Condensation transition in polydisperse hard rods

Martin Evans, S. N. Majumdar, I. Pagonabarraga, E. Trizac

Research output: Contribution to journalArticlepeer-review

Abstract

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=Sigma(N)(i=1)v(i), N being the total number of particles. The particles, referred to as p-spheres, have a linear size that behaves as v(i)(1/p) and our model thus represents a gas of polydisperse hard rods with variable diameters v(i)(1/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.

Original languageEnglish
Article number014102
Pages (from-to)-
Number of pages17
JournalThe Journal of Chemical Physics
Volume132
Issue number1
DOIs
Publication statusPublished - 7 Jan 2010

Keywords

  • condensation
  • density functional theory
  • liquid theory
  • stochastic processes
  • FACTORIZED STEADY-STATES
  • ZERO-RANGE PROCESS
  • EQUATION-OF-STATE
  • SPHERE FLUIDS
  • PHASE-TRANSITIONS
  • OPTIMAL PACKING
  • MODELS
  • SYSTEMS

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