Fast adsorption on nonideal surfaces

The initial adsorption kinetics in stagnant flow of both rigid spherical po ly(propylene imine) dendrimers as well as of flexible branched poly(ethylen e imine) with similar building-blocks on glass are quantitatively described as Smoluchowski-Levich convective-diffusion-controlled up to concentration s C-b approximate to 10 mg/L using a sticking probability beta, defined as the ratio between the experimental adsorption rate and the theoretical pred iction. This parameter beta accounts for the nonideality of the substrate: There is only a limited amount of surface sites in the glass get-layer avai lable for adsorption, and this affects the collision efficiency. beta is on the order of 0.03 for the small spheres and 0.8 for the flexible polyelect rolyte, perfectly in line with the expectation that the flexible polyelectr olyte, able to conform along the surface, has a much higher chance of findi ng a site within its contact area than the small dendrimers. At higher conc entrations, the experimental data no longer show the predicted linear conce ntration dependence. Whereas for parallel plate flow studies in the literat ure the breakdown can be related to the neglect of transient concentration effects in mass transport using the Smoluchowski-Levich approach, for stagn ant flow, such a simple relation does not exist. It is calculated for the l atter setup that the time scales needed for the concentration to settle thr oughout the cell would be longer for the larger poly(ethylene imine) than f or the dendrimers. This is in contrast with the experimentally observed tre nd: time scales over which deviations between the Smoluchowski-Levich appro ximation and the data occur are longer for the faster diffusing dendrimers than for PEI, and the breakdown can thus at least not directly be related t o transient concentration terms. It is suggested that the large difference in the sticking probability of these different types of materials on glass has to be taken into account in a complete numerical analysis of the mass t ransport equation, especially at short time scales.