Spinodal Region Research Articles

Phase transformations with stress generations in electrochemical reactions of electrodes: Mechanics-based multiscale model for combined-phase reactions

Phase transformations in most electrodes used for electrochemical energy storages follow the conserved dynamics of combined one- and two-phase reactions, which leads to complicated charge–discharge processes with various voltage plateaus; this could affect an electrochemical performance as a generic phenomenon in electrochemical system. In order to fully describe the combined-phase reactions from the atomic scale to the mesoscale, we propose a multiscale-based phase transformation model that also considers electrochemical states and mechanical deformations. This model predicts the miscibility gap, spinodal region, voltage profile, phase transformation, and stress generations of the combined-phase electrodes in the electrochemical reactions. We apply this multiscale model to high-rate cathode material LixFePO4 to fundamentally understand the experimental phase transformation behaviors (Yamada et al., 2006). This model is applicable to various electrodes for phase behaviors too complex to be detected experimentally due to combined-phase reactions.

Size effects of solvent molecules on the phase behavior and effective interaction of colloidal systems with the bridging attraction

There has been much recent research interest towards understanding the phase behavior of colloidal systems interacting with a bridging attraction, where the small solvent particles and large solute colloidal particles can be reversibly associated with each other. These systems show interesting phase behavior compared to the more widely studied depletion attraction systems. Here, we use Baxter’s two-component sticky hard sphere model with a Percus–Yevick closure to solve the Ornstein–Zernike equation and study the size effect on colloidal systems with bridging attractions. The spinodal decomposition regions, percolation transition boundaries and binodal regions are systematically investigated as a function of the relative size of the small solvent and large solute particles as well as the attraction strength between the small and large particles. In the phase space determined by the concentrations of small and large particles, the spinodal and binodal regions form isolated islands. The locations and shapes of the spinodal and binodal regions sensitively depend on the relative size of the small and large particles and the attraction strength between them. The percolation region shrinks by decreasing the size ratio, while the binodal region slightly expands with the decrease of the size ratio. Our results are very important in understanding the phase behavior for a bridging attraction colloidal system, a model system that provides insight into oppositely charged colloidal systems, protein phase behavior, and colloidal gelation mechanisms.

Nonequilibrium Dynamics and Phase Transitions in Holographic Models.

We study the poles of the retarded Green's functions of strongly coupled field theories exhibiting a variety of phase structures from a crossover up to a first order phase transition. These theories are modeled by a dual gravitational description. The poles of the holographic Green's functions appear at the frequencies of the quasinormal modes of the dual black hole background. We establish that near the transition, in all cases considered, the applicability of a hydrodynamic description breaks down already at lower momenta than in the conformal case. We establish the appearance of the spinodal region in the case of the first order phase transition at temperatures for which the speed of sound squared is negative. An estimate of the preferential scale attained by the unstable modes is also given. We additionally observe a novel diffusive regime for sound modes for a range of wavelengths.

Obtaining solid solutions of InGaAsPInGaAsP solid solutions in the spinoidal decomposition region

Technology for growing layers of InGaAsP solid solutions with Eg ∼⃒ 1.0 - 1.2eV on InP substrates in the spinodal decomposition region by the metalorganic vapour phase epitaxy (MOVPE) technique has been developed. Results of investigation of the obtained solid solution layers by the methods of photoluminescence, reflectance anisotropy spectroscopy and fractal analysis are presented.

Free surface liquid films of binary mixtures. Two-dimensional steady structures at off-critical compositions

We present steady non-linear solutions of films of confined polymer blends deposited on a solid substrate at off-critical concentrations with a free deformable surface. The solutions are obtained numerically using a variational form of the Cahn-Hilliard equation in the static limit, which allows for internal diffuse interfaces between the two components of the mixture. Existence of most of the branches of non-linear solutions at off-critical concentrations can be predicted from the knowledge of the branching points obtained with a linear stability analysis plus the non-linear solutions at critical concentrations. However, some families of solutions are found not to have correspondence at critical compositions. We take a value for surface tension that allows strong deformations at the sharp free upper surface. Varying the average composition and the length and thickness of the films we find a rich morphology of static films in the form of laterally structure films, layered films, droplets on the substrate, droplets at the free surface, and checkerboard structures. We show that laterally structured solutions are energetically favorable over homogeneous and other structured solutions within the whole spinodal region and even close to the absolute stability binodal boundary.

