Stochastic inference of surface-induced effects using Brownian motion

Maxime Lavaud,Yacine Amarouchene,Yann Louyer,Thomas Salez

doi:10.1103/physrevresearch.3.l032011

Abstract

Brownian motion in confinement and at interfaces is a canonical situation, encountered from fundamental biophysics to nanoscale engineering. Using the Lorenz-Mie framework, we optically record the thermally-induced tridimensional trajectories of individual microparticles, within salty aqueous solutions, in the vicinity of a rigid wall, and in the presence of surface charges. We construct the time-dependent position and displacement probability density functions, and study the non-Gaussian character of the latter which is a direct signature of the hindered mobility near the wall. Based on these distributions, we implement a novel, robust and self-calibrated multifitting method, allowing for the thermal-noise-limited inference of diffusion coefficients spatially-resolved at the nanoscale, equilibrium potentials, and forces at the femtoNewton resolution.

Highlights

Brownian motion is a central paradigm in modern science
We implement a robust and self-calibrated multifitting method, allowing for the thermal-noise-limited inference of diffusion coefficients spatially resolved at the nanoscale, equilibrium potentials, and forces at the femtonewton resolution
Measure the diffusion coefficient of confined colloids [10,11,12,13,14,15,16], or to infer surface forces [17,18,19,20,21,22]. Such a statistical inference is still an experimental challenge, and a precise calibration-free method taking simultaneously into account the whole ensemble of relevant properties, over broad spatial and time ranges, is currently lacking. In this Rapid Communication, we aim at filling the previously identified gap by implementing a method of statistical inference on a set of trajectories of individual microparticles recorded by holographic microscopy

Summary

Introduction

Brownian motion is a central paradigm in modern science. It has implications in fundamental physics, biology, and even finance, to name a few. We construct the time-dependent position and displacement probability density functions, and study the non-Gaussian character of the latter which is a direct signature of the hindered mobility near the wall.

Results

Conclusion