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Influence of surfactants on the structure of titanium oxide gels experiments and simulatio

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a r X i v :c h e m -p h /9511002v 1 22 N o v 1995Influence of surfactants on the structure of titanium oxide gels :experiments and simulationsF.Molino †J.M.Barthez †‡A.Ayral ‡,C.Guizard ‡,R.Jullien*,J.Marignan ††Groupe Dynamique des Phases Condens´e es,U.A.233C.N.R.S.,Universit´e Montpellier II,34095Montpellier,Cedex 05,France ‡Laboratoire des Mat´e riaux et Proc´e d´e s Membranaires,U.M.R.9987C.N.R.S.,E.N.S.C.M.,8,Rue de l’Ecole Normale,34053Montpellier,Cedex 01,France *Laboratoire de Science des Mat´e riaux Vitreux,U.A.1119C.N.R.S.,Universite Montpellier II,34095Montpellier,Cedex 05,France Abstract We report here on experimental and numerical studies of the influence of sur-factants on mineral gel synthesis.The modification of the gel structure whenthe ratios water-precursor and water-surfactant vary is brought to the foreby fractal dimension measures.A property of polydispersity of the initial hy-drolysis is proposed to explain these results,and is successfuly tested throughnumerical experiments of three dimensional chemically limited aggregation.I.INTRODUCTIONThe irreversible aggregation of molecules in a solution,leading to the formation of a three-dimensional(3D)network or gel,has been the focus of a wide range of studies,from the more theoretical to the more application-oriented ones[1],[7].The structure of the gel is a well-known case of fractal mass distribution[9].The polymerization of a mineral monomer in an organic solvent is an example of this sol-gel process.More specifically,a very studied class of monomers is the metal alcoxides one, which elements consist of a metal atom(as silicon(Si)or titanium(Ti))surrounded by alcoxy (alcohol)groups.In an organic solvent(decane,cyclohexane)and in the presence of water, they readily react in a two-step process leading to the fractal polymer.In thefirst step,hydrolysis,the interaction of monomers with water leads to the substitution of some alcoxy groups with short-OH(hydroxy)radicals(the number of groups modified depending at least of the total amount of water available):T i(OR)4+nH2O→(HO)n T i(OR)4−n+(4−n)ROH.Then the hydrolyzed monomers stick together throught-OH HO-(oxolation)or-OH RO-(alcoxolation)reactions,to form the inorganic backbone of the fractal polymer(this step is the polycondensation):−T i−OH+HO−T i−→H2O+−T i−O−T i−.Due to the presence of four potentially active sites,one obtains a branched polymer and the gelation of the structure.However,for some very reactive alkoxide precursors(as in our case tetraisopropyl orthoti-tanate[T i(O i P r)4]),the reaction is so fast,even for very small amounts of water,that the precipitation of the solution can be avoided only by introducing amphiphile molecules which control the sol-gel transition by interacting with water or hydroxyl radicals.Only this trap-ping effect obtained from the introduction of the surfactant allows the formation of the gel by slowing down the hydrolysis,as has been recently investigated[2][3][4].Rather surprisingly,considering the stability of the caracteristic fractal dimension of the gel with variations of many parameters,the amphiphilic molecules not only control the kinetics of the reaction,but induce structural variations in thefinal polymer.In the case where a gel could be synthetized,we have studied experimentally the influence on the process of the water-surfactant and water-precursor ratios.More specifically,we report here of the possibil-ity of understanding some of the observed variations of the gel structure from the following hypothesis:in reactions with very small amounts of water,not all the sites on the monomers will be hydrolyzed and the distribution among the monomers of the hydroxyl(-OH)radicals created in the hydrolysis on the precursor monomers could depend,for a given amount of water,on the[H2O]/[Surf.]ratio.Numerical experiments which have been done to test this idea are described in this paper,and explain some evolutions of the fractal dimension of thefinal gel.II.EXPERIMENTAL RESULTSThe gels have been synthetized in two different solvents(cyclohexane and decane)from a T i(O i P r)4monomer.For each solvent,two solutions were prepared,thefirst(S1)containing the surfactant(Triton X-35)and the water,and the second(S2)the precusor;S1was then tipped into S2.The characteristic parameters of the solution were the T i(O i P r)molality, alwaysfixed to0.1mol.kg−1,and the molar ratios:n=[H2O][T i(O i P r)4].These diluted sols exhibit long gelation times and produce gels with a large fractality range [4].The polymeric gelation could be obtained for h between2and3,and n between1and2. The structural characteristic of thefinal gel we were interested in was the fractal dimension, which was measured using ultra small angle x-ray scattering[5].One can see infig.1the evolution with h of the fractal dimension,for two values of n.As previously said,the kinetic of the sol-gel process can be decomposed in two steps:hy-drolysis of the isopropoxy group,and polycondensation of the hydroxyl radicals.Let’s go into some details.On the basis of the partial-charge model[6],alcoxolation(condensation between OH and OR groups)should be the favored condensation reaction between par-tially hydrolyzed,coordinatively saturated titanate precursors.As underlined by Brinker and Scherer[7],the same trend is predicted for silicate but29Si NMR investigations[8] have shown that oxolation(condensation between OH groups)is the favored reaction of condensation between partially hydrolyzed silicon alkoxides.Perhaps solvent interactions that are not accounted for by the partial-charge model influence the quality of the leaving group[7].In our case,the assumption that oxolation is the favored reaction can also be justified taking into account the stronger lyophobicity of the hydroxyl groups in the inverse micellar medium.An NMR study of the isopropanol amount in the solution[4]led us to the conclusion of an almost instantaneous hydrolysis compared with the gelation time.Therefore one can hope to study separately the effects of the surfactant presence on the two reaction steps,at least if no important”second hydrolysis”occurs,due to the water created during the condensation. Our modelization assumption concerns primarily the way the surfactants could control the hydrolysis.In the solution,the water is trapped on the hydrophilic heads of the amphiphils (with a limit of four molecules of H2O on every surfactant),which organize themselves in inverse micellar aggregates in the hydrophobic solvent.Quasielastic light scattering mea-surements[2]give us a hydrodynamic radius for these structures between3nm for n=1 and4nm for n=2,the surfactant itself having an average extension of1.5nm.One can estimate from these radii that the number of pseudo-micelles for one alkoxide is3.5times larger for n=1than for n=2.In order to be hydrolysed,the precursor molecules must penetrate into these aggregates.This was the motivation for introducing our”hydrolysis polydispersity”hypothesis:the number of hydroxyl radicals created on the alkoxide will vary between1and4,with a distribution dependent on n,due to the variation with this parameter of the available water in the micellar structure.III.THE MODEL AND THE SIMULATIONLet us describe the numerical experiments performed in order to test this assumption.In our three-dimensional algorithm,every particle has six potentially active sites(cubic sym-metry).Taking into account the titanium tetravalence,we hydrolyze at most four of these sites,always situated in the same randomly selected plane.The hydrolysis ratio parameter h is represented by a scalar q varying between0.5and0.75for h between2and3:for N particle samples,the hydrolysis stops when4Nq sites have been hydrolyzed.The implicit hypothesis in taking q=h/4is that all the water contained in the solution has been used in the hydrolysis(a conclusion we inferred from our NMR studies).It is far more difficult to introduce n in the algorithm,for many hypotheses on the molecular behavior are involved in the prediction of its influence on the hydrolysis.We have chosen a parameter p in[0,1] to govern directly the polydispersity in hydrolysis of the sample.The idea is as follows :during every round a monomer is randomly chosen and a random number z generated. Depending on wether z>p,p2<z<p,p3<z<p2,or z<p3,1,2,3,or4sites are si-multaneously hydrolyzed.Then a second particle is selected,among the ones which have not yet been hydrolyzed during this round.When every particle has been selected exactly once for hydrolysis in the round,a next round opens,and so on until the4Nq water molecules available have been used.The algorithmic interest of this procedure is to make the hydrolysis polydispersity vary strongly with p,which increases all eventual polydispersity effects.This does not happen, for example,if at every step the hydrolyzed particle is put again in the sample from which the next one is selected.But what about the physical point of view?Concerning the power law in p for the choice of the number of hydroxyl radicals created,an independence of the dif-ferent hydrolyses happening with the same probability when the precursor is in the micellar structure is implicit.It may appear more arbitrary to hydrolyse every particle exactely oncein ever round.As previously remarked,this is essentially in order to make the hydrolysis polydispersity vary more strongly in the algorithm.Concerning the aggregation dynamics,we have chosen a