2011年国际数模资料Polymer-Graphite Nanocomposites_Effective Dispersion and Major Property Enhancemen

2.The main methods of the preparation of Polymer-Organophilic nanocomposites 1．sol-gel
b) Covalent bonding between polymer and nano-phase inorganic phase is introduced in the side of the polymer or in the end of the backbone 。
inorganic materials：typical layered compounds（clay、phosphate,graphite, mica,MMT)
Ａ．Melt intercalation polymerization Ｂ．Solution intercalation polymerization
三、有机／无机纳米复合材料的性能特点
4.阻隔性能 （丙烯酸酯为例） Tab.2 Gas permeability of acrylic resin–clay hybrid film
Film samples MMT content (mass%) 0 0.7 2.2 3.4 5.6 O2 1 0.889 0.595 0.425 0.209 N2 1 0.875 0.581 0.416 0.203
3.原位聚合法（in-situ synthesise）
单体溶液↘ 超声波分散 中分散 ——〉 或（并） ——〉 单体聚合 纳米粒子↗ 机械共混
特点：反应条件温和，分散均匀。
2.The main methods of the preparation of Polymer-Organophilic nanocomposites 4．Intercalation

CERAMICSINTERNATIONALAvailable online at Ceramics International 40(2014)2047–2056Chemically modi fied boron nitride-epoxy terminated dimethylsiloxanecomposite for improving the thermal conductivityKiho Kim,Myeongjin Kim,Yongseon Hwang,Jooheon Kim nSchool of Chemical Engineering &Materials Science,Chung-Ang University,Seoul 156-756,KoreaReceived 30May 2013;received in revised form 22July 2013;accepted 24July 2013Available online 21August 2013AbstractThe thermal conductivities of composites with an epoxy-terminated dimethylsiloxane (ETDS)matrix and boron nitride (BN)powder fillers were investigated.Two surface curing agents,3-glycidoxypropyltrimethoxysilane (KBM-403)and 3-chloropropyltrimethoxysilane (KBM-703),were doped onto the surfaces of hydroxyl-functionalized boron nitride using a simple sol –gel process to act as fillers in the thermally conducting composites.These synthesized materials were embedded in epoxy resin via a solvent casting method.The surface modi fication had an appreciable effect on the thermal conductivity resulting in increased thermal conductivity up to 70wt%.The thermal conductivities of the composites containing 70wt%BN particles treated with the KBM-403and KBM-703curing agents were 4.11and 3.88W/mK,respectively,compared to 2.92W/mK for the composite without surface treatment.&2013Elsevier Ltd and Techna Group S.r.l.All rights reserved.Keywords:posites;C.Thermal conductivity;D.Nitrides;Surface treatment1.IntroductionDemands for the miniaturization and continuous perfor-mance improvements of electronic packages have led to the development of new microelectronic packaging techniques.The typical characteristics of future microelectronic packaging include high density,high frequency,and high speed [1–3].It is well known that the reliability of an electronic device is exponentially dependent on the operating temperature of the junction,whereby a small difference of the operation tempera-ture can result in a two-fold reduction of the lifespan of a device [4].Improvements of size and performance are likely to result in the generation of a greater amount of heat in a smaller volume of space.To ensure proper device operation,the unwanted heat must be removed as quickly and effectively as possible to maintain the operation temperature,suggesting that the packaging materials of the product needs to have good thermal conductivity [5,6].Epoxy resin has been widely applied in electronics,paints,electrical insulators,printed circuit boards,and packaging materials as a matrix [7,8].Unfortunately,epoxy used alone as an electronic packaging material cannot effectively dissipate the heat generated from high packing and power-density devices,given the relatively low thermal conductivity range of epoxy of 0.1–0.3W/mK.Several studies have been conducted to improve the thermal conductivity of epoxy.For example,polymers filled with thermally conductive fillers are emerging as a cost-effective means of coping with thermal management issues.Many researchers have investigated the thermal conductivity enhancement of composite materials including oxides (Al 2O 3,SiO 2,ZnO)[9–11],carbide (SiC)[12],and nitrides (AlN,BN,Si 3N 4)[13,14].The properties of these epoxy/inorganic filler composites depend on the nature of the inorganic filler including their chemical and physical composition,size,shape and dispersion in the epoxy matrix.Thermally conductive fillers,like those mentioned above,have attracted attention due to their high thermal and low electrical conductivities,while metallic particles have high thermal and electrical conductiv-ities.Among the fillers,boron nitride has been considered as/locate/ceramint0272-8842/$-see front matter &2013Elsevier Ltd and Techna Group S.r.l.All rights reserved./10.1016/j.ceramint.2013.07.117nCorresponding author.Tel.:þ8228205763.E-mail address:jooheonkim@cau.ac.kr (J.Kim).an attractive candidate due to its significantly high thermal conductivity($300W/mK),lack of toxicity,superior chemi-cal stability,electrical insulation properties,and relatively low cost.In order to obtain a higher thermal conductivity while maintaining the existing properties,filler loadings of60wt% or higher have traditionally been incorporated to form a heat conduction path in the matrix that is as continuous as possible. However,a highfiller content becomes rather inflexible with voids and cracks forming betweenfillers.Moreover,the BN/ epoxy slurry has a relatively low viscosity before drying, which facilitates the sedimentation of the BNfiller.As a result, BNfillers settle to the bottom of the compositefilm,the heat-conductive path is cut off,and the thermal conductivity decreases.In response to this issue,many studies have suggested fabrication of a surface-modified BN particle to preventfiller sedimentation[15,16].Recently,BN has been coated with a surface-curing agent to further enhance the thermal conductivity of polymer compo-sites,resulting in a reduction of sedimentation due to the lone-pair electron interaction of particle surfaces into the matrix.Gu et al.achieved a thermal