Dynamics Of Spinodal Decomposition Research Articles

Phase separation dynamics in binary systems containing mobile particles with variable Brownian motion

This study investigates the spinodal decomposition dynamics in binary mixtures containing mobile particles by combining the Cahn–Hilliard equation with Langevin dynamics for particles with Brownian motion changes proportional to their mobility. We solve the Cahn–Hilliard equation numerically using a semi-implicit Fourier spectral method, and show that the domain growth rate first increases with the increase in particle mobility, and then decreases. The effect of filler particle concentration on the domain growth depends on its mobility: when the particle mobility is low, the domain growth rate decreases with the increase in particle concentration; whereas when the particle mobility is high, the domain growth rate decreases and then increases and finally decreases again with the increase in particle concentration. The proposed model suggests the possibility of controlling macroscopic behaviour of binary alloys by altering filler particle properties.

Dynamics of Spinodal Decomposition in a Ternary Gelling System.

The phase diagram and phase transitions of the ternary system of gelatin, water and poly(ethylene glycol) oligomers were studied as a function of the weight fraction of gelatin and the weight fraction and molecular weight of poly(ethylene glycol) oligomers. It was found that both phase separation and the sol-gel transition occur in this ternary system. The relative position of the phase separation line and the sol-gel transition line depends on the weight fraction and the molecular weight of the poly(ethylene glycol) oligomer that coexists in the solution. All aspects of the phase diagram are sensitive to the molecular weight of the poly(ethylene glycol) oligomer. Since the phase separation line crosses the sol-gel transition line in the phase space that is created by the temperature and the weight fraction of gelatin, the phase space is typically divided into four regions, where each region corresponds to a definite phase. The transitions between mutual phases were studied using the light-scattering technique.

LB3D: A parallel implementation of the Lattice-Boltzmann method for simulation of interacting amphiphilic fluids

We introduce the lattice-Boltzmann code LB3D, version 7.1. Building on a parallel program and supporting tools which have enabled research utilising high performance computing resources for nearly two decades, LB3D version 7 provides a subset of the research code functionality as an open source project. Here, we describe the theoretical basis of the algorithm as well as computational aspects of the implementation. The software package is validated against simulations of meso-phases resulting from self-assembly in ternary fluid mixtures comprising immiscible and amphiphilic components such as water–oil–surfactant systems. The impact of the surfactant species on the dynamics of spinodal decomposition are tested and quantitative measurement of the permeability of a body centred cubic (BCC) model porous medium for a simple binary mixture is described. Single-core performance and scaling behaviour of the code are reported for simulations on current supercomputer architectures. Program summaryProgram Title: LB3DProgram Files doi:http://dx.doi.org/10.17632/9g9x2wr8z8.1Licensing provisions: BSD 3-clauseProgramming language: FORTRAN90, Python, CNature of problem: Solution of the hydrodynamics of single phase, binary immiscible and ternary amphiphilic fluids. Simulation of fluid mixtures comprising miscible and immiscible fluid components as well as amphiphilic species on the mesoscopic scale. Observable phenomena include self-organisation of mesoscopic complex fluid phases and fluid transport in porous media.Solution method: Lattice-Boltzmann (lattice-Bhatnagar–Gross–Krook, LBGK) [1, 2, 3] method describing fluid dynamics in terms of the single particle velocity distribution function in a 3-dimensional discrete phase space (D3Q19) [4, 5, 6]. Multiphase interactions are modelled using a phenomenological pseudo-potential approach [7, 8] with amphiphilic interactions utilising an additional dipole field [9, 10]. Solid boundaries are modelled using simple bounce-back boundary conditions and additional pseudo-potential wetting interactions [11].Additional comments including Restrictions and Unusual features: The purpose of the release is the provision of a refactored minimal version of LB3D suitable as a starting point for the integration of additional features building on the parallel computation and IO functionality. [1]S. Succi, The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond, Oxford University Press, 2001.[2]B. Dünweg, A. Ladd, Lattice Boltzmann simulations of soft matter systems, Adv. Poly. Sci. 221 (2009) 89–166[3]C. K. Aidun, J. R. Clausen, Lattice-Boltzmann Method for Complex Flows, Annual Review of Fluid Mechanics 42 (2010) 439.[4]X. He, L.-S. Luo, A priori derivation of the lattice-Boltzmann equation, Phys. Rev. E 55 (1997) R6333.[5]X. He, L.-S. Luo, Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E 56.[6]Y. H. Qian, D. D’Humiéres, P. Lallemand, Lattice BGK Models for Navier–Stokes Equation, Europhysics Letters 17 (1992) 479.[7]X. Shan, H. Chen, Lattice-Boltzmann model for simulating flows with multiple phases and components, Physical Review E 47 (1993) 1815.[8]X. Shan, G. Doolen, Multicomponent lattice-Boltzmann model with interparticle interaction, Journal of Statistical Physics 81 (1995) 379.[9]H. Chen, B. Boghosian, P.V. Coveney, M. Nekovee, A ternary lattice-Boltzmann model for amphiphilic fluids, Proceedings of the Royal Society of London A 456 (2000) 2043.[10]M. Nekovee, P. V. Coveney, H. Chen, B. M. Boghosian, Lattice-Boltzmann model for interacting amphiphilic fluids, Phys. Rev. E 62 (2000) 8282.[11]N. S. Martys, H. Chen, Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice-Boltzmann method, Phys. Rev. E 53 (1996) 743.