chemically-limited model[9],[10] which suppresses all effects due to the diffusion.More precisely,we start from a diffusion-limited model[9],in which the gel fractality results from the brownian motion of the particles which stick together with a probability c when happening to occupy nearest-neighbour lat-tice sites.Making then c going to0,we end at the chemical model mentioned above:the particle random path lenght before aggregation goes to infinity,with the consequence that all the free sites on the aggregate have an equal probability of stick to it,except for steric hindrance.Of course the fractal dimensions obtained are superior to the diffusion-limited model ones.In our algorithm,the folowing are associated with every particle at every step:(1)the list of its six sites and their state(hydrolyzed,non-hydrolyzed,or already used in condensation);(2)the reference number of the cluster to which it belongs;(3)its3D coordinates inside its cluster(i.e.its position relative to the other particles in the same cluster only).So each cluster is on a lattice but the whole process is not,at least not in a box[11].At every step,two bonds are selected randomly among the6N ones.In order for the ag-gregation process to take place,they must obey the following conditions:(P1)they both must be hydrolyzed sites;(P2)they must belong to two different particles not being in the same cluster;(P3)moreover,cluster rotation is excluded,so the two bonds must be on two opposites sites on the same symmetry axis of the monomer.Only if these conditions are fulfilled can one then check the steric possibility of the aggregation,due to the presence of other molecules already connected to the selected sites.Why this model?To neglect the hazards of the diffusion is equivalent to accelerating the aggregation dynamics;this is an important advantage since we wish to explore a two di-mensional parameter space,which requires many drawings.Although the physical polymer-ization process in our solutions is conceivably controlled in part by the diffusion,its effect is only to globally decrease the fractal dimension of thefinal aggregate,without modifyingthe relative variations due to polydispersity effects.So the same trends must be observed in this model for the dimension in the p and q phase space,unless other assumptions are made on the influence of surfactants during the polymerization process,as discussed below. Being not in a box,it was not possible to introduce a gelation test(like the existence of a percolation cluster)giving to the algorithm a systematic stopping condition.The end of the simulation happens when(1)all the particles are in one cluster(2)(6N)2successive attempts to select bonds fulfiling the(P1)-(P3)conditions have been unsucessful(3)N2 successive sticking attempts have failed due to steric reasons.None of these conditions,even thefirst,has anything to do with a physical gelation.One can obtain the fraction a N of the initial N particles sample found in the biggestfinal aggregate;to impose a N=1as a gelation criterion give a phase transition diagram in the p,q plane with a gelation domain narrowly limited around the q=1limit(value corresponding to total hydrolysis).This is clearly not correlated to the physical gelation domain,which contain all the h>2part of the phase space.Moreover it is obvious that the physical gelation does not necessitate all the monomers to be polymerized.After the conclusion of the aggregation process,we compute the fractal dimension of the biggest aggregate created.We obtain it from the double logarithm graph of the two points correlation function calculated with the following algorithm:for every particle the array of distances of the other monomers,by increasing order,is obtained;one then averages over all the arrays(i.e.over all the cluster monomers).With c(r)the two-points correlation function,and D the fractal dimension,one has:n R(D)= R0c(r)d3r=R D.And from the slope of the linear functionlogN=f logRthe fractal dimension is easily obtained.IV.DISCUSSIONWith this method,we have done numerical experiments to be compared with Fig.1,q varying from0.5to0.75and p from0to1.The step for q was5×10−2,and10−1for p.Due to the very nature of the simulation algorithm,the cluster self-similarity is obtained only on distances of approximately one-quarter of its maximum radius.Hence,to observe the linearity of the correlation function on many orders of magnitude,it should be necessary to work on particle samples of at least104elements.On a RISK workstation,the aggregation algorithm could take many hours to complete.Nevertheless,it is remarkable that on1000 particles samples,sufficient information can be obtained on the fractal dimension,a fact that has been observed in all the(p,q)-phase space.This is all the more true if one averages over many samples,a procedure which increases only linearly the execution time.Nevertheless the dimensions are a little smaller(of0.2approximately)than the physical ones.Fig.2 shows the proportion evolutions with p(”polydispersity”)of the different species for q=0.5 (h=2)and q=0.75(h=3).For the same two extremal values of q,Fig.3shows the fractal dimension evolution with p.To compare with the experimental evolutions,one must remember the correspondence q→h and p→n.The h=2plot of3can be compared to the bottom1experimental plot.The p variation at constant h corresponds moreover to vertical evolutions between the two plots of1(top).So we predict that the two evolutions with h will converge for values of q near1,and not cross,as in the experimental data.For all the q values,the fractal dimension increases with p.This is easily understood from fig. 2.When p=0,the distribution of differently hydrolyzed species shows no polydisper-sity:it is peaked on a value depending on q;for example for q=0.5,all the particles have two hydrolyzed sites,for q=0.75three hydrolyzed sites.As p increases,the proportion of particles having more hydrolyzed sites than this initial value increases,and forms a greater proportion of thefinal aggregate(remember that this cluster contains not necessarily all the particles of the sample).At the p=1limit,only four-hydrolyzed-site particles remain. The important point is that when q increases,the domain of variation of the fractal dimen-sion decreases with p.At the q=1limit(complete hydrolysis)of course the polydispersity cannot play any role,and p has no influence on the fractal dimension,since all the possible sites are hydrolyzed.The asymptotic value of the dimension is then the same as for p=1, since as previously said only particles with four hydrolyzed sites remain for this value.Now for the evolution with q of the dimension,as previously mentioned,one of the difficulties of this simulation is the gauging of the n and p scales.However,the increasing of the fractal dimension with h for n=1can clearly be associated with the same evolution with q for p=0.The ranges of evolution coincide rather well(Fig.3).For n=2,taking into account the error bars in the x-ray determination of the gel structure, one could interpret in at least two ways the evolution of the fractal dimension.Thefirst is a convergence of the n=1and n=2curves to a common asymptotic value(2.4),around which the n=2curve would not vary very much.This is in fact the prediction of our simulation for a pure hydrolysis effect.For p=1,the dimension is constantly equal to the asymptotic limit2.35.Taking for n=2values of p near1would give a slight increase of the dimension with h.However,the experimental evolution of the fractal dimension with h for large values of n seemed to point out another interpretation,and could definitively not be explained by our model.For n=2,due to one experimental point,the fractal dimension decreased with h, and crossed the increasing n=1curve.No mechanism based on the initial hydrolysis could account for this trend,since,given any kind of initial distribution of hydroxyl radicals,the fractal dimension must always increase with the hydrolysis rate,or at least stay constant if it appears that the hydrolysis has no effect on the structure of the gel.In any case,for h→4, the dimension must for any value of n converge to the same limit,correponding to the total hydrolysis case,for which the distribution of the radicals has no role to play.The lack of experimental points in this region of the n,h phase diagram led us to perform a second set of measures at n=2and2.5<h<3.With more values,the fractal dimension appears in this range remarkably constant(seefig.4),and coherent with the predicted asymptotic value2.35.We concluded that the n=2,h=3value offig.1was not reproductible.Theevolution in the(h,n)phase space predicted by the model seems to be confirmed.V.CONCLUSIONWe have succeeded in understanding through simulation the fractal dimension evolution for all the regions of the(h,n)phase diagram,with a hydrolysis polydispersity hypothesis in thefirst stage of the reaction.The dimension increases with h and n in a well understood way.Therefore it appears that the influence of the surfactants molecules on the sol-gel process could be limited to thefirst step of the gelification.Interactions occcuring later,in particular with the hydroxyl radicals,seem to be without effect on the structural properties of the gel.Aknowledgments.We wish to thank mbard,P.Lesieur,and T.Zemb,who allowed us to realize ultra small angle x-scattering experiments and data treatments in the”Service de Chimie Mol´e culaire”at the C.E.N.,Saclay.FIGURESFIG.1.Experiments:fractal dimension variation with h for n=1and n=2(bottom);same variation with n for h=2(top).FIG.2.Polydispersity variation with p for q=0.75(top)and q=0.5(bottom).FIG.3.Simulation:fractal dimension variation with p for h=2and h=3..FIG.4.Experiment:evolution of the dimension for n=2,2.5<h<3.REFERENCES[1]J.E.Martin and D.Adolf,Ann.Rev.Phys.Chem.,311(1991).