Solvent-Vapor Induced Spherulitic Growth in Multicomponent Elastic Films
- 41 Downloads
Herein we study isothermal spherulitic crystallization in multicomponent thin films under solvent-vapor annealing. Spherulitic crystallization is taken as a coherent phase transition between an amorphous phase and a crystalline phase. Both of the two phases of the film are modeled as (possibly prestressed) elastic solids, and no a priori assumption is made on the stresses in the two phases. The interface between the two bulk phases is treated as an evolving one-dimensional open thermodynamic system defined by various thermodynamic variables. In particular, each chemical component of the interface is generally endowed with a mass density and a chemical potential. The interface, as a continuum system, is composed of particles. We assign each particle of an evolving interface a well-defined interface velocity so that a moving interface with mass density carries linear momentum and kinetic energy. By appealing to free energy imbalance for isothermal processes and balance of mass and momentum, we derive dissipation inequalities for the bulk phases and for the interface, with which we obtain constitutive restrictions through the Coleman–Noll procedure. The driving force behind spherulitic crystallization is identified as the quantity conjugate to the normal velocity in the interfacial dissipation inequality. Finally we investigate the effect of prestress on the directional dependence of spherulitic growth.
KeywordsSpherulitic crystallization in elastic films Interface velocity Prestress effect on spherulitic growth Phase transition Solvent-vapor annealing
Mathematics Subject Classification (2010)74A20 74A50 74N20 80A17 82B26 82C26
D. Zhao would like to thank Prof. Michel Jabbour for helpful discussions and for the mechanics courses he offered at University of Kentucky. The research reported here was supported in part by the SOLAR Initiative of the National Science Foundation, USA, through Grant No. DMR-1035257.
- 5.Defay, R., Prigogine, I., Bellemans, A.: Surface Tension and Adsorption. Wiley, New York (1966) Google Scholar
- 7.Fitts, D.D.: Nonequilibrium Thermodynamics: A Phenomenological Theory of Irreversible Processes in Fluid Systems. McGraw-Hill, New York (1962) Google Scholar
- 10.Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs, Volume 1, Thermodynamics. Dover, New York (1961) Google Scholar
- 22.Lifshitz, E.M., Pitaevskii, L.P.: Physical Kinetics. Elsevier, Amsterdam (1981) Google Scholar
- 30.Man, C.-S., Jabbour, M.E., Paroni, R., Loo, Y.-L., Hailey, A.K., Lee, S.S., Anthony, J.E., Grimminger, M.A.: Spherulitic growth under solvent-vapor annealing: theory and experiments on thin-film blends of organic small-molecule semiconductors. Preprint Google Scholar
- 32.Münster, A.: Classical Thermodynamics. Wiley, Chichester, New York (1970) Google Scholar
- 35.Zhao, D.: Spherulitic growth and thermodynamic equilibrium in multicomponent elastic films under solvent-vapor annealing. Doctoral dissertation, University of Kentucky, Lexington (2018) Google Scholar