Electrostatic and Dispersion Interactions

Determine the net DLVO interaction (electrostatic plus dispersion forces) for two large colloidal spheres having a surface potential 0 = 51.4 mV and a Hamaker constant of 3 x 10 erg in a 0.002Af solution of 1 1 electrolyte at 25°C. Plot U(x) as a function of x for the individual electrostatic and dispersion interactions as well as the net interaction. 

Recently a comprehensive analysis of the adsorption energies of the TNB-siloxane surface systems has been published [197, 198]. The results are collected in Table 5. The following point needs to be highlighted the data obtained at MP2 level of theory are always considerably higher than the ones obtained at the HF and DFT levels. Therefore, there is a significant contribution of electron correlation energy to the total value of interaction energy. Thus, it has been concluded [197] that two physical forces, presumably electrostatic and dispersion interactions, mostly contribute to the interaction between TNB and the siloxane surface of clay minerals. 

If we neglect the difference between electrostatic and dispersion interaction energies, then, in accordance with the concept of volume filling of micropores described previously, the equation of adsorption of methane on zeolite L will be expressed by Ref. 3 as... 

What are the relative roles of electrostatic and dispersive interactions in the various adsorbate/adsorbent systems of interest ... 

Obviously, adsorption of complex mixtures of solutes such as NOM involves both electrostatic and dispersive interactions (see Section V), as well as molecular sieving effeets, and it will be the ultimate challenge for both manufacturers of... 

As abundantly documented in Section IV.B.I, some adsorption systems involving aromatic adsorbates are very much influenced by electrostatic interactions. Clearly, a model that takes into account both electrostatic and dispersion interactions is needed. Such a model has been presented by Muller and coworkers [523-525]. Radovic and coworkers [674] used this model to illustrate the possibly dramatic effects of modifications of carbon surface chemistry on equilibrium uptakes of / -nitrophenol they have also extended it to evaluate the relative importance of electrostatic and dispersive interactions [738]. This approach is summarized next. 

FIG. 33 Combined effects of electrostatic and dispersive interactions on changes in aniline uptake upon thermal treatment (e.g., in H or NH,) of an acidic" carbon and its conversion to a basic" carbon Cl. original acidic carbon C3-E, basic carbon (only electrostatic interaction adjusted) C3-E-Dx2, basic carbon (di.sper.sive attraction potential enhanced by a factor of 2) C3-E-Dx5, basic carbon (dispersive attraction potential enhanced by a factor of 5) C3-E-Dxl0, basic carbon (dispersive attraction potential enhanced by a factor of 10). 

As discussed above, in many instances the uptake of organics (especially aromatics) will be determined by a complex interplay of electrostatic and dispersion interactions. As discussed in Section III, adsorption of inorganic compounds will... 

In contrast, adsorption of organic compounds, and of aromatics in particular, is a decidedly more complex interplay of electrostatic and dispersive interactions. This is particularly true for phenolic compounds. The following arguments appear to have solid experimental and theoretical support ... 

A second modification that can be made concerns the use of pseudopotentials on the MM atoms. These provide a more accurate way of accounting for the electrostatic and dispersion interactions between the QM and MM atoms. They enter into the calculation in the same way as the electrostatic interactions — there will be a term for interaction with the nuclei of the QM atoms which is additive and a term which is incorporated into the one-electron matrix. They have been employed to describe the core electrons of atoms in QM calculations and also by Sprik and Klein [76], Estrin et al. [77] and Vaidehi et al. [29] and other groups to describe interactions between QM and MM atoms. Both pseudopotentials and polarizabilities can be included simultaneously as pseudopotentials, in general, do not describe charge distortion effects on the MM atoms. 

In the adsorption of inorganic solutes, the main fundamental challenge remains how to "activate" the entire surface to achieve maximum removal efficiencies. In the adsorption of organic solutes, the influence of carbon surface chemistry is decidedly more complex. Both electrostatic and dispersive interactions can influence or control the equilibrium uptake of a weak aromatic electrolyte. 

This assumption is in general rather poor and introduces two more parameters into the model, AE, and A/s, which are often related to the ionization potentials. Its only advantage is to make the evaluation of AAd feasible provided that one is able to compute the multipole polarizabilities. We proposed 2I] a convenient extension of the Kirkwood-Pople-Schofield variational method [22] which leads to reasonable values of AAd, and enables us to derive SCKV Hartree-Tock equations including the electrostatic and dispersion interactions 23]. 

The objective of the polarization model is to relate the material parameters, such as the dielectric properties of both the liquid and solid particles, the particle volume fraction, the electric field strength, etc., to the rheological properties of the whole suspension, in combination with other micro structure features such as fibrillatcd chains. A idealized physical model ER system—an uniform, hard dielectric sphere dispersed in a Newtonian continuous medium, is usually assumed for simplification reason, and this model is thus also called the idealized electrostatic polarization model. The hard sphere means that the particle is uncharged and there are no electrostatic and dispersion interactions between the particles and the dispersing medium before the application of an external electric field. For the idealized electrostatic polarization model, there are roughly two ways to deal with the suspensions One is to consider the Brownian motion of particle, and another is to ignore the Brownian motion and particle inertia. For both cases the anisotropic structure of such a hard sphere suspension is assumed to be represented by the pair correlation function g(r,0), derived by... 

Now using Stone s formalism [3.15], the case when the symmetry of the orientational distribution of the fi2 vector is lower than spherical is considered. In particular, possible contributions to potential of mean torque by electrostatic and dispersion interactions are briefly examined. A general expansion of the pair potential [Eq. (3.20)] as a product of a distance dependent and an angular dependent function is [3.15]... 

Moreover, the composition of a liquid may change at liquid-solid boundaries due to, for example, electrolyte concentration changes. This is expected to influence, to some extent, the value of the Hamaker constant. Thus, in the general case, the electrostatic and dispersion interactions are coupled in a complex nonlinear way, which violates the assumption of the DLVO theory. Due to the lack of appropriate theories, we should accept the hypothesis that this coupling is not too significant. 

Electrostatic and dispersion interactions are important for the attraction and directionality of the intermolecular interactions of aromatic molecules [8-10,16]. Quantitative evaluation of electrostatic and dispersion energies is essential for understanding the intermolecular interactions of aromatic molecules. An accurate evaluation of electrostatic energy is not difficult, as DMA provides an accurate value ( es) [15]. On the other hand, an accurate evaluation of the dispersion energy is very difficult. An IMPT calculation using a large basis set is necessary. 

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