[2]C.Guizard et al.,J.Chim.Phys.87,1901(1990).[3]S.Lebon et al.,J.Non Cryst.Solids.147-148,92(1992).[4]J.M.Barthez et al.,J.Sol-Gel Sci.and Techno.2,283(1994).[5]mbard,P.Lesieur,and T.Zemb,J.Phys.I France.2,1191(1992).[6]J.Livage,M.Henry,and C.Sanchez,Progr.Solid State Chem.18,259(1988).[7]C.J.Brinker and G.W.Scherer,in Sol-Gel Science:The Physic and Chemistry ofSol-Gel Processing(Academic Press,Boston,1990),p.44.[8]R.A.Assink and B.D.Kay,J.Non-Cryst.Solids99,359(1988);B.D.Kay and R.A.Assink,ibid.104,112(1988).[9]R.Jullien and R.Botet,Aggregation and Fractal Aggregates(World Scientific,Singapore,1987).[10]R.Jullien and M.Kolb,J.Phys.17,L639(1984).[11]R.Botet,R.Jullien,and M.Kolb,Phys.Rev.A30,2150(1984).1.81.922.12.22.32.42.52.62 2.2 2.4 2.6 2.83f r a c t a l d i m e n s i o n hydrolysis rate h n=2n=11.81.922.12.22.32.42.52.62.72.81 1.2 1.4 1.6 1.82f r a c t a l d i m e n s i o n water/surfactant ratio n h=200.10.20.30.40.50.60.70.80.9100.20.40.60.81f r a c t i o n o f d i s t r i b u t i o n polydispersity parameter p 1 HYDR. SITE 2 HYDR. SITES 3 HYDR. SITES 4 HYDR. SITES 00.10.20.30.40.50.60.70.80.9100.20.40.60.81f r a c t i o n o f d i s t r i b u t i o n polydispersity parameter p 1 HYDR. SITE 2 HYDR. SITES 3 HYDR. SITES 4 HYDR. SITES1.81.922.12.22.32.4f r a c t a l d i m e n s i o n h=2h=30.511.522.5f r a c t a l d i m e n s i o n。

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汉江中下游春季浮游植物群落结构特征

汉江中下游春季浮游植物群落结构特征

33 （ 1 ） ： 33－40 生态学杂志 Chinese Journal of Ecology 2014 ，汉江中下游春季浮游植物群落结构特征 * 及其影响因素潘晓洁＊＊朱爱民郑志伟乔晔邹清周莲凤邹曦( 水利部中国科学院水工程生态研究所，水利部水工程生态效应与生态修复重点实验室，武汉 430079 )摘 要 针对汉江中下游春季硅藻水华频繁暴发的现状 ， 研究了水华暴发不同时期浮游植 物群落结构特征， 并结合水体理化因子分析， 揭示硅藻水华发生的主要影响因子。

结果表 明： 汉江春季水华暴发期间， 共鉴定出浮游植物 7 门 48 属 64 种（ 含变种） ， 其中硅藻种类所 不同样点所占比例介于 44． 13% ～ 51． 29% ， 其次是绿藻类 （ 16 占比例最大（ 18 属 23 种） ， 属 22 种） ， 不同样点所占比例介于 28． 21% ～ 35． 14% ， 蓝藻门和隐藻门种类数在水华期间 较少， 各样点仅发现 2 ～ 3 种， 金藻门和甲藻门种类最少； 水华发生期间主要优势种为硅藻 门的小环藻， 水华暴发初期和中期往往形成单优种 ， 而水华末期随着其优势度的降低， 蓝藻 隐藻门和硅 藻 门 其 他 种 类 也 会 形 成 优 势 种； 水 华 暴 发 期 间 浮 游 植 物 密 度 最 高 可 达 门、 7 －1 2． 34×10 7 cells·L －1 ， 其中小环藻种群数量最高可达 2． 06 ×10 cells · L ， 占浮游植物群落 Margalef 物种丰富度指数无显著时空差异， Shannon 总数的 88% ； 浮游植物多样性指数中， ， ， BergerParker Simpson 多样性在水华中期较低 而水华初期和末期相对较高 指数变化与 指 浮游植物总数量与磷酸盐、 溶解氧、 数相反； 浮游植物与理化因子的冗余分析 （ ＲDA ） 发现， 总磷呈正相关， 与硝酸盐、 温度、 透明度呈负相关。

Effect of Surfactants on the Interfacial

Effect of Surfactants on the Interfacial

Effect of Surfactants on the Interfacial Tension and Emulsion Formation between Water and Carbon Dioxide Sandro R.P.da Rocha,Kristi L.Harrison,and Keith P.Johnston*Department of Chemical Engineering,University of Texas,Austin,Texas78712Received July8,1998.In Final Form:October7,1998 The lowering of the interfacial tension(γ)between water and carbon dioxide by various classes of surfactants is reported and used to interpret complementary measurements of the capacity,stability,and average drop size of water-in-CO2emulsions.γis lowered from∼20to∼2mN/m for the best poly(propylene oxide)-b-poly(ethylene oxide)-b-poly(propylene oxide)(PPO-b-PEO-b-PPO)and PEO-b-PPO-b-PEO Pluronic triblock copolymers,1.4mN/m for a poly(butylene oxide)-b-PEO copolymer,0.8mN/m for a perfluoropolyether (PFPE)ammonium carboxylate and0.2mN/m for PDMS24-g-EO22.The hydrophilic-CO2-philic balance (HCB)of the triblock Pluronic and PDMS-g-PEO-PPO surfactants is characterized by the CO2-to-water distribution coefficient and“V-shaped”plots of logγvs wt%EO.A minimum inγis observed for the optimum HCB.As the CO2-philicity of the surfactant tail is increased,the molecular weight of the hydrophilic segment increases for an optimum HCB.The stronger interactions on both sides of the interface lead to a lowerγ.Consequently,more water was emulsified for the PDMS-based copolymers than either the PPO-or PBO-based copolymers.IntroductionSupercritical fluid(SCF)carbon dioxide(T c)31°C,P c )73.8bar)is an environmentally benign alternative to organic solvents for waste minimization.It is nontoxic, nonflammable,and inexpensive.However,because of its very low dielectric constant, ,and polarizability per volume,R/v,CO2is a poor solvent for most nonvolatile lipophilic and hydrophilic solutes.1It may be considered a third type of condensed phase,different from lipophilic and hydrophilic phases.Consequently,it is possible to disperse either lipophilic or hydrophilic phases into CO2, in the form of microemulsions,emulsions,and latexes, given an appropriate surfactant.Because of the low values of and R/v for CO2,the most CO2-philic types of functional groups have low cohesive energy densities,e.g.,fluoro-carbons,fluoroethers,and siloxanes.2-6The solvent strength of carbon dioxide may be understood by the fact that the solubility of a polymer in carbon dioxide is highly correlated with the surface tension of the pure polymer melt.7For example,poly(fluoroacrylates)with low surface tensions of10-15mN/m are highly soluble,whereas poly-(dimethylsiloxanes)with surface tensions of20mN/m are moderately soluble,and hydrocarbon polymers with higher surface tensions show very low solubility.For nonpolar or slightly polar polymers,the surface tension is a measure of the van der Waals forces and is related to the cohesive energy density.Because R/v is so small for CO2,polymers with low cohesive densities and surface tensions are the most soluble.The first generation of research involving surfactants in SCFs addressed reverse micelles and water-in-SCF microemulsions,for fluids such as ethane and propane8,9 as reviewed recently.10,11Microemulsions are thermody-namically stable and optically transparent,with typical droplet diameters of about2-10nm.The mechanistic insight gained from these studies of phase equilibria, interfacial curvature,and droplet interactions in a su-percritical fluid is directly applicable to carbon dioxide. Attempts to form water-in-CO2(w/c)microemulsions have been elusive.6,12,13For PFPE COO-NH4+w/c microemul-sions,FTIR,UV-visible absorbance,fluorescence,and electron paramagnetic resonance(EPR)experiments have demonstrated the existence of an aqueous domain in CO2 with a polarity approaching that of bulk water,14as has also been shown by small-angle neutron scattering (SANS).15Organic-in-CO2microemulsions have also been formed for600molecular weight poly(ethylene glycol) (PEG600)and for polystyrene oligomers.16,17In many previous studies,surfactant activity in CO2has been characterized in terms of water uptake into a CO2 microemulsion.Since the results were negative most of the time,it has been difficult to determine how to design surfactants to the water-CO2interface.A more direct property,such as the interfacial tension,is needed to understand the activity of surfactants at various interfaces containing carbon dioxide.In SCF systems,only a few studies have measured the interfacial tension(γ)even for simple binary systems(1)O’Shea,K.;Kirmse,K.;Fox,M.A.;Johnston,K.P.J.Phys.Chem. 1991,95,7863.(2)McHugh,M.A.;Krukonis,V.J.Supercritical Fluid Extraction: Priciples and Practice,2nd ed.;Butterworth:Stonham,MA,1994.(3)Hoefling,T.A.;Newman,D.A.;Enick,R.M.;Beckman,E.J.J. Supercrit.Fluids1993,6,165-171.(4)Newman,D.A.;Hoefling,T.A.;Beitle,R.R.;Beckman,E.J.; Enick,R.M.J.Supercrit.Fluids1993,6,205-210.(5)DeSimone,J.M.;Guan,Z.;Elsbernd,C.S.Science1992,257, 945.(6)Harrison,K.;Goveas,J.;Johnston,K.P.;O’Rear,ngmuir 1994,10,3536.(7)O’Neill,M.L.;Cao,Q.;Fang,M.;Johnston,K.P.;Wilkinson,S. P.;Smith,C.D.;Kerschner,J.;Jureller,S.Ind.Chem.Eng.Res.1998, 37,3067-3079.(8)Fulton,J.L.;Smith,R.D.J.Phys.Chem.1988,92,2903-2907.(9)Johnston,K.P.;McFann,G.;Lemert,R.M.Am.Chem.Soc.Symp. Ser.1989,406,140-164.(10)Bartscherer,K.A.;Minier,M.;Renon,H.Fluid Phase Equilib. 1995,107,93-150.(11)McFann,G.J.;Johnston,K.P.In Microemulsions:Fundamental and Applied Aspects;Kumar,P.,Ed.;Dekker:New York,1998;Vol.in press.(12)Iezzi,A.;Enick,R.;Brady,J.Am.Chem.Soc.Symp.Ser.1989, No.406,122-139.(13)Consani,K.A.;Smith,R.D.J.Supercrit.Fluids1990,3,51-65.(14)Johnston,K.P.;Harrison,K.L.;Clarke,M.J.;Howdle,S.M.; Heitz,M.P.;Bright,F.V.;Carlier,C.;Randolph,T.W.Science1996, 271,624-626.