Omstein-Zemicke

An alternative derivation, which uses the Omstein-Zemicke equation ( equation (A2.4.12). was given by Lee [2], The Omstein-Zemicke equation can be written as... 

Using the Omstein-Zemicke equation, numerical solutions for the restricted primitive model can be. 

We have investigated theoretically film-thickness stability and structure formation inside a liquid film by Monte Carlo numerical simulations and analytical methods, using the Omstein-Zemicke (0-Z) statistical mechanics theory (21-24). The formation of longrange, ordered microstructures (giving rise to an oscillating force) within the liquid film leads to a new mechanism of stabilization of emulsions (3,4,25). In addition to the effective volume of micelles or other colloidal particles and polydispersity in micelle size, the film size is also found to be flic main parameter governing emulsion stability (15). 

For flexible molecules, the correlation functions are also functions of the molecular conformation. We consider small substances those for which conformation effects can be ignored. The molecular Omstein-Zemicke (OZ) equation defines the molecular DCF, c, (ri2, 0)i, otj) (Gray and Gubbins 1984),... 

This equation is known as the Omstein-Zemicke equation and if one were able to solve it, all the thermodynamic quantities, along with the density profiles, etc., would be known. To do so, or alternatively is required at least as a function of the other functions in Eq. (253). 

The adsorbed colloid systems also can be used for mimicking fluctuation phenomena occurring on molecular level. This is so because the adsorbed particle monolayer resembles a frozen fluctuation whose statistical analysis can furnish interesting structural information of general validity. In order to express quantitatively fluctuation phenomena, one usually determines the variance of the number of particles absorbed over equal-sized surface areas S [181-183]. This quantity is connected with the pair-correlation function by the Omstein-Zemicke relationship [132]... 

Since q 1, an Omstein-Zemicke type function is equally suitable to fit the data. This would only shift the parameters by a constant factor.)... 

Ifre size of the micelles could also be obtained by SAXS measurements. The background corrected and desmeared intensity distributions are depicted in Figure S. The intensity is divided by die respective concentration, all curves show the same behavior. Each dace can be approximated by either the Omstein-Zemicke fimction (eq 3, Figure 9) or a core-shell structure of spheres (eq 4). The correlation length and the radii Ri (core) and R2 (shell) were determined for several concentrations close to c (Table II). 

Figure 9. Intensity distribution of an aqueous solution with 0.7 wt% 57Tri07H and Omstein-Zemicke approximation.

The parameters R, and V represent the particle volume fraction, radius, and volume, respectively. The function is the particle form factor P Q, Rd. The contribution X(i j) is the Schultz function [50,51], which is characterized by an average radius R7 and root-mean-square (RMS) deviation o- = Rf/(Z 1)", where Z is a width parameter. With samples that were close to the low-pressure phase boimdary it was necessary to introduce into Eq. (2) an attractive Omstein-Zemicke structure factor S Q, C)- This S Q) is an effective function, accounting for additional scattering at low Q, and has been used before with CO2 microemulsions [11,13,16,17,30]. The O-Z function describes a decaying particle distribution with the correlation length, and the strength of interactions is related to S(0) via the isothermal compressibility [51]... 

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