A theoretical model for copolymer-bilayer interactions

We develop a theory to model the interactions between an amphiphilic copolymer and a bilayer. The copolymer is represented as a Gaussian chain, which contains an alternating arrangement of hydrophobic and hydrophilic sites along the length of the chain. The bilayer is modeled as a hydrophobic layer embedded in a hydrophilic environment. We use the transfer matrix technique to determine the polymer density profiles and the phase diagram for this system. Two distinct phases are observed. In one phase, the copolymer is localized at the surface or within the bilayer. In the second phase, the polymer is unbound or "delocalized." There is a continuous transition between the two phases. We also determine the scaling behavior for the density profiles. The scaling exponents agree with our analytical arguments. We discuss the implications of our findings on designing copolymers that can act as adhesives or macromolecular surfactants.