Force measurement in the presence of Brownian noise: Equilibrium distribution method vs. Drift method

TL;DR

This paper compares equilibrium distribution and drift methods for measuring forces on Brownian particles, highlighting the significance of thermal noise correction terms especially for small particles in nanotechnology applications.

Contribution

It provides a systematic analysis of the correction term in force measurements due to Brownian noise, clarifying its physical origin and dependence on experimental parameters.

Findings

Correction term increases for smaller particles.

Order of correction is several piconewtons for biomolecule-sized particles.

Equilibrium distribution method offers a reliable alternative to drift measurements.

Abstract

The study of microsystems and the development of nanotechnologies require new techniques to measure piconewton and femtonewton forces at microscopic and nanoscopic scales. Amongst the challenges, there is the need to deal with the ineluctable thermal noise, which, in the typical experimental situation of a spatial diffusion gradient, causes a spurious drift. This leads to a correction term when forces are estimated from drift measurements [Phys. Rev. Lett. 104, 170602 (2010)]. Here, we provide a systematic study of such effect comparing the forces acting on various Brownian particles derived from equilibrium distribution and drift measurements. We discuss the physical origin of the correction term, its dependence on wall distance, particle radius, and its relation to the convention used to solve the respective stochastic integrals. Such correction term becomes more significant for smaller particles and is predicted to be in the order of several piconewtons for particles the size of a biomolecule.