From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration
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There are diverse technological contexts where fluids and suspensions are perturbed by applied fields like interfaces or intrinsically governed by complex interparticle potentials. When these interactions act over lengthscales comparable to the fluid particle size and become strong enough to frustrate particle packing or rearrangements, they drive systems to exhibit microscopically inhomogeneous (i.e., position-dependent) structural and relaxation responses. We use computer simulations and statistical-mechanical tools to find connections between such frustrating interactions and inhomogeneous fluid responses, which can profoundly impact macroscopic material properties and processing requirements. We first consider how to measure and predict the position-dependent and average diffusion coefficients of particles along inhomogeneous free-energy landscapes (i.e., potentials of mean force). Characterizing diffusion in such inhomogeneous fluids is crucial for modeling, e.g., the transit of colloids across microfluidic devices and of solutes through biological membranes. We validate a practical technique based on the Fokker-Planck diffusion formalism that measures diffusivities based solely on particle trajectory data. We focus on hard-sphere fluids confined to thin channels or subjected to external fields that impose density fluctuations at various wavelengths. We find, for example, that hydrodynamic predictions of tracer diffusion in confinement are surprisingly robust given non-continuum solvents. We also demonstrate that correlations between fluid static structure and diffusivity can qualitatively depend on the lengthscale of density fluctuations or the onset of supercooling. We next examine fluids governed by competing short-range attractions and long-range repulsions that drive formation of equilibrium cluster phases, which comprise monodisperse aggregates of monomers. The formation of such morphologies greatly impacts, e.g., the manufacturing of therapeutic protein solutions. We first address a major challenge in probing the real-space structure of such suspensions: detecting and characterizing cluster phases based on the static structure factor accessible via scattering experiments. Using computer simulations and liquid-state theory, we validate rules for interpreting low-wavenumber features in the structure factor in terms of cluster emergence, size, spatial distribution, etc. We then validate a thermodynamic model that predicts cluster size based on the strengths of monomer interactions, adapting classical nucleation theory to incorporate new empirical scalings for the surface energies of small stable droplets.