Recent progress in drying of gels

IOURNAL

Journal of Non-Crystalline Solids 147&148 (1992) 363-374 North-Holland

OF

NON-CRYSTALLINE SOLIDS

Recent progress in drying of gels George W. Scherer Du Pont Co., Experimental Station 356/384, Wilmington, DE 19880, USA

The status of the theory and practice of drying is reviewed, with emphasis on work published in the last few years. Advances have been made in (1) the theory of drying stresses and the causes of cracking, (2) detailed and precise observations of phenomenology and drying, and (3) preparation of monolithic gels of commercial interest.

1. Introduction The difficulty of drying gels without cracking has prevented the economical production of large objects (monoliths) and thick films by sol-gel processing, so there is a strong incentive to improve our understanding of the physics of drying. In recent years, there has been some progress in the theory of stress development and cracking of gels. New techniques have been employed to obtain more detailed information about the kinetics of the process, and the physical and chemical changes that occur during drying. Some advances have also been made in the preparation of relatively large objects at reasonable rates. This review briefly describes the progress in the theory, phenomenology, and practice of drying, and suggests some topics requiring further study. To put these advances in perspective, we begin with a discussion of the origin of drying stresses and cracking.

2. Theory The initial period of drying is called the constant rate period (CRP), because the rate of evaporation of liquid is nearly constant. Evaporation gives rise to capillary tension in the liquid, P, and that tension is balanced by compressive stresses on the solid phase, which cause it to

contract. During the CRP, the volumetric shrinkage of the gel is equal to the volume of liquid that evaporates, so the pores remain full of liquid. As long as the network remains compliant, P remains small (because little force is required to produce a contraction rate equal to the evaporation rate). As the gel shrinks it becomes increasingly rigid and resistant to the compressive stresses exerted on it by the liquid, so P must increase. In some systems, the stiffness of the network may be strongly influenced by van der Waals and electrostatic forces [1]; in silicates it depends principally on condensation reactions that form new bridging bonds. Shrinkage stops at the 'critical point' when the gel network becomes stiff enough to resist the compressive stresses imposed by capillary forces; further evaporation forces the liquid/vapor interface to move into the pores of the gel. On a macroscopic scale, the interface (or, 'drying front') may be smooth or fractally rough, depending on the pore structure and drying rate [2,3]. When the front is rough, islands of saturated pores may be large enough to scatter light, making the gel opalescent or opaque; once all of the liquid has evaporated, the dry gel becomes clear again. The maximum capillary tension occurs at the critical point, when the menisci enter the pores, and the radius of curvature of the meniscus, rm, is related to the pore radius, rv, by r m = - r p / cos0, where 0 is the contact angle. Then the

0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

G.W. Scherer / Dryingof gels

364

tension at the drying surface is given by Laplace's equation: Pm,x -

2YLv

-rm

2YLv COS0 -

Yp

,

(1)

where 7LV is the l i q u i d / v a p o r interfacial energy. Very little shrinkage occurs after the menisci move into the pores, so the pore size measured in a dry gel is established by the forces exerted at the critical point. In very compliant materials, the network cannot resist the capillary forces (which increase continuously as rp decreases), so there is no critical point, and the pores collapse completely [4]. The stresses that cause shrinkage, warping, and cracking of the gel network during drying result from the capillary tension in the liquid. If P were uniform (i.e., hydrostatic), the solid network would be uniformly compressed, and there would be no warping or cracking. Instead, however, a pressure gradient, VP, develops within the drying body, leading to non-uniform contraction of the network. The theory of drying stresses has been discussed in detail in recent publications [5-7], so only the essential points will be repeated here. The liquid moves through a porous material, such as a gel, in response to a pressure gradient according to Darcy's law: D J = --VP, "OL

O'x~"

C {L~TLVEI N I 3D ] '

(4)

where CN=(1-2N)/(1-N), and N is the Poisson's ratio of the network; recent studies [9] indicate that N ~ 0.2, so C N ~ 0.75. Thus, the stress increases in proportion to the thickness of the gel; a similar expression describes the circumferential stress in a cylinder or sphere. Equation (4) shows that the total stress goes to zero as the evaporation rate does, so the drying stresses can be very small, even though the capillary tension in gels can be enormous (/°max --" 100-250 MPa at the critical point, because of the small pore sizes [6]). The explanation for this apparent contradiction is that the stress results from the gradient in P, not the absolute value of P, and the gradient is small when the evaporation occurs slowly. The total stress at the drying surface at the critical point is related to the tension in the liquid by ([6], p. 486) *

