Chain-length dependence of the polymer surface excess near the adsorption/depletion transition

The behavior of a solution of ideal polymers at a surface near the adsorption/depletion transition is investigated using a lattice model. A very simple relation was found for the surface excess theta(ex) of a polymer molecule of length N close to the adsorption/depletion transition: theta(ex)/phi(b) = A[B + (chi(s) - chi(SC)(infinity))N], where phi(b) is the bulk volume fraction of polymer, A approximate to 5/6 and B approximate to 1/5 are constants, chi(s) is the Silberberg adsorption parameter, and chi(SC)(infinity) is the critical adsorption energy for infinite chain lengths. The adsorption/depletion transition shifts to lower chi(s) values with decreasing chain length. This effect is strongly enhanced if the end segments of the chain adsorb preferentially. A continuum model was used to obtain analytical expressions. The agreement between lattice and continuum descriptions is quite good. The chain-length dependence of the adsorption/depletion transition for homopolymers is not found in the continuum model, however. The results in this paper may be relevant for example for critical chromatography.