Early Stage Of Spinodal Decomposition Research Articles

Phase Behavior and Morphology of Poly(Methyl Methacrylate)/Poly(α‐Methyl Styrene‐co‐Acrylonitrile) Blends Under Quiescent and Shear Flow

The kinetics of spinodal decomposition (SD) for the binary blend poly(methyl methacrylate), PMMA, and Poly(α‐methylstyrene‐co‐acrylonitrile), PαMSAN, with 31 wt% AN content (LCST‐type phase diagram) has been thoroughly studied using a time‐resolved light scattering technique. The early stage SD was dominated by a diffusion process and can be well described within the framework of the linearized Cahn‐Hilliard theory. The spinodal temperature could be evaluated from the analysis of the early stage SD based on the Cahn theory. In addition, viscoelastic properties of this system have been systematically investigated at temperatures below and above the LCST phase diagram. The linear viscoelastic properties of the blends were found to be greatly changed by phase separation in the two‐phase regime. This change in the linear viscoelastic properties attributed to an additional contribution of concentration fluctuations to the material functions at the phase separation temperatures. The phase diagram of the blends was also estimated rheologically through the dynamic temperature ramps of G′, G″ and η*. Furthermore, the phase behavior and morphology of this system has been studied under different shear rates using simple shear apparatus and transmission electron microscopy (TEM), respectively.

Dynamical density functional theory and its application to spinodal decomposition.

We present an alternative derivation of the dynamical density functional theory for the one-body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys. 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multibody interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our nonlinear theory is equivalent to the (generalized) linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wave number larger than that of the main peak.

Spinodal Decomposition in Binary Blend of Poly(methyl methacrylate)/Poly(α-methyl styrene-co-acrylonitrile): Analysis of Early and Late Stage Demixing

Summary: The phase separation kinetics of a poly(methyl methacrylate), PMMA, and poly(α-methylstyrene-co-acrylonitrile), PαMSAN, blend exhibiting a LCST-type phase diagram have been investigated as functions of temperature and demixing time for the near critical composition (PαMSAN/PMMA = 25:75) using a time-resolved light scattering technique. We found that the scattering data in the early stage spinodal decomposition (SD) can be well described by the linearized Cahn–Hilliard theory. Spinodal temperature Ts ∼ 171 °C was determined from Dapp versus T and qequation/tex2gif-stack-1.gif versus T based on the analysis of Cahn theory in the early stage SD, where Dapp is the apparent diffusion coefficient and qm is the scattering vector at the maximum scattering intensity. The value of Ts obtained from the analysis of light scattering data was in good agreement with the phase diagram obtained visually at the equilibrium condition. The LCST-type phase diagram of this blend was also calculated using the Flory–Huggen theory. The estimated interaction parameter used for the calculation of the phase diagram was found to be composition and temperature dependent. The coarsening behavior of the blend at the late stage SD was also studied by analyzing the magnitudes of qm and Im at various demixing times and temperatures based on the nonlinear statistical theories. Both of qm and Im obtained at different times and temperatures can be superposed and reduced to the respective master curves by horizontal shifting when they are plotted against log (t/aT) at a given reference temperature, where aT is the temperature-dependent shift factor. The shape of the phase separation domain structures as a function of time during the SD was also considered. The scaling structure function F(x,t;T) = qm(t;T)3I(q,t;T) versus q/qm was found to be time independent and falls onto a universal curve in the late stage SD as a result of the dynamical self-similarity accompanying with the phase separation process. Optical microscopy pictures for the structure development of spinodal decomposition for PαMSAN/PMMA = 25:75 blend at 180 °C for different demixing times.

Phase separation of off‐critical polymer blends of poly(styrene‐co‐maleic anhydride) and poly(methyl methacrylate). II. Morphology and mechanical properties

