviation from linearity in T g values from the end members is anticipated.In an ideal mixing series,a minimum occurs when half of each end member is mixed.This is analogous to the phenomenon that is clearly seen when dealing with the mixed alkali effect [29].A minimum in T g vs.Si/(Si+AlCa1=2)for the lines NBO/T¼0.5and1is observed[10,30].The increasing amount of Al–O–Si bonds relative to that of Si–O–Si bonds results in the decrease in T g when looking in the direction of decreasing Si/(Si+AlCa1=2)until a mini-mum in T g is reached.The minimum is followed by an increase in T g when additionally decreasing the Si/ (Si+AlCa1=2)ratio.This behavior is attributed to the increasing possibility for the charge-balancing cations and the network modifying cations to attract tetrahe-drons.The formation of clusters becomes easier with decreasing the Si/(Si+AlCa1=2)ratio.The consequence is a strengthening of the melt structure.The occurrence of a minimum in T g for the lines NBO/T¼0.5and1can be understood as a consequence of the mixing effect in the manner that S cðT gÞdepends non-linearly on the Si/(Si–AlCa1=2)ratio,but with a maximum at a certain Si/(Si+AlCa1=2)ratio.The mix-ing effect can be regarded as similar to that of the mixed alkali effect[29].For both melt series with NBO/T¼0.5186M.Solvang et al./Journal of Non-Crystalline Solids336(2004)179–188。

AbstractNumerical Analysis of Thermo-Fluid Flow and Crystal/Melt Interface Shape in Czochralski Crystal GrowthStudent: Shu-ShaoWangAdvisor: Prof. Long-SunChaoDepartment of Engineering Science National Cheng Kung UniversitySUMMARYNowadays, the Czochralski (CZ) method is the main silicon single crystal growth method. This method is a good commercial method for growing the larger, high-quality silicon crystal.The aim of this study is simulate the furnace of temperature and argon velocity distribution during difference Czochralski silicon single crystal growth stage by finite element software COMSOL Multiphysics.Heat shields can prevent the heat loss upward, and the optimized flow guide can decrease the SiO deposition on the upper wall. With this optimized hot zone, the temperature gradient near the crystal/melt interface increased and the CZ crystal could be grown at a faster rate.So heat shields and pulling rate are main parameters affecting the heat exchange and crystal growth conditions.Through analyses of the temperature distribution in the crystal and melt, the difference heat transfer conditions and melt flow patterns leading to the formation of convex shape interfaces, concave shape interfaces or W-shape interfaces.The results show that temperature field affected by buoyant force to cause distortion of isothermals in melt.As silicon ingot increases,the temperature and velocity of melt is decrease.And silicon surface will increase cooling that cause the interface is convex shape .The crucible rotation create three vortex in the melt and lead tostable of melt.Before adding heat shield and changing pulling rate, the crystal/melt interface is W-shape. After adding heat shield, the interface became concave shape.After increasing the pulling rate, the shape of the interface became flatter than before.Keywords:Czochralski method, Computer simulation, Interface, Single crystal growth,SiliconINTRODUCTIONThe Czochralski crystal growth process is nowadays commonly used to manufacture high quality crystals. This technology usually costs more than fabrication of poly-Si and therefore question of costs reduction in the CZ production of single crystals and wafers is very important. The melt is placed in a cylindrical crucible, located in a furnace, and is heated to melting temperature by heater. The Czochralski process involves all transport phenomena encountered in solid/liquid phase change systems, including the conduction, convectionand radiation heat transfer.Accordingto references that a flat crystal/melt interface or slight a convex interface to the melt could yield nice single crystals. Hence, it is essential to have accurate and fit condition of the heat transfer process to understand the CZ method and to grow good single crystals. In the CZ method, heat transfer due to conduction in the crystal and heat convection and conduction in the melt should be considered. And the continuous solidification at the crystal/melt interface should be also considered. According to the V/G ratio,when the heat field changes, it would result in the changes of the melt/crystal interface shape. By changing the heat field by heat shield that aim is to decrease the heater power and increase the pulling rate, while maintaining the crystal quality.MATHEMATIC MODEL AND METHODS OF STUDYThe axisymmetric CG6000 furnace geometry adopted in the present work is shown inFig. 1 for a 6 in diameter.The furnace components are made of several materials including steel,insulation material,graphite (heater and crucible), quartz (crucible), and silicon (crystal and melt).The gas phase is Argon.The axisymmetric global furnace model (Fig. 1) is built using the commercial softwareCOMSOL Multiphysics adopting aquasi-steady state approximation.Radiative heat transfer is considered between the crystal and heat component.The water cooled furnace wall in a constant temperature (300 K). The crystallization interface coincides with the melting point isotherm (1685 K).The energy balance at the crystal/melt interface is given by: s l s l s c T T k k u n nρ∂∂-=∆H ∂∂ Where s ρis the crystal density, ∆H the latent heat,s k and l k the crystal and meltconductivity,respectively, s T and l T thecrystal and melt temperature, respectively,c u is the local crystallization rate normal to the crystal/melt interface.The studied growth process is characterized by the 1.5 mm/min pulling rate.The effects of thermo-capillary forces and gas shear stresses on melt flow are taken into account as well as the buoyancy driven forces.The Boussinesq approximation is used to account for the buoyancy effects in the turbulent melt flow.The flow of the melt is governed by k-epsilon of the Reynolds-averaged Navier Stokes (RANS) equations in a rotatingframe which account for Coriolis and centrifugal forces.The gas is entering the furnace through the mass flow inlet at the top opening and leaves it through the pressure outlet at the bottom corner of the vessel.The gas inlet flowrate corresponds to 45 SLPM and the furnace pressure is kept at 20 torr.The study includes the following procedures: (1)Collect and process information of furnace (2)Calculation of the meniscus(triple junction point).The shape of the meniscus usually is found numerically solving the appropriate Laplace-Young equation. (3)Creating models(4)Creating meshes.In zones of special concern,such as the melt and crystal zonesnear the crystal/melt interface,grid meshes are refined.The number of computation grid cells is about 50000. (5)Thermal-fluid coupling analysis (6)Determinethe correct interface. (7)Processing and analyzing results.RESULTS AND DISCUSSIONA typical furnace temperature distribution is shown in Fig. 2. To demonstrate is correct of temperature filed result.The numerical results obtained are also quite similartoresults presented by reference.The crystal/melt interfaces results are shown in Fig. 3.Both are W-shape interface.The simulations are carried out keeping the crucible rotation rate constant (7 rpm). The flow pattern in the melt is composed of three vortices.In Fig. 4, after adding heat shield,Argon gas near the melt surface increases from about 5.27×10-6m/s to about 9.77×10-4m/s.Temperature near the heater decreases from about 1917K to about 1852K.Meaning the heat loss of the furnace is reduced, and the argon flow speeds up around the Heat shield by narrowed channel cross section.The shape of the interface usually shows four types: concave up, concave down, flat and W-shape.There are many factors influencing the shape of crystal/melt interface: heat transfer on interface, melt temperature and convection, pulling rate, crystal rotation rate, diameter and length of the crystal, etc.The above parameters can be adjusted to change the shape of the crystal/melt interface. In Fig. 5,when silicon ingot increases from 9% to 63%.The cooling rate of the crystal is enhanced that leading interface becomeconvex shape.In Fig. 6,before adding heat shield and changing pulling rate, the interface near the crystal axis is convex shape, while adjacent to the edge of the crystal it is concave shape. After adding heat shield, the interface is concave shape.We increase the pulling rate to 2 mm/min after adding heat shield, the shape of the interface become flatter than before.CONCLUSIONIn the study,using simulation software COMSOLMultiphysics, we simulate the heatand flow distributions in the furnace.we drawfollowing conclusions: (1)To demonstrate is correct of temperature filed and crystal/melt interfaces result.(2)Calculation of the meniscus. Meniscus height is 7mm. (3)add a heat shield. The aim is to reduce the heater power and to guide argon gas. (4)The velocity of melt is higher and the temperature of melt is lower,after considering surface tension effect. (5) As silicon ingot increases,the temperature and velocity of melt is decrease. (6)The crucible rotation create three vortex in the melt. (7) As silicon ingot increases,thecrystal/melt interfacebecomeconvex shape. (8)Before adding heat shield and changing pulling rate, the crystal/melt interface is W-shape. After adding heat shield, the interface became concave shape. After increasing the pulling rate, the shape of the interface became flatter than before.Figure1. CG6000 furnaceFigure2. Temperature distribution of GC6000 furnace(a)Dual-zone method (b)Single-zone methodFigure3. Interface deflectionDual-zone method and Single-zone method(a)(a)(b)Figure4. Velocity distribution of crucible rotation(a)Dual-zone method (b) Single-zone methodFigure5. Melt/crystal Interface deflection of differencecrystal lengthFigure6. Melt/crystal interface deflection before and afteroptimization.。

