Dept. of Materials Science
Oregon Graduate Center
The asymptotic behavior of the pair correlation functions of a one-dimensional binary mixture of simple model fluids is investigated. The method of investigation is an extension of a technique developed by Fisher and Widom (1) for simple one-component systems. The technique consists of examining the poles of the Laplace transform of the pair correlation function to determine the pole of least negative real part. The present investigation has been restricted to systems interacting through either hard-sphere or square-well intermolecular pair potentials. In all cases the pair potentials are short ranged and strictly nearest neighbor. The actual extraction of the poles of the Laplace transform of the pair correlation functions is carried out numerically. One specific case of a hard-sphere system has been solved analytically. In the case of hard spheres, a locus is generated in the density, concentration plane across which the pair correlation function abruptly changes its spatial frequency. Both linear continuum and lattice gas models are investigated for the hard-sphere systems and the results are found to be in qualitative agreement with each other. The square-well systems exhibit loci which divide the density temperature plane into several regions. Each region is characterized by the value of the spatial frequency associated with the damped sinusodial decay of the pair correlation function. The zero frequency region corresponds to monotonic exponential decay.
Perry, Paul M., "Asymptotic behavior of pair correlations in one-dimensional binary mixtures" (1973). Scholar Archive. 34.