Controlled Evaporative Assembly of Polymers from Confined Solutions

INTRODUCTION In the process of drying, nonvolatile solutes (e.g., polymers, proteins, viruses, bacteria, DNA, microspheres, nanocrystals, carbon nanotubes, etc.) contained within a sessile droplet (i.e., unconstrained liquid) readily assemble into a diverse range of intriguing oneor two-dimensional structures, possessing dimensions of a few hundred submicrons and beyond. It is, in principle, a nonequilibrium process. Two main characteristic patterns are often observed: ‘‘coffee rings’’ and irregular network structures (i.e., Benard cells). A ‘‘coffee ring’’ forms when, in the absence of natural convection and surface tension gradients, the contact line of an evaporating drop becomes pinned. This ensures that liquid evaporating from the edge is replenished by liquid from the interior, so the outward flow carries the nonvolatile dispersions to the edge. The evaporation flux varies spatially, with the highest flux observed at the edge of drop. A subset of the ‘‘coffee rings’’ phenomenon is the formation of concentric rings by repeated microscopic pinning and depinning events (i.e., ‘‘stick-slip’’ motion) of the three-phase contact line, that is, the competition between the friction force and surface tension of the solution. However, random concentric rings are generally formed. Moreover, based on Navier-Stokes equations with a lubrication approximation, the bulk of current theoretical work has centered on understanding a single ring formation using either analytical or numerical methods. By contrast, only a few elegant theoretical studies have focused, either analytically or numerically, on the formation of periodic multirings (i.e., concentric rings) during droplet evaporation on a substrate. A gradient of temperature normal to the droplet surface due to solvent evaporation can induce a Marangoni-Benard convection (i.e., closed-loop circular convection), which results in irregular Benard cells caused by the upward flow of lower, warmer liquid. The spatial variation of evaporative flux and possible convection mean, however, that these nonequilibrium, dissipative structures (e.g., ‘‘coffee rings,’’ cellular structures, fingering instabilities, etc.) are often irregular and stochastically organized.