AbstractThe effects of the phase‐separation temperature and time on the mechanical properties and morphology of poly(methyl methacrylate)/poly(styrene‐co‐maleic anhydride with 10 wt% ethyl acrylate) (SMA) blends were studied. Two compositions (20/80 and 40/60 w/w SMA/PMMAe) were prepared with a miniature twin‐screw extruder. Compared with those of the miscible blends, the Young's modulus values of the blends increased after the phase separation of the 40/60 SMA/PMMAe blend and within the early stage of spinodal decomposition of the 20/80 SMA/PMMAe blend. The mechanical properties, in terms of the tensile strength at break and the elongation, were better for the miscible blends than for the phase‐separation blends. This was believed to be the result of changes in the composition and molecular reorganization. The changes in the phase‐separating domains of both compositions, as observed by transmission electron microscopy, had no significant influence on the tensile moduli. Detailed studies of the morphology revealed a cocontinuous structure, indicating that the blends underwent spinodal decomposition. A morphological comparison of the two compositions illustrated the validity of the level rule. The growth rate of the droplet size was determined by approximation from the light scattering data and by direct measurements with transmission electron microscopy. The discrepancies observed in the droplet size growth rate were attributed to heat variations induced by the different sample thicknesses and heat transfer during the investigation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 886–897, 2004

Phase separation of off‐critical polymer blends of poly(styrene‐co‐maleic anhydride) and poly(methyl methacrylate). I. Kinetics of spinodal decomposition

AbstractThe kinetics of phase separation via the spinodal decomposition of poly(styrene‐co‐maleic anhydride)/poly(methyl methacrylate) from a delay time period to late stages were investigated with a light scattering technique. The standard procedure for identifying four stages of spinodal decomposition, based on the characteristics of concentration fluctuations, was clearly introduced with the light scattering method. The spinodal limits were divided into four stages: the delay time, the early stage, the intermediate stage, and the late stage. The validity of the linearized theory was reviewed because it was used as an indicator of the limit of the early stage of spinodal decomposition, which divided the delay time period from the early stage and the early stage from the intermediate stage. The linearized theory fit the experimental results very well after the delay time. The scaled structure function of the melt‐mixed blend was analyzed. The universality of the scale structure function, F(x) = S(q,t)qm3(t) (where S is the structure function, x is equal to q/qm, q is the scattering wave vector, qm is the maximum wave vector, and t is the time in seconds), indicated the late stage of phase separation and divided the late stage from the intermediate stage. The simple normalized scaling function profile for the cluster region proposed by Furukawa described the experimental data very well, whereas the profile for deep quenching, which was recently suggested, showed some discrepancies. As a result of the phase separation, the processing of this blend may be able to be developed to provide the most suitable morphology. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 871–885, 2004

Quench–jump sequence in phase separation in polymer blends

A two-step process of phase separation–mixing is analyzed for binary mixtures. The system is first quenched into the thermodynamical instability region (temperature T), where the mixture undergoes a process of spinodal decomposition, characterized for short times by the growth of the Cahn peak of a scattered intensity at fixed scattering wave vector. Next we heat up a system (make a temperature jump to temperature T1) above the spinodal line (temperature Ts) and compute the decay of this peak. The peak intensity decreases and the peak position moves toward short wave vectors. The integrated peak intensity decreases exponentially at short times with a characteristic decay time that depends on T, T1, and Ts. The increase of the Euler characteristic from large negative values toward zero suggests that the shift of the peak toward short wave vectors is associated with the disappearance of small connections in a bicontinuous structure formed in the early stages of spinodal decomposition. Slow decay of the surface area indicates that the domains keep their shape for a long time, despite the fast decay of the saturation of the concentration field inside them.

Spinodal decomposition in a binary polymer mixture: dynamic self-consistent-field theory and Monte Carlo simulations.

We investigate how the dynamics of a single chain influences the kinetics of early stage phase separation in a symmetric binary polymer mixture. We consider quenches from the disordered phase into the region of spinodal instability. On a mean field level we approach this problem with two methods: a dynamical extension of the self-consistent-field theory for Gaussian chains, with the density variables evolving in time, and the method of the external potential dynamics where the effective external fields are propagated in time. Different wave vector dependencies of the kinetic coefficient are taken into account. These early stages of spinodal decomposition are also studied through Monte Carlo simulations employing the bond fluctuation model that maps the chains-in our case with 64 effective segments-on a coarse grained lattice. The results obtained through self-consistent-field calculations and Monte Carlo simulations can be compared because the time, length, and temperature scales are mapped onto each other through the diffusion constant, the chain extension, and the energy of mixing. The quantitative comparison of the relaxation rate of the global structure factor shows that a kinetic coefficient according to the Rouse model gives a much better agreement than a local, i.e., wave vector independent, kinetic factor. Including fluctuations in the self-consistent-field calculations leads to a shorter time span of spinodal behavior and a reduction of the relaxation rate for smaller wave vectors and prevents the relaxation rate from becoming negative for larger values of the wave vector. This is also in agreement with the simulation results.

