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. This 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 single-file 1D
mobility 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
leads to the hard rod SFD theory for a Tonks gas.Comment: 4 pages, 4 figure