Theoretical determination of the dielectric constant of a two dimensional dipolar fluid

Abstract

Integral equations are solved to predict the pair correlation function, dielectric constant and thermodynamic properties of a two dimensional fluid. The results are compared with computer simulations including spherical truncation of the dipole potential, the reaction field method and spherical boundaries. The latter method has not yet been explored for dipolar systems and consists in placing the particles on the surface of a three dimensional sphere. Although the long range parts of the pair correlation functions predicted by these simulation methods all differ from that expected for an infinite system, the short range parts are sufficiently independent of boundary conditions and system size to permit an unambiguous test of the integral equations in this region. The most satisfactory is the QHNC equation. It gives very precise thermodynamic properties but dielectric constants which are too high compared to simulation results when the dipole moment μ* is larger then 1·5. The difference is of the order of 30 per cent for μ* = 2. The accuracy of ε obtained from the computer simulations is 10 per cent.