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Adsorption, Wetting, and Condensation on Energetically Heterogeneous Solid Surfaces? V. E. Smorodin Chemistry Department, Lomonosou Moscow State University, Moscow 119899,Russia Received November 25, 1992. I n Final Form: February 26, 1993@ Peculiarities of adsorption, wetting, and condensation on heterogeneous (colloidal scale) solid surfaces have been analyzed. In terms of the classical theory of capillarity, a generalization of the Young law for heterogeneous surfaces was achieved. The relationship between adsorption, wetting, and condensation has been investigated. A seriesof new physical phenomena, a “quasi-cavitation”mechanism of heterogeneous condensation, double barrier nucleation, and endothermic wetting effect, are predicted and studied.
Introduction According to numerous data, in the process of heterogeneous nucleation and growth as well as in the properties of a condensed phase on a surface, the essential role is played by the “active sites”, i.e. the lyophilic regions of the surface, which have a high value of the parameter m = cos 8, where 8 is the wetting angle. For example, heterophilization of aerosol particles increases their icenucleating activity; this fact is used for weather modification through the silver iodide aerosol systems.’ The artificial modificationof surfaces has become the principal mean for development of new methods and new materials. It becomes necessary to classify the data on the effects of energetic heterogeneities (of colloid scale)on the wetting, adsorption, and condensation and their relationships. Wetting of Heterogeneous Solid Surfaces The first important factor to be taken into account in this problem is a design (topology) of energetic heterogeneity of solid and film on their surfaces. It is possible to distinguish seven of the simplest topologicalstructures of solid heterogeneity: (1) a single lyophilic site on lyophobic substrate (“activecenter”);(2)lyophobic site on lyophilic substrates (“passive center”); (3) a system of parallel lyophilic and lyophobic strips; (4) concentric circumferences of lyophilic and lyophobic zones; (5) a lyophilic surface with regularly distributed “passive centers”; (6) a lyophobic substrate with regularly “active centers”; (7) stochastic structures. On analysis of the film topology structures, it is expedient to distinguish between three main types: (a) “island” (isolated clusters), (b) “mosaic” (partially merged clusters), and (c) continuous films. So, on the basis of the third and fourth models, some effects of heterophilicity on wettability have been explored in refs 2 and 3, where the authors disclosed, in part, the hysteresis effects. The next factor is the heterogeneity scale. Here we will consider the cases when an influence of gravitation is neglected compared to the capillary forces. Introduce a scale parameter linking the typical dimensions of surface heterogeneities (I) and those of the drop (R):1 = 1IR. Two typical cases can be singled out: 1 0). So, it is possible that the wetting heat, Q = -AH, is negative. It was shown in ref 18 that the maximal estimate (upper limit) of the endoeffect can be found assuming that the process of wetting is thermodynamically reversible. In this case, assuming that a change of the Gibbs free energy of the system AG = 0 in the Gibbs-Helmholtz equation AG = AH - TAS, we find
-Q = AB = NdTAcS"(JCR:/o)(h*/Ah)
(28)
calculated for unit heterogeneous surface and
-Qo = AE?, = TAS (JcR:/o)( h */Ah) (29) for one hydrophobic section. There Go is the mean change O
in entropy in the transition zone, o is the "landing area" of one molecule (water or polar liquid), h* is the critical film thickness corresponding to cavern closing up, and Ah is the thickness of the liquid monolayer. Considering the temperature relaxation of the endo effect, we may write the equation for heat transfer
-Qo = -AT C, e3tRi h* (30) where C,is the isochoric heat capacity of the layer averaged with respect to thickness, Q is its density, and -AT is the decrease in temperature of the layer owing to the endo effect. Comparing the right-hand sides of two last equations, we obtain a limiting value for the temperature effect of "heterophobic" wetting -AT = T A S o ( C gA~h -1
(31)
As example, consider the wetting by a supercooled aqueous film of the heterogeneous surface of a single crystal of the AgI. Let the hydrophobic-sections of the surface consist ofap-AgI pShase in the { l O l O > prismatic plane, where Ag' and I- ions alternate. The hydrophilic sections on this surface are clusters of silver formed as a result of m2, Ah = 3 x photolysis. Assuming o = 1.2 x m, C , = 4.18 x los J/(kg deg), e = lo3 kg/m3, gd = lo-@ m, Nd = 1014m'+, T = 263 K, and estimating ASo = 0 . 3 k ~ (where K B is the Boltzmann constant), we find Q = 3 x J and -AT = 30 K. These data were verified with the calorimeter experiment^.'^ (17)Smorodin, V. Ye. J . Aerosol Sci. 1991,22,Suppl. 1, 549. (18) Smorodin, V.Ye. In Aerosols: Proceedings of the Fifth Annual Conference of the U.K. Aerosol Society; 1991; p 145. (19) Tovbin, M. V.; et al. Kolloidn. Zh. 1982,44, 1119.
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Therefore, an additional cooling of film during the wetting of a heterogeneous surface may provoke its freezing at a low temperature. (This mechanism is discussed in greater detail in refs 14,17, and 18.) summary
For the case 2 e 1 (microscale heterogeneity), the Froumkin-Derjaguin equation was generalized. The resulting equation validated the correctness of the Cassietype semiempirical formulas. The volume dependencies of the equilibrium drop contact angle 8 = O(V, in terms of classical capillarity
Smorodin theory considered above can be interpreted like the generalization of the Young law for heterophilic surfaces (2 L 1). As a consequence of the thermodynamic instability of condensate on heterogeneous surfaces, the new physical phenomena were theoretically derived and studied double barrier nucleation and “quasi-cavitation” mechanism of heterogeneous condensation. Then the endothermic effect of wetting was analyzed together with the hydrodynamics of heterogeneous wetting. Some of these phenomena are experimentally verified, others need further investigation.
