f Change in the roles of physics and chemistry as ce- ramics move t, Notas de estudo de Engenharia de Produção

Baixe f Change in the roles of physics and chemistry as ce- ramics move t e outras Notas de estudo em PDF para Engenharia de Produção, somente na Docsity! Chem. Rev. 1990, 90. 33-72 93 The Sol-Gel Process LARRY L. HENCH' and JON K. WEST D q " n t of Materials Sc*mce and Enghwrhg, Advanced Materials Research Center, UnimrMy of Floryle. oakresville. Fknm 326 11 Received May 16. 1989 (Revised Manuscript Received October 27, 1989) Contents 1. Introduction 11. Sol-Gel Process Steps: An Overview 111. Hydrolysis and Polycondensation IV. Gelation VI. Aging VII. Drying V. Theoretical Studies VIII. Stabilization IX. Densification XI. Conclusions I. Infroducf/on X. Physical Properties 33 35 37 40 46 49 51 58 65 67 68 Interest in the sol-gel processing of inorganic ceramic and glass materials began as early as the mid-1900s with Ebelmanl,* and Graham's3 studies on silica gels. These early investigators observed that the hydrolysis of tet- raethyl orthosilicate (TEOS), Si(OC2H5),, under acidic conditions yielded Si02 in the form of a "glass-like material".l Fibers could be drawn from the viscous gel, and even monolithic optical lenses? or composites formed? However, extremely long drying times of 1 year or more were necessary to avoid the silica gels fracturing into a fine powder, and consequently there was little technological interest. For a period from the late 18008 through the 19209 gels became of considerable interest to chemists stim- ulated by the phenomenon of Liesegang Rings4& formed from gels. Many noted chemists, including OstwaldE and Lord Rayleigh,? investigated the problem of the periodic precipitation phenomena that lead to the formation of Liesegang rings and the growth of crystals from gels. A huge volume of descriptive literature re- sulted from these studiesg'O but a relatively sparse understanding of the physical-chemical principles? Roy and co-workersll-" recognized the potential for achieving very high levels of chemical homogeneity in colloidal gels and used the sol-gel method in the 19509 and 1960s to synthesize a large number of novel ceramic oxide compositions, involving AI, Si, Ti, Zr, etc., that could not be made using traditional ceramic powder methods. During the same period Iler's pioneering work in silica chemistry15 led to the commercial development of colloidal silica powders, Du Pont's colloidal Ludox spheres. Stober et a1.I6 extended Iler's findings to show that using ammonia as a catalyst for the TEOS hy- drolysis reaction could control both the morphology and size of the powders, yielding the so-called Stober spherical silica powder. The final size of the spherical silica powder is a function of the initial concentration of water and am- monia, the type of silicon alkoxide (methyl, ethyl, c , Lany L. Hend, is a eadaduate Research Professa in tb Cep" 01 Materials Science and Engineering at the University of Florida. where he has taught since 1964 after receiving B.S. (1961) and Ph.D. (1964) degrees in Ceramic Engineering at The Ohm State Universny. He is the Director of lha Boglass Research Center and CoDirectof of the Advanced Materials Research Center at the University of Florida. He has published more than 250 research articles and is the coauthor or coeditor of 12 books in the fields of biomateriak. ceramic processing. ceramic characterization. glass surfaces. electronic ceramics. nuclear waste disposal, and sol-gel processing. r 4-7 Jon K. West received his Ph.D. at the Univerrity of FkMa in 1979 while wwking full lime as an engineering manager wilh tb Battery Business Department of General Electric Co. His cment position is Associate-in-Engineering with the Department of Materials Science and Engineering at the University of Florida. His work in sol-gel silica includes mechanical testing, process control and instrumentation. and theoretical studies based on molecular wbtal calculations. He is the author of eight publications Including the recently published textbook Principles of Electronic Ceramics. by Hench and West. from John Wilev 8 Sons. pentyl, esters, e t 4 and alcohol (methyl, ethyl, butyl, pentyl) mixture used,16 and reactant tempe~ature.~' An example of a typical colloidal silica powder is shown in Figure la, made by the Stober process, and its uniform distribution of particle sizes is shown in Figure l b from Khadikar and Sacks work.ls 0009-2665/90/0790-0031$09.50/0 0 1990 American Chemical Society 34 Chemical Reviews. 1990. Vol. 90. No. 1 .J .n .. .E .5 .s .I Figure I. Top SEM of Stober spherical silica powders. Bottom: Histogram (number of particles in a given diameter class versus particle diameter) of a typical batch of Stoher spherical silica powders. Reprinted from ref 18: copyright 1988 University of Florida. PARnCtBDlAMETER @m) O~erbeek '~3 and SugimotoZ1 showed that nucleation of particles in a very short time followed by growth without supersaturation will yield monodispersed col- loidal oxide particles. Matijevic and c o - ~ o r k e r s ~ ~ - ~ ~ have employed these concepts to produce an enormous range of colloidal powders with controlled size and morphologies, including oxides (TiO,, a-FepO3, Fe304, BaTiO,, Ce02), hydroxides (AIOOH, FeOOH, Cr(OH),), carbonates (Cd(OH)CO,), Ce,O(CO3),, Ce(III)/Y HC03), sulfides (CdS, ZnS), metals (Fe(III), Ni, Co), and various mixed phases or composites (Ni, Co, Sr ferrites), sulfides (Zn, CdS), (Pb, CdS), and coated particles (Fe304 with AKOH), or Cr(OH),). The controlled hydrolysis of alkoxides has also been used to produce submicrometer Ti0z,26 doped Ti02.27 Zr0z,28 and doped Zr0z,28 doped SiOz,TJ SrTiO,." and even cordierite30 powders. Emulsions have been employed to produce spherical powders of mixed cation oxides, such as yttrium alu- minum garnets (YAG), and many other systems such as reviewed in Hardy et al." Sol-gel powder processes have also been applied to fissile elements31 where spray-formed sols of U 0 2 and U02-PuO, were formed as rigid gel spheres during passage through a column of heated liquid. Both glass and polycrystalline ceramic fibers have been prepared by using the sol-gel method. Compo- sitions include TiOz-Si02 and Zr02-Si02 glass high-purity SiO, waveguide f i b e r ~ ? ~ . ~ ~ A120b ZrO,, Hen& and West Tho,, MgO, TiO,, ZrSiO,, and 3AI2O3.2SiOz fibers.- Abrasive grains based upon sol-gel-derived alumina are important commercial products." A variety of coatings and films have also been de- veloped by using sol-gel methods. Of particular im- portance are the antireflection coatings of indium tin oxide (ITO) and related compositions applied to glass window panes to improve insulation c h a r a ~ t e r i s t i c s . ~ ~ Other work on sol-gel coatings is reviewed by Schroe- der,'8 Macken~ie,'~," and Wenzel.S1 Mackenzie's re- v i e ~ s ~ ~ 5 0 include many other applications of the sol-gel process, proven, possible, and potential. The motivation for sol-gel processing is primarily the potentially higher purity and homogeneity and the lower processing temperatures associated with sol-gels compared with traditional glass melting or ceramic powder methods. Ma~kenzie'~fl summarizes a number of potential advantages and disadvantages and the relative economics of sol-gel methods in general. Hench and colleague^^^^" compare quantitatively the merits of sol-gel-derived silica optics over the alternative high-temperature processing methods. During the past decade there has been an enormous growth in the interest in the sol-gel process. This growth has been stimulated by several factors. On the basis of Kistler's early work,% several teams have pro- duced very low density silica monoliths, called aerogels, by hypercritical point drying.5B Zarzycki, Prassas, and P h a l i p p o ~ ~ ~ . ~ demonstrated that hypercritical point drying of silica gels could yield large fully dense silica glass monoliths. Yoldassg showed that large monolithic pieces of alumina could be made by sol-gel methods. These demonstrations of potentially practical routes for production of new materials with unique properties coincided with the growing recognition that powder processing of materials had inherent limitations in ho- mogeneity due to difficulty in controlling agglomera- tion.60 , The first of a series of International Conferences on Ultrastructure Processing was held in 1983 to establish a scientific basis for the chemical-based processing of a new generation of advanced materials for structural, electrical, optical, and optoelectronic applications. Support by the Directorate of Chemical and Atmos- pheric Sciences of the Air Force Office of Scientific Research (AFOSR) for the Ultrastructure Conferences in 1983,6l 1985,6, 1987," and 198ga and the Materials Research Society Better Ceramics Through Chemistry annual meetings in alternate years in 1984,65 19S6,66 and 198Sa has provided constant stimulation for the field. In addition, AFOSR has provided a stable financial base of support for a number of university programs in sol-gel science throughout the 1980s under the technical monitoring of D. R. Ulrich. The primary goal in these conferences and the AFOSR research and development program was to es- tablish a scientific foundation for a new era in the manufacture of advanced, high-technology ceramics, glasses, and composites. For millennia, ceramics have been made with basically the same technology. Pow- ders, either natural or man-made, have been shaped into objects and subsequently densified at temperatures close to their liquidus. The technology of making glass has also remained fundamentally the same since pre- history. Particles are melted, homogenized, and shaped The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, NO. 1 37 priate control of the time-dependent change of viscosity of the sol, fibers can be pulled or spun as gelation oc- curs. Step 4: Aging. Aging of a gel, also called syneresis, involves maintaining the cast object for a period of time, hours to days, completely immersed in liquid. During aging, polycondensation continues along with localized solution and reprecipitation of the gel network, which increases the thickness of interparticle necks and de- creases the porosity. The strength of the gel thereby increases with aging. An aged gel must develop suffi- cient strength to resist cracking during drying. Step 5: Drying. During drying the liquid is removed from the interconnected pore network. Large capillary stresses can develop during drying when the pores are small (e20 nm). These stresses will cause the gels to crack catastrophically unless the drying process is controlled by decreasing the liquid surface energy by addition of surfactants or elimination of very small pores (method l), by hypercritical evaporation, which avoids the solid-liquid interface (method 2), or by ob- taining monodisperse pore sizes by controlling the rates of hydrolysis and condensation (method 3). After hypercritical drying (method 1) the aerogel has a very low density and is a very good thermal insulation when sandwiched between glass plates and eva~uated.5~ Step 6: Dehydration or Chemical Stabilization. The removal of surface silanol (Si-OH) bonds from the pore network results in a chemically stable ultraporous solid. Porous gel-silica made in this manner by method 3 is optically transparent with interconnected porosity and has sufficient strength to be used as unique optical components when impregnated with optically active polymers such as fluors, wavelength shifters, dyes, or nonlinear p o l y m e r ~ . ~ ~ t ~ ~ Step 7: Densification. Heating the porous gel at high temperatures causes densification to occur. The pores are eliminated, and the density ultimately becomes equivalent to fused quartz or fused silica. The densi- fication temperature depends considerably on the di- mensions of the pore network, the connectivity of the pores, and surface area, as illustrated in Figure 3.89 Alkoxide gels (method 3) have been densified as low as 1000 "C by Klein and Garvey,2w whereas gels made by the commercial colloidal process developed by Shoupw require 1500-1720 OC. However, colloidal silica gels with very carefully controlled dense packing can also be densified at low temperatures of 1000 "C, as shown by Sacks and T ~ e n g . ~ ' ~ ~ ~ The purity and homogeneity of dense gel-silica made by method 3 are superior to other silica glass processing methods. The ability to produce optics with nearly theoretical limits of optical transmission, lower coefficients of thermal expansion, and greater homogeneity, along with net shape casting, represents major advances resulting from sol-gel pro- cessing of monolith^.