Abstract
We present a molecular dynamics and theoretical study on the diffusion of interacting particles embedded on the surface of a sphere. By proposing five different interaction potentials among particles, we perform molecular dynamics simulations and calculate the mean square displacement (MSD) of tracer particles under a crowded regime of high surface density. Results for all the potentials show four different behaviors passing from ballistic and transitory at very short times, to sub-diffusive and saturation behaviors at intermediary and long times. Making use of irreversible thermodynamics theory, we also model the last two stages showing that the crowding induces a sub-diffusion process similar to that caused by particles trapped in cages, and that the saturation of the MSD is due to the existence of an entropic potential that limits the number of accessible states to the particles. By discussing the convenience of projecting the motions of the particles over a plane of observation, consistent with experimental capabilities, we compare the predictions of our theoretical model with the simulations showing that these stages are remarkably well described in qualitative and quantitative terms.
Highlights
In several physical and biological systems the mass transport phenomena is carried out in surfaces with non vanishing curvatures
Making use of irreversible thermodynamics theory, we model the last two stages showing that the crowding induces a sub-diffusion process similar to that caused by particles trapped in cages, and that the saturation of the mean square displacement (MSD) is due to the existence of an entropic potential that limits the number of accessible states to the particles
We present the results of the MSD for interacting particles in a crowded spherical surface by using Molecular Dynamics (MD) simulations and implementing five different pairwise-interaction potentials between the particles in a relatively high surface density medium
Summary
In several physical and biological systems the mass transport phenomena is carried out in surfaces with non vanishing curvatures. With the aim to provide a physical interpretation of the results of these numerical calculations, we formulate an analytic model based on the generalized Smoluchowski equation with timedependent coefficients [29,30,31,32,33,34] Using this tool, we can identify how the change of perspective, confinement and crowding are incorporated in an effective diffusion coefficient that takes into account the entropic confinement and the anomalous diffusion. We study the dynamics of the diffusion and the behavior of the MSD using the results provided by a Smoluchowski description which is presented in Sections 3.1 and 3.2, for free and interacting particles, respectively.
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