A general gel layer model for the transport of colloids and macroions in dilute solution

A general boundary element methodology for studying the dilute solution transport of rigid macroions that contain gel layers on their outer surfaces is developed and applied to several model systems. The methodology can be applied to particles of arbitrary size, shape, charge distribution, and gel layer geometry. Account is also taken of the steady state distortion of the ion atmosphere from equilibrium, which makes it applicable to the transport of highly charged structures. The coupled field equations (Poisson, ion-transport, low-Reynolds-number Navier-Stokes, and Brinkman) are solved numerically and from this, transport properties (diffusion constants, electrophoretic mobilities, excess viscosities) can be computed. In the present work, the methodology is first applied to a gel sphere model over a wide range of particle charge and the resulting transport properties are found to be in excellent agreement with independent theory under those conditions where independent theory is available. It is then applied to several prolate spheroidal models of a particular silica sol sample in an attempt to identify possible solution structures. A single model, that is able to account simultaneously for all of the transport behavior, which does not undergo significant conformational change with salt concentration, could not be found. A model with a thin (less than or equal to 1-nm) gel layer at high salt content that expands on going to low salt content is able to explain the salt dependence of the intrinsic viscosity, but not the electrophoretic mobility. However, a model with a fairly thick (2-nm) gel layer at high salt content, which expands slightly (2.5-nm) at low salt content, is in fairly good agreement with experiment. In addition, the influence of particle charge and the presence of a gel layer on the Scheraga-Mandelkern parameter are examined. This parameter is proportional to the product of the translational diffusion constant and the cube root of the intrinsic viscosity. It is found to be very robust with regard to net particle charge as well as properties of the gel layer. (C) 2003 Elsevier Science (USA). All rights reserved.