Nonlinear kinetics of spinodal decomposition,and dissolution of inhomogeneities formed by spinodal decomposition in polymer blends

Nonlinear kinetics of both spinodal decomposition at early stages, and the dissolution of homogeneities formed during spinodal decomposition, is studied. Variation of the scattering intensity during a complete cycle consisting of a step temperature change from T₁ in the one-phase region to T₂ in the two-phase region, a period of spinodal decomposition followed by a temperature drop from T₂ back to T₁, and the subsequent relaxation to the original equilibrium state, is investigated at various wavenumbers. Step temperature changes within one-phase region are also investigated.     

Computational analysis of spinodal decomposition dynamics in polymer solutions

In this work a model, composed of the nonlinear Cahn-Hilliard and Flory-Huggins theories, is used to numerically simulate the phase separation and pattern formation phenomena of oligomer and polymer solutions when quenched into the unstable region of their binary phase diagrams. This model takes into account the initial thermal concentration fluctuations. In addition, zero mass flux and natural nonperiodic boundary conditions are enforced to better reflect experimental conditions. The model output is used to characterize the evolution and morphology of the phase separation process. The sensitivity of the time and length scales to processing conditions (initial condition c) and properties (dimensionless diffusion coefficient D) is elucidated. The results replicate frequently reported experimental observations on the morphology of spinodal decomposition (SD) in binary solutions: (1) critical quenches yield interconnected structures, and (2) off-critical quenches yield a droplet-type morphology. As D increases, the dominant dimensionless wave number k increases as well, but the dimensionless transition time t from the early stage to the intermediate stage decreases. In addition, t is shortest when c is at the critical concentration, but increases to infinity when c is at one of the two spinodal concentrations. These results are found when the solute degree of polymerization N₂ is in the range 1 ≤ N₂ ≤ 100. When N₂ > 100, however, a problem of numerical nonconvergence due to diverging relaxation rates occurs because of the very unsymmetric nature of the phase diagram. A novel scaling procedure is introduced to explain the phase separation phenomena due to SD for any value of N₂ during the time range explored in this study.     

Viscoelastic effects on early stage of spinodal decomposition in dynamically asymmetric polymer blends

Spinodal decomposition induced by a rapid pressure change was investigated for a dynamically asymmetric polymer blend [deuterated polybutadiene (DPB)/polyisoprene (PI)] with a composition of 50/50 wt/wt by using time-resolved small angle neutron scattering. The time change in the scattered intensity distribution with wave number (q) during the spinodal decomposition was found to be approximated by the Doi-Onuki theory [M. Doi and A. Onuki, J. Phys. II 2, 1631 (1992)]. The theoretical analysis yielded the q dependence of the Onsager kinetic coefficient which is characterized by the q(-2) dependence at qxive > 1 with the characteristic length xive being much larger than the radius of gyration of DPB or PI. The estimated xive agrees well with that obtained previously in the relaxation processes induced by pressure change within the one phase region for the same blend.     

Lamellar morphology induced by two-step surface-directed spinodal decomposition in binary polymer mixture films

A novel process for obtaining ordered morphology on the basis of two-step surface-directed spinodal decomposition is numerically investigated. The formation mechanism and evolution dynamics of this process are also discussed in detail. The calculated results of the chemical potential demonstrate that the equilibration state at the first quench affects the competition between the surface potential and the chemical potential in the bulk, leading to a surprising lamellar structure at the second further quench. It is also found that the lamella formation obeys the logarithmic growth. These results could provide a new approach for fabricating ordered structure of polymer materials and stimulate experimental studies based on this subject.     

Digital image analysis of polymer blends morphology

Application of digital image analysis (DIA) to polymer blends morphology is discussed with examples. Various operations in DIA including two-dimensional Fourier transformation (2DFT), intensity distribution, recursive region extraction, etc. are applied to morphology of polymer blends due to spinodal decomposition (SD), nucleation 6 growth (NG), and eutectic solidification (ES). Merits and drawbacks of DIA to study polymer blends morphology are discussed and the possibility of future development is presented.     

