Binodal Decomposition Research Articles

Theoretical formulation of the distribution function of critical nuclei under precipitation polymerization conditions

Precipitation Polymerization (Pre-Poly) can be considered a nucleation and growth process in which complex and high molecular weight branched polymers are involved. From an experimental point of view, it is well-known that under Pre-Poly conditions the phase transition (nucleation) occurs in the first minutes of polymerization, and then a long growth stage is observed in which the critical nuclei simultaneously grow until reaching a highly monodisperse distribution of microspheres (characteristic mechanism of binodal decomposition). The high rate at which nucleation and growth processes usually take place when radical polymerization (extremely high polymerization rate) under Pre-Poly conditions is used, makes it very difficult to study experimentally some aspects of these processes, such as the size and concentration of critical nuclei, among others. Based on the thermodynamic principles of Pre-Poly, this analytical paper covers for the first time, to the best of our knowledge, the theoretical formulation of the distribution function of critical nuclei under Pre-Poly conditions. In addition, a simple empirical method to calculate the concentration of critical nuclei was also developed using only three global, physical experimental parameters, and good agreement was found between empirical and theoretical calculations.

Short-range positional order in phase separated indium gallium oxide islands deposited in a reducing atmosphere

We report a spontaneous phase separation in indium gallium oxide thin films with a nominal composition of (In0.006Ga0.994)2O3 grown on sapphire (0001) substrates using a powder sputtering method in a reducing atmosphere. The In-rich (In0.24Ga0.76)2O3-x domains are non-stoichiometric and located underneath the surface islands, whereas the In-poor domains are nearly stoichiometric Ga2O3, forming a continuous flat surface, though both domains have a monoclinic crystal structure. Furthermore, the In-rich domains exhibit a short-range positional order with a correlation length of approximately 1 μm because the phase separation occurs along the binodal decomposition accompanying periodic concentration profiling of In atoms. The analysis of X-ray photoelectron spectroscopy confirmed that the non-stoichiometry of the thin films originated from the formation of Ga sub-oxide (Ga2O) and metallic Ga, whereas the chemical state of the In atoms was close to In2O3 rather than metallic In. Our results indicate that the spontaneous phase separation occurs in (InxGa1-x)2O3 thin films even at an In content of 0.6 at%. Also, the non-stoichiometry associated with oxygen vacancies is an important parameter for causing spontaneous phase separation via the segregation of In atoms.

The dynamics of single-to-multi layer transition in bacterial swarms

Wet self-propelled rods at high densities can exhibit a state of mesoscale turbulence: a disordered lattice of vortices with chaotic dynamics and a characteristic length scale. Such a state is commonly studied by a two-dimensional continuum model. However, less is known about the dynamic behaviour of self-propelled rods in three- or quasi-two- dimensions, which can be found in biological systems, for example, during the formation of bacterial aggregates and biofilms. In this study, we characterised the formation of multi-layered islands in a monolayer of swarming cells using the rod-shaped bacteria B. subtilis as a model system. We focused on how bacteria form multiple layers and how the presence of stress affects the multiple layer formation. Following our previous study where we reported that the initiation of the multilayer formation can be accounted by the framework of motility-induced phase separation (MIPS), this study analysed how this phase separation is impacted by the presence of stress, specifically under the exposure to a gradient of antibiotic. The analyses show that in the presence of an antibiotic gradient, the multi-layer formation happens by a nucleation and growth of well-defined multilayered clusters instead of by the uncontrolled emergence of the multilayer, resembling the traditional thermodynamic processes of binodal and spinodal decomposition respectively. Finally, the multilayer gives place to waves of bacteria that can travel towards high concentrations of antibiotics and that resemble travelling waves predicted by simulations of mixtures of passive and active particles.

Biased-angle effect on diffusion dynamics and phase separation in anisotropic active particle system.

A deep understanding for collective behavior in an active matter system with complex interactions has far-reaching impact in biology. In the present work, we adopt Langevin dynamics simulations to investigate diffusion dynamics and phase separation in an anisotropic active particle system with a tunable biased angle α defined as the deviation between the active force direction and anisotropic orientation. Our results demonstrate that the biased angle can induce super-rotational diffusion dynamics characterized by a power-law relationship between the mean square angle displacement (MSAD) and the time interval Δt in the form of MSAD ∼ Δtβ with β > 1 and also result in non-trivial phase separation kinetics. As activity is dominant, nucleation time shows a non-monotonic dependence on the biased angle. Moreover, there arises a distinct transition of phase separation, from spinodal decomposition without apparent nucleation time to binodal decomposition with prominent nucleation delay. A significant inhibition effect occurs at right and obtuse angles, where the remarkable super-rotational diffusion prevents particle aggregation, leading to a slow nucleation process. As active force is competitive to anisotropic interactions, the system is almost homogeneous, while, intriguingly, we observe a re-entrant phase separation as a small acute angle is introduced. The prominent super-rotational diffusion under small angles provides an optimum condition for particle adsorption and cluster growth and, thus, accounts for the re-entrance of phase separation. A consistent scenario for the physical mechanism of our observations is achieved by properly considering the modulation of the biased angle on the interplay between activity and anisotropic interactions.

