A Computational Study of the Polymerization‐Induced Phase Separation Phenomenon in Polymer Solutions under a Temperature Gradient

This paper studied the polymerization‐induced phase separation phenomenon (spinodal decomposition) in a model binary polymer solution under a linear spatial temperature gradient for the purpose of fabricating anisotropic polymeric materials by using mathematical modeling and computer simulation. Reaction kinetics were incorporated with the non‐linear Cahn‐Hilliard theory and the Flory‐Huggins free energy expression in the model. Moreover, the slow mode theory and Rouse law were used to account for polymer diffusion. It was found that an anisotropic morphology was obtained when a temperature gradient was imposed along the polymer solution sample. The direction of the structural anisotropy, however, depended significantly on the overall phase separation time. The presence of a temperature gradient along the polymer solution sample generated a spatial variation in polymerization rate, which resulted in a spatial variation of quench depth. Consequently, at a given instant, the phase separation at different locations of the polymer solution was at different stages of spinodal decomposition. The droplet size formed along the polymer solution was therefore dependent on the polymerization rate, the quench depth and the stage of spinodal decomposition. Furthermore, the spatial temperature gradient produced a spatial variation in the process induction time, which contains the polymerization induction time and phase separation induction time. It was also found that the polymerization induction time played a significant role on the spatial variation in the overall process induction time.

     

Wetting-layer formation mechanisms of surface-directed phase separation under different quench depths with off-critical compositions in polymer binary mixture

Focusing on the off-critical condition, the quench depth dependence of surface-directed phase separation in the polymer binary mixture is numerically investigated by combination of the Cahn-Hilliard-Cook theory and the Flory-Huggins-de Gennes theory. Two distinct situations, i.e., for the wetting, the minority component is preferred by the surface and the majority component is preferred by the surface, are discussed in detail. The simulated results show that the formation mechanism of the wetting layer is affected by both the quench depth and the off-critical extent. Moreover, a diagram, illustrating the formation mechanisms of the wetting layer with various quench depths and compositions, is obtained on the basis of the simulated results. It is found that, when the minority component is preferred by the surface, the growth of the wetting layer can exhibit pure diffusion limited growth law, logarithmic growth law, and Lifshitz-Slyozov growth law. However, when the majority component is preferred by the surface, the wetting layer always grows logarithmically, regardless of the quench depth and the off-critical extent. It is interesting that the surface-induced nucleation can be observed in this case. The simulated results demonstrate that the surface-induced nucleation only occurs below a certain value of the quench depth, and a detailed range about it is calculated and indicated. Furthermore, the formation mechanisms of the wetting layer are theoretically analyzed in depth by the chemical potential gradient.     

Uniform to Accelerated Crystal Twisting Transition in Deuterate Polyethylene/Poly（ethylene-alt-propylene） Blend Films

A uniform to accelerated crystal twisting transition is observed in deuterate polyethylene/poly（ethylene-alt- propylene） （d-PE/PEP） blend films. And the band period is a function of initial d-PE concentration, quench depth and annealing time of phase separation. As Keith and Padden suggested, twisting of lamella is due to the unbalanced stress on its both sides, which can supply a satisfying explanation to banded spherulites formed in homogeneous systems. When it comes to d-PE/PEP blend system, in homogeneous 99% d-PE/PEP （weight fraction of d-PE） blend film, the formation of banded spherulite is observed as a result of uniform twisting of ribbon like d-PE lamellae along the radial direction. With the amorphous PEP piling up, it transfers into accelerated edge-on to fiat-on twisting due to crystallization assisted phase separation. The mechanism can be interpreted as following： d-PE molecules must inter-diffuse to the twisting growth front to continue the secondary nucleation and growth process. Meanwhile, the amorphous PEP molecules are rejected and accumulated at the twisting growth front. Once the d-PE lamella begins to twist because of unbalanced stress on both sides, the accumulated rubber phase at the growth front strengthens the unbalance and accelerates the edge-on to flat-on twisting. The concentration wave propagates further away with constant speed, and leads to concentric ring pattern with periodic nonuniform twisting along the radial direction. Since this is a kinetic effect, the band period can be controlled through initial d-PE concentration, quench depth and annealing time of phase separation. Our result shows that crystallization assisted phase separation can modify lamella growth kinetic pathway, thereby assisting concentric ring pattern formation.     

