Spinodal decomposition (phase transitions via unstable states)

Skripov, V. P.; Skripov, A. V.

doi:10.1070/pu1979v022n06abeh005571

Cited by 128 publications

(66 citation statements)

References 4 publications

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“…11,37,38 It is derived from the continuity equation, where the mobility M is the ratio of the negative flux to the gradient of the functional derivative of the total free energy. The total free energy contains two terms.…”

Section: Problem Formulation and Numerical Methodsmentioning

confidence: 99%

Polymerization-Induced Phase Separation. 2. Morphological Analysis

Chan

Rey

1997

Macromolecules

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A model composed of the nonlinear Cahn-Hilliard and Flory-Huggins theories for spinodal decomposition (SD) and a second-order rate equation for polymerization for the self-condensation of a trifunctional monomer is used to study the polymerization-induced phase separation (PIPS) phenomena. The numerical results are consistent with experimental observations. These observations include the formation and evolution of a droplet-type morphology. In addition, the time evolution of the maximum value of the structure factor S(km,t) exhibits an exponential growth during the early stage but saturates during the intermediate stage of SD. Moreover, the dominant dimensionless wavenumber km* decreases during the intermediate stage. The numerical results, however, also indicate that km* increases during the early stage, which has not yet been observed experimentally. Furthermore, the morphological analysis is also consistent with experimental observations. The droplet size and shape distributions indicate that the average droplet size and shape prevail during the PIPS phenomena, and statistical analysis of the Voronoi polygons indicates that the droplets are randomly positioned within the matrix. Lastly, the characteristic time τ, average dimensionless equivalent droplet diameter 〈d*〉, and droplet number density Nd depend on the magnitudes of a scaled diffusion coefficient D for phase separation and a scaled rate constant K1 for polymerization. Consistent with experimental observations, τ and 〈d*〉 decrease while Nd increases as K1 increases. Similarly, as D increases, τ and 〈d*〉 decrease while Nd increases. The parameters K1 and D have no effect on the average shape factor.

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Section: Problem Formulation and Numerical Methodsmentioning

confidence: 99%

Polymerization-Induced Phase Separation. 2. Morphological Analysis

Chan

Rey

1997

Macromolecules

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“…The maximum decrease in enthalpy is found to be 1.03 J for rate 30 K min À1 . It is noteworthy to mention that it was deduced within the framework of the mean-field theories [12][13][14] that there is a discontinuity of the mechanism of decomposition kinetics at the boundary between the metastable and unstable regions. Langer [15] developed unified theory on the basis of a non-linear spinodal theory as well as Binder et al [16] who chose the cluster kinetics approach by treating spinodal decomposition in the form of a generalized nucleation theory.…”

Section: Differential Thermal Analysismentioning

confidence: 99%

“…Such information is very important to give an insight about the spinodal and binodal phase decomposition and the verification of different theories about them. On one hand, the mean-field theories [12][13][14] suggest a discontinuity of the mechanism of the decomposition kinetics at the boundary between the metastable and instable regions. On the other hand, Langer [15] developed the unified theory while Binder et al [16] chose the cluster kinetics approach by treating spinodal decomposition in the form of a generalized nucleation theory.…”

Section: Introductionmentioning

confidence: 99%

Thermal analysis study for the phase determination and instable to metastable transformation of the Co–13Cu alloy

et al. 2009

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The differential thermal analysis (DTA) is utilized to determine the phase boundary and phase equilibria of Co-Cu alloy having a miscibility gap. Regions for various phase i.e., spinodal and coherent binodal, peritectic, magnetic and the transformation from the two phases to phase transformations are distinctly determined for the Co-13 at%Cu alloy. The obtained results might indicate the continuity of the decomposition kinetics at the boundary between instable and the metastable regions but an activation barrier is needed. The activation energy for the magnetic transformation is determined to be 182.2 AE 2.1 kJ mol À1 .

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“…In parallel with a detailed analysis and tests against experimental data [3,4] the theory of Cahn and Hilliard has been further explored and developed. In particular, it has been demonstrated that there is a boundary for the critical quenching above which the classic Cahn-Hilliard approach has to be extended to the case of strongly non-equilibrium decomposition provided by deep supercooling into the spinodal region of a phase diagram [5,6].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the dispersion relation in spinodal decomposition of a binary system

Galenko

Лебедев

2007

Philosophical Magazine Letters

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A model for diffusion and phase separation which takes into account hyperbolic relaxation of the solute diffusion flux is developed. Such a 'hyperbolic model' provides analysis of 'hyperbolic evolution' of patterns in spinodal decomposition of binary systems. Analytical results for the dispersion relation and critical parameters (such as wavelength and amplification rate of decomposition) are analyzed in comparison with outcomes of classic CahnHilliard theory. It is shown that the hyperbolic model predicts the amplification rate behaviour that is typically observed in experiments on spinodal decomposition.

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Spinodal decomposition (phase transitions via unstable states)

Cited by 128 publications

References 4 publications

Polymerization-Induced Phase Separation. 2. Morphological Analysis

Polymerization-Induced Phase Separation. 2. Morphological Analysis

Thermal analysis study for the phase determination and instable to metastable transformation of the Co–13Cu alloy

Analysis of the dispersion relation in spinodal decomposition of a binary system

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