From random walk to single-file diffusion

Binhua Lin, Mati Meron, Bianxiao Cui, Stuart A. Rice, Haim Diamant

Research output: Contribution to journalArticlepeer-review


We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. The ansatz asserts that the inverse mean squared displacement is the sum of the inverse mean squared displacement for short time normal diffusion (random walk) and the inverse mean squared displacement for asymptotic single-file diffusion (SFD). The dependence of the 1D mobility in the SFD on the concentration of the colloids agrees quantitatively with that derived for a hard rod model, which confirms for the first time the validity of the hard rod SFD theory. We also show that a recent SFD theory by Kollmann [Phys. Rev. Lett.PRLTAO0031-9007 90, 180602 (2003)10.1103/PhysRevLett.90.180602] leads to the hard rod SFD theory for a Tonks gas.

Original languageEnglish
Article number216001
JournalPhysical Review Letters
Issue number21
StatePublished - 3 Jun 2005


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