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 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.     

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.     

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.     

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.     

Kinetics of formation of polymer dispersed liquid crystals in a liquid-crystalline polymer matrix

With the use of optical polarization microscopy, the kinetics of phase separation during cooling of molten mixtures of a nematic low-molecular-mass liquid crystal and a liquid crystalline polymer is studied to produce polymer dispersed liquid crystals. The statistical drop-size distribution of a low-molecular-mass liquid crystal is described in the terms of equilibrium thermodynamics of irreversible processes. For a nematic polymer component of a mixture, the analysis of time dependences of the average diameter of drops of a low-molecular-mass liquid crystal makes it possible to reveal two stages in the kinetics of their growth and to describe this process according to the universal law of cluster growth. For a smectic polymer component, the Avrami equation is used to quantitatively describe the kinetics of growth of low-molecular-mass liquid-crystal drops.     

Kinetics of phase separation in polymer blends for deep quenches

Electro microscopy was used to study the phase separation kinetics of a polystyrene/polyvinylmethylether system subjected to a critical deep quench. The size of the phase-separated domains was found to increase linearly with time, implying that hydrodynamic effects control the rate of growth of the domains in the time scale and temperature range under consideration. From these measurements the growth velocity and approximate diffusion constants can be determined for three different temperatures. Comparison of these results with those obtained by light scattering on other systems and with theoretical predictions is possible by replotting in dimensionless units.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

Ｔｈｅｐｈａｓｅｂｅｈａｖｉｏｒｉｎｍｕｌｔｉｐｌｅｃｏｍｐｏｎｅｎｔｐｏｌｙｍｅｒｓｃｏｎｓｔｉｔｕｔｅｓａｌｏｎｇｓｔａｎｄｉｎｇａｃｔｉｖｅａｃａｄｅｍｉｃｓｕｂｊｅｃｔｂｏｔｈｉｎｐｏｌｙｍｅｒｓｃｉｅｎｃｅａｎｄｃｏｎｄｅｎｓｅｄｓｔａｔｅｐｈｙｓｉｃｓ.Ｉｔｉｓｅｓｐｅｃｉａｌｌｙｓｉｇｎｉｆｉｃａｎｔｉｎｇｕｉｄｉｎｇｔｈｅｆａｂｒｉｃａｔｉｏｎｏｆｐｏｌｙｍｅｒａｌｌｏｙｓ[1].Ｄｕｒｉｎｇｔｈｅｌａｓｔｄｅｃａｄｅｓｍｕｃｈａｔｔｅｎｔｉｏｎｈａｓｂｅｅｎｐａｉｄｔｏｔｈｅｃｏｍ…     

Flow of a liquid-crystalline polymer solution around an obstacle

The behaviour of an anisotropic solution of hydroxypropylcellulose around an obstacle is investigated in shear and during relaxation. Experiments were carried out with an optical rheometer equipped with transparent cone-and-plate. The obstacle is a 200 micron glass sphere stuck on the plate. A typical Reynolds number past the obstacle is about 10^-5. The flow of the anisotropic solution perturbed by the obstacle shows specific phenomena: distorted downstream streamlines, a very long wake behind the obstacle during shear which persists a long time after the ceasing shear, a change in the behaviour at very high shear rates and in particular, the appearance of a wake in front of the obstacle. To date there has not been any theoretical bases with which to explain these new findings. An interesting point is that the wake behind the obstacle is a good illustration of the problem of weldlines in injection moulding.     

Kinetics of polymer decomposition

Kinetic equations have been developed for polymers that decompose by the zipper mechanism. The usual assumption of steady state kinetics has not been made. Plots of the fraction decomposed α, as a function of time demonstrate a variety of patterns depending upon the relative values of the fraction k₁, of chains becoming activated per second and the fraction k₂ of an activated chain that decomposes per second.     

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.     

Kinetics of thermally induced phase separation in ternary polymer solutions. I. Modeling of phase separation dynamics

Simulations based on Cahn–Hilliard spinodal decomposition theory for phase separation in thermally quenched polymer/solvent/nonsolvent systems are presented. Two common membrane‐forming systems are studied, cellulose acetate [CA]/acetone/water, and poly(ethersulfone) [PES]/dimethylsulfoxide [DMSO]/water. The effects of initial polymer and nonsolvent composition on the structure‐formation dynamics are elucidated, and growth rates at specific points within the ternary phase diagram are quantified. Predicted pore growth rate curves exhibit a relative maximum with nonsolvent composition. For shallow quenches (lower nonsolvent content) near a phase boundary, the pore growth rate increases with increasing quench depth, whereas for deep quenches, where the composition of the polymer‐rich phase approaches that of a glass, the pore growth rate decreases with increasing quench depth. With increasing initial polymer concentration, the overall rate of structure growth is lowered and the growth rate maximum shifts to higher nonsolvent compositions. This behavior appears to be a universal phenomenon in quenched polymer solutions which can undergo a glass transition, and is a result of an interplay between thermodynamic and kinetic driving forces. These results suggest a mechanism for the locking‐in of the two‐phase structure that occurs during nonsolvent‐induced phase inversion. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1449–1460, 1999     

