Pair correlation functions coefficient

The pair correlation functions can be expressed directly in terms of the computed coefficients from Eq. (61) in particular, the number-number pair distribution function gN ir) and the number-number structure factor SNN k). Thus,... 

Local Average Density Model (LADM) of Transt)ort. In the spirit of the Flscher-Methfessel local average density model. Equation 4, for the pair correlation function of Inhomogeneous fluid, a local average density model (LADM) of transport coefficients has been proposed ( ) whereby the local value of the transport coefficient, X(r), Is approximated by... 

It is thus entirely expressed in terms of the zero wave number Fourier coefficient pQ(p t). Similarly, the pair correlation function in a spatially homogeneous system is defined by17... 

An alternative, already implicit in van der Waals theory of the surface tension [237], exploits an interconnection between the coefficient Co and the pair correlation function g(ra, rp) of the inhomogeneous system. As the local density distribution determining g(ra, rp) is unknown, one has to resort to a... 

Here d> is the matrix of pair correlation functions obeying the auxiliary equation (3.529) with helpful initial condition (r, 0) = W(r). Still the problem remains rather complex. Solving it in Ref. 194, all the kernels were specified using as input data only the diffusion coefficients and transfer rates W/ (r), WB (r), Wr (r), and Wrr(r). 

The simulation of the liquid has given a vaporization energy underestimated by 7%, while pressure appears to be overcorrected with respect to MCY at 305 K (P =-1180 + 470atm). Experimental specific heat is well reproduced, as pair correlation functions, apart from the usual shift to larger distance of the first peak of the 0-0 g(r). The effective dipole moment is 2.8 D and diffusion coefficient (r> = 2.5 0.110" cmVs) compares well with the experimental data at 25 C, = 2.4-10" cm /s). Experimental is reproduced... 

Thus, the virial coefficient B2 in (6.44) depends on the pair potential. The virial coefficient depends on the pair correlation function (or equivalently on the potential of the mean force). 

In the site-site representation, the virial pressure involves higher spherical harmonic coefficients of the site-site pair correlation functions. The difficulties involved in the standard virial route to the pressure in polymer systems have been well illustrated in recent work. ... 

This observation constitutes the basic idea of the local equilibrium model of Prigogine, Nicolis, and Misguich (hereafter referred to as PNM). One considers the case of a spatially nonuniform system and deduces from (3) an integral equation for the pair correlation function that is linear in the gradients. This equation is then approximated in a simple way that enables one to derive explicit expressions for all thermal transport coefficients (viscosities, thermal conductivity), both in simple liquids and in binary mixtures, excluding of course the diffusion coefficient. The latter is a purely kinetic quantity, which cannot be obtained from a local equilibrium hypothesis. 

The partial structure factorSab(k) is an equilibrium solution property that is not a thermodynamic coefficient, but that can be measured in scattering or diffraction experiments/ It is given in terms of the pair correlation function gab(r) (Section 4.1) by the equation... 

It may be noted that at present only the cluster expansion methods are reliable for the investigation of the higher-order limiting laws. Also, the relative quality of different approximation methods is most often judged on the basis of comparison of calculated values for only a small number of thermodynamic coefficients. One compares values for the osmotic coefficient < > or the excess energy B = as determined by different methods, or else (for primitive model calculations) the values of the pair correlation functions of the ions at contact. While it is necessary that all of these coefficients be given with high accuracy, relatively little is known about the accuracy of various approximation methods in the determination of the other measurable coefficients summarized in Section 3. 

Among the most useful quality tests are those for self-consistency, which determine whether the pair correlation functions calculated using a particular approximation method give identical results when used to calculate a certain thermodynamic function by different routes. For example, in an ionic solution calculation we can apply the virial-compressibility consistency test as follows From the pair correlation functions, we calculate the osmotic coefficient 4> ... 

The general expressions for the flexoelectric coefficients obtained using the density functional approach can be used to estimate the contributions from different types of intermolecular correlations, including short-range dipole-dipole correlations. We use the following approximation for the direct pair correlation function ... 

The dielectric constant can be obtained from the rotational invariant coefficients of the pair correlation function. For example, following Fries et al., it can be evaluated using the Kirkwood g factor ... 

Static pair correlation functions are not very sensitive to the establishment of long range connections. This implies that dynamic parameters, such as the diffusion coefficient >co p, ate not very sensitive to the establishment of a weak gel phase. 

In the previous four sections we have dealt with some aspects of very dilute aqueous solutions. From the formal point of view, it is sufficient to study the solvation properties of one solute j in a pure solvent. We now proceed to the next step and study a pure solvent with two solutes. In the absence of a solvent, two-particles-in-a-system determines the second virial coefficient in the density expansion of the pressure (section 1.8). Likewise, two-solute-in-a-solvent determines the second virial coefficient of the osmotic pressure (section 6.11). This quantity is expressed in terms of the pair correlation function by... 

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