Asymmetric landscapes of early spinodal decomposition

We address the effect of an asymmetric concentration-dependent mobility on the early stages of spinodal decomposition in polymer blends and solutions, and characterise it quantitatively. This is particularly important when one of the components has a slower dynamics than the other, e.g., because it is closer to its glass transition, or is weakly cross-linked. Composition mode coupling is proposed as the underlying physical mechanism, and then investigated by means of numerical simulations of the Cahn-Hilliard equation in one (1d) and two (2d) dimensions. In general, this coupling broadens the peak in the structure factor: in 1d an asymmetric concentration profile is obtained, with sharpened interfaces, whereas in 2d the formation is favoured of sharp peaks of the phase rich in the more mobile component. It is shown how the changing morphology of this phase-separating system can be described with the aid of Minkowski functionals.

Spinodal Decompositions Driven by Orientation Fluctuations

We study early stages of spinodal decomposition (SD) in polymer/liquid crystal mixtures by solving linearized time-dependent Landau-Ginzburg equations for concentration (conserved order parameter) and orientation (nonconserved order parameter). We calculate structure factors for concentration and for orientation, depending on a quench temperature and concentration. We find a new SD process driven by instability of the orientational order parameter.

Experimental studies of stress–diffusion coupling in semi-dilute polymer solutions. I. ‘Viscoelastic length’ and viscoelastic effects on early stage spinodal decomposition

We investigated the viscoelastic effects on the early stage spinodal decomposition (SD) in semi-dilute polymer solutions where the coupling between stress and diffusion plays an important role. The so-called viscoelastic length, ξve, within which the stress suppresses the growth of the concentration fluctuations, was quantitatively evaluated experimentally. The evaluated value was found out to be about 10 times larger than the radius of gyration of polymer. We measured the interdiffusion coefficient, the cooperative diffusion coefficient, the zero-shear viscosity, and the plateau modulus in the one phase region and evaluated ξve independently from the SD experiment. The value ξve obtained in the early stage SD agrees well with that estimated from the diffusion and viscoelasticity measurements, confirming the validity of the Doi–Onuki theory.

Instability in Si(110) etched with tetramethyl ammonium hydroxide

Experimental data for the morphological evolution of etched Si(110) is presented. The observed results are interpreted using a continuum equation. The results reveal the presence of unstable etching which leads to the formation of elliptical hollows on the surface. The early stage of the formation of hollows can be explained by a linear theory similar to that which describes the early stage of spinodal decomposition. This instability is caused by anisotropic surface tension.

Early stages of spinodal decomposition in binary liquid crystal mixtures

We study the early stages of spinodal decomposition in binary liquid crystal mixtures by solving linearized time-dependent Landau–Ginzburg equations for concentration (conserved order parameter) and two orientation (nonconserved) order parameters, one for each component. The theory takes into account a cross term between concentration and orientation gradients, which becomes an important factor for phase separation kinetics. We calculate growth rates and structure factors for the order parameters, following thermal quenches from a stable isotropic state into an unstable region. Depending on the quenched temperature and concentration, we find five unstable regions which are characterized by the time evolutions of the structure factors.

Validity of linear analysis in early-stage spinodal decomposition of a polymer mixture

A two-step phase separation was imposed to a binary mixture of deuterated polybutadiene and protonated polyisoprene with nearly critical composition in the following way: the system was first subjected to phase separation via spinodal decomposition (SD) so that the system developed coexisting two phases characteristics of the late stage of SD (the first-step phase separation). It was then brought into a deeper quench so that both two phases again fell into spinodal region and hence further SD took place within each phase (the second-step phase separation at T2). In the very early stage after this second-step phase separation, the two-phase structure developed in the first-step phase separation was almost unchanged with time, but the composition fluctuation was newly developed within each phase, giving rise to an excess light scattering (LS) at large scattering vectors. The very early stage in this second-step phase separation process was studied by time-resolved LS. We found that the early-stage SD after the second-step phase separation at T2 can be well described by the linearized theory of SD. However the characteristic parameters, especially the collective diffusivity, obtained from the linear analysis, were different from those obtained by the single-step SD at T2 for the corresponding single-phase mixtures. The results unveil an intriguing effect of initial structure or space confinement on early stage SD, reflecting an intrinsically nonlinear phenomenon.

