Statistics of Particle Trajectories at Short Time Intervals Reveal fN-Scale Colloidal Forces

TL;DR

This paper introduces a method to extract colloidal forces from particle trajectory relaxation at short time scales, leveraging normal mode analysis and fluctuation-dissipation relations, applicable without prior calibration or force assumptions.

Contribution

The authors develop a calibration-free technique using normal mode analysis and fluctuation-dissipation to measure colloidal forces from particle trajectories at short intervals.

Findings

Successfully measured electrostatic interactions of polymer microspheres

Method implicitly accounts for hydrodynamic interactions

No prior knowledge of material properties needed

Abstract

We describe and implement a technique for extracting forces from the relaxation of an overdamped thermal system with normal modes. At sufficiently short time intervals, the evolution of a normal mode is well described by a one-dimensional Smoluchowski equation with constant drift velocity, v, and diffusion coefficient, D. By virtue of fluctuation-dissipation, these transport coefficients are simply related to conservative forces, F, acting on the normal mode: F = k_BT v/D. This relationship implicitly accounts for hydrodynamic interactions, requires no mechanical calibration, makes no assumptions about the form of conservative forces, and requires no prior knowledge of material properties. We apply this method to measure the electrostatic interactions of polymer microspheres suspended in nonpolar microemulsions.