晶格的热平衡的英文Lattice Thermal Equilibrium。

In solid-state physics, the concept of lattice thermal equilibrium plays a crucial role in understanding the behavior of materials at the atomic level. It refers to the state in which the lattice vibrations, or phonons, within a crystal are in a state of balance, resulting in a uniform distribution of energy throughout the material. This phenomenon has significant implications for various properties of solids, including thermal conductivity, specific heat capacity, and even the stability of crystal structures.At the heart of lattice thermal equilibrium lies the principle of energy conservation. In a crystal lattice, energy can be transferred between neighboring atoms through phonons, which are quantized vibrations of the lattice. These phonons carry both energy and momentum, allowing the lattice to exchange thermal energy. However, for the lattice to be in thermal equilibrium, the rate of energy transfer between neighboring atoms must be equal in all directions.To understand this concept further, let us consider a simplified model of a one-dimensional crystal lattice. Imagine a row of identical atoms, each connected to its nearest neighbors by springs. When a phonon is created at one end of the lattice, it propagates through the lattice by transferring energy to the neighboring atoms. As the phonons travel, they undergo scattering events, where they can be absorbed or emitted by the atoms. These scattering events are essential for maintaining thermal equilibrium.In a system at thermal equilibrium, the rate of energy transfer due to phonon absorption must equal the rate of energy transfer due to phonon emission. This balance ensures that the lattice remains in a steady state, with no net flow of energy. If there were a significant imbalance in energy transfer, the lattice would either heat up or cool down, leading to a departure from thermal equilibrium.The concept of lattice thermal equilibrium becomes particularly relevant when considering the thermal conductivity of materials. Thermal conductivity measures amaterial's ability to conduct heat, and it is directly influenced by the efficiency of phonon transport. In materials with strong phonon-phonon scattering, such as amorphous solids, the lattice thermal conductivity is significantly lower compared to crystalline materials. This is because the random arrangement of atoms in amorphous solids disrupts the regular phonon propagation paths, leading to increased scattering events.Furthermore, lattice thermal equilibrium also affects the specific heat capacity of materials. Specific heat capacity measures the amount of heat required to raise the temperature of a given mass of material by a certain amount. In a system at thermal equilibrium, the specific heat capacity is constant and independent of temperature. This is because the energy supplied to the lattice is evenly distributed among the phonons, resulting in a uniform increase in temperature throughout the material.In summary, lattice thermal equilibrium is a fundamental concept in solid-state physics that governs the behavior of materials at the atomic level. It ensures a uniform distribution of energy within a crystal lattice, influencing properties such as thermal conductivity and specific heat capacity. Understanding and controlling lattice thermal equilibrium is crucial for designing materials with desired thermal properties, and it continues to be an active area of research in the field of materials science.。

CHINESE JOURNAL OF CHEMICAL PHYSICS JANUARY25,2016ARTICLECrystallization Behavior and Properties of B-Doped ZnO Thin Films Prepared by Sol-Gel Method with Different Pyrolysis Temperatures Bin Wen a,Chao-qian Liu a∗,Nan Wang a,Hua-lin Wang a,Shi-min Liu a,Wei-wei Jiang a,Wan-yu Ding a,Wei-dong Fei b,c∗,Wei-ping Chai aa.Engineering Research Center of Optoelectronic Materials&Devices,School of Materials Science andEngineering,Dalian Jiaotong University,Dalian116028,Chinab.School of Materials Science and Engineering,Harbin Institute of Technology,Harbin150001,Chinac.School of Mechanical Engineering,Qinghai University,Xining810016,China(Dated:Received on June11,2015;Accepted on August14,2015)Boron-doped zinc oxide transparent(BZO)films were prepared by sol-gel method.The effectof pyrolysis temperature on the crystallization behavior and properties was systematicallyinvestigated.XRD patterns revealed that the BZOfilms had wurtzite structure with apreferential growth orientation along the c-axis.With the increase of pyrolysis temperature,the particle size and surface roughness of the BZOfilms increased,suggesting that pyrolysistemperature is the critical factor for determining the crystallization behavior of the BZOfilms.Moreover,the carrier concentration and the carrier mobility increased with increasingthe pyrolysis temperature,and the mean transmittance for everyfilm is over90%in thevisible range.Key words:Transparent conduction oxide,Thinfilm,Boron-doped ZnO,Pyrolysis tem-perature,Sol-gelI.INTRODUCTIONZinc oxide(ZnO)is a direct wide band gap semicon-ductor with E g=3.37eV,and is naturally an n-type semiconductor due to oxygen vacancies and interstitial zinc atoms.In addition,ZnO is abundant,nontoxic, and stable in reducing atmosphere.It is considered as a promising candidate to replace indium tin oxide as transparent conducting electrodes in solar cell devices andflat panel display[1−3].To enhance the electri-cal properties of ZnO,various atoms(e.g.Al,In,Ga, B,F)have been employed as donors[4−7].Wherein, boron-doped ZnO has not only high transparency over the visible and near-infrared range,and low electrical resistivity,but also excellent light scattering property [8,9].Therefore,B-doped ZnO thinfilm has attracted some attention in recent years.Generally,B-doped zinc oxide(BZO)thinfilms were primarily synthesized by chemical vapor deposition [10−15]and spray pyrolysis[16,17].Also,there are a few studies on the BZO thinfilms deposited by sol-gel method[18−23].The sol-gel process has many advan-tages in preparing thinfilms,including low cost,excel-lent compositional control,easy handling and feasibility of deposition on large-area substrate[24].In previous studies on the BZOfilms prepared by sol-gel process,∗Authors to whom correspondence should be addressed.E-mail: cqliu@,wdfei@ the effects of annealing temperature[18],doping con-centration of boron[19−23],and pH of precursor sol [1]on the crystallization,microstructure,electrical and optical properties of BZOfilms were reported system-atically.To the best of our knowledge,the effect of py-rolysis temperature on the properties of BZOfilm has not been reported.In this work,BZOfilms were pre-pared by sol-gel spin coating and pyrolyzed at different temperatures,and the dependence of the properties of the BZOfilms on the pyrolysis temperatures was inves-tigated.II.EXPERIMENTSBoron-doped ZnO precursor solution was prepared from zinc acetate di-hydrate(Zn(Ac)2·2H2O,AR)and boric acid(H3BO3,GR)as sources for Zn and B,where the B/Zn atomic ratio wasfixed at0.5at.%.The de-tailed solution preparation was described in our previ-ous work[23].Thefilms were prepared by spin-coating the solution onto cleaned quartz glass substrates under 2000r/min for10s atfirst.Then,each layer was di-rectly put into a homemade tube furnace at350−500◦C for2min to evaporate the solvent and pyrolyze organ-ics,where the heating time from room temperature to pyrolysis temperature was0.5min.The details of the homemade tube furnace were also described in our pre-vious work[25].The spin-coating pyrolyzing procedure was repeated5times for eachfilm.Finally,the de-positedfilms were annealed at500◦C for5min in ArDOI:10.1063/1674-0068/29/cjcp1506116c⃝2016Chinese Physical SocietyChin.J.Chem.Phys.Bin Wen et al. atmosphere.The thickness of all thefilms was about160nm measured by a step profiler(Veeco Dektak6M).The crystal structure of thefilms was analyzed byan X-ray diffractometer(PANalytical Empyrean)withCu Kα1radiation(λ=1.54056˚A)and a G¨o bel mirror at40kV and40mA,where the step size and the count-ing time were0.05◦and0.5s respectively.The surfacemorphologies of the thinfilms were characterized usingan atomic force microscope(AFM,Bruker Multimode8).A Hall effect measurement system(Swing HALL8800)was employed to measure the electrical propertiesof thefilms.Optical transmittance measurements wereperformed by an ultraviolet-visible spectrophotometer(Hitachi U-3310)in the wavelength range from300nmto900nm.III.RESULT AND DISCUSSIONA.StructureThe XRD scan patterns of the BZO thinfilms py-rolyzed at different temperatures are shown in Fig.1(a).It is clear that thefilms exhibit a single-phase hexagonalstructure(wurtzite ZnO JCPDS No.36-1451)and havethe preferred orientation of(002)(i.e.,c-axis preferredorientation).Moreover,the intensity of(002)reflectionwas enhanced with increasing the pyrolysis tempera-ture,suggesting that the pyrolysis temperature is thecritical factor determining the crystallization behaviorof the BZOfilms in the present work.To estimate theaverage grain size of the samples,the Scherers equationis employed:D=0.89λβcosθ(1)where D is the grain size,λis the X-ray wavelength of1.54056˚A,θis Bragg