scholarly journals Using the Cahn–Hilliard Theory in Metastable Binary Solutions

2019 ◽  
Vol 3 (3) ◽  
pp. 75 ◽  
Author(s):  
Viet-Nhien Tran Duc ◽  
Philip K. Chan
Keyword(s):  
Phase Separation ◽  
Spinodal Decomposition ◽  
Activation Barrier ◽  
Binary Solution ◽  
Functional Materials ◽  
Nucleation And Growth ◽  
Unstable Region ◽  
Unstable Phase ◽  
Spinodal Line ◽  
Model Phase

A solution may be in one of three states: stable, unstable, or metastable. If the solution is unstable, phase separation is spontaneous and proceeds by spinodal decomposition. If the solution is metastable, the solution must overcome an activation barrier for phase separation to proceed spontaneously. This mechanism is called nucleation and growth. Manipulating morphology using phase separation has been of great research interest because of its practical use to fabricate functional materials. The Cahn–Hilliard theory, incorporating Flory–Huggins free energy, has been used widely and successfully to model phase separation by spinodal decomposition in the unstable region. This model is used in this paper to mathematically model and numerically simulate the phase separation by nucleation and growth in the metastable state for a binary solution. Our numerical results indicate that Cahn–Hilliard theory is able to predict phase separation in the metastable region but in a region near the spinodal line.

scholarly journals A computational study of phase separation in polymer solutions under a double quench

2021 ◽  
Author(s):  
Ehsan Hosseini
Keyword(s):  
Phase Separation ◽  
Polymer Solution ◽  
Spinodal Decomposition ◽  
Computational Study ◽  
Stable State ◽  
Thermal Quenching ◽  
Nucleation And Growth ◽  
Two Dimensions ◽  
Numerical Work ◽  
Binary Polymer

Polymer-dispersed liquid crystals (PDLCs) are a relatively new class of materials used for many applications ranging from switchable windows to projection displays. PDLSs are formed by spinodal decomposition induced by thermal quenching or polymerization. The objective of the present study is to introduce a new mechanism of phase separation in a binary polymer solution and develop a mathematical model and computer simulation to describe the phase separation during the early and intermediate stages of nucleation and growth and spinodal decomposition induced by thermal double quenching. The growth equilibrium limits of phase separation as well as phase transition are calculated by taking into consideration the Flory-Huggins theory for the free energy of mixing. A two step quench is modeled using Cahn-Hilliard theory for asymmetric binary polymer solution which is quenched from a stable state in the one-phase region to a metastable region where nucleation and growth occurs. The solution is allowed to coarsen for different time periods before a second quench was applied to a point further inside the phase diagram. The numerical results in two dimensions replicate the experimental and numerical work that has been recently done and published.

scholarly journals A computational study of phase separation in polymer solutions under a double quench

2021 ◽  
Author(s):  
Ehsan Hosseini
Keyword(s):  
Phase Separation ◽  
Polymer Solution ◽  
Spinodal Decomposition ◽  
Computational Study ◽  
Stable State ◽  
Thermal Quenching ◽  
Nucleation And Growth ◽  
Two Dimensions ◽  
Numerical Work ◽  
Binary Polymer

Polymer-dispersed liquid crystals (PDLCs) are a relatively new class of materials used for many applications ranging from switchable windows to projection displays. PDLSs are formed by spinodal decomposition induced by thermal quenching or polymerization. The objective of the present study is to introduce a new mechanism of phase separation in a binary polymer solution and develop a mathematical model and computer simulation to describe the phase separation during the early and intermediate stages of nucleation and growth and spinodal decomposition induced by thermal double quenching. The growth equilibrium limits of phase separation as well as phase transition are calculated by taking into consideration the Flory-Huggins theory for the free energy of mixing. A two step quench is modeled using Cahn-Hilliard theory for asymmetric binary polymer solution which is quenched from a stable state in the one-phase region to a metastable region where nucleation and growth occurs. The solution is allowed to coarsen for different time periods before a second quench was applied to a point further inside the phase diagram. The numerical results in two dimensions replicate the experimental and numerical work that has been recently done and published.

scholarly journals Computational study of comprehensive methods of initiating phase separation within metastable regions and obtaining some notable patterns in unstable region

2021 ◽  
Author(s):  
Viet-Nhien Tran Duc
Keyword(s):  
Phase Separation ◽  
Spinodal Decomposition ◽  
Thermal Noise ◽  
Complex Geometry ◽  
Activation Barrier ◽  
Computational Study ◽  
Polymeric Materials ◽  
Mixed Solution ◽  
Flat Panel Displays ◽  
Energy Behavior

Binary phase polymer solution is interesting in that they expresses double-well local energy behavior, which means phase separation is preferred when condition is right. It is a feature that has been used to fabricate functional polymeric materials such as PDLC films for electro-optical devices (e.g. flat-panel displays and switchable windows). A uniformly mixed solution may be in one of three state: unstable, stable, or metastable. If the solution is unstable, then phase separation is spontaneous and proceeds by spinodal decomposition. If the solution is metastable, then the solution must overcome certain activation barrier for phase separation to proceed spontaneously. The activation barrier is usually the thermal noise or the fluctuation created by some external influence. This mechanism is called nucleation-and-growth. Manipulating morphology of phase separation has been of some great research interest because of its practical use. While spinodal decomposition has been well-studied, there are several other methods to further control morphology. For this thesis, the following methods are considered: double quench, anisotropic quenching with varying temperature or polymerization, surface-directed wetting, and concentration gradient. The methods are carried out within metastable or unstable regions or both. To numerically model, Cahn-Hilliard theory and FloryHuggins’ theory are used. This thesis is to also demonstrate that, present numerical method is very efficient and can work on complex geometry.