Investigation of spinodal decomposition of InGaAsP solid solutions grown by the MOCVD technique

Technology for growing layers of InGaAsP solid solutions with Eg ∼ 1.0 - 1.2 eV on InP substrates by the MOCVD technique in the spinodal decomposition region has been elaborated. Results of the investigation of solid solution layers by the methods of photoluminescence, reflectance anisotropy spectroscopy and fractal analysis are presented.

Phase behavior near and beyond the thermodynamic stability threshold.

The phase behavior of stabilized dispersions of macromolecules is most easily described in terms of the effective interaction between the centers of mass of solute particles. For molecules such as polymer chains, dendrimers, etc., the effective pair potential is finite at the origin, allowing "particles" to freely interpenetrate each other. Using a double-Gaussian model (DGM) for demonstration, we study the behavior of the system as a function of the attraction strength η. Above a critical strength η(c), the infinite-size system is Ruelle unstable, in that it collapses to a cluster of finite volume. As η(c) is approached from below, the liquid-vapor region exhibits an anomalous widening at low temperature, and the liquid density apparently diverges at the stability threshold. Above η(c), the thermodynamic plane is divided in two regions, differing in the value of the average waiting time for collapse, being finite and small on one side of the boundary line, while large or even infinite in the other region. Upon adding a small hard core to the DGM potential, stability is fully recovered and the boundary line is converted to the spinodal line of a transition between fluid phases. We argue that the destabilization of a colloidal dispersion, as induced by the addition of salt or other flocculant, finds a suggestive analogy in the process by which a strengthening of the attraction pushes a stabilized-DGM system inside the fluid-fluid spinodal region.

Non-equilibrium theory of arrested spinodal decomposition.

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ramŕez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.

Study of the submicron heterogeneity of aqueous solutions of hydrogen-bond acceptor molecules by laser diagnostics methods

Three independent experimental laser techniques (dynamic light scattering, nanoparticle tracking analysis, and laser phase microscopy) have been used to find and quantitatively characterize a lowconcentration domain of existence for the droplet-stratified phase in an aqueous solution of tetrahydrofurane (THF) molecules acting as hydrogen bond acceptors. The concentration and temperature dependences of the light scattering intensity and droplet sizes in the solution have been measured. It is shown that the nanodroplets found have a higher light refractive index than that of water and that they are highly enriched with THF molecules. An estimation of the volume number density of 300-nm droplets, based on the data obtained, yields a value on the order of 108 cm-3. The droplet lifetime is limited by the effect of the buoyancy force and amounts to several days. A crossover is found in the temperature dependence of scattering intensity in the droplet phase, which indicates possible interaction of two order parameters: the THF concentration and the number of hydrogen bonds of THF and H2O molecules. A model stochastic theory is proposed to describe the stratification of solutions with cross hydrogen bonds, which predicts stratification in the low-concentration range adjacent to the spinodal decay region.

Miscibility Gap in the Phase Diagrams of Thermoelectric Half-Heusler Materials CoTi $$_{1-x}Y_x$$ 1 - x Y x Sb (Y = Sc, V, Mn, Fe)

The half-Heusler system CoTi $${_{1-x}Y_x}$$ Sb (Y = Sc, V, Mn, Fe) has been investigated by means of an ab initio-based mean-field model which provides phase diagrams of alloys. Co(Ti,Y)Sb materials show a miscibility gap, which leads to spontaneous demixing within a spinodal region. The results are compared with experimental investigations of microstructure and transport properties of the alloys. The thermoelectric properties of the solid solution were investigated comprehensively by measuring the temperature dependence of the Seebeck coefficient as well as electrical and thermal conductivity. Compared with pure CoTiSb, the thermal conductivity of substituted CoTi $${_{0.9}Y_{0.1}}$$ Sb was significantly reduced by approximately 53% for Y = V. Here, we report on the effect of phase separation in the Co(Ti,Y)Sb system and its consequences for the thermoelectric figure or merit.