Phase separation behavior in polyvinyl alcohol/ethylene glycol/water ternary solutions

In this work, the effects of mixed solvent on the phase separation behavior in PVA/EG/water ternary solutions were studied through the time-resolved light scattering, pulsed NMR and X-ray measurements. The Cahn–Hilliard–Cook (CHC) linear theory at the early stage of spinodal decomposition was first used to discuss the phase separation behavior in PVA solutions. The results showed that an unusual behavior is observed in this system. At the water content above 30 vol% in EG/water mixed solvent, the phase separation of PVA solutions was found to yield the mechanism of spinodal decomposition as described by the linear CHC theory. On the contrary, phase separation may occur simultaneously with crystallization and then does not correspond to the linear CHC theory at water content below 30 vol%. The apparent diffusion coefficient of PVA chains in solution decreases rapidly and then approaches zero at water content above 50 vol%, implying that the phase separation of PVA solutions is very difficult to achieve in this work. Finally, the structural change in gel network with water content was investigated through X-ray and 1H pulsed NMR measurements. The X-ray result shows that the crystallinity of PVA gels decreases with water content. The (1 0 1) diffraction peak related to PVA crystal vanishes for the gels with water content above 30 vol%, indicating that the gelation at this condition should form a low crystalline or an amorphous gel structure. The spin–spin relaxation time T S 2 in the polymer-rich phase of gel changes discontinuously with water content i.e. the increment of the T S 2 value rises rapidly at about 30 vol%. This phenomenon must be related to the change of chain mobility in polymer-rich phase with various gel structures.

Surface enrichment effect on the morphological transitions induced by directional quenching for binary mixtures

The morphological transitions during directional quenching-induced spinodal decomposition in binary mixtures are investigated by computer simulation. By setting the quenching front between the stable and unstable phases, and shifting the front with a constant velocity, the evolution of the domain morphologies is examined numerically on the basis of the time-dependent Ginzburg–Landau (TDGL) equation. Three different types of morphologies are found for the critical quenching. One is irregular morphology (IM), which is essentially equivalent to that produced by homogeneous quenching. The other two are regular, representing the characteristics of the directional quenching process. One is regular lamellar morphology (RLM) and the other is regular column morphology (RCM). By varying the shifting velocity of the cooling front, two morphological transition velocities, va from IM to RLM, and vi from RLM to RCM, are observed. In contrast to that, for the case of off-critical quenching, a new transition velocity vb from RCM back to RLM can be found if the cooling front is further shifted slower. This characteristic morphological transition is attributed to the surface enrichment effect appearing in the nonequal volume fraction system, which competes with linear instability triggered by initial thermal fluctuation in the early stage of spinodal decomposition. Detailed studies reveal that RLM can be easily formed and thus the region of RCM is reduced when the surface enrichment effect is stronger. On the other hand, RCM will be preferred if the initial thermal fluctuation is stronger. The quantitative relation between lamella width and shifting velocity of the cooling front is also presented.

Two-step phase separation of a polymer mixture. II. Time evolution of structure factor

Nonlinear time evolution of phase-separating structures in the two-step phase separation process was investigated for a deuterated polybutadiene–polyisoprene mixture by using a time-resolved light scattering technique. The mixture studied has a lower critical solution temperature type phase diagram with a spinodal temperature of 36 °C. The first-step phase separation via spinodal decomposition (SD) was conducted by a temperature jump (T-jump) from 23 °C to 42 °C, and to the late stage of the SD for varying time periods, t0, in order to develop phase-separated domains with varying characteristic size Λm,1. This phase separation was followed by the second-step T-jump to a higher temperature of 70 °C so that each phase-separated domain is again quenched into thermodynamically unstable region. Nonlinear time evolution processes of phase-separating structures after the second-step SD were explored as a function of size of the initial structures Λm,1. We found the following intriguing effects of the initial structures on further evolution of phase-separating structure via the second-step SD: (1) When Λm,1≫Λm,0 (characteristic length of composition fluctuations developed in the early stage SD after quenching the system from a single-phase state to 70 °C), small domains were evolved within the initial domains (defined as large domains) developed during the first-step SD process, while (2) when Λm,1⩽Λm,0, the small domains were not developed, but only the large domains grew at a growth rate larger than that at 42 °C. In the former case (1), we succeeded in separating the scattering due to the small domains and that due to large domains from the observed scattering profile. The separation allows us to investigate a coupling of the time evolution of the large and small domains and nonlinear pathways for the system to achieve a new equilibrium structure after the second-step SD process.