diffraction angle,andβis the full-width at half-maximum(FWHM)of the diffraction peak corresponding to2θ.The FWHM values and cal-culated average grain sizes of thefilms pyrolyzed at dif-ferent temperatures are shown in Fig.1(b).It is clear that the grain size increased with increasing the pyrol-ysis temperature.B.MorphologyIn order to understand deeply the influence of pyrol-ysis temperature on the crystallization behavior of the BZOfilms,the surface morphologies of thefilms were characterized by AFM in contact mode and are shown in Fig.2.From the two-dimensional AFM images,the combined tendency of the particles in thefilms can be clearly observed with increasing pyrolysis temperature. This result also suggests that the pyrolysis temperature is the critical factor for determining the crystallization behavior of the BZOfilms.FIG.1(a)XRD2θscan patterns and(b)FWHM valuesand average crystallite sizes of the BZOfilms deposited atdifferent pyrolysis temperatures.The influence of the pyrolysis temperature on thegrowth behavior of the sol-gel derived BZOfilms canbe understood on the basis of the understanding ofthe pyrolysis process.Primarily,the source material ofZn(Ac)2·2H2O involved in two chemical reaction pro-cesses in the precursor solution[26].Thefirst was areversible hydrolysis reaction:Zn(CH3COO)2·2H2O↔(ZnCH3COO)++CH3COO−+2H++2OH−(2) Then hydrolysis products reacted with mo-noethanolamine in the solvent of2-methoxyethanol through the following chemical reaction:CH3COOZn++CH3COO−+2H++2OH−+NH2CH2CH2OH→Zn(OH)2+CH3COONH2+CH3COOCH2CH3+H2O(3) Evidently,the reaction resultant of Zn(OH)2in the precursor solution is the source of the primary sol par-ticles,and then can form the gel network in the spin-coating processes and can be adsorbed onto the sub-strate to form precursorfilm.According to the previ-ous studies[27,28],it can be known that the organic solvents and reaction resultants in the precursorfilmDOI:10.1063/1674-0068/29/cjcp1506116c⃝2016Chinese Physical SocietyChin.J.Chem.Phys.B-doped ZnO Thin Films(a)(c)(e)(b)(d)(g)(f)(h)0.0 1.0 µm-12.3 nm11.6 nm-20.0 nm12.9 nm13.1 nm16.0 nm-12.3 nm-12.2 nm0.0 1.0 µm0.0 1.0 µm0.0 1.0 µm−0.411.6 0.20.40.60.80.312.9 0.20.40.60.80.20.40.60.80.20.40.60.80.413.1 -0.2 16.0 nm µmµmµmµm0.20.40.60.80.20.40.60.80.20.40.60.80.20.40.60.8nm nm nm FIG.2Two-and three-dimensional AFM images of the BZO films deposited at (a,b)350◦C,(c,d)400◦C,(e,f)450◦C,(g,h)500◦Ccan be entirely evaporated or pyrolyzed at the pyrolysis temperature below 350◦C.Moreover,the decomposi-tion temperatures of Zn(OH)2and H 3BO 3are about 125and 185◦C,respectively.The above discussion in-dicates that there should not be any residual organic component or other volatile matter in the as-pyrolyzed films.Kang et al .[29]considered that the residual or-ganic components in the as-pyrolyzed films would sup-press the crystal growth of the films.Therefore,in our present work,the effect on the particle size in the an-nealed films should be controlled mainly by the pyroly-sis temperature.As for the further understanding about the effect of the pyrolysis temperature on the growth behavior of the sol-gel derived BZO films,it is described as the follow-ing.It is clear that the particle size is very small and less than 20nm in diameter in the film pyrolyzed at 350◦C shown in Fig.2(a).Thus it can be reasonably deduced that the sol particle size in the precursor solu-tion should be smaller than 20nm.As is well known,generally,the smaller the nanoparticle size is,the higher the specific surface energy of the nanoparticle is.There-fore,in the pyrolysis process for preparing the BZO films,the sol particles in the precursor films were easy to merge,and the merging process was susceptible to the pyrolysis temperature.However,the grain growth in the as-pyrolyzed films was difficult in the post anneal-ing process at 500◦C for 5min.Generally,the grain growth due to post annealing corresponds to a recrys-tallization process.When the annealing temperature and time is not high or long enough,the grain growth is difficult.Therefore,although the as-pyrolyzed BZO films were annealed at 500◦C for 5min,the particle size in the films was still mainly controlled by thepyrolysisFIG.3RMS roughness of the BZO films deposited at dif-ferent pyrolysis temperatures.temperature.From that discussed above,we think the pyrolysis temperature is the critical factor affecting the crystallization behavior of the BZO films.The root-mean-square (RMS)roughness of the BZO thin films is shown in Fig.3.It can be seen that the RMS roughness of the thin films increased with increasing py-rolysis ly,the RMS roughness value of the BZO film pyrolyzed at 350◦C was about 2.5nm,and then that of the BZO film pyrolyzed at 500◦C in-creased to about 4.9nm.Evidently,the increase of the RMS roughness originated from the grain growth with increasing pyrolysis temperature.C.Electrical propertiesHall measurements were carried out at room tem-perature to investigate the electrical properties of BZODOI:10.1063/1674-0068/29/cjcp1506116c ⃝2016Chinese Physical SocietyChin.J.Chem.Phys.Bin Wen et al.FIG.4Electrical properties of the BZOfilms as a function of the pyrolysis temperature.films.The resistivity,Hall carrier concentration,and mobility of thefilms as a function of the pyrolysis tem-peratures are presented in Fig.4.When the pyrolysis temperature was raised from350◦C to500◦C,the carrier concentration of the BZOfilms increased from 5.27×1018cm−3to1.77×1019cm−3,and the carrier mo-bility increased from2.04cm2/(V·s)to7.58cm2/(V·s). The increases in the carrier concentration and mobility should be attributed to the crystallization enhancement with increasing pyrolysis temperature.Logically,when the crystalline state of the sample of B-doped ZnO is poor,there will be a large amount of amorphous ZnO and boron oxide in the sample.The crystallization en-hancement means more B atoms were doped into the crystal lattice of ZnO to replace the Zn2+,and then more free charge carrier was released.As a result,the carrier concentration increased with increasing pyroly-sis temperature.Moreover,the crystallization enhance-ment also means the defect concentration in thefilms decreased with increasing pyrolysis temperature.Cor-respondingly,the carrier mobility of the BZOfilms in-creased with increasing pyrolysis temperature.At the pyrolysis temperature of500◦C,the BZOfilm has the lowest resistivity(4.64×10−2Ω·cm)in the present work.D.Optical propertiesThe transmittance spectra(T)of the BZOfilms were measured at room temperature by an ultraviolet-visible spectrophotometer,and are shown in Fig.5(a).All the transmittance spectra show mean values higher than 90%in the visible range.Moreover,it can be observed that the mean transmittances of thefilms in the visi-ble range arefluctuant with pyrolysis temperature.The mean transmittance of thefilm pyrolyzed at350◦C was lower than that of thefilm pyrolyzed at400◦C in the visible range,which may be attributed to the difference in the crystalline states of the twofilms.According to the calculated grain size shown in Fig.1(b)and the two-dimensional AFM images shown in Fig.2,the crystalline state of thefilm pyrolyzed at350◦C was slightly weaker than that of thefilm pyrolyzed at400◦C.Therefore, the defect concentration in the former was higher than that in the latter,and then the mean transmittance of the former was lower than that of the latter in the visible range.When the the pyrolysis temperature ex-ceeded400◦C,the mean transmittance decreased with increasing pyrolysis temperature,which should be due to the increase of carrier concentration with increasing pyrolysis temperature.Generally,the higher the free carrier concentration is,the more serious the free car-rier absorption and reflection in the visible range are. Therefore,according to the Hall measurement results, the mean transmittance of transmittance of thefilms pyrolyzed at higher temperature is lower in the visible range.Generally,boron-doped ZnO is considered as a direct energy gap semiconductor,thus the relationship among absorption coefficient,photon energy,and optical band gap is(αhν)2=A(hν−E g)(4) where A is a constant for a direct transition,hνis pho-ton energy,αis the optical absorption coefficient,and E g is the optical energy gap.To identifyαfor the BZO films,Lambert’s law is used:α=1dln1T(5)where d is thefilm thickness and T is the transmit-tance spectra.The E g was obtained by extrapolating downwards the corresponding straight lines till the in-tersection with energy axis,as shown in Fig.5(b).The determined optical band gaps are shown in the inset of Fig.5(b).The slight blue-shift in optical energy gap is clear with increasing the pyrolysis temperature.The in-crease in optical band gap of the BZO thinfilms should be attributed to Burstein-Moss effect.IV.CONCLUSIONWe have investigated the effect of pyrolysis temper-ature on the crystallization behavior,electrical and optical properties of sol-gel-derived boron-doped ZnO (BZO)films,and found that pyrolysis temperature was a critical factor affecting the crystallization behavior of the sol-gel-derived BZOfilms.XRD patterns revealed that all the BZOfilms had wurtzite structure with a preferential growth orientation along the c-axis.With increasing the pyrolysis temperature,the grain size ofDOI:10.1063/1674-0068/29/cjcp1506116c⃝2016Chinese Physical SocietyChin.J.Chem.Phys.B-doped ZnO Thin FilmsFIG.5(a)Transmittance spectra and(b)(αhν)2versus hνplot of the BZOfilms deposited at different pyrolysis temperatures.Inset:the optical band gap of thefilms.the BZOfilms increased,and the RMS roughness of thefilms also increased.The mean transmittance for everyfilm was over90%in the visible range,and the optical band edge of the BZOfilms exhibited blue shift with increasing pyrolysis temperature.Moreover,with increasing pyrolysis temperature,the carrier concentra-tion and the carrier mobility increased.V.ACKNOWLEDGMENTSThis work was supported by the National Natural Sci-ence Foundation of China(No.51302024,No.51002018 and No.51472039),the Program for Liaoning Excel-lent Talents in University(No.LJQ2012038),the Higher Specialized Research Fund for the Doctoral Program (No.20122124110004),the Project of Education Depart-ment of Liaoning Province(No.L2013179),the Project of Open Research Foundation of State Key Laboratory of Advanced Technology for Float Glass(No.KF1301-01),the Dalian Science and Technology Plan Project (No.2011A15GX025),the Dalian Science and Technol-ogy Plan Project(No.2010J21DW008),and the Qinghai Province Science and Technology Project(No.2012-Z-701).