Mar 12, 2005 - S. CHAKRABARTI, J. SAHU, A. BISWAS, H. N. ACHARYA. Central Research Facility, Indian Institute of Technology, Kharagpur 721 302, India.
JOUII~NAL OF MATERIALS SCIENCE LETTERS 11 (1992) 763-766
Relationship between weight loss and shrinkage during gel drying S. CHAKRABARTI, J. SAHU, A. BISWAS, H. N. ACHARYA Central Research Facility, Indian Institute of Technology, Kharagpur 721 302, India
The phenomenon of drying in porous bodies has long been a subject of interest to ceramicists. Non-uniform shrinkage during drying creates residual stresses in clay bodies and gel monoliths, and often causes cracking and warping in them. However, whereas in clay bodies the drying shrinkage is only a few per cent, gels may undergo several hundred per cent shrinkages (on a dry basis) as a result of drying. Such enormous volume changes are usually avoided by hypercritical evaporation. Another distinguishing feature between clay drying and drying of gel is that whereas clay bodies always warp with an upward curvature, warping of gels is associated with a reversal of curvature from the upward to the downward direction with progressive drying [1, 2]. Cooper's analysis [3] of stresses and strains that appear during the drying of clay bodies is based on the assumption that the loss of moisture from wet clay is a diffusion-controlled process similar to the flow of heat from a heated body. According to Dwivedi [4] the assumption was arbitrary and is certainly untenable in explaining gel drying as was done by Zarzycki [5]. Dwivedi's studies on the drying of alumina gel provided a basis for the theoretical modelling of gel drying by Scherer and co-workers [2, 6]. Scherer divided the process of drying in gel into three stages; namely, the constant-rate period (CRP) and the first and second falling-rate periods (FRP1 and FRP2, respectively). As mentioned above, this division was based on Dwivedi's studies of the rate of water loss from alumina gels [assumed by him to be a solution of boehmite (AOOH) in water] of different thicknesses versus the water content of the gel. Dwivedi noted that the rate of water loss was constant during the initial period of drying, after which it reduced significantly (Fig. 1). It is also seen from the figure that during the constant-rate period the rate of water loss from the gel was similar to that of evaporation from a fresh layer of distilled water. It was suggested that the gel lost pore liquid at a constant rate and the decrease in volume of the gel was equal to the volume of liquid lost by evaporation. This automatically assumes that the gel network is compliant and deforms and shrinks due to the large capillar of forces acting within it [8]. The plot (Fig. 1) by Dwivedi, however, showed remarkable deviation from the theoretically predicted curve for the constant-rate period, i.e. the horizontal portion of the curve. He admitted "the 0261-8028 ©1992 Chapman & Hall
o
o Evaporation - a - _ o < } _ _ - • _ _ _ _ rate of o distilled ~ofer
'c . . . . E 0.20
= 0.15
o •
"~ 0.10
,__First
o ¢=;
•
Tronsition~Second
0.05
o 100
t
I
00
60
~ ~0
Water
in gel ( % )
l 20
0
Figure I Rate of water loss plotted against the water in the gel for various initial thicknesses of gel sections: (O) 7.5, ( 0 ) 3.0, (D) 1.8 and (ZX) 0.8 mm [4].
significant experimental errors expected in these studies because of cracking of gels and continuous change in the surface area of gel during drying". As is described below, this problem has largely been avoided here while studying the shrinkage-weight loss characteristics of silica gels. Another interesting point to note is that the gels Dwivedi used were colloidal in nature, being prepared by the method used by Yoldas [9]. It is well known that colloidal or base-catalysed alkoxide gels have a microstructure different from that of an acid-catalysed (polymeric) alkoxide gel (Fig. 2). It is easy to understand that colloidal gels have larger pores (> 20 nm average pore diameter [8]) whereas pores within the polymeric gels are smaller (< 20 nm). It was therefore expected that the two types of gels (colloidal and polymeric) would behave differently during the course of drying. Recently, Hench and West [8] have shown that for certain acid-catalysed alkoxide gels the initial rate of drying is not constant, but decreases significantly. We carried out the shrinkage versus weight loss studies for acid (HC1)-catalysed tetra-ethyl orthosilicate (TEOS)-derived gels. Gels were prepared with and without the addition of alcohol to establish the relatively unimportant role played by alcohol in influencing the drying characteristics. As noted by Anvir and Kaufman [10], alcohol is an unnecessary additive in the silica alkoxide sol-gel process, but its addition dramatically reduces the drying schedules from almost 1 month (in an alcohol-less system) to only 3-4 days (in a system using water and alcohol in equal proportions). 763
/~~
~.~]~
Farfromgelpoint
Far from gel po~nt branched clusters
/.~10 nm-~ ~ ~
NeargeIpoint Entangledprimarily [inear molecules
Near get point growth and a d d i t i o n a l branching
\ Get point Gel point
a dditional crosslink s
tinked c l u s t e r s
at junctions (a)
Figure2
(b) Polymer growth and gel formation in (a) acid- and (b) base-catalysed systems [7].
