DENSITY FIELD THEORY TO STUDY ASSOCIATION IN A YUKAWA FLUID. ROLE OF THE FLUCTUATIONS

In this paper we study the effect of the interaction potential in a liquid where there is an equilibrium of association of a molecule into dimers. We use a field theory where the fields represent the densities of the species and of its dimer. The Hamiltonian is a generalization to binary mixtures of the Hamiltonian studied in the previous work for a one component liquid interacting with a Yukawa potential. In the binary mixture, the dimerization equilibrium is taken into account as a condition on the chemical potential of the monomers and dimers. In this paper we compare the effect of the interaction potentials on the equilibrium densities as predicted by the mean field approximation to their effect as a consequence of the fluctuations. The fluctuations play an important role in the field theoretical analysis. To obtain the effect of the fluctuations, we have used a relation equivalent to the `equation of motion' in the field theory for the interacting quantum particles. We find that in a number of physical cases the mean field analysis can be entirely modified by the effect of the potential in relation with the fluctuations