Most methods for measuring colloidal interactions use digital video microscopy (9,8,2) to track particles' motions. They differ in how the particles are handled during the measurement and in how the pair potential is recovered from the measured trajectories. For instance, colloids' interactions can be inferred from the pair distribution function of dispersions in equilibrium. Imaging measurements of the distribution function (10,12,11) involve large numbers of particles with sufficiently uniform properties that interpreting the many-particle statistics in terms of an effective pair potential is meaningful. This approach is limited, therefore, to measuring interactions among identical particles and cannot be applied to heterogeneous samples. Acquiring sufficient statistics to measure interactions at small separations requires large data sets and long experimental runs (3). Maintaining sufficiently uniform conditions can be challenging (13,14). Increasing the particles' concentration to speed the measurement introduces many-body correlations that can obscure the pair potential (16,15). Even imaging an equilibrium dispersion poses challenges because high-resolution microscopes have a limited depth of field (18,17), three-dimensional imaging techniques can be too slow to acquire snapshots of the particle distributions, and confining the particles to a plane can modify their interactions (5,20,19). The images themselves can be subject to artifacts (8) that must be addressed with care to obtain meaningful results (5).
Many of the limitations and much of the time and difficulty involved in equilibrium interaction measurements can be avoided by using optical tweezers (21) to arrange pairs (22) or clusters (16) of particles into appropriate configurations. Colloidal interaction measurements based on optical tweezer manipulation generally fall into two categories: measurements performed with intermittent or blinking traps, and those performed with continuously illuminated traps. In the former case, particles positioned by optical tweezers are released by extinguishing the traps (23,19,22) and the resulting nonequilibrium trajectories can be analyzed by Markovian dynamics extrapolation (22) to yield the equilibrium pair potential. This approach has the benefit that the particles' interactions are measured while the tweezers are extinguished, ensuring that the results are not contaminated by light-induced phenomena (22). It also lends itself to measurements of dissimilar particle pairs (19). Such ``blinking tweezer'' measurements also require large data sets, however, and only work if the relaxation to equilibrium is free from kinematic effects, such as hydrodynamic coupling (24,25,27,26). Demonstrating the absence of such artifacts is difficult.
Both long sampling times and nonequilibrium effects can be avoided by measuring the motion of particles trapped in optical tweezers. Accurate measurements of dynamic interactions, such as hydrodynamic coupling, can be extracted from observations of the coupled diffusion of particles individually trapped in optical tweezers (28,29). Fast pair potential measurements can be realized by replacing the discrete optical tweezers with extended optical line traps (1,32,34,30,35,36,31,33), which allow trapped objects freedom of motion in one dimension. Appropriately sculpting the trap's one-dimensional force landscape optimizes statistical sampling (35). Unfortunately, all tweezer-based measurements rely on accurate calibration of the traps' potential energy wells, and can be sensitive to optically induced interactions. Previous reports of line-trap interaction measurements have relied on separate calibrations of the lines' longitudinal potential energy landscape (37), and have extrapolated from measurements over a range of laser powers to account for light-induced interactions (38,34,35). These calibrations and background measurements can be time-consuming and exacting, particularly if optical forces cannot be described simply, or if measuring optically-induced interactions is one of the goals.
Using holographic methods to project line traps (1,7,39) and optimal statistical methods (6) for analyzing the particles' trajectories addresses all of these issues. In particular, this combination eliminates the need for single-particle calibrations and explicitly distinguishes particles' intrinsic interactions from one- and two-particle optically-induced interactions. The result is a reliable, robust and, above all, rapid method for measuring colloidal interactions.