July, 19%
HYDRATION OF COLLOIDAL SILICA PARTICLES
piston to the right. This will continue until the line of contact, by small movements, is no longer able to find a sufficient number of planes of proper orientation to provide the apparent contact angle demanded by the relationships of eq. 4 and 8. At that point, the equilibrium becomes unstable, and the liquid climbs the wall. The contact angle hysteresis is determined, therefore, not by the inclination or height of the barrier (within reasonable limits), but by the predominant orientation of the surface roughnesses. If the roughnesses consist of a series of ridges whose sides are inclined to the horizontal by an angle, 9, we would expect ea = e., 'p (21) This relationship was in fact, observed by Bartell and Shepard3for liquids of high surface tension spreading over blocks of paraffin whose surfaces had been ruled to give asperities of known inclination. Eliminating runs in which large amounts of air were obviously entrapped, it was found that the height of the asperities had little effect, and that eq. 21 was obeyed, if 8eq. is taken as 8,, instead of (ea 8,)/2, as is usually done, for want of more precise knowledge. The situation is complicated here by the fact that their surfaces were ruled in two directions, so that spreading within the valleys, as climbing over the ridges, was an important mode of advance and recession. For this reason, presumably, their data for liquids of low surface energy do not follow eq. 21 so well (Table I).
+
+
IN
AQUEOUS SOLUTION
955
TABLE I ADVANCING AND RECEDING:CONTACTANGLES I N THE SPREADING: OF LIQUIDDROPS OVER MACHINED PARAFFIN SURFACES (DATA,OF SHEPARD AND BAR TELL^) Liquid Water 3 M CaClz Glycerol Ethylene glycol Methyl cellosolve Methanol
y, Smooth dynes/ surface om. 8s or
f a
-
30' or
72 110' 9Q0 129O 99' 84.5 119 109 136 114 63.2 97 90 115 92 47.5 81 74 93 65 30 62 42 76 12 22.6 42 27 58 0
% = 45' + = 60o'r or
142O 149 127 102 82 50
94" 115 83 49 0 0
Be
160' 96' 174 125 145 68 120 17 93 0 0 0
Conclusions (1) A semi-infinite sheet of liquid would be expected t o display no time-independent hysteresis of contact angle, ie., hysteresis attributable to surface roughness. ( 2 ) A method is given for calculating the reversible free energy change of a finite sheet of liquid upon climbing a barrier of known height and inclination. This corresponds roughly to the "contortional energy,'' and hence gives a measure of the contact angle hysteresis to be expected on advancing over a surface whose roughnesses have random inclinations and orientations. If, however, the roughnesses have a predominant inclination, this will tend to determine the contact angle hysteresis, in accordance with eq. 21.
DEGREE OF HYDRATION OF' PARTICLES OF COLLOIDAL SILICA I N AQUEOUS SOLUTION BY R. K. ILER AND R. L. DALTON Grasselli Chemicals Department, Experimental Station, E. I . du Pont de Nemours and Company, Inc. Received January 16, 1966
The viscosity of colloidal dispersions of silica has been studied, with the objective of determining the amount of water bound to the surface of the discrete, spherical amorphous particles. By applying the Mooney equation for the viscosity of a dispersion of spheres in a liquid medium, i t is calculated from the viscosity data that there is a monomolecular layer of water molecules immobilized, probably through hydrogen bonding, at the hydroxylated surface of the silica particles.
The degree to which the molecules in water are immobilized a t the surface of a highly polar solid apparently varies with the nature of the surface. For example, Bertil Jacobson' concluded that near the surface of molecules of sodium desoxyribonucleate, water molecules are oriented to form an immobilized lattice-oriented layer similar to ice. On the other hand, Vand2 has concluded that the viscosity of an aqueous solution of sucrose is consistent with the assumption that there is approximately a single layer of water molecules hydrogen bonded to the hydroxyl groups of the sugar molecule. It was of interest to determine whether the surface of amorphous silica immobilizes or otherwise binds water molecules. The viscosity of colloidal dispersions of amorphous silica has therefore been studied with the objective of determining the amount of water bound to the surface. ,
(1) B. Jacobson, J . Am. Chem. Soc., 77,2919 (1955). ( 2 ) V. Vand, TEIIE JOURNAL,52, 314 (1948).