(2)

where J is the flux of liquid, D is the permeability, and ~TL is the viscosity of the liquid; P is defined as a stress, rather than pressure, so it is positive when tensile. Diffusion may be important if the pores contain a solution of liquids whose intrinsic diffusion coefficients differ greatly [8]; generally, however, diffusion is expected to be less important than flow. During the CRP, the flux to the surface of the drying body matches the evaporation rate, l)'z, so eq. (2) requires VP[surface =

ability of gels is very small compared with that of ordinary ceramics; the smallness of D (in addition to low strength) is why slower evaporation rates must be used for gels than for conventional ceramics. For a plate of gel (with thickness 2 L ) dried at a moderate evaporation rate, the total stress at the surface is [5]

"qL~ZE/D.

(3)

Thus the gradient in tension that causes damage to the gel is proportional to the evaporation rate (so slower drying is safer), and is inversely proportional to the permeability. Since D is related to the square of the pore diameter, the perme-

O'x=

C N ( L2"0L ] 3----D--K~G ] Vmax ~

(5)

where K G is the bulk viscosity of the network; this approximation applies when the quantity in parentheses is < 1. From eqs. (4) and (5), we find that the critical point occurs when /°max =

KGG/L" I)E/3L is the

(6)

Since volumetric shrinkage rate of the gel, eq. (6) states that the capillary tension is equal to the stress needed to deform the network at such a rate that the pores remain full liquid. When K G becomes so large (as a result of stiffening during shrinkage) that the required tension * Here we do not use the approximation N-~-0, C N = 1 employed in ref. [6].

365

G.W. Scherer /Drying of gels

is > Pmax, t h e n t h e C R P is over a n d t h e m e n i s c u s moves into the p o r e s . If the n e t w o r k is very c o m p l i a n t (so t h a t t h e q u a n t i t y in p a r e n t h e s e s in eq. (5) is >> 1), t h e n a d i f f e r e n t a p p r o x i m a t i o n applies: o'× ~ CNI)E~/HGrlL/D ,

(7)

w h e r e H o is the l o n g i t u d i n a l viscosity of the gel, HG = 3 K o ( 1 - N ) / ( 1 + N ) . In this case, t h e gel m a y s h r i n k Until t h e p o r e s c o l l a p s e c o m p l e t e l y , a n d the stress will n e v e r b e large b e c a u s e o f t h e small v a l u e of H o. I n d e e d , if t h e p o r o s i t y goes to zero, t h e n t h e n e t w o r k b e c o m e s i n c o m p r e s s i b l e , so N ~ 0.5 a n d C N + 0, a n d t h e stress d e c r e a s e s accordingly. T h e t o t a l stress is t h e sum of t h e forces on the n e t w o r k a n d on t h e liquid, so o-x can be positive (tensile) w h e n t h e stress o n t h e n e t w o r k itself, ~×, is compressive. T h e s e q u a n t i t i e s a r e r e l a t e d by [5,61 * * o-x = ~x + (1 - p ) P

,

a X

Fig. 1. The curvature of the meniscus in a crack, rm, depends on the capillary tension in the liquid, P, according to Laplace's equation, P = 2 T L v / r m . If P is large enough that r m = rc, where r e is the radius of curvature of the crack tip, then the crack is empty and the total stress, %, acts on the faces of the crack. The stress, ~rc, at the tip of a crack of length c is = 2AG ct/7/77, where A -~ 1 [10].

(8)

w h e r e p is the r e l a t i v e d e n s i t y of (volume f r a c t i o n of solids in) t h e gel. O n e might r e a s o n a b l y expect t h a t t h e stresses on t h e n e t w o r k w o u l d cause f r a c t u r e , b u t t h e s i t u a t i o n is n o t so simple. It is t h e total stress t h a t acts on t h e faces of a flaw, such as t h a t shown in fig. 1, so t h e c r a c k will o p e n w h e n e v e r o-x > 0. F o r large e n o u g h flaws, t h e crack o p e n i n g will cause s t r e t c h i n g o f the solid p h a s e at t h e c r a c k tip, r e v e r s i n g the local stress s t a t e from c o m p r e s s i v e (Sx < 0) to tensile, a n d allowing t h e c r a c k to p r o p a g a t e . T h e stress conc e n t r a t e d at the c r a c k tip is %= 2A% c~,

X

(9)

w h e r e A is a c o n s t a n t ( A ~ 1), c is t h e l e n g t h o f t h e crack, a n d ro is t h e r a d i u s o f t h e c r a c k tip.