conductivity of1.052W/mK using a hot disk instrument for epoxyfilled with silane-modified BN at a solid loading of60wt%[17].Yung et al.reported the effect of multi-modal particle size mixing on the formation of a thermally conductive network[18].Unfortunately,these previous experiments used nano-scale BN particles($1μm). Due to the small size of thefiller-containedfilm,heat passing through the boundary of the particles is more frequently the main cause of the phonon scattering.The diffuse boundary scattering due to the short wavelength in comparison to interface roughness of dominant phonon heat carriers not only reduces the phonon mean free path,but can also destroy the coherence of the phonons[19].Thermal resistance at particle junctions known as thermal boundary resistance or Kapitza resistance is one of the primary causes of heat transfer property reduction.In the presence of a heatflux across the boundary,this thermal resistance causes a temperature dis-continuity at the boundary.Due to the differences of the electronic and vibrational properties of various materials,an energy carrier will scatter when attempting to traverse the interface[20–22].It is known that hexagonal BN particles have a plate-like shape withflat surfaces corresponding to the basal planes of the hexagonal crystal structure.The basal plane of BN is molecularly smooth and has no surface functional groups available for chemical bonding or interactions.In contrast,the edge planes of the platelets have functional groups such as hydroxyl and amino groups.These functional groups allow the BNfiller to disperse in an organic solvent and chemically bond with other rge BN particles are significantly decreased in the edge plane areas,resulting in difficulty obtaining uniform dispersion and chemical bonding.To this end,Sato et al.employed0.7μm BN particles as a thermal conductivefiller on polyimide resin[23,24].For the effective use of micro-scale BN as afiller,another surface treatment is necessary to make the reaction site of the particle surface.In this study,a polymer matrix,dimethyl siloxane-basedepoxy,was employed to fabricate a thermally conductivecomposite and a12μm BN particle was adopted as acompositefiller to reduce phonon scattering and improve thethermal conductivity.To increase the affinity and dispersibilityof thefiller in the epoxy matrix,which is expected to provide agood thermal conductivity,two types of surface curing agentswere employed.The resulting surface curing agent-coated BNpossessed electrical insulating properties in addition toenhanced thermal conductivity due to reduced thermal resis-tance at the junction.The mechanical properties of thefabricated composites were measured and the data demon-strates that a small amount of surface curing agent enhancesthe thermal and mechanical properties.2.Experimental2.1.Synthesis of ETDSThe epoxy-terminated dimethysiloxane(ETDS)oligomerwas obtained from Shin-Etsu silicon(KF-105,equivalentweight(E.E.W)=490g/eq,density=0.99g/cm3).In ourprevious study,the weight ratio of the epoxy to the curingagent was determined to provide efficientflexibility of thematrix.In this study,the equivalent weight ratio of ETDS toDDM(4.4′-diamino diphenylmethane)was1:2.1.9g of DDMwas placed in a four-neck roundflask equipped with a refluxcondenser and was preheated to363K.9.5g of the ETDSresin was added and heated in an oil bath at363K for1hunder a N2atmosphere.The bubbles in the mixture wereremoved by placing the mixture in a vacuum oven for30minat room temperature.The mixture was then placed in an oilbath at323K for10min in a N2atmosphere.Thefinaldegassing was performed in a vacuum oven for1h at roomtemperature to remove air bubbles[25].2.2.Surface modification of BNThe detailed synthesis procedure is shown in Fig.1.First,micro-BN particles were suspended in a5M sodium hydro-xide solution at1101C for18h to attach more hydroxide ionsonto the surfaces.Because micro-BN particles have fewfunctional groups,surface treatment is necessary to facilitatechemical bonding with the surface curing agent.After basesolution dipping,the particles were rinsed with D.I.water and filtered several times to adjust the pH from basic to neutral. The micro-BN hydroxide particles were left in the furnace at801C for5h,cooled to room temperature,and then stored indesiccators.The BN particles were modified with two surface curingagents,KBM-403and KBM-703,obtained from Shin-EtsuSilicon by a sol-gel reaction.An appropriate amount of3-glycidoxypropyltrimethoxysilane(KBM-403;3–5%based onthe weight of the micro-BN particles)and3-chlorop-ropyltrimethoxysilane(KBM-703)were added to D.I.waterand stirred at501C for30min to achieve hydrolysis.Themicro-BN hydroxide particles were then dipped into theK.Kim et al./Ceramics International40(2014)2047–2056 2048resulting solution and stirred at 701C for 1h,followed by rinsing with D.I.water and filtering three times.The particles were then vacuum dried at 801C for 5h to remove the solvent.The amount of the coating solution necessary is preferably 0.05–10%by weight,based on the weight of the particles.When the amount of the coating solution is less than 0.05%by weight,there is a tendency for insuf ficient and non-uniform particle coating to occur.When the amount of the coating solution exceeds 10%by weight,the obtained particles may possess excessive thermal resistance,thereby causing a decrease of the thermal conductivity of the composite films [26].2.3.Preparation of the BN/epoxy compositesThe composites were prepared by solution blending and a casting method consisting of (a)adding surface curing agent-coated micro-BN to the ETDS epoxy resin (50,60,70wt%)for approximately 3h in N,N-dimethylformamide (DMF)until the synthesized materials were completely mixed,(b)fabricat-ing the composite films to a uniform thickness via a doctor blade on the Te flon mold,(c)pre-curing the films at 1501C for 3h until no air bubbles appeared on