(15)Zielinski,R.G.;Kline,S.R.;Kaler,E.W.;Rosov,ngmuir 1997,13,3934-3937.419Langmuir1999,15,419-428including carbon dioxide and a liquid phase.18-20None of these studies included a surfactant.Surfactants have been studied for the generation of CO2foams in water21typically for water-soluble surfactants.The effects of various surfactants on theγbetween supercritical CO2and PEG (600MW)were reported recently.16At276bar,the addition of1%PFPE COO-NH4+reducesγfrom3.2to2.1mN/m, and the interfacial area of the surfactant is437Å2/ molecule.Interfacial tension measurements have also been made between poly(2-ethylhexyl acrylate)(PEHA)and CO222and styrene oligomers and CO2.23As is well-known for water-in-oil(w/o)emulsions and microemulsions,the phase behavior,γ,and curvature are interrelated,as shown in Figure1.24A minimum inγis observed at the phase inversion point where the system is balanced with respect to the partitioning of the surfactant between the phases.25,26Upon change of any of the formulation variables away from this point,for example,the temperature or the hydrophilicity/hydro-phobicity ratio(in our case the hydrophilic/CO2-philic ratio),the surfactant will migrate toward one of the phases. This phase usually becomes the external phase,according to the Bancroft rule.27Unlike the case for conventional solvents,a small change in pressure or temperature can have a large influence on the density and thus on the solvent strength of a supercritical fluid.By“tuning”the interactions between the surfactant tail and the solvent,it becomes possible to manipulate the phase behavior,and therefore the activity of the surfactant at the interface and curvature,and also the extension of the surfactant tails.As an example of pressure tuning,a water-in-propane microemulsion is inverted to a propane-in-water microemulsion by varying the pressure by50bar in the C12EO6/brine/propane system, at constant temperature.28This system undergoes a phase inversion density,by analogy with the phase inversion temperature,for conventional systems.If the density is changed so that the surfactant prefers either phase over the other,the surfactant is less interfacially active and γincreases.16,22,23The objective of this study is to achieve a fundamental understanding of the lowering of the water-CO2inter-facial tension by different classes of surfactants and to use this knowledge to explain the formation and stability of water-in-CO2(w/c)emulsions.The surfactants include PFPE COO-NH4+,Pluronic R(PPO-b-PEO-b-PPO)and Pluronic L(PEO-b-PPO-b-PEO)triblock copolymers,poly-(butylene oxide-b-ethylene oxide)(PBO-b-PEO),and poly-(dimethylsiloxane)(PDMS)copolymers with PEO-PPO grafts(PDMS-g-PEO-PPO).Fromγmeasurements ver-sus concentration,the adsorption is investigated for PFPE COO-NH4+and used to determine the critical micro-emulsion concentration.For the PPO-and PDMS-based surfactants,the concept of a hydrophilic-CO2-philic bal-ance(HCB)is introduced by relatingγand the distribution coefficient of the surfactant to the EO fraction(see Figure 1).To understand howγand the HCB influence colloid stability,we chose to study w/c emulsions in contrast to previous studies of microemulsions,since so few of these surfactants form microemulsions.Emulsions are ther-modynamically unstable,but may be kinetically stable, with droplets from100nm to several micrometers in diameter.The presence of the surfactant at the interface lowers theγand thus the Laplace pressure,reducing the energy necessary to deform the interface.29The emulsions may be stabilized against flocculation due to van der Waals forces by steric stabilization,as has been analyzed theoretically,30-33and/or Marangoni stresses,due to gradients in interfacial tension at the interface.To characterize emulsion capacity,stability,and the average droplet size of the emulsions,an in-situ turbidity technique has been applied in addition to visual observations.The ability to design surfactants for the interface between CO2 and an aqueous phase based upon knowledge of the relationship between colloid formation and stability,phase behavior,andγis of interest for a wide variety of heterogeneous reactions and separation processes in CO2. Examples include dry cleaning,extraction with micro-(16)Harrison,K.L.;Johnston,K.P.;Sanchez,ngmuir1996, 12,2637-2644.(17)McClain,J.B.;Betts,D.E.;Canelas,D.A.;Samulski,E.T.; DeSimone,J.M.;Londono,J.D.;Cochran,H.D.;Wignall,G.D.;Chillura-Martino,D.;Triolo,R.Science1996,274,2049.(18)Heurer,G.Ph.D.Thesis,The University of Texas at Austin, 1957.(19)Chun,B.-S.;Wilkinson,G.T.Ind.Eng.Chem.Res.1995,34, 4371-4377.(20)Schiemann,H.;Wiedner,E.;Peter,S.J.Supercrit.Fluids1993, 6,181-189.(21)Lee,H.O.;Heller,J.P.;Hoefer,A.M.W.SPE Reservoir Eng. 1991,11,421-428.(22)O’Neill,M.;Yates,M.Z.;Harrison,K.L.;Johnston,P.K.;Canelas,D.A.;Betts,D.E.;DeSimone,J.M.;Wilkinson,S.P.Macromolecules1997,30,5050-5059.(23)Harrison,K.L.;da Rocha,S.R.P.;Yates,M.Z.;Johnston,K. P.;Canelas,D.;DeSimone,ngmuir1998,14,6855-6863.(24)Aveyard,R.;Binks,B.P.;Clark,S.;Fletcher,P.D.I.J.Chem. Technol.Biotechnol.1990,48,161-171.(25)Bourrel,M.;Schechter,R.S.Microemulsions and Related Systems:Formulation,Solvency and Physical Properties;Marcel(27)Ruckentein,ngmuir1996,12,6351-6353.(28)McFann,G.J.;Johnston,ngmuir1993,9,2942.(29)Walstra,P.Chem.Eng.Sci.1993,48,333-349.(30)Peck,D.G.;Johnston,K.P.Macromolecules1993,26,1537.(31)Meredith,J.C.;Johnston,K.P.Macromolecules1998,31,5507-5555.(32)Meredith,J.C.;Sanchez,I.C.;Johnston,K.P.;Pablo,J.J.d.Figure1.Schematic representation of phase behavior andinterfacial tension for mixtures of water,CO2,and nonionicsurfactants as a function of formulation variables.420Langmuir,Vol.15,No.2,1999da Rocha et al.emulsions and emulsions,phase transfer reactions,34,35and emulsion polymerization.36Experimental SectionMaterials.All of the surfactants were used as received,unless indicated.The CF 3O(CF 2CF(CF 3)O)∼3CF 2COO -NH 4+(PFPE COO -NH 4+),a gift from A.Chittofrati,37was stored in a desiccator.The single tail Krytox-sulfate,R -COOCH 2CH 2OSO 3--Na +,where R )CF 3(CF 2CF(CF 3)O)n CF 2CF 2-,and the triple tail Krytox-sorbitol surfactants were synthesized by E.Singley and Dr.E.J.Beckman at the University of Pittsburgh.38Pluronic L,PEO-b -PPO-b -PEO (PEO -PPO -PEO),and Pluronic R,PPO-b -PEO-b -PPO (PPO -PEO -PPO),surfactants were a gift from BASF.The block copolymer PEO-b -PBO (EO 15-BO 12,SAM185)(where the subscripts indicate the number of repeat units of each moiety)was provided by Pittsburgh Paint and Glass.The surfactant (CH 3)3SiO[Si(CH 3)2O]20[Si(CH 3)(R)]2OSi(CH 3)3,with graft R )(CH 2)3O(C 2H 4O)∼11H,(PDMS 24-g -EO 22),M w ∼2600,was a gift synthesized by Unilever.7SILWET L-7500(M w )3000),(CH 3)3SiO(Si(CH 3)2O)x (Si(CH 3)(R))y OSi(CH 3)3,with R )(CH 2)3O-(C 3H 6O)n Bu (PDMS 11-g -PO 39),with n ,x ,and y not specified,and SILWET L-7622(M w )10000),with a similar backbone,but R )(CH 2)3O(C 2H 4O)m Me (PDMS 105-g -EO 68),were provided by OSi Specialties,Inc.ABIL B 8851(M w ∼6000),(CH 3)3SiO(Si-(CH 3)2O)22(Si(CH 3)(R)O)4Si(CH 3)3,with R )(CH 2)3O(C 2H 4O)∼17-(C 3H 6O)∼4H (PDMS 28-g -EO 67-PO 17),and ABIL B 88184(M w ∼13000),(CH 3)3SiO(Si(CH 3)2O)73(Si(CH 3)(R)O)4Si(CH 3)3,with R ∼(CH 2)3O(C 2H 4O)∼32(C 3H 6O)∼7H (PDMS 79-g -EO 126-PO 28)were obtained from Goldschmidt AG.PDMS homopolymer with a M w of 13000was synthesized by J.M.DeSimone at U.N.Carolina.Poly(ethylene glycol)with a molecular weight of 600was obtained from Polysciences,Inc.Poly(butylene glycol)monoether,composed of an ethylene oxide backbone with an ethyl side group (PBO,800g/mol)was supplied by Air Products.Poly(propylene glycol)(1025g/mol)was obtained from Polysciences,Inc.,and used as received.Deionized water (NANOpureII;Barnstead)and instrument grade carbon dioxide (99.99%)were used for all experiments.Phase Behavior.Phase boundaries were determined in the variable-volume view cell as described in further detail else-where.7For a given weight of surfactant and CO 2,the pressure of the system was increased until a single phase was observed in the view cell.The pressure was then decreased slowly until the solution became slightly turbid.The pressure was then increased again,and the process was repeated.The pressure where the system became turbid was classified as the cloud point pressure.The pressure and temperature were measured to (0.2bar and (0.1°C,respectively.Interfacial Tension Measurements.The tandem variable-volume pendant drop tensiometer described previously 16was used to measure the interfacial tension between CO and water (γ).The apparatus consisted of two variable volume view cells (the drop phase cell and the measurement cell (continuous phase cell)),an optical rail for proper alignment,a light source,a video camera,and a computer.The drop phase cell contained water saturated with an excess amount of pure CO 2,and the continuous phase cell contained CO 2and surfactant (if present).In this configuration,the surfactant only has to diffuse short distances in the small volume of the droplet phase.Pendant drops were formed on the end of a stainless steel or PEEK capillary tube with an inside diameter ranging from 0.01to 0.03in.Once a suitable drop was formed,the six-port switching valve connecting the two cells was closed and timing of the drop age was started.Several images were recorded as a function of drop age.Images of the drop were obtained in a tagged imagefile format (TIFF)and the edge of the drop was extracted from data at various global threshold values using a C ++program.From the shape of the interface,the γmay be obtained from the Laplace equationwhere ∆P is the pressure differential across the interface,R 0is the radius of curvature at the apex of the drop,and z is the vertical distance from the apex.A set of three first-order differential equations was used to express Laplace’s equation,and a computer program 39,40was used to solve for γ.The density difference between the two phases was calculated by using an equation of state for pure CO 241and steam tables for pure water.The aqueous phase density was assumed to change less than 0.0025g/cm 3for the concentrations of surfactant studied.Emulsion Formation,Stability,and Average Droplet Size Estimation.Figure 2shows a schematic representation of the experimental apparatus,similar to a previous version,for turbidimetric measurement and visual observation of emulsion formation and stability.22The system consists of a 28-mL variable-volume view cell,an optical cell (0.1cm path length)which was mounted in a spectrophotometer (Cary 3E UV -vis),a high-pressure reciprocating pump (minipump with a flow rate of 8-80mL/min),and a manual pressure generator (High-Pressure Equip.,model 87-6-5).A six-port switching valve (Valco Instru-ments Co.,Inc.)with an external sampling loop was used to add water to the system.The pressure was monitored to (0.2bar with a strain gauge pressure transducer (Sensotec),and the temperature was controlled to within (0.1°C.Surfactant was initially loaded into the view cell,and the desired amount of CO 2was added with the pressure generator.The pressure was increased,and the system equilibrated at the desired T ,for ∼2h,by using a magnetic stir bar.The cloud point of the surfactant was obtained as described above.The solution was then recirculated,and deionized water was injected into the system via the 150-µL sample loop in the switching valve.The solution was sheared through a 130µm i.d.