Auto-calibrated colloidal interaction measurements with extended optical traps

Marco Polin, Yohai Roichman and David G. Grier
Department of Physics and Center for Soft Matter Research, New York University, New York, NY 10003

Abstract:

We describe an efficient technique for measuring the effective interaction potential for pairs of colloidal particles. The particles to be tested are confined in an extended optical trap, also known as a line tweezer, that is projected with the holographic optical trapping technique. Their diffusion along the line reflects their intrinsic interactions with each other, the influence of the line's potential energy landscape, and also inter-particle interactions mediated by scattered light. We demonstrate that measurements of the particles' trajectories at two laser powers explicitly correct for optically-induced forces and that statistically optimal analysis for optically-induced forces yields auto-calibrated measurements of the particles' intrinsic interactions with remarkably few data points.

Colloidal interactions tend to be diminutive, often no greater than a few femtonewtons, and typically are masked by vigorous Brownian motion. Nevertheless, they govern the microscopic stability and macroscopic properties of colloidal dispersions. Monitoring these interactions therefore is useful for understanding and controlling the many natural and industrial processes governed by colloidal dynamics.

This Article introduces a rapid and accurate method for measuring the interactions between a pair of colloidal particles. Combining optical micromanipulation (1), digital video microscopy (4,5,2,3) and a new analytical scheme based on adaptive kernel density estimation (6), this method requires just minutes to characterize the pair potential of micrometer-scale particles in water. It corrects for experimental artifacts identified in previous studies of colloidal interactions, accounts for any optically-induced interactions, and provides results in near-real time.

Section 1 reviews methods for measuring colloidal interactions with an emphasis on the practical considerations that have limited their widespread adoption. This section also highlights some of the benefits and challenges of confining colloidal particles to one dimension using extended optical traps known as line tweezers. Section 2 briefly describes our holographic implementation of line traps, which have been described in detail elsewhere (7,1). The principal contributions of this Article are presented in Sec. 3, which addresses the statistical mechanics of interacting colloidal particles on a line trap. This discussion develops a statistically optimal analysis of trapped particles' trajectories that yields accurate results for the pair potential with exceedingly small data sets. We apply these methods to a well-studied model system in Sec. 4 to demonstrate that just 4,000 samples of two particles' trajectories can suffice to measure their pair potential to within $\pm 0.5~k_B T$ .