Modeling of protein electrophoresis in silica colloidal crystals having brush layers of polyacrylamide.

Sieving of proteins in silica colloidal crystals of millimeter dimensions is characterized for particle diameters of nominally 350 and 500 nm, where the colloidal crystals are chemically modified with a brush layer of polyacrylamide. A model is developed that relates the reduced electrophoretic mobility to the experimentally measurable porosity. The model fits the data with no adjustable parameters for the case of silica colloidal crystals packed in capillaries, for which independent measurements of the pore radii were made from flow data. The model also fits the data for electrophoresis in a highly ordered colloidal crystal formed in a channel, where the unknown pore radius was used as a fitting parameter. Plate heights as small as 0.4 µm point to the potential for miniaturized separations. Band broadening increases as the pore radius approaches the protein radius, indicating that the main contribution to broadening is the spatial heterogeneity of the pore radius. The results quantitatively support the notion that sieving occurs for proteins in silica colloidal crystals, and facilitate design of new separations that would benefit from miniaturization.