Condensation transition in polydisperse hard rods

摘要

We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume v, with the constraint of a fixed total volume V = ∑i = 1Nvi, N being the total number of particles. The particles, referred to as p-spheres, have a linear size that behaves as vi1/p and our model thus represents a gas of polydisperse hard rods with variable diameters vi1/p. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard-rod system, under the constraints of fixed N and V. Complementary approaches (explicit construction of the steady state distribution on the one hand; density functional theory on the other hand) completely and consistently specify the behavior of the system. A real space condensation transition is shown to take place for p>1; beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles. © 2010 American Institute of Physics Article Outline INTRODUCTION Summary of results MODEL Dynamics Factorized steady state THERMODYNAMICS IN GRAND CANONICAL ENSEMBLE Ensembles Reduced volume fraction ϕ∗ and scaling variable u Entropy The case p ≤ 1 The case p>1 The large p limit MICROCANONICAL ANALYSIS OF THE CONDENSED PHASE FOR p>1 THE FREE ENERGY FUNCTIONAL ROUTE Free energy functional for polydisperse hard rods Optimal polydispersity distribution The condensation transition COMPARISON WITH SIMULATION RESULTS Control parameter and critical point Monte Carlo simulations CONCLUSION