Phase Separation In Binary Systems Research Articles

Influence of thermal effects on the morphological patterns developed through phase separation in binary systems

This paper is concerned with the modelling and numerical simulation of temperature-induced phase separation (TIPS) coupled with non-uniform temperature fields. The spontaneous phase separation of an initially homogeneous blend can be used, in principle, as a reliable and scalable process to reproduce specific morphologies at the microscopic scale in two-phase composite materials, such as rubber-reinforced resins, or in microstructured porous media. The size of the microstructures that are formed and the degree of anisotropy can be controlled through the imposition of an adequate temperature field. In order to understand the potential use of a temperature gradient to control phase separation, we developed a qualitative model for TIPS based on the Cahn–Hilliard approach and we proposed a computational strategy to obtain numerical solutions for phase separation in confined domains taking into account the thermal interaction with the walls. While the method is based on a volume penalization technique, the novelty of the proposed approach relies on the fact that the penalization term of the equation is constructed on the same theoretical basis from which the Cahn–Hilliard equation is derived. The advantage offered by this technique is that the same pseudo-spectral Fourier discretization schemes that are classically used to solve the Cahn–Hilliard equation in periodic domains can be straightforwardly applied to the case of bounded domains. The application examples shown in this paper emphasize the key role of the dimensionless number given by the ratio of the characteristic heat propagation time and the characteristic time of the phase separation, and demonstrate how control of the microstructure anisotropy could be achieved through TIPS.

Phase separation in binary systems with competing internal and external multiplicative noises

We have considered phase separation processes in binary stochastic systems with thermal diffusion and ballistic mixing representing irradiation influence. Introducing fluctuations of thermal flux and an external source of atom relocations due to ballistic diffusion into dynamics of a globally conserved field, we have shown that there are two competing mechanisms of phase transitions type of “order-disorder”: thermally assisted diffusion and irradiation induced atomic exchange. We have studied dynamics of the structure function at early stages of decomposition. In the framework of the mean field theory we have derived the effective Fokker-Planck equation to describe phase separation processes. It was shown that the ordering processes can be controlled by both regular and stochastic parts of external source influence. A reentrant behavior of a mean field order parameter versus the external noise intensity and fluctuations correlation radius is found.

Phase separation of binary systems

In this paper, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a nondimensional parameter K such that if K > 0 , the transition is first order with latent heat and if K < 0 , the transition is second order. Here the parameter K is defined in terms of the coefficients in the quadratic and cubic nonlinear terms of the Cahn–Hilliard equation and the typical length scale of the container. Second, a phase diagram is derived, characterizing the order of phase transitions, and leading in particular to a prediction that there is only a second-order transition for molar fraction near 1 / 2 . This is different from the prediction made by the classical phase diagram. Third, a T L -phase diagram is derived, characterizing the regions of both homogeneous and separation phases and their transitions.

Cahn-Hilliard equations and phase transition dynamics for binary systems

The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical Cahn-Hilliard equation or the Cahn-Hilliard equation coupled with entropy, leading to some interesting physical predictions.The analysis is based on dynamic transition theory for nonlinear systems and new classification scheme for dynamic transitions, developed recently by the authors.

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.

Phase Separation in Binary Systems: the Possibility of Gas-Gas Equilibrium at Subcritical Conditions

The possibility of gases exhibiting limited solubility under subcritical conditions is analyzed and discussed. It is shown that a binary gas mixture will always behave like a regular solution and that phase splitting is theoretically feasible whenever the condition (Pdelta12)/(RT) > 2 is fulfilled where delta12 = 2B12-B11-B22. The value of delta12 required for phase splitting to occur is extremely large so that although the phenomena is theoretically possible, it will occur rarely or at all.

Structure of liquid metals determined by scattering techniques

Liquids structure is characterized by a short range order, which can be determined by X-ray and neutron scattering. The important function measured by these techniques is the structure factor. It is the Fourier transform of the pair correlation function, which describes the instantaneous spatial positions of the atoms. Partial pair correlation functions describe the local arrangements of the atoms constituting the alloy. They can be determined, in particular by neutron scattering. Metastable states are usually related to nucleation processes. Their study is also possible by small angle scattering (SAS). The kinetics of phase separation in binary systems can be followed in real time by SAS. Some fundamental notions of scattering techniques applied to the study of liquid metals structure and to the kinetics of phase separation during nucleation processes are presented.