the surface followed by post-curing at 1801C for 5h,and (d)cooling to room temperature.2.4.CharacterizationFourier transform infrared (FT-IR;Parkin-Elmer Spectrum One)spectroscopy and X-ray photoelectron spectroscopy (XPS;VG-Microtech,ESCA2000)were employed to analyze the surface curing agent-coated BN.For FT-IR spectroscopy,the ATR mode was used to avoid the in fluences of moisture adsorbed on the potassium bromide (KBr)particles and the scans were performed using radiation in the frequency range of 400–4000cm À1.In the XPS analysis,a monochromatic Mg K αX-ray source was used at 1253.6eV and the Gaussian peak widths obtained by curve fitting were constant in each spectrum.Thermogravimetric analysis (TGA;TGA-2050,TAinstrument)of the samples was carried out to examine the thermal degradation of BN,BN-403,and BN-703.4mg of the samples were heated to 8001C at a heating rate of 101C/min under a nitrogen atmosphere.Field emission scanning electron microscopy (FE-SEM;Sigma,Carl Zeiss)was carried out to con firm the cross-sections of the component films before and after the silane treatment.The samples were sputtered with a thin layer of platinum to avoid the accumulation of charge before the FE-SEM observations.The thermal diffusivity (δ,mm 2s À1)at room temperature was measured on disk samples using a laser flash method (Netzsch Instruments Co.,Nano flash LFA 447System).The speci fic heat (C ,J g À1K À1)at room temperature was measured on disk samples via differential scanning calorimetry (DSC;Perkin-Elmer Co.,DSC-7System)and the bulk density (ρcomp ,g cm À3)of the specimens was measured using the water displacement method.The thermal conductivity (Ф,W mK À1)was calcu-lated using the following equation:Ф¼δC ρcompTo study the mechanical properties of the composite materials,mechanical analysis (DMA;Triton Instrument,Triton DMTA)was carried out.The storage modulus of the solid films was measured at a frequency of 1Hz.The temperature range was À180to 1801C with cooling and heating rates of 101C/min.3.Results and discussion3.1.Structure analysisThe chemical structures of the surface-modi fied BN were determined using Fourier transform infrared spectroscopy (FT-IR),thermogravimetric analysis (TGA),and X-ray photo-electron spectroscopy (XPS).Fig.2(a –c)shows the FT-IR spectra of pristine BN,BN-403,and BN-703,respectively.For pristine BN,the bands at 1400and 800cm À1indicate stretching vibration in the hexagonal BN.The absorption band of pristine BN at 2300–2380cm À1represents absorbed CO 2.Fig.1.Reaction scheme for the preparation of surface curing agent treated BN particle (BN-403,BN-703).K.Kim et al./Ceramics International 40(2014)2047–20562049Comparing the pristine BN and the surface curing agent-treated BN (BN-403and BN-703),the new band at 1100cm À1corresponds to stretching of the Si –O bonds,which existed in the pure surface curing agent.Detailed surface information of pristine BN,BN –OH,BN-403,and BN-703was collected by X-ray photoelectron spectroscopy (XPS)and the corresponding results are pre-sented in Fig.3.In the spectrum of pristine BN,there are only two elements of B and N.However,the O 1s signal emerges in the spectrum of BN –OH.This result implies that the hydroxyl groups were effectively introduced on the BN surfaces and edges via the sodium hydroxide treatment.These hydroxyl groups,acting as anchor sites,enabled attachment between the BN particles and surface curing agent.Moreover,the new peaks of C 1s and Si 2p can be assigned in the spectra of both BN-403and BN-703,indicating that both surface curing agents,403and 703,were successfully attached to the surface and edges of pristine BN particles.The detailed chemical bonding of fabricated,surface-treated BN particles was con firmed from the de-convoluted B 1s,Si 2p,and C 1s spectra,the results of which are shown in Fig.4.Fig.4(a and b)show the de-convoluted B 1s spectra of BN-403and BN-703,respectively.The B 1s spectra of both BN-403and BN-703showed a strong binding energy peak for the B –N bond and a weak binding energy peak for the B –OH bond at 190.4eV and 192eV,respectively [27,28].The B –OH peak resulted from the introduction of a hydroxyl group by the base treatment.In order to provide clearer evidence of chemical bonding between the BN particles and the silane curing agent,the Si 2p peak of these synthesized materials can be fitted by a curve with several component peaks.Fig.4(c and d)shows the de-convoluted Si 2p spectra of BN-403and BN-703,respectively.In the spectra of both BN-403and BN-703,the strong peak at the binding energy of 102.1eV represents the bond between silicon and oxygen originating from the BN particles (B –O –Si),indicating that the surface curing agent and BN particles are connected through the hydroxyl groups.The peak at 103.3eV is attributed to siloxane (Si –O –Si)resulting from the partial hydrolysis of the silane curing agent molecules during the silanization reaction.Moreover,the peak at 100.8eV is attributed to Si –C bonding in the silane curing agent molecules.These results are in agreement with the reaction mechanism of silane,including the hydrolysis of –OCH 3,condensation to oligomers,hydrogen bonds between oligomer and hydroxyl groups on the substrate,and the formation of the covalent linkage between silane and the substrate.The peak at 102.5eV is attributed to Si –OH bonding,indicating that some hydroxyl groups did not hydro-lyze and a small amount of hydroxyl group remained [29,30].This implies that the amount of hydroxyl groups on the BN surface was not suf ficient to make a uniform siloxane network and some hydroxyl groups in the surface curing agent were not hydrolyzed.This is due to the basal plane of the boron nitride particle surface having no functional groups.In addition,the silane coupling agent does not coat the surface uniformly such that the hydroxyl groups of the surface curing agent remained.The C 1s spectra of both BN-403and