On the localization of random heteropolymers at the interface between two selective solvents

Abstract:

To study the localization of random heteropolymers at an interface separating two selective solvents within the model of Garel, Huse, Leibler and Orland, [Europhys. Lett. 8, 9 (1989)], we propose a disorder-dependent real space renormalization approach. This approach allows to recover that a chain with a symmetric distribution in hydrophobic/hydrophilic components is localized at any temperature in the thermodynamic limit, whereas a dissymmetric distribution in hydrophobic/hydrophilic components leads to a delocalization phase transition. It yields in addition explicit expressions for thermodynamic quantities as well as a very detailed description of the statistical properties of the heteropolymer conformations in the high temperature limit. In particular, scaling distributions are given for the lengths of the blobs in each solvent, for the polymer density, and for some correlation functions. In the case of a small dissymmetry in hydrophobic/hydrophilic components, the renormalization approach yields explicit expressions for the delocalization transition temperature and for the critical behaviors of various quantities: in particular, the free energy presents an essential singularity at the transition (the transition is thus of infinite order), the typical length of blobs in the preferred solvent diverges with an essential singularity, whereas the typical length of blobs in the other solvent diverges algebraically. Finite-size properties are also characterized in details in both cases. In particular, we give the probability distribution of the delocalization temperature for the ensemble of random chains of finite (large) length L, and the distribution of the numbers of blobs for the chains that are still localized at a given temperature. Finally, we discuss the non-equilibrium dynamics at temperature T starting from a zero-temperature initial condition.