Perturbation theories for the dipolar fluids

We derive here four different perturbation equations for the calculation of the angular pair correlation functions of dipolar fluids; namely, the first order y-expansion, the modified Percus--Yevik (MPY) expansion, the modified hypernetted chain (MHNC) expansion, and the modified linearized hypernetted chain (MLHNC) equation. Both the method of the functional expansion and the method of the cluster integrals are utilized. Comparison with other perturbation theories (e.g., the Melnyk--Smith equation) is made. While none of the theories is exact, as shown by the cluster diagrams, the MLHNC and the MHNC contain more diagrams than, say, the MPY and y-expansion. The y-expansion equation can be improved by including the correction terms to the Kirkwood superposition approximation for the triplet correlation function. For example, the inclusion of the correction term rho∫d4h(14)h(24)h(34) in a formula given by Henderson, is shown to improve substantially the y-expansion equation. We examine the performance of two of the theories: the y-expansion and the MLHNC equation for a Stockmayer (dipolar) fluid with a reduced dipole moment μ/sup asterisk2/ [ = μ2/(epsilonsigma3)] = 1.0. Comparison with Monte Carlo simulation results of Adams et al. and with other theories (e.g., the QHNC equation) shows that our results are reasonable. Further improvements of the equations are also pointed out