Dynamics of spinodal decomposition coupled with chemical reaction in thermosetting phenol-formaldehyde resin-based solutions and its application in monolithic porous materials

A model comprised of a rate equation for polymerization and cross-linking reaction and the time-dependent Ginzburg–Landau equation for spinodal decomposition was utilized to describe reaction-induced spinodal decomposition (RISD). The effects of initial composition, curing temperature, and scaled diffusion coefficient and rate constant on the RISD dynamics were investigated numerically in thermosetting phenol-formaldehyde resin (PF)-based polymer solutions. As the initial composition increased, the final morphology varied from the regular droplet-like to interconnected pattern, and then transformed into another droplet-like one. The greater initial composition or higher curing temperature contributed to accelerate the RISD dynamics and caused the smaller dominant wavelength. When the curing point was determined, the increase of scaled diffusion coefficient gave rise to reduction of characteristic size and maximum structure factor, while the raise of scaled rate constant merely resulted in acceleration of the curing reaction. Based on the theoretical analyses, experiments were carried out to verify the influence of initial composition and curing temperature on the morphology of monolithic porous carbons. The results were in good agreement with the theoretical analyses and can provide guidance for synthesizing monolithic porous polymer and carbon materials with tunable pore morphology.

Acousto-spinodal decomposition of compressible polymer solutions: Early stage analysis

The structure and dynamics of early stage kinetics of pressure-induced phase separation of compressible polymer solutions via spinodal decomposition is analyzed using a linear Euler-Cahn-Hilliard model and the modified Sanchez Lacombe equation of state. The integrated density wave and Cahn-Hilliard equations combine the kinetic and structural characteristics of spinodal decomposition with density waves arising from pressure-induced couplings. When mass transfer rate is slower that acoustic waves, concentration gradients generate density waves that cycle back into the spinodal decomposition dynamics, resulting in oscillatory demixing. The wave attenuation increases with increasing mass transfer rates eventually leading to nonoscillatory spinodal demixing. The novel aspects of acousto-spinodal decomposition arise from the coexistence of stable oscillatory density dynamics and the unstable monotonic concentration dynamics. Scaling laws for structure and dynamics indicate deviations from incompressible behavior, with a significant slowing down of demixing due to couplings with density waves. Partial structure factors for density and density-concentration reflect the oscillatory nature of acousto-spinodal modes at lower wave vectors, while the single maximum at a constant wave vector reflects the presence of a dominant mode in the linear regime. The computed total structure factor is in qualitative agreement with experimental data for a similar polymer solution.

Deterministic and Stochastic Dynamics in Spinodal Decomposition of a Binary System

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 in systems supercooled below critical temperature. Analytical results for the hyperbolic model of spinodal decomposition are summarized in comparison with outcomes of classic Cahn−Hilliard theory. Numeric modelling shows that the hyperbolic evolution leads to sharper boundary between two structures of a decomposed system in comparison with prediction of parabolic equation given by the theory of Cahn and Hilliard. Considering phase separation processes in stochastic systems with a field-dependent mobility and an internal multiplicative noise, we study dynamics of spinodal decomposition for parabolic and hyperbolic models separately. It is that the domain growth law is generalized when internal fluctuations are introduced into the model. A mean field approach is carried out in order to obtain the stationary probability, bifurcation and phase diagrams displaying re-entrant phase transitions. We relate our approach to entropy-driven phase-transitions theory.

