Computational analysis of spinodal decomposition dynamics in polymer solutions

Abstract

SUMMARY: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:) 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 wavenumber k& increases as well, but the dimensionless transition time t: from the early stage to the intermediate stage decreases. In addition, f; is shortest when c8 is at the critical concentration, but increases to infinity when c: is at one of the two spinodal concentrations. These results are found when the solute degree of polymerization N, is in the range I 5 N2 5 100. When N2 > 100, however, a problem of numerical nonconvergence due to diverging relaxation rates occurs because of the very unsymrnetric nature of the phase diagram. A novel scaling procedure is introduced to explain the phase separation phenomena due to SD for any value of N2 during the time range explored in this study.

The Ludwig‐Soret Effect on the Thermally Induced Phase Separation Process in Polymer Solutions: A Computational Study

“…The Phase-Separated Structure and Patterns [42] and Tanaka et al [43] In addition, these results are also in good agreement with the numerical results presented by Copetti and Elliott, [44] Chakrabarti, [45] Brown and Chakrabarti, [46] Chan and Rey, [8,9] and Jiang and Chan. [18] Moreover, analyzing the spatial concentration profiles and patterns in Figure 2 to 4, it is interesting to note that the initiation of the phase separation phenomena begins at the low temperature region (i.e., close to x à ¼ 0) of the polymer solution sample at early times and the phase separated regions grow over time increasingly from the region x à ¼ 0 to 1 to occupy the entire solution sample area.…”

Kinetics of thermally induced phase separation in ternary polymer solutions. I. Modeling of phase separation dynamics

“…20 The position of the maximum of the structure factor, k m , and the first zero of the pair correlation function, r 1 , are used as measures of the domain size, because both are proportional to the position of the light scattering intensity maximum. Owing to discretization, k m is difficult to determine accurately, particularly at larger times where the spinodal ring is collapsing.…”

A Computational Study of the Polymerization‐Induced Phase Separation Phenomenon in Polymer Solutions under a Temperature Gradient

“…[ 22] The dimensionless expression of the initial infinitesimal concentration fluctuations is written as: [8] c*ðx*; t* ¼ 0Þ ¼ c o * þ dc*ðx*; t* ¼ 0Þ ð 12Þ…”

“…the initial average concentration is not equal to the critical concentration) results in a droplettype morphology. [8] In the PIPS method on the other hand, the cure point of the phase separating system remains in the off-critical position of the binary phase diagram throughout the phase separation process once it has been thrust into the unstable region; a droplet-type morphology is expected.…”