Colloidal transport and diffusion over a tilted periodic potential: dynamics of individual particles

Abstract

A tilted two-layer colloidal system is constructed for the study of force-assisted barrier-crossing dynamics over a periodic potential. The periodic potential is provided by the bottom layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top layer diffusing particles. By tilting the sample at an angle θ with respect to the vertical (gravity) direction, a tangential component of the gravitational force F is applied to the diffusing particles. The measured mean drift velocity v(F, Eb) and diffusion coefficient D(F, Eb) of the particles as a function of F and energy barrier height Eb agree well with the exact results of the one-dimensional drift velocity (R. L. Stratonovich, Radiotekh. Elektron, 1958, 3, 497) and diffusion coefficient (P. Reimann, et al., Phys. Rev. Lett., 2001, 87, 010602 and P. Reimann, et al., Phys. Rev. E, 2002, 65, 031104). Based on these exact results, we show analytically and verify experimentally that there exists a scaling region, in which v(F, Eb) and D(F, Eb) both scale as ν'(F)exp[-E(F)/kBT], where the Arrhenius pre-factor ν'(F) and effective barrier height E(F) are both modified by F. The experiment demonstrates the applications of this model system in evaluating different scaling forms of ν'(F) and E(F) and their accuracy, in order to extract useful information about the external potential, such as the intrinsic barrier height Eb.

Enhanced diffusion with abnormal temperature dependence in underdamped space-periodic systems subject to time-periodic driving

“…The potential barrier height and the free diffusion coefficient were treated as fit parameters. Similarly, diffusivity in [24] (Fig. 7) showed peaked at F 0 behavior, and agreed fairly well with analytic predictions from [19] with the potential form inferred from independent study of the colloidal particle spatial distribution function.…”

Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions

“…The relaxation time τ is shortened if a larger external force F is used. This is because with increasing F , the effective energy barrier is reduced and so does the mean first passage time [40,47]. We numerically solve the 2D version of Eq.…”

“…The values of F c /F T for the two colloidal samples used are given in Table I. When F F c , the particle flux density J ss (or drift velocity v) becomes the same as that over an incline without an energy barrier [40]. It can be shown that the effective friction coefficient ξ eff (F ) in Eq.…”

“…Details about the apparatus and the experimental method have been described elsewhere [19,40], and here we mention only some key points.…”

“…More recently, we carried out a systematic study of the effects of an external force F on the barrier crossing dynamics of the diffusing particles over a periodic potential [40]. By tilting the entire two-layer system at an angle θ with respect to the vertical (gravity) direction, a tangential component of the gravitational force F is applied to the top-layer particles.…”