Scaling properties of chain interactions in amphiphilic aggregates

We outline a connection between recent mean-field theories of short-chain packing in micellar systems and earlier approaches developed for treating phase separation in polymer blends. These theories are easily unified on the basis of a common variational principle, thereby allowing a single route for deriving lateral pressures, local ordering, and thermodynamic properties. In this approach the search for conformational probability distribution functions is mapped into a constrained random walk problem, using the monomer propagator formalism first exploited by Edwards. As an application, the case of a compact (uniform density-"dry") amphiphilic bilayer is studied in detail. We show that the "core" free energy can be described via a single reduced variable relevant to both short and long chains: convenient scaling relations are proposed and discussed.