BN-703were de-convoluted to compare the structural differences of the two silane curing agents and the results are shown in Fig.4(e and f),respectively.In the spectra of both BN-403and BN-703,the strong peak at a binding energy of 284.7eV indicates the C –C bond and the weak peak at the binding energy of 283.44eV represents the C –Si bond,which exists in the surface curing agent structure.The primary difference between KBM-403and KBM-703is that KBM-403has ether and epoxide groups,whereas KBM-703has a chloride atom at the end of the carbon chain.In the C 1s spectrum of BN-403,C –O bonding is observed at a binding energy of 286.2eV,which originates from the ether and epoxide groups.However,in the case of BN-703,the peak at 285.9eV is attributed to C –Cl bonding,which can be explained by the existence of a chloride atom at the end of the carbon chain [31].Based on these results,it can be concluded that the silane treatment can effectively introduce the surface curing agent onto the surface ofBN.Fig.2.FT-IR spectra of (a)raw BN,(b)BN-403and (c)BN-703.Fig.3.X-ray photoelectron spectroscopy survey scans of (1)raw BN,(b)BN-OH,(c)BN-403,and (d)BN-703.K.Kim et al./Ceramics International 40(2014)2047–20562050Fig.4.XPS spectra of BN-403and BN-703.(a)XPS B 1s spectrum of BN-403:(b)XPS B 1s spectrum of BN-703:(c)XPS Si 2p spectrum of BN-403:(d)XPS Si 2p spectrum of BN-703;(e)XPS C 1s spectrum of BN-403:(f)XPS C 1s spectrum of BN-703.K.Kim et al./Ceramics International 40(2014)2047–20562051The compositions of the as-prepared BN,BN-403,and BN-703composites were further investigated via TGA (Fig.5).The experiments were performed up to 8001C in air at a heating rate of 101C min À1.Under these conditions,weight loss was not observed up to 8001C for pristine BN,whereas weight losses of about 4%and 3.6%were observed for BN-403and BN-703,respectively,due to thermal decomposition of the surface curing agents attached to the BN.The mass ratios of KBM-403/BN and KBM-703/BN for BN-403and BN-703were calculated to be 0.042/1and 0.037/1,respec-tively.Moreover,these ratios between BN and the surface curing agent are optimal to mix the surface curing agent-treated BN as a filler and the silane-based epoxy as a matrix [32].As reported by Itoh et al.,the surface curing agent is poorly dispersed in the particles when too little is added and the desired effect of improved crack formation resistance in the cured resin composition cannot be achieved [33].An excess of surface curing agent in the resin composition leads to a decreased thermal conductivity.This is because the redundant coupling agent causes phonon scattering and gives rise to a decreased thermal conductivity of the composites,resulting in low thermal conductivity materials.3.2.Thermal propertiesThe thermal conductivity of the composites is controlled by the intrinsic conductivities of the filler and matrix as well asthe shape,size,and loading level of the filler.Table 1shows the variations of the thermal conductivity of the BN/ETDS composites with nano-BN ($1μm),micro-BN (8μm,12μm),and a filler content ranging from 50to 70wt%.The thermal conductivity of pristine ETDS is approximately 0.2W/mK.It can be seen that as the weight fraction of these fillers increased,the thermal conductivity also increased consider-ably.With 12μm particles at loadings of 50wt%,60wt%,and 70wt%,the thermal conductivity increased by factors of 11.1,13.35,and 14.58,respectively,compared to the pure resin ($0.2W/mK).As shown for the three types of particles,the thermal conductivity is also a function of the particle size,where the results parallel the effect of the particle type.The highest thermal conductivity values were obtained from the 12μm particle-filled composites at all filler loading levels.This result can be explained by the thermal interface resistance caused by phonon boundary scattering.In theory,the scatter-ing of phonons in composite materials is primarily due to the existence of an interfacial thermal barrier from acoustic mismatch or damage of the surface layer between the filler and the rge particles tend to form fewer thermally resistant polymer-layer junctions than small particles at the same filler rge particles are therefore used as a thermal conducting filler because of their negligible phonon scattering effect and excellent thermal conductivity [34,35].In this paper,the use of a micro-filler to improve the thermal conductivity of composites was studied.The in fluence of the BN concentration and surface treatment on the thermal conductivity of BN/ETDS composites is presented in Fig.6.It can be seen that as the weight fraction of these synthesized materials increased,the calculated thermal conductivity of all of the investigated composites increased considerably.The use of surface curing agents clearly improved the thermal con-ductivities of the composites.At 12μm BN particle loadings of 50,60,and 70wt%,the thermal conductivities of the KBM-403-and KBM-703-treated BN/ETDS composites increased by factors of 1.17,1.23,and 1.41and 1.15,1.19,and 1.33compared to the untreated BN/ETDS composite,respectively.This effect could be explained by the enhanced dispersibility of particles in the composite caused by the surface curing agent.The two surface curing agents used contain an epoxide group and chloride functional groups that interact with the active groups of the epoxy matrix.Thus,the organic active groups or long molecular chains on the surface of the modi fied BN either react or entangle with the reactive groups of the epoxy matrix.The addition of surface curing agents totheFig.5.TGA thermograms of pristine BN,BN-403and BN-703.Table 1Thermal conductivity of various particle size and filler contents (W/mK).Size of BN particlesThermal conductivity at various filler concentration [W/mK]50wt%60wt%70wt%$1m m 1.49 1.67 2.158m m 2.16 2.35 2.7712m m2.322.732.92K.Kim et al./Ceramics International 40(2014)2047–20562052epoxy matrix