Intimately mixed sols were poured into 100 ml volumetric flasks. These flasks with lids from their narrow stems removed provided conditions in which the gels could shrink without being fragmented into too many pieces. Forty cm 3 T E a s was added to 30 cm 3 ethanol and 30 cm 3 acidified (HC1 to alcoholate molar ratio rHa = 0.03) water to make 100 cm 3 alcohol-containing sol. Alcohol-less sol was prepared by mixing 33 cm 3 T E a S with 67 cm 3 similarly (rHCl = 0.03) acidified water. Different drying rates were achieved by keeping the gel-filled flasks in a controlled temperature-curehumidity cabinet. The weight loss and concomitant volume shrinkage were noted at regular intervals for gels kept under different drying conditions. However, the shrinkage-loss characteristics used here require the following mathematical steps for better understanding. Assuming the volume of a gel (v) to be constituted of a solid porous network structure with pores filled with liquid,
where o~ and vl are the volumes of the solid and liquid phases, respectively. If the specimen reacts to volatile loss by shrinkage (case I) do = dvl However, if the specimen reacts to volatile loss by forming pores (case II) du = 0 Let f be the volume fraction of liquid. Then f = v,/o Therefore,
dVl/O
764
dv
5--
for case I for case II
(1)
1 dv v df
1/(l-f) 0
cr =
forcaseI for case II
In reality, there may be a region where loss of volatiles is accounted for both by shrinkage and pore formation, and then, 0 < ~ < 1/(1-f) Considering that only shrinkage occurs, from Equation I
or don v ) = gives
1 dv
d(ln v)
1
v df
df
1- f
d[ln ( 1 - f)], which on integration
-ln(~o)=ln((1-f)i,(1- f)o]
(2)
with suffix 0 indicating initial values. Thus, a plot of versus should give a slope of unity where no pores occur. In practice, the instantaneous gel volume v was measured by the water displacement method. The water used was kept at the same temperature inside the cabinet. The terms ( l - f ) denotes the volume fraction of the solid phase at any instant and was measured assuming the evaporation of constantcomposition volatiles. In alcohol-containing gel, the evaporating liquid was assumed to have a time average specific gravity of 0.9 and in alcohol-less gel (although, strictly, ethyl alcohol and diethyl ether form during copolymerization of hydrolysed orthosilicates) the liquid within the gel was taken to be water, having a specific gravity of unity. The weight-loss measurement always preceded the measurement of volume shrinkage and the volume
ln[(1-f)/(1-f)o]
0 = Us + Ol
df f (l/v) ( l - f )
Defining
-In(viva)
1.2 (a)
1.0
0
0.5
0
0.6
1.0
1.5
2.0
(b)
0.5-
0.4
E 0.2
0.1 0 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-In (V/v 0 )
Figure3 Plot of In [(1 - f)/(1 - f)0] versus - In (V/Vo) for (a) alcohol-containinggel (drying temperature O, 50 °C; /x, 70 °C; and [3, 90 °C) and (b) alcohol-lessgel (dryingtemperature 70 °C). of the pore liquid was calculated as j~__
/31 /)
_
#L/Pl - /)
where #1 is the difference between the mass of the gel at any instant (mi) and the final mass of the dried gel (m~). It is obvious that rn~ can have no absolute value, as drying may proceed indefinitely for a very long time and the value of #~ taken for calculation corresponding to the weight of gel after the entire drying campaign. ~ , the density of the pore liquid,
was assumed to be 0 . 9 g c m -3 in the case of alcohol-containing gel and unity for the alcohol-less gel. Fig. 3a and b shows that the plot of l n [ ( 1 - f ) / ( 1 - f ) o ] versus -ln(v/Vo) indeed has a certain linear region with a slope of unity. In this region the gel is perfectly compliant and the loss of volatiles corresponds to an equivalent decrease in gel volume, and the contraction rate is controlled by the rate of transport of liquid in the pores. This portion of the curve refers to the CRP and the 765
portion of the curve that lies beyond it indicates the FRP in which pores begin to form. The region where the curve finally becomes horizontal (this is even less noticeable in alcohol-less gel due to the difficulty in removing water from such gels) corresponds to the FRP2. However, the most interesting point to note is that, except for the case of alcohol-containing gel held at 90 °C, the slope at the early steps of drying is non-uniform and is significantly less than unity. This may be described as microsyneresis. In other words, the gel is so turgid that the expulsion of liquid from the pores does not create a corresponding increase in the fraction of the solid phase in the gel. Brinker and Scherer [6] described this as a process of phase separation in which the polymeric chains within the gel cluster together creating regions of free liquid. Here the driving force is the greater affinity of the polymer for itself than for the pore liquid. This is not unexpected, since polycondensation reactions continue even after the gel point is reached. It seems logical to expect the effect of microsyneresis to be more conspicuous at lower temperature where the gel gets longer time to dry. The studies described above complement in a certain way the findings of Hench and West [8], but suffer from the limitation that the initial rate of drying could not be correlated with the average pore size of the gels. Also, the measurement of the gel
766
volume by the water displacement method assumes the drying gels to have no hygroscopic nature.
Acknowledgement The authors thank the University Grant Commission (UGC) for partly financing support for the reported work.
References 1. 2. 3.
S. CHAKRABARTI, PhD thesis, IIT, Kharagpur (1988). G.W. SCHERER, J. Amer. Ceram. Soc. 73 (1990) 3. A. R. COOPER, in "Ceramic processes before firing", edited by G. Y. Onoda and L. L. Hench (Wiley, New York, 1978) p. 261. 4. R.K. DWIVEDI, J. Mater. Sci. Lett. 5 (1986) 373. 5. J. ZARZYCKI, in "Ultrastructure processing of ceramics, glasses and composites", edited by L. L. Hench and D. R. Ulrich (Wiley, New York, 1984) p. 88. 6. C.J. BRINKER and G. W. SCHERER, "Sol-gel science" (Academic Press, New York, 1990). 7. Idem, J. Non-Cryst. Solids 70 (1985) 301. 8, L.L. HENCH and J. K. WEST, Chem. Rev. 90 (1990) 33. 9. B . E . YOLDAS, J. Mater. Sci. 10 (1975) 1056. 10. D. ANVIR and V. R. KAUFMAN, J. Non-Cryst. Solids 192 (1987) 180.
Received 12 March and accepted 25 April 1991