^^^^^ Details of these seven sol-gel processing steps follow. The emphasis is on sol-gel-derived silica monoliths made by the alkoxide process (method 3) processed under ambient pressures. I I I . Hydrolysis and Polycondensation As shown in Figure 3 the structure of a gel is estab- lished at the time of gelation. Subsequent processes such as aging, drying, stabilization, and densification all depend upon the gel structure. Since it is the rela- tive rates of hydrolysis (eq 2) and condensation (eq 3) that determine the structure of the gel, it is essential to understand the kinetics of the hydrolysis and con- densation reactions and the ratio of their rate constants As discussed by Orcel et a1.,93-95 Hench and Orce1,96 Klemperer et al,,w*98 Scherer and Brinker,70 and Artaki et al.,% many factors influence the kinetics of hydrolysis and condensation, and the systems are considerably more complex than represented by the simplified eqs 2-4. Many species are present in the solution, and furthermore, hydrolysis and polycondensation occur simultaneously. The variables of major importance are temperature, nature and concentration of electrolyte (acid, base), nature of the solvent, and type of alkoxide precursor. Pressure influences the gelation process also; kH increases with pressure as shown by Artaki et a1.,100-102 but pressure is usually not a processing vari- able. There are relatively few studies of the dependence of kH and kc on independent processing variables. In fact many studies have reported the variation of the gelation time, viscosity, or textural characteristics (e.g., specific surface area) of the gel as a function of exper- imental conditions without determining kH or kc.102-107 However, several investigations do provide a scientific foundation for understanding the processing depen- dence of kH and kc. Aelion's study of the influence of electrolyte concen- tration on the hydrolysis of TEOS in different solvents showed that kH increases linearly with the concentration of H+ or H30+ in acidic media and with the concen- tration of OH- in basic medium.lo3 The reaction rate varies from 4.12 X lo4 L mo1-ls-l for a 0.063 mol L-l HC1 solution. This corresponds to a rate constant per unit concentration of electrolyte of 0.091 mol L-l s-' [H+]-l. Similar values are observed in basic media where the rate constant is about 0.040 L mol-' s-l [OH]-'. There is a variation in the concentration of TEOS of 0.2 mol L-l for the basic conditions versus 0.6 mol L-' for the acid-catalyzed sol. The increase in [TEOS] can account for the increase in rate constant. As discussed by OrceP the nature of the solvent (dioxane, methanol, or ethanol) has a "secondary" effect on kH, as well as the temperature dependence of the reaction (10-fold increase when the temperature varies from 20 to 45.5 "C). NMR experiments by Artaki, Zerda, and Jonas'OO show that k H varies in the different solvents as follows: acetonitrile > methanol > di- methylformamide > dioxane > formamide, with kH- (acetonitrile) being about 20 times larger than ItH(for- mamide) . An increase of the R ratio (moles of water/moles of TEOS) from 1.86 to 3.72 induces kH to increase from 0.042 to 0.059 L mol-' s-l [acid]-l.lo3 However, Schmidt et al.lo4 found that the hydrolysis rate decreases when the R ratio increases from 0.5 to 2. Schmidt attributes this to the "special experimental conditions and the water acting as a proton acceptor which decreases the proton activity".lo5 The nature of the alkoxy groups on the silicon atom also influences the rate constant. As a general rule, the longer and the bulkier the alkoxide group, the slower the rate constant.105J08J09 For example, in the case of (kH/kC) * 38 Chemical Reviews, 1990, Vol. 90, No. 1 the hydrolysis of kH = 51 X L mol-l s-l [H+]-' for R = C2H5 and kH = 3 X 10" L mo1-ls-l [H+]-' for R = (CH3)2CH(CH2)3CH(CH3)CH2. From these results it is apparent that the dominant factor in controlling the hydrolysis rate is the electrolyte con~ent ra t ion .~~ However, the nature of the acid plays an important role. As outlined above, a minute addition of HCl induced a 1500-fold increase of kH. However, Aleion reported "hydrolysis in glacial acetic acid as solvent is not particularly fast".lo3 Although these have been called "secondary" effectslo3 and they are very small compared to those induced by addition of electrolyte, they are relatively important (e.g., the 10-fold increase of kH with a variation of the processing temperature of 25.5 "C) and might be re- sponsible for numerous observations in systems inves- tigated in other works. For example, a systematic study of Mackenzie shows that the type of acid catalyst and nature of solvent have a large effect on TEOS gela- tion.l1° Although the polycondensation of silicic acids has been studied extensively, as reviewed by Iler15376 there are little data on the rate constant of the condensation reaction.93 A value of kc = 3.3 X lo+ L molW1 s-l has been reported by Artaki et al. for the dimerization of monosilicic acid.lo2 However, no value of kH is available for the same system. Artaki et al. showed that appli- cation of a pressure of 5 kbar to the system increased the polycondensation rate constant by a factor 10.'O2 There are many problems associated with the com- putation of reaction rate constants and especially the determination of the mechanisms of the reactions as well as the order of the reactions with respect to the constituents, as discussed by Schmidt et al.lo5 When the order of the reaction varies with time, such as in Uhlmann et al.'s experiments, determining the rate constant becomes even more difficult.lW For short periods of time, the order of the reaction can be con- sidered constant. However, one must keep in mind that there are several hydrolysis and condensation reactions possible, each having its own rate c ~ n s t a n t . ~ ~ ~ J ' ' Con- sequently, assumptions are necessary to allow the com- putation of kH and kc, which limits the characterization of the reactions to the early stages of the process. Because of the above limitations, early studies of the influence of the experimental factors on the sol-gel process were primarily phenomenological, without specific values of the ratio k H / k c being determined for a single system. This situation has changed dramati- cally in the past few years. Many investigators have pursued the kinetics of silicon alkoxide hydrolysis using 29Si NMR. It is one of the most useful techniques to follow the hydrolysis and first-stage polymerization of silicon alkoxide, because it allows the determination of the concentration of the different Si(Or),(OH), and (OH),(OR),Si-0-Si(OR)x(OH), species. Each of the monomer and dimer species has a specific chemical shift with respect to the metal alkoxide.'12 employed 29Si NMR as early as 1977 to investigate the condensation of aqueous silicates a t high pH. Their results indicate that a typical se- quence of condensation products is monomer, dimer, linear trimer, cyclic trimer, cyclic tetramer, and a higher order generation of discrete colloidal particles which are commonly observed in aqueous systems. This sequence Engelhardt et Hench and West Figure 4. Variation of the concentration of M1 (Si(OH)(OCH,),) and D1 ((OCH3),Si-O-Si(0CH3),) as a function of time for the different solution^.^^ of condensation requires both depolymerization (ring opening) and availability of monomers (species that may be produced by depolymerization). However, in alcoholic solutions especially a t low pH the depolym- erization rate is very low. Iler15 speculates that under conditions where depolymerization is least likely to occur, so that the condensation is irreversible and si- loxane bonds cannot be hydrolyzed once they are formed, the condensation process may resemble clas- sical polycondensation of polyfunctional organic mo- nomers resulting in a three-dimensional molecular network. Owing to the insolubility of silica under these conditions, the condensation polymer of a siloxane chain cannot undergo rearrangement into particles. In sol-gel systems commonly employed for glass prepara- tion, the water/alcohol ratio and pH are widely varied. Thus the importance of the reverse reactions depends on processing conditions, and it is anticipated that condensation may result in a spectrum of structures ranging from molecular networks to colloidal particles. Yoldas114 concluded that the hydrolysis reaction and the condensation reaction are not separated in time but take place simultaneously. It has been well established that the presence of H30+ in the solution increases the rate of the hydrolysis reaction, whereas OH- ions in- crease the condensation reaction.'15 Orcel et al.9*953116 explored the effect of acid catalysis and formamide (a drying control chemical additive) on the hydrolysis and polycondensation rates of a TMOS silica system, using 29Si NMR. By plotting the variation of the concentration of the species of interest from the NMR data as a function of time (Figure 4), one can obtain the rate constants for hydrolysis ( k H ) and poly- condensation (k,) of the Si alkoxide, in this case TMOS. Even though the assumptions involved in the com- putation of the rate constants are crude, such as first- order kinetics and no influence of the degree of sub- stitution of Si atoms on the reaction rates, the order of magnitude of kH and kc, Table I, demonstrates im- The Sol-Gel Process I / f d d Chemical Reviews, 1990, Vol. 90, No. 1 39 TABLE I. Physicochemical Characteristics of the Different Gel Solutions sample SW 55 SF 25 SF 50 SF 23 vol formamide/vol formamide + 0 25 50 25 MeOH D1 D1 D1 p H = 3 12 I 2 25 H20 103kH, L mol" h-I k c , L mol-' h'' 29 31 25 6 d , nm 2 2.2 2.5 portant differences. These data show that acid catalysis increases the hydrolysis rate constant, kH, by a factor of 2. The data also show that formamide decreases the hydrolysis rate and slightly increases the condensation rate. This can be attributed to the ability of HCONH2 to form hydrogen bonds and to its high dielectric con- stant ( E = 110).ll6 The presence of formamide also decreases the time of gelation (tg). Additional details regarding the use of formamide and other drying control chemical agents (DCCAs) are discussed in refs 93 and 117. The studies of Klemperer and colleagues97~98 provide some of the most detailed evaluation of the extent of hydrolysis and condensation of silica prior to the onset of gelation. To identify the polysilicate intermediates formed during sol-gel processing, Klemperer et al.97 used a protocol that combined quenching by diazo- methane, fractionation using spinning band column distillation, identification by capillary gas chromatog- raphy, and structural characterization using 29Si(1Hj NMR techniques (one-pulse, 1D-INADEQUATE, and 2D- INADEQUATE) to provide structural assignments and response factors for the components separated by gas chromatography. Theyg8 showed that under acidic conditions the polysilicate molecular size distributions, expressed in terms of mole percent of total silicon present as a function of degree of polymerization, ex- hibit maxima near the number-average degree of po- lymerization. There are mostly linear structures under acidic conditions. In contrast, under basic conditions the maximum of the distribution is a t the monomer percent and extends to very high molecular weights. Thus, the distribution of polysilicate species is very much broader for basic conditions of hydrolysis and condensation, characteristic of branched polymers with a high degree of cross-linking, whereas for acidic con- ditions Klemperer et aLgs conclude that there is a low degree of cross-linking due to steric crowding. Raman spectroscopy is one means of assessing qualitatively the size of particles or scale of struc- ture1l8Jl9 when gelation occurs. Since the Raman in- tensity is proportional to the concentration of scatterers, sols and gels prepared with different experimental conditions can be compared by using a proper internal standard. In the study of the Si02-formamide system, methanol was used for calibration.9H5 According to the NMR data, the concentration of CH30H is constant after 0.7t a t 23 "C, and the solvent is significantly expelled hom the gel after -6tg. Thus the calibrated Raman intensities are valid in the time frame 0.7tg-6t,. Results for several gel solutions, with and without formamide, under basic and acidic conditions, are given in Figure Lg6 These curves demonstrate that when formamide is present, i.e., samples SF 50 and SF 25, larger particles are formed at the gelation point. This is in good agreement with the NMR result^.