therefore improves the interface bonding between the BN particles and matrix,leading to an enhanced thermal conductivity.In addition,this result could beexplained by the reduction of the phonon diffuse boundary scattering that constitutes a signi ficant part of the thermal resistance accompanying an imposed temperature gradient.The phonon scattering at interfaces,both for free surfaces and those bonded to other materials,observed for most real interfaces has yet to be quantitatively explained.The boundary resistance between two carefully bonded solids appears to be satisfactorily described by the acoustic impedance mismatch between the two media.The silane coupling agents acted as phonon transfer bridges between the polymer and the ceramic filler,which reduced the phonon boundary scattering and improved the thermal conductivity at low concentrations.As demonstrated in this study,the KBM-403treatment was more effective than KBM-703in enhancing the thermal conductivity.This can be explained by the ETDS/DDM polymerization mechanism.When the composite curing was performed at high temperature,epoxide groups in the ETDS react with DDM,and the ring opening and polymerization reactions proceed continuously.Similarly,epoxide groups in KBM-403react with DDM and are polymerized with ETDS.As a result,the boron nitride filler linked with the matrix through covalent bonding.However,KBM-703has a chloride group that instead forms non-covalent bonding,a dipole-dipole interaction,with the ETDS matrix.Therefore,KBM-403-Fig.6.Effect of surface treatment of BN particles on the thermal conductivity of BN/ETDS composites at various fillerconcentration.Fig.7.SEM cross section image of (a)–(b)BN/ETDS,(c)–(d)BN-403/ETDS and (e)–(f)BN-703/ETDS composites with 50wt%filler concentration.K.Kim et al./Ceramics International 40(2014)2047–20562053treated BN has a stronger interaction with the ETDS matrix along with good dispersibility and a higher thermal conduc-tivity than the KBM-703-treated BN composite.The differences in the cross-sectional images of each composite can be correlated to the existence of a silane coupling agent.Fig.7shows FE-SEM images of the cross-sections of50wt%BN/ETDS and two kinds of surface coupling agent-treated BN/ETDS compositefilms.As observed in Fig.7(a,c and e),all of the compositefilms appear to be homogeneously distributed.However,when the BN/epoxy compositefilm is observed at higher magnification (Fig.7(b)),it can be seen that the BNfiller settled to the bottom and a non-uniform distribution can be observed in the top of thefilm.This phenomenon is due to sedimentation of thefiller,which is an endemic problem of the casting method. BNfillers were well mixed for a sufficient time with the epoxy resin,maintaining goodfluidity at the high temperature,but sedimentation of thefiller progressed in the post curing step. On the other hand,the images in Fig.7(d and e)show a uniform cross-section of the silane coupling agent-treated BN, which was dispersed more uniformly and embedded in theepoxy,creating superior interface adhesion with the BN in the epoxy matrix.Uniform distribution of BN particles develops in the conduction carrier path.Moreover,BN has an idiopathic high surface energy,indicating that the phase interaction force between the epoxy and BN particles is very weak and suggesting that a low energy is needed to pull BN particles out from the matrix[36].The images in Fig.7(d and f)show an enhanced homogeneous distribution of BN particles throughout and a decrease of cracks and voids between the BN particles.This is further evidence that the surface curing agent enhanced the BN particle affinity with the matrix. Fig.7shows that the use of surface coupling agents effectively improves the homogeneous dispersion of BN particles in the epoxy,eliminates the agglomeration offiller, and decreases the void content and defects in the composites, resulting in an increased thermal conductivity.3.3.Mechanical propertiesThe mechanical properties of the composites with enhanced thermal conductivities were also measured by dynamic mechanical analysis(DMA).This was carried out to determine the improvement of the mechanical properties after the surface modification of the boron nitride particles in the polymer matrix.Since the operation temperature of the electronic package is generally about1501C,the stability of the composites was examined up to this temperature.The storage modulus of compositefilms with afiller content of70wt%is displayed in Fig.8as a function of temperature.As expected, the slopes of the curves tended to decrease near the glass temperature(T g).It can be clearly seen that the storage modulus of the composites increased withfiller surface modification,which is due to the mechanical reinforcement resulting from the strong interactions between BN and the ETDS matrix.As mentioned above,silane coupling agents improved the adhesive property between thefiller and matrix, as the stress is not well transferred when the same force is applied to the composite.The KBM-403in the composites prevented efficient treeing of the propagation of stress and,as a result,the storage modulus could be improved where the modulus of the KBM-403treated with the BN composite was higher than that of the KBM-703-treated BN composite. The tanδpeak position,which is a measure of the glass transition temperature(T g),shifted to higher temperatures with surface modification.The peak height was reduced when compared to that of the surface-untreated BN composite because the well dispersedfiller and sufficient incorporation of epoxy restricted the mobility of the epoxy chains,resulting in the higher mechanical properties observed for the surface-treated BN composites.4.ConclusionBN/epoxy compositefilms with different BN particle sizes and contents were successfully fabricated with a surface curing agent using a solvent casting method.The thermal conductiv-ities of polymer compositesfilled with various types of particles were evaluated and the thermal interface resistance theory was applied.Various particle tofiller ratios were tested and the12μmfiller demonstrated a higher performance,in the range of136–149%,than the nano-sizefiller($1μm). Furthermore,by applying micro-sized particles,the formation of conductive networks was maximized while minimizing the thermal interface resistance along the heatflow path.This thermal interface resistance is caused by phonon scattering in the interface of materials,which is the primary cause of decreased thermalconductivity.Fig.8.Storage modulus of ETDS and ETDS composites with70wt%filler concentration.K.Kim et al./Ceramics International40(2014)2047–2056 2054。