A Calorimetric Study of Phase Separation in Liquid Crystal/Matrix Systems: Determination of the Excess Specific Heat of Mixing

Abstract The effects of concentration and state of cure on mixing and phase separation of binary systems of a low molecular weight liquid crystal (LC) and an organic matrix have been determined for the first time. We found that, as temperature is increased, mixing in uncured LC/matrix systems is accompanied by a step-like decrease in specific heat at T mix, the mixing temperature. This decrease is due, for the most part, to the (negative) excess specific heat of mixing. ΔC mix. The excess enthalpy of mixing. ΔH mix, may also contribute to the thermal effect. A plot of ΔC mix versus LC concentration exhibits a minimum, as expected from theory. Such a plot for a mixture of a specific LC (E7) with uncured matrix (NOA65) allows us to estimate the solubility limit of E7 in the matrix-rich phase (∼15%) and of NOA65 in the LC-rich phase (∼5%). Uncured E7/NOA65 mixtures exhibit phase diagrams with an upper critical solution temperature (UCST) slightly above 300 K. To avoid undesired phase separation prior to fina...

A mathematical model of dynamics of non-isothermal phase separation

A mathematical model of thermally activated phase separation in binary systems is proposed. The construction is based on the Landau-Ginzburg theory of phase transitions and non-equilibrium thermodynamics. The proposed system of differential equations represents an extension of the Cahn-Hilliard model to the non-isothermal situation. The model is shown to be consistent with the first principles of thermodynamics. The stability solutions is considered, and for the one-dimensional case numerical results are presented.

The effect of surfactants on the dynamics of phase separation

The dynamics of phase separation in binary systems containing surfactants is investigated by means of a time-dependent Ginzburg-Landau model. The Langevin equations for two scalar fields are solved numerically in two spatial dimensions. One of these fields is the order parameter representing the local difference in the concentrations of the two phase-separating components and the second is the local surfactant concentration. Different conservation laws of the fields, which represent different models for the dynamics of phase separation, are investigated. In all models, the average domain size for intermediate to late times is characterized by anomalously slow dynamics caused by the accumulation of surfactants at the interfaces and by the concomitant decrease in the driving force. Although all models exhibit similar slow growth, the domain structure is found to depend strongly on the nature of the conservation law. Indeed, the structure factor exhibits a peak at k>0 when the order parameter is conserved, whereas the peak is found to lie at k=0 if the order parameter is not conserved. Finally, dynamical scaling in both real- and Fourier-space correlation functions for the order parameter is found during the intermediate time regime.

Dynamics of phase separation in binary systems

Abstract The present understanding of the dynamics of phase separation in various binary systems is reviewed and discussed in order to find universal aspects, such as scaling properties of the structure function, the evolution power law of the length scale, and the asymptotic behaviour of the structure function for small and large wave vector and the kinetics of kinks, interfaces and patterns. Emphasis is placed on how the early linear theories of phase separation have been developed, through non-linear theory, to the scaling theories and how computer simulation and experimental observations have confirmed such ideas on historical grounds. The importance of the acquisition of information about the microscopic atomic viewpoint and the macroscopic motion of phase boundaries, clusters and interfaces is stressed in order to advance investigations on this subject in the future.

Scaling and mean-field-like behaviour in phase separation processes

Extensive Monte Carlo calculations are used to study the still not well understood process of phase separation in binary systems. The results show that for a separation dominated by long-wavelength fluctuations a mean-field description holds in certain concentration regions. This, however, is only true for short times after the system has been brought into a non-equilibrium state. A crucial parameter is the interaction range. It determines the region and the time where the mean field description is valid. At later times the structure factor exhibits dynamical scaling. Scaling is also investigated for the metastable states. The results are applicable to polymer blends with long chains or binary alloys with long-range forces.