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Project C3: Modeling late stages of the spin coating process

Principal Investigators: A. Blumen (Freiburg) / J. Baschnagel (Strasbourg)
Collaborators: H. Meyer (Strasbourg)
PhD-Student: Julian Helfferich

Current state of the research

Spincoating of dilute polymer solutions onto substrates is a powerful technique that allows the deposition of thin polymer films of nanoscopic dimensions [1].  However, the glassy polymer film produced by rapid evaporation of the solvent (“solvent quench”) differs from that obtained from temperature quenches in that there are still “unwanted” solvent molecules present when the film vitrifies.  Annealing of the films at temperatures greater than the bulk Tg is typically performed after spincoating to remove trapped solvent and to allow the chains to relax.  The duration for which this treatment can be applied is, however, limited because the films tend to dewet.  Therefore, it is unclear to what extent annealing is able to relax nonequilibrium states possibly produced by the spincoating process.

One viewpoint is that spincoated polymer films “represent highly metastable forms of matter” [2].  It is argued that “residual stresses” [2] are created after the completion of the spincoating process during the final stage of solvent evaporation because chains below a critical, low solvent concentration are no longer mobile enough to fully relax and adapt their conformations to the changing environment as the solvent continues to evaporate. The resulting stresses are supposed to decay only very gradually upon annealing, thus hampering chain entanglement which is expected to be fairly weak after spin coating. These out-of-equilibrium features should determine the stability of polymer films by controlling e.g. the propensity of the films for nucleation and growth of holes in dewetting experiments [3].


Contributions of the participating groups

The Freiburg group has recently studied by molecular dynamics (MD) simulations one aspect of the scenario sketched above, the entanglement process from nonentangled chains [4]. To this end, a dilute solution of a coarse-grained model of long polymer chains is rapidly compressed to a thin film, and the building up of entanglements in course of the chain interdiffusion process is monitored. It is found that this process is indeed fairly slow, already at temperatures T far above Tg, where the simulations were done [4]. On the other hand, the Strasbourg group has recently performed simulation studies of short, only weakly entangled chains, but with explicit solvent and for T close to Tg. These simulations explored equilibrium properties of supercooled polymer solutions in a supported film geometry [5] and the solvent evaporation from such films at the bulk Tg [6].  For the polymer solutions, it was found that the structure and dynamics of the films is spatially heterogeneous near Tg. For instance, at both the substrate and free interfaces the solvent dynamics is fast, but smoothly crosses over to the bulk dynamics when moving from the interfaces toward the center of the film.  This smooth gradient can be parametrized by a formula consisting of two opposing factors: a factor leading to a slowing down of the dynamics as the solvent concentration decreases and a factor which accounts for the dependence of the relaxation time on the distance to the interfaces [5]. It is crucial to include both factors when modeling solvent evaporation close to Tg, an effect which is usually not considered in the modeling of the spin coating process (see e.g. [7]).


Research project and collaborations

c3We use MD simulations (mainly Strasbourg) and theoretical modeling via Continuous Time Random Walks (CTRWs; mainly Freiburg) to explore the final stage of spincoating after the completion of the spinning process. The MD simulations will study coarse-grained models of solvent-polymer mixtures on a substrate near and below the bulk Tg (see figure at right), using much larger chains than in previous studies [5,6]. The analysis will focus on two main aspects: (i) The study of solvent evaporation from the films and its modeling in terms of CTRW theory [8] and of fractional calculus [9]. Guided by the theory, the simulation will determine input quantities (waiting time distributions, probability density for displacements, etc.) which the theory requires to predict the film behavior on solvent evaporation (e.g., the decrease of the film thickness). These predictions shall then be compared with the simulation. The comparison will show which features of CTRW model vary with the molecular properties of the simulation model (chain flexibility, polymer-solvent interactions, etc.) and which are robust, and possibly also suggest improvements of the CTRW model. (ii) Recent research suggests that bulk polymer glasses are dynamically and mechanically heterogeneous (see e.g. [10] and references therein). These features should also be present in glassy polymer films and could be related to the “residual stresses” [2] of spin coated films. By extending the work of Ref. [10] to polymer films we propose to explore local mechanical properties and their correlation with the chain conformations for dry films of the same thickness but prepared in different ways, i.e., through solvent quenches and temperature quenches.

In all stages of this project, the direct contact with experimental projects of this IRTG, in particular with projects C4 and C5 (as well as with project B3), will be extremely beneficial. We hope that this joint work will lead to a theoretical model that makes testable predictions about experimentally controllable factors which are important for the spin-coating process.

[1]M. Alcoutlabi and G. B. McKenna, J. Phys.: Condens. Matter 17, R461 (2005).
[2]G. Reiter and P. G. de Gennes, Eur. Phys. J. E 6, 185 (2001).
[3]T. Vilmin and E. Raphaël, Phys. Rev. Lett. 97, 036105 (2006).
[4]J. Zabel, Diplomarbeit Freiburg (2009).
[5]S. Peter, H. Meyer, and J. Baschnagel, J. Chem. Phys. 131, 014902 (2009).
[6]S. Peter, H. Meyer, and J. Baschnagel, J. Chem. Phys. 131, 014903 (2009).
[7]D. E. Bornside, C. W. Macosko, and L. E. Scriven, J. Appl. Phys. 66, 5185 (1989); T. Okuzono, K. Ozawa, and M. Doi, Phys. Rev. Lett. 97, 136103 (2006).
[8]J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987)
[9]I. M. Sokolov, J. Klafter, and A. Blumen, Physics Today 55, 48 (Nov. 2002)
[10]G. J. Papakonstantopoulos, R. A. Riggleman, J.-L. Barrat, and J. J. de Pablo, Phys. Rev. E 77, 041502 (2008).

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