2011年全国大学生数学建模竞赛D题及评阅参考
来源：吕梁学院数学系发布时间：2011-09-27 查看次数：1092
D题天然肠衣搭配问题
天然肠衣（以下简称肠衣）制作加工是我国的一个传统产业，出口量占世界首位。

肠衣经过清洗整理后被分割成长度不等的小段（原料），进入组装工序。

传统的生产方式依靠人工，边丈量原料长度边心算，将原材料按指定根数和总长度组装出成品（捆）。

原料按长度分档，通常以0.5米为一档，如：3-3.4米按3米计算，3.5米-3.9米按3.5米计算，其余的依此类推。

表1是几种常见成品的规格，长度单位为米，∞表示没有上限，但实际长度小于26米。

表1 成品规格表
为了提高生产效率，公司计划改变组装工艺，先丈量所有原料，建立一个原料表。

表2为某批次原料描述。

表2 原料描述表
根据以上成品和原料描述，设计一个原料搭配方案，工人根据这个方案“照方抓药”进行生产。

公司对搭配方案有以下具体要求：
(1) 对于给定的一批原料，装出的成品捆数越多越好；
(2) 对于成品捆数相同的方案，最短长度最长的成品越多，方案越好；
(3) 为提高原料使用率，总长度允许有±0.5米的误差，总根数允许比标准少1根；
(4) 某种规格对应原料如果出现剩余，可以降级使用。

如长度为14米的原料可以和长度介于7 -13.5米的进行捆扎，成品属于7-13.5米的规格；
(5) 为了食品保鲜,要求在30分钟内产生方案。

请建立上述问题的数学模型，给出求解方法，并对表1、表2给出的实际数据进行求解，给出搭配方案。

Superhydrophobic and conductive carbon nanofiber/PTFE composite coatings for EMI shieldingArindam Das a ,Harun T.Hayvaci b ,Manish K.Tiwari c ,Ilker S.Bayer d ,Danilo Erricolo b ,Constantine M.Megaridis a ,⇑aMechanical and Industrial Engineering,University of Illinois at Chicago,Chicago,IL 60607,USA bElectrical and Computer Engineering,University of Illinois at Chicago,Chicago,IL 60607,USA cMechanical and Process Engineering,Swiss Federal Institute of Technology,Zurich 8092,Switzerland dSmart Materials Group,Italian Institute of Technology,Arnesano,LE 73010,Italya r t i c l e i n f o Article history:Received 14July 2010Accepted 5September 2010Available online 15September 2010Keywords:Superhydrophobic ConductiveCarbon nanofibers Composite coating EMI shieldinga b s t r a c tThis paper presents a solvent-based,mild method to prepare superhydrophobic,carbon nanofiber/PTFE-filled polymer composite coatings with high electrical conductivity and reports the first data on the effectiveness of such coatings as electromagnetic interference (EMI)shielding materials.The coatings are fabricated by spraying dispersions of carbon nanofibers and sub-micron PTFE particles in a polymer blend solution of poly(vinyledene fluoride)and poly(methyl methacrylate)on cellulosic substrates.Upon drying,coatings display static water contact angles as high as 158°(superhydrophobic)and droplet roll-off angles of 10°indicating self-cleaning ability along with high electrical conductivities (up to 309S/m).100l m-thick coatings are characterized in terms of their EMI shielding effectiveness in the X-band (8.2–12.4GHz).Results show up to 25dB of shielding effectiveness,which changed little with frequency at a fixed composition,thus indicating the potential of these coatings for EMI shielding applications and other technologies requiring both extreme liquid repellency and high electrical conductivity.Ó2010Elsevier Inc.All rights reserved.1.IntroductionElectrostatic dissipation,microwave absorption and electro-magnetic interference (EMI)shielding of sensitive electrical/elec-tronic circuitry and devices,antenna systems,aerospace and military equipment (e.g.lightning-protection aircraft composite panels),stealth technology,radar absorbing materials,avionics line replaceable unit (LRU)enclosures,etc.,are just few of many tech-nologies where metal-based materials have been considered almost exclusively to this date.Flexible and lightweight,electri-cally-conducting,polymer-based coatings have tremendous poten-tial for such technologies,as recent studies indicate [1–6].Added functionalities,such as chemical inertness and water repellency,further contribute to the value of polymer-based coatings by pre-venting contamination and corrosion when exposed to outdoor conditions.The first report of superhydrophobic,conductive,polymer-based coatings was made by Zhu et al.[7]who electrospun stable,polyaniline/polystyrene,large-area films well suited for corrosive environments.The conductivities of these films are too low (10À2S/m)for EMI shielding.Han et al.[8]created transparent ,conductive and superhydrophobic films using carbon nanotube/si-lane sol solutions.Their high-quality nanotubes (3–5nm dia.)raise the cost of these coatings.Luo et al.[9]used solution processing and vacuum filtering to produce superhydrophobic carbon nano-tube/nafion nanocomposite films with conductivities up to 1700S/m,which were maintained even after 1000bending cycles.How-ever,since the films were formed on the filtration membranes,their transfer and adherence to other surfaces might pose chal-lenges.Meng and Park [10]applied transparent,conductive,super-hydrophobic films on glass using fluoropolymer grafted multiwall carbon nanotubes.The high quality of the carbon nanotubes does not classify their process as low-cost.Zou et al.