** In my earlier publications in this journal [JNCS 87 (1986) 199-225; 92 (1987) 375-382], the distinction between total and network stresses was not handled correctly. The analysis was corrected in ref. [5], and is employed in later publications (e.g,, refs. [6-8], and analyses of syneresis, JNCS 108 (1989) 18-27, and permeability, JNCS 113 (1989) 107-118), but the terminology is sometimes careless. That is, % is sometimes improperly called the 'stress on the network', in view of its role in crack propagation.

T h e c r a c k will p r o p a g a t e w h e n [10] ( 2 / ~ - ~ ) K i c - 4(~rc % > 2 A ~ - - ~/7~ '

(10)

w h e r e K~c is t h e critical stress intensity. Since the t e r m s in r c a r e small, this r e d u c e s to the usual f r a c t u r e criterion, A~,~

> K~.

(IX)

T h u s it is t h e total stress t h a t controls f r a c t u r e d u r i n g drying. W h e n a gel is d e p o s i t e d on a rigid substrate, the n e t w o r k is p r e v e n t e d f r o m c o n t r a c t i n g in t h e p l a n e o f the s u b s t r a t e , a n d the total stress is very n e a r l y e q u a l to t h e t e n s i o n in t h e liquid ( G = P ) [6]. This is such a large stress t h a t cracking o f films w o u l d s e e m to be inevitable. H o w e v e r , it is c o m m o n l y o b s e r v e d t h a t films can easily b e p r e p a r e d with no c o n t r o l over the drying rate, if t h e thickness of t h e film is b e l o w s o m e critical value, hc; typically, hc = 0.5 - 1 txm [6]. T h e r e a s o n for this s u r p r i s i n g b e h a v i o r is t h a t very thin films do n o t r e l e a s e e n o u g h e n e r g y w h e n t h e y c r a c k to c o m p e n s a t e for the e n e r g y e x p e n d e d in m e c h a n i -

366

G.W. Scherer / Drying of gels

cal damage at the crack tip. For the propagation of cracks [11] or the growth of pinholes [12], the critical thickness is given by h e = (K~c/~xS?) 2,

(12)

where g2 is a function that depends on the ratio of the elastic moduli of the film and substrate; for the small values of this ratio expected for gel films, g2 ~ 1. The stresses created by drying are macroscopic, in the sense that the pressure gradient extends through the thickness of the body. If the stresses were localized on the scale of the pores, the body would crumble to dust as the drying front advanced; instead, drying bodies often crack into only two or three pieces, because the crack propagation is driven by a stress field that extends across the body. Warping during drying is another clear indication of the macroscopic nature of the stresses. On the other hand, the flaws that lead to failure might be created by local stresses [13] (resulting, for example, from nonuniform pore sizes [14]), then propagated by the macroscopic stresses.

3. Phenomenology 3.1. Stages o f drying

If the pores of a gel contain a pure liquid (e.g., water), the rate of evaporation is constant until the critical point is reached [6,15]. However, most alkoxide-derived gels contain a mixture of water and alcohol, so the composition of the vapor changes with time, and a CRP may not be observed. Kawaguchi et al. [16] found that the evaporation rate and vapor composition were initially constant, and the slope of a plot of gel mass versus volume was equal to the density of the pore liquid, OK" Later, the evaporation rate slowed and the w a t e r / e t h a n o l ratio in the vapor increased; curiously, the composition of the vapor was that of the pore liquid ( ~ 89 wt% ethanol), not the azeotrope (95.5 wt% [17]). Wilson [18] found a continuously decreasing evaporation rate (i.e., no CRP) in his silica gels. This was attributed [18,19] to the depression of the vapor