Phase separation in binary systems with internal multiplicative noise

A study of a phase separation process in stochastic systems with a field dependent kinetic coefficient and an internal multiplicative noise is presented. Dynamics of spinodal decomposition at early and late stages is investigated by computer simulations where the domain growth law is generalized. A mean field approach was carried out in order to obtain the stationary probability, bifurcation and phase diagrams displaying reentrant phase transitions. We relate our approach to entropy driven phase transitions theory.

Non-linear dynamics of spinodal decomposition in multi-component polymer systems. I. General approach

Abstract Spinodal decomposition of multi-component systems is analyzed within the framework of a new approach focusing on the description of this dynamic process in terms of the Langevin equation for the one-time structure factor S(q, t) treated as an independent dynamic object. We apply this approach, in particular, to multi-component incompressible polymer systems (binary polymer solutions, ternary polymer blends etc.). The dynamic equation describing the simultaneous relaxation of both the order parameters (component concentrations) and the matrix of the component-component dynamic correlation functions ∥S ij(q, t)∥, including the explicit expression for the corresponding effective kinetic coefficients, is derived.

Shock wave stability under the spinodal decomposition of binary mixtures

A diffusion equation for a binary mixture and spinodal decomposition in the case of phase separation are considered. It is shown that, if the binding force between polymer chain links is weak, the diffusion equation for a binary mixture allows for the reduction to the Burgers equation with “viscosity”; that is, the coexistence of rarefaction waves and shock density waves is a possibility. The effect of strong bonds between polymer chain links on the spinodal decomposition dynamics is studied. It is demonstrated that strong bonding may cause a multiflux wave system with alternate stability to arise when the viscosity varies.

Non-linear dynamics of spinodal decomposition

We develop a new technique describing the non linear growth of interfaces. We apply this analytical approach to the one dimensional Cahn-Hilliard equation. The dynamics is captured through a solvability condition performed over a particular family of quasi-static solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the non-linear growth is also well characterized. Numerical simulations are compared in a satisfactory way with the analytical results through three different fitting methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.

Dynamics of spinodal decomposition in finite-lifetime systems: Nonlinear statistical theory based on a coarse-grained lattice-gas model.

We study theoretically dynamics of the spinodal decomposition in finite-lifetime systems to clarify effects of the interparticle interactions beyond the Ginzburg-Landau-Wilson phenomenology. Our theory is based on the coarse-grained Hamiltonian derived from the interacting lattice-gas model with a finite lifetime. The information of a system is reduced to closed-form coupled integrodifferential equations for the single-point distribution function and the dynamical structure factor. These equations involve explicitly the interparticle interactions. The finite lifetime prevents the phase separation and the order formation in the cw creation case; domains cannot grow to be larger than an asymptotic characteristic size [k(max)(t --> infinity)](-1). Power-law dependence of k(max)(t --> infinity) on the interparticle interaction and the particle lifetime is also found numerically. The finite lifetime prevents the phase separation, i.e., the lower critical wave number k((1))(c) appears and domains of size larger than [k((1))(c)](-1) cannot grow.

Dynamics of spinodal decomposition in finite-lifetime systems

We present a statistical theory of the phase-separation dynamics in many-particle systems with a finite lifetime. Temporal evolution of the spinodal decomposition is traced with the single-point distribution function and the dynamical structure factor under the situation where the mean particle number is constant by balancing between decay and creation of the particles. The finite lifetime prevents phase separation and order formation; hence the lower critical wave number ${k}_{\mathrm{c}}^{(1)}(t)$ appears; domains of larger size than $[{k}_{\mathrm{c}}^{(1)}(t){]}^{\ensuremath{-}1}$ cannot grow. Differences between the infinite- and finite-lifetime cases are clarified in terms of this critical wave number. A universal relation between the lifetime and the asymptotic $(\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty})$ critical wave number is confirmed numerically. Comparison with the nucleation process is also made.

