Previous studies establish that adsorbed layers of telechelic polymers can exchange ends, increasing the entropy and allowing the loops to relax. The resulting, entropic attraction amounts to approximately 1 kT per bridging chain for ideal chains but decreases with increasing degree of stretching. From the interactions between planar brushes of highly stretched chains, we calculate the pair potential between spheres via the Derjaguin approximation. The softness of the repulsion and the depth of the attraction depend on the degree of stretching of the chains, the aggregation number or adsorption density, and the ratio of the overall size to the layer thickness. From the interaction potential, second virial coefficients in the osmotic pressure and the high-frequency modulus, characterizing dilute micellar solutions, follow directly. The second virial coefficient in the osmotic pressure is very negative with modest stretching but approaches the hard sphere limit as the chains become very strongly stretched. The coefficient of the leading O(phi(2)) term for the high-frequency modulus depends nonmonotonically on the stretching with the attractive well dominating for modest stretching and the repulsive core taking over for strong stretching. Combining these calculations with estimates of the relaxation time for end exchange should provide useful predictions of low shear viscosities for these Maxwellian fluids. (c) 2006 The Society of Rheology.