Compressing polymer “brushes”: A quantitative comparison of theory and experiment

A recent measurement of the force-height relation for two layers of end-grafted polystyrene chains in toluene is shown to be in excellent quantitative agreement with our recent theory, which is an exact solution of self-consistent field equations applicable in the limit of strongly stretched chains. Two undetermined parameters in the theory, corresponding to the chain persistence length and excluded volume parameter, are fixed by measurements of the radius of gyration and osmotic pressure in a moderate-density solution. The effect of polydispersity in chain molecular weight may be accounted for in the theory; the experimental estimate of M_W/M_N = 1.02 makes a significant difference, as the polydisperse brush is predicted to be taller than the monodisperse brush by an amount of order (M_W/M_N - 1)^1/2.