Molecular diameters for fluid

Next, let us consider the application of Equation (21) to a particle migrating in an electric field. We recall from Chapter 4 that the layer of liquid immediately adjacent to a particle moves with the same velocity as the surface that is, whatever the relative velocity between the particle and the fluid may be some distance from the surface, it is zero at the surface. What is not clear is the actual distance from the surface at which the relative motion sets in between the immobilized layer and the mobile fluid. This boundary is known as the surface of shear. Although the precise location of the surface of shear is not known, it is presumably within a couple of molecular diameters of the actual particle surface for smooth particles. Ideas about adsorption from solution (e.g., Section 7.7) in general and about the Stern layer (Section 11.8) in particular give a molecular interpretation to the stationary layer and lend plausibility to the statement about its thickness. What is most important here is the realization that the surface of shear occurs well within the double layer, probably at a location roughly equivalent to the Stern surface. Rather than identify the Stern surface as the surface of shear, we define the potential at the surface of shear to be the zeta potential f. It is probably fairly close to the... 

Interfacial rheology deals with the flow behavior in the interfacial region between two immiscible fluid phases (gas-liquid as in foams, and liquid-liquid as in emulsions). The flow is considerably modified by surface active agents present in the system. Surface active agents (surfactants) are molecules with an affinity for the interface and accumulate there forming a packed structure. This results in a variation in physical and chemical properties in a thin interfacial region with a thickness of the order of a few molecular diameters. These... 

Often the liquid structure close to an interface is different from that in the bulk. For many fluids the density profile normal to a solid surface oscillates about the bulk density with a periodicity of about one molecular diameter, close to the surface. This region typically extends... 

The pair correlation function is a short range quantity in liquids, decaying to unity after a few molecular diameters, the correlation length However, in supercritical fluids g(r) has a much longer range and t, becomes considerably larger than the mean inter-molecular separation at the critical density. For instance, for carbon dioxide , = 5.5 nm at Tc compared to the mean intermolecular separation of 0.55 nm (Eckert, Knutson and Debenedetti 1996). 

Water Is a strongly three-dlmenslonally structured fluid (sec. 1.5.3c) with structure-originating Interactions reaching several molecular diameters. Considering this, simple models and/or simulations with a limited number of molecules are not really helpful. By "simple" we mean models in which water molecules are represented as point dipoles, point quadrupoles, or as molecules with Lennard-Jones Interactions plus an additional dipole, etc., and by "limited" less than, say 10 molecules, i.e. 10 molecules in each direction of a cubic box. Admittedly, for a number of simpler problems more embryonic models may suffice. For example, electrochemists often get away with a dipole Interpretation when focusing their attention solely on the Stern layer polarization. Helmholtz s equations for the jf-potential 3.9.9] is an illustration. 

For simple adsorbates composed of spherical molecules in pores of simple geometry, it is possible to map out freezing phase diagrams based on the simulation studies [3,6]. A corresponding states analysis [3] of the partition function for such a system shows that the freezing temperature in the pore, 7/pore, relative to the value for the bulk material, Tfbutk, is a function of three variables H/aff, a, and Ofjoff, where H is pore width, CT is the molecular diameter, subscripts / and w refer to fluid and wall, respectively. 

As a typical example of CEDFT calculations, we present in Fig. 1 the capillary condensation isotherm of N2 in a cylindrical pore mimicking the pore channel in MCM-41 mesoporous molecular sieves. The isotherm is presented in co-ordinates adsorption N versus chemical potential p Calculations were performed at 77 K for the internal diameter of 3.3 nm up to the saturation conditions, point H. We used Tarazona s representation of the Helmholtz free energy [6] with the parameters for fluid-fluid and solid-fluid interaction potentials, which were employed in our previous papers [7]. We distinguish three regions on the isotherm. The adsorption branch OC corresponds to consecutive formation of adsorption layers. Note that the sharp transitions between the consecutive layers are not observed in experiments. They are caused by a well-known shortcoming of the model employed, which ignores intrinsic to real... 

These imperfections have occasioned to review the spherical DFT approach with respect to a more correct description for fluids which consists of non-spherical particles. The paper applies a statistic thermodynamic approach [7, 8] which uses density functional formulation to describe the adsorption of nitrogen molecules in the spatial inhomogeneous field of an adsorbens. It considers all anisotropic interactions using asymmetric potentials in dependence both on particular distances and on the relative orientations of the interacting particles. The adsorbens consists of slit-like or cylinder pores whose widths can range from few particle diameters up to macropores. The molecular DFT approach includes anisotropic overlap, dispersion and multipolar interactions via asymmetric potentials which depend on distances and current orientations of the interacting sites. The molecules adjust in a spatially inhomogeneous external field their localization and additionally their orientations. The approach uses orientation distributions to take the latter into account. 

There have been many analytic and numerical studies of the structure that solids induce in an adjacent fluid. Early studies focussed on layering in planes parallel to a flat solid surface. The sharp cutoff in fluid density at the wall induces density modulations with a period set by oscillations in the pair correlation function for the bulk fluid [169 173]. An initial fluid layer forms at the preferred wall fluid spacing. Additional fluid molecules tend to lie in a second layer, at the preferred fluid fluid spacing. This layer induces a third, and so on. The pair correlation function usually decays over a few molecular diameters, except near a critical point or in other special cases. Simulations of simple spherical fluids show on the order of 5 clear layers [174 176], while the number is typically reduced to 3 or less for chain or branched molecules that have several competing length scales [177 180]. 

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