Growth of spinodal instabilities in nuclear matter. II. Asymmetric matter

As an extension of our previous work, the growth of density fluctuations in the spinodal region of charge asymmetric nuclear matter is investigated in the basis of the stochastic mean-field approach in the non-relativistic framework. A complete treatment of density correlation functions are presented by including collective modes and non-collective modes as well.

Ab initio study of domain structures in half-metallic CoTi1−xMnxSb and thermoelectric CoTi1−xScxSb half-Heusler alloys

We present first-principles calculations of the electronic density of state, the structures in CoTi1−xScxSb and CoTi1−xMnxSb. In addition for the latter we calculate magnetic moments. Systems with different stoichiometries are compared and low energy configurations are determined using a cluster expansion procedure. For all studied manganese concentrations, x>0, CoTi1−xMnxSb is half-metallic and magnetic, which make it interesting for spintronic applications. In contrast, with increasing scandium concentration, the band gap of CoTixSc1–xSb closes continuously, while the material changes from a semiconductor to a non-magnetic metal. For low Sc doping this material is well suited for thermoelectric applications. The electronic states close to the Fermi energy are strongly influenced by the distribution of Ti and Mn (or Ti and Sc). This has important consequences for the usage of materials in application fields like spintronics and thermoelectrics. In general, a phase separation of the alloys into a Ti rich and a Ti poor phase is energetically favored. Using mean field theory we create a phase diagram that shows the coexistence and the spinodal region. A spontaneous demixing can be used for the creation of nanodomains within the material. In the case of CoTi1−xScxSb, the resulting reduced lattice thermal conductivity is beneficial for thermoelectric applications, while in CoTi1−xMnxSb the nanodomains are detrimental for polarization.

Quasi-atomistic modeling of the microstructure evolution in binary alloys and its application to the FeCr case

In this work, we present a comprehensive quasi-atomistic Object Kinetic Monte Carlo (OKMC) model for diffusion-mediated decomposition in binary alloys, which is applied to the particular case of phase nucleation and spinodal decomposition in the iron–chromium system. The model describes atomistically the defects driving diffusion, while following the evolution of alloy concentrations by tracking the number of alloy atoms in the elements of an uniform mesh. Input parameters are defect diffusivities, tracer diffusivity ratios, and mixing energies, and they have been calibrated according to reported experiments and ab-initio calculations. Simulations based on this model are able to reproduce both phase nucleation in the metastable composition region and spontaneous phase decomposition and coarsening within the spinodal composition region. The convergence into the correct thermodynamics has been shown by comparing the simulation results to theoretical predictions, while the time evolution has been validated with experimental data for different alloy compositions. The simulation approach has proven to be suitable for extended annealing times and for domain sizes up to hundreds of nanometers.

Trapping citronellal in a microporous polyethylene matrix

The Flory–Huggins theory was used to model the phase behaviour of linear low density polyethylene–citronellal binary mixtures. The model parameters were obtained from fitting the bimodal phase envelope using data points from cloud point determinations. This allowed the prediction of the melting point depression curve as well as the location of the spinodal region. A microporous polyethylene matrix was obtained by quenching homogeneous liquid mixtures at temperatures well below the spinodal phase boundary. This strategy makes it possible to trap, and effectively solidify, large amounts of citronellal in a polyethylene (LLDPE) matrix. This has potential implications for the development of long-lasting insect repellent bracelets and anklets.

Phase Separations in Mixtures of a Flexible Polymer and a Cholesteric Liquid Crystal in the Presence of an External Field

We present a mean field theory to describe phase behaviors in mixtures of a flexible polymer and a cholesteric liquid crystal under an external magnetic or electric field. Taking into account a chiral coupling between liquid crystals under the external field, we examine twist-untwist phase transitions and phase separations in the mixtures. Depending on the strength of the external field, we predict cholesteric-paranematic (Ch + N), nematic-paranematic (N + pN), cholesteric-nematic (Ch + N) phase separations on the temperature-concentration plane. We also calculate spinodal regions, which are important in phase separation kinetics inside binodal lines.

