The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Effects of unique ion chemistry on thin-film growth by plasma–surface interactions

Plasma processing is a standard industrial method for the modification of material surfaces and the deposition of thin films. Polyatomic ions and neutrals larger than a triatomic play a critical role in plasma-induced surface chemistry, especially in the deposition of polymeric films from fluorocarbon plasmas. In this paper, low energy CF3+ and C3F5+ ions are used to modify a polystyrene surface. Experimental and computational studies are combined to quantify the effect of the unique chemistry and structure of the incident ions on the result of ion-polymer collisions. C3F5+ ions are more effective at growing films than CF3+, both at similar energy/atom of ≈6 eV/atom and similar total kinetic energies of 25 and 50 eV. The composition of the films grown experimentally also varies with both the structure and kinetic energy of the incident ion. Both C3F5+ and CF3+ should be thought of as covalently bound polyatomic precursors or fragments that can react and become incorporated within the polystyrene surface, rather than merely donating F atoms. The size and structure of the ions affect polymer film formation via differing chemical structure, reactivity, sticking probabilities, and energy transfer to the surface. The different reactivity of these two ions with the polymer surface supports the argument that larger species contribute to the deposition of polymeric films from fluorocarbon plasmas. These results indicate that complete understanding and accurate computer modeling of plasma–surface modification requires accurate measurement of the identities, number densities, and kinetic energies of higher mass ions and energetic neutrals.