EXCHANGE KINETICS IN SPHERICAL GEOMETRY

The decay of the surface concentration Gamma(t) of polymers undergoing exchange kinetics between a spherical adsorbent and the bulk solution is studied. The influence of bulk diffusion and the radius R of the s pherical adsorbent on the decay rate has been examined. It is shown th at the influence of bulk diffusion is reduced when the radius of the a dsorbent particle is small. However, in contrast to the case of planar adsorbents, for which a simple-exponential decay of Gamma(t) correspo nds to detachment-controlled desorption, a simple-exponential decay in the case of spherical adsorbents is not necessarily an indication of detachment-controlled decay. It is shown that when R is small (relativ e to the recapture length, Q, given by the ratio of the coefficients o f reattachment and detachment), the decay of Gamma(t) is close to a si mple-exponential function with a decay lifetime tau approximate to tau (det) + QR/D, where tau(det) is the detachment lifetime of the polymer from the surface and D is the diffusion coefficient of the polymer in solution. Only when R is small enough so that QR/D < tau(det), does t he measured decay lifetime become the true detachment lifetime. The re sults may also be extended to understand the exchange rate of surfacta nt molecules among micelles or bilayers.