[11]synthesized polymer-based superhydrophobic coatings with very high conduc-tivities in the range 3Â103À104S/m (as compared to 6Â107S/m for Ag);these coatings were created by a one-step solution casting process that involved a carbon-nanotube-conjugated block copoly-mer dispersion.Attractive features of this method included the ability to apply on various substrates ranging from glass and silica wafers,to metals,fabrics or even paper.However,the higher cost of the carbon nanotubes (10–20nm dia.)hinders scale-up to large-area applications.While electrical conductivity of superhydrophobic polymer-based coatings/films has been measured in the sporadic works [7–11]published in this area,and the potential of such materials0021-9797/$-see front matter Ó2010Elsevier Inc.All rights reserved.doi:10.1016/j.jcis.2010.09.017Corresponding author.Fax:+13124130447.E-mail address:cmm@ (C.M.Megaridis).has been mentioned[8,11]in conjunction with EMI shielding,no study exists on EMI shielding properties of super-repellent,poly-mer-basedfilms.Since the EMI shielding effectiveness of a material depends not only on its conductivity but also its permeability[4], EMI shielding does not correlate directly with conductivity.Fur-thermore,EMI shielding effectiveness varies with frequency[12], thus requiring EMI measurements to be performed over a fre-quency range or the entire spectrum,when necessary.In response to the need for defining the EMI shielding effectiveness of novel superhydrophobic and conductive,polymer-basedfilms,the pres-ent study examines water repellent,composite coatings comprising of carbon nanofiber/PTFEfillers dispersed in a hydrophobic poly-mer matrix and applied by spray.The work utilizes only solu-tion-processable,commercially available,raw materials,and is therefore inherently low-cost.Water droplet sessile contact angle, roll-off angle and electrical conductivity measurements are performed on coatings applied on glass microscope slides.EMI shielding measurements are performed over the range8.2–12.4GHz(X-band)on identical coatings applied on cellulosic paper substrates,which in their uncoated state,have typical thickness of $100l m.The underlying hypothesis is that coatings deposited on either glass or paper have similar properties and structure when applied under identical conditions.2.ExperimentalA solution blend of poly(vinylidenefluoride)(PVDF)and acrylic poly(methyl methacrylate)(PMMA)forms the composite polymer matrix,which has a good degree of hydrophobicity and interfacial adhesion properties.PVDF with its environmental durability, hydrophobicity and electroactivity,combined with its chemical inertness,is an ideal choice for the hydrophobic component in the binder polymer,while adhesion and particle dispersion is im-parted by the acrylic PMMA.PMMA on its own generally forms brittle coatings with much lower mechanicalflexibility and stress bearing capacity[13].Sub-micron PTFE particles are used as hydro-phobicfillers to tune the coating microstructure and reduce sur-face energy[14],whereas the electrical conductivity is manipulated using heat-treated,vapor-grown carbon nanofibers (CNFs)[15,16].To prepare the composite coatings,60/40wt.%solution blends of PVDF(530kDa;Sigma–Aldrich,USA)in Dimethylformamide (DMF)and PMMA(996kDa;Sigma–Aldrich,USA)in acetone were mixedfiFs(averagefiber dia.100nm,PR24XT-HHT Pyrog-raf III;Applied Sciences Inc.,USA)and sub-micron PTFE particles (average dia.260±54.2nm;Sigma–Aldrich,USA)in dispersions were added asfillers to create sprayable solutions which,after application on glass and cellulosic substrates,were heat-dried at 90°C for1.5h to remove any residual solvent.The CNFs are free of CVD carbon with highly graphitized structure developed by high temperature treatment,resulting in higher electrical and thermal conductivity compared to as-grownfibers[17].The composite films were superhydrophobic and had electrical conductivities spanning over six orders of magnitude for the following weight composition range:Polymer matrix/PTFE/CNF1/5.76/0.068-1.1.A more detailed description of the suspension preparation and coat-ing application is provided in Supplemental material section.The dried coating thickness was measured using an optical microscope calibrated for depth measurement(top vs.bottom of the coating).At least three different thickness measurements at different locations were performed on each sample to assess point-to-point thickness uncertainty.Typical coating thickness was near100l m.The electrical conductivity of the coatings ap-plied on glass slides was measured using a Keithley6517electrom-eter/ammeter and the two-probe method.The coating areas slated for contact with the measuring probes were coated with a conduc-tive silver paint to ensure good electrical contact.A Lab-view based program was used to generate I–V curves and extract the electrical resistance of the coatings,which was then used to determine con-ductivity using the measured values of the coating thickness,width and length.Electrical conductivity of the coatings rose with CNF loading.Water droplet contact and roll-off angle measurements were performed using an in house goniometer-type optical setup described previously[14].3.Results and discussionFig.1shows the results of wettability tests and conductivity measurements for composite coatings with different CNF loadings expressed in terms of CNF/polymer weight ratio.As shown in Fig.1a,static water contact angles for all CNF loadings remained above150°.At the maximum CNF loading of1.1,contact angle reached a value of158°.It is worth noting that the corresponding contact angle for CNF-free coating was158°(see Fig.S1),which indicates that super-repellency is not contingent on the presence of CNFs.As Fig.1b indicates,water droplet roll-off angles for all CNF loadings remained close or below10°,confirming the self-cleaning water repellent nature of these coatings.Self-cleaning is promoted by low roll-off angles when the water droplet carries impurities off the tilted surface.As expected,Fig.1a shows an increase in conductivity of the composite coatings with rising content of conductive CNFs.It can be seen that the electrical percolation threshold for the coatings falls within the0.068–0.138CNF loading range,which corresponds to CNF content of1–2wt.