Investigation Of Phase Instability And Correlation Lengths In Ionic Fluid

The theoretical investigation in ionic fluids has been done with analytical or numerical calculation of integral equations. The integral equations consist of two equations: the Ornstein-Zernike (O. Z.) equation and the closure. The O. Z. equation describes the relation between the direct and total correlation functions, and this relation can be interpreted that the total correlation function of two particles is the sum of direct correlation and indirect correlation transferred by all other particles. O. Z. equation is for two unknown functions and so another equation for the direct correlation function C(r,T,p) and the total correlation function h(r,T,p) is necessary, which is usually called the "closure" of the open problem. Some functions in the closure can not be obtained exactly and must be approximated, so the closure is an approximate relation between the correlation functions and the interaction potential. According to the different kinds of approximations, there many kinds of closures, the mostly used are the Percus-Yevick (PY) approximation, the mean sphere approximation (MSA) and the hypernetted chain (HNC) approximation. PY approximation and the MSA are applicable for the systems with short range interaction, and only the HNC approximation can be used in the systemswith strong long range interaction. With the numerical iteration method we use the HNC integral equations to calculate the direct correlation function C(r,T,p) andthe total correlation function h(r,T,p) in a soft-sphere ionic fluid which something like the system of the alkali-metal salts. We discuss the phase instability of the system with the grand potential functional and find only gas-liquid phase transition happens and the demixing phase transition does not happen. After numerical calculation we want to draw the phase transition line, but failed in low density because of the divergence in calculation. Then we calculate three correlation lengths in order to see what happens in low density. The second moment density-density correlation length N,1 is from the density-density structure factor,the second moment charge-charge correlation length Z,1 is from the charge-charge structure factor, and the Lebowitz length L is related to the charge fluctuation. All of the correlation lengths diverge in low density, N,1 as -1/4 , Z,1 , and L as -1/2 , and these results are the same as the S. Bekiranov and M. E. Fisher's. S. Bekiranov and M. E. Fisher analytically calculated these correlation lengths with two methods: the first is HNC and Meeron's resummation, the second is generalized Debye-HUckel theory. Their results of N,1 and L are the same toours only when the reduced density is less than 10-3 . The divergence of the correlations gives as the signal of something happens in the system in low density.L is the linear dimension of neutral clusters in the ionic system. The lower density with the larger L means the forming of larger neutral clusters. Then when wewant to use the integral equations in low density, we must consider not only the interaction between ions but also the effects of the neutral clusters.