Vand3 and Mooney4 have developed equations for a dispersion of spheres in a liquid, relating the relative viscosity of the dispersion to the volume fraction of the dispersed phase. The dispersed phase includes the volume of the solid particle plus any part of the medium ivhich is bound to the surface of the particles. With spheres larger than 100 mp diameter, the presence of a single molecular layer of solvent bound to the surface of the particle would have little effect on the volume fraction of the dispersed phase. However, in the case of spherical particles smaller than 10 or 20 mp in diameter, one or two molecular layers of solvent attached to the surface would appreciably increase the volume of the dispersed phase. This would have a marked influence on the viscosity. In the case of particles 5 mp in diameter, for example, the presence of two molecular layers of water, having a thickness of the (3) V. Vand, ibid., 52, 277. 300 (1948). (4) M. Mooney, J . CoZZoid Sci., 6 162 (1951).
,
R. K. ILER AND R. L. DALTON
956
order of 0.5 mp would increase the over-all diameter of the dispersed unit to about 6 inp. This would increase the volume fraction of the dispersed phase by about 70%. Assuming the above equations to be applicable to spheres of very small diameter, it is thus possible to calculate from the viscosity the degree to which spherical silica particles are “hydrated.” On this basis, our results, described below, indicate that uncharged particles of amorphous silica in suspension in water a t pH 2 are associated with only a monomolecular layer of water molecules, probably hydrogen bonded to the silanol (-SiOH) groups which make up the surface of the particles.
Experimental Preparation of Sols.-A series of silica sols containing discrete, non-aggregated particles having specific surface areas of 400 to 800 square meters per gram of SiOl, corresponding to average particle diameters of about 7 to 3.5 mp, were prepared for viscosity studies. That the particles are discrete and not aggregated in solution was shown by examining electron micrographs taken of deposits on a supporting film from sols at high dilution. In these micrographs the discrete particles lie as a single layer on the supporting film with very few aggregates which are deposited less regularly and form darker clumps more than one particle deep on the film. It is possible to prepare sols of discrete particles free from aggregates by slow deionization of a dilute solution of sodium silicate (3% SiO,), while maintaining the pH above 7, at elevated temperature. The specific surface area of the product may be varied by changing the temperature and rate of deionization while maintaining the pH between 11 and 9.6 For example, a dilute solution of sodium silicate (Si0P:NasO weight ratio 3.25) containing 3% Si03 was maintained at 47”, and “Nalcite” HCR, a sulfonic type cation-exchange resin in the hydrogen form, was added slowly over a 13-min. period, lowering the pH from 11.3 to 9.1. The pH was then maintained at ea. 9.0 by careful addition of resin. Samples were removed after 1 and 3 hours, cooled and filtered. The second sample was further deionized to p H 8.6 and again filtered. Additional sols were prepared by varying the time and temperature of deionization, as showu in Table I. TABLE I PREPARATION A N D CHARACTERIZATION OF SILICASOLS Time required for preparation,
hr.
A, 1 B, 3 Cl 2
Temp.
of prep-
aration, OC.
47 47 61 64 64 90 90 90
p H of
final sol
9.07 8.57 8.80 9.4 7.9 8.9 9.12 9.34 9.27
Molar ratio SiOn: NaiO
where d and t are the density and the time of flow of the silica sol, and d, and tw are the density and time of flow of water, res ectively. 8 n the assumption that the solution contains dispersed spherical particles, the relative volume fraction of the dispersed phase is then calculated from the viscosity data, using the Mooney equation4
where c is the volume-fraction of the “dis ersed phase.” A t concentrations of silica employed in t i i s study, the Mooney and Vand equations give essentially the same value for c . The “dispersed phase” consists of particles of anhydrous SiOz together with any water which is immobilized a t the surface of the particles. The relat,ion between c and S, the per cent. by weight of silica in the dispersed phase, in a sol containing P per cent. by weight of silica, may be calculated as follows. Assume 100 g. of sol containing P g. of silica. Since the volumes of silica and water in the system are additive,* the volume of the 801 is (Pl2.3 100 - P) ml. The dis ersed phase thus has a volume of c(P/2.3 100 P) ml. $he dispersed phase thus consists of P / 2 . 3 ml. of silica and
+
m.a/g.
