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Computational analysis of spinodal decomposition dynamics in polymer solutions
Author(s) -
Chan Philip K.,
Rey Alejandro D.
Publication year - 1995
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.1995.040040502
Subject(s) - spinodal decomposition , thermodynamics , dimensionless quantity , phase diagram , spinodal , scaling , work (physics) , isothermal process , statistical physics , phase (matter) , percolation (cognitive psychology) , materials science , chemistry , physics , mathematics , geometry , organic chemistry , neuroscience , biology
In this work a model, composed of the nonlinear Cahn‐Hilliard and Flory‐Huggins theories, is used to numerically simulate the phase separation and pattern formation phenomena of oligomer and polymer solutions when quenched into the unstable region of their binary phase diagrams. This model takes into account the initial thermal concentration fluctuations. In addition, zero mass flux and natural nonperiodic boundary conditions are enforced to better reflect experimental conditions. The model output is used to characterize the evolution and morphology of the phase separation process. The sensitivity of the time and length scales to processing conditions (initial condition c 0 * ) and properties (dimensionless diffusion coefficient D ) is elucidated. The results replicate frequently reported experimental observations on the morphology of spinodal decomposition (SD) in binary solutions: (1) critical quenches yield interconnected structures, and (2) off‐critical quenches yield a droplet‐type morphology. As D increases, the dominant dimensionless wave number k m *increases as well, but the dimensionless transition time t t *from the early stage to the intermediate stage decreases. In addition, t t *is shortest when c 0 *is at the critical concentration, but increases to infinity when c 0 *is at one of the two spinodal concentrations. These results are found when the solute degree of polymerization N 2 is in the range 1 ≤ N 2 ≤ 100. When N 2 > 100, however, a problem of numerical nonconvergence due to diverging relaxation rates occurs because of the very unsymmetric nature of the phase diagram. A novel scaling procedure is introduced to explain the phase separation phenomena due to SD for any value of N 2 during the time range explored in this study.