Investigation Of Phase Instability In The Binary Gaussian Core Model

In recent years increasing attention has been paid to the soft-particle models of fluids. One of the soft-particle models is the Gaussian core model(GCM) where particle interaction Gaussian. This model serves as a good approximation for the effective interaction between the centers of mass of two polymer chains in the polymer mixtures and has been investigated extensively. In this thesis the phase instability of binary Gaussian core model has been investigated with the type of the phase instability be characterized also.Normally the investigations of phase behaviour of binary fluids are based on the concentration-concentration structure factor S_cc(k) with S_cc{0) = NkBT t,p,n- If S_cc(0) goes to infinity, will approach zero and the system becomes unstable.This criterion determines the boundary of stability which has been called the spinodal. With this criterion it is impossible to distinguish between the demixing and condensation phase instability in a binary fluid. By considering the fluctuation of grand potentialΩ . around equilibrium with respect to small density fluctuations δpα(l): we can determine not only the spinodal, but also clearly characterize the phase instability from its direct correlation functions. The phase instability of binary Gaussian core model has been investigated and characterized.The correlation functions of the binary Gaussian core model are obtained numerically from the integral equations which consist of the Ornstein-Zernike(O.Z.)equation and a closure equation. The O.Z.equation relates the direct and total correlation functions. To determine the correlation functions another relationship between them, which is usually called the closure, is needed. The closure can be obtained only approximately. Different kinds of closure have been discussed in the literature. One of the closures is the hypernetted chain(HNC) approximation which has been shown to be very accurate in comparison with the Monte Carlo simulation of fluids. Here we use the HNC integral equations to calculate the correlation functions of binary GCM with the numerical iteration method. We choose the parameters of the model systems according to the simulation of a mixture of two polymers with length ratio 2:1. After getting the correlation functions in HNC approximation we can determine the spinodal of this model. Our analysis shows that this phase transition is predominately demixing.In the random phase approximation(RPA),the direct correlation functions are set to be equal to the interaction potential between two particles. The approximation made in RPA is much stronger than in the HNC approximation. It is the advantage that the direct correlation functions in RPA are analytic. Previously the spinodal of GCM has been investigated without the characterization of the phase instability. Here we have investigated the phase instability of the binary GCM with the correlation functions obtained in the HNC approximation. The correlation functions in HNC approximation deviates from the RPA's results. Correspondingly the spinodal in HNC approximation deviates from theRPA's. From the eigenvector corresponding the eigenvalue approaching zero in the density fluctuation plane (δρ1, δρ2), the phase instability of the GCM is predominately demixing. In the random phase approximation the phase transition is shown to be also predominately demixing.