^^-^^ Since formamide decreases the hydrolysis rate, fewer sites are 3001 . I - , , 1 a Reduced t ime ( t / tq l Figure 5. Variation with time of the relative Raman intensity of the 830-cm-' band of the various gel solutions.% available for condensation and larger particles are formed in the so1.93J17 The reaction of silica colloids with molybdic acid, a technique widely used for the characterization of soluble silicates,120 can also be used to assess the size of particles developed in the sol. Si02 particles depolymerize in an acidic medium, and the monosilicic acid thus formed gives a yellow complex with Mo, which can be measured optically. A plot of the absorbance as a function of time allows the computation of the depolymerization rate constant, kD, as a function of time.93p96 For example, the values of kD a t 0.5tg for several SO2-formamide solutions can be used to calculate the particle diameter. Ultimately, kD can be related to the particle diameter d through an empirical law: (5) where a and b are constants (see Iler120) depending on experimental conditions, mainly solution pH. Since the solution pH of samples 55, 25, and 50 are nearly equivalent, it is possible to compare relative particle sizes by using eq 5 and assuming the values for a and b from Iler.120 (Note: This is only an approximation since Iler's values are based on a pH = 2, SiOp solution.) The calculated values a t the gelation point, shown in Table I, increase with increasing formamide concen- tration. It has been shown93194 that the calibrated Raman in- tensity I R is inversely proportional to kD Thus, I R can be related to the sol particle size as I R = Adlfb (6) where A is a function independent of d. For the con- ditions described by Iler" l / b = 3.48. The theoretical basis for this value is developed in refs 93 and 94. By use of l / b and the values of d (eq 5 ) calculated from the Mo test, it is possible to compute an empirical value of 6.8 for A in eq 6. By use of eq 6 and the measured values of Raman intensity (Figure 5), the time-dependent change in sol particle size can be cal- culated. The results are shown in Figure 5 on the right-hand particle-size axis. By the time of gelation, the size of the sol particles grows to 2 nm without formamide, and with 50% formamide they grow to 2.5 nm. These findings are similar to those of Klemperer et a1.97998 in their studies of the effects of base vs acid log d = a + b log kD 42 Chemical Reviews, 1990, Vol. 90, No. 1 sw 55 Hench and West I .75 I- 0.40 -2.01 I I 1 I t 1 I I -5 0 -2.25 -1.5 -0.75 0 Loo h Figure 8. Variation with time of log I (h) vs log h curves for a SW55 sample (no f ~ r m a m i d e ) . ' ~ ~ during the gelation process. Only a few techniques are available to follow struc- tural evolution at the nanometer scale of sol-gels. They include small-angle X-ray scattering (SAXS), neutron scattering, and light scattering, each of them giving complementary information, and transmission electron microscopy. Small-angle X-ray scattering allows the determination of a characteristic length of the particle (Guinier's radius of gyration, or electronic radius of gyration) 145-147 and a fractal dimension, which gives some information on the structure of the polymer (branched vs linear) and on the growth mechan i~m. '~~ The application of SAXS to a number of gel systems has been reported by various a ~ t h o r s . ~ ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ Small-angle neutron scattering (SANS) has also been applied to the study of silica ~ 0 l s . l ~ ~ Results similar to those from SAXS are obtained, but further develop- ments of the SANS technique may produce additional insight to the sol-gel process.158 Light scattering has been used for a long time to characterize macromolecular solutions. Although this technique should be useful in following the sol-gel transition, it has received very little attention in the sol-gel literature. However, the characteristic dimen- sion probed by visible light scattering is >10 nm, and therefore it cannot be used to characterize the early stages of the gelation process.149 Recent development of short-wavelength UV lasers may make it possible to extend light-scattering studies to the range of 3 nm and thereby could follow most of the gelation process. The major conclusion of the various scattering studies is that acid-catalyzed sols develop a linear structure with very little branching. In contrast, base-catalyzed systems are characterized by highly ramified struc- tures. 150,?51 Figure 8 is a Porod plot showing SAXS scattering curves typical of a sol prepared by hydrolyzing TMOS.93J56 The log of the scattering intensity, I , is plotted as a function of the scattering factor h. The scattering factor is defined as h = (4r/X) sin (8/2). As time increases from the sol stage ( t / t , = 0.11) toward gelation ( t / t , = 1.00), there is an increase in the size of X-ray scatterers. However, after a critical time ( t / t , Figure 9. 2 = 3; N = total number of bond sites = 43; n = total number of node bonds = 81: P = 0.7. = 0.28) no new scattering centers are formed. When formamide is present, the critical reduced time for formation of scattering centers is longer.93 The fractal nature of the network formed can be calculated from the slope of the Porod plot and is discussed in a later section, as are additional SAXS investigations. D. Classical or Mean-Field Theory of Gelation The classical or mean-field theory of polymerization was developed by F10ry .~~ The basis structure of this model looks like a tree and is called a Cayley tree or Bethe lattice. Figure 9 shows a Cayley tree model for a polymer that forms a connected, gel-forming cluster without forming rings. In this tree, the functionality or maximum number of bonds, z , that are allowed to form a t each numbered bond site is 2 = 3 Other polymers have different values for this parameter. For example, silicic acid has a functionality of z = 4. Four bonds may form a t every site where silicon is present. Returning to our model with z = 3, we can define the probability, P, of a bond forming a t each site: (9) P = n / ( N z ) (10) number of bonds total number of node bonds p = where n = number of node bonds, N = number of sites, and z = dimensionality of the polymer. Thus, in our simple example, shown in Figure 9 N = 43; z = 3; n = 81 (11) This means that some bonds are counted twice. The number of connections for each numbered node is counted. For example (a) node 34 has one bond, (b) node 27 has two bonds, and (c) node 1 has three bonds. Therefore, the probability for a connection for each site in this example is P = n / ( N z ) ; P = 81/[(43)(3)]; P = 0.6 (12) This example forms a gel, as we have conceptually defined it, since the cluster is continuously connected from one side to the other. Thus, there must be at least two connections per node for the cluster to be a gel. This defines the critical probability, P,, for gel forma- tion to be P, = 1/2 (13) (14) or in terms of the functionality of the polymer324 P, = l / ( z - 1) The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, No. 1 43 a Figure 11. Bond percolation model. b Figure 10. Site percolation model: (a) empty grid; (b) Raman filling of grid. This defines then the degree of reaction a t the gel point. The distribution of molecular weights can also be determined. However, there is a fatal flaw in this model. Because no rings are allowed, there is an in- creasing number of nodes as the radius of the cluster increases. In fact, the mass of this type of cluster increases as the fourth power of the radius as shown by Zimm and S t ~ c k m a y e r ' ~ ~ and de Gennes." In real materials the mass must increase linearly with volume as the third power of the radius. However, this model is still useful in visualizing the gelation of silica sol-gels. It yields a degree of reaction of one-third: P, = l / ( ~ - 1) = 1/3 (15) a t the time of gelation. That means that two-thirds of the connections are still available and play a role in subsequent processing. This value is lower than the experimental evidence as we shall see in the next sec- tion. It does however represent the minimum degree of reaction before gelation can occur as presented by F 1 0 r y . ~ ~ ~ E. Percolation Theory Percolation theory and its relationship to gelation has been reviewed by ZallenlG1 and Stauffer et Per- colation allows for rings or closed loops to form, and thus the mass of percolation models increases with the cube of the radius. Figure 10 shows a simple percolation model. Starting with an empty grid (Figure loa), intersections are ran- domly filled with particles (filled circles). If two circles or particles are adjacent, then bonding will occur (Figure lob). Loops of various sizes may form as the structure expands. This eliminates the fatal error of the classical model and is called a site percolation model. In a manner similar to the classical model, the probability, P, that a site may be filled is defined as P = n / N (16) where n = number of filled sites and N = total number of sites. With the simple example in Figure 10 n = 32 (17) N = 64 (18) P = 1 / 2 (19) Thus This simple model shows that for this value of site filling, complete connectivity or gelation is unlikely for the site model. Experimental results indicate that 0.6 C P, I 0.84 (20) for silica sol-gel systems, as reviewed by Zarzycki.81 Thus, this model must be modified to increase the connectivity. By starting with all the sites filled and randomly adding bonds, the connectivity increases over the site model. Figure 11 shows a bond percolation model. Again we can define the probability of bonding as P = n / N (21) where n = number of bonds and N = total number of bond sites. In the case of the example in Figure 11 we have n = 39 (22) N = 112 (23) P = 0.35 (24) where gelation appears likely. The bond percolation model is dependent on the lattice. Table IV shows a summary of the percolation threshold for various lattices based on Brinker and Scherer.'O The table also shows the volume fraction, &, of the gel a t gelation and the filling factor, u. F. Fractal Theory The fractal model of structures was designated as such by M a n d e l b r ~ t l ~ ~ and gives order to the many seemingly random patterns generated by nature, such 44 Chemical Reviews, 1990, Vol. 90, No. 1 Hench and West TABLE IV. Percolation Threshold for Various Lattices (from Brinker and Scherer'O) dimensionality d latticea coordination z 1/(z - 1) Pc pesite filling factor u @c = up,Bib bond I chain 2 1 1 1 1 1 1 triangular 6 0.200 0.347 0.500 0.907 0.45 2 square 4 0.333 0.500 0.593 0.785 0.47 2 kagom6 4 0.333 0.45 0.653 0.680 0.44 2 honeycomb 3 0.500 0.653 0.698 0.605 0.42 3 fcc 12 0.091 0.119 0.198 0.741 0.147 :i bcc 8 0.143 0.179 0.245 0.680 0.167 3 SC 6 0.200 0.247 0.311 0.524 0.163 3 diamond 4 0.333 0.388 0.428 0.340 0.146 :i repb -8 -0.143 -0.27 -0.637 -0.16 4 sc 8 0.143 0.160 0.197 0.308 0.061 4 fcc 24 0.043 0.098 0.617 0.060 2 SC 10 0.111 0.118 0.141 0.165 0.023 7 fcc 40 0.026 0.054 0.465 0.025 6 SC 12 0.091 0.094 0.107 0.081 0.009 fcc = face-centered cubic; bcc = body-centered cubic; sc = simple cubic; rep = random closed-packed. bLess precise values, determined experimentally. t CL x U ul c a .- n \ F r a i t a i Size, R - Figure 12. Density of fractal objects. as trees,163 galaxies,164 or the surface of the sun.165 Witten and S a r ~ d e r l ~ J ~ ~ and Witten and Cates168 have demonstrated the fractal nature of diffusion-limited aggregation of particles. Growth processes that are apparently disordered also form fractal objects.168 Sol-gel particle growth has also been modeled by using fractal c o n c e p t ~ . ~ ~ J ~ ~ J ~ ~ The nature of fractals requires that they be invariant with scale. This is a symmetry that requires the fractal to look similar no matter what level of detail is chosen. For example, a tree as a whole has a very similar structure as a small branch within that tree. The second requirement for mass fractals is that their density decreases with size (see Figure 12). Thus, the fractal model overcomes the problem of increasing density of the classical model yet retains many of its desirable features. Fractal objects are quantified by their fractal di- mension, df. Figure 13 shows objects with increasing fractal dimension.70 For linear-like structures 1 < d , < 2 (25) (as shown in Figure 13B). Fractally rough structures have a mass fractal dimension 2 < d , < 3 (26) C. 