[1]B.Houng, C.L.Huang,and S.Y.Tsai,J.Cryst.Growth307,328(2007).[2]A.Banejee and G.Guha,J.Appl.Phys.69,1030(1991).[3]J.Y.Liu,X.X.Yu,G.H.Zhang,Y.K.Wu,K.Zhang,N.Pan,and X.P.Wang,Chin.J.Chem.Phys.26,225 (2013).[4]Y.S.Kim and W.P.Tai,Appl.Surf.Sci.253,4911(2007).[5]J.C.Wang,F.C.Cheng,Y.T.Liang,H.I.Chen,C.Y.Tsai,C.H.Fang,and T.E.Nee,Nanoscale Res.Lett.7,270(2012).[6]N.A.Estrich,D.H.Hook,A.N.Smith,J.T.Leonard,ughlin,and J.P.Maria,J.Appl.Phys.113,233703(2013).[7]J.Wen,C.Y.Zuo,M.Xu,C.Zhong,and K.Qi,Eur.Phys.J.B80,25(2011).[8]S.Fa¨y,J Steinhauser,N.Oliveira,E.V.Sauvain,andC.Ballif,Thin Solid Films515,8558(2007).[9]X.G.Xu and H.L.Yang,Appl.Phys.Lett.97,232502(2010).[10]G.Kim,J.Bang,Y.Kim,and S.K.Rout,Appl.Phys.A97,821(2009).[11]X.L.Chen,B.H.Xu,J.M.Xue,Y.Zhao,C.C.Wei,J.Sun,Y.Wang,X.D.Zhang,and X.H.Geng,Thin Solid Films515,3753(2007).[12]S.Y.Myong,J.Steinhauser,R.Schluchter,S.Fay,E.V.Sauvain,A.Shah,C.Ballif,and A.Rufenacht,Sol.Energy Mater.Sol.Cells91,1269(2007).[13]J.Hu and R.G.Gordon,J.Electrochem.Soc.139,2014(1992).[14]W.W.Wenas,A.Yamada,and K.Takahashi,J.Appl.Phys.70,7119(1991).[15]W.W.Wenas,A.Yamada,M.Konagai,and K.Taka-hashi,Jpn.J.Appl.Phys.30,L441(1991).[16]B.N.Pawar,S.R.Jadkar,and M.G.Takwale,J.Phys.Chem.Solids66,1779(2005).[17]B.J.Lokhande,P.S.Patil,and M.D.Uplane,PhysicaB302,59(2001).[18]V.Kumar,R.G.Singh,F.Singh,and L.P.Purohit,J.Alloy Compd.544,120(2012).[19]M.Caglara,S.Ilican,Y.Caglar,and F.Yakuphanoglu,pd.509,3177(2011).[20]R.B.H.Tahar and N.B.H.Tahar,J.Mater.Sci.40,5285(2005).[21]S.Jana, A.S.Vuk, A.Mallick, B.Orel,and P.K.Biswas,Mater.Res.Bull.46,2392(2011).[22]V.Kumar,R.G.Singh,L.P.Purohit,and R.M.Mehra,J.Mater.Sci.Technol.27,481(2011).[23]B.Wen,C.Q.Liu,W.D.Fei,H.L.Wang,S.M.Liu,N.Wang,and W.P.Chai,Chem.Res.Chin.Univ.30, 509(2014).[24]H.H.Huang,B.Orler,and G.L.Wilkes,Polym.Bull.14,557(1985).[25]N.Wang,C.Q.Liu,B.Wen,H.L.Wang,S.M.Liu,and W.P.Chai,Mater.Lett.122,269(2014).[26]A. 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Study of the Phase Behavior of LiquidCrystalsLiquid crystals are materials that exhibit an intermediate state of matter between a liquid and a solid crystal. This unique phase is characterized by anisotropic properties that are similar to those of crystals, such as the ability to align in one direction, while maintaining the ability to flow like a liquid. Liquid crystals are a vital component in the technology behind liquid crystal displays (LCDs), which are widely used in televisions, computer monitors, and mobile phones.The study of the phase behavior of liquid crystals is of great importance in the design and development of new liquid crystal materials and devices. It involves understanding the behavior of liquid crystals in different phases and under different conditions, such as temperature and pressure. The following will discuss the key concepts related to the study of phase behavior in liquid crystals.Phases of Liquid CrystalsLiquid crystalline phases are characterized by the orientation and positional order of the molecules. The three main phases of liquid crystals are nematic, smectic, and cholesteric.Nematic liquid crystals are characterized by their orientation order. The molecules in a nematic phase are aligned in one direction, forming a long-range orientation order, but the positional order remains random. This results in the ability of nematic liquid crystals to flow like a liquid but maintain their alignment.Smectic liquid crystals are characterized by their positional order. The molecules in a smectic phase are aligned in layers, forming a long-range positional order, but the orientation order is random. This results in the ability of smectic liquid crystals to flow like a liquid within the layers but remain rigid in the perpendicular direction.Cholesteric liquid crystals are characterized by a periodic twisting of the orientation order. The molecules in a cholesteric phase are aligned in one direction, but the direction twists periodically. This results in the ability of cholesteric liquid crystals to reflect light of a specific wavelength and form colors.Phase TransitionsPhase transitions in liquid crystals occur when external conditions, such as temperature, pressure, or electric fields, cause changes in the orientation or positional order. These transitions result in changes in the physical properties of the liquid crystal, such as viscosity, thermal expansion, and refractive index.The most common phase transition is the nematic–isotropic transition, which occurs when a nematic liquid crystal changes to an isotropic liquid. This transition typically occurs at a specific temperature, called the clearing point, and is characterized by a sudden change in the physical properties of the liquid.Another important phase transition is the smectic–nematic transition, which occurs when a smectic liquid crystal changes to a nematic liquid crystal. This transition is characterized by changes in molecular orientation and the formation of defects in the layers.Effects of External FieldsExternal fields, such as electric or magnetic fields, can have a significant effect on the phase behavior of liquid crystals. The response of liquid crystals to external fields is known as electro-optic effect or magneto-optic effect, depending on the type of field used.In an electric field, the orientation of the liquid crystal molecules can be controlled, resulting in changes in the refractive index and the reflection of light. This effect is used in LCDs to create images by controlling the orientation of the liquid crystal molecules through the application of an electric field.Magnetic fields can also change the orientation of liquid crystal molecules. This effect is used in magneto-optic devices, such as optical isolators and switches.ConclusionThe study of the phase behavior of liquid crystals is an important area of research that has led to significant advances in the development of liquid crystal materials and devices. The understanding of the different phases and phase transitions is essential for the design and development of new liquid crystal technologies. The ability to control the behavior of liquid crystals through external fields has led to a range of applications in displays, sensors, and optical devices. Further research in this area will undoubtedly lead to new and exciting developments in liquid crystal technology.。

16 CrystallizationOn both large and small scale crystallization is the most important method for the purification of solid organic compounds. A crystalline organic substance is made up of a three-dimensional array of molecules held together primarily by vender wades forces. These intermolecular attractions are fairly weak; most organic solids melt in the range of room temperature to 250 ℃．Crystals can be grown from the molten state just as water is frozen into ice, but it is not easy to remove impurities from crystals grade in this way. Thus most purification in the laboratory involves dissolving the material to be purified in the appropriate hot solvent. As the solvent cools, the solution becomes saturated with respect to the substance. Soluble impurities stay in solution because they are not concentrated enough to saturate the solution. The crystals are collected by filtration, the surface of the crystals is washed with cold solvent to remove the adhering impurities, and then the crystals are dried. This process is carried out on an enormous scale in the commercial purification of sugar.In the organic laboratory, crystallization is usually the most rapid and convenient method for purifying the products of a reaction. Initially you will be told which solvent to use to crystallize a given substance and how much of it to use; Later on you will judge how much solvent is needed, acid finally the choice of both the solvent and its volume will be left to you. It takes both experience and knowledge to pick the correct solvent for a given purification.The process of crystallization can be broken into seven discrete steps: choosing the solvent, dissolving the solute decolorizing the solution, removing suspended solids, crystallizing the solute. Collecting and washing the crystals and drying the product. The process involves dissolving the impure substance in all appropriate hot solvent, removing some impurities by decolorizing and/ or filtering the hot solution, allowing the substance to crystallize as the temperature of the solution falls, removing the crystallization solvent, and drying the resulting purified crystals.16. 