pressure by capillary tension, but that cannot be correct, because the capillary forces are too small at the early stages of drying to have a noticeable effect; the variation in VE must result from composition change. (The evaporation rate from a gel cannot be expected to equal that from a dish containing a solution of the same composition as the pore liquid, because there is no convection within the gel; the composition in the dish is homogenized by convection, but only diffusion operates within the pore liquid. §) If a gel is partially dried (i.e., before the critical point), then immersed in liquid, it expands [16]. This is expected, because the l i q u i d / v a p o r interface and the corresponding capillary forces are eliminated, so the elastic strains stored in the network are released; in addition, there may be a chemical reaction, as the amount of expansion was found to be greater in water than in ethanol. A similar, but smaller, effect is seen beyond the critical point: when the last of the liquid evaporates, so that the volume of liquid exerting capillary forces on the network decreases, the compressive forces on the network decrease and the gel expands by ~ 1% linearly [20]. Kawaguchi et al. [16] examined the dilatation of a gel during the last stage of drying as a function of the e t h a n o l / w a t e r ratio in the pore liquid. They found that t h e total shrinkage increased with water content (presumably because of the higher surface tension of water), but the springback decreased (probably because irreversible viscous deformation is easier in the presence of water [9]). Measurements of the weight and volume of • drying gels show that the pores remain full of liquid until shrinkage stops [16,20]. Recently the same observation has been made using magnetic resonance imaging [21]. As the l i q u i d / v a p o r interface recedes into the pores, opacity may occur as light scatters from isolated pockets of liquidfilled pores. Wilson [18] observed an opaque transition region between the fully saturated and fully dried parts of the gel, as indicated schematically i n f i g . 2. § Note that movement of the liquid relative to the network occurs by hydrodynamicflow (except in certain cases. [8]), but movement within the liquid phase occurs by diffusion.

G.W. Scherer / Drying of gels

367

Pro~e

II

Section

II

I

I I

Beginning

I

I

I

Late middie

I

End

Drying front leading edge Drying front trailing edge

Transparent

Opaque

Fig. 2. Schematic illustration of opaque region in drying gel disk, seen from top (profile) and in cross-section. (From ref. [18].)

Once the gel is fully dried, it tends to crack on :e-wetting. This phenomenon has been systematically studied by Adachi and Sakka [22-24]. The pore liquid in their gels at the last stage of drying was dimethyl formamide (DMF), and they found that the gels could be rewet safely with liquids having a surface tension, 7LV, less than or equal to that of DMF; liquids with higher YLV caused cracking. Damage results from contraction of the surface of the body relative to the interior as liquid condenses in, or flows into, surface pores. Some gels are so compliant that the pores collapse completely during drying. This has been observed in certain acid-catalyzed silica films [25], in which the silicate polymers are expected to be relatively lightly crosslinked; in sols at higher pH, the silicate polymers are more robust, and the films made from such sols are highly porous. Pore collapse is also observed in gels containing 47 A120 3 • 53 SiO 2 (by weight), if the pore liquid is mostly water [26]; remarkably, compositions differing only slight in alumina content retain open pores and high surface areas [27]. Presumably there is an anomaly in the mechanical properties of gels at this composition, but this has not yet been investigated.

3.2. Structural euolution A novel method for characterizing the pore structure of saturated gels is nuclear magnetic resonance (NMR) [28]. Since the mobility is different for solvent molecules near the wall of a pore and for those in bulk liquid, an analysis of the kinetics of relaxation of the magnetization permits calculation of the surface-to-volume ratio of the pore space in the gel; the hydrodynamic radius ( = ratio of pore volume to surface area) is then reported as the apparent pore size. This technique reveals that the surface area of the network drops rather suddenly during the last stage of drying [29], presumably as a result of the high capillary stresses generated at that time. Another method of microstructural characterization is a calorimetric technique called thermoporometry [30,31]. This method depends on the fact that the pore liquid freezes at a lower temperature than bulk liquid, because of the curvature imposed on the tiquid)/crystal interface by the pore wall. Thermoporometry directly measures the size and volume distribution of mesopores (radii of 1-30 nm); liquid in smaller pores (micropores) does not freeze [30], and liquid in

368

G.W. Scherer /Drying of gels

larger pores (macropores) freezes too close to the normal melting point, Tin, for the undercooling to be accurately determined. However, the volume of macropores can be determined indirectly by comparing the amount of liquid that freezes at Tm with the known amount of bulk liquid outside the gel sample. In that way, it has been shown [32] that both acid- and base-catalyzed silica gels contain considerable volumes of macropores; indeed, it is well known that such pores exist in aerogels made by supercritical extraction of the pore liquid [33,34]. In the supercritical state, there is no liquid/vapor interface, so there is no capillary pressure [35]; shrinkage occurs only as a result of chemical reactions, not drying stresses [36]. Nevertheless, thermoporometry reveals that those processes can substantially reduce the macropore volume and virtually eliminate micropores during supercritical drying [32]. Kawaguchi et al. [16] found that macropores were partially collapsed during evaporative drying of gels if the pore liquid was pure ethanol, and were completely collapsed if it was water; this difference is expected, because 7LV is higher for water than for ethanol.