Growth and characterization of III-N ternary thin films by plasma assisted atomic layer epitaxy at low temperatures

We report the growth and characterization of III-nitride ternary thin films (AlxGa1−xN, InxAl1−xN and InxGa1−xN) at ≤500°C by plasma assisted atomic layer epitaxy (PA-ALE) over a wide stoichiometric range including the range where phase separation has been an issue for films grown by molecular beam epitaxy and metal organic chemical vapor deposition. The composition of these ternaries was intentionally varied through alterations in the cycle ratios of the III-nitride binary layers (AlN, GaN, and InN). By this digital alloy growth method, we are able to grow III-nitride ternaries by PA-ALE over nearly the entire stoichiometry range including in the spinodal decomposition region (x=15–85%). These early efforts suggest great promise of PA-ALE at low temperatures for addressing miscibility gap challenges encountered with conventional growth methods and realizing high performance optoelectronic and electronic devices involving ternary/binary heterojunctions, which are not currently possible.

Photovoltaic converters of concentrated sunlight, based on InGaAsP(1.0 eV)/InP heterostructures

Results obtained in the development of a metal-organic vapor-phase epitaxy (MOVPE) technology and in studies of the electrical parameters of photovoltaic converters based on heterostructures in the InP/InGaAsP system for the spectral range 0.95–1.2 μm are presented. A MOVPE technique is developed for obtaining and doping InGaAsP solid solutions around the spinodal dissociation region with a band-gap width of about 1.0 eV. Photovoltaic converters of 1000-× concentrated sunlight are fabricated.

Registered and Antiregistered Phase Separation of Mixed Amphiphilic Bilayers

We derive a mean-field free energy for the phase behavior of coupled bilayer leaflets, which is implicated in cellular processes and important to the design of artificial membranes. Our model accounts for amphiphile-level structural features, particularly hydrophobic mismatch, which promotes antiregistration, in competition with the direct transmidplane coupling usually studied, which promotes registration. We show that the phase diagram of coupled leaflets allows multiple metastable coexistences, and we illustrate the kinetic implications of this with a detailed study of a bilayer of equimolar overall composition. For approximate parameters estimated to apply to phospholipids, equilibrium coexistence is typically registered, but metastable antiregistered phases can be kinetically favored by hydrophobic mismatch. Thus, a bilayer in the spinodal region can require nucleation to equilibrate, in a novel manifestation of Ostwald’s rule of stages. Our results provide a framework for understanding disparate existing observations in the literature, elucidating a subtle competition of couplings and a key role for phase-transition kinetics in bilayer phase behavior.

From the depletion attraction to the bridging attraction: the effect of solvent molecules on the effective colloidal interactions.

Depletion attraction induced by non-adsorbing polymers or small particles in colloidal solutions has been widely used as a model colloidal interaction to understand aggregation behavior and phase diagrams, such as glass transitions and gelation. However, much less attention has been paid to study the effective colloidal interaction when small particles/molecules can be reversibly attracted to large colloidal particles. At the strong attraction limit, small particles can introduce bridging attraction as it can simultaneously attach to neighbouring large colloidal particles. We use Baxter's multi-component method for sticky hard sphere systems with the Percus-Yevick approximation to study the bridging attraction and its consequence to phase diagrams, which are controlled by the concentration of small particles and their interaction with large particles. When the concentration of small particles is very low, the bridging attraction strength increases very fast with the increase of small particle concentration. The attraction strength eventually reaches a maximum bridging attraction (MBA). Adding more small particles after the MBA concentration keeps decreasing the attraction strength until reaching a concentration above which the net effect of small particles only introduces an effective repulsion between large colloidal particles. These behaviors are qualitatively different from the concentration dependence of the depletion attraction on small particles and make phase diagrams very rich for bridging attraction systems. We calculate the spinodal and binodal regions, the percolation lines, the MBA lines, and the equivalent hard sphere interaction line for bridging attraction systems and have proposed a simple analytic solution to calculate the effective attraction strength using the concentrations of large and small particles. Our theoretical results are found to be consistent with experimental results reported recently.

Growth of spinodal instabilities in nuclear matter

Early growth of density fluctuations of nuclear matter in spinodal region is investigated employing the stochastic mean-field approach. In contrast to the earlier treatments in which only collective modes were included in the calculations, in the present work non-collective modes are also included, thus providing a complete treatment of the density correlation functions. Calculations are carried out for symmetric matter in non-relativistic framework using a semi-classical approximation.