Abstract
The dynamics of colloidal particles at infinite dilution, under the influence of periodic external potentials, is studied hereviaexperiments and numerical simulations for two representative potentials. From the experimental side, we analyzed the motion of a colloidal tracer in a one-dimensional array of fringes produced by the interference of two coherent laser beams, providing in this way an harmonic potential. The numerical analysis has been performedviaBrownian dynamics (BD) simulations. The BD simulations correctly reproduced the experimental position- and time-dependent density of probability of the colloidal tracer in the short-times regime. The long-time diffusion coefficient has been obtained from the corresponding numerical mean square displacement (MSD). Similarly, a simulation of a random walker in a one dimensional array of adjacent cages with a probability of escaping from one cage to the next cage is one of the most simple models of a periodic potential, displaying two diffusive regimes separated by a dynamical caging period. The main result of this study is the observation that, in both potentials, it is seen that the critical timet*, defined as the specific time at which a change of curvature in the MSD is observed, remains approximately constant as a function of the height barrierU0of the harmonic potential or the associated escape probability of the random walker. In order to understand this behavior, histograms of the first passage time of the tracer have been calculated for several height barriersU0or escape probabilities. These histograms display a maximum at the most likely first passage timet′, which is approximately independent of the height barrierU0, or the associated escape probability, and it is located very close to the critical timet*. This behavior suggests that the critical timet*, defining the crossover between short- and long-time regimes, can be identified as the most likely first passage timet′as a first approximation.
Highlights
A colloidal particle undergoing Brownian motion presents deviations from pure diffusion when such a particle interacts with an external potential or when it moves in a crowded environment
As only a few particles remain withing the field of view for more than 100 s, the long time dynamics is found to be affected by statistical noise
We have studied some dynamic properties of a Brownian tracer in two periodic potentials at short- and longtimes
Summary
A colloidal particle undergoing Brownian motion presents deviations from pure diffusion when such a particle interacts with an external potential or when it moves in a crowded environment. Some examples of crowded environments that affects colloidal motion include the colloidal motion of proteins or organelles in the interior of a cell [1,2,3], the motion of a tracer particle in complex fluids [4,5,6,7,8,9] and colloidal motion near the glass transition [10, 11]. The main effect of external potentials, or crowded environments, in colloidal dynamics is to promote the appearance of time regimes in which particles might slow down (subdiffusion) or speed up (superdiffusion) their motion as compared with normal diffusion. The dynamics of a colloidal tracer provides useful information about the concentration of other colloidal macromolecules, the degree of coupling between the tracer and an applied external field, as well as the competition between the energy associated to the external potential and the thermal energy [4, 10, 17, 22]
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