Homogeneous crystal nucleation triggered by spinodal decomposition in polymer solutions

We report dynamic Monte Carlo simulations of polymer crystal nucleation initiated by prior spinodal decomposition in polymer solutions. We observed that the kinetic phase diagrams of homogeneous crystal nucleation appear horizontal in the concentration region below their crossovers with the theoretical liquid-liquid spinodal. When the solution was quenched into the temperature beneath this horizontal boundary, the time evolution of structure factors demonstrated the spinodal decomposition at the early stage of crystal nucleation. In comparison with the case without a prior liquid-liquid demixing, we found that the prior spinodal decomposition can regulate the nanoscale small polymer crystallites toward a larger population, more uniform sizes, and a better spatial homogeneity, whereas chain folding in the crystallites seems little affected.     

Cluster kinetics and dynamics during spinodal decomposition

Spinodal decomposition (barrierless phase transition) is a spontaneous phase separation caused by conditions that force the system to become thermodynamically unstable. We consider spinodal decomposition to occur under conditions of large supersaturation S and/or small ratio of interfacial to thermal energies omega, such that the computed number of monomers in a critical nucleus xi*=(omega/ln S)3 is less than unity. The small critical nucleus size is consistent with a negligible energy barrier for initiating condensation. Thus, in contrast to conventional opinion, it is suggested that the spinodal decomposition is related to the homogeneous nucleation of metastable fluids. Population balance equations show how clusters aggregate and rapidly lead to phase separation. Different mass dependences of aggregation rate coefficients are proposed to investigate the fundamental features of spinodal decomposition. When the mass dependency is an integer, the equations are solved by the moment technique to obtain analytical solutions. When the mass dependency is a noninteger, the general cases are solved numerically. All solutions predict the two time regimes observed experimentally: the average length scale of condensed-phase domains increases as a power law with an exponent of 1/3 at early times, followed by a linear increase at longer times.     

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

Time-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.     

Glass transition temperatures in binary polymer blends

Knowledge of the glass transition temperatures (T_gs) as function of composition reflects miscibility (or lack of it) and is decisive for virtually all properties of polymer‐based materials. In this article, we analyze single blend‐average and effective T_gs of miscible polymer blends in full concentration ranges. Shortcomings of the extant equations are discussed to support the need for an alternative. Focusing on the deviation from a linear relationship, defined as ΔT_g = T_g ? φ₁T_g,1 ? φ₂T_g,2 (where φ_i and T_g,i are, respectively, the weight fraction and the T_g of the i‐th component), a recently proposed equation for the blend T_g as a function of composition is tested extensively. This equation is simple; a quadratic polynomial centered around 2φ₁ ? 1 = 0 is defined to represent deviations from linearity, and up to three parameters are used. The number of parameters needed to describe the experimental data, along with their magnitude and sign, provide a measure of the system complexity. For most binary polymer systems tested, the results obtained with the new equation are better than those attained from existing T_g equations. The key parameter of the equation a₀ is related to parameters commonly used to represent intersegmental interactions and miscibility in binary polymer blends. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 80–95, 2008     

Kinetics of phase separation by spinodal decomposition in a liquid-crystalline polymer solution

Time-resolved light scattering studies have been undertaken for elucidating the dynamics of phase separation in aqueous HPC (hydroxypropyl cellulose) liquid-crystalline solutions. The HPC/water system phase separates during heating and returns to a single phase upon cooling. The phase diagram of thermally induced phase separation was subsequently established on the basis of cloud point measurements. For kinetic studies, T (temperature) jump experiments of 10 per cent aqueous HPC solutions were undertaken. Phase separation occurs in accordance with the spinodal decomposition mechanism. At low T jumps or in reverse quenched experiments, the scattering maximum remains invariant as predicted by the linearized Cahn-Hilliard theory. However, at large T jumps, the SD is dominated by non-linear behaviour in which scattering peaks move to low scattering angles. The latter process has been identified to be a coarsening mechanism associated with the coalescence of phase separated domains driven by a surface tension. A reduced plot has been established with dimensionless variables Q and t. It was found that the scaling law is not valid over the entire spinodal process. The time evolution of the scattering profiles of 10 per cent HPC solutions, following a Tjump to 49°C, is tested with the scaling law of Furukawa. It seems that the kinetics of phase separation at 10 per cent solution resemble the behaviour of off-critical mixture.     

