The Polarization Model

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

The potential model has been applied to the adsorption of mixtures of gases. In the ideal adsorbed solution model, the adsorbed layer is treated as a simple solution, but with potential parameters assigned to each component (see Refs. 76-79). 

An interesting alternative method for formulating f/(jt) was proposed in 1929 by de Boer and Zwikker [80], who suggested that the adsorption of nonpolar molecules be explained by assuming that the polar adsorbent surface induces dipoles in the first adsorbed layer and that these in turn induce dipoles in the next layer, and so on. As shown in Section VI-8, this approach leads to 

Thus a plot of log log (P /P) versus n should give a straight line (see Fig. XVII-14). If Eq. XVII-83 is applied to typical type II isotherms, such as CO or N2 on silica C [81] or N2 on KCl [82], a/d comes out to be about 0.4, from which d is about an atomic radius. 

The polarization model suggests strongly that orientational effects should be present in multilayers. As seen in Section X-6, such perturbations are essential to the explanation of contact angle phenomena. 

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Stillinger FH (1979) Dynamics and ensemble averages for the polarization models of molecular interactions. J Chem Phys 71(4) 1647... 

The pyroelectric coefficient at constant strain, p is expressed by the polarization model, using the quasi-harmonic approximation, as... 

The polar model applies to all other compounds for which the fragments can be linked to a corrective contribution in the Pf list ... 

We shall remove an important drawback of the polarization model described in Section VI by considering another variant of a composite model than that described in previous Section VILA. We use again a linear-response theory to find the contribution of a vibrating dipole to the total permittivity . We split the total concentration N of polar molecules into the sum Nm and Nv b, where each term refers to rotation of a like rigid dipole (viz. with the same electric moment p) but characterized by different law of motion ... 

Because the double layer force vanishes in the absence of surface charges, one expects the attractive van der Waals force to cause the coagulation of all neutral (or even weekly charged) colloids. The absence of such a behavior has been explained by the existence of an additional (non-DLVO) force, the hydration interaction, which is due to the structuring of water in the vicinity of hydrophilic surfaces. This chapter is devoted to the identification of the microscopic origin of the hydration force, and to the presentation of a unified treatment of the double layer and hydration forces, the Polarization Model. 

The monotonic decay of the polarization in the Schiby— Ruckenstein model (the main critique of the polarization models) is a consequence of the assumption of the homogeneous distribution of water molecules in the vicinity of the surface. However, when the water was assumed to be structured in icelike layers in the vicinity of the surface, the polarization became an oscillatory function of the distance from the interface.13 This result was due to the particular locations of the water molecules... 

One cannot yet rule out that other interactions contribute to the hydration, such as the disruption of the hydrogen bond networks when two surfaces approach each other. However, at least a part of this disruption is already contained in the dipole—dipole interactions included in the polarization model. In addition, the polarization model of hydration can relate the magnitude of the hydration force to the density of dipoles on the surface. This can explain the dependence of the hydration repulsion on the surface dipolar potential18 or the restabilization of some colloids at high ionic strength16 observed experimentally.10... 

M. Manciu, E. Ruckenstein The polarization model for hydration/double layer interactions the role of the electrolyte ions ADVANCES IN COLLOID AND INTERFACE SCIENCE 1.12 (2004) 109-128. 

The polarization model predicts that the interaction between nanoparticles depends not only on the surface charge density, but also on the surface dipole density. As the concentration of electrolyte increases, the surface charge density decreases, due to the recombination of ions with surface groups, but the density of surface dipoles increases. At relatively low salt concentrations, the repulsion due to the dou-... 

By combining the thermal undulations of membranes with the polarization model it is shown that an increase in... 

Whereas the coupled equations of the polarization model can be solved analytically in the linear approximation (which is valid only for small potentials), in the general case one must rely on numerical solutions [7.5]. The polarization model can explain the restabilization of protein-stabilized polymer latexes, for which the increase in the repulsive force generated by the surface dipoles more than compensates for the decrease in repulsion caused by the decrease in the surface charge and the increase in the screening of the electrostatic field by the increasing ionic strength [7.5]. 

The polarization model is extended to account for additional interactions, not included in the mean field, such as the ion-hydration forces [7.8]. 

In order to explain the interactions between silica surfaces, the polarization model is adapted to poorly-organized surfaces. To account for the disorder induced in water by the rough surfaces of silica, the dipole correlation length Am, which is the main parameter of the polarization model, is allowed to decrease from Am=14.9A obtained for water perfectly organized in ice-like layers in the vicinity of a surface to smaller values. For Am=4A, good agreement with experiment is obtained for reasonable values of the parameters involved (such as surface dipole and charge densities) [7.9],... 

Predictions of the polarization model for hydration forces between bilayers... 

The polarization model can be combined with ion-specific effects induced by the ions that approach the surface (with preference for the bulk water for structure making (SM) ions and... 

Let us also note that at large separations, the polarization model provides a very large repulsion, hence that the swelling... 

Fig. 7. Experimental values for the osmotic pressure as a function of separation distance from Ref. [13] (stars water, circles 1 M KC1 triangles 1 M KBr) are compared with calculations that combine the polarization model for hydration forces with the statistical treatment of the undulation, for the following values of the parameters = 9 Debyes, A = 60 A , A = 1 A, o = 0,...

One of the models for the hydration force, the polarization model,5 assumes that the hydration force is generated by the local correlations between neighboring dipoles present on the surface and in water. The macroscopic continuum theory, in which water is assumed to be a homogeneous dielectric, predicts that there is no electric field above or below a neutral surface carrying a uniform dipolar density. However, at microscopic level the water is hardly homogeneous, and the electric interactions... 

Strong specific anion effects were reported particularly at low electrolyte concentrations (10 4—10 2 M),1 a range in which the DLVO theory is considered accurate. However, as shown later, the present experimental data cannot be reproduced by the traditional theory in this range of electrolyte concentrations. In the past, no agreement could be obtained, on the basis of the traditional theory, because small changes in the values of the parameters, caused by the nonuniformity of the particles, affected strongly the stability ratio.18 The polarization model provides similar results in the above range of electrolyte concentrations, when the dipole densities are sufficiently low and cannot explain the data. 

The polarization model for hydration/double layer interactions the role of the electrolyte ions... 

The present article is structured as follows. In the first section, the physical basis of the polarization model for the hydration/double layer interactions proposed by the authors... 

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