Spinodal Wave Research Articles

Symmetry constraints during the development of anisotropic spinodal patterns.

Spinodal decomposition is a phase-separation phenomenon occurring at non-equilibrium conditions. In isotropic materials, it is expected to improve the physical properties, in which modulated structures arise from a single system of spinodal waves. However, in anisotropic materials this process is controversial and not very well understood. Here, we report anisotropic spinodal decomposition patterns in single crystals of K-rich feldspar with macroscopic monoclinic 2/m symmetry. The periodicity of the spinodal waves at ~450 nm produces a blue iridescence, typical of the gemstone moonstone. Stripe patterns in the (010) plane, labyrinthine patterns in the (100) plane, and coexistence of the two patterns in the (110) plane are first resolved by scanning Rayleigh scattering microscopy. Two orthogonal systems of spinodal waves with the same periodicity are derived from the features and orientations of the patterns on the crystal surfaces. The orthogonality of the waves is related to the perpendicularity of the binary axis and the mirror plane. Thus, the spinodal patterns must be controlled by symmetry constraints during phase separation at early stages. Unusual and new properties could be developed in other anisotropic materials by thermal treatment inducing two orthogonal systems of periodic spinodal waves.

A computational study of long range surface-directed phase separation in polymer blends under a temperature gradient

The surface-directed phase separation phenomena of a model binary polymer blend quenched into the unstable region of its binary symmetric phase diagram was studied numerically using the nonlinear Cahn–Hilliard theory coupled with the Flory–Huggins–de-Gennes theory. Long range surface potential within a square geometry, where one side of the domain is exposed to a surface with preferential attraction to one component of a binary polymer blend under a temperature gradient in the x-direction, was incorporated in the model. No transition from complete wetting to partial wetting for all quench depths and/or long range surface potentials was observed. The structure factor analysis for the bulk presented an exponential growth rate at the early stage of phase separation, which slowed down at the intermediate stage with a slope of 0.33, which is in agreement with the Lifshitz–Slyozov power law. As the diffusion coefficient increased, the rate of phase separation increased accordingly in the bulk. This led to faster transition time from the early to intermediate stage within the bulk. In deeper quenches, a higher rate of phase separation was observed along with lower surface enrichment. Deeper quenches also led to the faster rupture of spinodal waves in the bulk. The process of surface enrichment, however, was continuous for all quench depths studied. The effect of different temperature gradient values on the surface enrichment rate was studied for the first time within a long range surface potential setting. No noticeable change in surface enrichment was observed for different temperature gradients.

A computational study of short-range surface-directed phase separation in polymer blends under a linear temperature gradient

The nonlinear Cahn–Hilliard theory and the Flory-Huggins-de-Gennes theory were used to study numerically the surface-directed phase separation phenomena of a model binary polymer blend quenched into the unstable region of its binary symmetric upper critical solution temperature phase diagram. Short-range surface potential within a square geometry, where one side of the binary polymer blend is exposed to a surface with preferential attraction to one component of the blend that is under a linear temperature gradient along the direction perpendicular to the surface, was integrated into the model. The structure factor analysis showed a faster exponential growth at the early stage of phase separation and a slower growth rate at the intermediate stage with a slope of 0.31 within the bulk, which is consistent with the Lifshitz–Slyozov growth law. The investigation of surface enrichment rate at the surface wall demonstrated faster growth rate at the early stage with the slope of 0.5. This growth rate became slower at the intermediate stage with a slope of 0.13 near the surface. The effect of various temperature gradient values on the surface enrichment rate with constant temperature T1* at the surface preferentially attracting one of the polymer components and different temperature T2* at the opposite surface, where T1*>T2*, was studied for the first time. The results showed that the thickness of the wetting layer increased with increasing temperature difference ΔT*, where ΔT*=T1*−T2*. The structure factor analysis of the surface potential h1 effect on the phase separation within the bulk close to the surface showed earlier transition time for higher values of h1. However, there was no difference observed for transition time within the bulk at distances farther away from the surface. As the surface potential increased, spinodal wave became more visible in the bulk and the transition time from complete wetting to partial wetting occurred at a later time on the surface.

