Late Stage Of Spinodal Decomposition Research Articles

On the mechanism of pinning in phase-separating polymer blends

We reexplore the kinetics of spinodal decomposition in off-critical polymer blends through numerical simulations of the Cahn–Hilliard equation with the Flory–Huggins–De Gennes free energy functional. Even in the absence of thermal noise, the solution of the discretized equation of motion shows coarsening in the late stages of spinodal decomposition without evidence of pinning, regardless of the relative concentration of the blend components. This suggests this free energy functional is not sufficient to describe the physics responsible for pinning in real blends.

Correlation between shear viscosity and anisotropic domain growth during spinodal decomposition under shear flow.

To investigate the influence of a simple shear flow on the late stage spinodal decomposition of a binary polymer blend, the shear viscosity and the domain growth have been studied by a combined rheo--small-angle-light-scattering technique. In a representation versus the applied strain, the viscosities as well as the structure deformation can be scaled on single curves for different shear rates. Both quantities show two characteristic crossovers at the same strain values. The behavior is compared with results of a recent computer simulation.

Scaling in late stage spinodal decomposition with quenched disorder.

We study the late stages of spinodal decomposition in a Ginzburg-Landau mean field model with quenched disorder. Random spatial dependence in the coupling constants is introduced to model the quenched disorder. The effect of the disorder on the scaling of the structure factor and on the domain growth is investigated in both the zero temperature limit and at finite temperature. In particular, we find that at zero temperature the domain size R(t) scales with the amplitude A of the quenched disorder as R(t)=${\mathit{A}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$f(t/${\mathit{A}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$) with \ensuremath{\beta}\ensuremath{\simeq}1.0 and \ensuremath{\gamma}\ensuremath{\simeq}3.0 in two dimensions. We show that \ensuremath{\beta}/\ensuremath{\gamma}=\ensuremath{\alpha}, where \ensuremath{\alpha} is the Lifshitz-Slyosov exponent. At finite temperatue, this simple scaling is not observed and we suggest that the scaling also depends on temperature and A. Comparisons of the scaled structure factors for all values of A at both zero and finite temperature indicate only one universality class for domain growth. We discuss these results in the context of Monte Carlo and cell dynamical models for phase separation in systems with quenched disorder and propose that in a Monte Carlo simulation the concentration of impurities c is related to A by A\ensuremath{\sim}${\mathit{c}}^{1/\mathit{d}}$.

Computational study of effects of uniaxial compression during processes of spinodal decomposition.

We present a computational study on the effects of a uniaxial compression with compression ratio 1/2 on the ordering processes via spinodal decomposition (SD), by numerically integrating the time-dependent Ginzburg-Landau equation. We investigate the pattern growth and two-dimensional structure factors both after a compression in the intermediate stage SD and after a compression in the late stage SD. The results indicate that the compression in the intermediate stage SD causes the phase-separated structure to orient with its interfaces in the direction parallel to the compression axis, and that the compression in the late stage SD causes the phase-separated structure to orient with its interfaces in the direction perpendicular to the compression axis.

Phase Separation Dynamics of Blends of Telechelic Epoxy Terminated Polybutadiene and Maltene

Abstract Thermally induced phase separation in a mixture of telechelic epoxy terminated polybutadiene (ETPB) and maltene has been studied by means of time-resolved light scattering and optical microscopy. Maltene, consisting of various hydrocarbon derivatives, was extracted from asphalt with n-heptane and isolated by centrifugation. The cloud point studies of the ETPB/maltene mixture showed an upper critical solution temperature (UCST) which is thermally reversible. Several deep temperature quench experiments were conducted at an off-critical composition (27/73 ETPB/maltene) from a single phase (80°C) to a two-phase region (27, 29, 31 and 33 °C). The time-evolution of the structure factor for the late stage of spinodal decomposition (SD) was analyzed in the framework of nonlinear and dynamical scaling laws. The reverse quench experiments were also undertaken to elucidate the phase dissolution process.

