Localization transition of random chains at interfaces

We consider a simple model of a random chain at an interface between two fluids, and suppose that its monomers have random affinities with both fluids (e.g., a Gaussian distribution with mean value ζ₀). Simple statistical arguments and replica theory lead to the prediction of a localization transition of the chain (for the generic case of nonzero ζ₀). This transition separates a low-temperature phase, in which the random chain is localized at the interface, from a high-temperature phase in which it is delocalized in one solvent. This physical picture is qualitatively confirmed by numerical studies.