Entropic Effects of Interacting Particles Diffusing on Spherical Surfaces

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.

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

“…The GCMS representation is 'expandable' to include multiple steps and wells depending on the physical system being considered. Most recently, Ledesma-Durán and co-workers [83] investigated the entropic effects associated with the diffusion of colloidal particles on spherical surfaces using a GCMS representation. The GCMS potential can also be extended to capture anisotropic contributions: this variant has been successfully applied to MD simulations of Janus particles in which the attractive domain of a softened SW interaction contains an orientation-dependent term [84].…”

Adiabatic limit collapse and local interaction effects in non-linear active microrheology molecular simulations of two-dimensional fluids

“…We used the GCMS potential due to its ability to provide continuous representations of discrete potentials like the square-well and square-shoulder potentials, among others. 47,48 This ability is useful for its implementation in conventional MD algorithms.…”

Fast and precise inference on diffusivity in interacting particle systems

“…This problem has been studied by physicists for the last few decades, see for example (Spiechowicz and Łuczka 2017 ) and (Ledesma-Durán et al. 2021 ). Thus, just considering the MSD of our particle system will not suffice to draw conclusions regarding the diffusion coefficient in the cases of dense, highly correlated particles.…”