Dynamic aspects of phase decomposition in reactive blends of polycarbonate and syndiotactic polymethyl methacrylate

AbstractDynamics of phase separation in bisphenol‐A polycarbonate (PC)/syndiotactic polymethyl methacrylate (sPMMA) blends has been investigated by means of time‐resolved light scattering. Solvent‐cast films of the PC/sPMMA blends were transparent, suggestive of miscible character. Several temperature jumps were carried out at a 50/50 PC/sPMMA composition from a homogeneous state (room temperature) into a two‐phase regime. The process of phase separation first occurred for some considerable period, then it was followed by phase dissolution driven by chemical reaction. The thermodegradative reaction of sPMMA triggered the dissolution process by probably forming PC/sPMMA graft or random copolymers at the interface, which eventually resulted in a single phase. However, annealing at elevated temperatures for an extended period could lead to cross‐linking, and thus a two‐phase structure could be fixed permanently. The early stage of spinodal decomposition was interpreted in terms of the linearized Cahn‐Hilliard theory. In the late stages of spinodal decomposition, the relationship between scattering peak wavenumber and time was found to obey a power law, but the exponents showed a strong dependence on temperature jumps. The temporal universal scaling failed due to the influence of the chemical reaction. © 1995 John Wiley & Sons, Inc.

Morphological studies of late‐stage spinodal decomposition in polystyrene–cyclohexanol system

AbstractWe studied the late‐stage spinodal decomposition of the polystyrene–cyclohexanol system in relation to membrane formation. Phase separation was effected by the removal of thermal energy from the homogeneous polymer solution. The ultimate morphology of the phase‐separated systems has been studied using electron microscopy and has been found to be strongly affected by the quenching time. A shift from a highly interconnected open‐cell structure to a closed‐cell structure has been observed, indicating the transition of the spinodal decomposition from early to late stages. The cell growth in the late stage has been quantitatively analyzed and a power‐law relationship between the cell size and quenching time has been found. The resulting exponent of 0.61 is consistent with literature values from light‐scattering measurements, as well as from theoretical derivations. © 1995 John Wiley & Sons, Inc.

A melt rheometer with integrated small angle light scattering

A stress-controlled commercial rheometer has been equipped with small-angle light scattering (SALS) instrument working in a range of wave-vectors between 0.5 and 4.2 μm−1 By a specially designed optical system the scattered light is focused directly on the square chip of a CCD-detector with high dynamical range allowing quantitative two-dimensional (2 D) intensity measurements of polarized and depolarized scattering. The rheo SALS system is suited for simultaneous fast measurements of 2D SALS and rheological material functions of polymer melts and liquid crystals. As a first application results on the influence of shear rate on the late stage of spinodal decomposition of a polybutadiene/polyisoprene blend are reported. A second application concerns a creep experiment in the liquid crystalline phase of a lyotropic non-ionic surfactant with simultaneous measurement of the time-dependent compliance and associated changes of the 2D intensity patterns of the polarized and depolarized scattering.

Late stage spinodal decomposition in binary critical fluids: scaling function obtained over a wide q-space of 4 orders of magnitude

Space-time organization of the pattern in late stage spinodal decomposition was explored over an extremely wide q-space amounting to 4 orders of magnitude by a combined use of the time-resolved small-angle neutron and light scattering methods for a binary fluid mixture of perdeuterated polybutadiene and polyisoprene near the critical point. The scaled structure factor F( x) = S( q, t) q m( t) 3 with x = q q m (t) was explored in detail where S( q, t) is the scattering structure factor at time t as a function of magnitude of scattering vector q and q m( t) is the q value at the maximum of the structure factor at t. A dynamical evolution of the mean value of the absolute interface curvature H( t) was estimated evolution of the mean have a particular relationship with that of q m( t), i.e., H(t) q m (t) ≅ 2 , both being controlled by the hydrodynamic interaction effect. The dynamical scaling law was found to be valid for the global feature of the pattern growth, i.e., F( x,t) at x < 2. However, this is not the case for the local feature, giving rise to “extrinsic” and “intrinsic” nonuniversalities in F( x,t) at x > 2.

Late stage spinodal decomposition in binary fluids: comparison between computer simulation and experimental results

Abstract We present detailed comparisons of results on the late stage dynamics of spinodal decomposition obtained by the computer simulation of the time-dependent Ginzburg-Landau equation with hydrodynamic interaction and experiments of a polymer mixture of polybutadiene and polyisoprene. We show that the temporally linear domain growth law, which is characteristic for viscous fluids, is observed in both simulation and experiment in the late stage. Some quantities obtained in such a hydrodynamic domain growth region, such as the interface area density and the scaling function, are compared in detail. Especially, we show that the scaling functions for the two systems are in quantitative agreement.