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     

混合高聚物分相过程标度、分形与Monte Carlo模拟

基于光散射、Monte Carlo模拟标度理论和分形(Fractal)概念研究和分析了高分子混合体系不稳相分离过程结构函数的标度行为和成因, 结果表明相分离的形态是一种分形结构, 其分形维数不随时间变化. 结构函数的标度行为起源于相态的分形结构. 相态的分形结构是不稳相分离特征之一.     

Phase separation by continuous quenching: similarities between cooling experiments in polymer blends and reaction-induced phase separation in modified thermosets

Small angle light scattering (SALS) has been applied to study the phase separation kinetics in a binary polymer mixture of poly(ethyl methyl siloxane) (PEMS) and poly(dimethyl siloxane) (PDMS). The phase separation was induced by cooling an initially homogeneous mixture with well defined cooling rates. The results have been compared to time resolved SALS and microscopy in the course of reaction-induced phase separation in mixtures of an epoxy resin and polysulfone (PSU). For the critical PEMS/PDMS mixture with an upper critical point it was found in a continuous quenching experiment that the time evolution of the scattered light intensity I(q,t) scales with the cooling rate. The similarity to the scaling behavior of I(q,t) in isothermal experiments after fast quenches (scaled by the quench depth) is discussed. A secondary phase separation was found and has been explained by the competition between the growth of the two phase structure during cooling and the mutual diffusion without the assumption of gelation or vitrification. For the epoxy/PSU mixture with 15% PSU, after the appearance of a bicontinuous structure a secondary phase separation was observed. Mixtures with higher PSU-contents formed epoxy-rich droplets in the PSU-rich matrix by nucleation and growth mechanism. The frustration of the structure growth can be explained by approaching vitrification of one or both phases. The similarity between continuous cooling experiments in blends and the reaction-induced phase separation have been discussed in the generalized χN vs. composition phase diagram (N: degree of polymerization, χ: Flory-Huggms interaction parameter).     

Spinodal patterns indicating unstable regime of polymer crystallization

It has been considered that crystallization of polymer from melt proceeds via the coexistence of molten matrix and growing crystals that have once overcome a nucleation barrier to a critical size. The nucleation process has often been explained analogously with so-called nucleation and growth (NG) behavior of the phase separation of a binary mixture in metastable conditions, although the crystallization in one-component polymer is not a real component separation but a phase transition. Among the mechanisms of polymer crystallization, the topic is whether a liquid–liquid transition between states of different densities within one-component polymers takes place before the aforementioned nucleation process. The liquid–liquid transition between states, which is probably driven by chain orientation, is also categorized into NG and the controversial spinodal decomposition (SD) type processes depending on the quenching depth. This article provides the optical microscopic observations that favor the occurrence of the SD-like process when a one-component polymer melt is very rapidly quenched below a stability limit, including a drastic morphological change from a spherulitic to a spinodal pattern at the critical (or spinodal) temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1817–1822, 2004     

The phase dynamics and wetting layer formation mechanisms in two-step surface-directed spinodal decomposition

The two-step quench process of surface-directed spinodal decomposition is numerically investigated by coupling the Flory-Huggins-de Gennes equation with the Cahn-Hilliard-Cook equation. The phase dynamics and formation mechanisms of the wetting layer in two-step surface-directed spinodal decomposition have been concerned in detail. The results demonstrate that a parallel strip structure forms near the wetting layer and propagates into the bulk, when the first quench depth is very shallow and the bulk does not undergo phase separation, and the second quench depths are various points with deeper quench depths. In this case, the wetting layer turns to be unchangeable at the intermediate and later stages of the second quench process, compared to the growth with a time exponent 1/2 during the first quench process. When the first quench depth is deeper and phase separation occurs in the bulk during the first quench process, it is found that a deeper second quench depth can stimulate a more obvious secondary domain structure, and the formation mechanism of the wetting layer changes from logarithmic growth law to Lifshitz-Slyozov growth law.     

