A model is presented for the shear (or frictional) forces Fs between two surfaces a distance D apart as they slide past each other while bearing mutually compressed polymer brushes, on the assumption that sliding takes place at the brush-brush interface. The predictions of the model for the rapid increase in Fs at increasing compressions are in reasonable agreement with experiments on polystyrene brushes immersed in toluene over two decades in Fs. At higher compressions (smaller D) the experimental shear forces increase only slowly, and diverge from the calculated ones which continue to increase rapidly; at the same time the form of the shear force response at these higher compressions reverts from a viscous-like one to a stick-slip behaviour. These observations strongly indicate that at sufficiently high compressions the plane of slip crosses over from the brush-brush interface to the polymer-solid surface.
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Klein, J. Sliding Friction between Polymer-brush-bearing Surfaces: Crossover from Brush-brush Interfacial Shear to Polymer-substrate Slip.. MRS Online Proceedings Library 651, 321 (2000). https://doi.org/10.1557/PROC-651-T3.2.1