't 0. Figure 13. Fractal objects: (A) linear structures, 1 < df < 1.5; (B) fernlike structures, 1.5 < df < 2; (C) fractally rough structures, 2 < df < 3; (D) solid structure, df = 3. Reprinted from ref 70; copyright 1989 Academic Press. TABLE V Keefer's hydrolyzed monomer fractal dimension df nonfractal 100% triple 3 fractal 33% double 1.8 33% triple 33% fully fractal 50% double 1.67 50% fully (as shown in Figure 13C). Finally, uniform nonfractal objects have a fractal dimension d f = 3 (27) (as shown in Figure 13D). The mass of a fractal then is related to the fractal dimension and its size or radius, R , by M a Rdi (28) Therefore, computer models can be constructed to generate particle growth and measure the resulting fractal dimension. One such fractal gelation model was developed by Keefer.153 He postulated that sol particles grow from partially hydrolyzed TEOS (Si(OC,H,),). When fully hydrolyzed TEOS was used in the model, a fully dense particle was formed that had no fractal nature. The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, No. 1 47 philic species that can complex to form hypervalent intermediates. They applied semiempirical molecular orbital calculations to examine the formation of pen- tacoordinate silicic acid complexes with hydroxide ion and fluoride ion, as well as neutral adducts with hy- drogen fluoride, ammonia, and formamide. They also have calculated reaction paths for water elimination from silicic acid complexes with hydroxide ion, fluoride ion, and hydrogen fluoride. The qualitative semi- empirical picture of the reaction surface has been quantified by employing high-level ab initio calculations for selected intermediates and transition-state struc- tures. The adducts studied were chosen because of their potential as catalysts or drying control agents in sol-gel processing chemistry. For example, as discussed earlier, formamide is used as a drying control additive for sol-gel chemistry to control the ratio of rates of siloxane hydrolysis and silanol polymerization. The semiempirical methods used in Davis and Burggrafs research are part of the MOPAC program available from the Quantum Chemistry Program Ex- change (QCPE) a t the University of Indiana.lE3 Semiempirical molecular orbital calculations were performed using MNDO6 and AM17 methods devel- oped by Dewar and c ~ - w o r k e r s . ' ~ J ~ ~ Revised silicon parameters were used for MNDO calculations.'@ All stationary points on the potential surfaces were fully optimized by using procedures of the MOPAC program. Force constant calculations and intrinsic reaction co- ordinate calculations were performed for each station- ary point to determine the nature and connectivity of the potential surface. Ab initio calculations were performed using the GAUSSIAN86 program and basis sets it contains.'s7 All ab initio calculations in their work were single-point calculations at AM1 geometries. Estimates of energies a t the MP1/6-31++G(d) level'@ were calculated by assuming correlation effects and polarization effects are Comparisons of ab initio results and semiempirical results are used to establish a quantita- tive benchmark for semiempirical energies in order to solve problems that are too large for high-level ab initio methods.lg2 For reaction of any nucleophile with silicic acid, two possible outcomes are (1) addition and (2) abstraction. By studying the possible reaction paths for the removal of water, the proton-abstracting pentacoordinated sil- icon has no activation energy for water removal. In contrast, the pentavalent silicon has a relatively large activation energy for removal of water if the proton is added and constrained to form its most stable structure before the water is removed. Figure 17 shows both the proton abstraction and hydroxyl paths that include the addition of penta- coordinated silicon as an intermediate in the conden- sation reaction. The more favorable proton abstraction path is one where a proton from a silanol moves toward the hydrogen-bonded OH as the OH moves toward the silicon. This forms a pentacoordinated silicon inter- mediate where water easily escapes. If, on the other hand, the OH is moved toward the silicon to form a stable pentacoordinated structure, the energy is much lower. From this structure, a significant activation energy is then required to eliminate the water. f C o n d e n s a t i o n .. t a Forrr Watw: 5 1 (OH 'Kp -50 1 D r o t o n A +,( , A d d i t i o n = -93 -103 S I ( O H ) ~ R e a c t i o n Coord ina t i o n Figure 17. Formation of pentacoordinate silicon. Burggraf and Davisla2 used MNDO, AM1, and ab initio molecular orbital models to predict the proton abstraction and resulting pentacoordinate silicon. They constructed similar models for HF ammonia and form- amide adducts on silicic acid. For HF they also predict that the pentacoordinated silicon created by proton abstraction is the more favorable path to water elimi- nation. The difference is that water elimination from HF adducts has a slight energy barrier. This indicates a shift to a slower condensation rate for the HF-silanol system over the OH-silanol system. Ammonia and formamide adducts with silicic acid form by hydrogen bonding. Formamide is predicted to form a bistable bond in which one oxygen-silicon bond is shorter than the other. The long bond oxygens permit more favorable hydrogen-bonding interactions. Burggraf and DavislE2 also calculated the energy of water adducts on silicic acid. They found that there were very small energy differences between the penta- coordinated water adducts and the corresponding hy- drogen-bonded water adducts. This result is important when considering the effect of water adducts on rings of silica tetrahedra discussed in a later section. B. Gelation In the previous sections, we saw that experimental analyses of silica gelation using SAXS, Raman spec- troscopy, and a Mo dissolution technique led to the conclusion that a gel network is preceded by the for- mation of very small clusters, or primary particles, of silica tetrahedra. The primary particles are apparently formed by polycondensation that favors nearly closed clusters of tetrahedra rather than linear chains. This conclusion regarding the gelation and resulting ultrastructure of acid-catalyzed alkoxide-derived silica gels has been tested by West et al.lg3 and Davis and Burggraflg4 using semiempirical quantum calculations. The calculations done by West e t al. used an inter- mediate neglect of differential overlap (INDO) molec- ular orbital mode1.1g3 The INDO program was made available by the Quantum Theory Project a t the University of F10rida.l~~ The calculations done by Davis and Burggraf used the AM1 mode1.1g4 The silica structures evaluated contain from one to six silica tetrahedra. In each model two bridging oxy- gens and two nonbridging oxygens are bonded to each silicon. One hydrogen is bonded to each of the non- bridging oxygens to terminate the structure and balance the charge. Both ring and chain models of silica tet- rahedra were evaluated, and their energies compared. 48 Chemical Reviews, 1990, Vol. 90, No. 1 8 8 9 Hench and West -50 1 1 Uncorreclee for water Secondav I particle Q 4 Figure 18. TABLE VI. INDO Calculations for Silica Structures INDO HOMO-LUMO no. of silica energy per uv cutoff tetrahedra struct Tetrahedra, au wavelength, nm 1 tetrahedra -73.82 87.1 2 2 3 chain ring chain ring chain ring chain ring chain ring -64.72 -55.82 -61.74 -55.86 -60.25 -55.80 -59.35 -rr - JJ. 16 -58.55 -5,579 130.7 112.8 132.7 106.2 139.6 114.3 134.2 144.3 135.8 114.1 Figure 18 shows the 2-D projections of chain and ring structures for four silica tetrahedra that have been geometrically optimized to minimize the molecular en- ergy by using INDO calculations. These projections are typical of the hydroxylated silica structures modelled by West et al.lg3 and Davis and Burggraf.lg4 The clusters were each optimized for the minimum energy by using a molecular mechanics (MM2)'% routine. The molecular orbitals were determined by using geome- trically optimized INDO calculations. The molecular energies were evaluated and compared to establish the relative stability of each structure. The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for the single states and the corresponding UV cutoff wavelength were determined. The calculated optical properties are compared with experimental values in the properties section of this review. Table VI, summarizing the INDO calculations, is shown to compare the relative stability of the INDO structures. The more negative the energy, the more stable the structure. These differences are exaggerated because each chain structure has an extra water mole- -65 0 2 4 6 8 1 0 1 2 Number of SI tetrahedra Figure 19. TABLE VII. Cluster Sizes for Rings and Chains of Tetrahedra INDO no. of silica cluster size, A tetrahedra N rings chains (chain-ring), au 2 6.6 9.1 8.9 3 7.1 12.7 5.9 4 9.3 16.3 4.4 5 11.3 19.8 3.6 6 11.9 23.4 2.8 cule when compared to the ring structure. Figure 19 shows the INDO energy per silica tet- rahedra for rings and chains as a function of the number of tetrahedra. It suggests that the chain structures are more stable than the rings for small number of silica tetrahedra. This has been observed experimentally by Klemperer and Ramamurthig7 and Orcel and Hench1lG using NMR spectroscopy, where a linear, as opposed to a ring, growth model most consistently interprets the experimental structural evidence prior to gelation. As mentioned earlier, investigatorsg4 have proposed models for the structure of acid-catalyzed silica gels containing two levels of structure formed before gela- tion. These models propose the formation of primary particles, of diameter 1-2 nm, which agglomerate to form secondary particles of about 4-6 nm before drying. The secondary particles give rise to the pore structure after drying. Table VI1 shows the differences in the INDO struc- tural energies between chains and rings (C-R). The relative stability of chains compared to rings decreases as the number of silica tetrahedra increases by the decrease in the difference between their calculated INDO energies. The difference is estimated to reach zero as the number of tetrahedra reaches about 10 or 12, when the driving force for rings becomes more fa- vorable than for chains. This result is similar to the size range where secondary particle growth stops in acidic silica Acid catalysis ensures complete hydrolysis of the silica tetrahedra, as used in these calculations. The size of the INDO-calculated rings or clusters for 10-12 tetrahedra appears to fall within the range of the radius of gyration of the primary particles calculated from SAXS analysis of acid-catalyzed silica so1s.94J56 As gelation occurs, the cross-linking of the structure becomes more dominant. A statistical analysis con- ducted by Zarzyckis1 indicates that chain growth is limited by this process and rings must be formed. The energy differences in the ring structures in the INDO model are very small. This indicates that a broad distribution of ring sizes may be possible in a gel as they The Sol-Gel Process Chemical Reviews, 1990, Vol. 90, No. 1 49 - 8 " 2 3 4 Number of Si tetrahedra F i g u r e 20. AMI corrected energy difference. TABLE VIII. AM1 Enthalpies of Rings and Chains at 25 "C (kcal/mol) no. of silica A H f tetrahedra N chain ring water differences 1 -296.8 2 -545.4 -458.2 -59.2 +28.0 4 -104.3 -991.7 -59.2 -4.6 3 -794.0 -727.6 -59.2 +7.2 become energetically more favorable. Davidg4 recalculated the energetics of rings and chains using AM1. His calculations were corrected for the extra water molecule in the chains as compared to the rings. The AM1 energies were also corrected for zero-point energy and converted to enthalpies a t 25 "C. These corrections moved the crossover energy from 10 to 12 tetrahedra to 3 or 4 tetrahedra (see Figure 20). Table VI11 shows the enthalpies, AH,, in kcal/mol for rings and chains and their differences. Chains are still the most likely to occur in the early stages of hydrolysis and condensation. The important feature is that chains and rings are reversed in energy difference when three to four tetrahedra or more are formed. The driving force to produce chains is elimi- nated, and therefore 4-fold rings are very likely. This corresponds very closely to the 1-2-nm primary silica particles that form prior to agglomeration, as shown in Tables I11 and VII. Thus, results from quantum me- chanical calculations compare quite favorably to ex- perimental observations for the ultrastructure devel- opment in alkoxide-derived s i l i ~ a s . ' ~ ~ - ~ ~ ~ VI . Aghg When a gel is maintained in its pore liquid, its structure and properties continue to change long after the gel point. This process is called aging. Four pro- cesses can occur, singly or simultaneously, during aging, including polycondensation, synerisis, coarsening, and phase transformation. Although there is an extensive literature on aging by Iler,15*76J20 and Scherer has made an effort to describe aging phenomena theoretically,7°*205 there is relatively little detailed knowledge of aging mechanisms and kinetics and even less quantitative analysis of the effects of aging on gel structure and properties.206 Polycondensation reactions, eqs 3 and 4, continue to occur within the gel network as long as neighboring silanols are close enough to react. This increases the connectivity of the network and its fractal dimension. Syneresis is the spontaneous shrinkage of the gel and resulting expulsion of liquid from the pores. Coarsening is the irreversible decrease in surface area through dissolution and reprecipitation processes. Disintegrated o p F i g u r e 21. Stages in aging of gel: (A) Gel as formed and dried. Shrinks on drying, giving small pore volume and pore diameter. (B) Wet heat-aged-increased coalescence. Little shrinkage on drying. Pore diameter larger than the dried sample A. (C) Further heat aged or autoclaved. Structure-coarsened small area and large pores but same pore volume as sample B. (D) Disintegration to irregular round particles. A. Polycondensation Usually in alkoxide-based gels the chemical hydrolysis reaction is very rapid and is completed in the early stage of sol preparation, especially when the sol is acid cat- alyzed. For silica gels synthesized in alcoholic solutions, i.e., made by hydrolysis and condensation of alkoxides, nuclear magnetic resonance (NMR,207p208 Figure 21) and Raman spectroscopies209 show that the number of bridging bonds increases long after gelation. The con- densation reaction continues to occur because of the large concentration of silanol (SiOH) groups in a newly formed gel. As the hydroxyls are lost during aging, new bonds are formed, creating more cross-linked structures. 29Si NMR results of Kelts et al.'07 show substantial amounts of Q2 species a t the gel point, and the pro- portions of Q3 and Q4 species increase with time long after gelation. As discussed earlier, &" represents a Si atom bonded through a bridging oxygen to n other Si atoms. Since the chemical reaction is faster a t higher tem- perature, aging can be accelerated by hydrothermal treatment, which increases the rate of the condensation reaction. B. Syneresis The shrinkage of the gel and the resulting expulsion of liquid from the pores is called syneresis.76~205*210 Syneresis in alcoholic gel systems is generally attributed to formation of new bonds through condensation reac- tions, which increases the bridging bonds and causes contraction of the gel network. In aqueous gel systems, or colloidal gels, the structure is controlled by the balance between electrostatic repulsion and attractive van der Waals forces. Therefore, the extent of shrink- age is controlled by additions of electrolyte. Vysotskii and colleagues211*212 have shown that the rate of con- traction of silica gel during syneresis has a minimum a t the isoelectric point (IEP). For silica this point is a t a pH of 2, a t which the silicate species are un- 52 Chemical Reviews, 1990, Vol. 90, No. 1 by the large capillary forces, which causes shrinkage of the object. In classical large-pore systems, this first stage of drying is called “the constant rate period” be- cause the evaporation rate per unit area of the drying surface is independent of A detailed review of the drying phenomena associated with the constant rate period is presented in Brinker and S ~ h e r e r . ~ ~ This behavior is applicable to gels made by colloidal pre- cipitation (method 1) or base-catalyzed alkoxide gels (method 3) that have pores >20-nm average diameter. However, a recent quantitative analysis by Wilson237 and Wilson and H e n ~ h ~ ~ ~ q ~ ~ ~ of the drying kinetics of acid-catalyzed alkoxide gels shows that for gels with pores <20 nm the rate of drying in stage 1 is not con- stant but in fact decreases substantially. As discussed below, this behavior is due to changes in pore radii during drying, which cause substantial reductions in vapor pressure of the liquid in the small pores. For large or small pore gels the greatest changes in volume, weight, density, and structure occur during stage 1 drying. Stage 1 ends when shrinkage ceases. Stage 1 ends and stage 2 begins when the “critical point” is reached; classical drying theory calls this the “leatherhard point”.232-236-240 The critical point occurs when the strength of the network has increased, due to the greater packing density of the solid phase, sufficient to resist further shrinkage. As the network resistance increases, the radius of the meniscus is reduced. Eventually, a t the critical point, the contact angle ap- proaches zero and the radius of the meniscus equals the radius of the pore. This condition creates the highest capillary pressure, and unable to compress the gel any further, the pores begin to empty, which is the start of stage 2. In stage 2 liquid transport occurs by flow through the surface films that cover partially empty pores. The liquid flows to the surface where evapora- tion takes place. The flow is driven by the gradient in capillary stress, as described by Whitaker.241 Because the rate of evaporation decreases in stage 2, classically this is termed “the first falling rate period”.242-244 Stage 3: The third stage of drying is reached when the pores have substantially emptied and surface films along the pores cannot be sustained. The remaining liquid can escape only by evaporation from within the pores and diffusion of vapor to the surface. During this stage, called the “second falling rate period”,225 there are no further dimensional changes but just a slow progressive loss of weight until equilibrium is reached, determined by the ambient temperature and partial pressure of water. Whitaker230.241 has developed a theoretical analysis of the second falling rate period. Brinker and Scherer70 review the factors in this stage that are relevant to the drying of gels. A comparison of Dwivedi’s results235 on the drying of an alumina gel with those of Wilson and H e n ~ h ~ ~ ~ * ~ ~ ~ for an acid-catalyzed alkoxide silica gel illustrates the importance of pore size in gel drying behavior. Dwivedi prepared the alumina gels using the Y01das~~ method, which yields gels with pores >>20 nm. Samples up to 3 mm thick were weighed a t periodic intervals during drying at 80 “C. Figure 23, from D ~ i v e d i , 2 ~ ~ shows that the rate of water loss was constant from his gels during stage 1 (within the range of the considerable experi- mental error caused by removing the sample from the oven for weighing). He showed that the rate was similar .- c ‘E 0.20 N 6 0) 0.15 v u) u) 0 - 0.1 0 (L, m L u 3 0.05 0, m CI: - Hench and West - Evaporation rate of --- -------- - ‘7 T distiled water ILL‘ - - L Second Stage - First Stage 4 P - I I The Sol-Gel Process Chemical Reviews. 1990, Vol. 90, No. 1 53 0 25 50 71 I W I75 150 (75 Time lhourr) Figure 24. Time dependence of (A) temperature and weifhG (B) absolute loss rate; (C) loss rate per unit area for gel A. 37 atmosphere after casting. It also is consistent with the fact that traditional porous ceramic bodies are much more crack resistant during drying. Since the perme- ability of a 50% porous body with 1-pm pores has a value of D i; cm2, the stress will be lo4 smaller than in a gel drying a t the same rate. When the pores in a gel are <5 nm, characteristic of acid-catalyzed alkoxide gels, the analysis of drying stresses is complicated by the fact that stage 1 is not a constant-rate period of drying. This is in dramatic contrast to all classical drying experiments. As shown in Figure 24, from Wilson and Hench,239 the evaporation rate from the gel during stage 1 dropped from a max- imum of 0.034 to 0.013 g/(h cm*) a t the critical point, even though the meniscus remained at the surface throughout this stage, as required by the definition of stage 1. These data were taken by use of a specially designed drying apparatus developed by Wilsonu7 that permitted simultaneous monitoring of sample dimen- sions, weight, and optical properties a t constant tem- perature and atmosphere without removing the samples from the drying chamber?% Consequently, high accu- racy was obtained. Wilson and Henchm show the time dependence of weight and dimensions of a representa- tive silica gel monolith in Figure 25. The relationship between relative weight (W/ Wo) and relative volume (V/Vo) of the gel during the various stages of drying is shown in Figure 26. The change between stage 1 and stage 2 is very clear. The reason for the decrease in drying rate in stage 1 for these gels is associated with the effect of pore 0 ii) 2n 10 40 IO fa 70 so 90 I W wlwo c. Figure 26. WJW, percent vs VIVO percent for gel B.” radius on evaporation rate. Recall that acid-catalyzed alkoxide gels have very small pores, <5 nm. The evaporation rate from the gel is dictated by the dif- ference between the vapor pressure at the evaporating surface, Ps, and the vapor pressure of the ambient at- mosphere, Pw Evaporation continues as long as P. > Pa with a rate (VJ: v, = u p , - Pa) (36) where Ke is a constant. The vapor pressure of a surface comprised of a large number of very small pores, Pv, will be influenced by the radii of the pores, as described hy the Gibbs-Kelvin equation (37) 54 Chemical Reviews, 1990, Vol. 90, No. 1 x < 1 $ 2 - I - . n - 1.0 I C 26 BID0 * I 9 BSW 0650 _.__.____________.__..-------- m = ..- Y *BW * 6 i D i I W , , ' . ' ' Hench and West 0 a. e" 0 1 2 3 4 5 6 7 8 9 10 Meniscus radius (nm) Figure 27. Reduction of vapor pressure with decreasin meniscus radius as predicted by the Gibbs-Kelvin equation.23f i n 5 3 . -.1 I I 0.9 1 0.8 0.7 0.6 0.5 - WPo no Round wstpr layer 0.0 1 ' 1 ' 1 ' 1 ~ 1 ' 1 ' 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Pore/ meniscus radius (nm) Figure 28. Comparison of observed evaporation rate ( V J Vo) to that predicted by the Gibbs-Kelvin equation. where P, is the vapor pressure over the meniscus of the pore, Po is the vapor pressure over a flat surface (760 Torr), B is the molar volume of the liquid (0.18 g/cm3), R is the gas constant (8.314 X T i s temperature (kelvin), r m the radius of curvature of the meniscus (meters), and y the difference in the solid-vapor and liquid-vapor interfacial energies (y = 0.072 J/m2). Figure 27 plots the dependence of vapor pressure on the pore radius, using the values above in the Gibbs-Kelvin equation, from Wilson and H e n ~ h . ~ ~ ~ The average pore radius of the acid-catalyzed alk- oxide silica gels when dry is 2.3 nm. The structural density can be assumed to remain constant during drying. Therefore, the decrease in dimension during drying (Figure 2 5 ) should also be indicative of the de- crease in pore radius during shrinkage of the gel. This assumption yields an average pore radius of the wet gel to be -4.1 nm. Thus, the change in the ratio of evaporation rate between a free surface ( Vo) and the gel surface ( V J Vo) during stage 1 should be comparable to the drop in vapor pressure (P,/Po) predicted by the Gibbs-Kelvin equation as the gel shrinks.239 Figure 28 - RbfromDSC e-' ---e-- h b S l r o m D S C 1 I 0.0 4 i 0 1 1 6 n \?erago Pore Radius R [nm] Figure 29. Dependence of the bound water thickness on the average pore *-- DRS Samples 1 c1s compares the measured ratio of evaporation rates (V,/ V,) for the gel in stage 1 as a function of the pore radii in the gel. The ratio of evaporation rates predicted by the Gibbs-Kelvin equation is also plotted in Figure 28. The Gibbs-Kelvin equation predicts higher evap- oration rates than are observed. An important contribution to the depressed evapo- ration rate from the small pore gel is the