The expressions for the 2nd-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities

In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding (TB) modelling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather `technical' and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-centre matrix element is aligned along the z-axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.Comment: 9 pages, no figure

Driven colloidal suspensions in confinement and density functional theory: Microstructure and wall-slip

We theoretically investigate general properties of driven (sheared) colloidal suspensions in confinement, based on methods of classical density functional theory. In the absence of an exact closed (Smoluchowski-) equation for the one-particle density under shear, we formulate a set of general conditions for approximations, and show that a simple closure fulfills them. The exact microscopic stress tensor is identified. Exemplifying the situation near a wall (oriented parallel to the direction of shear), we note that the microscopic shear stress is not necessarily homogeneous. Formulating a second equation additional to the Smoluchowski equation, we achieve a homogeneous shear stress, and thereby compute the local flow velocity near the wall. This finally leads to a slip length of the complex fluid at the wall.Comment: 11 pages, 8 figure

Theory of rheology in confinement

The viscosity of fluids is generally understood in terms of kinetic mechanisms, i.e., particle collisions, or thermodynamic ones as imposed through structural distortions upon e.g. applying shear. Often the former is less relevant, and (damped) Brownian particles are considered good fluid model systems. We formulate a general theoretical approach for rheology in confinement, based on the many particle diffusion equation, evaluated via classical density functional theory. We discuss the viscosity for the situation of two parallel walls in relative motion as a function of wall-to-wall distance.Comment: 5 pages, 3 figure