Kinetic energy of flexible aggregates and universal power-law behavior of self-assembling in a thermal bath

Abstract

I am drawing the readers’ attention to the importance of the kinetic energy contribution which has been systematically ignored in the partition functions of worm-like objects in a thermal bath. The kinetic energy of linear aggregates is shown to play a unique role when they are reversibly assembled from solute molecules in a solvent. The kinetic energy contribution to the partition function of an n-mer is modeled by the term n q , where q is determined by the persistence lengths of different translation-rotation modes (e.g., q = 5 for a rigid rod and q ≈ 0 for a very flexible chain). The model gives rise to different aggregation regimes for lower and higher solute concentration. The concentrations of different n-mers and total aggregate concentration, which is the main order parameter of the system, are found to depend on the solute concentration via its powers that are different in different regimes, but are always determined solely by the parameter q. The approximate analytical and numerical solutions of the model are in quantitative agreement and clearly show the universal power-law q dependencies. At the same time, it is imposible to express the exact analytical solution in a simple form. The model is pertinent to self-assemblies of plank-like dye molecules dissolved in an isotropic solvent (related to lyotropic chromonic liquid crystals).