Different dominating mass transport mechanisms for drying and sorption of toluene-PMMA films – Visualized with Raman spectroscopy

Phase-Field Simulation of Liquid-Vapor Equilibrium and Evaporation of Fluid Mixtures

In solution processing of thin films, the material layer is deposited from a solution composed of several solutes and solvents. The final morphology and hence the properties of the film often depend on the time needed for the evaporation of the solvents. This is typically the case for organic photoactive or electronic layers. Therefore, it is important to be able to predict the evaporation kinetics of such mixtures. We propose here a new phase-field model for the simulation of evaporating fluid mixtures and simulate their evaporation kinetics. Similar to the Hertz-Knudsen theory, the local liquid-vapor (LV) equilibrium is assumed to be reached at the film surface and evaporation is driven by diffusion away from this gas layer. In the situation where the evaporation is purely driven by the LV equilibrium, the simulations match the behavior expected theoretically from the free energy: for evaporation of pure solvents, the evaporation rate is constant and proportional to the vapor pressure. For mixtures, the evaporation rate is in general strongly time-dependent because of the changing composition of the film. Nevertheless, for highly nonideal mixtures, such as poorly compatible fluids or polymer solutions, the evaporation rate becomes almost constant in the limit of low Biot numbers. The results of the simulation have been successfully compared to experiments on a polystyrene-toluene mixture. The model allows to take into account deformations of the liquid-vapor interface and, therefore, to simulate film roughness or dewetting.

Critical Solutal Marangoni Number Correlation for Short-Scale Convective Instabilities in Drying Poly(vinyl acetate)-Methanol Thin Films

A new empiric correlation for the critical solutal Marangoni number as function of the Péclet and Schmidt numbers is proposed. It is based on previously published experimental flow field data in drying poly(vinyl acetate)-methanol films with an initial thickness in the range of 20–100 μm and an initial solvent load of 1 to 2 gMeOH/gPVAc, as well as newly derived concentration profile measurements and 1D drying simulations. The analysis accounts for realistic transient material properties and describes the occurrence of short-scale convective Marangoni (in)stabilities during the entire drying process with an accuracy of 9%. In addition, the proposed correlation qualitatively follows trends known from theory. As convective Marangoni instabilities in drying polymer films may induce surface deformations, which persist in the dry film, the correlation may facilitate future process design for either thin films with uniform thickness or deliberate self-assembly.

Drying Kinetics from Micrometer- to Nanometer-Scale Polymer Films: A Study on Solvent Diffusion, Polymer Relaxation, and Substrate Interaction Effects

The drying behavior of two different polymers [polyvinyl pyrrolidone (PVP) and polyisobutylene (PIB)] with different glass transition temperatures are investigated and compared as a function of film thickness from micrometer (∼3 μm) to nanometer scale (∼10 nm). The focus of this study is to distinguish between solvent diffusion, polymer relaxation, and substrate confinement of polymer chain mobility toward the interface as the dominating mechanism of drying kinetics. Relaxation kinetics becomes more dominant when the film thickness is reduced, which is shown experimentally for the first time for nanometer-scale film thicknesses. Identical drying curves regardless of the film thickness of PVP/methanol indicate the limitation of solvent transport by relaxation kinetics. The viscoelastic relaxation behavior of the polymer/solvent film is modeled by a Maxwell element. The results are in accordance with the experimental drying curves and allow for the determination of the characteristic relaxation time. Relaxation limitation becomes relevant at high diffusion Deborah numbers when the relaxation time-which is a function of the deployed material and the polymer/solvent composition-is higher than the characteristic diffusion time in the film. The latter is a function of the polymer/solvent composition and the thickness of the film. Drying curves of PIB/toluene films show additional effect in a substrate-near region of about 5 nm in which polymer chain mobility is confined, resulting in decelerated solvent diffusion. Although this effect near the substrate interface is expected to be present regardless of the film thickness, it becomes more dominant when the substrate-near region represents a significant fraction of the total film thickness. The key to the derived methodology for characterization of the polymer/solvent drying process is to vary dry film thickness from micrometers to a few nanometers which allows us to determine the dominating mechanism of drying kinetics.

Transient Three-Dimensional Flow Field Measurements by Means of 3D µPTV in Drying Poly(Vinyl Acetate)-Methanol Thin Films Subject to Short-Scale Marangoni Instabilities

Convective Marangoni instabilities in drying polymer films may induce surface deformations, which persist in the dry film, deteriorating product performance. While theoretic stability analyses are abundantly available, experimental data are scarce. We report transient three-dimensional flow field measurements in thin poly(vinyl acetate)-methanol films, drying under ambient conditions with several films exhibiting short-scale Marangoni convection cells. An initial assessment of the upper limit of thermal and solutal Marangoni numbers reveals that the solutal effect is likely to be the dominant cause for the observed instabilities.