×50mm long stainless steel capillary tube upstream of the optical cell.Emulsion formation and stability were characterized based upon turbidity measurements versus time (t )at a constant wavelength (λ)650nm)and also visual observation.The turbidity is a measure of the reduction in transmitted intensity,τ)(1/l )ln(I 0/I ),where l is the path length and I 0and I are the incident and transmitted intensities,respectively.After the injection of each increment of water,the emulsion was stirred and recirculated for ∼20min (approximate time required for the absorbance to reach a maximum value).Immediately after recirculation and stirring were stopped,τmeasurements started.The stability was assessed from τas a function of t ,while the(34)Jacobson,G.B.;Lee,C.T.;daRocha,S.R.P.;Johnston,.Chem.,in press.(35)Jacobson,G.B.;Lee,C.T.;Johnston,.Chem.,in press.(36)Adamsky,F.A.;Beckman,E.J.Macromolecules 1994,27,312-314.(37)Chittofrati,A.;Lenti,D.;Sanguineti,A.;Visca,M.;Gambi,C.M.C.;Senatra,D.;Zhou,Z.Prog.Colloid Polym.Sci.1989,79,218-(39)Jennings,J.W.;Pallas,ngmuir 1988,4,959-967.Figure 2.Apparatus for emulsion formation and turbidimetry measurement.∆P )2γ/R 0+(∆F )gz(1)Surfactant Effect on Interfacial Tension Langmuir,Vol.15,No.2,1999421effective average droplet size was determined fromτversusλ.For a monodisperse system of nonabsorbing spheres in theabsence of multiple scatteringτis given byτ)3K*φ/2D,42where φis the dispersed phase volume fraction,D is the droplet diameter, and K*is the scattering coefficient.According to Mie theory,Κ*is a complex function of R(R∼D/λ,whereλis the wavelengthof the incident light)and m the ratio of the refractive indices ofthe dispersed and continuous phases.The refractive indices wereapproximated by those of the pure components,water(1.333)and CO2.43By evaluation of turbidities at two wavelengths,theaverage droplet size can be determined by an iteration proce-dure.44Results and DiscussionInterfacial Tension of the CO2-Water Binary System.The interfacial tension between pure CO2and water is shown in Figure3for two temperatures as a function of pressure,along with the data of Heurer18and Chun and Wilkinson.19Our interfacial tensions were measured1h after drop formation.Theγvalues obtained by Chun and Wilkinson19were measured with the capillary rise technique.Whereas local equilibrium was achieved within the capillary tube,the entire system was not at equilibrium.Heurer used the pendant drop technique; however,the values reported were obtained from the drop profile within10s of drop formation.Therefore,the lower values ofγin the present study suggest a closer approach to true equilibrium.A simple physical picture may be used to explain the behavior for most of the pressure range studied.16At pressures below70bar,γdecreases with increasing pressure.The cohesive energy density or free energy density of CO2is well below that of water at all pressures. The density and free energy density of CO2change over a wide range with pressure,whereas the values for essentially incompressible water are constant.As the density of the CO2phase increases,its free energy density becomes closer to that of water,andγdecreases.At low pressures where the density and free energy density change a great deal with pressure,the decrease inγis pronounced.At high pressures,where CO2is more “liquidlike”,it is much less compressible and the decrease inγwith pressure is small.For the CO2-PEG600interface,γwas predicted quantitatively with a gradientmodel and the lattice fluid equation of state.16The latticefluid model is less applicable for water due to thecomplexities resulting from hydrogen bonding and car-bonic acid formation.A cusp in the curve ofγversus pressure is observed attemperatures and pressures near the critical point of CO2.The region of the cusp inγshifts to slightly higherpressures as the temperature is increased above the criticaltemperature of CO2.For supercritical temperatures,themagnitude of the cusp increases as the temperature isdecreased toward the critical temperature.At25,1935,and38°C,the cusp in the interfacial tension is verynoticeable,while it becomes small at45°C and is notvisible at71°C.18The following argument explains how the cusp is relatedto the large compressibility of CO2.An upward pointingcusp has been observed for the surface excess of ethyleneon graphitized carbon black.45The excess adsorption canbe defined in terms of the density of the bulk phase andthe density of the interfacial region46where F(z)is the molar density of the fluid at a distancez from the surface.At pressures below the critical pressureregion,F(z)can be much larger than F,due to attractionof solvent to the surface,leading to a largeΓex.At higherpressures,the bulk fluid is much denser,so that thedifference between F(z)and F is much smaller resultingin a smallerΓex.As temperature increases above thecritical temperature of the solvent,the tendency of thesurface to raise F(z)to“liquidlike”densities diminishesandΓex decreases.Similar arguments apply to theadsorption of CO2at the water-CO2interface.TheenhancedΓex is manifested as the downward cusp inγ.Inboth examples,the cusps become broader and shift tohigher pressures at higher temperatures.Similar behavioris observed for peaks in plots of the isothermal compress-ibility of pure CO2versus pressure at constant temper-ature.To put the above results in perspective,new interfacialtension data are shown for the PEG600-CO2interface tocomplement earlier data16only at45°C(Figure4).Thevalues ofγfor the water-CO2interface are considerablylarger than those for the PEG600-CO2,PS(M n)1850),23CO2-PEHA(M n)32k)interfaces.22This result is dueprimarily to the much larger surface tension of water,∼72mN/m,versus that of PEG,∼35mN/m,and PEHA, 30mN/m.However,it is interesting thatγbetween CO2and water at high pressures,20mN/m,is below that forwater-hydrocarbon interfaces.For heptane and octane,the hydrocarbon-waterγis about50mN/m.This lower γis consistent with the higher miscibility between CO2 and water47versus hydrocarbons and water.The stronger interactions between CO2and water versus hydrocarbons and water are due to the small size of CO2which causes a smaller penalty in hydrophobic hydration,CO2’s quad-rupole moment,and,finally,Lewis and Bronsted acid-base interactions.Over the entire pressure range for PEG600-CO2at25and45°C,the interfacial tension decreased monotonicallywith increasing pressure,unlike the case for CO2-water(42)Yang,K.C.;Hogg,R.Anal.Chem.1979,51,758-763.(43)Burns,R.C.;Graham,C.;Weller,A.R.M.Mol.Phys.1986,59,(45)Findenegg,G.H.In Fundamentals of Adsorption;Myers,A.L., Belfort,G.,Eds.;Engineering Foundation:New York,1983;p207.Figure3.Interfacial tension at the CO2-water interface asa function of pressure at various temperatures.Γex≡∫(F(z)-F bulk)d z(2) 422Langmuir,Vol.15,No.2,1999da Rocha et al.at 35°C.The lack of a dip near the critical pressure may be due to the much lower compressibility at 25and 45°C versus 35°C.This contrast in behavior may also be due to a difference in the density gradient and thickness in the interfacial region for the two systems,for example,greater miscibility for the CO 2-PEG600system.Interfacial Tension:PFPE Ammonium Carboxy-late.The addition of small amounts of PFPE COO -NH 4+decreases γsubstantially as shown at 45°C and 276bar in Figure 5.As the concentration is raised above 0.03%surfactant,a discontinuity is observed,and the magnitude of the slope becomes much smaller.Because it has been shown that w/c microemulsions are formed in this system,14the discontinuity can be attributed to a critical microemulsion concentration (c µc)for the PFPE COO --NH 4+surfactant,as has been done for oil -water inter-faces.24At concentrations above the c µc,the less negative slope is caused by the addition of surfactant primarily to adsorption at the pendant drop interface,the change in γis reduced.The adsorption obtained from the Gibbs’adsorption equationfor the PFPE COO -NH 4+surfactant was 1.77×10-10mol/cm 2,which corresponds to a surface coverage of ∼100Å2/molecule.Such a high surface coverage is sufficient for the formation of microemulsions.A comparable value of ∼140Å2/molecule was measured by Eastoe et al.48at 500bar and 25°C for the hybrid hydrocarbon -fluorocarbon C 7F 15CH(OSO 3-Na +)C 7H 15surfactant in CO 2.This value was determined by assuming that all the surfactant is adsorbed at the interface of spherical droplets of 25Å2radius,as measured by SANS,with a polydispersity of ∼0.2.The substantial reduction in γand relatively high surfactant adsorption explain why it was possible to form a w/c microemulsion with PFPE COO -NH 4+.The same surfactant had an absorption of 400Å2/molecule at the CO 2-PEG interface.16Phase behavior studies indicated that PEG-in-CO 2microemulsions are also formed with this surfactant,but the nature of the core has not been characterized.16Interfacial Tension:Fluoroether Sulfate and Sorbitol Surfactant.The phase behavior of fluoroether sulfates and fluoroether sorbitols was measured by Singley et al.38for various molecular weights of single-,twin-,and triple-tailed surfactants.The surfactants were soluble in CO 2at 33°C and moderate pressure (<300bar).The sorbitol surfactants were found to be more soluble in CO 2than the sulfate ones,as expected