3.3. Structure/property relations With regard to avoiding cracking, the most important mechanical property of the gel is the critical stress intensity, Kic. Unfortunately, however, there has only been a single report of measurement of that quantity for a wet gel [37]. By contrast, there have been many studies of the modulus of rupture and elastic moduli of gels. It has been shown that silica gels are viscoelastic when the pore liquid is a w a t e r / a l c o h o l solution [38]; the relaxation process is assumed to result from chemical attack by water on strained siloxane bonds. When the pore liquid is replaced by pure alcohol, syneresis is arrested [39] and so is viscoelastic load relaxation [9]. The elastic shear modulus of the network, G p , increases rapidly as the gel contracts, and the relation between modulus and density is only weakly dependent on the means used to produce the shrinkage (e.g., aging in various liquids or partial drying) [40]. Poisson's ratio for a cellular material, such as a gel, is

1000

Kp = 0.4 (VNo)3"8

f

oo"

lO0 -

o

¢>0

/

po~ "

lO-

g c~ 1

0

0.1 VIV

0.1 0

Fig. 3. Bulk modulus of B2-type silica gel versus volume (data from ref. [40].)

expected to be independent of density [41], and this is supported by measurements made on aerogels [42], hydrothermally aged gels [36], and alcogels [9] of silica, all of which yield a value of N = 0.2. Ttrerefore, the trends found for Gp are expected to apply for Young's modulus, Ep, and the bulk modulus, Kp. Assuming N ~ 0.2, the results of ref. [40] for alcogels can be fitted to

Kp = Ko( Vo/V ) m = Ko (P/Po) m,

(13)

where K 0 is a constant, and V0 and P0 are the initial volume and relative density of the gel, respectively. Figure 3 shows the quality of the fit, with K 0 = 0.4 MPa and rn = 3.8. The same type of power law relates the elastic moduli of aerogels to their density [43,44], with a very similar exponent (3.2-3.8). The modulus of rupture increases much more slowly [40]; for aerogels, the power law relating the strength to the density has an exponent of 2.6 [45]. Percolation theory suggests such a power law [46]. However, as Woignier and co-workers point out [43,45], it is not clear what feature of gel structure (e.g., density, monomer concentration) should be used to represent the 'bonds' or 'sites' of percolation theory. The moduli of gels are much lower than would be expected merely on the basis of their porosity [40]. In part, this is a result of the low connectivity of the solid phase; that is, there is a high number of non-bridging bonds (resulting in a skeletal density much lower than that of the corresponding oxide [6]) that reduces the rigidity

G.W. Scherer / Drying of gels

of the solid phase. Another important factor is the apparent weakness of the connectivity on a macroscopic scale (perhaps reflecting the relatively small number of links between the clusters that grew to form the gel). This was demonstrated by Dumas et al. [47], who prepared a series of gels with different solids contents and used thermoporometry to evaluate the pore structure. The moduli of the gels varied dramatically, while the mesoporous volumes changed little; however, the moduli were related to the volume of macropores. Thus, the large-scale structure of the gel seems to have a profound influence on the mechanical behavior. 3.4. Film deposition Whereas monolithic gels are usually molded, aged, and then dried, the deposition and drying of films are concurrent processes. Hurd and Brinker [48] have undertaken an elegant series of experiments using ellipsometry and F T I R spectroscopy to follow the physical and chemical evolution of a sol to a film during dip-coating; this work has recently been reviewed by Brinker et al. [6,49]. As a substrate is drawn out of a sol, a steady state is achieved, as indicated schematically in fig. 4. At the drying line ( x = 0 ) the thickness, h, of the film decreases rapidly, varying approximately as h ~ x 1/2. The sudden variation in h reflects the relative ease of vapor transport near the drying line: at large x, vapor can only diffuse away from the film in a direction normal to the substrate, but at x = 0, it can also diffuse parallel to the substrate. The structure of the dry film depends on competition between two factors: capillary forces that compress the network, and condensation reactions that stiffen the network (allowing it to resist compression). The same factors control the structure of monolithic gels, but the timescale is very different, since film drying occurs in a matter of seconds and monoliths dry over days or weeks. Consequently, there is little time for network formation during film deposition, and the structure of the film is largely controlled by the structure of the clusters in the sol from which it is formed [6,50]. If those clusters arc compliant, the enormous capillary forces can

