Cluster conformations and multipole distributions in ionic fluids. I. Two-dimensional systems of mobile ions

A new association-biased Monte Carlo (MC) method is proposed for efficient simulation of association and dissociation of ions in an ionic fluid. The method is then utilized to carry out extensive MC simulations, in order to study the properties of ionic fluids in two-dimensional systems that consist of mobile ions. The size distributions of the ionic clusters, their conformations, as well as the clusters' multipole distributions are computed over wide ranges of temperature T and ions' density rho. At any given T, bonded dipolar pairs are dominant in the insulating phase, but larger clusters with an even number of ions are also present. In the conducting phase at the same T, however, single (free) ions are abundant, while clusters of larger sizes are also present. As for the conformations of the clusters, at any T, perturbed folded structures are dominant in the insulating phase, whereas perturbed linear chains are the dominant conformation in the conducting phase at the same T. Moreover, ionic clusters with closed loops are rarely formed, if at all, over the range of T that we study. As T decreases, more clusters with symmetrical conformations are formed. The multipole distributions are shown to be accurate indicators for the various types of conformations of the ionic clusters. They are also shown to be accurate means of differentiating the conformations of ionic clusters that may appear to be only slightly different, and may be difficult to distinguish otherwise, as the multipoles are sensitive to the details of the conformations. Some exact results are presented for the dipoles and quadrupoles of several types of cluster conformations. These results give rise, for the first time, to a numerical "spectroscopy" of ionic fluids, whereby each conformation is associated with distinct values of the dipole and quadrupole of the ionic cluster. We also suggest a new method of locating the critical locus T(c)(rho) that separates the conducting and insulating phases-the Kosterlitz-Thouless transition-based only on the size distribution of the ionic clusters and its dependence on the ions' density.