Destabilization of polystyrene latex particles induced by adsorption of polyvinylamine: mass, size and structure characteristics of the growing aggregates

The obviously visible aggregation of suspended colloidal particles resulting from the addition of polyvinylamine to the aqueous dispersion of polystyrene latex particles bearing surface sulfate groups set in with a delay of 24 h. The aggregation mechanisms and the fractal dimension of the aggregates were derived from the variations with time of the weight and number averaged masses of the aggregates as well as of the weight averaged harmonic mean diameter of the size distribution. Since the establishment of starved layers was determined to be relatively fast and to leave the liquid phase free of polymer, the delay for the obvious destabilization was attributed to the reconformation of adsorbed macromolecules that was expected to be extremely slow. This reconformation promoted the emergence of the diffusion-limited aggregation process that accompanies the permanent reaction-limited aggregation process. The fractal dimension of the latex particles/polyvinylamine aggregates was determined to be 2.12.     

A mimetic porous carbon model by quench molecular dynamics simulation

A mimetic porous carbon model is generated using quench molecular dynamics simulations that reproduces experimental radial distribution functions of activated carbon. The resulting structure is composed of curved and defected graphene sheets. The curvature is induced by nonhexagonal rings. The quench conditions are systematically varied and the final porous structure is scrutinized in terms of its pore size distribution, pore connectivity, and fractal dimension. It is found that the initial carbon density affects the fractal dimension but only causes a minor shift in the pore size distribution. On the other hand, the quench rate affects the pore size distribution but only causes a minor shift in the fractal dimension.     

Surface-directed phase separation via a two-step quench process in binary polymer mixture films with asymmetry compositions

Surface-directed phase separation via a two-step quench process in asymmetry polymer mixtures is numerically investigated by coupling the Flory-Huggins-de Gennes equation with the Cahn-Hilliard-Cook equation. Two distinct situations, i.e., the minority component is preferred by the surface and the majority component is preferred by the surface, are discussed, respectively. The morphology and evolution dynamics of the phase structure, especially the secondary domain structure, are analyzed. The wetting layer formation mechanisms during the two-step quench process are examined. The simulated results demonstrate that different secondary domain structures in these two situations can be induced by the second quench with deeper quench depth, which can be used to tailor phase morphology. It is also found that, in the second quench process, the evolution of the wetting layer thickness can cross over to a faster growth when the preferential component is the minority component. In this situation, the formation mechanism of the wetting layer will change and is eventually determined by the second quench depth. However, when the preferential component is the majority component, a deeper second quench depth corresponds to a slower growth of the wetting layer thickness. The chemical potential is calculated to explain the difference regarding the growth dynamics of the wetting layer thickness between these both situations.     

Does conventional nucleation occur during phase separation in polymer blends?