1 Choosing the Solvent“Like dissolves like'', some common solv ents are water, methanol, ethanol, ligroin and toluene. When you use a solvent pair, dissolve the solute in the bettersolvent and add the poorer solvent to be hot solution until saturation occurs. Some common solvent pairs are ethanol-water, diethyl ether ligroin, and toluene-ligroin.16. 2 Dissolving the SoluteTo the crushed or ground solute in the Erlenmeyer flask or reaction tubes add solvent; heat the mixture to boiling. Add more solvent as necessary to obtain a hot, saturated solution.16. 3 Decolorizing the SolutionIf it is necessary to remove colored impurities, cool the solution to near room temperature and add more solvent to prevent crystallization from occurring. Add decolorizing charcoal in the form of palletized. Norit to the cooled solution, and then heat it to boiling for a few minutes, taking care to swirl the solution to prevent bumping. Remove the norit by filtration, and then concentrate the filtrate.16. 4 Filtering Suspended SolidsIf it is necessary to remove suspended solids, dilute the hot solution slightly to prevent crystallization from occurring during filtration. Filter the hot solution. Add solvent if crystallization begins in the funnel. Concentrate the filtrate to obtain a saturated solution.16. 5 Crystallizing the SoluteLet the hot saturated solution cool spontaneously to room temperature. Do not disturb the solution. Then cool it in ice. If crystallization does not occur, scratch the inside of the container or add seed crystals.16. 6 Collecting and Washing the CrystalsCollect the crystals using the pasteur pipet method or by vacuum filtration on a Hirsh funnel or a buchner funnel. If the latter technique is employed, wet the filter paper with solvent, apply vacuum until solvent just disappears, break vacuum, add cold wash solvent, apply vacuum, and repeat until crystals are clean and filtrate cones through clear.16. 7 Drying the ProductPress the product on the filter to remove solvent. Then remove it from the filter, squeeze it between sheets of filter paper to remove more, and spread at on a watch glass to dry.。

Role of Heat Transfer and Thermal Conductivity in the Crystallization Behavior of Polypropylene-Containing Additives:A Phenomenological ModelS.Radhakrishnan,Pradip S.SonawanePolymer Science&Engineering,National Chemical Laboratory,Pune411008,IndiaReceived5June2002;accepted5November2002ABSTRACT:The thermal conductivity of afiller and the thermal conductivity of a composite made from thatfiller influence the heat-transfer process during melt processing. The heat-transfer process from the melt to the mold wall becomes an important factor in developing the skin–core morphology.These aspects were examined in this study. The thermal conductivity of polypropylene–filler compos-ites was estimated with a standard model for variousfillers such as calcium carbonate,talc,silica,wollastonite,mica, and carbonfibers.The rate of cooling under given condi-tions,including the melting temperature,mold wall temper-ature,mass of the composite,andfiller content,was esti-mated with standard heat-transfer equations.The time to attain the crystallization temperature for polypropylene was evaluated with a regression method with differential tem-perature steps.The crystallization curves were experimen-tally determined for the differentfillers,and from them,the induction period for the onset of crystallization was esti-mated.These observations were correlated with the ex-pected trends from the aforementioned formalism.The ex-cellentfit of the curves showed that in all these cases,the thermal conductivity of thefiller and composite played a dominant role in controlling the onset of the crystallization process.However,the nucleation effects became important in the later stages after the crystallization temperature was attained.©2003Wiley Periodicals,Inc.J Appl Polym Sci89: 2994–2999,2003Key words:poly(propylene)(PP);crystallization;thermal properties;fillers;additivesINTRODUCTIONPolymers are generally used with different types of additives,such as stabilizers,processing aids,coloring agents,andfillers.In the polymer processing industry, many types offillers are incorporated into resins for different reasons,including improvements in the me-chanical properties,color matching,surfacefinishing, gloss,and cost reduction.1–3Polypropylene(PP)has drawn considerable attention in recent years because it can be modified by additives andfillers to obtain properties that are comparable to those of engineering plastics.4,5These various additives are known to affect the crystallization behavior of the polymer.Studies have been reported by several groups,including our own,on the crystallization behavior of PPs containing calcium carbonate,calcium sulfate,talc,mica,and wollastonite.In most of these studies,the emphasis was placed on the nucleation,preferential growth,and so forth.6–10However,it is well known that the rate of cooling plays an important role in determining the crystallinity and/or morphology obtained in thefinal product made by melt processing.11Because the ther-mal conductivity of thefiller and that of the composite containing thatfiller are important factors governing the heat-transfer process,we felt that a systematic investigation into the role of thermal conductivity in the crystallization of PPs containing differentfillers would lead to a better understanding of these phe-nomena.However,until now,no work has been re-ported on developing the corelationships of the ther-mal conductivity,induction time,cooling time,crys-tallinity value,and so forth.Furthermore,because the crystal structure and the morphology are responsible for the properties of thefinal product,a knowledge and understanding of the crystallization process are important for designing the material for a given prod-uct.This article addresses these issues,and an attempt has been made to correlate the different parameters with the help of a phenomenological model described here.PHENOMENOLOGICAL MODEL Polymers are usually processed in industry by either injection molding or extrusion techniques.The crys-tallization of a polymer from the melt takes place while it cools in the mold or as it extrudes out in the cooling zone(usually a water trough).During this step,the heat from the melt has to be transferred to the surroundings.In the injection-molding and compres-Correspondence to:S.Radhakrishnnan(srr@che.ncl.res.in). Journal of Applied Polymer Science,Vol.89,2994–2999(2003)©2003Wiley Periodicals,Inc.sion-molding processes(considered for simplicity), the polymer is in contact with the mold,and the heat is conducted away from the melt by the mold walls. Because the polymer(melt or solid)has a quite low thermal conductivity(ca.0.01W/m),the heat transfer from the central portion of the melt is much slower than that at the surface.This leads to uneven crystal-lization rates through the polymer,giving rise to a skin–core morphology,as indicated in Figure1.Such morphological features have been reported previously by some authors,but they have not been correlated with the rate of heat transfer or the thermal conduc-tivity.12,13The addition offillers to the polymer leads to large changes in the thermal conductivity,giving rise to faster cooling.Therefore,this aspect isfirst considered in this formalism.The thermal conductivity(K)of polymers contain-ingfillers can be estimated by different models devel-oped for such composites,including the simple rule of mixtures,series/parallel models,the Hashin–Schtrik-man model,the Hamilton–Crosser model,and Niels-en’s model.14,15Among these,Nielsen’s model16is known to be most accurate in predicting the values of K.Therefore,it was used here.According to this model,the K value of a composite is given byK c K p ϭ͓1ϩ͑AϪ1͒B␾͔͑1Ϫ␺B␾͒(1)␺ϭ1ϩ͑1Ϫ␾max͒␾␾max2(2)Bϭ͑K f/K pϪ1͒͑K f/K pϩAϪ1͒(3)where␾is thefiller concentration(volume fraction);A and B are parameters;␾max is the maximumfiller packing for a given geometry;and the subscripts c,f, and p give the corresponding values for the composite,filler,and polymer,respectively.The coefficient A de-pends on the geometry and orientation of thefiller particles.Nielsen provided values of A for a wide range of commonfiller types.For sphericalfiller par-ticles,A is2.5.The values used for the parameters A and␾max in Nielsen’s equation are2.5and0.637,re-spectively.The values of K,the specific heat(C p),and ␾max for thefillers used are indicated in Table I.PP byitself has K and C p values of0.23W/mK and0.427 cal/g°C,respectively.17The K value for each of the compositions was estimated with these values in eqs.(1)–(3).These are indicated in Tables II and III.The rate of cooling of a molten composite can be estimated as follows.Initially,when the melt comes in contact with the external mold wall surface,the heat is transferred according to the Fourier equation for un-steady heat transfer in one dimension(x).A heat bal-ance for the object being cooled then gives the amount of heat transferred in the time interval(⌬t)as follows:⌬Q⌬tϭͫKA1⌬T⌬xͬ⌬Qϭ͑mC p⌬T͒(4)where⌬T is the temperature difference between the melt and the external medium,A1is the cross-section area,⌬x is the thickness of the sample,and m is the mass.It is assumed that the heat,once transferred to the wall,is rapidly conducted away(the metalbeingFigure1Schematic diagram of polymer melt cooling in themold with the formation of a skin layer.TABLE IReported Standard Values for K and C pfor Different Fillers21–24Filler typeK(W/mK)C p(cal/g.