CAPILLARY RISE OF A LIQUID ON A SOLID GRAFTED WITH LONG POLYMER-CHAINS

Very long grafted chains on a solid surface may turn out to be interes ting adhesion promoters. Systems of this sort are now chemically acces sible and must be characterized through their wetting properties. Here we discuss the climbing of a liquid along a vertical plane covered wi th long grafted polymer chains (N monomers per chain). Assuming that t he liquid is a good solvent for the polymer, we calculate the thicknes s L of the swollen polymer brush as a function of the graft density ph i(s) and reduced altitude h=kappa2ah (where kappa-1 is the capillary l ength and a is the monomer size). (1) At small altitudes (h<h(c1)=phi( s)4/3), L(h) results mainly from a balance between excluded-volume and entropic effects, L(h)=Naphi(s)1/3-DELTAL. The shift DELTAL is-approx imately-equal-to Nah1/2phi(s)-1/3 is not linear in h and is large. Thi s remarkable effect reflects the existence of a parabolic concentratio n profile in the unperturbed brush, first derived by Milner, Witten an d Cates (a simpler, Flory, model with a step function profile would gi ve a much smaller effect). (2) At altitudes h>h(c1) the solvent conden sation energy becomes the leading term and L(h)=Naphi(s)h-1/2. At even higher altitudes (h>h(c2)=N2phi(s)3, a third 'mushroom' regime may sh ow up if the polymer does not wet the solid. Our results are consisten t with some preliminary observations of Deruelle and Leger on very lon g brushes of p-dimethylsiloxane (N is similar to 4000). Their brushes show colour variations with altitude (h is similar to 1 cm). The corre sponding values of DELTAL are rather large; thus the colour effect may give a rather direct experimental proof of the parabolic profiles.