8, %b
no
79 0.9 80 84 0.6 6i 81 0.9 Dl 28 81 0.9 113 83 0.9 F, 1 100 82 0.8 G, 6 5 100 85 1.1 J.00 89 0.8 H, 23 8 90 100 89 1.0 I, 50 Av. 0 . 9 * S, per cent. by a A , specific surface area of the silica. weight of anhydrous silica in the “dispersed phaRe.” n, calculated nuinher of molecular layers of water held a t the silanol surface of the particles. For the preparation of samples C and D, the deionbation was carried out still more slowly, initial samples of the sodium fiilicate solution being treated with ion-exchange resin to remove sodium over a period of 30 minutes, to lower the pH to 9.1, and then maintajbinjng the pH at this value for 1 and 2 hours, respectively. Similarly, by aging these sols at about pH 9 for 1 and 6.5 hours at 90°, samples F to I were prepared. 38
Characterization of Sols.-The specific surface area of the particles, A , was determined by a titration method described by G. W. Sears.‘ The per cent. by weight of silica in the dispersed phase, S, was calculated from the relative viscosity of the sols and the densities of water and silica. In order to avoid electroviscous effects, the viscosity of the colloidal solution was measured at pH 2, where the charge on the silica particles is at a minimum.’ The solution of the freshly prepared colloidal d i c a is alkaline and the particles are negatively charged. However, just before measuring the viscosity, the pH must be reduced to about 2, in order to minimize the charge on the particles. ThiR is done by adding wet, freshly regenerated “Nalcite” HCR resin, in the hydrogen form, in sufficient quantity to remove all the sodium ions, filtering and then adding sufficient l N HC1 to lower the pH to about 2.0. The concentration of SiOz in the solution is then determined, either gravimetrically, or by measuring accurately the specific gravity of the solution. The viRcosity of the solution was then measured a t 25” with an Ostwald pipet, and the relative viscosity calculated from the following expression
c Ana
827 717 690 705 612 615 478 406 360
(5) R. K. Iler and F. J. Wolter, U. S. Paten6 2,631,134 (E. I. du Pont de Nemours & Co.,Inc., 1953).
Vol. 60
+
[& + 100 - P] - & ml. of water
Then
s _ 100 -
P
P
+
P
whence S = 0.00566P ~ ( l 0.00566P) The values of S for the sols in Table I were calculated from this equation, using the values of c calculated from viscosity data. Effects of pH, Salts and Aggregation.-The virscosity of an acidic sol is relatively independent of pH. For example, a 7.6% ROI at p H 2.0 and 3.2 exhibited viscosities of 1.239 and 1.250. In alkaline solution, a change in pH from 8.0 to 9.0, produced a viscosity change from 1.478 to 1.580. The value of 8 as measured by viscosity, is unchanged when the viscosity is measured over a two-fold concentration of silica. Thus, a t pH 2, increasing the concentration of silica from 3.77 to 6.63%, increased the viscosity from 1.149 to 1.295 but the calculated value for S was 53% in both cases.
-
(6) G. W. Sears. paper to be submitted for publication. (7) N. E. Gordon, Colloid Ssmposium Monograph, Vol. 11, Chemical Publishing Co., New York, N. Y., 1925, pp. 114-125. (8) It waa verified experimentally that the density of a colloidal dispersion of ailica in water can be calculated from the composition and densities of amorphous ailia8 (2.3 g./ml.) and of water (1.0 g h l . ) .
APPLICATION OF ABSOLUTE RATETHEORY OF ADHESION
July, 1956
At pH 2, where there is little charge on the particles, the addition of an electrolyte has very little effect. In the aforementioned sols containing 3.77 and 6.63% silica, addition of 1.5% of sodium sulfate did not change the viscosity. It is necessary to measure the viscosity promptly when the pH of the sol has been reduced to 2, even though the rate of gelling of colloidal silica is a minimum at about this point.9 Over a period of several days a t 25”, aggregation of the particles occurs, and eventually the solution will form either a precipitate or gel. However, during the first hour or so, a t ordinary temperature, colloidal solutions a t the indicated concentrations increase very little in viscosity. It should be pointed out that the volume fraction of the dispersed phase, C, may be increased not only by the amount of water associated with the surface of the individual silica particles, but also by the degree of aggregation of the particles. If a number of particles were joined together to form a porous aggregate, the water within the pores would be essentially immobilized from a hydrodynamic standpoint, so that the “dispersed phase” would include more water than if the particles were not aggregated. Thus aggregation decreases the value of 8. This effect of aggregation accounts for the low value of S (Le., 53%) for the sols mentioned above. However, since the sols referred to in Table I are not aggregated, the relationship between viscosity and surface area can be accounted for by the hydration of the surface, as shown below. Calculation of the Composition of the “Dispersed Phase.” -It is known that the hydrated surface of amorphous silica is covered with silanol groups (-SiOH).’O The composition of discrete spherical particles, in terms of SiOz and HzO present as hydroxyl groups, can be calculated from the specific surface area. Thus A = 2720/d where A = specific surface area of the particles in square mfters per gram and d = average particle diameter in millimicrons. The particle composition9 has been calculated as 22?r x = - d8 and y = (2.80d)2 6 where the composition is represented as ( S ~ O Z ) ~ ( H ~ O ) ~ .
