Generalized Flory Theory for Rotational Symmetry Breaking of Complex Macromolecules

Abstract

We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. We analyze this transition using a variational mean-field theory that combines the Gibbs-Bogolyubov-Feynman inequality with the concept of the Laplacian matrix. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of this Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension Eventually, the variational free energy landscape develops a complex structure with multiple competing minima.

References in corpus (4)

• Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications
• Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications
• Extended Vicsek fractals: Laplacian spectra and their applications
• From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers