Chain statistics in micelles and bilayers: Effects of surface roughness and internal energy

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Abstract
A recently developed mean field (‘‘single‐chain’’) theory for amphiphile chain organization and thermodynamics in micellar aggregates is applied to rotational isomeric state, model chains. The theory provides explicit, simple expressions for the probability distribution of chain conformations and related molecular and thermodynamic properties applicable to aggregates of arbitrary geometries. Bond order parameter profiles calculated from the theory for a planar bilayer, assuming a compact hydrophobic core, show very good agreement with experimental data and molecular dynamics simulations. For small spherical micelles comparison between theory and experiment suggest the existence of a somewhat rough (few angstroms wide) hydrocarbon–water interfacial region. Cylindrical aggregates reveal intermediate behavior. The extent of ‘‘surface roughness’’ is introduced into the theory via a density profile of the hydrophobic core which decreases gradually from the bulk liquid (compact core) density to zero. A series of calculations is presented to analyze the effects of internal chain (gauche/trans) energy and micellar geometry on the conformational and thermodyamic properties of the hydrocarbon chains. It is found that the internal energy plays only a secondary role, compared to the primary role of the packing constraints. (This is qualitatively consistent with our previous findings for approximate, ‘‘cubic,’’ model chains.) The conformational free energy cost associated with chain packing in aggregates is shown to depend on the micellar geometry (i.e., on the curvature of, and the average area per head group at, the hydrocarbon–water interface) and to be comparable with the surface (head group) contributions treated exclusively in the prevailing theories of surfactant self‐assembly. Finally, a ‘‘corresponding‐states’’ behavior is demonstrated for packed chains (in planar bilayers) by referencing all thermodynamic functions and configurational properties to those of the associated ‘‘free’’ chain.