°C)⌽maxWollastonite0.8240.240.62Silica 1.490.190.70Glassfiber 1.170.1970.42Talc 2.090.2030.45Mica 2.50.2070.38Calcium carbonate 2.70.210.80Carbonfiber70.20.40TABLE IIDependence of the Induction Period on the K Values ofPP with Fillers at10wt%Composition(10wt%)K a(W/mK)Induction period b(s)Pure PP0.23263PPϩwollastonite0.263191PPϩglassfiber0.271183PPϩsilica0.277138PPϩtalc0.285135PPϩmica0.286140PPϩcalciumcarbonate0.286130PPϩcarbonfiber0.292108a Estimated from eqs.(1)–(3).b Samples isothermally crystallized at115°C from thestarting melt at200°C.HEAT TRANSFER AND THERMAL CONDUCTIVITY29951000times better as a conductor than the polymer). The cooling curve(the temperature at any given time) was generated with a⌬t value of1min.Equation(4) was used for estimating the temperature difference for the initial step,which gave the temperature attained by the melt after⌬t,which was then subsequently used for the next step and so on.The values of K and C p were those estimated for that type offiller and composition with the Nielsen model,which was de-scribed previously.To estimate the induction time for the onset of crys-tallization,we assumed that the melt had to reach the temperature at which maximum crystallization was observed for that polymer.Therefore,a line through this temperature was drawn parallel to the time axis on the cooling curve,and the common points gave the induction times for crystallization for that composi-tion.The nucleation effects were not taken into con-sideration,but they are discussed later in the article.EXPERIMENTALPP(Indothane,SM85N,MFI8-12,IPCL,India)was made into afine powder form by the precipitation of its solution followed by thorough washing with ace-tone and drying for24h in vacuo;this yielded the pure form of the PP powder.To study the crystallization behavior of PPfilled with different types offillers(e.g., wollastonite,silica,glassfiber,talc,calcium carbonate, mica,and carbonfiber),we mixed the additive,avail-able in a particulate form,in a desired quantity with PP powder in an agate pestle and mortar and thor-oughly ground the mixture for30min.The samples were subjected to isothermal melt crystallization on the hot stage of a polarizing microscope(melting tem-peratureϭ200°C,crystallization temperature ϭ115°C).The crystallization behavior was investi-gated by the continuous recording of the growth of spherulites and the intensity of transmitted light in the cross-polar mode of the optical polarizing microscope (Leitz,Germany)coupled to an image analyzer system (VIDPRO32,Leading Edge,Australia).The details of these experiments have been described else-where.18–20Care was taken to avoid any loss of time in the transfer of the sample from the hot plate to the microscope stage.From the isothermal crystallization curve,the induction period,crystallization half-time, growth rate,and so forth were evaluated.RESULTS AND DISCUSSIONThe cooling curves for PP melts containing different fillers(10%),for which K values were estimated with the aforementioned phenomenological model,are shown in Figure2.The melting temperature was as-sumed to be200°C,the mold wall temperature was 25°C,the specimen thickness was3mm,the cross-section area was1cm2,and⌬t was1min.The K and C p values in Table I were used in eq.(4)for the calculations with the same unit system.The density of PP was taken to be0.95g/cm3.The higher thermal conductivity of thefiller produced faster cooling,as expected from the model.The induction time,esti-mated with the method outlined earlier in this article, is shown in Figure3(10%filler concentration).The time required for the melt to attain the temperature for the onset of crystallization decreased with an increase in the thermal conductivity of thefiller present in the composite.Therefore,we expected that the induction period for the crystallization would also depend on the thermal properties of thefiller.The results of experiments on the isothermal crys-tallization kinetics,carried out at120°C,are depicted in Figure4for PPs containing different additives (10%).The onset of crystallization was found to de-pend on the type of additive.From these curves,the induction time was deduced from the time at which the onset of crystallization was observed,and it was compared with the expected value of the cooling time, which was determined for each composition with the aforementioned theory.Figure5compares these val-ues with those estimated from the melt cooling curves described earlier in this article.We have depicted the data in normalized scales with respect to the original PP to avoid any errors arising from sample-to-sample variations and PP grades,which may be different from those reported in the literature.Figure5shows that the overall trend for the experimentally observed data follows the same trend expected from the theory. There was some difference in the actual values:the experimentally noted induction time in some cases was lower than that expected from thermal conduc-tion.This might be due to nucleation effects,whichTABLE IIIVariation of K and Skin-Layer Thickness in PP with␾Composition (wt%)K a(W/mK)Skin-layer thickness b(mm)PP with5%TC0.2530.3810%TC0.2850.4120%TC0.3450.4430%TC0.4360.5440%TC0.5730.57PP with5%CC0.2570.4110%CC0.2860.4820%CC0.3540.5630%CC0.4540.5840%CC0.6120.64TCϭtalc;CCϭcalcium carbonate.a Estimated from Nielsen’s model with eqs.(1)–(3).b Data reported for injection-molded3-mm-thick samples(refs.12and13).2996RADHAKRISHNNAN AND SONAWANEFigure 2Effect of the thermal conductivity of the additive in the polymer melt on its cooling rate:(A)pure PP,(B)PP with wollastonite,(C)PP with silica,(D)PP with talc,(E)PP with mica,(F)PP with calcium carbonate,and (G)PP with carbon fiber.The filler concentration was 10wt %in allcases.Figure 3Variation of the induction time derived from the cooling curves with respect to the thermal conductivity of PPs filled with different fillers at 10wt %.HEAT TRANSFER AND THERMAL CONDUCTIVITY 2997depended on the filler–polymer interaction,the nucle-ating efficiency of the filler particle,and so forth.The rate of cooling of the melt has a profound effect on the morphology that develops in semicrystalline polymers during processing.For example,during the injection molding of PP,there is a faster cooling rate near the mold walls due to rapid heat transfer than in the central portion of the melt.This leads to uneven crystallization rates,and a skin–core morphology is known to present in final products,especiallythick-Figure 4Isothermal crystallization curves for PPs containing fillers (10wt %):(A)pure PP,(B)PP with silica,(C)PP with talc,(D)PP with calcium carbonate,(E)PP with mica,and (F)PP with carbonfiber.Figure 5Comparison of experimental data and theoretically estimated values for the induction time of crystallization with the thermal conductivity of the PP composite.The solid line has been drawn only as a guide.2998RADHAKRISHNNAN AND SONAWANEwalled items (see Fig.1).To determine the effect of a faster cooling rate on the crystallization process of PPs containing additives,we compiled data for the skin-layer thickness of injection-molded samples of PP with calcium carbonate and talc in Figure 6.The skin-layer thickness depended on the amount of the additive present in each PP sample.These data were redrawn in terms of the thermal conductivity of PP containing a filler,which was estimated with Nielsen’s model (see Table I).This graph clearly indicates the impor-tance of the thermal conductivity of a composite on its crystallization process and the morphology developed in the PP samples containing additives.This can be associated with the fact that a high thermal conduc-tivity filler content leads to better heat transfer and a faster cooling rate,which,in turn,produces greater skin-layer thickness than that of the original polymer.CONCLUSIONSThe crystallization behavior of polymers is dependent on the heat-transfer process from the melt to the sur-roundings (e.g.,quenched air and mold walls).A phe-nomenological model has been developed for estimat-ing the cooling rate for any given polymer with known K and C p values.The addition of fillers to the polymer leads to an increase in the thermal conduc-tivity of the composite,and so faster cooling is ex-pected for such systems.The role of the thermal con-ductivity of the filler/additive in the crystallization behavior of PP has clearly been presented in this arti-cle.The experimental results for PPs containing dif-ferent types of fillers clearly support the aforemen-tioned hypothesis.Also,the reported data on the skin-layer thickness for injection-molded PPs containing talc and calcium carbonate can be understood in terms of this model.References1.Deanin,R.D.;Schott,N.R.Fillers for Reinforcement for Plastics;American Chemical Society:Washington,DC,1974;pp 41and 114.2.Lutz,J.T.,Jr.Thermoplastic Polymer Additives:Theory and Practice;Marcel Dekker:New York,1989;p 255.3.Flick,E.W.Plastic Additives:An Industrial Guide;Noyes Data:Park Ridge,NJ,1993;p 140.4.Karger-Kocsis,J.Polypropylene;Kluwer Academic:Dordrecht,Netherlands,1999;pp 329,519,and 663.5.Van Der Ven,S.Polypropylene and Other Polyolefins;Elsevier:Amsterdam,1990;p 347.6.Vasile,C.;Seymour,R.B.Handbook of Polyolefins;Marcel Dekker:New York,1993;p 681.7.Pukanszky,B.;Tudos,F.;Kelen,T.In Polymer Composites:Proceedings of the Microsymposium on Macromolecules;Sed-lacek,B.,Ed.;de Gruyter:Berlin,1986;p 167.8.(a)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,42,2739;(b)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,42,2749.9.Khare,A.;Mitra,A.;Radhakrishnan,S.J Mater Sci 1996,31,5691.10.Radhakrishnan,S.;Saujanya,C.J Mater Sci 1998,33,1069.11.Saujanya,C.;Tangarilla,R.;Radhakrishnan,S.Macromol MaterEng 2002,287,272.12.Karger-Kocsis,J.Polypropylene Structure,Blends and Compos-ites;Chapman &Hall:London,1995;p 167.13.(a)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,43,57;(b)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,43,97.14.Bigg,D.M.Adv Polym Sci 1995,119,1.15.Torquado,S.Rev Chem Eng 1987,4,151.16.Nielsen,L.E.Ind Eng Chem Fundam 1974,13,17.17.Powell,T.;Klemens,H.Thermophysical Properties of Matter;Plenum Publishers:New York,1970;Vol.2,p 943.18.Radhakrishnan,S.;Saujanya,C.J Mater Sci 1998,33,1069.19.Radhakrishnan,S.;Saujanya,C.Polymer 2001,42,6723.20.Radhakrishnan,S.;Saujanya,C.Macromol Mater Eng 2001,286,1.21.Katz,H.S.;Milewski,J.V.Handbook of Fillers for Plastic;VanNostrand Reinhold:New York,1987;p 117.22.Plastic Additives and Modifiers Handbook;Edenbaum,J.,Ed.;Chapman &Hall:London,1996.23.Karian,H.G.Handbook of Polypropylene and PolypropyleneComposites;Marcel Dekker:New York,1999;p 237.24.Buyco,T.Thermophysical Properties of Matter;Plenum Pub-lishers:New York,1970;Vol.3.Figure 6Variation of the skin-layer thickness of injection-molded PPs containing different amounts of fillers:calcium carbonate (top)and talc (bottom).The data are plotted di-rectly in terms of the composite thermal conductivity esti-mated from Nielsen’s equation.HEAT TRANSFER AND THERMAL CONDUCTIVITY 2999。