Orientation fluctuation-induced spinodal decomposition in polymer–liquid-crystal mixtures

We study the early stages of spinodal decomposition (SD) in polymer--liquid-crystal mixtures by solving linearized time-dependent Landau-Ginzburg equations for concentration (conserved order parameter) and orientation (nonconserved order parameter). The theory takes into account a cross term between concentration and orientation gradients, which becomes an important factor for phase separation kinetics. We calculate structure factors for concentration and for orientation, depending on a quench temperature and concentration. We find a new SD process driven by instability of the orientational order parameter. In this case, the average domain size initially grows as a nontrivial and evolving power of time, which starts as ${t}^{1/3}$ in our minimal model. The domain growth is advanced by the coupling between the two order parameters.

A new kinetic description for phase separation of materials

This Letter presents a new kinetic description for phase separation of materials. The unstable non-uniform regions fluctuate to form the steadily critical non-uniform regions, which diffuse to grow by either nucleation growth or Spinodal decomposition mechanism. The equation describing fluctuation stage is c(r,t)−c0=Pcos(βWt)cos(β·r), and the equations describing diffusion stage are λ2=Ht (nucleation growth) and c(r,t)−c0=PQ2exp[R2(β)t]cos(β·r) (early stage of Spinodal decomposition). The process of forming a steadily critical non-uniform region is that the region size fluctuates near the critical one, the amplitude of fluctuation decreases gradually, and the composition of region tends to stable.

Phase separation kinetics in mixtures of flexible polymers and low molecular weight liquid crystals

SUMMARY: A dynamic Monte Carlo (MC) simulation is performed to investigate the phase behavior of mixtures of flexible polymers and low molecular weight thermotropic liquid crystals (LCs). The polymer is represented by three-dimensional self-avoiding lattice chains, while the LC is described by the LebwohlLasher nematogen model. The initially homogeneous rod-coil mixture is, following a deep quench, separated into an isotropic phase rich in coils and a nematic phase rich in rods. The underlying spinodal decomposition (SD) process is then simulated and studied extensively. This is the first simulation of SD in a rod-coil mixture where the nematic ordering is included. Concentration fluctuations with a conserved order parameter are thus coupled with orientation fluctuations with a nonconserved order parameter. It is found that the early stage SD in the rod-coil mixture still exhibits the dominant spatial wavelength and that the scalar scattering functions in the late stage of SD obey the Furukawa scaling law. The kinetic difference between the so-called isotropic and anisotropic SD regions is, however, much less pronounced than predicted recently by the mean-field theory.

Evolution of a dispersed morphology from a co-continuous morphology in immiscible polymer blends

We observed, via transmission electron microscopy, the evolution of a dispersed morphology from a modulated co-continuous morphology in immiscible blends of two amorphous polymers, poly(methyl methacrylate) (PMMA) and polystyrene (PS). Upon rapid precipitation of a homogeneous solution, which can be regarded as being equivalent to spinodal decomposition via temperature quenching, we observed a modulated co-continuous morphology for all three blend compositions, 70/30, 50/50, and 30/70 PMMA/PS blends. This observation is interpreted with the Cahn's linearized theory, which has been found to be accurate in describing phase separation in the early stage of spinodal decomposition. When a rapidly precipitated PMMA/PS blend specimen having asymmetric (70/30, 60/40, 55/45 or 30/70) blend composition was annealed under isothermal conditions at 170°C for varying periods, the modulated co-continuous morphology evolved into a dispersed morphology, in which the major component formed the continuous phase and the minor component formed the discrete phase, and into a `dual mode' of dispersed morphology in the symmetric (50/50) PMMA/PS blend. This observation is interpreted in terms of the percolation-to-cluster transition mechanism proposed by Hashimoto and co-workers. The morphology evolution, during isothermal annealing, of a rapidly precipitated blend may be regarded as being equivalent to late stages of spinodal decomposition, which is controlled by diffusion and coalescence. The rate of morphology development in PMMA/PS blend during isothermal annealing was found to depend on the zero-shear viscosity ratio of the constituent components. This observation is interpreted in terms of Siggia's theory for late stages of spinodal decomposition.