Electrostatic Interaction Between Different Surfaces

Contrary to the case of two identically charged surfaces, which always repel each other (see Equation 5.178), the electrostahc interaction between two plane-parallel surfaces of different potentials, /j, and /j2, can be either repulsive or attractive. - Here, we will restrict our considerations to the case of low surface potenhals, when the Poisson-Boltzmann equation can be linearized. Despite that it is not too general quantitatively, this case exhibits qualitatively all features of the electrostatic interaction between different surfaces. 

The difference in adsorption energy is therefore given by the one-electron energy difference plus the difference in electrostatic interaction between the surface and the adsorbate in the two situations ... 

Hogg, Healy, and Fuerstenau [7] developed their HHF theory to describe the interactions of two particles of different size. In 1985, Matijevi and Barouch [8] evaluated the validity of the HHF theory for the electrostatic interaction between two surfaces of different sizes for both unlike particles with potentials opposite in sign, and for particles with same sign potentials. The computational calculations overcame the problem of the accuracy in the evaluation of incomplete elliptic integrals of the first kind, which is a direct consequence of a non-linearity of the Poisson-Boltzmann equation. They concluded that for systems with dissimilar particles with either opposite signs or the same sign, the approximation of the HHF theory achieved good results. However, when potential differences increased, marked deviations from the HHF theory were found. 

Several different analytical and ultra-micropreparative CEC approaches have been described for such peptide separations. For example, open tubular (OT-CEC) methods have been used 290-294 with etched fused silicas to increase the surface area with diols or octadecyl chains then bonded to the surface.1 With such OT-CEC systems, the peptide-ligand interactions of, for example, angiotensin I-III increased with increasing hydrophobicity of the bonded phase on the capillary wall. Porous layer open tubular (PLOT) capillaries coated with anionic polymers 295 or poly(aspartic acid) 296 have also been employed 297 to separate basic peptides on the inner wall of fused silica capillaries of 20 pm i.d. When the same eluent conditions were employed, superior performance was observed for these PLOT capillaries compared to the corresponding capillary zone electrophoresis (HP-CZE) separation. Peptide mixtures can be analyzed 298-300 with OT-CEC systems based on octyl-bonded fused silica capillaries that have been coated with (3-aminopropyl)trimethoxysilane (APS), as well as with pressurized CEC (pCEC) packed with particles of similar surface chemistry, to decrease the electrostatic interactions between the solute and the surface, coupled to a mass spectrometer (MS). In the pressurized flow version of electrochromatography, a pLC pump is also employed (Figure 26) to facilitate liquid flow, reduce bubble formation, and to fine-tune the selectivity of the separation of the peptide mixture. 

The usually accepted approach is to adopt an ionic model for the superoxide ion on the surface. In this model, an electron is transferred from the surface to the oxygen to form 02, and there is an electrostatic interaction between the cation at the adsorption site and the superoxide ion. A calculation of the g tensor based on this model (Section 111,A,1) accounts for nearly all the data from adsorbed 02 and is consistent with the evidence that the spin density on both oxygen nuclei is the same (Section III,A,2). However, there are examples of oxygen adsorbed on the surface where the g values do not fit the predictions of the ionic model (Section IV,E) and also a few cases where the spin density on the two oxygen nuclei is found to be different. In these situations it seems likely that a covalent model in which a a bond is formed between the cation and the adsorbed oxygen, is more relevant. 

In the sections that follow, we first outline and summarize, in the context of contemporary ET theory, the experimental behavior of systems involving only weak, electrostatic interactions between dye molecules and the semiconductor surface. This is followed by (1) a description of the behavior of covalently linked dye-semiconductor combinations, which is remarkably different from that seen with weakly interacting systems, (2) a discussion of the fundamental energetics for the reactions—which again appears to differ significantly for the two reaction subclasses—and (3) a comparative discussion of possible interfacial reaction mechanisms. 

It is important to note that the concept of osmotic pressure is more general than suggested by the above experiment. In particular, one does not have to invoke the presence of a membrane (or even a concentration difference) to define osmotic pressure. The osmotic pressure, being a property of a solution, always exists and serves to counteract the tendency of the chemical potentials to equalize. It is not important how the differences in the chemical potential come about. The differences may arise due to other factors such as an electric field or gravity. For example, we see in Chapter 11 (Section 11.7a) how osmotic pressure plays a major role in giving rise to repulsion between electrical double layers here, the variation of the concentration in the electrical double layers arises from the electrostatic interaction between a charged surface and the ions in the solution. In Chapter 13 (Section 13.6b.3), we provide another example of the role of differences in osmotic pressures of a polymer solution in giving rise to an effective attractive force between colloidal particles suspended in the solution. 

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

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