CONFORMATIONAL ENTROPY OF A BRANCHED POLYMER

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