The mobility of molecules on a solid surface plays a key role in diverse phenomena such as friction and self-assembly and in surface-based technologies like heterogeneous catalysis and molecular targeting. To understand and control these surface processes, a universally applicable model of surface transport at solid-liquid interfaces is needed. However, unlike diffusion at a solid-gas interface, little is known about the mechanisms of diffusion at a solid-liquid interface. Using single-molecule tracking at a solid-liquid interface, we found that a diverse set of molecules underwent intermittent random walks with non-Gaussian displacements. This contrasts with the normal random walk and Gaussian statistics that are commonly assumed for molecular surface diffusion. The molecules became temporarily immobilized for random waiting times between surface displacements produced by excursions through the bulk fluid. A common power-law distribution of waiting times indicated a spectrum of binding energies. We propose that intermittent hopping is universal to molecular surface diffusion at a solid-liquid interface.

Control and transport of nanoscale objects in fluids is challenging because of the unfavorable scaling of most interaction mechanisms to small length scales. We designed energy landscapes for nanoparticles by accurately shaping the geometry of a nanofluidic slit and exploiting the electrostatic interaction between like-charged particles and walls. Directed transport was performed by combining asymmetric potentials with an oscillating electric field to achieve a rocking Brownian motor. Using gold spheres 60 nanometers in diameter, we investigated the physics of the motor with high spatiotemporal resolution, enabling a parameter-free comparison with theory. We fabricated a sorting device that separates 60- and 100-nanometer particles in opposing directions within seconds. Modeling suggests that the device separates particles with a radial difference of 1 nanometer.

The dynamics of polymers adsorbed to a solid surface are important in thin-film formation, adhesion phenomena, and biosensing applications, but they are still poorly understood. Here we present tracking data that follow the dynamics of isolated poly(ethylene glycol) chains adsorbed at a hydrophobic solid-liquid interface. We found that molecules moved on the surface via a continuous-time random walk mechanism, where periods of immobilization were punctuated by desorption-mediated jumps. The dependence of the surface mobility on molecular weight (2, 5, 10, 20, and 40 kg/mol were investigated) suggested that surface-adsorbed polymers maintained effectively three-dimensional surface conformations. These results indicate that polymer surface diffusion, rather than occurring in the two dimensions of the interface, is dominated by a three-dimensional mechanism that leads to large surface displacements and significant bulk-surface coupling.

The efficiency of chromatographic separations decreases markedly when peaks exhibit asymmetry (e.g., "peak tailing"). Theoretically, these effects can arise from heterogeneous adsorption kinetics. To investigate the nature and consequences of such heterogeneity, we used a combination of single-molecule imaging and reversed-phase liquid chromatography (RPLC). In both single-molecule and macroscopic RPLC experiments, the stationary phase was hydrophobic end-capped (trimethylsilyl-functionalized) silica, which we exposed to different methanol/water solutions (50%-62% methanol), containing a fluorescent fatty acid analyte. Super-resolution maps based on single-molecule observations revealed rare, strong adsorption sites with activity that varied significantly with methanol concentration. The adsorption and desorption kinetics on the strong sites were heterogeneous and positively correlated, suggesting a broad underlying distribution of site binding energies. Adsorption equilibrium on the strong sites was more sensitive to solution conditions than overall retention measured in RPLC experiments, suggesting that the effect of strong sites on the overall adsorption kinetics should change with solution conditions. Interestingly, in RPLC experiments, peak tailing had a nonmonotonic dependence on methanol concentration within the range studied. Using the stochastic model of chromatography, we showed quantitatively that our single-molecule kinetic results were consistent with this macroscopic trend. This approach to identifying and quantifying adsorption sites should be useful for designing better chromatographic separations and for identifying the role of heterogeneous surface chemistry in molecular dynamics.

The inherent pore-scale heterogeneity of many natural and synthetic porous materials can make it difficult to model and predict porous transport because the underlying microscopic processes are often poorly understood. Here we present the results of single-particle tracking experiments in which we followed the pore-scale diffusion of individual nanoparticles, deep within a three-dimensional porous material of moderate porosity. We observed significant hydrodynamic damping of particle motion at subpore length scales, resulting in heterogeneous and spatially dependent mobility. The accessibility of the void space was strongly dependent on particle size, and related to the heterogeneous hydrodynamics. Our results suggest that pore-scale diffusion is more heterogeneous and volume accessibility more limited than previously expected. The method demonstrated here will enable studies of a broad new class of materials including porous polymers of technological interest.