Coupled transport at the nanoscale: the unreasonable effectiveness of equilibrium theory.

T he Soret effect, also known as thermodiffusion, is a classic example of coupled transport (1) in which directed motion of a particle or macromolecule is driven by f low of heat down a thermal gradient. Generally, a particle moves from hot to cold, but the reverse is also seen under some conditions. Although it has been known for 150 years, the microscopic explanation of the Soret effect has remained unclear. In a recent issue of PNAS, Duhr and Braun (2) shed important light on the molecular mechanisms of the Soret effect by using a technique of singleparticle tracking, which allows very sensitive measurements of how thermodiffusion can be inf luenced by changes in the environment, as well as how the effect scales with parameters such as particle size and surface charge. Although there are numerous examples (3, 4) of exciting possibilities for technological uses of thermodiffusion, the importance of understanding the mechanism of the Soret effect goes beyond the practical applications. Ultimately, similar coupled processes in which a chemical reaction drives directed motion of a protein may lie at the heart of the mechanism of the biological motors and pumps essential for life. Detailed understanding of a variety of coupled transport processes, including the Soret effect, may lead to important advances in our ability to inf luence biological molecules and to use the insight gained from natural systems to help design synthetic nanoscale machines. The Soret effect can be characterized in terms of two parameters: the thermal diffusion coefficient DT, defined by the assumed linear relationship between the velocity and the thermal gradient v DT T, and the Soret coefficient, ST DT/D, which is the ratio between DT and the scalar diffusion coefficient D. To unravel the molecular mechanism for thermodiffusion, it is essential to understand how the parameters DT and ST depend on the properties of the solvent and solute (or colloidal particles) and to determine the general mechanisms by which particles move along a thermal gradient. There are two generic classes of mechanisms by which thermodiffusion can occur: one based on f luid dynamics and the other based on thermodynamics. In the class based on hydrodynamics (5), the temperature gradient leads directly to some imbalance over the surface of the molecule that results in a net mechanical force F that drives the particle motion. A similar mechanism, although not involving a thermal gradient, has been proposed as a description of a selfpropelled molecular motor driven by a chemical reaction catalyzed by the motor that creates an osmotic gradient that pushes the motor along (6). In the second type of mechanism, the local thermodynamic environment of the particle is effectively isotropic (7). The chemical potential of the particle depends on temperature and hence on space, but gently, in comparison with the radius of the particle itself. The particle moves preferentially to the colder regions, in which it is thermodynamically more stable, by random diffusion that is biased by the increasing stabilization in the colder regions, similar to a Brownian motor mechanism for molecular motors (8). The relative importance of these two types of mechanisms for a given particle of radius a depends on the ratio of the time to diffusively explore a region as large as itself, tdiff a2/D, vs. the time to move the same distance by deterministic thermodiffusion, tT a/v a/DT T. These two times are approximately equal when T (aST) 1, so for aST T 1, we expect the motion to be governed by the deterministic component of the velocity and the mechanical force mechanism to be operative, whereas for aST T 1, the particle has time to diffusively explore its environment, and the second, Brownian-type mechanism is probably operative. The experiments of Duhr and Braun (2) were carried out in the diffusive regime, where the particle is always in local equilibrium. Their results are consistent with a mechanism in which the dominant factor governing the Soret coefficient is the temperature dependence of the entropy change associated with hydration and with ionic shielding, resulting in the expression