Fabrication of Al-Bi frozen emulsion alloys due to high-intense ultrasound irradiation

The aim of this study is to develop an ultrasound-assisted process for fabrication of frozen emulsion alloys, which are a type of miscibility gap alloys (MGAs). Al-Bi system was used to produce 2-kg ingots of Al-Bi frozen emulsion alloys in the following two steps: (1) emulsification treatment of Al-Bi melt by introducing high-intense ultrasound vibrations into it in a temperature range of Al-Bi binodal decomposition, and (2) casting of the melt into a book mold. The ingot samples were analyzed with SEM/EDX for the alloy microstructure and bismuth particle distribution. Besides, cold model experiments, thermodynamic and CFD numerical simulations were performed to elucidate the underlying mechanisms of emulsification including droplet fragmentation and acoustic streaming.The results reveal that the alloys with Bi concentration of 4%~9.4% can be fabricated by the proposed technique. Within this range, 90% of Bi particles have a diameter under 10 µm, and the majority of them are incorporated into aluminum grains. Especially, a uniform microstructure is obtained when concentration of Bi is less than 6%. Emulsification was found to occur at the interface between two liquids when cavitation bubbles collapse in the interface vicinity followed by high-velocity micro-jetting which is responsible for the emulsion droplet formation. Another positive effect of ultrasound is acoustic streaming which is responsible for the effective agitation of molten bath preventing the sedimentation of Bi droplets during the ultrasound treatment and casting operation.

Morphological evaluation and phase behavior of PVDF/PEO blends in the presence of graphene nanoplatelets through rheological measurements

ABSTRACTIn this study, graphene nanoplatelets (GNPs) were incorporated into poly(vinylidene fluoride) (PVDF), poly(ethylene oxide) (PEO), and PVDF/PEO blends using solution casting method in order to achieve binary and ternary polymer nanocomposites. The focus of the work is on the compatibilizing effects of the GNPs on partially miscible PVDF/PEO blends. X‐ray diffraction method, rheological measurements, scanning electron microscopy (SEM), and atomic force microscopy observations enabled us to track the dispersion state and localization of the graphene nanosheets in the nanocomposites. The results exhibited that the nanoplatelets were preferentially distributed through the PVDF phase and/or at the interface of the PVDF/PEO phases. Evaluation of the wetting parameter for the PVDF/PEO/GNPs nanocomposite also verified better affinity of the selected nanofiller with the PVDF component. Extend of the miscibility in the nanocomposites was studied by a well‐known rheological method. A tangible increment in binodal (Tb) and spinodal (Ts) decomposition temperatures by addition of a very low content of the GNPs (0.5 wt %) revealed well‐defined compatibilization effects of the graphene on this binary polymer blend. SEM images at different temperatures confirmed the rheologically determined liquid–liquid phase diagram. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 48017.

Robust, ultra-insulative and transparent polyethylene-based hybrid silica aerogel with a novel non-particulate structure

Aerogels derived from pre-polymerized vinyl trimethoxy silane (VTMS) precursor with nano-size particles are known to exhibit outstanding mechanical and insulation properties. However, the density reduction has been limited by the poor connectivity. This paper presents an innovative technology to generate a new class of VTMS-based hybrid silica aerogels that possess outstanding non-particulate, reticulated structure and superior properties. This technology relies on spinodal decomposition instead of conventionally exploited binodal decomposition, which leads to a particulate structure. This new aerogel technology has significantly increased the void fraction of the pre-polymerized VTMS-based aerogel, which could not be achieved previously using binodal decomposition. The increased void fraction in the form of nano-pores with an average pore size of 21.75 nm nullifies the gas thermal conductivity effectively. Another consequence of the non-particulate structure is decreased processing time by removing the aging step. These improvements are due to the non-particulate structure’s increased connectivity produced by spinodal decomposition. This novel structure was then compared to a particulate counterpart aerogel of the same material derived from the conventional binodal decomposition of the pre-polymerized VTMS precursor. To further decrease the processing cost, a lower molecular-weight polymeric precursor was synthesized under milder polymerization conditions. The effects of the polymeric precursor’s molecular weight on the mechanical and thermal properties of the aerogel created via spinodal decomposition were also investigated.