2“
(9) R. K. Iler, “The Colloid Chemiatry of Silica and Silioates,”
The Cornel1 Presa, Ithaca, N. Y., 1965, p. 45.
957
Let us now assume that in addition to the chemically bound layer of silanol groups, there are n layers of water molecules adsorbed or fixed in some way to the surface as far a~ their hydrodynamic behavior is concerned. The association of hydrogen-bonded water molecules with the silanol layer, in view of the large volume of the oxygen atom relative to hydrogen, suggests that in the first layer there may be one water molecule associated with each underlying silanol group.11 Since the hydrogen atoms of two silanol groups are equivalent to one molecule of water reacted with one unit of anhydrous SiOz, the composition of the “dispersed phase” may be represented as
(Si02)=(HzO),(HzO ) n ( ~ u ) Thus for every molecule of water present in the silanol layer there would be two water molecules in each physically bound water layer. From the above formula, using the formula weights for SiOz and H20, the dispersed phase has the composition, by weight
Substituting for x, y and d from the above relationships 1 8480(100
n = -2 [
- S)
SA
-
Degree of Hydration.-Applying this formula to the values of S and the specific surface area, A , in Table I, the values of n for each sol were calculated. For example, for sol E having a specific surface area of 612 m.z/g. and a viscosity corresponding to a value of S of 83%, n was calculated to he 0.9. For n to have been 0 or 2, the required value of S would have been about 94 or 74%, respectively. Such values are well outside the range of experimental error in deterniiniiig viscosity. Thus, for discrete silica particles ranging in size from 3.3 mp diameter in sol A to 7.5 mp in sol I, the value of n remains constant a t a value of about unity. It therefore appears that there is about a monomolecular layer of water molecules immobilized a t the hydroxylated surface of the silica particles. (11) Ref. 9, p. 240.
(10) Ref. 9, pp. 99, 103, 234.
APPLICATION OF THE ABSOLUTE RATE THEORY TO ADHESIOIV* BY MARSHALL R. HATFIELD AND GEORGE B. RATHMANN Contribution No. 96, Central Research Department, Minnesota Mining & Manufacturing Company, St. Paul 1, Minnesota Received January 19, 1966
Attempts to treat adhesion of a deformable adhesive to a rigid surface in terms of a simple fuse model for the bond are shown to be inadequate for explaining the time dependence of adhesion failure. Modification of this model to include the effects of a time dependent modulus of elasticity for the adhesive does not appear to be a satisfactory solution. The application of the absolute rate theory is based upon the assumption that bonding and debonding are rate processes and do not occur instantaneously which automatically results in a time dependent failure. The general implications of the theory are that: (1) loads below a critical force will never produce failure (2) the work of adhesion will have a profound effect on the time to breakage for a given load, although it represents a smafl fraction of the energy expended, and (3) the free energy of activation for viscoelastic flow of the adhesive also has a profound effect on the time to breakage for a given load. Precise and simplified forms of the rate equation are given for adhesion failure of a bond under tensional load. For comparison of similar systems, the simplified form may be adequate. I n addition, proper use of the simplified form may permit some information concerning work of adhesion to be derived from experimental adhesion data.
Introduction Adhesion, as discussed in this paper will be restricted to the bonding together of two solids, one soft and deformable (adhesive) and the other rigid and non-deformable (adherend). The primary purpose is to demonstrate that the rate theory offers a plausible mechanism for the direct approach t o the
* Presented at the 128th National American Chemical Sooiety Meeting, Cincinnati, Ohio, April, 1955.
failure of such an adhesive bond under tensional stress. The fact that small variations in the applied stress have a pronounced effect on the time required for bond failure is well established experimentally. The introduction of the rate theory provides a natural explanation for this time-dependency. Other explanations, which consider the adhesive bond as a fuse, introduce time-dependency through the viscoelastic properties of the adhesive
