Dielectric continuum theory 696 INDEX

The Hamaker constant can be evaluated accmately using the continuum theory, developed by Lifshitz and coworkers [40]. A key property in this theory is the frequency dependence of the dielectric permittivity, e( ). If this spectrum were the same for particles and solvent, then A=0. Since the refractive index n is also related to t ( ), the van der Waals forces tend to be very weak when the particles and solvent have similar refractive indices. A few examples of values for for interactions across vacuum and across water, obtained using the continuum theory, are given in table C2.6.3. 

The theories of van der Waals and double-layer forces are both continuum theories wherein the intervening solvent is characterized solely by its bulk properties such as refractive index, dielectric constant, and density. When a liquid is confined within a restricted space, it ceases to behave as a structureless continuum. At small surface separations, the van der Waals force between two surfaces is no longer a smoothly varying attraction instead, there arises an additional solvation force that generally oscillates between attraction and repulsion with distance, with a periodicity equal to some mean dimension of the liquid molecules. 

Truchon, f.-F., Nicholls, A., Roux, B., Ifiimie, R.I., and Bayly, C.I. (2009) Integrated continuum dielectric approaches to treat molecular polarizability and the condensed phase refractive index and implicit solvation. Journal of Chemical Theory and Computation, 5 (7), 1785-1802. 

J.-F. Truchon, A. Nicholls, B. Roux, R. I. Iftimie,and C. I. Bayly,/. Chew. Theory Cowpat, 5(7), 1785-1802 (2009). Integrated Continuum Dielectric Approaches to Treat Mole ar Polarizability and the Condensed Phase Refractive Index and Implicit Solvation. 

This quantitative theory fails for a monolayer or submonolayer of adsorbed molecules, because it is impossible to define a complex dielectric constant 2 for a film of molecular thickness since the layer is not a continuum. However, it is possible, in a first approximation, to treat the monolayer like the film and to define an effective index of refraction (or dielectric constant) for a submonolayer and an effective thickness d = ddo, where do is the thickness of a full monolayer and 0 is the degree of coverage of the surface by adsorbed species. It turns out that if d in Eq. (15) is replaced by 6do, the normalized reflectivity change Al /R will be, in a first approximation, proportional to the degree of coverage 0. 

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