HEATSOF IMMERSION IN WATEROF CHARACTERIZED SILICAS
11, though present together, diffuse independently; in the latter process the diffusion coefficients would be
D1-11 = D11-1 = 0; DI-I
=
a
-D1; Y
D11-11=
?Da
P
(A21 The solutions of the difference equations are then either equal to those for initial distributions a and b of Table 111,or constant. For one initial distribution the values of A(cJc0) have been plotted in Figure 4. The general character of the results for the initial distributions c and f is the same. At least as far as
2169
their sign is concerned, the results are as can be expected qualitatively from eq 13 and Tables I and 11. I n agreement with qualitative and quantitative expectations, A(cf/co) for initial distribution d came out to be zero for all E. It might well be, therefore, that the influences of I and I1 on each other's diffusion are adequately described by the A(cf/co) as found with the computer. If so, the complete distributions, (ct/co) a t chosen 5 values and a t t -t m , should be found by adding these A(cf/co) values to the exact solutions for independent diffusion (preferably to be derived from error functions, using D1-I and D11-11, as given in eq A2).
Heats of Immersion in Water of Characterized Silicas of Varying Specific Surface Area
by J. A. G. Taylor' and J. A. Hockey Chemistry Department, Faculty of Technology, University of Manchester, Manchsster, England (Received November 29, 1965)
The heat of immersion ( M I )in water of annealed, fully hydroxylated amorphous silica is 160 =k 3 ergs/cm2. This value is independent of the specific surface area in the range 8.5-147.5 m2/g. Higher values were obtained for samples containing microporous defects.
Introduction Although absolute values for the surface energy of solids cannot be obtained from heat of immersion ( A H I ) studies, this technique has been widely used in recent years to measure variations between surfaces of The results obtained have in differing some cases been interpreted in terms of the crystallinity of the solid. It has been suggested that as the particle size of the solid increases, the surface corresponds more closely to that of the pure crystalline material and so the energy change on formation of the solid-liquid interface increases. This hypothesis has been used to interpret the marked increase in AH1 on passing from high to low surface area solids.2 I n
the present work, values for AH1 in water of wellcharacterized silicas of similar surface properties but varying particle size have been determined. (1) Chemical Physics Division, Unilever Research Laboratory, Port Sunlight, Cheshire, England. (2) W. H. Wade, H. D. Cole, D. E. Meyer, and N. Hackerman, Advances in Chemistry Series, No. 33, American Chemical Society, Washington, D. C., 1961,p 35. (3) (a) A. C. Makrides and N. Hackerman, J. Phys. Chem., 63, 594 (1959); (b) W. H.Wade, R. L. Every, and N. Hackerman, ibid., 64, 355 (1960). (4) R. L. Venables, W. H. Wade, and N. Hackerman, ibid., 69, 317
(1965). (5) J. W. Whalen, ref 2, p 281. (6) M. M. Egorov and V. F. Kiselev, Zh. Fiz. Khim., 36, 158 (1962).
(7) D. Kolar, Croat. C h m . Acta, 35, 123, 289 (1963).
Volume YO, Number 7 July 1966
J. A. G. TAYLOR A N D J. A. HOCKEY
2170
Table I : Characteristics of the Silica Samples Specific surface area,
Initial
Preparation
ml/g
NOH
Heated a t 700" for 48 hr Heated at 940" for 4 hr Heated to 940" for 16 hr Heated to 980" for 4 hr Heated to 980" for 16 hr Heated to 1040" for 16 hr Heated to 1060" for 4 hr Heated to 1040" for 4 hr Prepared by precipitation
147.5 99.3 87.1 79.0 64.7 29.9 8.2 35.5 47.1
Sample no.
a
A: heated in air a t 115' for 6 hr.
' €3:
AH1 values were determined a t
27.0 f 0.05" by means of a differential calorimeter mounted in an ethylene glycol-water bath thermostated to =t0.002" during the experimental run. Up to three sample bulbs could be mounted in each calmimetric vessel, where the temperature changes by means of two 105were measured to f 5 X ohm thermistors mounted in opposing arms of a Wheatstone bridge circuit. At least two electrical calibrations were performed after each experiment, the agreement between these pairs always being better than 0.3%. All the values for AH1 in Table I are the result of at least two independent determinations, The 3- to 15-g samples were contained in thin-walled Pyrex glass bulbs, 22 mm in diameter and 50 mm long, which had an exothermic heat of bulb breaking of 0.22 =t 0.05 cal. A correction of 0.0075 cal/g of sample, calculated from the heat of vaporization of water, was applied to the experimentally determined heats to allow for the change in the free volume available for evaporation. The bulbs were completely shattered to ensure rapid and complete dispersion of the solid. In an experimental determination, the heat liberated varied from 3 to 15 cal; this corresponded to a 1-5 X temperature rise. The accuracy of the data is &3y0for the lowest surface area sample but considerably bettsr in the other cases. 2. Materials. Samples 1-8 (see Table I) were all derived from a 2-kg batch of "Aerosil" (from Degussa) which had been rehydrated by heating in liquid water a t 95" for 5 hr and then dried at 115" in air.* This material (coded R.A.2) had a specific surface area (ssa) of 158 m2/g and a surface hydroxyl population of 6.25 groups per 100 A2, ;.e., NOH = 6.25. Sample 1 was prepared by heating a portion of this material a t 700" for 48 hr; it was then rehydrated and dried The Journal of Physical Chemistry
*.. 5.50
>8.0
0.006 0.005 0.004
... ... 0.005
... 0.018 0.110
-AHI~ Set Aa
165 158 158 158 153 155 163 186 1330
ergs/cm-Set Bb
170 154 144 160 159
...
173 177 1320
heated in vacuo a t 115' for 6 hr.
Experimental Section 1. Apparatus.
4.71 4.61 4.64 4.62 4.68 4.31
Microporosity, ml/g
as described above. There was little change in the surface area (ssa = 147.5 mz/g) as a result of this treatment, but the NOHvalue fell to 4.71. This NOHvalue corresponds closely with that expected for one hydroxyl group per silicon atom in a 0-cristobalite or ptridymite structure. Samples 2-8 of varying particle size were obtained by heating portions of R.A.2 for differing lengths of time at temperatures between 940 and 1060" (see Table I), then rehydrating and drying, as described above. Sample 9 was a highly microporous precipitated silica which was used, after drying, without further rehydration. Finally the bulbs were loaded, weighed, and glass-blown onto a vacuum line separated by means of a liquid nitrogen trap from any portion of the system having greased joints. One set (A) was heated in air a t 115" for 16 hr, followed by evacuation to a pressure of
