Single-molecule diffusion in freely suspended smectic films

We present a study of the molecular diffusion in freely suspended smectic-$A$ liquid crystal films with thicknesses ranging from 20 down to only two molecular layers. The molecular mobility is directly probed by determining the trajectories of single, fluorescent tracer molecules. We demonstrate, using several different smectic compounds, that a monotonic increase of the diffusion coefficient with decreasing film thickness is a general phenomenon. In two-layer films, the diffusion is enhanced by a factor of 3 to 5 compared to the corresponding bulk smectic phase. Molecular dynamics simulations of freely suspended smectic films are presented which support the experimental results.

Figure 1

Diffusion coefficient in freely suspended 8CB films as a function of the film thickness. The solid line is a fit according to Eq. (1). The error bars are determined by the standard error of the mean. The inset shows a typical trajectory for a time interval $\Delta t=6.5$ s.

Figure 2

Thickness dependence of the diffusion coefficient $D$ (normalized by the respective bulk diffusion coefficients $D_0$) in freely suspended films of C7, 8CB, pyrimidine, and 9O.4. The solid lines are fits using Eq. (1).

Figure 3

Diffusion coefficients obtained from MD simulations of freely suspended smectic films. The $D$ values are obtained in arbitrary units and scaled such that the numerical value of the two-layer film is the same as measured experimentally (in $\mu {\mathrm{m}}^2/\mathrm{s}$) for 8CB. The solid line is the same as in Fig. 1, corresponding to the experimental values obtained for 8CB. The inset shows the $D$ values obtained for the individual layers of a five-layer film, illustrating the larger $D$ values in the two surface layers.

Figure 4

Temperature dependence of the diffusion coefficient in 8CB films for three to seven smectic layers thickness. All films show an Arrhenius behavior with the same activation energy.