369

SOL-GEL DIP-COATING DEPOSITED FILM l Ua~ | ./ /

x:O t FiLMCOLLAPSEANDI

GELATION

ALCOHOL/WATER EVAPORATI ~ ON ~:,v, ~~' v~* ,*X~" Y *~*~ *~" ,~"~ ~' x~' '~~"

AGGREGATION GRAVITATIONAL DRAINING +

EVAPORATION

J

' '~

• . ,v.~ : . ~

~.. (q Uoi2/3/YLVlJ6(pg11,'2 ~ ENTRAINEDDILUTESOl ~ RESERVOIR SURFACE DILUTESOL

Fig. 4. Schematic illustration of dip coating showing steadystate thickness profile, h(x), which extends over a distance, X0, from the drying line ( x = 0) to the reservoir of sol; deposited film is dry above x = 0. The substrate is withdrawn from the sol at speed, U0; the initial thickness of the liquid layer is A =(rlUo/pg) 1/2, where r/ and p are the viscosity and density of the sol, and g is the gravitational acceleration. (Figure courtesy of C.J. Brinker.)

cause complete collapse of the network, resulting in a non-porous film [25], even though a monolith from the same sol would have high porosity and surface area. The solvent is generally not a pure liquid, and differences in evaporation rates of the constituents result in compositional variation along x, typically leaving a water-rich region near x = 0 [6]. Consequently there is a gradient in "/Lv along the surface of the film, resulting in flow of liquid toward regions of higher surface tension (a phenomenon known as the Marangoni effect). The influence of such factors on the thickness and structure of gel films is under study by direct observation and numerical simulation [49]. The stresses produced during drying of films have been measured by Voncken et al. [51] by depositing a film (of alumina) on a flexible substrate and observing the deflection of the substrate. Stresses on the order of 200 MPa are routinely measured, in keeping with expectations [6]. Such stresses create cracks if the film is too

370

G.W. Scherer /Drying of gels

thick, and the crack patterns observed experimentally [52] are in qualitative accord with those predicted by computer simulations [53,54]: initially isolated defects appear and the rate of bond breaking is slow; then the concentration of forces on bonds near defects causes cracks to appear and grow, relaxing the stresses and decreasing the rate of bond breaking. The result is a fractal pattern resembling mud-cracking. The mean spacing of the cracks can be estimated theoretically, and experiments by Atkinson and Guppy [55] show semi-quantitative accord with predictions based on the assumption that partial delamination occurs along the crack [56]. It would be desirable to have more studies of this type, combined with measurements of the elastic properties and critical stress intensity for the film materials.

4. Practice

The most practical and important applications of sol-gel processing are in the preparation of films and powders, and that situation is not likely to change. However, optical quality silica glass monoliths made from gels are now commercially available [57-59], and considerable progress has been made toward the preparation of optical fibers from gel-derived rods [60]. Generally the details of fabrication are not available for such products, but unofficial information indicates that aging at elevated temperatures and slow, careful drying are required. We have seen that the drying stress decreases in proportion to the evaporation rate, but the 'safe' rates are so slow that objects thicker than ~ 1 cm usually require uneconomically long times to prepare. (There is speculation [61] that Libyan desert glass, nearly pure silica found in pieces as large as 30 cm, was formed by a natural sol-gel process, but successful industries do not operate on a geological timescale!) Fortunately, several procedures are known that can substantially increase the permissable drying rate, most of which are based on long established principles [14].