A small-angle x-ray scattering study of microstructure evolution during sintering of sol-gel-derived porous nanophase titania

The evolution of microstructure as a function of firing temperature in sol-gel derived porous titania xerogels was investigated by small-angle x-ray scattering (SAXS). SAXS curves for xerogels fired below 550 °C exhibit a well-defined structure peak. This peak indicates the presence of a high degree of order in the electron density correlations associated with the interparticle structure factor. Results from electron microscopy and SAXS give a primary particle mean diameter of 50 Å, while scaling analysis of the scattered intensity at large momentum transfer values yields the Porod exponent 4, indicating a sharp transition zone between the solid and void phases. The pore volume fraction of the unfired xerogel is consistent with random close-packing of spheres. The internal surface area decreases almost linearly with increasing firing temperature. Rapid grain growth and pore coarsening begin near 90% of theoretical density, and lead to a breakdown in pore interconnectedness and the development of isolated pores. Observed enhanced sintering properties may be attributed primarily to the large surface-to-mass ratio of the sol-gel particles. The SAXS curves were adequately fit using a bicontinuous phase model developed for late-stage spinodal decomposition structures. Alternatively, the microstructure can be described by a hierarchical close-packing of spheres model. SAXS results are compared with data from gas adsorption and electron microscopy.

Spinodal decomposition in a critical isobutyric acid and water mixture.

Light scattering was used to study the time evolution of phase separation of a critical isobutyric acid and water mixture in the spinodal region. A shoulder is observed in the larger-scattering-angle region of the main dominant peak in the structure factor, and the time dependence of the position of shoulder is well scaled by the same characteristic wave number and interdiffusion coefficient as those for the main peak. The tail in the large-scattering-angle region of the structure factor is well expressed by the Porod law in the intermediate and late stages of spinodal decomposition.

Phase separation in mixtures of poly(ethylene glycol monomethylether) and poly(propylene glycol) oligomers

AbstractTime‐resolved light scattering was employed to investigate kinetics of phase separation in mixtures of poly (ethylene glycol monomethylether) (PEGE)/poly (propylene glycol) (PPG) oligomers. Phase diagrams for PEGE/PPG of varying molecular weights were established by means of cold point measurements. The oligomer mixtures reveal an upper critical solution temperature (UCST). Several temperature quench experiments were carried out with a 60/40 PEGE/PPG blend by rapidly quenching from a single phase (69°C) to two‐phase temperatures (66–61°C) at 1°C intervals. As is typical for oligomer mixtures, the early stage of spinodal decomposition (SD) was not detected. The kinetics of phase decomposition was found to be dominated by the late stage of SD. Time‐evolution of scattering intensity was analyzed in accordance with nonlinear and dynamical scaling theories. The time dependence of the peak intensity Im and the corresponding peak wavenumber qm was found to follow the power‐law {Im(t)˜ tα, qm(t)˜ t‐β} with the values of α = 3 ± 0.3 and β = 1 ± 0.2, which are very close to the values predicted by Siggia. This process has been attributed to a coarsening mechanism driven by surface tension. In the temporal scaling analysis, the structure function reveals university with time, suggesting self‐similarity. Phase separation dynamics in 60/40 PEGE/PPG resembles the behavior predicted for off‐critical mixtures.

Simulation of bicontinuous microemulsions: comparison of simulated real-space microstructures with scattering experiments

The ubiquitous scattering peak found in all disordered bicontinuous microemulsions, when scattering measurements are made with an oil-water contrast, is attributed to the existence of two length scales in the system. The two lengths, d and ξ, appear explicitly in the Debye correlation function for the microemulsion in a phenomenological model proposed by Teubner & Strey [J. Chem. Phys. (1987), 87, 3195–3200] (T–S model). The precise physical meaning of these two lengths, however, was not clear in the original paper. Cahn's scheme for simulating the morphology of the late-stage spinodal decomposition of a phase-separating two-component alloy is extended to the case of bicontinuous microemulsions with an equal volume fraction of oil and water. In the simulation, a length scale {\bar d}=2π/{\bar k}, representing the average interdomain distance (proportional to the average domain size), and another parameter z, relating to the dispersion of the domain size by Δk/{\bar k} = (z + 1)−1/2, are imposed. It is shown that the ratio ξ/d in the T–S model is a unique function of the parameter 1/z. The extended Cahn model gives both the real-space structure of a disordered bicontinuous microemulsion and the exact Debye correlation function for the calculation of the corresponding scattering intensity. A criterion is given for the realisation of the disordered bicontinuous structure in terms of a universal range for the dispersion (i.e. ξ/d). The existence of the two lengths, having a universal ratio, also implies that the scattering function I(Q) satisfies a certain scaling relation. Our SANS data are used to support the validity of such a scaling relation.