due to the low solubilities of ions in CO 2,because of its low dielectric constant.The results showed that branching depresses the cloud point curve of a surfactant until the solubility becomes domi-nated by the overall molecular weight.These surfactants were used to form CO 2-in-water and middle-phase emul-sions with excess CO 2and water.38The interfacial tension was measured at the water -CO 2interface for the single-tailed M w 2500sulfate and the triple-tailed (7500g/mol total)sorbitol surfactants.Our measured cloud point for the 1.4%(w/w)CO 2sorbitol surfactant was 215.6bar at 45°C.For 0.56%sulfate surfactant,it was 139.8bar at 45°C.The sulfate surfactant did not lower the interfacial tension significantly over the pressure range of 180-283bar 45°C at a concentration of 0.56%.The interfacial tension was difficult to determine accurately,because bubbles and possibly surfactant precipitate appeared on the surface of the pendant drop within 15min of drop formation.The interfacial tension was estimated to be ∼15mN/m by using manual edge detection of the pendant drop.For the sorbitol surfactant,the interfacial tension decreased to ∼5.5mN/m at 276bar and 45°C with a concentration of 1.4%.Relative to other surfactants reported in this study,these surfactants were less successful in lowering the interfacial tension.Interfacial Tension:PPO -PEO -PPO,PEO -PPO -PEO,and PBO -PEO Surfactants.Block co-polymers containing CO 2-philic and hydrophilic (CO 2-phobic)functional groups may be designed to be active at the CO 2-water interface.In this section,the CO 2-philic blocks are poly(propylene oxide)and poly(butylene oxide),while the CO 2-phobic block is poly(ethylene oxide).TheFigure 4.Interfacial tension for the PEG600-CO 2interface at varioustemperatures.Figure 5.Interfacial tension for the water -CO 2-PFPE COO -NH 4+system at 45°C and 276bar.The dotted line is used to determine the surfactant adsorption via the Gibbs adsorption equation.A discontinuity is present at the critical micromemulsion concentration.Γ2)-1RT (d γd ln c 2)T ,P(3)Surfactant Effect on Interfacial Tension Langmuir,Vol.15,No.2,1999423。

The influence of structure on the pre-failure behaviour of a natural clay

The influence of structure on the pre-failure behaviour of a natural clay

The in¯uence of structure on the pre-failure behaviour of a naturalclayF.COTECCHIA Ãand R.J.CHANDLER {Results are presented of an extensive laboratory and ®eld investigation of a Pleistocene stiff clay in its natural and reconstituted states,including constant rate of strain oedometer and triaxial tests over a wide stress range,scanning electron microscopy and chemical micro-analysis.The relationships between the structure of the clay,its geological history and its mechanical re-sponse are demonstrated.The structure of the clay is strongly in¯uenced by bonding,appar-ently largely due to a ®lm of amorphous calcite which developed in situ at the end of normal consolidation.The effects of structure on the stiffness of the clay are identi®ed,with sensitiv-ity as the parameter quantifying the mechanical effects of structure.A frictional ¯ow rule is found generally to be applicable over a wide strain range,including yield,even when strong bonding is present,although its form is in¯u-enced by structure.A new normalization shows that the gross yield surface is isotropically hardening in terms of both volume and struc-tural change.KEYWORDS:constitutive relations;fabric a structure of soils;in situ testing;microscopy;shear strength;stiffness.L 'article preÂsente les re Âsultats de recherches approfondies,en laboratoire et sur le terrain,sur une argile raide du PleÂistoce Áne a Ál'e Âtat naturel et reconstitueÂe,y compris des essais oedomeÂtriques et triaxiaux a Átaux de contrainte constant,sur un large eÂventail de contraintes,ainsi que les reÂsultats de travaux de microscopie eÂlectronique a Ábalayage et de micro-analyse chimique.Les auteurs montrent les rapports entre la structure de l'argile,son histoire geÂologique et sa re Âaction me  struc-ture de l'argile est fortement in¯uenceÂe par l'adheÂrence,qui semble en grande partie due a Áune pellicule de calcite amorphe qui s'estformeÂe sur place a Ála ®n de la consolidation normale.Les auteurs identi®ent les effets de lastructure sur la rigiditeÂde l'argile,la sensibilite ÂeÂtant le parame Átre qui quanti®e les effets meÂcaniques de la structure.On constate qu'un eÂcoulement de frottement s'applique ge Âne Ârale-ment aÁun large e Âventail de contraintes,y compris aÁla limite d'e Âlasticite Â,me Ãme quand l'adheÂrence est forte,bien que sa forme soit in¯uenceÂe par la structure.Une nouvelle nor-malisation montre que la surface brute d'e Âcou-lement subit un durcissement isotrope tant en volume qu'en changement structural.INTRODUCTIONIn a soil mechanics context,the terms `structure'and `bonding'have generally been used to attempt to identify elements that may or may not be phys-ical components of the soil.Here,following,for example,Lambe &Whitman (1969),the term `structure'is used to combine `fabric',the arrange-ment of the component particles,and `bonding',de®ned as those interparticle forces which are not of a purely frictional nature.Bonding is not neces-sarily (although it may be)a solid link,particularlywith clays,but is the consequence of such pheno-mena as electrostatic,electromagnetic or other forces acting to connect the particles which have developed during the geological life of the soil.Bonding is thus the combined result of such factors as the minerology,water chemistry during deposi-tion,pressure,temperature and organic content,and it depends on mechanical conditions such as deposition and consolidation rates and strain paths (Mitchell &Houston,1969;Sides &Barden,1970;Sfondrini 1975;Mitchell,1976).The structure of a natural soil thus depends on the physical and chemical conditions that applied during deposition,consolidation,ageing and unloading.The basic elements of structure exist in all clays,and thus structure should be seen as the source of similarities in the behaviour of different clays.It follows that,in comparing the mechanical behaviour of natural and `reconstituted'(Burland,Cotecchia,F .&Chandler,R.J.(1997).GeÂotechnique 47,No.3,523±544523Manuscript received 23rd October 1996;revised manu-script accepted 21March 1997.Discussion on this paper closes 1November 1997.ÃFormerly Imperial College of Science,Technology and Medicine,London;now Politecnico di Bari.{Imperial College of Science,Technology and Medicine,London.1990)clays with a view to contributing to a better understanding of an overall clay behaviour,one should®rst look to the similarities in behaviour.Of course,there will be differences,of which sensitiv-ity(Terzaghi,1944;Skempton&Northey,1952), which often characterizes the behaviour of natural clay,though not reconstituted clay,is perhaps the most important.Following this approach,this study endeavours to make a contribution to the understanding of pre-failure soil behaviour by comparing the mechanical behaviour of a strongly bonded natural clay with the behaviour of the same clay when reconstituted, the two clays having different structure and sensi-tivity.The pre-failure consequences of the structure of the clay that are examined here are the in situ stress state of the natural clay,and the oedometer and triaxial compression behaviour.Full details of sampling,testing and interpretation procedures,as well as other background material,are given in Cotecchia(1996);for reasons of space much of this information is presented here only in outline.THE GEOLOGICAL HISTOR Y AND INDEX PROPERTIES OF PAPP ADAI CLA YThe natural clay that is the subject of this study is the Pappadai Clay,a Pleistocene clay from the Montemesola Basin,near Taranto,Italy,the basic engineering geology of which is described by Cotecchia&Chandler(1995).In summary,this clay was deposited about1.3million years ago,in a quiet sea where reducing conditions applied. There was subsequent erosion of some120m at the sampling location,resulting in the clay being overconsolidated.Block samples were taken from a depth of 25´4m during the construction of a reservoir draw-off shaft.Fig.1shows the present geological and hydrogeological situation.The current vertical ef-fective stress at the sampling depth is415kPa, while the preconsolidation stress deduced from geo-logical evidence is about1300kPa.Typical index and other properties of the clay, together with the mineralogical composition,are given in Table1.The high proportions of illite, chlorite and smectite,sedimented in a saline mar-ine environment,will have resulted in¯occulation,giving rise to a bookhouse-type of fabric(Fig.2). The decrease in the proportion of smectites with depth,along with an increase in the proportions of non-swelling minerals and a decrease in activity, all suggest that diagenesis(i.e.chemical and a or other modi®cations to both soil particles and bond-ing during the period of burial)has occurred in the Pappadai Clay.It is likely,therefore,that there will have been substantial changes to the structure of the clay,which will have occurred at the stress levels required to generate the mineralogical changes,that is,at the stresses that applied towards the end of normal consolidation.In an attempt to explain the observed present-day depth±water content pro®le,the geological his-tory of the Pappadai Clay was modelled(Cotecchia &Chandler,1995),assuming a sequence of stages of(i)normal deposition,(ii)erosion,(iii)deep drying,and(iv)weathering and re-establishment of the ground water to the present level(Fig.3(a)). The normal consolidation of the natural