The most obvious thing to do is to increase the pore size, since it is the small pores of gels that create the low permeability and high capillary pressures that result in cracking. This method was pioneered by Shoup [62], who used colloidal silica particles as 'seeds' for the growth of silica gel from a potassium silicate solution. A similar approach was adopted by Toki et al. [63], who mixed silica particles (made either in the vapor phase or by a sol-gel method) with tetraethoxysilane to produce gels with relatively large pores. Okazaki et al. [60] have shown that this procedure also increases the strength of the gel. Some workers [64-68] have used flame-generated colloidal particles to make gels that are relatively easy tO dry, and yield glass of optical quality. The disadvantage of this approach is that the large pores reduce the driving force for sintering, so relatively high firing temperatures are needed to obtain a dense ceramic. If low-temperature processing is the goal (as when a layer is to be deposited on a substrate), then the use of large pores is counter-productive. If high stresses cannot be avoided (because of the need for small pores to facilitate sintering), then it is helpful to increase the strength of the gel. It is well known, for instance, that hydrothermal treatment reduces the shrinkage duringsubsequent drying [69], presumably by accelerating condensation reactions that stiffen and strengthen the gel, and this has been applied to reduce cracking [70]. The same chemical processes can be enhanced by chemical treatments, such as the 4 N HC1 rinse used by Mizuno et al. [71,72] that reportedly increases that allowable drying rate by an order of magnitude. Even extended aging at modest temperatures reduces drying shrinkage [73,74] and increases the strength of the gel [14,75]. A recent study by Wijnen et al. [76] found that aging produced an increase in connectivity of the silica network (revealed by 29Si NMR); small angle X-ray scattering indicated slow growth of the primary particles and a decrease in the fractal dimension of the network. The latter effect was attributed to migration of material from the tenuous fringes of the constituent clusters toward their centers, thus reducing the net surface area

G.W. Scherer / Drying of gels

and increasing the density gradient within the clusters. The rate of aging was found to be much faster at higher pH, where the solubility of silica is greater. The capillary pressure can be directly reduced by use of surfactants [14] or choosing a solvent with a low surface tension. In alkoxide-derived gels, the pore liquid is usually a w a t e r / a l c o h o l solution, but the alcohol (with YLv ~ 0.025 J / m 2) evaporates first, leaving mostly water (YLv = 0.072 J / m 2 ) . This situation can be reversed by using a solvent with a lower volatility than water that also has a low YLv. For example, Adachi and Sakka [22] added dimethyl formamide (DMF) to tetramethoxysilane in the preparation of a base-catalyzed gel, and dried the gel by slowly increasing the temperature to 150°C. This procedure caused the methanol and water to evaporate first, leaving the D M F (YLv = 0.036 J / m 2) in the pores; in addition, the elevated temperature (and possibly some chemical effect produced by DMF) resulted in larger pores in the dry gel. Similarly, Mori et al. [77] report reducing defects by immersing a gel into perfluoroalkyl polyether, then gradually heating to 105°C, and finally heating to 300°C to remove the polyether. It is probable that the thermal aging involved in these processes is more important than the reduction of YLv, because, as eq. (4) indicates, the drying stress does not depend on the magnitude of the capillary pressure. The surface tension of a liquid can be reduced simply by increasing the temperature, and beyond the critical temperature and pressure there is no tension at all [69]; of course, when P = 0, VP must be zero, so no stresses can appear. Supercritical drying has been extensively studied and has led to the production of large gels with relative densities as low as p ~ 0.0013 [78]. The process has recently been reviewed [79] and is the subject of a series of biennial conferences [80,81], so further discussion here is not warranted. A method for avoiding interracial tension that has been less successful is freeze-drying (to produce 'cryogels'). Frozen gels are generally reduced to powder [82] or develop a very coarse pore structure [83,84], apparently as a result of damage done by growing crystals of the solvent. A gel must be cooled below the normal melting point

371

for crystals to form [30,85], so it is likely that crystallization will nucleate outside (or on the surface of) the gel, whereupon liquid will flow from the pores to the crystal at the surface. This will produce a flux toward the surface in a manner strictly analogous to evaporative drying, and will produce similar stresses. Therefore, it is not surprising that freezing usually produces cracking. The driving force that draws liquid from the gel to the crystal is proportional to the entropy of fusion, which is much lower for organic liquids than for water; this may help explain the observation [82] that less damage is produced if the pores initially contain butanol, rather than water. The only report of successful preparation of a monolithic cryogel from water is in a patent application by Yoshida et al. [86] that describes a process involving immersion of a gel in water, followed by slow heating to 95°C to remove all alcohol from the pores, then freeze-drying at - 5 ° C . If all the liquid freezes at - 5 ° C , then (according to the Gibbs-Thompson equation) the smallest pore must have a diameter exceeding 27 nm. Such large pores, presumably produced by the hightemperature aging in water, could account for the absence of cracking. A version of freeze-drying that has been proposed [6], but apparently never applied, is to use a glass-forming liquid in the pores of the gel to avoid all damage associated with crystallization. The use of certain organic compounds (including glycerol, formamide, and oxalic acid) as 'drying control chemical additives' (DCCA) [87] has attracted considerable attention, because it is reported that gels > 1 cm thick can be dried in ~ 1 day by their use. The exact role of these compounds during drying is not clear, but is is known that they increase the hardness (and presumably the strength) of the wet gel [88]; unfortunately, they are hard to remove [89], and tend to cause foaming when the gel is sintered. Glycerol has been found beneficial for preventing cracking in alumina gels [90] and alumina-matrix composites [91], but Hench [89] notes that it tends to form carbonates when decomposed at high temperatures. By adding 5-10 vol.% glycerol, Luo and Tian [92] were able to make large silica gel disks (68 mm × 13 mm) with drying times of 3 - 4 days,

