The Kinetics of Polymer Brush Growth in the Frame of the Reaction Diffusion Front Formalism.

We studied the properties of a reaction front that forms in irreversible reaction-diffusion systems with concentration-dependent diffusivities during the synthesis of polymer brushes. A coarse-grained model of the polymerization process during the formation of polymer brushes was designed and investigated for this purpose. In this model, a certain amount of initiator was placed on an impenetrable surface, and the "grafted from" procedure of polymerization was carried out. The system consisted of monomer molecules and growing chains. The obtained brush consisted of linear chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions only. The simulations were carried out for high rafting densities of 0.1, 0.3, and 0.6 and for reaction probabilities of 0.02, 0.002, and 0.0002. Simulations were performed by means of the Monte Carlo method while employing the Dynamic Lattice Liquid model. Some universal behavior was found, i.e., irrespective of reaction rate and grafting density, the width of the reaction front as well as the height of the front show for long times the same scaling with respect to time. During the formation of the polymer layer despite the observed difference in dispersion of chain lengths for different grafting densities and reaction rates at a given layer height, the quality of the polymer layer does not seem to depend on these parameters.