Kinetics of phase separation by spinodal decomposition in a liquid-crystalline polymer solution

Abstract

Time-resolved light scattering studies have been undertaken for elucidating the dynamics of phase separation in aqueous HPC (hydroxypropyl cellulose) liquid-crystalline solutions. The HPC/water system phase separates during heating and returns to a single phase upon cooling. The phase diagram of thermally induced phase separation was subsequently established on the basis of cloud point measurements. For kinetic studies, T (temperature) jump experiments of 10 per cent aqueous HPC solutions were undertaken. Phase separation occurs in accordance with the spinodal decomposition mechanism. At low T jumps or in reverse quenched experiments, the scattering maximum remains invariant as predicted by the linearized Cahn-Hilliard theory. However, at large T jumps, the SD is dominated by non-linear behaviour in which scattering peaks move to low scattering angles. The latter process has been identified to be a coarsening mechanism associated with the coalescence of phase separated domains driven by a surface tension. A reduced plot has been established with dimensionless variables Q and t. It was found that the scaling law is not valid over the entire spinodal process. The time evolution of the scattering profiles of 10 per cent HPC solutions, following a Tjump to 49°C, is tested with the scaling law of Furukawa. It seems that the kinetics of phase separation at 10 per cent solution resemble the behaviour of off-critical mixture.     

Rheology and morphology of compatibilized polymer blends

Research into the compatibilization of immiscible polymer blends has, during the past few years, begun to focus on the role of block co-polymers (bcp) on various morphological processes. Considerable advances have been made, from both a theoretical and an experimental point of view, in relating the presence of compatibilizers to structure development during flow.     

Processing/morphology/rheology relationships in polymer blends

In this paper certain aspects concerning the influence of rheological parameters on the morphology of immiscible polymer blends are considered. The author reviews his own work with reference to other key studies carried out in the field. The influence of the viscosity ratio on morphology for compatibilized and non-compatibilized systems are treated, as well as the influence of shear stress. The role of viscosity and viscosity ratio in controlling co-continuous and complex composite droplet morphologies are also discussed.     

The crystallization and morphology of melt-miscible polymer blends

The morphology and kinetics of crystallization from melt-miscible blends is reviewed for binary systems in which either one or both polymer components are crystallizable. In systems in which one component (component A) crystallizes first, the other component (B) may reside finally between spherulites, between growth arms (composed of a stack of A crystalline lamellae), or between crystal lamellae of A. The kinetics of component redistribution dictates which site must become primary. It is shown that the diffusivity D of the components in the melt and the velocity V of spherulite growth combine through the diffusion length δ = D/V to define the final location for component B and to also define whether spherulite propagation will be linear or parabolic in time. When crystallization of both components proceeds concurrently, by forming spherulites of A and of B, the spherulites are prone to interpenetrate or to form concentric spherulites. Cooperative crystallization, in which the kinetics of a rapidly crystallizing component and a slowly crystallizing component are both affected such that the two crystallize nearly simultaneously, is discussed. Finally, the competition between liquid-liquid phase separation and crystallization in systems with either an upper or lower critical solution temperature is reviewed.     

