Physical Clusters, Surface Tension, and Critical Phenomena

Abstract

A physical‐cluster theory of condensation and critical phenomena is developed in which primary emphasis is placed on collective modes of oscillation of clusters under the restoring force of their surface tension. A procedure is advocated for self‐consistent inclusion of surface mode interaction leading to a nonlinear integral equation whose solution yields a wavelength‐dependent surface tension. An explicit expression is derived for the physical‐cluster‐size distribution near condensation, and from it follows prediction of critical exponents δ (critical isotherm degree), γ′ (initial compressibility below T_c), ν′ (correlation length), and η (deviation from Ornstein—Zernike pair distribution at the critical point), in terms of the phenomenological coexistence curve (β) and surface tension (σ) exponents, as well as a parameter v, which is not directly measureable. The predictions are not consistent with the so‐called ``scaling laws,'' except for special v values that seem experimentally unacceptable. Reasons are listed indicating fundamental differences between the critical phenomena in lattice gases enjoying high current theoretical fashionability, and continuum fluid models. For a range of v values, the physical cluster theory predictions agree well with experiment. Appendices are devoted to an interfacial fluctuation theorem, and to an outline of the present physical‐cluster theory in two dimensions.