Experimental evidence for the divergence of a transport coefficient in a quasi-two-dimensional fluid.

Abstract

We report experimental evidence for the divergence of the collective diffusion coefficient in a quasi-two-dimensional fluid. The system studied is a monolayer of nearly monodisperse self-assembled disks of the diblock copolymer polystyrene-b-polymethylmethacrylate, supported in the air/water interface, and the method used to measure the collective diffusion coefficient is dynamic evanescent wave light scattering. In all cases studied, in a system of interacting particles the collective diffusion coefficient, which depends on the sum of the time integrals of the velocity autocorrelation and crosscorrelation functions for all pairs of particles, is proportional to the self-diffusion coefficient. It has been predicted that the self-diffusion coefficient of a two-dimensional fluid does not exist, i.e., that the apparent self-diffusion coefficient defined by the time integral of the velocity autocorrelation function diverges as t\ensuremath{\rightarrow}\ensuremath{\infty}, implying that so, also, will the collective diffusion coefficient of a two-dimensional fluid. Our experimental data are consistent with this qualitative expectation and they also agree with the asymptotic dependence on time (t\ensuremath{\rightarrow}\ensuremath{\infty}), wave vector (Q\ensuremath{\rightarrow}0), and surface density of the self-diffusion coefficient of a two-dimensional fluid predicted by Yuan and Oppenheim [H.H.-H. Yuan and I. Oppenheim, Physica 90A, 1 (1978); 90A, 21 (1978); 90A, 561 (1978)].