Theoretical characterization of C doped SiGe monolayer

Two dimensional Si1−xGeCx (SGC) alloys have been investigated within the framework of density functional theory using the hybrid functional of Heyd-Scuseria-Ernzerhof for the electron exchange correlation potential. The site occupancy disorder program is used to predict the most stable configuration for different values of carbon (C) concentration (x). With increasing C content, the lattice constant decreases almost linearly, while there is a reversal in the bandgap bowing for x>0.50. Besides the ideal solid solutions, we have also studied the effect of the C dimer. The calculated mixing enthalpy suggests that the growth of the alloys follows the endothermic reaction. The spinodal and binodal decomposition curves for Si and C rich phases have been explained along with a growth temperature equal to 2675 K. The valence and conduction band edges are aligned with respect to the vacuum level. The calculated optical absorption coefficient of SGC alloys is greater than 104cm−1, suggesting that these alloys are promising materials for opto-electronic applications. Our results may motivate experimentalists to synthesize these alloys which show promise for efficient thin film devices.

Thermodynamic assessment of Fe–Ti–S ternary phase diagram

A thermodynamic analysis of the Fe-Ti-S ternary system was performed by incorporating first-principles calculations into the calculation of phase diagrams (CALPHAD) method. To evaluate the Gibbs energy, the Debye-Grüneisen model was applied for some sulfides of the Ti-S binary system. In addition, the cluster expansion and cluster variation methods were used for the solid solution phases in the Ti-S binary and (Fe,Ti)S phases. The calculated Ti-S binary phase diagram showed good agreement with the experimental results. The very low solubility of the Ti solid solution in the Ti-S system, as reported by Murray, agreed well with our calculated results. A binodal phase decomposition of the liquid phase was expected in the S-rich region. The Gibbs energy curve of (Fe,Ti)S between FeS and TiS was found to be convex downward. This is characteristic of an isomorphic solid solution, attributed to the attractive interaction between Fe and Ti in (Fe,Ti)S. The vertical phase diagram between FeS and TiS, obtained using the thermodynamic database, was in good agreement with the experimental results of Mitsui et al. The solubility products of (Fe,Ti)S have been experimentally estimated previously. The calculated solubility product agreed with the experimental value of TiS.

Conjugated dual-phase transitions in crystalline/crystalline blend of poly(vinylidene fluoride)/poly(ethylene oxide)

Blends of two semi-crystalline polymers, poly(vinylidene fluoride) (PVDF) and poly(ethylene oxide) (PEO), were prepared via solution mixing method over the whole composition range. The research focuses on the liquid–liquid phase separation (LLPS) and miscibility window in the PVDF/PEO blends by employing several techniques. Small-amplitude oscillatory shear measurements were carried out to detect LLPS and determine spinodal and binodal decomposition temperatures in its early stages. An asymmetrical lower critical solution temperature (LCST) phase diagram was observed from dynamic temperature sweep experiments in which the system became immiscible after the solid–liquid phase transition (SLPS) temperatures in the PEO-rich blends. In fact, a one-way partial miscibility of PEO in the PVDF-rich phase blends was observed. The rheologically determined phase diagram was also verified by means of optical microscopy and cloud point technique. The results revealed that the PVDF/PEO blends undergo a viscoelastic phase separation (VPS). This was attributed to the large viscoelastic asymmetry of the components in the blend. A compressible regular solution free energy model was employed to determine the spinodal temperatures theoretically. The comparison between the experimental results and the mathematical modeling indicated that the model is able to predict the phase behavior qualitatively.

High temperature phase decomposition in TixZryAlzN

Through a combination of theoretical and experimental observations we study the high temperature decomposition behavior of c-(TixZryAlzN) alloys. We show that for most concentrations the high formation energy of (ZrAl)N causes a strong tendency for spinodal decomposition between ZrN and AlN while other decompositions tendencies are suppressed. In addition we observe that entropic effects due to configurational disorder favor a formation of a stable Zr-rich (TiZr)N phase with increasing temperature. Our calculations also predict that at high temperatures a Zr rich (TiZrAl)N disordered phase should become more resistant against the spinodal decomposition despite its high and positive formation energy due to the specific topology of the free energy surface at the relevant concentrations. Our experimental observations confirm this prediction by showing strong tendency towards decomposition in a Zr-poor sample while a Zr-rich alloy shows a greatly reduced decomposition rate, which is mostly attributable to binodal decomposition processes. This result highlights the importance of considering the second derivative of the free energy, in addition to its absolute value in predicting decomposition trends of thermodynamically unstable alloys.

