Chain organization and thermodynamics in micelles and bilayers. I. Theory

Abstract

Starting from the partition function of a micellar aggregate, the various assumptions involved in decomposing the aggregate’s standard chemical potential into surface and core terms are explicitly stated and discussed. The conformational statistics of the amphiphiles’ hydrocarbon chains (tails) composing the hydrophobic core is assumed to be governed by the hard core repulsive interactions between chain segments. The density within the core is assumed uniform and liquid-like. By appropriate expansion of the aggregate’s configurational integral, explicit expressions are derived for the (singlet) distribution function of chain conformations and the chain’s conformational partition function (free energy). These quantities depend on the thickness and curvature (geometry) of the hydrophobic core via the lateral pressures representing the geometric packing constraints. (The same distribution function has been previously derived by us using the maximal entropy formalism.) It is argued that the variations in the conformational contribution to the aggregate’s chemical potential may be comparable to those due to the surface term. (In the prevailing models of amphiphile aggregation only the latter are included.) Detailed numerical analyses for model chains packed in spherical, cylindrical, and planar aggregates are presented in the subsequent paper (part II). One of the major conclusions from the calculations is that geometric packing constraints rather than internal energy (gauche–trans) effects are the dominant factors determining chain statistics.