The kinetics of liquid–liquid phase separation in off-critical polymer blends was studied with time-resolved small-angle neutron scattering. Our objective was to study the nature of the nuclei that formed during the initial stages of the phase transition. The blends were composed of model polyolefins—deuterium-labeled poly(methyl butylene) (PMB) and poly(ethyl butylene) (PEB)—with molecular weights of about 200 kg/mol. A direct examination of the initial clustering of molecules before macroscopic phase separation was possible because of the large size of the polymer chains and concomitant entanglement effects. We discovered that the scattering profiles obtained during nucleation merged at a well-defined critical scattering vector. We propose that this is the signature of the critical nucleus and that the size of the critical nucleus is inversely proportional to the magnitude of the critical scattering vector. The kinetic studies were preceded by a thorough characterization of the equilibrium thermodynamic properties of our PMB/PEB blends. The locations of the binodal and spinodal curves of our system are consistent with predictions based on the Flory–Huggins theory. This combination of thermodynamic and kinetic experiments enabled the quantification of the dependence of the size and structure of the critical nuclei on the quench depth. Our results do not agree with any of the previous theories on nucleation. Some aspects of our results are addressed in recent theoretical work by Wang in which the effects of fluctuations on the classical binodal and spinodal curves in polymer blends are incorporated. Both theory and experiment support the notion that the traditional stability limit (spinodal) should be replaced by a metastability limit. Although Wang's theory provides an explanation for some of our observations, many fundamental issues regarding nucleation in polymer blends remain unresolved. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1793–1809, 2004     

Neutron scattering and monte carlo determination of the variation of the critical nucleus size with quench depth

We have used a combination of neutron scattering experiments and Monte Carlo simulations to study the initial stages of first-order phase transitions. We focus on quenches wherein the nascent phase is formed by homogeneous nucleation, and we approach the spinodal, i.e., the quench depth at which the original phase becomes unstable. In this regime, we show how critical nuclei sizes are determined from neutron scattering structure factors. Prevailing thought is that the size of the critical nucleus should increase with increasing quench depth and diverge at the spinodal. To the contrary, our experiments and simulations indicate that the critical nucleus size decreases monotonically as quench depth is increased and is finite at the spinodal.     

聚合物共混物的相容性及相分离

综述了聚合物共混物相容性和相分离的研究现状。介绍了聚合物共混物的相容性理论,影响相容性的因素及改善和相容性的方法和表征相容性的手段。聚合物共混物的相分离机理制约着材料的性能,旋节分离和成核－增长相分离分别形成不同的形态结构。旋节分离和成核－增长相分离所对应的动力学过程是不同的,散射光强与相分离时间分别满足指数和幂指数关系。     

Associative phase separation of beta-lactoglobulin/pectin solutions: a kinetic study by small angle static light scattering

Interpolymer complexation between beta-lactoglobulin (beta-lg) and pectin led to phase separation. Small angle static light scattering and phase contrast microscopy were used to monitor the phase separation of beta-lg/low-methoxyl or high-methoxyl-pectin (LM- or HM-pectin) dispersions as they were slowly acidified from pH 7 to 4 with glucono-delta-lactone (GDL). The monotonic decrease in scattered light intensity with the wave vector was associated with a nucleation and growth phase separation mechanism. Microscopic observations and turbidity measurements showed the increase of complex amounts with lower pH and at higher beta-lg/pectin ratios. The formation of intrapolymer complexes was initiated at pH 6.4 with the LM-pectin and at pH 5.0 with the HM-pectin. Local ordering with increasing amounts of small complexes was observed as scattered light intensity increased at intermediate q values. The beta-lg/LM-pectin complexes at the 5:1 and the 2:1 weight ratios and the beta-lg/HM-pectin complexes at 5:1 weight ratio have fractal structures. The formation of large amounts of small assemblies and sedimentation would be responsible for the decrease in the number and volume mean diameters and fractal dimension of beta-lg/LM-pectin complexes over time.     

多相聚合物体系熔体动态过程中相形成与发展——PS/PcBR非相容体系的扫描电子显微镜图样分析

以连续共混过程间歇出料法研究了PS/PcBR非相容体系共混过程中的扫描电子显微镜图样演化过程 ,从平均粒径、特征长度Λ和平均特征长度Λm 多个方面讨论了非相容体系的共混过程 ,并以标度函数P(Λ/Λm)证明非相容体系共混过程在一定时间和空间范围内具有自相似性 ,且分形维数D可以作为一个参数描述熔体动态过程     

Viscoelastic Effects on the Dynamics of Spinodal Decomposition in Binary Polymer Mixtures