Evolution of the heterogeneous structure of model sodium silicate glasses during binodal decomposition: X-ray small-angle scattering investigation

The kinetics of binodal decomposition in model glasses of the Na2O-SiO2 system from the initial stage to the stage of the Ostwald ripening inclusive has been investigated in situ. It has been found that the spatial-temporal evolution of the heterogeneous structure during binodal decomposition has a multistage character. The characteristic size of the phase regions at each stage of the binodal decomposition varies with time according to the power law L ∼ tβ. The values of exponents β for different stages of the binodal decomposition are as follows: 1/20 (fluctuation stage), 1/2 (growth stage), 0 (transient stage), and 1/3 (Ostwald ripening stage). The particle size distributions for all stages of the binodal decomposition have been presented.

Colour and multicolour tuning of InGaN quantum dot based light-emitting diodes

InGaN quantum dots (QDs) formed via spinodal and binodal decomposition are used as an optically active region for light-emitting diodes (LEDs). It is shown that the emission wavelength of the electroluminescence (EL) can be shifted from blue to green by adjusting the deposition time of the InGaN QD layer. A first approach towards a monolithic multicolour emitting diode is presented. Strong difference of the EL on the InGaN QD stacking sequence is observed and is attributed to both low hole concentration and mobility.

Hierarchical sol–gel derived porous titania/carbon nanotube films prepared by controlled phase separation

Titania/carbon nanotube (CNT) composite films containing hierarchical interconnected porous structure have the advantages of high surface area of mesoporous structure and micro-channels of titania as well as high conductivity and charge separation properties of CNTs. In this research, the composites were prepared with controlled phase separation of titania sol. The main parameters to control the phase separation and macroporous morphology of the films including water content, stabilizer content, polyethylene glycol content, sol concentration, and deposition speed were investigated. X-ray diffraction and Raman spectroscopy confirmed the presence of CNTs together with anatase titania phase. Transmission electron microscopy showed that a very thin layer of titania was formed on CNT surface which improved interface of TiO2/CNT. It was found that macropores grew either with increasing water or polyethylene glycol content. However, stabilizer content and deposition speed had an inverse effect on macropores formation. Furthermore, sol concentration caused binodal decomposition and hence widened the pore size distribution. Although CNTs were ineffective in macropores formation, they strongly affected the transparency and charge separation of the composite films.

Determination of Phase Behavior of Poly(ethylene oxide) and Chitosan Solution Blends Using Rheometry

Aqueous solutions of PEO exhibit a lower critical solution temperature (LCST) phase diagram. In this work, phase separation behavior of PEO/water solutions was investigated using small-amplitude oscillatory shear and steady shear rheological measurements. Binodal decomposition temperatures were determined from the sudden changes in the slope of the dynamic temperature sweep of storage modulus and loss tangent. The spinodal decomposition points were also estimated by a mean-field theoretical approach. Comparing the obtained critical points with other conventional methods revealed that rheological measurements are powerful and sensitive to detect even the early stage of phase separation of PEO solutions. This successful method was employed to investigate phase separation and miscibility of chitosan/PEO solutions at different compositions in aqueous acetic acid solutions that have already showed anomalous behavior in a forming process. Lower critical solution temperature (LCST) phase behavior was observed for chitosan/PEO solution blends. Phase separation temperature, miscibility range, and correlation length of the solutions were determined from isochronal dynamic temperature sweep experiments. The effect of chitosan/PEO ratio on the binodal and spinodal decomposition temperatures was studied. Finding phase separation information on polymer solutions through rheological measurement is very promising. Isothermal steady shear rheological measurements were also carried out on chitosan/PEO solutions over a temperature range in which phase separation occurs. Viscosity increase at low shear rates above but in the vicinity of phase separation temperature was observed, which confirms the validity of the theoretical approach employed to determine the critical temperatures through dynamic rheological measurements. Finally, the Flory–Huggins interaction parameters were estimated from critical solution temperature and concentration results.

