Self-consistent Treatment of Copolymers with Arbitrary Sequences

Using the Gaussian Ansatz for the monomer-monomer correlation functions we derive a set of the self-consistent equations for determination of the conformational state in the bead-and-spring copolymer model. The latter is based on the Edwards type effective free energy functional with arbitrary two-body interaction matrix. The rate of conformational changes in kinetics may be expressed via the instantaneous gradients of the variational free energy functional in the space of the averaged dynamical variables. We study the equilibrium and kinetics for some periodic and random aperiodic amphiphilic sequences in infinitely diluted solution. Typical equilibrium phase diagrams are elucidated and the conformational structure of different states is discussed. The kinetics of compaction of an amphiphilic copolymer to the globular state proceeds through formation of locally frustrated non-equilibrium structures. This leads to a rather complicated multistep kinetic process. We observe that even a small modification in the primary sequence of a copolymer may significantly change its kinetic folding properties.