Calculation of spreading profiles for molecularly-thin films from surface energy gradients

The one-dimensional diffusion equation is solved numerically to calculate t he spreading profile of a molecularly-thin liquid on a solid surface. The t hickness-dependent diffusion coefficient of the liquid is derived from the thickness dependence of the dispersive and polar surface free energies. Cha nges in the gradient and curvature of the total free energy with respect to film thickness give rise to distinct features in the calculated spreading profile. In the sub-monolayer thickness regime, a rapid spreading front dev elops as a result of the steep gradient in the dispersive force with film t hickness. For polar end-group terminated perfluoropolyethers, a shoulder fo llows behind the rapid spreading front. At the top of the shoulder, a step increase in the film thickness is observed. This vertical step results from film thicknesses that correspond to negative disjoining pressures and henc e are thermodynamically unstable. The profiles calculated from the thicknes s dependence of the total surface energy account for all of the features ob served experimentally during the spreading of perfluoropolyethers onto soli d surfaces. (C) 1999 Elsevier Science B.V. All rights reserved.