Metastable liquid phase separation in undercooled molten Pd40.5Ni40.5P19

1997 ◽  
Vol 12 (2) ◽  
pp. 314-317 ◽  
Author(s):  
C. W. Yuen ◽  
K. L. Lee ◽  
H. W. Kui
Keyword(s):  
Phase Separation ◽  
Spinodal Decomposition ◽  
Liquid State ◽  
Microstructural Analysis ◽  
Nucleation And Growth ◽  
Transition Regime ◽  
Metastable Liquid ◽  
Temperature Liquid ◽  
Kinetic Crystallization ◽  
Metastable Liquid Phase Separation

It was demonstrated that molten Pd40.5Ni40.5P19 undergoes liquid state phase separation in the undercooling regime δT = T1 − T where T1 is the liquidus of Pd40.5Ni40.5P19 and T is the kinetic crystallization temperature. Liquid state phase separation by nucleation and growth takes place for δT ≤ 60 K while that by spinodal decomposition occurs for δT ≥ 100 K. Microstructural analysis of the undercooled specimen obtained in the undercooling regime of 60 ≤ δT ≤ 100 K indicates that it is the transition regime. Finally, it was found that when undercooled molten Pd40.5Ni40.5P19 undergoes liquid state spinodal decomposition, it first decomposes into two liquid networks, which is finally replaced by a system of three liquid networks.

Investigation of Solid-State Immiscibility and Thermoelectric Properties of the System PbTe – PbS

2009 ◽  
Vol 1166 ◽  
Author(s):  
Steven N Girard ◽  
Jiaqing He ◽  
Vinayak P Dravid ◽  
Mercouri G Kanatzidis
Keyword(s):  
Phase Separation ◽  
Solid State ◽  
Spinodal Decomposition ◽  
Thermoelectric Properties ◽  
Nucleation And Growth ◽  
Thermoelectric Systems ◽  
Precipitation Phenomena ◽  
Decomposition Phase

AbstractWe have shown that (Pb1-mSnmTe)1-x(PbS)x where m = 0.05 and x = 0.08 exhibits a ZT of ˜1.4 at 700 K. This system incorporates two thermoelectric systems: PbSxTe1-x and Pb1-xSnxTe. Here we report the thermoelectric properties of PbSxTe1-x (x = 0.08 and 0.30). The material PbS0.08Te0.92 exhibits nucleation and growth of PbS precipitates, while PbS0.30Te0.70 exhibits PbS precipitation through spinodal decomposition phase separation. We report the thermoelectric properties of this system as a result of the differing precipitation phenomena.

scholarly journals Computational study of comprehensive methods of initiating phase separation within metastable regions and obtaining some notable patterns in unstable region

2021 ◽  
Author(s):  
Viet-Nhien Tran Duc
Keyword(s):  
Phase Separation ◽  
Spinodal Decomposition ◽  
Thermal Noise ◽  
Complex Geometry ◽  
Activation Barrier ◽  
Computational Study ◽  
Polymeric Materials ◽  
Mixed Solution ◽  
Flat Panel Displays ◽  
Energy Behavior

Binary phase polymer solution is interesting in that they expresses double-well local energy behavior, which means phase separation is preferred when condition is right. It is a feature that has been used to fabricate functional polymeric materials such as PDLC films for electro-optical devices (e.g. flat-panel displays and switchable windows). A uniformly mixed solution may be in one of three state: unstable, stable, or metastable. If the solution is unstable, then phase separation is spontaneous and proceeds by spinodal decomposition. If the solution is metastable, then the solution must overcome certain activation barrier for phase separation to proceed spontaneously. The activation barrier is usually the thermal noise or the fluctuation created by some external influence. This mechanism is called nucleation-and-growth. Manipulating morphology of phase separation has been of some great research interest because of its practical use. While spinodal decomposition has been well-studied, there are several other methods to further control morphology. For this thesis, the following methods are considered: double quench, anisotropic quenching with varying temperature or polymerization, surface-directed wetting, and concentration gradient. The methods are carried out within metastable or unstable regions or both. To numerically model, Cahn-Hilliard theory and FloryHuggins’ theory are used. This thesis is to also demonstrate that, present numerical method is very efficient and can work on complex geometry.

Anomalous patterns of Saffman–Taylor fingering instability during a metastable phase separation

2021 ◽  
Author(s):  
Ryuta X. Suzuki ◽  
Hikari Tada ◽  
Sae Hirano ◽  
Takahiko Ban ◽  
Manoranjan Mishra ◽  
...  
Keyword(s):  
Phase Separation ◽  
Spinodal Decomposition ◽  
Metastable Phase ◽  
Nucleation And Growth ◽  
Growth Type ◽  
Fingering Instability ◽  
Metastable Phase Separation

A phase separation is important in biology, biochemistry, industry, and other areas, and is divided into two types: a spinodal decomposition type and a nucleation and growth type. It has...

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