Conformational Entropy of a Branched Polymer

We consider the globular state of a randomly branched polymer macromolecule with an annealed structure of branchings. We extend for a branched polymer the main steps of the Lifshitz theory of the globular phase and arrive at a generalized Lifshitz equation for conformational entropy. Both the ensemble with given density distributions for all types of particles (ends, branch points, linear chains, etc.) and the one with given total density and chemical potentials of different particles are considered. The entropy of a branched polymer confinement up to some scale R is shown to scale as N(a/R)⁴, contrary to N(a/R)² for linear polymers; simple scaling arguments are given to explain this difference. The effect of nonlocality, or correlations between ends and branch points, is shown to cause a tendency toward microphase segregation in a branched system.