372

G.W. Scherer / Drying of gels

but the glass bloated after densifying, probably as a result of decomposition of residual glycerol. Hayashi et al. [93] report that the DCCA (formamide, in their gels) can be removed and bloating can be avoided if the gel is dipped in a 1/1 mixture of water and ethanol for 1 day before drying; however, the drying period is then ~ 10 days, so it is not clear that the use of a DCCA provides any advantage. Another type of organic modification is the addition of polymerizable organic groups along with metal alkoxides to produce hybrid o r g a n i c / inorganic networks. These materials, pioneered by Schmidt [94] and now widely studied [95], are readily dried because the organic constituents provide resilience (i.e., lower K G and higher K~c) to the network. They collapse to non-porous solids because of their compliance; given the absence of pores, the last stages of drying probably involve diffusion rather than flow of liquid, and that tends to reduce stress [8]. Usually the organics in this type of hybrid have a beneficial effect on properties, and are not burned out. H o w e v e r , Schmidt et al. [96] point out that the organics can be used to reduce the connectivity of the network and thereby help 'relax stresses', a n d can then be burned out to yield dense monolithic ceramics. In terms of the theory presented in section 2, we expect that the stresses in these compliant gels remain low in obedience to eq. (7). Reduced connectivity can be achieved by binding chelates to the metal atoms (e.g., acetyl acetonate on aluminum butoxide) or by using a silica precursor with non-hydrolyzable groups. As an example of the latter method, the phenyl ligands on Si(OH)2(C6Hs) 2 were used to reduce connectivity in a sodium aluminosilicate composition that was deposited as a film 20 txm thick without cracking; some cracking did occur when the organics were burned out [96]. Schlichting [97] has prepared films ~ 10 t~m (after firing) by dipping a substrate in neat alkoxides and allowing hydrolysis by ambient moisture, a procedure that probably results in a high concentration of retained organics (and many non-bridging bonds) in the dried film. Garino [52] deposited films of similar thickness by using a low w a t e r / a l k o x i d e ratio, but they cracked when fired to ~ 400°C.

5. Topics for further study Although progress is being made in our understanding of drying, there are many things that remain to be done. Theoretical expressions are available for the distribution of stress in drying bodies [5], but no direct measurements of o-x or P have yet been made (except in films [51] where it is expected [6] that o-x ~ P). The role of diffusion in the liquid phase, which is predicted to have a profound impact on stress [8], has not been explored. Transient opacity is often observed after the critical point, but it is not known what factors (pore size distribution, liquid viscosity, evaporation rate) control that phenomenon, nor is it known whether the irregular interface does harm by generating defects [13], or beneficially diffuses the stress. The problem of crack initiation and growth is of critical importance, but very little effort seems to have been devoted to it. Freeze-drying of gels is a potentially valuable way of preparing monoliths, but it has not yet been particularly successful. To date, little relevant work has been reported on the mechanism of crystal nucleation and growth in gels, or the mechanisms by which damage occurs during freeze-drying. Some measurements are now available of the properties of gels that are relevant to drying stresses (permeability, rheology, strength), but no systematic study has yet been done of the dependence of structure on properties. In particular, it is essential to know how the properties change during aging and drying. It is remarkable that only one study has been reported on the critical stress intensity of a wet gel [37]. The influence of structure - and particularly of organic additions - on K~c must be established. Several studies indicate that macropores exist in alcogels, but pore size distributions have not been determined. More information on structure on the macropore scale is important, because that level of structure seems to have a strong influence on the modulus and strength of the gel, and should be important to the permeability. Finally, the connectivity (i.e., the spatial distribution of bonds) must be known so that the structure can be related to the mechanical properties.

G.W. Scherer / Drying of gels

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