%.This range is well below the theoretical values calculated for spherical particlefillers[18].The reason for this difference is the high aspect ratio of CNFs[19].Thisfigure also delineates the required electrical conductivities for three different applications of conductive coatings using two horizontal lines[20]. EMI shielding requires the highest conductivity(top)band.Various electronic products require protection of their internal circuitry and magnetic memory based components(microchips or ICs)from interference of outside electromagneticfields.Materials with high-er values of conductivity can block incoming EM waves more effec-tively.On the other hand,for electrostatic dissipation(lowest band in Fig.1a),lower conductivities suffice to reduce charge accumula-tion on insulator surfaces to avoid damage through electrostatic discharge.As far as electrostatic painting is concerned,this is a pro-cess in which materials of moderate to high conductivity(middle band in Fig.1a)are deposited on substrates by electrostatic attrac-tion.Corrosion resistant and conductive lightweight polymer coat-ings in the automobile industry offer one such example.The conductivity values achieved by these coatings are above the elec-trostatic dissipation range and can reach into the EMI shielding range;metals can be painted using this process.It is clear from Fig.1a that CNF loading can be used as a tuning parameter to vary conductivity of the coatings by more thanfive orders of magnitude without compromising superhydrophobicity.A maximum conductivity value of309S/m was obtained for coat-ings with CNF loadings around1.This underscores the potential of such coatings for numerous applications,and especially EMI shielding.Fig.2shows scanning electron micrographs of the surface mor-phology of the composite coatings for the two extreme CNF load-ings studied(a–b0.068,c–d1.1).In both cases,good dispersion of PTFE particles and CNF was achieved within the polymer blend matrix.As mentioned earlier,more than15-fold increase in CNF loading did not alter the degree of superhydrophobicity of the coatings(see Fig.1a),although their surface morphology was al-tered from predominantly PTFE clustered spheres with some CNF312 A.Das et al./Journal of Colloid and Interface Science353(2011)311–315strands to a mix of PTFE spheres and nanofibers(compare Fig.2b and d).No phase separation or segregation of the particles is ob-served even for the highest CNF loading.Moreover,micro to nano-scale surface features are preserved in both cases.The main factor responsible for the good dispersion of PTFE and CNF,as well as the preservation of the rough surface features responsible for water repellency is the existence of the PVDF/PMMA polymer blend ma-trix.Individually,PVDF is a low-interfacial-energy inert polymer, hence particle dispersion within PVDF is rather e of pristine PMMA polymer,on the other hand,can result in coat-ings with brittle andflaky structure and morphology[21]although PMMA is compatible with thefiller particles due to its high inter-facial energy.To this end,the60/40PVDF/PMMA blend was found to be optimal for maintaining a good degree offiller dispersion and high hydrophobicity.The EMI shielding effectiveness of the coatings was measured through S parameter measurements in a two-port configuration [22](see Fig.S2)using an HP8719D vector network analyzer (VNA)with operating range50–13.5GHz.An in house assembly consisting of two opposing WR-90waveguides coupled together to fully encase one coated sample at a time was used to evaluate the EMI shielding performance of the coatings(Fig.S3).The capa-bility of a thin planar barrier(coating in the present case)to shield from electromagnetic waves is measured in terms of its signal attenuation,defined[23]as10logP iP t¼20log E iE t½dB ;ð1Þwhere P i is the incident power on one side of the barrier and P t is the power transmitted through the barrier to the other side.The power ratio may also be expressed in terms of the ratio of the magnitudes of the incident electricfield E i and transmitted electricfield E t by assuming that thefields are plane waves.Moreover,this same ratio can be expressed in terms of the ratio of voltages associated with the ports of an appropriate network,and thus be determined through S parameter measurements[24].In general,systems that carry electromagnetic waves may be given a simpler description by treating them as networks and focusing only on the exchange of electromagnetic energy at their ports.According to Eq.(1),whichconductivity and sessile water contact angle for various(PVDF+PMMA)/PTFE/CNF composite coatings as a function of CNF loading weight ratio.In all cases the PTFE/polymer weight ratio was5.76.The conductivity regimes suitable for different applications droplet roll-off angle on coatings with different CNF loadings.micrographs of(PVDF+PMMA)/PTFE/CNF coatings for the two extreme CNF loadings considered in this study(a,bmagnification)correspond to50l m;the ones in the right(high magnification)to2l m.(reflection)and S21(transmission),for coatings with different CNF loading in the8.2–12.4GHz frequency range(X-band), setup shown in Fig.S3.to1.1.An important outcome of the measurements drawn in Fig.3 is that both transmission and reflection parameters S11and S21re-main fairlyflat in the frequency range8.2–12.4GHz.This indicates that the present coatings are equally effective in shielding over this entire frequency range.4.ConclusionWe describe fabrication and characterization of superhydropho-bic,carbon nanofiber/PTFE-filled polymer composite coatings with high electrical conductivity.The polymer matrix was a PVDF/PMMA blend,which,even in the absence of particlefillers displayed a good degree of hydrophobicity,interfacial adhesion andflexibility.The electrical conductivity of the coatings was tuned by varying CNF loading,and reached up to309S/m without sacrificing self-clean-ing water repellent ability.We report thefirst measurements on EMI shielding effectiveness of superhydrophobic,conductive poly-mer-based coatings over the X-band(8.2–12.4GHz).Shielding val-ues as high as$25dB(with a corresponding transmission power of only$0.5%)were obtained for coating thickness under$100l m. 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