Wetting, Spreading, and Adsorption on Randomly Rough Surfaces

The wetting properties of solid substrates with customary (i.e., macroscopic) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. Analytic expressions are derived which allow for any given lateral correlation function and height distribution of the roughness to calculate the wetting phase diagram, the adsorption isotherms, and to locate the percolation transition in the adsorbed liquid film. Most features turn out to depend only on a few key parameters of the roughness, which can be clearly identified. It is shown that a first order transition in the adsorbed film thickness, which we term 'Wenzel prewetting', occurs generically on typical roughness topographies, but is absent on purely Gaussian roughness. It is thereby shown that even subtle deviations from Gaussian roughness characteristics may be essential for correctly predicting even qualitative aspects of wetting

Equation of State of Wet Granular Matter

A theory is derived for the nonequilibrium probability currents of the capillary interaction which determines the pair correlation function near contact. This yields an analytic expression for the equation of state, P = P(N/V,T), of wet granular matter for D=2 dimensions, valid in the complete density range from gas to jamming. Driven wet granular matter exhibits a van-der-Waals-like unstable branch at granular temperatures T<T_c corresponding to a first order segregation transition of clusters. For the realistic rupture length of the liquid bridge, s_crit=0.07 d, the critical point is located at T_c = 0.274 E_cb. While the critical temperature weakly depends on the rupture length, the critical density phi_c is shown to scale with s_crit according to s_crit = 4d (sqrt(phi_J / phi_c) -1). The segregation transition is closely related to the precipitation of granular droplets reported for the free cooling of one-dimensional wet granular matter [Phys. Rev. Lett. 97, 078001 (2006)], and extends the effect to higher dimensional systems. Since the limiting case of sticky bonds, E_cb >> T, is of relevance for aggregation in general, simulations have been performed which show very good agreement with the theoretically predicted coordination K of capillary bonds as a function of the bond length s_crit. This result implies that particles that stick at the surface, s_crit=0, form isostatic clusters.Comment: 29 pages, 20 figure

Generic morphologies of viscoelastic dewetting fronts

A simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid coatings. It demonstrates that by taking into account the elastic properties of the coating, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.Comment: 4 pages, 2 figure

The Glass Transition of Thin Polymer Films: Some Questions, and a Possible Answer

A simple and predictive model is put forward explaining the experimentally observed substantial shift of the glass transition temperature, Tg, of sufficiently thin polymer films. It focuses on the limit of small molecular weight, where geometrical `finite size' effects on the chain conformation can be ruled out. The model is based on the idea that the polymer freezes due to memory effects in the viscoelastic eigenmodes of the film, which are affected by the proximity of the boundaries. The elastic modulus of the polymer at the glass transition turns out to be the only fitting parameter. Quantitative agreement is obtained with our experimental results on short chain polystyrene (Mw = 2 kg/mol), as well as with earlier results obtained with larger molecules. Furthermore, the model naturally accounts for the weak dependence of the shift of Tg upon the molecular weight. It furthermore explains why supported films must be thinner than free standing ones to yield the same shift, and why the latter depends upon the chemical properties of the substrate. Generalizations for arbitrary experimental geometries are straightforward.Comment: 7 pages, 4 figure