Viscoelastic Effects on the Dynamics of Spinodal Decomposition in Binary Polymer Mixtures

Numerical simulations based on the modified time-dependent Ginzburg-Landau (TDGL) equation have been performed on the domain growth dynamics of binary polymer mixtures. An elastic relaxation term was introduced into the equation to take the entanglement effects of the polymer chains into account. A cell dynamical scheme (CDS) is employed in this paper to improve the computing efficiency. The dynamics of the phase separation in polymer blends was investigated through to a very late stage. In the system without viscoelastic effects, there exists an apparent early stage, and in the late stage the modified Lifshitz-Slyozov law and dynamical scaling law are satisfied very well. In the system with viscoelastic effects, there are some unique characteristics. A morphology with a rough interface between the domains is obtained and suppression of order-parameter fluctuations is observed. The growth behavior of domains was altered and there exits an intermediate stage between the early and late stage, in which the growth rate of domains slows down drastically. The intermediate stage was prolonged with enhanced entanglement effects. Entanglement effects also enhance the quench-depth effects on the correlation and diminish the discrimination of correlation induced by criticality. After the relaxation of entanglements, the growth exponents with the model employed in this paper are independent of entanglements and are essentially consistent with the modified Lifshitz-Slyozov law. In addi tion, the pair correlation function and the structure function are shown to exhibit the dynamical scaling law at the late stage.

膜の構造制御と機能 熱誘起相分離法による多孔膜の作製と微細構造制御

The thermally induced phase separation (TIPS) process is a valuable way of making microporous materials, such as membranes and foams. TIPS process consists of the following steps.1. A homogeneous solution is formed at an elevated temperature by blending the polymer with a high-boiling, low molecular weight liquid (diluent).2. The solution is formed into the desired shape (flat sheet, tube, hollow fiber).3. The solution is cooled at a controlled rate or quenched to induce phase separation.4. The diluent is removed typically by solvent extraction.5. The extracatnt is removed typically by evaporation to produce a microporous structure.This paper mainly focuses on the kinetics of phase separation in the TIPS process. The studies on phase separation by the light scattering method, kinetics of droplet growth in the latter stage of phase separation and the computer simulation on dynamics of spinodal decomposition are reviewed briefly. Accurate engineering of the TIPS process is essential for control of microstructural properties such as pore size, pore size distribution and porosity, since these properties ultimately determine the performance of the microporous membranes.

Non-linear dynamics of spinodal decomposition

A new approach is proposed to describe the spinodal decomposition, in particular, in polymer binary blends. In the framework of this approach, the spinodal decomposition is described as a relaxation of one-time structure factor S(q,t) treated as an independent dynamic object (a peculiar two-point order parameter). The dynamic equation for S(q,t), including the explicit expression for the corresponding effective kinetic coefficient, is derived. In the first approximation this equation is identical to the Langer equation. We first solved it both in terms of higher transcendental functions and numerically. The asymptotic behaviour of S(q,t) at large (from the onset of spinodal decomposition) times is analytically described. The values obtained for the power-law growth exponent for the large-time peak value and position of S(q,t) are in good agreement with experimental data and results of numerical integration of the Cahn-Hilliard equation.

Spinodal decomposition and inflation: Dynamics and metric perturbations

We analyse the dynamics of spinodal decomposition in inflationary cosmology using the closed time path formalism of out of equilibrium quantum field theory combined with the non-perturbative Hartree approximation. In addition to a general analysis, we compute the detailed evolution of two inflationary models of particular importance: lambda Phi^4 new inflation and natural inflation. We compute the metric fluctuations resulting from inflationary phase transitions in the slow roll approximation, showing that there exists a regime for which quantum fluctuations of the inflaton field result in a significant deviation in the predictions of the spectrum of primordial density perturbations from standard results. We provide case examples for which a blue tilt to the power spectrum (i.e. n_s > 1) results from the evolution of a single inflaton field, and demonstrate that field fluctuations may result in a scalar amplitude of fluctuations significantly below standard predictions, resulting in a slight alleviation of the inflationary fine tuning problem. We show explicitly that the metric perturbation spectrum resulting from inflation depends upon the state at the outset of the inflationary phase.

Interfacial curvature in phase-separating binary fluids: comparison between computer simulation and experiments

We present comparisons of results on the late stage dynamics of spinodal decomposition (SD) obtained by the computer simulation based on the time-dependent Ginzburg-Landau equation with hydrodynamic interaction and experiments of a polymer mixture of deuterated polybutadiene and polybutadiene. We especially focus on the curvatures of the interface of phase-separated structures formed by SD and show that the scaling functions of the curvature distributions for the two systems are in good agreement.

