Evaluation of cooperativity for phase transitions in two- and three-dimensional systems

Abstract

Use of the so-called "cooperative unit" (readily obtainable from the midpoint slope of phase transition curves) is discussed for the determination of cluster sizes and cooperative interaction energies. This quantity has been commonly employed in a rather empirical way since its correct interpretation is known only for some special cases (linear systems, all-or-none transitions). It is shown in the framework of a lattice model (Ising model) that the cooperative unit may be interpreted in terms of correlation functions and that it defines an average cluster corresponding to the patch size as obtained from scattering experiments. Relations between the cooperative unit and a cooperativity parameter are given for various lattices. Different types of transition curves are discussed using a simple analytical formalism, the quasichemical approximation. Some important nonideality effects are investigated which may lead to a "smearing-out" of first-order transitions.