Archimedean solidlike superconducting framework in phase-separatedK0.8Fe1.6+xSe2(0≤x≤0.15)

The superconducting (SC) phase in phase-separated (PS) ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6+x}\mathrm{S}{\mathrm{e}}_{2}\phantom{\rule{0.16em}{0ex}}(0\ensuremath{\le}x\ensuremath{\le}0.15)$ materials is found to crystallize on Archimedean solidlike frameworks, and this structural feature originates from a spinodal phase separation (SPS) at around ${T}_{s}\ensuremath{\approx}540\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, depending slightly on the Fe concentration, as revealed by in situ heating TEM observations and shown in a phase diagram. Two stable phases in ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6+x}\mathrm{S}{\mathrm{e}}_{2}$ are demonstrated to be the SC ${\mathrm{K}}_{0.5}\mathrm{F}{\mathrm{e}}_{2}\mathrm{S}{\mathrm{e}}_{2}$ and antiferromagnetic (AFM) ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6}\mathrm{S}{\mathrm{e}}_{2}$. The spinodal waves go along the systematic $[113]$ direction and result in notable lamellar structure as illustrated by strain-field theoretical simulations. The three-dimensional SC framework is constructed with hollow truncated octahedron similar to that discussed for Archimedean solids. Based on this structural model, we can efficiently calculate the volume fraction of the SC phase in this type of PS SC material.

What determines the critical size for phase separation in LiFePO4 in lithium ion batteries?

LiFePO4 characteristically shows a plateau voltage due to a two-phase (LiFePO4/FePO4) separation during the charge/discharge process in Li ion batteries. In this study, we clearly show that monodispersed nano-sized (about 10 nm) LiFePO4 particles exhibit a complete single-phase reaction without showing any plateau voltage. Since the elastic strain due to lattice mismatch between LiFePO4 and FePO4 would be easily released near the surface, elastic effects are usually expected to weaken, but, in contrast to this expectation, phase separation does not occur experimentally in such small nanoparticles. Consideration on the basis of only static thermodynamics is insufficient to explain why such a single-phase reaction occurs in nano-sized particles. In contrast, the mechanism of the single-phase reaction can be naturally understood, when we consider a kinetics concept based on the preferred wavelength for stable growth of the spinodal wave under such an elastic constraint.

Dynamic Density Functional Study on the Structure of Thin Polymer Blend Films with a Free Surface

Using the dynamic density functional method, we studied the structural evolution of a thin film of polymer blends placed between the solid substrate and free surface. We observed various types of structural instabilities such as the spinodal wave and the roughening of the free surface due to droplet formation. We proposed a simple theoretical argument based on the Neumann triangle condition among the interfacial tensions to construct a phase diagram for the instability of the free surface and confirmed this by a series of dynamic density functional simulations.

Phase separation of polymer blend films near patterned surfaces

The effect of a patterned surface on the phase separation kinetics of a thin polymer film has been investigated using the Cahn–Hilliard–Cook model in three dimensions with the addition of a short range surface potential. We have observed pattern-induced spinodal waves perpendicular to the surface creating “checkerboard”-like composition fluctuations for a wide range of patterns used in this study. The number of such layers strongly depends on the magnitude of the thermal noise. For sufficiently thin films, where the film thickness is smaller than the spinodal wavelength, spinodal decomposition can be arrested if the surface potential and the characteristic size of the pattern are chosen accordingly, enabling the transfer of surface patterns to the film material. The kinetic pathways through which the equilibrium states are reached delicately depend on the particular pattern, its size, and the film thickness.