Spinodal decomposition induced by cross-linking reaction in a binary polymer mixture

Phase separation of a binary polymer mixture of poly{styrene-co-[p-2,2,2-trifluoro-1-hydroxy-1-trifluoromethylethyl-α-methylstyrene]} (PS(OH)) and poly[(methyl methacrylate)-co-(glycidyl methacrylate)] (PMMA(G)) upon cross-linking reaction was studied using time-resolved light scattering (TRLS) and optical microscopy. The blends of PS(OH)/PMMA(G), in which PMMA(G) containing 1.4 mol-% epoxy groups can be selectively cross-linked with the multifunctional agent 4,4′-methylenebis(o-chloroaniline) (MOCA) and PS(OH) contains 1.8 mol-% of the strongly proton-donating group C(CF3)2OH, exhibit a lower critical solution temperature (LCST). The cross-linking reaction was carried out for two compositions of PS(OH)/PMMA(G)/MOCA, 50/50/0.7 and 40/60/0.8 (w/w/w), at various temperatures located in the one-phase region between the coexistence curve and the glass transition temperature of the blends. TRLS investigation shows that the phase separation takes place via spinodal decomposition (SD) induced by the increase in the molecular weight of PMMA(G) during the cross-linking reaction. A modulated phase structure with the characteristic features of periodicity and dual connectivity of the phases was developed in this case. The dynamics of SD were investigated in terms of changes of the peak scattering vector qm(t) as a function of time. They are dependent on the reaction temperature and composition. A scaling relation qm(t) ∝︁ t−af(x) describing the behavior of the evolution of phase separation upon reaction was supported by the experiments.

Spinodal decomposition induced by cross-linking reaction in a binary polymer mixture

Phase separation of a binary polymer mixture of poly{styrene-co-[p-2,2,2-trifluoro-1-hydroxy-1-trifluoromethylethyl-α-methylstyrene]} (PS(OH)) and poly[(methyl methacrylate)-co-(glycidyl methacrylate)] (PMMA(G)) upon cross-linking reaction was studied using time-resolved light scattering (TRLS) and optical microscopy. The blends of PS(OH)/PMMA(G), in which PMMA(G) containing 1.4 mol-% epoxy groups can be selectively cross-linked with the multifunctional agent 4,4′-methylenebis(o-chloroaniline) (MOCA) and PS(OH) contains 1.8 mol-% of the strongly proton-donating group C(CF3)2OH, exhibit a lower critical solution temperature (LCST). The cross-linking reaction was carried out for two compositions of PS(OH)/PMMA(G)/MOCA, 50/50/0.7 and 40/60/0.8 (w/w/w), at various temperatures located in the one-phase region between the coexistence curve and the glass transition temperature of the blends. TRLS investigation shows that the phase separation takes place via spinodal decomposition (SD) induced by the increase in the molecular weight of PMMA(G) during the cross-linking reaction. A modulated phase structure with the characteristic features of periodicity and dual connectivity of the phases was developed in this case. The dynamics of SD were investigated in terms of changes of the peak scattering vector qm(t) as a function of time. They are dependent on the reaction temperature and composition. A scaling relation qm(t) ∝︁ t−af(x) describing the behavior of the evolution of phase separation upon reaction was supported by the experiments.

Dynamics of Spinodal Decomposition in Polymer Solutions near a Glass Transition

A model based on the Cahn−Hilliard formalism is used to simulate structure formation in thermally quenched polymer solutions in the vicinity of a glass transition. Simulation results for the system poly(methyl methacrylate)/cyclohexanol are correlated with light scattering and microscopy measurements recently reported in the literature. Good qualitative and quantitative agreement with experimental observations indicates the applicability of current free-volume and thermodynamic theories to quantify the dynamics near a glass transition. The model accurately predicts late-stage scaling exponents, and results show that the early stage of phase separation occurs on time scales ≪ 1 s. Pore growth rates based on zero-free-parameter calculations agree well with experimental observations. Simulations also show that quenching a phase-separated structure below a glass transition can result in the formation of a secondary droplet structure within the polymer-rich phase, prior to freezing-in of the preexisting morphology. Such secondary structures, which have also been observed experimentally, appear to have little or no effect on the calculated structure factor, which is also consistent with light-scattering measurements.