Time-resolved small-angle neutron scattering in intermediate- and late-stage spinodal decomposition of perdeuterated polybutadiene-protonated polyisoprene blends

Etude de l'evolution temporelle de la difference de composition entre les 2 domaines coexistant dans les stades intermediaire et final de la decomposition spinodale d'un melange critique de polybutadiene perdeuterie et de polyisoprene protone ayant un diagramme de phase de type LCST

Micellar formation and correlation in the cavity of porous silica glass.

Small-angle neutron scattering (SANS) is used to study the scattering length density correlations in a dry porous silica glass (Vycor) and in the glass filled with anionic and cationic surfactant molecules dispersed in water. SANS intensity distributions from empty pores of the glass can be satisfactorily analyzed using a standard late stage spinodal decomposition model in which the porous structure is described by a superposition of random density waves. This model, however, agrees with experiment only if one allows for a suitable distribution of wave numbers for the density waves. Micellar formation is observed in Vycor filled with surfactant solutions. We discuss the interpretation of the intermicellar correlations, measured by SANS, within the pores of the Vycor glass.

Phase separation dynamics of polycarbonate/polymethyl methacrylate blends. I. Temperature jumps into an immiscibility loop

Time-resolved light scattering was employed to elucidate the dynamics of phase separation in mixtures of polycarbonate (PC) and polymethyl methacrylate (PMMA). Blends of PC and PMMA of moderately low molecular weight reveal the coexistence of an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST), forming an immiscibility loop. Temperature jump (T jump) experiments were conducted on the 40/60 PC/PMMA composition from a single phase (150 °C) to a two-phase immiscibility loop region (180 and 190 °C). Phase separation takes place through spinodal decomposition (SD). The early stage of SD is explicable in terms of the linearized Cahn–Hilliard theory. The late stage of SD follows the power law relationship with the exponents of −1/3 and 1 as predicted by the cluster theory of Binder and Stauffer. The universal curve with reduced variables Qm and τ was established. The late stage data were analyzed in accordance with the recent scaling law of Furukawa. The temporal phase decomposition appears to be self-similar. The shape of the structure function can be scaled with slopes of 2 and −6 for q&amp;lt;qm and q&amp;gt;qm regions, respectively.

Phase separation dynamics of polycarbonate/polymethyl methacrylate blends. II. Temperature jumps above an immiscibility loop

Blends of polycarbonate (PC) and moderately low molecular weight polymethyl methacrylate (PMMA) reveal an immiscibility loop in which an upper critical solution temperature (UCST) is located above a lower critical solution temperature (LCST). Temperature jump (T jump) experiments were conducted on a 40/60 PC/PMMA composition from a single phase (150 °C) to two-phase temperatures above the immiscibility loop (205–241 °C). Phase separation first occurs, then is accompanied by phase dissolution. The early stage of phase separation is explicable in terms of the linearized Cahn–Hilliard theory. The late stage of SD follows the power-law relationship with the exponents of −1/3 and 1 as predicted by the cluster theory of Binder and Stauffer. The universal curve was established with dimensionless variables of Qm and τ. The late stage data were analyzed in accordance with the recent scaling laws of Furukawa. Time evolution of structure function exhibits universality in the late stages of spinodal decomposition. The shape of the structure function can be scaled with slopes of 2 and −6 for q&amp;lt;qm and q&amp;gt;qm regions, respectively. At a later time, phase dissolution takes place and the system returns to a single phase.

Aspects of late-stage dynamics of ordering processes

We discuss two examples of the late-stage dynamics of ordering processes. First, we describe time evolution of cellular patterns of polycrystals in the solidification transition where a new set of models called the vertex models is introduced and studied. We also discuss a non-classical Ostwald ripening occuring at the late stage of spinodal decomposition.

Scaling tests of late stages of spinodal decomposition in PC/PMMA blends

AbstractTime‐resolved light scattering studies were undertaken to elucidate the kinetics of phase separation in polycarbonate (PC)/polymethyl methacrylate (PMMA) blends. The 40:60 PC/PMMA blend undergoes thermally induced phase separation through spinodal decomposition. Temperature jump experiments were carried out from a single‐phase to a two‐phase temperature region. The general trend of spinodal decomposition in this blend system is nonlinear in character and obeys the power laws. The time evolution of scattering curves was analyzed in accordance with dynamical scaling laws for self‐similarity and the shape of scaled structure functions.