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Low density properties of a two dimensional dipolar fluid

Second and third pressure and dielectric virial coefficients are calculated for a two dimensional fluid of hard discs with embedded central point dipoles. These exact results are compared with the predictions of various integral equation theories based upon the hypernetted chain (HNC) approximation. The linearized (LHNC) equation gives poor pressure virial coefficients B p* and C p*, but good results for the dielectric coefficients B e* and C e*. The quadratic (QHNC) equation gives a good approximation to B p* and C p*, even for large values of the dipole moment μ*, but C e* is very poor and is of the wrong sign for μ*2≳2·5. This failure is traced to the arbitrary neglect of rotational invariants other than 1, Δ(12) and D(12) in the eigenfunction expansion of the pair correlation functions h(12) and c(12) of the fluid. We also compute the critical point of the fluid. The critical constants are very different from those previously calculated in the mean spherical approximation (MSA).