Introduction

The theme of transport through modulated potential-energy landscapes pervades solid-state physics and arises in many natural and industrial processes. This problem has been studied extensively in the quantum-mechanical limit. Considerably less attention has been paid to the classical limit, where effects such as viscous damping and thermal randomization complicate the analysis. This article focuses on noninertial transport of classical objects driven through periodically modulated potential-energy landscapes by constant, uniform forces. The one-dimensional variant of this problem has been thoroughly investigated (1), and its results have been applied profitably to such processes as gel electrophoresis. We focus instead on the overdamped motions of classical objects as they flow through two-dimensional periodic landscapes, about which far less is known. Such higher-dimensional periodic landscapes have shown exceptional promise in a new category of sorting techniques. Our discussion draws upon recent experimental realizations of this process in which macromolecules or mesoscopic colloidal particles are observed while moving through arrays of microfabricated posts (3,2) and through regular arrays of optical traps (6,5,4). In both cases, particles' differing interactions with the physical landscape and their differing responses to the external driving force can cause them to follow radically different paths, thereby providing a novel basis for dispersing small fluid-borne objects into distinct fractions.

Section 2 introduces the theoretical framework for describing driven objects' interactions with inhomogeneous environments in the context of recent experimental realizations. We then apply this in Sec. 3 to the particularly simple case of transport across a linear barrier or potential trench. Such a landscape can continuously sort mixtures of objects into two distinct fractions, but with only algebraic sensitivity to properties such as size. Generalizing to periodic landscapes in Secs. 4 and 5 leads generally to fractionation with exponential size selectivity. Exploiting this exceptional resolution for practical separations may be difficult, however, in the most straightforward implementations. Other potential landscapes, such as a line of discrete potential wells, discussed in Sec. 6, offer exponential size selectivity with good prospects for practical implementations.