Spinodal Decomposition In Systems Research Articles

Dissipative spinodal decomposition in systems with nonreciprocal effective interactions

Reciprocity of action and reaction, well known as the third Newtons law, can be violated in open complex systems of different nature. We analyze the dynamic behavior of the binary system with variable nonreciprocal interactions. We demonstrate that the resulting state in these systems is determined by interplay between dissipation and energy release (due to the interaction nonreciprocity), allowing bi-stability and corresponding dissipative phase transitions. The results of the Article shed light to a role of interactions nonreciprocity, intrinsic for different classes of open dynamical systems, from chemical physics and materials science to multi-agent systems and financial markets.

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.

Spinodal decomposition in systems with initially quenched fluctuations of the order parameter

Early time kinetics of a system with conserved order parameter quenched into unstable two-phase region of the phase diagram is considered. We study the influence of random inhomogeneities of the order parameter distribution, present already in the system before the quench, on the process of phase separation. The combined effect of this quenched fluctuations and persistent thermal fluctuations on the structure factor is discussed. For large-scale inhomogeneities even for small times the maximum instability of Cahn–Hilliard type shifts to the larger wavelengths. This may be interpreted as a start of coarsening.

Freezing of spinodal decomposition by irreversible chemical growth reactions

We present a description of the freezing of spinodal decomposition in systems, which contain simultaneous irreversible chemical reactions, in the hydrodynamic limit approximation. From own results we conclude, that the chemical reaction leads to an onset of spinodal decomposition also in the case of an initial system which is completely miscible and can lead to an extreme retardation of the dynamics of the spinodal decomposition, with the probability of a general freezing of this process, which can be experimetally observed in simultaneous IPN formation.

Spinodal decomposition in systems containing surfactant molecules

The spinodal decomposition is studied, by using light scattering, in two critical systems containing surfactant molecules. Time evolution of the characteristic wave vector and the intensity distributions are discussed. The data obtained agree with the findings of recent Molecular Dynamic simulations carried out in analogous systems. A comparison with MD data gives indication that in the two systems studied the phase separation process occurs through the formation of different structural coalescing domains. Whereas in a AOT microemulsion system the separation occurs through the formation of irregular bicontinuous-like domains, in a micellar mixture the separation is dominated by micellar domains which depend by thermal fluctuations.

A light scattering study of spinodal decomposition in systems containing surfactant molecules

We have performed a series of spinodal decomposition measurements on two critical systems containing surfactant molecules, i.e. (i) a three-component microemulsion made up of a surfactant (aerosol-OT), water and decane, and (ii) a water - butoxyethanol micellar-like mixture. The measurements were performed, via a temperature jump crossing the coexistence line along the critical isovolume fraction line, using the time-resolved light scattering intensity technique. All of the three stages of the evolution were studied. The time evolution of intensities for the initial stage closely follows the linearized theory. The time evolution of the characteristic wavevector, the maximum scattered intensity, and the intensity distribution in the intermediate and late stages are discussed in the framework of dynamical scaling theories and compared with the findings of recent molecular dynamics simulations. Such a comparison of the data obtained with the numerical analysis carried out for binary mixtures containing surfactant gives a clear indication that in the systems investigated the phase-separation process occurs through the formation of different structural coalescing domains. Whereas in the AOT microemulsion system the separation occurs through the formation of irregular bicontinuous-like domains, in the water - mixture the separation is dominated by a process of formation of micellar domains. In addition, in the latter case thermal fluctuation processes have a significant effect on the coarsening of the domain structures.

Theory of spinodal decomposition.

The general evolution equation describing spinodal decomposition in systems with conserved or nonconserved order parameter is developed. It is shown that if in the system thermodynamic potential expression the coefficients at order parameter square and at order parameter gradient square can change sign near the spinodal point, some different decomposition scenarios are possible, which result in system transformation from disordered to ordered, modulated, patterned, or ordered-patterned states.

Nonlinear Theory of Sound Waves near Critical Points. II: -- Periodic Spinodal Decomposition in Systems with Nonconserved Order Parameter --

Nonlinear Theory of Sound Waves near Critical Points. II: -- Periodic Spinodal Decomposition in Systems with Nonconserved Order Parameter --

Coherency strains in the elastic free energy

A semi-discrete model for the elastic free energy of systems with coherent composition fluctuation has been developed. It applies to systems of orthorhombic and higher symmetry. The treatment is carried through the continuous theory of elasticity and hence involves the elastic constants which makes it readily applicable to any system. Moreover, the distortions may assume isotropic as well as anisotropic form in this model. The total strain may be isotropic but the (stress-free) coherency strain and subsequently the elastic strain tensors will in general be anisotropic. This results in the anisotropic kinetics of the mechanism of the spinodal decomposition. This treatment can be applied to study strain-dependent physical properties through a Green's function method and the mathematical formalism presented here. It is currently being applied to study the effect of the coherency strains on the structure of compositionally modulated systems of various symmetries. Calculations of the biaxial elastic modulus of these modulated systems as well as application of the present development to spinodal decomposition in systems with orthorhombic, tetragonal and hexagonal symmetry will be presented in a future report.

Spinodal decomposition in the tetragonal system

The method of Cahn has been used to study spinodal decomposition in systems with tetragonal symmetry. The gradient energy and diffusion mobility in tetragonal systems have been considered in addition to the elastic free energy, previously treated by Stubican, Schultz, and Bitler. The results have been applied to the system TiO2–SnO2. In this system the theory predicts that spinodal decomposition will take place along the [001] direction, the additional anisotropies considered in this paper reinforcing the effects treated by Stubican, Schultz, and Bitler.