Solvent depletion and other effects on linear aggregation

摘要

The exclusion of solvent from solute clusters provides an additional contribution to aggregation. A derivation of the well known equations for equilibrium aggregation is given, and an explicit expression for the solvent-exclusion effect is obtained for linear aggregates. The analytical result is shown to be in qualitative agreement with recent Monte Carlo simulations of model discotic solutions, which found a concentration dependence of the equilibrium constant. The latter behaviour is argued to stem from a peculiarity in the simulation protocol, namely that the total pressure was fixed, which means that the solvent pressure must increase due to the decreased osmotic pressure at lower solute concentrations. Finite size effects are shown to have a small effect in the simulations. Two further contributions to the observed increased aggregation at low temperatures and concentrations are analysed. For intra-column aggregation it is argued that it is more appropriate to use the length of the column rather than the volume of the system in the definition of the aggregation constant. The possibility is raised that the increased aggregation seen at low solute concentrations could manifest a type of phase transition, either to one-dimensional columns, driven by feedback between the solvent pressure and the number of aggregates, or to a solvent-depleted globule.