二氧化钛高温不同的产生的晶像英文版Titanium Dioxide: The Formation of Crystalline Structures at Elevated TemperaturesTitanium dioxide, commonly known as titania, is a widely studied material due to its unique physical and chemical properties. Its behavior at high temperatures is particularly intriguing, as it undergoes structural transformations that lead to the formation of different crystalline structures.At room temperature, titanium dioxide exists primarily in the anatase form, which is a tetragonal crystal structure. However, when exposed to high temperatures, anatase transforms into a different crystal structure known as rutile. Rutile is a tetragonal structure that is more thermally stable than anatase.The transformation from anatase to rutile occurs gradually as the temperature increases. The rate of transformation depends on various factors such as the purity of the titania, thepresence of impurities, and the rate of heating. During the transformation, the lattice parameters and atomic arrangements within the crystal change, resulting in distinct physical and chemical properties.The formation of these different crystalline structures at high temperatures has important implications in various applications of titanium dioxide. For instance, the anatase-to-rutile transformation is exploited in photocatalysis, where titania is used as a photocatalyst to split water into hydrogen and oxygen. The transformation enhances the photocatalytic activity of titania by promoting charge separation and enhancing the formation of reactive oxygen species.In addition, the high-temperature stability of rutile makes it suitable for use in high-temperature applications such as ceramic coatings and solar cells. The ability of rutile to maintain its structure at elevated temperatures ensures durability and long-term stability in these applications.In summary, the behavior of titanium dioxide at high temperatures is fascinating, as it undergoes structural transformations that lead to the formation of different crystalline structures. These transformations have significant implications in the applications of titania, ranging from photocatalysis to high-temperature materials.中文版二氧化钛：高温下产生的晶像变化二氧化钛，通常被称为二氧化钛，是一种因其独特的物理和化学性质而广受研究的材料。

crystallizeCrystallize: A Comprehensive Guide to the Process of CrystallizationIntroductionCrystallization is a fundamental process in chemistry that involves the formation of a solid crystalline material from a solution or a melt. It is utilized in various fields, including pharmaceuticals, materials science, and food production. In this guide, we will delve into the intricacies of the crystallization process, exploring its principles, techniques, and applications.I. The Science of CrystallizationA. Crystallization Basics1. Definition and NatureCrystallization is the process by which atoms, ions, or molecules arrange themselves in a highly ordered and repetitive pattern, forming a crystal lattice structure. This structure imparts distinctive physical properties to the resulting crystal.2. Types of CrystalsCrystals can be classified into two categories: organic and inorganic. Organic crystals are composed of carbon-based molecules, such as sugar or protein crystals, while inorganic crystals consist of non-carbon-based materials, like salt or metal crystals.B. The Factors Affecting Crystallization1. SolubilitySolubility plays a crucial role in the crystallization process. It is influenced by factors such as temperature, pressure, solvent properties, and the presence of impurities.2. NucleationNucleation is the initial step in crystallization, where tiny clusters of atoms, ions, or molecules aggregate to form a stable nucleus. This process can be either spontaneous or induced.3. Crystal GrowthOnce nucleation occurs, crystal growth follows. It involves the addition of new particles to the existing crystal lattice, leading to an increase in crystal size.II. Crystallization TechniquesA. Solvent-Based Crystallization1. Cooling CrystallizationCooling crystallization is a widely employed technique that capitalizes on the decrease in solubility with decreasing temperature. It involves the gradual cooling of a solution, leading to the precipitation of the solute in the form of crystals.2. Evaporative CrystallizationEvaporative crystallization relies on the evaporation of the solvent to achieve supersaturation and subsequent crystallization. It is commonly used for the production of salt crystals and certain pharmaceutical compounds.B. Anti-Solvent CrystallizationAnti-solvent crystallization involves the addition of a non-solvent to a solution, resulting in a decrease in solute solubility and subsequent crystallization. This technique is particularly advantageous for the purification of solid materials.C. Reactive CrystallizationReactive crystallization involves simultaneous crystal growth and chemical reaction. It is employed in various industries, including pharmaceuticals and fine chemicals, where selective product formation is desired.III. Applications of CrystallizationA. Pharmaceutical IndustryCrystallization plays a vital role in drug discovery, development, and manufacturing. It is used for purification, separation, and formulation of active pharmaceutical ingredients (APIs) and drug delivery systems.B. Materials ScienceCrystallization is extensively utilized in materials science for the production of single crystals, polymers, and composite materials with controlled properties. Single crystals find applications in electronic devices, while polymers and composite materials are used in various structural and functional applications.C. Food and Beverage IndustryCrystallization is involved in the manufacture of various food products, including sugar, chocolate, and salt. It is used tocreate desired textures, improve stability, and enhance organoleptic properties.D. Energy SectorCrystallization is utilized in the energy sector for the purification of crude oil, natural gas, and nuclear fuels. It helps remove impurities and improve the quality of these energy resources.ConclusionCrystallization is a fascinating and versatile process with numerous applications across various industries. Understanding the principles, techniques, and applications of crystallization is crucial for scientists and engineers working in fields ranging from chemistry to materials science. By harnessing the power of crystallization, researchers can design new materials, develop innovative pharmaceuticals, and improve the efficiency of industrial processes. This guide serves as a starting point for exploring the vast world of crystallization and its manifold possibilities.。

a r X i v :c o n d -m a t /0403132v 1 [c o n d -m a t .s o f t ] 3 M a r 2004Cooling rate,heating rate and aging effects in glassy waterNicolas Giovambattista 1,H.Eugene Stanley 1and Francesco Sciortino 21Center for Polymer Studies and Department of PhysicsBoston University,Boston,MA 02215USA2Dipartimento di Fisica,Istituto Nazionale per la Fisica della Materia,and I.N.F.M.Center for Statistical Mechanics and Complexity,Universit`a di Roma La Sapienza,P.le A.Moro 2,I-00185Roma,ITALYWe report a molecular dynamics simulation study of the properties of the potential energy land-scape sampled by a system of water molecules during the process of generating a glass by cooling,and during the process of regenerating the equilibrium liquid by heating the glass.We study the dependence of these processes on the cooling/heating rates as well as on the role of aging (the time elapsed in the glass state).We compare the properties of the potential energy landscape sampled during these processes with the corresponding properties sampled in the liquid equilibrium state to elucidate under which conditions glass configurations can be associated with equilibrium liquid configurations.PACS numbers:One recent activity in the physics of supercooled liq-uids and glasses[1,2]is the search for the conditions un-der which a glass can be considered a liquid whose struc-tural properties have been “frozen”during the prepa-ration process.If the glass can be connected to a liq-uid state,then a thermodynamic description of the glass state can be developed[3,4,5,6].Many routes can bring a system to an arrested disordered state [7],such as va-por deposition,pressure induced amorphization,hyper-quenching or standard cooling.Only the last two provide a continuous path from the liquid to