Continuum-scale modelling of polymer blends using the Cahn–Hilliard equation: transport and thermodynamics

Abstract

The Cahn–Hilliard equation is commonly used to study multi-component soft systems such as poly-mer blends at continuum scales. We first systematically explore various features of the equationsystem, which give rise...

Clapeyron.jl: An Extensible, Open-Source Fluid Thermodynamics Toolkit

“…However, another type of bulk property one might be interested in is mixing and excess functions. These can be of use in continuum models such as the Cahn–Hilliard equation . As presented in Table , the mixing and excess functions are provided using a single function, rather than for each bulk property.…”

“…These can be of use in continuum models such as the Cahn−Hilliard equation. 6 As presented in Table 7, the mixing and excess functions are provided using a single function, rather than for each bulk property. This allows for users to obtain mixing or excess functions for any bulk property directly; for example, These functions are exemplified in Figure 8a,b.…”

“…Thermodynamic models, such as equations of state and activity coefficient models, are used to predict the properties of bulk matter at specified conditions. Today, they have found applications in natural gas, electrolyte, , polymer, − metallic, pharmaceutical, , and biological systems. They have become ubiquitous in modeling for both the academia and industry, and moreover, as the needs and demands placed upon this modeling have grown ever larger, these models have become more sophisticated.…”

Multiphase flow applications of nonintrusive reduced-order models with Gaussian process emulation

“…We now apply the analysis pipeline to polymer precipitation dynamics, of importance to engineering design problems in high-performance plastics and membrane systems. The complex dynamics and rich pattern formation were considered recently by Inguva et al (2020Inguva et al ( , 2021 (see also references therein) who used Cahn-Hilliard theory to model and simulate the spatio-temporal evolution of the emergent phase separation patterns; the relevant equations for a binary polymer blend are expressed by where ϕ represents the volume fraction of one of the polymers in the blend, M is a constant mobility parameter, and μ is a generalized chemical potential, which can be derived from the variational derivative of the Gibbs free energy functional: here, f denotes the homogeneous contribution to the Gibbs free energy per monomer, which is a nonconvex function of ϕ, and λ is a gradient free energy parameter. Numerical solutions of the above equations are obtained subject to Neumann conditions:…”

Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures

“…Coarsening of the morphology is therefore expected to have a significant impact on the material properties. Hence, coarsening is a long lasting subject of interest, mostly investigated together with SD in binary systems with experimental methods [7][8][9][10] , numerical simulations [11][12][13][14][15][16] , analytical models 1,17,18 and still an active area of research [19][20][21][22][23][24] . Being able to predict the actual time-dependent average domain size or characteristic length scale L(t) is crucial for understanding the morphology-property relationship.…”