CLIMBING OF A HIGH-MOLECULAR-WEIGHT LIQUID ON A VERTICAL SOLID-SURFACE GRAFTED WITH LONG POLYMER-CHAINS

We discuss the climbing of a high molecular weight liquid (P monomers per chain) on a vertical solid surface grafted with long polymer tails (N monomers per chain). We assume the liquid and the grafted tails to be chemically identical. Using a Flory-type approach, we calculate the thickness L of the film as a function of the reduced altitude h = h/h(c), the degrees of polymerization P and N, and the grafting density sigma. The characteristic height hc is defined by h(c) = kT/(rhoga3), where rho is the liquid density and a a molecular size. Several regimes are found. In the particular case where at h = 0 the grafted tails are stretched and some mobile chains are still present in the brush, we predict that (a) at small altitude (h < P-1/3sigma4/3), gravity is a small perturbation and L is-approximately-equal-to aNP-1/3sigma1/3(1-hP1/3sigma-4/3) and (b) at higher altitude, gravitational effects are important and L is-approximately-equal-to aNP-1/3sigma1/3(hP1/3sigma-4/3)-1/2.