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Force versus distance profiles acquired by atomic force microscopy probe the structure and interactions of polymer brushes. An interpretation utilizing the Derjaguin approximation and assuming local compression of the brush is justified when colloidal probes are utilized. The assumptions underlying this approach are not satisfied for sharp tips, and deviations from this model were reported for experiments and simulations. The sharp-tip force law proposed assumes that the free energy penalty of insertion into the brush is due to the osmotic pressure of the unperturbed brush. This static force law is in semiquantitative agreement with the simulation results of Murat and Grest (Murat, M.; Grest, G. S. Macromolecules 1996, 29, 8282).
Halperin et al. (Fri,) studied this question.