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Condensation Transition in Polydisperse Hard Rods | | M.R. Evans
; S.N. Majumdar
; I. Pagonabarraga
; E. Trizac
; | | Date: |
28 Sep 2009 | | 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 $V=sum_{i=1}^N v_i$, $N$ 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 behaviour 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. | | Source: | arXiv, 0909.5054 | | Services: | Forum | Review | PDF | Favorites | |
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