Percolation-to-droplets transition during spinodal decomposition in polymer blends, morphology analysis

Phase separation kinetics of the off-critical mixture of polystyrene and poly(methylphenylsiloxane) is studied by the time-resolved light scattering and optical microscopy. The results from the light scattering experiments are correlated with the images obtained by the optical microscopic observation in order to find characteristic features of the scattering intensity during the percolation-to-droplets morphology transition. At the beginning of the spinodal decomposition process only a bicontinuous network is present in the system and the light scattering intensity has only one peak. The network coarsens and at the same time small droplets appear in the system resulting in a growth of the scattering intensity at very small wave vectors. When the large network starts to break up into disjoint elongated domains a second peak in the scattering intensity appears. Finally, both peaks merge into a single peak at zero wave vector, indicating a complete transformation of elongated domains into spherical droplets of variable sizes. The comparison of the direct microscopic observations with the light scattering spectra shows that the process of breaking up of the bicontinuous network starts when the growth of the first peak, corresponding to the bicontinuous pattern, becomes very slow (essentially pinned down).     

Diffusion and phase separation in polymer solution during asymmetric membrane formation

Most of the commercially available polymeric membranes are prepared by the phase inversion process. In this process a thermodynamically stable polymer solution is brought to phase separation by immersing the solution in a surplus of nonsolvent, followed by an exchange of solvent and nonsolvent. The ultimate membrane structure is the result of an interplay of mass transfer and phase separation. Asymmetric membranes as well as symmetrical porous membranes can be obtained. Two types of demixing processes (l-l phase separation and formation of aggregates) can be distinguished by the kinetics of phase separation, as the formation of aggregates is supposed to be a slower process than l-l demixing. Because it is impossible to measure the composition changes during the demixing processes experimentally, a theoretical analysis has to be applied. A suitable formalism to calculate the diffusion induced composition changes in the immersed casting solution, as a function of thermodynamic and hydrodynamic interaction parameters will be described. With this theory it can be shown that two distinctly different mechanisms of membrane formation may occur resulting in two different types of membranes. One type has a relatively thick toplayer and mostly exhibits reverse osmosis, gas separation and pervaporation properties; the other type results in a porous type of membrane, which will exhibit ultra- and microfiltration properties. Model calculations are in agreement with light transmission experiments on membrane forming systems. Therefore, it could be concluded that the elucidation of the diffusion behavior in the immersed polymer film is the key to better understanding of membrane formation by means of immersion precipitation.     

New polymer liquid-crystalline CdS nanocomposites forming a chiral nematic phase

A new approach has been developed for the design of liquid-crystalline polymer nanocomposites combining the unique properties of polymer cholesterics and quantum dots of CdS.     

Two‐dimensional model of phase separation of the binary polymer blend in spinodal and binodal regions

It had been shown in two‐dimension case that the Chan‐Hilliard‐de‐Gennes model describes the processes of phase separation both in spinodal and metastable regions. The nature of the structures birth different for different regions. It is rigid in metastable regions, while in spinodal regions it may be both rigid and smooth. Analytical expression for the boundaries separating the regions with rigid and smooth birth of the structures is obtained.     

Kinetics of phase separation in polymer blends. Calculations based on nonlinear theory

Suzuki's scaling theory for transient phenomena is applied to the calculation of the kinetics of phase separation in the early-to-intermediate stage based on a nonlinear theory proposed by Langer, Bar-on, and Miller (LBM). Calculated results are compared with experimental data on light scattering from a polymer blend system. Deviations from predictions of Cahn's linearized theory in the early time range of phase separation can be explained well by the proposed method of calculation. Nonlinear effects are found to play an essential role in characterizing the light scattering behavior of phase separation in the intermediate stage. Time evolutions of the single-point distribution function of composition are calculated, and the results are in good agreement with those reported in digital imaging analysis experiments and computer simulations of the time-dependent Ginzburg-Landau equation. The influence of asymmetry of free-energy on the single-point distribution function is also investigated in this study. © 1993 John Wiley & Sons, Inc.     

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.