Spinodal decomposition of an ABv model alloy: Patterns at unstable surfaces

We develop mean-field kinetic equations for a lattice gas model of a binary alloy with vacancies (ABv model) in which diffusion takes place by a vacancy mechanism. These equations are applied to the study of phase separation of finite portions of an unstable mixture immersed in a stable vapor. Due to a larger mobility of surface atoms, the most unstable modes of spinodal decomposition are localized at the vapor-mixture interface. Simulations show checkerboard-like structures at the surface or surface-directed spinodal waves. We determine the growth rates of bulk and surface modes by a linear stability analysis and deduce the relation between the parameters of the model and the structure and length scale of the surface patterns. The thickness of the surface patterns is related to the concentration fluctuations in the initial state.

A model of multiscaling dynamics for spinodal decomposition

A model is developed for analysing small-angle scattering data for systems which are undergoing spinodal decomposition. This model is expressed as an integration of a series of Fourier components of the density fluctuation A( β)sin( βr + ϕ) based on Cahn's linear theory of spinodal decomposition. Hence the time evolution of the growth kinetics can be calculated analytically using a multiscaling function. The characteristic crossover phenomenon and the width of the crossover of the scaling function of the structure factor measured by small-angle scattering techniques are predicted to be associated with the maximum spinodal wave number β m and the correlation length ξ m, respectively.

Surface-Induced Asymmetries during Spinodal Decomposition in Off-Critical Polymer Mixtures

We have studied the growth of the wetting layer formed at the surfaces of symmetric and nonsymmetric mixtures of poly(ethylenepropylene) (PEP) and perdeuterated poly(ethylenepropylene) (dPEP) during spinodal decomposition. For off-critical quenches, the growth rat is found to be strongly dependent on the bulk composition of the mixtures. If the minority phase wets the surface, the wetting layer is found to grow slower than in the reverse situation, where the majority phase wets the surface. In the latter case, hydrodynamic effects may play a role, increasing the rat of wetting layer growth. The surface spinodal waves are shallower for the case of off-critical compositions as compared to critical compositions

Quantification of the spinodal wave in Cu2.5Mn0.5Al by dark-field image analysis

Abstract The spinodal decomposition of the alloy Cu2.5Mn0.5Al is assessed using a transmission electron microscopy imaging method for the characterization of the form and amplitude of the composition changes. The conditions under which the quantification of the dark field image contrast can allow the reliable evaluation of the composition are also discussed.

Real space observation of dynamic scaling in a critical polymer mixture

We have studied the growth of the wetting layer formed at the surface of a critical mixture of poly(ethylene propylene) and perdeuterated poly(ethylene propylene) during spinodal decomposition. The wavelength of the surface spinodal wave is found to grow as ${\mathit{t}}^{1/3}$ over the entire range of times accessible in the experiment. The composition profiles exhibit universal scaling behavior in the near-surface region. These results are in excellent agreement with a recent numerical study on surface-directed spinodal decomposition.

Interference of spinodal waves in thin polymer films

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTInterference of spinodal waves in thin polymer filmsGeorg Krausch, Chi An Dai, Edward J. Kramer, John F. Marko, and Frank S. BatesCite this: Macromolecules 1993, 26, 21, 5566–5571Publication Date (Print):October 1, 1993Publication History Published online1 May 2002Published inissue 1 October 1993https://doi.org/10.1021/ma00073a006RIGHTS & PERMISSIONSArticle Views535Altmetric-Citations114LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts Get e-Alerts

Study of the spinoidal mechanism of phase separation of polystyrene solutions in decalin

Rayleigh light scattering was used in the angular region of 20 to 2° to study the phase separation of metastable and unstable PS solutions ( M w=3·33 × 10 6, M w/ M n= 1·06 ) in decalin of three concentrations: critical c cr=1·96 and c=1·18 and 3·6 g/dl. It was found that there is an interference maximum in the angular range of 1·5−3·5° on curves showing the angular relation of the intensity of light scattering I of unstable solutions of C cr. The interference maximum is absent for unstable systems of other concentrations and for metastable systems. It was shown that in the first 3–5 min phase separation of unstable solutions of c cr = 3·6 g/dl is described by Cahn's theory. Diffusion coefficients, which are negative and dimensions of spinodal wave lengths were calculated using this theory. As the temperature of the system approximates to the spinodal, structural dimensions increase and diffusion slows down.