Reports: AC6
46569-AC6 Developing Inverse Density Functional Theory as an Analytical Tool for Diffusing Colloidal Probe Microscopy
In the first year of this grant we were successful in applying density-functional theory (DFT) in an inverse fashion, to interpret the diffusing colloidal probe microscopy (DCPM) experiments of our collaborator Professor Michael A. Bevan. Specifically we were able to employ density profiles of concentrated colloidal suspensions near surfaces, as measured by confocal microscopy, and invert them through DFT to yield the potential energy function describing the interaction between a single colloidal particle and the surface. In the second year of this grant we have moved in a slightly different direction. We have developed a closure-based perturbative DFT of fluid-solid transitions in which the higher-order terms in the free energy expansion are re-summed as a bridge functional. Using the hard-sphere system as a model, we found that the bridge functional shows distinct regions of uniqueness and non-uniqueness when expressed in terms of the indirect correlation function. Yet simple polynomial functions that capture the correct behavior in the unique region are capable of predicting exactly the properties of the hard-sphere system at the freezing transition. These observations have parallels in liquid-state Ornstein-Zernike theory, although the mathematical forms of the bridge functional closures developed here are quite different. We envision this line of work leading to highly accurate perturbative DFTs of freezing, where an appropriate closure is chosen based on the type of interparticle potential model (e.g. hard-sphere, soft-sphere, Lennard-Jones, Coulombic).