Enthalpic relaxation and the glass transition in polymer blends

The kinetics of enthalpic relaxation are reviewed and applied to the ageing of a range of blends made from polyether imide and polyether ether ketone. DSC has been used to follow the development of enthalpic relaxation and a Williams-Watt stretched exponential equation relating the extent of relaxation, ϕ(t), to the ageing time t and an average relaxation time, t́_a', has been used to quantify the ageing process. where β' is inversely related to the breadth of the relaxation spectrum such that 0<β>1.0. The relationship was modified to incorporate non-linearity in the relaxation behaviour. ϕ(t) was measured directly from the enthalpy change observed in the endotherms on heating aged specimens through the glass transition in the DSC. The PEI/PEEK blends were compatible over the full composition range in that they exhibited a single glass transition with a temperature that varied almost linearly with composition between those of the homopolymers. Enthalpic relaxation was found to be a useful technique for probing the molecular relaxations of polymer blends and confirming the degree of compatibility of the system. The β' values changed systematically with the blend composition between those of the homopolymers suggesting that the breadth of the relaxation spectra were similar in the blends to that in the homopolymers. Physical ageing was observed to embrittle the blends, and there was a close correlation between the extent of enthalpic ageing and the change in mechanical and impact behaviour. The yield stress increased and the elongation to break decreased progressively with ϕ(t) in addition to a reduction in impact strength. The model of enthalpic relaxation and the kinetic relationships, outlined above, have been used to determine the onset of the glass transition temperature and subsequent progress of enthalpic relaxation at fixed ageing temperatures, for direct comparison with the change in specific heat observed in DSC experiments. Good agreement was observed between experiment and calculated glass transitions and the effect of variables, such as activation enthalpies, pre-exponential factors, non-linear factors such as X and β' and fictive temperature on the observed glass transition temperatures and the temperature range over which the glass transition occurred determined. Modifications to the model for the enthalpic relaxation have been suggested.     

Influencing the morphology of polymer blends through graft copolymers

Graft copolymers have a potential as compatibilizers in two-component thermoplastic polymer blends, and also as impact-modifiers in one-component thermoplastics. The compatibility of the blocks of the copolymer (i.e. the grafts and the main chain) with the chains of the matrix polymers must be adjusted carefully. Blends of various polymers, especially of polystyrene (PS) and poly(vinyl chloride) (PVC), with graft copolymers on the basis of polybutadiene are discussed. An excellent compatibilizer, for blends PS/PVC, is a block-graft copolymer, derived from a diblock copolymer of Styrene and butadiene, with grafts of cyclohexyl methacrylate monomelic units.     

The early stage of the morphology development of immiscible polymer blends during melt blending: Compatibilized vs. uncompatibilized blends

The early stage of the morphology development has been studied for the blending of two immiscible polymers. Controlled experiments were carried out in a batch mixer in such a way that the rate of melting was low enough to follow up the morphology development of dilute and concentrated systems. For a dilute or semidilute polypropylene and polyamide 6 (PP/PA6) blend with 0.5, 5, or 10 wt % PA6, particles formed in the very early stage of melt blending were very small, of the order of 0.25 to 0.3 μm in radius. They immediately began to grow in size when no compatibilizer was added, indicative of coalescence even in the very early stage of melt blending and/or in very dilute systems (0.5 wt % PA6). Further growth of the particles was eliminated with the introduction of a graft copolymer compatibilizer providing evidence of the stabilizing effect of the copolymer from the very beginning of melting blending. However, the behavior of the morphology development of a concentrated PP/PA6 (80/20) system was similar to that reported in the literature. The average radius of the particles of the uncompatibilized blend decreased with increasing mixing time, whereas that of the compatibilized blend remained almost constant during mixing. The most favorable conditions to obtain a fine morphology seems to be the following: rate of melting/plastification of pellets < rate of dispersion (deformation + breakup) of the polymer melt to small particles < rate of stabilization (with an adequate copolymer). © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 601–610, 2001     

Rheology and morphology of polymer blends in melt and solid state

The rheological properties of polymer mixture melts containing polysulfone and LC-polyester have been investigated in this work in terms of the morphology and physical-mechanical characteristics of extrudates. The perculiarities of rheological behaviour are accounted for by morphology of stream which is maintained also in solid extrudates. The reinforcement of an isotropic mixture by LC-polymers as well as formation of an anisotropic surface layer lead to a specific change in the strength properties of compositions. An increase in strength and initial modulus was observed for blends containing not more than 10% LC-polymer.     

Kinetics of phase separation at the early stage of spinodal decomposition in epoxy resin modified with PEI blends

The behavior at the early stage of spinodal decomposition (SD) for polyetherimide (PEI)/epoxy blends was investigated. It was found that the phase separation of PEI/epoxy blends took place by SD mechanism. The development of molar mass in the epoxy resin was gradual and then the three blends could still be considered as concentrated solutions of thermoplastic. The kinetics at the early stage of phase separation for these blends could be described by the Cahn–Hilliard–Cook linearized theory.