SOME DYNAMIC PROPERTIES OF GRAFTED POLYMER LAYERS

We present a study of the dynamics of a densely grafted layer (brush) using a mean-field approach. Each chain of the layer interacts with many others. The interaction probed by a monomer is represented by a mean potential. However, locally the chain interacts mainly with itself. In a good solvent this causes local swelling which is taken into account. To include hydrodynamic interactions, the theory must describe local correlations accurately. We consider the cases of a theta solvent and a good solvent. In both cases, the relaxation time of a chain configuration is found to be tau congruent-to etah3/k(B)T where k(B) is the Boltzmann constant, T is temperature and h is the solvent viscosity. Our approach does not account for entanglements. A recent simulation by Chakrabarti and Marko suggests, however, that the current experiments belong to the unentangled regime. We also discuss the expulsion of a desorbed chain by a grafted layer. The scaling obtained for the velocity of the centre of mass agrees well with simulations by Wittmer and Binder. The expulsion time should be the Rouse-Zimm time of the grafted chain, but for reasonable grafting densities the centre of mass spends additional time in the dilute brush edge.