Strong phase separation of strained InxGa1−xN layers due to spinodal and binodal decomposition: Formation of stable quantum dots

InGaN quantum dots were grown by metal-organic vapor phase epitaxy using a phase-separation process based on spinodal and binodal decomposition. Uncapped structures were grown which show InGaN phases with two different In contents on the surface. The high-In-content phase accumulates to huge islands while the low-In content phase forms flat meander and quantum-dot-like structures on the surface. The dissolution of the high-In-containing phase is very sensitive to the growth temperature of the GaN capping while there is no significant change of the InGaN quantum dot structures. The samples were investigated with transmission and scanning electron microscopy, photoluminescence measurements, and x-ray diffraction. A narrow growth window concerning the InxGa1−xN composition was found in which the formation of quantum dots takes place. This growth window is in good agreement with the InGaN miscibility gap calculated for a strained InGaN layer. A detailed theoretical discussion is presented and the quantum dot and island formation will be explained by a strain-modified spinodal and binodal decomposition model.

Density-functional study of U–Mo and U–Zr alloys

The ground-state properties of U–Mo solid solutions are studied by density functional theory and compared to the similar U–Zr system. We discuss how the heat of formation in both alloys correlates with the charge transfer between the alloy components, and how the specific behavior of the density of states in the vicinity of the Fermi level promotes the stabilization of the U 2Mo compound. Our calculations suggest that, due to the existence of a single γ-phase over the typical fuel operation temperatures, γ-U–Mo alloys should indeed have much lower constituent redistribution than γ-U–Zr alloys for which binodal decomposition causes a high degree of constituent redistribution.

Biaxial strain-induced suppression of spinodal decomposition in GaMnAs and GaCrAs

The thermodynamic properties of the magnetic semiconductors GaMnAs and GaCrAs are studied under biaxial strain. The calculations are based on the projector augmented wave method combined with the generalized quasichemical approach to treat the disorder and composition effects. Considering the influence of biaxial strain, we find a tendency to the suppression of binodal decomposition mainly for GaMnAs under compressive strain. For a substrate with a lattice constant 5% smaller than the one of GaAs, for GaMnAs, the solubility limit increases up to 40%. Thus, the strain can be a useful tool for tailoring magnetic semiconductors to the formation or not of embedded nanoclusters.

Fabrication of Nanostructured Poly(3-thiophene methyl acetate) within Poly(vinylidene fluoride) Matrix: New Physical and Conducting Properties

Nanostructured poly(3-thiophene methyl acetate) (PTMA) within the poly(vinylidene fluoride) (PVDF) matrix is achieved by reactive blending technique under melt-cooled condition. The nanoparticles are almost spherical showing a minimum size with 5% (w/w) PTMA concentration (PTMA5), and they become agglomerated at > or = 25% (w/w) PTMA concentration. Different phase separation mechanisms are used to explain the above variation of nanoparticle size. The lower size nanophase in the PTMA5 blend is attributed to spinodal decomposition, while the larger size nanophases are produced from binodal decomposition. The TGA study indicates increasing thermal stability of PVDF in the nanoblends. DSC study shows increasing melting and crystallization temperature of the nanoblends; the former is due to the attractive forces of PTMA nanostructure, and the latter is for the nucleating effect of nanophase PTMA. The long distance, lamellar distance, and amorphous overlayer distance decrease to different extents. The pi-pi* transition band of UV-vis spectra shows a red shift with increasing PTMA concentration, but the photoluminescence spectra of the nanoblends show a blue shift. The former is attributed to intrachain aggregation of PTMA, while the latter is caused from "static excimer" formation at the ground state. PTMA1 and PTMA3 show approximately 8 times increase in PL intensity except PTMA5 where interconnectivity between the nanodomains makes the nonradiative decay similar to bulk PTMA. The temperature variation of conductivity indicates a conformational transition of PTMA chain with increasing temperature facilitating better charge transport. The I-V characteristic curves are really interesting; the nanoblends show a negative hysterisis, but PTMA5 shows a memory effect attributed to the electrical bistability originated from the interconnected nanophases arising from spinodal decomposition.

First Principle Study of Spinodal Decomposition Thermodynamics in Half-Heusler Alloy CoTi1−x Fe x Sb

A possibility of half-metallic ferromagnetism for the homogeneous phase in the half-Heusler alloy-based DMS CoTi1−xFexSb is predicted. A phase diagram of the spinodal and binodal decomposition is constructed through the evaluation of the mixing free energies. By applying the Monte Carlo simulation method to the Ising model with realistic chemical pair interactions between Fe magnetic impurities, we simulate the spinodal decomposition and nanoscale separation in this alloy.