Stretching of grafted polymer layers

We calculate the osmotic pressure in a semi-dilute solution of stretched polymers in a good solvent. The results are applied to polymer brushes where polymers are stretched either directly or by application of shear. It is shown that when a brush is sheared against the solvent, the stretching proceeds always within the nonlinear regime of polymer elasticity. When the brush is subjected to a combination of compression and shear forces and the shear is gradually increased, there is a crossover between low-shear linear elastic behaviour to a nonlinear regime in which the brush swells and eventually reaches its full uncompressed thickness at high shear stress. The relevance of our results to present and future experiments is discussed.