Spin coating with slow evaporation

Abstract

The spin coating of polymer solutions is discussed, with emphasis on the nature of the evaporation boundary condition. A dimensional analysis reveals that the appropriate condition is a constant small evaporation rate, which is determined by the mass transfer in the adjacent atmosphere. An error in previous work [Phys. Fluids 31, 2786 (1988)] is brought to light, and it is shown that the previous paper would be valid for rapid evaporation, such as might occur if the ambient condition were near vacuum. The transport of solvent in the liquid film is described by a boundary layer diffusion equation with large Peclet number P0. When the dimensionless evaporation rate ê is small, the diffusion equation has a self-similar solution in which the boundary layer thickness and polymer concentration increase in proportion to the decrease in film thickness. The final film thickness is determined by the boundary layer thickness, which is controlled by P0 and is independent of ê. Thus the final film thickness is found to be the same as for the case of rapid evaporation. © 1990 American Institute of Physics.