presence of a bound layer of water on the pore surfaces. The bound water layer has a structure that is substantially more ordered than free water and possesses properties, such as melting point, that are markedly different than bulk water. Wallace and H e n ~ h ~ ~ " ~ ~ ~ used dielectric relax- ation spectroscopy (DRS) and differential scanning colorimetry (DSC) to analyze the properties and cal- culate the thickness of the bound water layer in acid- catalyzed alkoxide silica gel monoliths with porosity nearly identical with those used in the Wilson and H e n ~ h ~ ~ ~ - ~ ~ ~ drying experiments. A fundamental assumption made in relating the DRS and DSC studies to drying kinetics is that the structure of water adsorbed into the pore network of a dried gel, the starting condition for the Wallace and H e n ~ h ~ ~ ~ study, is nearly equivalent to the structure in the gel during stage 1 drying. This appears to be a reasonable assumption since Wallace and H e n ~ h ~ ~ ~ show that bound water thickness appears to be dependent upon pore radius and temperature (Figure 29). This result is valid for two different models: a bound cylindrical layer and a bound statistical layer of water. The pore radius is also independent of surface silanol concen- tration (Figure 30). When H 2 0 is adsorbed onto the surface of silica, the first H20 molecules form H bonds with, on average, two The Sol-Gel Process 1 1 1 1 I I I IO ,I la 25 I Su,tuuamra Figure 35. Schematic representation of gel surface at the end of stage 1 (critical point). Drawn to the same relative scale as Figure 34.237 of the effective pore radius decreasing from 3.2 to 1.3 nm. The bound water is apparently not removed until much higher temperatures in the stabilization regime. This analysis of effects of pore radius on stage 1 evaporation also explains why DwivediB5 and Kawag- u c h P observed a classical constant rate period during the drying of their gels. The magnitude of vapor pressure reduction required to produce a noticeable decrease in evaporation rate during stage 1 does not occur until menisci of r, < 10 nm are formed. Menisci of this radius cannot form in pores of the dimensions reported for their gels, and no significant change in the evaporation rate was seen. B. Stage 2 The Opaque Stage The second stage starts a t the critical (or leatherhard) point. At this point the meniscus radius is equal to the pore radius and is able to penetrate the bulk. The loss rate of the acid-catalyzed alkoxide silica gelsm steadies at a constant, low value of -0.008 g/(h cm?. This stage is consistent with the stage Scherer'O terms the "first falling rate period". Liquid is driven to the surface by gradients in capillary pressure, where it evaporates due to the ambient vapor pressure being lower than inside the pores. Shortly after entering the second stage, the gel is seen to turn opaque, starting a t the edges and progressing linearly toward the center. There are several possible causes of this phenomena, including phase separation of the pore liquid or exsolution of gas from the liquid. The most plausible explanation is that put forward by Shaw,2& who suggests that this phenomenon is caused by light scattering from isolated pores (or groups of pores) in the process of emptying, of such a dimension that they are able to scatter light. The data obtained during stage 2 indicate an increase in open porosity from -0.012 to -0.364 cm3/g during the opaque transition, which started at -16% (&1.5%) moisture and ended a t 6% (f1.5%) for both samples in Wilson Chemical Reviews. 1990, Vol. 90. No. 1 57 and Hench's e~periment;'~'see Figure 24. C. Stage 3 After transparency is regained, Figure 2j shows that the loss rate of the acid-catalyzed alkoxide silica gel monolith gradually falls to a value of -0.001 g/(h cm') until no further weight changes occur. The transition to stage 3 is the hardest to identify, and its start is probably best defined as the end of the opaque stage. Scherer'O describes stage 3 as the "second falling rate period", where the temperature of the body is not as strongly suppressed as when evaporation rates were higher. The remaining liquid evaporates within the pores and is removed by diffusion of its vapor to the surface. It is unaffected by local changes in tempera- ture, ambient vapor pressure, flow rate, etc., as dem- onstrated for gel B in Wilson and Hench's study.wg By the start of stage 3 the gel is to all intents and purposes dry. It can be removed from the drying chamber and dehydrated under much more severe conditions (180 "C at 0.1 Torr) without risk of cracking. Stress birefrigence measurements during drying indicate a gradual reduc- tion in residual stress during stage 3 and the end of stage 2, because of the reduction in number of bire- frigent lines and eventual elimination of the isogyres caused by biaxial strain.23' D. Cooling During the cooling period (which can be rapid) the samples gained weight as shown in Figure 24. On cooling, gel B gained almost all of the weight lost during stage 3. As the chamber cools, the vapor pressure in the chamber rises until Pa > P. and condensation occurs within the pores. E. Drying Failure The drying times reported in Wilson and Hench's study" are the experimentally determined minimum for gels of 2-4-cm diameter without cracking. When samples fail, they do so a t distinct points within the drying sequence. Cracking during stage 1 is rare but can occur when the gel has had insufficient aging and strength (see S ~ h e r e r ' ~ * ~ - ~ ) and therefore does not possess the dimensional stability to withstand the in- creasing compressive stress. If the loss rate is increased (by lowering the vapor pressure of the ambient atmo- sphere or increasing the draft rate), there comes a point where it exceeds the maximum rate of shrinkage. If this occurs, localized pore emptying results and surface cracks develop. Most failure occurs during the early part of stage 2, the point a t which the gel stops shrinking. This is the point at which the meniscus falls below the surface. A distribution of pore sizes exists in these materials, and some pores must empty before others. At the start of stage 2 the modulus of the gel is very high and the compressive stress is in the order of -100 MPa. The pores that empty first (at the larger end of the distri- bution) stop shrinking a t the point of emptying and can only passively shrink under the influence of nearby saturated pores. The possibility of cracking a t this point is great due to the high stresses and low strain tolerance of the material. Cracking during stage 3 does not occur, in the experience of Wil~on.~ ' The moisture 58 Chemical Reviews. 1990. Vol. 90. NO. 1 level and thus the stress is considerably diminished by this point, and cracking generally will not occur even under fairly extreme dehydration conditions unless very large defects are present. Hench et al. have discussed the types of defects that can be introduced during gel processing and their effects on strain ~oncentration.5~ Successful drying of large gel monoliths requires control of the drying rate through the opaque stage and elim- ination of processing defects during mixing, casting, and gelation. VIII. Stabilization A. Introduction Optically transparent dried silica gel monoliths have been made by Hench et al."$ of over 80-mm diameter. This new type of optical material is termed type VI and its physical characteristics are described in the properties section of this review. A critical step in preparing type VI gelsilica is stabilization of the porous structure as indicated in Figure 3. Both thermal and chemical stabilization is required for the material to be used in an ambient environment. The reason for the stabilization treatment is the very large concentration of silanols on the surface of the pores of these large surface area (>400 m2/g) materials. Chemical stabilization involves removing the con- centration of surface silanols below a critical level so that the surface does not rehydroxylate in use. Thermal stabilization involves reducing the surface area suffi- cient to enable the material to be used a t a given tem- perature without reversible structural changes. The mechanisms of thermal and chemical stabilization are interrelated because of the extreme effects that surface silanols and chemisorbed water have on structural changes. In fact, full densification of the silica gels, transforming them to a glass, is nearly impossible without dehydration of the surface prior to pore closure. Dehydration, dilation, and contraction of the silica network with adsorption and desorption of water are equally important in forming a stable porous gel mon- olith (type VI) or a fully dense gel3lass monolith (type B. Dehydration A major problem in producing gel-silica optics is removal of gel surface hydroxyl groups and hydrogen- bonded pore water, which give rise to atomic vibrational energy absorption in almost the entire range of ultra- violet to infrared wavelengths (16C-4500 nm) and de- creases the optical applications of silica-gel monoliths. Consequently, to achieve the theoretical optical per- formance of silica, complete dehydration is imperative. Many chlorine compounds-some of these include methylated chlorosilanes, such as CISi(CH,),, C12Si(C- H3)2, Cl3Si(CH3), silica tetrachloride (SiC14), chlorine (C12), and carbon tetrachloride (CC14)-can completely react with surface hydroxyl groups to form hydrochloric a ~ i d , 2 ~ - ~ ~ ~ which then desorbs from the gel body a t a temperature range (400-800 "C) where the pores are still interconnected. In a study by Wang and Hench,52wm carbon tetrachloride was used successfully to achieve complete dehydration of ultrapure gelsilica monoliths. V),52,53,256 Hench and West Y H ti \ Reversible (25°C <-----> 170°C) Figure 36. Physical water decreases and silanol~oups condense in the range of room temperature and 170 O C . 6o To achieve dehydration it is necessary to recognize that "water" is present in two forms: free water within the ultraporous gel structure (i.e., physisorbed water) and hydroxyl groups associated with the gel surface (i.e., chemisorbed water). The amount of physisorbed water adsorbed to the silica particles is directly related to the number of hydroxyl groups existing on the surface of silica. During the 1950s and 19605, researchers YoungY61 Benesi and Jones,"2 Hockey and PethicaYm Kiselev,% and McDonaldB5 contributed much infor- mation regarding the hydration/dehydration charac- teristics of the silica gel/water system, as summarized below: (1) The physisorbed water can be eliminated, and surface silanol (Si-O-H) groups condensed starting a t about 170 "C, as shown in Figure 36.260 (2) The dehydration is completely reversible, up to about 400 "C, as shown in Figure 37.260 Decomposition of organic residuals, up to 400 "C, was also confirmed by using DSC and TGA for TMOS-derived silica gels, as discussed by Wang.2" (3) Above 400 "C, the dehydration process is irre- versible as a result of shrinkage and sintering across pores, as shown in Figure 38.2@' Thus, the amount of existing hydroxyl groups on the gel surface is an inverse function of the temperature of densification. UV-vis- NIR absorption data also show that the reduction of surface hydroxyl groups occurs above 400 "C. (4) Viscous flow occurs above 850 "C with the exact temperature depending on the pore size of a specific gel. The isolated hydroxyl groups on the gel surface react with each other, bringing particles together, thereby eliminating voids within the gel. If surface water is unable to be desorbed prior to pore closure, it is trapped inside the densified gel. The Sol-Gel Process H Figure 37. Surface silanol groups are reversible in the range 17C-400 'Cm H Figure 38. Irreversible elimination of adjacent hydroxyl Young, in his early work,261 found that the decrease in surface area of silica gel a t high temperatures is a function of the time and temperature of the heat treatment. This supports the concept that the sintering mechanism is essentially the result of viscous flow, Chemical Reviews. 