the glass state and hence are the best candidates for studying the connection between glass and liquid configurations.Since water can be glassified by cooling only using hy-perquenching techniques (i.e.with rates of the order of 105K/s[8]),understanding the connection between the liquid state and glasses generated with different cooling rates is important.When the hyperquenched glass of wa-ter is properly annealed at T =130K[8],a reproducible weak endothermic transition is observed which has been associated with the calorimetric glass transition temper-ature T g .For water,the standard cooling rate is not suf-ficiently fast to overcome crystallization,so active debate [9,10,11]concerns how to relate the T g of hyperquenched water to the unmeasurable T g of the slowly cooled glass.In this work we use molecular dynamics (MD)simu-lations to address the relation between liquid and glass configurations.We reproduce the same procedure fol-lowed experimentally to generate glasses.We use two cooling rates q c differing by almost three orders of mag-nitude.We also study the heating rate and aging effects in the glass,an aspect novel to numerical simulations.We work in the framework of the potential energy land-scape (PEL)approach,in which the 6N -dimensional con-figurational space —defined by the 3N center of mass coordinates and by the 3N Euler angles —is partitioned into a set of basins,each associated with a different localminimum of the PEL [12,13].We focus in particular on the depth of the local minimum closest to the system point,and on the local curvatures of the PEL around the local minimum.We discover that with slow cooling rates,the glass retains a configuration very similar to a configuration sampled by the liquid at higher T ,and hence all structural properties of the glass can be related to the structural properties of the liquid.In this case,a fictive temperature can be defined,the temperature at which the glass configuration is sampled by the liquid.In the case of a fast cooling rate,aging phenomena are very active already during the cooling process.Dynamics moves the configuration in regions of the PEL which are never explored in equilibrium [14].Further aging at low temperature increases the differences between the glass and the liquid.When this is the case,the glass does not possess a structure corresponding to the equilibrium liquid at any temperature and hence it is not possible to associate an unique fictive T with the glass configuration.We perform MD simulations for a system of N =216molecules at fixed density,ρ=1g/cm 3,interacting with the SPC/E potential[15],with periodic boundary condi-tions.Interactions are cut offat a distance of r =2.5σ(σparameterizes the Lennard-Jones part of the SPC/E potential)and reaction field corrections are added to ac-count for the long range interactions.Quantities are aver-aged over 32independent trajectories.We perform three types of MD calculations:(i)cooling scans at constant rate,starting from equilibrium liquid configurations at T =300K ,(ii)heating scans at constant rate (from glass configurations at ≈5K),and (iii)aging runs at constant aging temperature (at T age =100K and T age =180K,where significant aging effects are observed).The two cooling rates are q c =−3×1010K/s and q c =−1013K/s,and the two heating rates are q h =+3×1010K/s and q h =+1013K/s.We will denote by fast-quenched glass the glass obtained with the fast cooling rate and byslow-quench glass the glass obtained with the slow cool-ing rate.An averaged slow scan requires a simulation lasting320ns,close to the maximum possible by our method.This limitation prevent us from studying larger systems[20].The location of the system on the PEL is studied performing numerical minimizations(conjugate gradient algorithm)along the runs to estimate the clos-est local minimum configuration or inherent structure (IS),its energy e IS and the set of6N eigenvaluesω2i of the Hessian matrix[18].The local curvatures around the minimum define in the harmonic approximation the multi-dimensional parabolic shape of each PEL basin.As a global indicator of shape we use the shape function de-fined asS IS≡ 6N−3i=1ln( ωi/A0)in water,the slow-quenched glass would be character-ized by a different T g compared to the fast-quenched glass[9,10,11].The analysis of simulated configura-tions has allowed us to clarify the differences between the slow-and the fast-quenched glass.The differences lie not only in the expected difference in e IS but,more significantly,in the fact that the fast-quenched glass dur-ing cooling loses contact with the liquid state and starts to explore regions of the PEL which are never explored in equilibrium.The fast-quenched glass does not pos-sess a structure corresponding to the equilibrium liquid structure at any temperature,and hence it is not pos-sible to associate with it a uniquefictive temperature. 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[18]The Hessian matrix is the matrix formed by the sec-ond derivatives of the potential energy with respect to the center of mass coordinates and Euler angles of each molecule.[19]F.Sciortino et al.,Phys.Rev Lett.91,155701(2003).[20]A previous study for a Lennard-Jones system has con-vincingly shown that size effects in the supercooled state do not significantly alter statistical properties of the PEL provided that the number of particles is larger than≈65 [S.B¨u chner and A.Heuer,Phys.Rev.Lett.84,2168 (2000)].−60−59−58−57−56−55e I S [k J /m o l ]0100200300T [K]−60−59−58−57−56−55e I S [k J /m o l ]7.87.988.18.28.3S IS−60−59−58−57−56e IS [kJ/mol]7.87.988.18.28.3S I SFIG.1:(a)Cooling of equilibrium liquid configurations at T =300K to T ≈0K with a fast (q c =−1013K/s)and slow (q c =−3×1010K/s)cooling rate to generate fast-quenched and slow-quenched glasses,respectively.While during fast cooling the system is out of equilibrium already at T =290K,slow cooling allows the system to sample the equilibrium IS10−110101102103104105t age [ps]−59.6−59.1−58.6−58.1−57.6e I S [k J /m o l ]T age =100KT age =180K(a)−60−59−58−57e IS [kJ/mol]88.058.18.158.28.258.3SI SFIG.2:(a)Time dependence of e IS and (b)relation between basin shape S IS and basin depth during aging of the fast-quenched glass at two temperatures T age =100K and T age =180K.For both cases,for long t age ,e IS ≈log(t age )(dashed lines).Note that during aging at low T age ,the system explores basins for which the relation between shape and depth does not correspond to the equilibrium S IS (e IS )relation.At large T age ,aging moves the system closer to equilibrium.At each T age ,open diamonds correspond to (from right to left)t age =20ps,t age =200ps,t age =2ns,and t age =20ns.−60.5−59.5−58.5−57.5−56.5−55.5−54.5e I S [k J /m o l /N ]0100200300T [K]−60.5−59.5−58.5−57.5−56.5−55.5−54.5e I S [k J /m o l /N]7.958.058.158.258.35S IS−59.25−58.25−57.25e IS [kJ/mol]7.958.058.158.258.35S ISFIG.3:Inherent structure energy e IS and basin shape func-tion S IS during heating of the fast-quenched glass with (a,c)slow and (b,d)fast heating rates after aging for different times t age at a temperature T age =100K.Results for T=180K are qualitatively similar.Filled circles correspond to data for equi-librium liquid configurations from Ref.[19]For comparison,in (a)and (b)we show e IS during the heating scan from the slow-quenched glass.In (c)and (d),we only show S IS in the heating scans after aging for t age =20ps and t age =20ns.。

MELTING CRYSTALLIZATION BEHAVIOR OF NYLON66Qing-xin Zhang;Zhi-shen Mo State Key Laboratory of Polymer Physics & Chemistry Changchun Institute of Applied Chemistry Chinese Academy of Sciences, Changchun 130022, China【期刊名称】《高分子科学：英文版》【年(卷),期】2001()3【摘要】Analysis of isothermal and nonisothermal crystallization kinetics of nylon 66 was carried out using differential scanning calorimetry (DSC). The commonly used Avrami equation and that modified by Jeziorny were used, respectively, to fit the primary stage of isothermal and nonisothermal crystallizations of nylon 66. In the isothermal crystallization process, mechanisms of spherulitic nucleation and growth were discussed. The lateral and folding surface free energies determined from the Lauritzen-Hoffman tr eatment are σ= 9.77 erg/cm2 and σe = 155.48 erg/cm2, respectively; and the work of chain folding is q = 33.14 kJ/mol. The nonisothermal crystallization kinetics of nylon 66 was analyzed by using the Mo method combined with the Avrami and Ozawa equations. The average Avrami exponent n was determined to be 3.45. The activation energies (ΔE) were determined to be -485.45 kJ/mol and -331.27 kJ/mol, respectively, for the isothermal and nonisothermal crystallization processes by the Arrhenius and the Kissinger methods.【总页数】10页(P237-246)【关键词】Nylon;66,;Crystallization;kinetics,;Activation;energy【作者】Qing-xin Zhang;Zhi-shen Mo State Key Laboratory of Polymer Physics & Chemistry Changchun Institute of Applied Chemistry Chinese Academy of Sciences, Changchun 130022, China【作者单位】【正文语种】中文【中图分类】O63【相关文献】1.Crystallization Kinetics and Melting Behavior of PA1010/Ether-based TPU Blends [J], ZHANG Shu-ling;ZHAO Yan;SUN Xiao-bo;JIANG Zhen-hua;WU Zhong-wen;WANG Gui-Bin2.Study on the crystal morphology and melting behavior of isothermally crystallized composites of short carbon fiber and poly(trimethylene terephthalate) [J], Mingtao RUN;Hongzan SONG;Yanping HAO3.MULTIPLE MELTING AND CRYSTALLIZATION BEHAVIOR OF NYLON 1212 [J], 莫志深4.Melting Behavior of PA6 and PA6/PE Blends Crystallized from Amorphous State [J], 仇武林;罗运军;罗善国;谭惠民;李政军;麦堪成;曾汉民5.CRYSTALLIZATION AND MELTING OF NYLON 610 [J], 王国明;颜德岳;卜海山因版权原因，仅展示原文概要，查看原文内容请购买。