Scaling properties of chain interactions in amphiphilic aggregates

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Abstract
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 conformationalprobability 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.