Anurag Verma, Chemical Engineeering, University of Massachusetts, Amherst., 1040 North Pleasant Street , Apartment 103., Amherst, MA 01002 and David M. Ford, Department of Chemical Engineering, University of Massachusetts, Amherst, 209 Goessmann Laboratory, 686 North Pleasant Street, Amherst, MA 01003.
The self- or directed-assembly of colloidal particles from the fluid phase into solid structures is important for a wide range of technologies, ranging from photonic crystals to reconfigurable nanowires. The inter-particle potential energies in these systems can be complex, with long-range attraction or repulsion as well as short-range steric (hard core) contributions. A fast and accurate method for mapping out fluid-solid phase transitions in such systems would be a useful design tool; we explore classical density functional theory (DFT) for this purpose. We employ a novel DFT approach using a partitioning of the direct correlation function suggested by S.Q. Zhou, coupled with a technique to simplify the integrals in the free energy expansion. A general form of the second order direct correlation function, which is applicable to different types of inter-particle potential and exactly represents the first order direct correlation function as per the Lagrangian theorem of differential calculus, is discussed. We present the theoretical predictions for several different colloidal potential models.