clay (the 4060801001200100mCalcareousbedrock61 m.o.d.111 m a.s.l.Borehole A ShaftPiezometer Block sampleGrey-blueclayGravinaCalcarenitesY ellowishblueclay m a.s.l.Fig.1.Geological and hydrogeological conditions at the sampling siteTable1.Properties and minerology of natural Pappa-dai ClayProperties Speci®c gravity2´69Liquid limit65%Plastic limit30%Natural water content%31%Organic content2´4%Carbonate content28% Mineralogy Quartz3%Feldspar1%Carbonate22%Dolomite6%Kaolinite12%Chlorite14%Illite20%Smectite12%Intergrades10%Total100%524COTECCHIA AND CHANDLERsedimentation compression curve,SCC;Terzaghi, 1941)was assumed to be that of a clay of low to medium sensitivity and thus is assumed to lie in the middle of the range of natural clay compaction behaviour reported by Skempton(1970)(Fig.3(b)). The model makes reasonable predictions of the present water content pro®le(stage(iv);Cotecchia &Chandler,1995),the non-linear shape of which (dotted line,Fig.3(a))is the consequence of deep desiccation followed by weathering at shallow depths.The predicted history of the block samples tested,from original deposition(O)to the present state(B),is given by the path O±P±N±M±B.The observed present state,at"B,lies marginally be-low B,consistent with the predictions of the mod-el.The intrinsic compression line(ICL;Burland, 1990),obtained from a disaggregated sample of the Pappadai Clay prepared at a water content of 1´63liquid limit,consolidated in an oedometer to a vertical stress(óv9)of200kPa,is also shown in Fig.3(a).The distance between the ICL and the SCC re¯ects the difference in structural strength between the natural and the reconstituted clay that developed during normal consolidation.THE STRUCTURE OF NATURAL AND RECONSTITUTED PAPP ADAI CLA YThe microstructure of the Pappadai Clay from the block samples was compared with samples of the clay reconstituted to point A in Fig.3(a).A Cambridge500scanning electron microscope,an apparatus well documented in the literature(e.g. see Smart&Tovey,1982),was used to examine the microfabric of the Pappadai Clay.The samples were prepared by freeze-drying,and were then broken to form approximately vertical and horizon-tal surfaces,which were gold coated.The resulting electron microscope images were then examined visually.Natural clayAt medium magni®cation the fabric of the nat-ural clay seen on vertical fractures is densely packed(Fig.4).The clay particles are generally aggregated in`domains',that is,groups of parallel particles(see Fig.2),which originated as¯ocs during deposition(Sides&Barden,1970;Cotec-chia et al.,1982).Groups of subhorizontally or-iented domains can be seen in Fig.4,suggesting that the fabric is well oriented.However,some areas are more densely packed than others,such as regions A and B,and both`stacks'of domains in face-to-face contact(see Fig.2),and irregularly intersecting domains can be seen,forming voids of up to10±20ìm in size(Fig.5).Stacks also occur interbedded with zones of randomly¯occulated fabric(Fig.6),and individual particles in edge-to-face contact are seen in Fig.7.These observations appear to con®rm that the natural Pappadai Clay at deposition had a`book-house'fabric,subsequently compressed so that there are areas of oriented clay,intermixed with remnants of the original fabric.Fabric of this type, a`compacted bookhouse fabric'(Sides&Barden, 1970),is very similar to that anticipated by Sfond-rini(1975)for one-dimensionally normal consolid-ated¯occulated clay(Fig.8).Uniform orientation is not observed;rather,non-uniform strains occurred during compression,so that an open honeycomb fabric is interspersed with densely packed,well-oriented stacks of domains.In spite of the relatively high carbonate content (Table1)there is little evidence of calcite crystals, which may in part be explained by the relatively high incidence of carbonate fossils.Reconstituted clayFigure9shows the fabric on a vertically frac-tured surface of reconstituted clay.The fabric appears more open than the natural clay,re¯ecting the considerable difference in the preconsolidation pressures of the two clays.This fabric has,none the less,much in common with that of the natural clay.Oriented areas,with stacks of domains,can be recognized,together with randomly oriented ¯occulated areas.Fig.10shows an example of open honeycomb fabric.Thus,as with the natural clay,a non-uniform reorientation of the clay parti-cles has occurred during compression.The natural clay is,however,far more complex,with less regular alternations of oriented and¯occulated fabrics,probably the consequence of diagenesis.Bookhouse DomainHoneycombTurbostratic StackChemical micro-analysis:methods and results A microprobe analysis was used in the electron microscope to examine the chemical composition of selected areas of samples of the natural clay.Carbon-coated freeze-dried samples were used,and locations as small as 1ìm were investigated,the results being presented as diffractograms indicating the chemical elements present.The technique was `calibrated'by scanning such fabric elements as framboid pyrite crystals and fossil fragments,and in two such cases the size of the sulphur and iron peaks (Fig.11(a))and the calcium peak (Fig.11(b))are as expected.The diffractogram of Fig.11(c),typical of many,relates to a clay particle and shows the expected mica components (Si,Al and K),but also shows a high proportion of calcium,which seems to be coating the clay particle.The diffractogram of Fig.11(d),Fig.3.State history of the natural and reconstituted Pappadai Clay:(a)results of modelling geological stages (i)±(iv),and (b)SCC assumed to apply to natural Pappadai Clay (from Skempton,1970).10100100010000σv ′: kPa Ϫ0.20.00.20.40.60.81.01.2L i q u i d i t y i n d e xOANBB MP Diagenesis ICLSCC natural clayBookhouse fabricIN SITUMEASUREMENTSStage (i)Stage (ii)Stage (iiI)Stage (iv)MODEL RESULTS Clay states through the deposit at the end of:(a)0.0010.010.111030100P 0: kg/cm2(b)Ϫ0.50.511.52L i q u i d i t y i n d e xSCC of naturalPappadai Clay ICL of reconstituted Pappadai Clay526COTECCHIA AND CHANDLERagain typical,relates to a `bridge'between two domains.As before,the basic mica components appear,together with a considerable proportion of calcium.These results show that calcium is widespread throughout the fabric of the clay,the calcium con-tent being higher at interparticle contacts.As pre-viously noted,calcium is not generally present in crystalline form,so it is presumably amorphous,and since it is ubiquitous it doubtless coats and binds the particles.The deposition of the carbonate coating is un-likely to have occurred during deposition since precipitation of calcite from solution produces cry-stalline,not amorphous,calcite.Moreover,the model of the geological history of the clay (see Fig.3(a))would not explain the present water content pro®le unless it were controlled by normalFig.4.Undisturbed Pappadai Clay:overall view of the fabric on a verticalfractureBALess densely packed domains Example of stratum of densely packed domains Fossil printFig.5.Undisturbed Pappadai Clay:fabric on a ver-tical fracture.Detailsof parallel and intersecting domains;calcite crystals occur within the dashed lineCoccolithsPRE-FAILURE BEHAVIOUR OF A NATURAL CLAY527consolidation,so the diagenetic calcite ®lm was probably deposited after normal consolidation as a result of precipitation from supersaturated pore ¯uid.Similar formation of authigenic calcite has been observed elsewhere in soils rich in carbonate fossils (e.g.see Sfondrini,1975;O'Brien &Slatt,1990).THE CURRENT STATE OF PAPP ADAI CLA Y IN SITU AND AFTER SAMPLINGA series of self-boring pressuremeter tests was carried out at depths to 45m in a boring 80m from the shaft where the block samples were ob-tained (borehole A,Fig.1).The pressuremeter was of the type designed for soft rock,with a capacity of 20MPa (Clarke &Allan,1989).Since the ground surface level and depths correspond in boring and shaft,it is assumed that the in situ stresses for the block samples are those for the pressuremeter tests at the corresponding depth.The horizontal effective stresses were deter-mined noting the piezometric measurements made in borehole A.Zero pore pressures were taken to apply down to a depth of 18´4m,below which either hydrostatic pressures with respect to this depth (assumption 1),or pressures lower than hydrostatic to allow for downward seepage into the underlying bedrock (assumption 2;Fig.1),were assumed.Fig.12shows that this range of values of pore pressure does not have much effect on the value of K 0,which at the sample depth (25´4m)is about 1´6,corresponding to a mean effective stress of about 575kPa.This compares quite well with the suctions in the block samples,which were measured using various techniques to be about 650kPa.Effect of diagenesis on the values of K 0The K 0±depth pro®les shown in Fig.12for the four geological stages were calculated using K 0 (1Àsin ö9)(1)for stage (i),K 0 (K 0)nc OCR sin ö9(2)for stages (ii)and (iv),andFig.6.Undisturbed Pappadai Clay:fabric on a ver-tical fracture.Stacks and random ¯occulatedfabricFig.7.Undisturbed Pappadai Clay:fabric on a ver-tical fracture.Edge to edge and edge to face particle contacts5 µmFig.8.Scheme of ¯occulated fabric compressed one-dimensionally.