(80f) Quantitative Measurements of Colloid-Surface Interactions from Microscopic Imaging and Inverse Density Functional Theory

We present a modeling technique, based on an inversion of classical density functional theory (DFT), that allows us to determine the potential energy of a single colloidal particle with a surface, based on particle density profiles measured in a dense colloidal system. The equilibrium particle density profiles are obtained with a unique combination of total internal reflection and confocal scanning laser microscopy, proposed by Wu and Bevan under the name of Diffusing Colloidal Probe Microscopy (DCPM). In this paper, the authors' previous inverse DFT work on hard spheres [Lu et al., J. Chem. Phys. 122, 224710 (2005)] is extended to soft particle-particle interaction potentials characteristic of many colloidal fluids. Both simulated (Monte Carlo) and real DCPM data were used to test the approach. For model screened electrostatic, van der waals, and depletion systems, we found that the inversion procedure reproduces the true particle-surface potential energy to an accuracy within typical DCPM experimental limitations (~0.1 kT) at low to moderate bulk colloidal densities. Sedimentation equilibrium of colloidal suspensions is also studied. The choice of DFT closures for different interaction potential was obtained. For the DCPM experiments, some numerical challenges were overcome in the conversion of raw image data to particle density profiles before applying the inverse DFT. This combination of DCPM and DFT holds great promise for rapid mapping of O(kT) surface energetics in a variety of nano- and bio-technology applications.