Compression of Finite Size Polymer Brushes

We consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects ξ∝h0(h0/h)1/2 is larger than the natural height h0 and the actual height h. For a brush of finite lateral size S (width of a stripe or radius of a disk), the lateral extension uS of the border chains follows the scaling law uS=ξφ(S/ξ). The scaling function φ(x) is estimated within the framework of a local Flory theory for stripe-shaped grafting surfaces. For small x, φ(x) decays as a power law in agreement with simple arguments. The effective line tension and the variation with compression height of the force applied on the brush are also calculated.