(After Sfondrini,1975)528COTECCHIA AND CHANDLERK 0 (K 0)nc [OCR a OCR max34(1ÀOCR a OCR max )](3)for stage (iii)(Mayne &Kulhawy,1982).Thevalue of ö9used is 238,which,as is seen later,is consistent with the value at critical state.The mea-sured values of K 0are higher than calculated using equations (1)±(3),perhaps not surprising sincethese empirical expressions for K 0were derived from data for soft and reconstituted clays and thus do not apply to clays such as the Pappadai Clay that have undergone diagenesis.To illustrate the differences between the ob-served stress state and the Mayne &Kulhawy predictions,the relationships between q and p 9for the sampling depth have been calculated for geolo-gical stages (i)±(iv)(Figs 3(a)and 12),and are plotted in Fig.13,where they are compared with the measured in situ stress state at about the depth of sampling.It is seen that the natural clay is subject to a higher mean stress and lower deviato-ric stress than would be expected if overconsolida-tion resulted from simple unloading,as implicitly assumed by equations (1)±(3).Although the Cam Clay model (Scho®eld &Wroth,1968)simply assumes non-linear elastic behaviour in unloading and does not model the hysteresis of the unload±reload loops,it is none the less of value in helping to identify the various factors that contribute to the observed values of K ing the Cam Clay model,the increase in K 0on unloading depends on the value of Poisson's ratio,which in turn can be shown to vary with the overconsolidation ratio and shear modulus (Cotec-chia,1996).Thus the increase in K 0with the overconsolidation ratio is greater with higher va-lues of shear modulus.Thus if,after normal con-solidation,the natural clay became stiffer as a result of diagenesis,the observed higher values of K 0would be expected.This seems to be the caseFig.9.Reconstituted Pappadai Clay:fabric on a verticalfractureStrata of oriented particlesFloccu-latedfabricFig.10.Reconstituted Pappadai Clay:fabric on a vertical fracture.Detail of honeycomb fabricPRE-FAILURE BEHAVIOUR OF A NATURAL CLAY529for Pappadai Clay,whose bonding was strength-ened by diagenesis prior to unloading.OEDOMETER TESTINGOedometer tests with incremental loading (test series OED)were carried out,to a maximum stress of about 7MPa in a conventional oedometer,and also with constant rate of strain compression (test series CRS)in a high-pressure oedometer to a vertical stress about 25MPa,with drainage to the upper boundary of the sample and pore pressures measured at the base.In the following ®gures,both the OED and CRS tests on the reconstituted clay are distinguished from those on the natural clay by the suf®x `R'.The constant rate of strain tests were interpreted using a modi®ed version of the theory developed by Wissa et al .(1971).In all tests,corrections were applied for machine compliance.More details of the apparatus and testing will be published elsewhere,but some of the data which highlight the effect of the structure of the clay are discussed brie¯y.Representative compression and swelling curves for natural and reconstituted clay are shown in Fig.14.For clarity,some compression stages prior toswelling are omitted;only the swelling stage prior to compression is shown in the case of OED7.In the case of the reconstituted clay the average yield stress is about 200kPa,consistent with the maxi-mum stress attained in the consolidometer.Beyond yield,the CRS reconstituted sample de®nes the ICL for the Pappadai Clay to 22MPa.The initial swelling curve of OED7shows the very stiff response of the natural clay.On compres-sion,the clay is similarly stiff,with `gross yield',the threshold of major plastic strains (subsequently referred to as `yield')occurring beyond the ICL line.The yield stress (óy 9)of the natural clay from the OED tests is about 2600kPa,much higher than the equivalent vertical stress (óe à 750kPa)re-quired to bring the reconstituted clay to the same void ratio.The stress ratio óy 9a óe à 3X 5is a measure of the higher strength of the structure of the natural clay compared to the reconstituted clay,and is presumably related to the sensitivity of the clay.Since the yield stress of the natural clay exceeds the geological preconsolidation stress,óp 9,it lies to the right of the SCC.Thus the ratio óy 9a óe Ã,already greater than unity during normal consolidation (see Fig.3(a)),has increased further to 3´5as a result of diagenetic bonding.Conse-X-RAY:Live:Real:0 – 20keV50s Preset:54s 7% Dead50s Remaining:0sX-RAY:Live:Real:0 – 20keV50s Preset:58s 14% Dead50s Remaining:0sX-RAY:Live:Real:0 – 20keV50s Preset:58s 14% Dead50s Remaining:0sX-RAY:Live:Real: 0 – 20d keV50s Preset:59s 15% Dead50s Remaining:0sFS ϭ 1KMEM1: A allineamento pirite3.020keV ch 161 ϭ 10cts8.1 ϾFS ϭ 2KMEM1: A-PORO 2 particella3.040keV ch 162 ϭ 73cts8.2 ϾFS ϭ 2KMEM1: A FOSSIL 13.020keVch 161 ϭ 49cts8.1 ϾFS ϭ 2KMEM1: A-PORO 3 particella3.020keV ch 161 ϭ 60cts8.1 Ͼ(a)(c)(b)(d)SCK N a N gA l S iC a C a T i TiF eF eN a N gAl S i S Cl KK CaC aT i T iF eF eN a N aN gA lS iS ClKK C aCa T i TiF eF eN g A lS iS ClKKC aC a Ti T iF eF eFig.11.Diffractograms resulting from the micro-chemical analysis530COTECCHIA AND CHANDLERquently the yield stress ratio,YSR,óy 9a óv 9( 6´0),of the natural clay is greater than the geo-logical overconsolidation ratio,which is 3´1.The swell sensitivity (de®ned as the ratio of the swelling index of the reconstituted clay to that of the natural clay,C s Ãa C s ;Schmertmann,1969;Burland,1990)is about 2´5preyield.This ratio reduces rapidly beyond yield,becoming unity at vertical stresses about 5000kPa.As bonding will restrain swelling,this reduction in swell sensitivity illustrates the loss of some bonding with straining beyond yield,which is not observed with the stable,insensitive reconstituted clay.None the less,the convergence of the compression curves of the two clays shown in Fig.14is slow,the natural clay still carrying higher stresses than the reconstituted clay even at a void ratio as low as 0´3.Thus the natural clay retains a structure stronger than the reconstituted substantially beyond yield,and per-haps at all stages of loading.Despite their different structures,the two clays follow similar patterns of behaviour,with,in quali-tative terms,similar trends of variation with stress level of such properties as compression index,stiffness and permeability,and with a similar mag-nitude of strain-rate dependency (Cotecchia,1996).As an example,one aspect of the similarity of the clays that is of particular relevance to pre-failure behaviour,the variation with YSR of stiff-ness in K 0compression,M ( 1a m v ),will be discussed.Fig.15shows the typical variation of the values of M with vertical stress observed in the tests on the natural and the reconstituted clay.The M nc Àóv 9relationship for the natural clay is similar to that observed for the reconstituted clay,but with different values of the coef®cient and exponent.Similar linear relationships to those shown in Fig.15are obtained for all tests on both natural and reconstituted clay specimens.Since the mechanical behaviour of reconstituted clays can generally be normalized with respect to volume,as with the critical state model (Scho®eld &Wroth,1968),it is to be anticipated that the stiffness,M ,should be capable of similar normal-ization.Such a result may be obtained by normal-izing the current value of M along each oedometer loading curve by the value of the stiffness at yield,M nc (Fig.16).This is equivalent to normalization by volume,since,ignoring strain-rate effects,for a given value of óv 9the void ratio is related to a single yield stress (Fig.16),which in turn is related uniquely to M nc .The normalized stiffnesses of the reconstituted clay are shown in Fig.17for different loading paths.In tests CRSR2and CRSR4the clay was continuously compressed,whereas in test OEDRb the clay was ®rst compressed beyond yield (OEDRb(1))and then unloaded and reloaded to successively higher consolidation pressures (OEDRb(2)and OEDRb(3)).(Only the reloading stiffness is plotted for OEDRb(2)and OEDRb(3).)If a similar normalization is applied to the stiffness of the natural clay both during ®rst load-ing and in reloading beyond yield,the normalized stiffness of the clay postyield is less than thatSample depthStage (i)Stage (ii)Stage (iii)Stage (iv)1234K 05040302010D e p t h : mFig.12.Values of K 0measured in situ (squares and circles)compared with the variation of K 0with depth obtained by modelling stages (i)±(iv)of the geological history of the clay.The squares correspond to piezo-matic assumption 1(see text);the circles to assump-tion 2(i)(ii)(iii)(iv)Acquisition of bondingin situ40080012001600p ′: kPaϪ600Ϫ400Ϫ20002004006008001000q : k P aFig.13.Modelled q ±p 9states at the sampling depth at end of each geological stage (solid squares),compared with the measured in situ stress state of the clay (open squares)PRE-FAILURE BEHAVIOUR OF A NATURAL CLAY531exhibited by the clay during ®rst loading,theconsequence of the degradation of structure post-yield.However,this structural effect may be elimi-nated by further normalizing M a M nc by the stressratio óy 9a óe Ã.This is shown in Fig.18,where the data points OED10(2)and OED10(3)refer to reloading beyond yield.A near unique relation with the YSR is obtained,similar to that obtainedOED5OED7OED8OEDRCRS (natural clay)CRS (reconstituted clay)PreconsolidationYieldσe*σp ′σy′10100100010000σv′: kPa 0.30.40.50.60.70.80.91.01.11.21.3V o i d r a t i o epression behaviour of the natural and reconstituted clayNatural clay:M nc ϭ 0.187 σv ′1.432Reconstituted clay:M nc ϭ 3.286 σv ′1.18310100100010000100000σv′: kPa 102103104105106M : k P aFig.15.M ±óv 9relationships for the natural and the reconstituted clay532COTECCHIA AND CHANDLER。

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FM 对自动喷淋系统要求

Approval Standard for Steel Pipe for Automatic Fire Sprinkler Systems
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November 2013
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