Numerical simulations based on the modified time‐dependent Ginzburg‐Landau (TDGL) equation have been performed on the domain growth dynamics of binary polymer mixtures. An elastic relaxation term was introduced into the equation to take the entanglement effects of the polymer chains into account. A cell dynamical scheme (CDS) is employed in this paper to improve the computing efficiency. The dynamics of the phase separation in polymer blends was investigated through to a very late stage. In the system without viscoelastic effects, there exists an apparent early stage, and in the late stage the modified Lifshitz‐Slyozov law and dynamical scaling law are satisfied very well. In the system with viscoelastic effects, there are some unique characteristics. A morphology with a rough interface between the domains is obtained and suppression of order‐parameter fluctuations is observed. The growth behavior of domains was altered, and there exits an intermediate stage between the early and late stage, in which the growth rate of domains slows down drastically. The intermediate stage was prolonged with enhanced entanglement effects. Entanglement effects also enhance the quench‐depth effects on the correlation and diminish the discrimination of correlation induced by criticality. After the relaxation of entanglements, the growth exponents with the model employed in this paper are independent of entanglements and are essentially consistent with the modified Lifshitz‐Slyozov law. In addition, the pair correlation function and the structure function are shown to exhibit the dynamical scaling law at the late stage.     

Mathematical modeling of polymer-induced flocculation by charge neutralization

A detailed mathematical model for flocculation of colloidal suspensions in presence of salts and polymers is described and validated. In former case, the classical DLVO theory, which accounts for relevant variables such as pH and salt concentration, is incorporated into a geometrically sectioned discrete population balance model. For processes involving polymers, flocculation via simple charge neutralization is modeled using a modified DLVO theory in which the effect of adsorbed polymer layers on van der Waals attraction is included. The fractal dimension of aggregates is obtained by dynamic scaling of experimental data for time evolution of mean aggregate size. The particle surface potential is assumed to be approximately equal to the zeta potential. The model predictions are in close agreement with experimental results for flocculation of colloidal hematite suspensions in the presence of KCl and polyacrylic acid at different concentrations. In particular, given values of model parameters, e.g., Hamaker constant, fractal dimension, surface potential, and thickness of adsorbed polymer layer, the model can realistically describe the kinetics of flocculation by a simple charge neutralization mechanism and track the evolution of floc size distribution. Representative examples of sensitivity of the flocculation model to perturbations in surface potential and fractal dimension and to modification in the DLVO theory for polymer-coated particles are included.     

Controllable size, shape and morphology of molybdic acid self-aggregated with rhodamine B to construct functional material

Controllable size, shape and morphology of rhodamine B/molybdic acid (RBMA) aggregates were prepared from a self-aggregation reaction in a molybdic acid and rhodamine B (RhB) coexisting solution. Nanodisks, as well as microcrystal rods and polyhexagonal microcrystal rods, have been obtained in conventional bulk solutions at different temperatures. Large-sized network microcrystal rods and branched fractal aggregates constructed with nanosubunits after the nucleation duration of an ice-water-cooled process have also been achieved under the evaporation-enhanced conditions on glass substrates. The factors affecting the size, shape and morphology of RBMA aggregates including temperature, nucleation and growth, and processing conditions are discussed. The results show that photofunctional molecules (RhB) modified the surface of the molybdic acid particles and influenced their self-aggregation. The temperature and nucleation play key roles in the formation of RBMA aggregates. The structures of RBMA aggregates were characterized by X-ray diffraction, infrared spectra and elemental dispersive spectroscopy. The results indicate that the aggregates show the characteristics of RhB-mediated hydrated ammonium molybdenum bronze with the metastable hexagonal phase. Visible-light-induced electrons transfer reactions in the RBMA aggregates from rhodamine B molecules to MoO3 matrixes were measured by UV-vis spectra and X-ray photoelectron spectra, and the fluorescent image was observed by laser scanning confocal microscopy.     

Fractal structure of asphaltene aggregates

A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.