Statistical thermodynamics of molecular organization in mixed micelles and bilayers

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Abstract
The conformational and thermodynamic characteristics of molecular organization in mixed amphiphilic aggregates of different compositions and geometries are analyzed theoretically. Our mean‐field theory of chain conformational statistics in micelles and bilayer membranes is extended from pure to mixed aggregates, without invoking any additional assumptions or adjustable parameters. We consider specifically binary aggregates comprised of long‐chain and short‐chain surfactants, packed in spherical micelles, cylindrical rods, and planar bilayers. Numerical results are presented for mixtures of 11‐ and 5‐carbon chain amphiphiles. The probability distribution functions (pdfs) of the (different types of) chains are determined by minimizing the conformational free energy, subject to packing constraints which reflect the segment density distribution within the hydrophobic core. In order to analyze the relative thermodynamic stabilities of mixed aggregates of different compositions (long/short chain ratios) and different geometries, the aggregate’s free energy is expressed as a sum of conformational, surface, and mixing contributions. The conformational free energy is determined by the pdfs of the chains and the surface term is modeled in terms of the ‘‘opposing forces’’ operative at the hydrocarbon–water interface. An interesting coupling between these terms arises from the special geometric (surface/volume) limitations associated with packing short and long chains in a given ratio within a given aggregate. In particular, it is found that the minimal area per surfactant head group in a mixed spherical micelle is significantly lower than that in a pure micelle (similarly, though less drastically so, for cylindrical micelles). The most important qualitative conclusion of our thermodynamic analysis is that the preferred aggregation geometry may vary with composition. For example, we find that under certain conditions (areas per head group, chain lengths) the preferred micellar geometry of pure long or short‐chain aggregates is that of a planar bilayer, whereas at intermediate compositions spherical micelles are more stable. Our analysis of chain conformational properties provides quantitative information on the extent of long (or short) chain distortion attendant upon chain mixing. For example, the results for bond order parameter profiles and segment density distributions reveal enhanced stretching of the long chain towards the central regions of the hydrophophic core as the fraction of short chains is increased.