Polydisperse Brush with the Linear Density Profile

Macromolecules densely end-grafted to a planar solid surface form a polymer monolayer (brush). It is known that, in a good solvent, the density profile of monodisperse brushes parabolically decays on moving away from the plane. Using the analytical theory and computer simulation methods, we studied the structure of a polydisperse brush from homopolymers, for which molecular-mass distribution is set by the Schulz–Zimm distribution. It is found that, at a polydispersity index of 1.143, the polymer brush in a good solvent has a linear density profile. In this brush, the average distance of chain ends to the grafting plane is proportional to the square of their contour length. If any chain of the brush is chemically modified so that it will be able to adsorb on the grafting surface, then the adsorption of this chain inside the brush will proceed via a discontinuous first-order phase transition with the bimodal distribution of the order parameter (free end height). This transition has unusual features: the energy of adsorption corresponding to the midpoint of the transition is proportional to the contour length of the adsorbing chain N, the sharpness of the transition is proportional to N², and the height of the barrier separating adsorbed and desorbed states is proportional to N³. The predicted dependences are verified by computer simulation.