Concentration Dependence of Linear Self-Assembly and Exactly Solvable Models

Exactly solvable one-dimensional models of amphiphilic solutions are used to investigate the concentration dependence of isodesmic chemical equilibria (linear self-assembly). Highly efficient methods are developed for solving directly for the equation of state and for obtaining the cluster statistics. Remarkably, at fixed pressure, it is the low concentration limit where the equilibrium constant is both maximized and shows the strongest concentration dependence.