Dynamics of Phase Separation in Polymer Blends Revisited: Morphology, Spinodal, Noise, and Nucleation

Fiałkowski, Marcin; Hołyst, Robert

doi:10.1002/mats.200800020

Cited by 29 publications

(16 citation statements)

References 58 publications

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“…We have shown that the Ludwig-Soret effect may be neglected in the model without any significant effect on the resulting transient morphology. Other morphological measures, [53,54] such as interface surface area, genus, Euler characteristic and homogeneity index, were not evaluated in this paper but may provide more insight about the effect that the Ludwig-Soret effect has on the TIPS phenomena.…”

Section: Resultsmentioning

confidence: 99%

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

Kukadiya

Chan

Mehrvar

2009

Macro Theory & Simulations

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The Ludwig‐Soret effect was investigated in the thermally induced phase separation process via SD in polymer solutions under an externally imposed spatial linear temperature gradient using mathematical modeling and computer simulation. The mathematical model incorporated non‐linear Cahn‐Hilliard theory for SD, Flory‐Huggins theory for thermodynamics, and the Ludwig‐Soret effect for thermal diffusion. 2D simulation results revealed that the Ludwig‐Soret effect had negligible impact on the phase separation mechanism in binary polymer solutions under a non‐uniform temperature field, as reflected by the time evolution of the dimensionless structure factor and the transition time from the early to the intermediate stages of SD.magnified image

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Section: Resultsmentioning

confidence: 99%

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

Kukadiya

Chan

Mehrvar

2009

Macro Theory & Simulations

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“…4.2, we perform numerical simulations for initial valuesφ 0 = 0.3 with order parameters (4.1) and time step δt = 0.001. The red domain, corresponding to the larger values of φ, indicates the concentrated polymer segments [14], and the blue region, corresponding to the smaller values of φ, indicates the macromolecular microspheres (MMs). We observe that the polymer chains are too short to entangle with each other, therefore, they graft on the surface of the MMs.…”

Section: Spinodal Decomposition In 2dmentioning

confidence: 99%

On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

Yang¹,

Jia²

2019

CICP

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In this paper, we consider the numerical approximations for the fourth order Cahn-Hilliard equation with concentration dependent mobility, and the logarithmic Flory-Huggins potential. One challenge in solving such a diffusive system numerically is how to develop proper temporal discretization for nonlinear terms in order to preserve the energy stability at the timediscrete level. We resolve this issue by developing a set of the first and second order time marching schemes based on a novel, called "Invariant Energy Quadratization" approach. Its novelty is that the proposed scheme is linear and symmetric positive definite because all nonlinear terms are treated semi-explicitly. We further prove all proposed schemes are unconditionally energy stable rigorously. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy and efficiency of the proposed schemes thereafter.

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“…Thus in the following 3D simulations, we simply set β = 0.9 and α = 0. The red domain, corresponding to the larger values of φ = 1, indicates the concentrated polymer segments [24], and the blue region, corresponding to the smaller values of φ = −1, indicates the macromolecular microspheres (MMs). In Fig.…”

Section: Spinodal Decomposition In 3dmentioning

confidence: 99%

Linear, second order and unconditionally energy stable schemes for the viscous Cahn–Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method

Yang

Zhao

2018

Journal of Computational and Applied Mathematics

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In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system numerically is how to develop high order temporal discretization for the hyperbolic and nonlinear terms, allowing large time-marching step, while preserving the energy stability, i.e. the energy dissipative structure at the time-discrete level. We resolve this issue by developing two second-order time-marching schemes using the recently developed ''Invariant Energy Quadratization'' approach where all nonlinear terms are discretized semi-explicitly. In each time step, one only needs to solve a symmetric positive definite (SPD) linear system. All the proposed schemes are rigorously proven to be unconditionally energy stable, and the second-order convergence in time has been verified by time step refinement tests numerically. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy and efficiency of the proposed schemes.

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Dynamics of Phase Separation in Polymer Blends Revisited: Morphology, Spinodal, Noise, and Nucleation

Cited by 29 publications

References 58 publications

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

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

On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

Linear, second order and unconditionally energy stable schemes for the viscous Cahn–Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method

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