# Exchange kinetics in spherical geometry

## Abstract

The decay of the surface concentration Γ(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 spherical adsorbent on the decay rate has been examined. It is shown that the influence of bulk diffusion is reduced when the radius of the adsorbent particle is small. However, in contrast to the case of planar adsorbents, for which a simple-exponential decay of Γ(t) corresponds 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 (relative to the recapture length, Q, given by the ratio of the coefficients of reattachment and detachment), the decay of Γ(t) is close to a simple-exponential function with a decay lifetime τ ≈ τdet + QR/D, where τdet 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 < τdet, does the measured decay lifetime become the true detachment lifetime. The results may also be extended to understand the exchange rate of surfactant molecules among micelles or bilayers.

## Publication Title

Langmuir

## Recommended Citation

Wang, Y., Diermeier, R., & Rajagopalan, R.
(1997). Exchange kinetics in spherical geometry.* Langmuir**, 13* (8), 2348-2353.
https://doi.org/10.1021/la9607666