Dynamics of polymeric brushes: End exchange and bridging kinetics

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Abstract
We study some dynamical aspects of grafted polymer layers in a solvent. The structure of the brush is described in a θ solvent by the self‐consistent mean field theory and in a good solvent using scaling laws. The Rouse–Zimm model including hydrodynamic interactions is used for the dynamic properties. A given chain end explores the entire thickness of a free grafted layer in a time Te proportional to the cube of the thickness. The exploration time is much larger than the Rouse time that characterizes the relaxation of the fluctuations of the chains conformations. In a θ‐solvent we give a detailed study of the relaxation of the density of a few labeled chain ends towards its equilibrium value. The bridging kinetics between a grafting plate and a plate adsorbing the free ends is also discussed. When adsorption proceeds, an exclusion zone grows in the vicinity of the adsorbing plate. To cross the exclusion zone and adsorb, a chain end must overcome an energy barrier. The typical adsorption time is the first passage time through this barrier. Except in the very late stages where the fraction of chains η forming bridges saturates at its equilibrium value, the energy barrier against adsorption increases as a power law of η and the bridging fraction increases very slowly (logarithmically) with time. Both weak bridging where only a small fraction of chains form bridges and total bridging where all the chains form bridges are studied.