1990. VOI. 90. No. 1 59 Tkl- H H u@16 88 nm Figure 39. Reabsorption of physical water below 400 O C W rather than surface diffusion. Impurities (i.e., surface water) effectively lower surface energy and thereby decrease the sintering temperature, presumably by fa- cilitating viscous flow; Phalippou et dm confirmed this point. Hair (see p 87 in ref 268) also proved that heating silica gel in the 170-400 "C range causes reversible dehydration via elimination of surface water and the formation of both single and adjacent surface hydroxyl groups, as illustrated in Figure 37. Hair found that at 400 "C, no more than half of the surface hydroxyl groups had been desorbed and that most of the re- maining surface hydroxyl groups were adjacent to each other and therefore situated for preferential water ad- sorption (Figure 39). He stated that heating the gel above 400 "C causes a drastic, irreversible elimination of adjacent hydroxyl groups, as shown in Figure 38, until a t about 800 "C, only single hydroxyl groups re- main (Figure 40). As the temperature increases, single hydroxyl groups depart from the gel surface until the gel is densified; this occurs in the 850-1000 "C range. However, some single hydroxyl groups are still unable to escape from the gel surface and therefore can con- tribute to foaming of the gel as the temperature in- creases. More importantly, Hair describes2@ that when the silica gel has been completely dehydrated, there are no surface hydroxyl groups to adsorb the free water; in other words, the surface is essentially hydrophobic. Clearly, it is the realization of this critical point that is the focus for making stable monolithic gels. The vibrational overtones and combinations of hy- droxyl groups and their associated molecular water, occurring in the 1251F3000-nm range, have been studied 62 Chemical Reviews, 1990, Vol. 90, No. 1 UV TRANSMISSION Hench and West to be rate-determined by a diffusion process that is probably governed by the adsorption and desorption of chlorine atoms. Susa et a1.256 indicate that reducing the surface area by a presintering process is useful for reducing both the hydroxyl and chlorine content in the densified silica glass. C. Structural Characterization The structure of alkoxide-derived silica gels has been examined in some detail, by using Raman spectroscopy, from the dry gel through to the fully dense amorphous Si02.326-330 Gottardi et al.326 report the Raman spectra of a silica gel heated from 140 to 800 " C , showing the interrelated changes in intensity of the SiOH peaks a t 980 and 3750 cm-', the cyclotrisiloxane D2 and cyclo- tetrasiloxane D, "defect'! peaks, a t 495 and 605 cm-l, respectively, and the main Si02 structural vibrations at 440, 800, 1060, and 1195 cm-l. These results were reproduced by Krol et a1.,3271328 confirming the D1 and D2 peak assignments to be four- and three-membered siloxane rings respectively, and the formation of large concentrations of cyclotrisiloxane D2 rings on the in- ternal pore surface as the hydroxyl concentration and the internal pore surface area decrease with increasing temperature. The three-membered D2 rings are strained in comparison to the four-membered D, rings and consequently can form only above 250 "C on the surface of the gels via the condensation of adjacent isolated surface silanols. In contrast the four-membered D, rings form initially in the sol stage and are retained until the gel is dense.282 The existence of another peak has been postulated by Mulder et al.329 to explain the behavior of the peak at 490 cm-' between 100 and 800 "C. He proposes that the symmetric stretch vibration of network oxygen at- oms coupled to a network-terminating SiOH group gives rise to a strongly polarized Raman peak a t 490 cm-', which he called the Do peak and which is transformed to the D, peak as the condensation reaction goes to completion. However, Brinker et a1.282 dispute this interpretation of the 495-cm-' peak behavior with tem- perature. Recent analysis of the structure of silica gels using low-frequency (0-200 cm-l) Raman scattering has been interpreted by assuming that the gels are fractal. This infers that the scattering was characteristic of the scattering from fractons,m,331 where fractons are defined as phonons with vibrational modes localized by the fractal nature of the structure. Most of this work has been done on hypercritically dried aerogels. Raman scattering from gels involves a large contribution due to the tail of the Rayleigh scattering peak. The inten- sity of this peak is proportional to the heterogeneous density fluctuations, and therefore in porous gels it can be up to 8 orders of magnitude more intense than the Raman peaks. Consequently, this tail is removed by thermal reduction using Bose-Einstein statistics, and the reduced Raman spectra is then analyzed.330 Con- sequently, the reduced data must be interpreted cau- tiously due to the magnitude of the thermal correction. D. Stralned Defects Brinker et a1.279-283 have used solid-state 29Si magic- angle spinning NMR, XPS, 'H cross-polarization MASS NMR, and Raman spectroscopy to investigate the local 100 7. , GELSIL 7 5 % - 50% - 0 INCREASING OH CONCENTRATION 794a CORNING DYNASIL WAVELENGTH O U A N N M BASED QUANTUM BASED THEORETICAL RING OF FIVE 6 MOLE % OH SlUCA TETRAHEDRA IN SIUCA Figure 45. Improvements in UV transmission of alkoxide gel- silicas with time compared with quantum mechanics predictions of UV cutoff ~ a v e l e n g t h . ~ ~ Carbon tetrachloride treated samples were prepared at 850,950, 1050, and 1150 "C, and their characteristic UV-vis-NIR absorption spectra compared, as shown in Figures 43 and 44 (from refs 260 and 266). Absorp- tion peaks were visible a t 2890.1, 2768.9,2698.9,2668.8, 2207.5, and 1897.6 nm for the 850 "C sample and a t 2884.3, 2765.4, 2698.3,2669.4,2207.5, and 1897.6 nm for the 950 "C sample. Stretching vibrations of the adsorbed physical water gives rise to typical broad absorption peaks at 2890.1 and 2884.3 nm, which are shifted from 2919.70 nm (YJ within a broad range from 2700 to 3200 nm. Absorption peaks a t 2698.3 and 2698.9 nm are suggested260p266 to be the result of the stretching vibrations of hydrogen- oxygen bonds of adjacent silanol groups. The 2768.9 and 2765.4-nm peaks are proposedmsm to be the result of stretching of the hydrogen bonds to the neighboring silanol oxygens, as shown in Figure 37. These two kinds of absorption peaks in general cannot be distinguished and thus form the combined broad peak a t 2732.24 nm, which is observed by many r e ~ e a r ~ h e r ~ . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ The sharp peaks a t 2668.8 and 2669.4 nm are identified to be caused by vibrating surface isolated silanol groups (Le., free hydroxyl groups). The intensity of all absorption peaks decreases as the temperature increases. The spectrum from the 1050 "C sample shows only one peak, as shown in Figure 44,260 occurring at 2668.8 nm ( v J , which is caused by isolated hydroxyl groups. The sample heated to 1150 "C has a spectrum in which the water peaks have been elimi- nated, as shown in Figures 44 and 45 (from ref 260 and 53). The absorption loss due to water approaches zero as no water or hydroxyl absorption peaks are present at any wavelength. The quality of optical transmittance of this sample is significantly higher than that of tra- ditional fused silica glass and equivalent to that of op- tical fibers used in communication systems. One of the complications associated with use of chlorine compounds in the dehydration of silica gels is the incorporation of chlorine ions in the densified gel-glass structure. Susa et al.256 describe a dechlori- nation treatment using an oxygen atmosphere a t 1000-1100 "C after chlorination a t 800 "C to remove the hydroxyl ions. The dechlorination reaction seems The Sol-Gel Process 800 7 600 - 400 - h ' 2 0 0 - 0 - 0 - \ -200- _I ___ - 4--- - I - R.1.21 NM - Rz4 .18NM - R=8.98NM 2.15 R = HYDRAULIC PORE RADIUS 2.10 -."" . 2 0 0 400 600 8 0 0 1000 1 2 0 0 TEMPERATURE ["C] (HELD FOR 12 HRS) Figure 46. Dependence of the structural density p s (g/cm3) of alkoxide-derived porous silica gels, as a function of sintering temperature, for three different average hydraulic pore radii, R (nanometers). silicon environment and siloxane ring vibrations in amorphous alkoxide (TEOS) derived silica gels. Their results relate the 608-cm-' Raman "defect" mode in amorphous Si02 with reduced Si-0-Si bond angles in- dicative of strained three-membered rings of silicate tetrahedra.282g283 They showB3 that dehydroxylation of the silica surface results in cyclotrisiloxane species that have altered acid-base characteristics due to the strained bonds. Their XPS experimentsm indicate that the expected 0.35-eV shifts in silicon and 2p oxygen 1s binding energies which are due to the reduced bond angles are hidden within broad peaks due to the re- maining hydroxyls. Brinker et al. also observe addi- tional silicon 2p oxygen 1s and carbon peaks which are postulated to result from preferential absorption of extrinsic 1s carbon-containing species on sites with enhanced acid-base properties. Molecular orbital calculations by O'Keefe and Gibbs2% have established that the optimized geometry of the cyclic trisiloxane molecule, H6Si303, is planar with D3h symmetry with a bond angle 4 = 136.7", which is 10" less than the 147" angle characteristic of traditional vitreous silica. Spectroscopic investigations of isolated model molecules by Galeener285 show that the symmetric oxygen ring breathing vibration occurs at 586 cm-l, which is close to the D2 Raman bond observed for gels and glasses.286 The change in structural density of alkoxide-derived silica gels during thermal processing is apparently caused by a t least four interrelated mechanisms. These mechanisms include the elimination of metastable three-membered rings (see above), the loss of hydroxyls, the loss of organic groups, and the relaxation of the Si02 structure. Figure 46, from Wallace and H e n ~ h , ~ ~ shows the structural density ps (g/cm3) of a series of silica gel powders, held for 12 h at each temperature with average hydraulic pore radii R of 1.21, 4.18, and 8.98 nm. The true or structural density was measured by using He pycnometry. The structural density ps starts out below that for amorphous silica (p , = 2.20 g/cm3) and goes through a maximum of about 2.30 g/cm3 before equilibrating a t full densification at about 2.22 g/cm3. The average standard deviation of the measurements is about 0.004 g/cm3. The observed variation of ps with temperature is potentially due to a number of effects, including reducing the surface alkoxide and hydroxyl 0 r w -400 n -800 6 0 200 400 600 Temperature ("C) Figure 47. Expansion and contraction of 950 "C stabilized gel-silica cycled to 600 0C.278 -5001 I - I I 9 I - 0 100 200 300 400 500 TEMPERATURE ("C) Figure 48. Repeated cycling of gel-silica above 250 0C,278 concentration, formation and elimination the metasta- ble three- and four-membered siloxane ring surface defects (D2 and D1, respectively, in the Raman spec- troscopy nomenclature), structural relaxation, comple- tion of condensation reactions, and viscous flow. Con- siderable additional research is required to isolate each of these contributions to the observed changes in structural density of the gels. E. Dilation of Sol-Gel Silica Monoliths with Adsor bed Water The expansion of porous gel-silica monoliths has been studied by using a dual pushrod Theta dilatometer.27s The expansion and contraction showed a hysteresis with heating and cooling. Figure 47 shows this hysteresis for a sample stabilized to 950 "C. As long as the sample was cycled below approximately 500 "C, there was no hysteresis and the monolith appeared to be thermally stable.278 If thermal cycling is performed on the gel monolith, the hysteresis is reduced significantly. Figure 48 shows the thermal cycles performed on a porous gel monolith between 250 and 400 "C before cooling to room tem- perature. The material shrinks a lot initially, but during thermal cycling the expansion behavior is totally re- versible. It is postulated that the expansion of porous gel-silica upon cooling below 250 "C was due to ab- sorption of water onto the pore walls of the material. This was tested by running diatometry and thermo- gravimetric analysis (TGA) under an ambient atmo- sphere.278 Figure 49 shows expansion in the dilatometer over 23 h at 23 "C due to water absorption onto the pore surfaces of the gel. Thus, adsorption of water into the 64 Chemical Reviews, 1990, Vol. 90, No. 1 Hench and West TABLE X. Silica Dilation diagonals Si-Si dist, A av neighbor water av expansion INDO 4 fold ring energy, au (1)-(14) (6)-(7) Si-Si dist, 8, content, wt Yo UIL, PPm without H,O -223.4 4.6 4.5 3.2 0 0 with H,O -241.4 5.2 4.0 35c r-- -50 C - r - 7 ~- ~- T - - T 7 - - - -T -1 0 4 0 12 16 2 C 2 4 -IME (hours) Figure 49. Expansion of porous gel-silica a t room temperature over 24-h in ambient air. porous sol-gel silica appears to dilate the gel structure. F. Quantum Calculations of Water Adsorption onto Sol-Gel Silica The INDO models presented earlierlg39lg4 attempted to show the energetics of rings and chains of silica tetrahedra during the sol to gel transition. After con- densation is complete and thermal processing has oc- curred, the sol-gel silica monoliths should be primarily made up of rings. There is roughly an equal distribu- tion of 4-fold, 5-fold, 6-fold, and 7-fold rings of silica tetrahedra in vitreous silica and equivalent structures are believed to be present in silica gels (Klemperer et aLg7). The 4-fold ring shown in Figure 50 shows the structure selected by West et a1.288 to study the theo- retical effect of water on silica rings. The water was hydrogen bonded to the silica cluster as predicted by T a k a h a ~ h i . ~ ~ ~ Intermediate neglect of differential overlap (INDO) molecular orbital theory developed by Zerner et was used to optimize the structure in Figure 50. The 4-fold ring was geometrically optimized with and without the adsorbed water molecule. Table X shows the results of the calculations for the dilation of the 4-fold silica ring. The distances between the diagonal silicon atoms are shown. The ring without water is uniform. However, the ring with the water adsorbed is elongated along the axis with the water. Also, the average silicon-silicon distance for neighboring atoms increases. In an amorphous structure there should generally be a random orientation of the structural elongation. Some orientation can be imposed on an amorphous material through fiber drawing or spin casting. In gel monoliths with random structures some of the water-induced ex- pansion will occur in regions of the glass where con- traction of the rings can compensate, thereby inducing strain. However, on the average there is predicted to be a small expansion when the water is bonded to the structure. ci ( 2 7 ) W a t e r H ( 26: Figure 50. The 4-fold silica structure with one absorbed water molecule.251 TABLE XI water water content. wt 70 ALIL, rmm content, wt % U J L , ppm 5.8 836 0.725 104 2.9 418 0.36 52 1.45 209 The average bond length between neighboring silicon atoms increases with the bonding of water. This in- crease can be used to estimate the expansion and con- traction ( U / L ) of porous sol-gel silica associated with adsorption and desorption of water. When the porous material is heated, there are two competing contribu- tions to the observed thermal dilation: (1) the uniform increase in dimension due to thermal expansion of the silica structure; (2) a decrease in dimension due to contraction resulting from desorption of water from the surface of the pores. Upon cooling, the reverse occurs, i.e., there is an intrinsic contraction of the structural network and an extrinsic expansion as water is adsorbed (Figure 49). If the effect is linear, then the calculated expansion is shown in Table XI. For the observed expansion, we have ( u / L ) o b s = (AL/L)H,O + ( u / L ) i n t r j n s i c (38) then, solving for the extrinsic effect of water on heating the sample: (BL/L)H,O = ( u / L ) o b s - ( u / L ) i n t r i n s i c (39) where the thermal expansion of the material can be calculated from Figure 47, shown earlier. Thus ( u / L ) i n t r i n s i c = 60 P P ~ (40) with ( U / L ) O , S = 200 PPm (41) Then (WL)I-I,O = 140 PPm (42) The SOl-Gel Rocess 0 0 200 400 600 800 1000 1200 TEMPERATURE (C) Figure 55. Variation of the number of branches (B.) BS a function of temperature for structures of 24- and 64-A pore diameter."' of the third stage of densification Vasconcelos shows that @ is given by B(G,=O) = 1 - (2/CN0) (46) Application of the cylindrical topological model to structures of different pore sizes (24- and 64-.& average diameter) is shown in Figure 55. While B, for the 24-.& structures decreases sharply after about 800 "C, B, for the 64-A structure remains roughly the same (in fact it increases slightly) over a much broader temperature range. An explanation for the apparently larger thermal stability of the large pore size structure is the smaller driving force for sintering associated with the smaller pore-solid surface area present in the large-pore structure. such as those studied by Rhines and DeHoff:Ism show similar paths of topological evolution during densification (particu- larly a decrease in G. as V, decreases), indicating the broad spectrum of applications of the topological con- cepts. The path of microstructural evolution described for silica gel monoliths is similar to the path associated with the sintering of larger ~tructures.2~' Thus, application of topological modeling to the densification of sol-gel-derived nanometer-scale struc- tures reveals the same principles as determined for the sintering of micrometer to millimeter scale powder structures. As shown in the next section, the topological evolution of the gel structure can be related to physical properties and presents potentially useful information that is complementary to traditional metric parameters. X. Physical Propertes There are relatively few papers .describing the ther- mal, mechanical, and optical properties of gel-derived monoliths. This is because of the difficulty of producing large stable structures, as reviewed in the previous sections. During 1988-89, processing optimization has been achieved for the production of gel-derived silica optical components. Hench et al?2.53 described the processing and properties of these new materials, termed type V (fully dense) gel-silica and type VI (optically transparent porous gel-silica). The properties of types V and VI are compared with commercial fused quartz optics (types I and 11) and synthetic fused silica optics (types 111 and IV)?2 T y p V gelsilica has excellent transmission from 160 to 4200 nm with no OH absorption peaks. As shown in Figure 45, the UV cutoff is shifted to lower wave- numbers by removal of OH from the gel glass. Also, Much larger structures (G, = 106 Figure 56. Sol-gel silica monoliths in the (A) dry state, (B) stabilized state (porous type VI), and (C) fully dense state (type w . 5 3 quantum calculations, discussed earlier, predict this effect.lq3 Other physical properties and structural character- istics of type V gel-silica are similar to high-grade fused silica but offer the advantages of near net-shape casting, including internal cavities, and a lower coefficient of thermal expansion of 0.2 X lo6 cm/cm compared with 0.55 X lo6 Optically transparent porous gel silica (type VI) has a UV cutoff ranging from 250 to 300 nm. Type VI gel-silica optics has a density as low as 60% of types I-V silica and can be impregnated with up to 30-4070 by volume of a second-phase opti- cally active organic or inorganic compound. Photo- graphs of a dried alkoxide silica gel monolith, a type VI porous Gelsil sample and a fully dense type V G e l d sample are shown in Figure 56. Shoup and Hagy has shown that the colloidal method of making reflective silica opticsm (method 1) yields a different thermal expansion behavior than types 1-111 vitreous silica, presumably due to the rapid quenching of the gel-glasses from 1720 oC."2 Bachman et aLS3 describe the use of centrifugal de- position of 12-40-nm colloidal silica powders to produce synthetic silica t u b e used in the manufacture of optical telecommunication fibers. They report optical losses of a13w = 0.97 dB/km and d5% = 0.77 dB/km for o p tical fibers made by using the tubes. A Rayleigh scattering coefficient of aR = 1.1 dB/(km pm') was measured for the bulk sintered tubes, equivalent to that of the single-mode fibers. One of the main advantages of the sol-gel technique was very high accuracies (*0.05%) for the diameter, cross-sectional area, and wall thickness of the tubes. Mechanical properties of the type VI porous gel-silica monoliths have been determined by Vasconcelos et al.8q.251 and related to the topological and metric fea- tures. The variation of flexural strength as a function of V, shows relatively scattered data (Figure 57a). The flexural strength correlates better with @, as shown in Figure 57b. for the topological cylindrical model dis- cussed in the Densification section. The points in Figure 57 represent an average; the total number of mechanical tests performed is 27. The true density data are incorporated into the topological modeling. The true density of some selected samples (of 24-.& pore diameter) is as follows: dried, 2.10 g/cm3; 800 O C , 2.31 g/cm3; 1150 "C, 2.20 g/cm3. Additional details of ultrastructure-poroperty cor- relations of various gelsilica monoliths are to be pub- 68 Chemical Reviews, 1990, Vol. 90, No. 1 Hench and West n 5. E a z W [I: c v) -I [I: 3 x W A U. a 0 4 0 0 42 0 44 0 46 0.48 0 50 v v 60 5 0 4 0 30 20 i n fl Figure 57. Variation of the flexural strength (a) as a function of the volume fraction of pores (V,) and (b) as a function of the topological index p.251 lished later by Hench and V a s c o n ~ e l o s . ~ ~ ~ X I . Conclusions The goal of sol-gel processing is to control the structure of a material on a nanometer scale from the earliest stages of processing. For pure silica powders, fibers, and even monoliths this goal has been achieved. The potential of improved properties due to ultra- structural processing, control of higher purity, and greater homogeneity has been realized. Other engi- neering advantages of the lower temperature chemically based sol-gel processing such as net-shape casting, fiber pulling, and film coating have also reached economic potential. Advances in understanding the science of sol-gel processing are less conclusive. General aspects of the chemistry of each of the seven sol-gel process steps are established. However, understanding of the molecular reaction mechanisms and the thermodynamics and kinetics of sol-gel systems is meager. Many studies involve model systems that yield self-consistent data but may not necessarily apply to processing formulas that yield useful materials. Only a few studies use multiple experimental methods to confirm reaction mechanisms or determine kinetics. Likewise, there are few investigations of the interrelationships between the seven processing steps. For example, many investiga- tors have shown that base catalysis yields gels with a coarser texture than acid catalysis. However, there is little understanding as to how the differences in gel texture influences aging, drying, stabilization, or den- sification of the gels. Systematic studies on multicom- ponent gel systems are especially rare. A major difficulty in developing molecular level un- derstanding of the sol-gel processing is the extremely small scale of the structures involved. After gelation occurs, and often even at t > 0.3-0.5tg, the substance usually must be treated analytically as a solid. Since the solid phase a t t , can be as little as 1-1070 of the mass of the object, a cross section of the solid web is only a few molecules wide, but the length of the mo- lecular chains extend throughout the object with an enormous number and complexity of interconnections. The molecular structure of the liquid phase in these gels is as important as the structure of the solid phase. However, the liquid characteristics deviate from clas- sical liquids in many ways. The concept of phase boundary is stretched to the quantum mechanical limit. Consequently, it is quite likely that quantum mechan- ical based models are much more likely to yield the next level of understanding of sol-gel processes rather than a macroscopic fractal approach. In some ways it may be useful to think of sol-gel science in terms of a few fundamental questions, i.e., How does the gel structure form? How does the structure evolve? How does it interact with its envi- ronment? How does it collapse? These questions parallel the fundamental questions in the biological sciences. It is fitting that they do, for silicon is the fiith most abundant element in the biosphere, and life forms with hydrated silicon exoskeletons, diatoms, are re- sponsible for more than half of the carbon and nitrogen biochemical fixation that occurs annually on the earth.334 The biological silicon-based structures of both plants and animals form a t low temperatures and with elegant highly repetitive ultrastructures. 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