Polymer chains in good solvent within attracting walls

It is known that a polymer chain in an ideal solvent confined within parallel attracting walls undergoes a second-order transition at the temperature T* satisfying the equation exp-ε/(k_BT*)]=6/5; here the model consists of a chain placed on a cubic lattice, and ε (<0) is the attractive energy experienced by a chain segment contacting a wall. We then investigate the effect induced by a good solvent upon the chain behavior. A single chain is considered; within the Gaussian approximation, we assume that its partition function may be factorized in two terms, one across the wall planes and another parallel to them. For an interplanar distance L significantly smaller than the average radius of gyration the compressed chain is assumed to reach a uniform density, so that the free energy contribution due to the intrachain atomic contacts is a function of the density alone. It may be shown that the effective value of ε/(k_BT*)(=σ) is the difference between the value to be expected “in vacuo” and β/(z-2), where z is the degree of coordination of the lattice and β is the excluded-volume parameter. As a result, for large values of L we may have an attractive effect exerted by the chain on the walls whereas at small L's we invariably have a repulsion. For the cubic lattice we have a repulsion and an attraction for large L approximatively for σ < ln(6/5)+β/(z-2) and for σ > (ln(6/5)+β/(z-2), respectively, whereas we have inversion between the two regimes at some distance L for intermediate values of σ. In the limit of an infinite molecular weight the inversion translates into a thermodynamic transition. We believe the present model may explain some important features seen in polymer adhesion.