Analysis of polymer membrane formation through spinodal decomposition

A phenomenological model used in a previous work for spinodal decomposition of polymer-solvent systems is further analyzed. From the dimensionless form of the nonlinear Cahn-Hilliard equation, the dimensionless induction time is found to be a constant number for suddenly quenched systems. Computer simulation is carried out for prediction of early stage behavior with thermal history corresponding to a linear temperature drop followed by a constant temperature vs. time. In the areas of polymer membrane formation and phase separation studies, the universality of the constant dimensionless Induction time for suddenly quenched systems allows the determination of the minimum time needed for phase separation via spinodal decomposition. Also, simulation results for the double linear temperature history allows the convenient prediction of early stage spinodal decomposition behavior at every point of a membrane cross section undergoing thermal inversion phase separation.     

Analysis of polymer membrane formation through spinodal decomposition. III: Two-dimensional simulations of early-stage behavior

A nonlinear diffusion equation is used to study early-stage spinodal decomposition of polymer solutions, in relation to the membrane formation, in two dimensions. The effects of overall polymer composition and composition-dependent mobility and diffusivity are included in our simulations. Our results show a kinetically stable structure is established during the early stages, which corresponds to a circular range of peaks in the two-dimensional frequency spectrum. Such a spectrum is found to result in an interconnected cell structure in the two-dimensional real space. A decrease in the level of polymer interdomain interconnectedness is obtained as time increases, which indicates the influence of interfacial tension. As the overall polymer composition is increased, an increase in interdomain distances is observed, although the same early stage morphological structure is obtained. Finally, calculated interdomain distances from the two-dimensional simulation are larger than those obtained in equivalent one-dimensional model systems.     

Analysis of polymer membrane formation through spinodal decomposition. Part 4: Computer simulation of early-stage coarsening

In a previous work, an early-stage coarsening mechanism was proposed, whereby continued growth of structure (via spinodal decomposition) in a polymer-solvent system will occur because some of the polymer-rich domains are being depleted. Such a mechanism was explained based on the situation wherein portions of the solvent-rich domains have already reached their binodal composition while the polymer-rich domains are still on their way to their corresponding binodal composition. In this work. we have simulated the nonlinear version of the Cahn-Hilliard theory to verify this phenomenon. Moreover, we have observed that the depleted polymer-rich domains seem to be uniformly distributed in space. Finally, as a validation of the proposed mechanism, we did not observe this uniform depletion of the domains when portions of the solvent-rich and polymer-rich domains reach their respective binodal compositions almost simultaneously.     

Numerical simulation of substrate effects on spinodal decomposition in polymer binary mixture: morphology and dynamics

The characteristic features of the morphology and dynamics of binary mixture for substrate-directed spinodal decomposition (SDSD) in three dimensions have been studied using numerical simulations. The simulation results show that the formation of the wetting layer on the substrate interface follows the power-law growth. It is found that the continuous influence of anisotropic diffusive behavior arose by wetting of substrate induces the wetting component spreading onto the interface of the substrate randomly. The phase morphology and averaged size in the vicinity of the substrate fluctuate greatly due to the wetting of the substrate. The self-similar evolution of the cross-sections parallel and perpendicular to the substrate interface is discussed by relevant scale law functions, respectively. And the mechanisms of the growth in both the parallel and perpendicular directions are also investigated.     

Membrane transport of organics. II. Permeation of some carboxylic acids through strongly basic polymer membrane

The permeability characteristics of the strongly basic polymer membrane Neosepta® AFN‐7, (Tokuyama Soda) have been studied for acetic, propionic, lactic, tartaric, oxalic, and citric acid. The results were interpreted by using the model of transport in reactive membranes. The specific constants, that is, the maximum flux J_max, the reactivity constant K, and the permeability coefficient (P), were calculated using the experimental quasi‐stationary fluxes and the equation derived as a sum of reaction–diffusion (Michaelis–Menten‐type), and the solution–diffusion transport equation. The constants K and J_max were found to range from 0.1 to 5 dm³ mol⁻¹ and from 0.4 × 10⁻⁷ to 2.5 × 10⁻⁷ mol cm⁻² s⁻¹ depending, on the acid properties. The values of K and J_max were correlated with the dissociation constants K_dis.acid, and the diffusion coefficients D_aq.acid in aqueous media, respectively. It was found that the reaction–diffusion flux is predominating for all acids, except for the lactic one, when the feed concentration is lower than 0.5 mol dm⁻³. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 2179–2190, 1999     

Numerical simulation of substrate effects on spinodal decomposition in polymer binary mixture: Effects of the surface potential

The surface-directed spinodal decomposition (SDSD) of polymer binary mixture with different values of surface potential is numerically simulated in three-dimension (3D) by cell dynamic systems (CDS). Furthermore, the growth laws of the wetting layer are theoretically analyzed by the current equation and the dynamical scaling. The results show that the thickness of the wetting layer increases with the increasing surface potential. The crossover, which is later for larger values of surface potential, appears in the evolution curve of the wetting layer. Before the crossover, the growth law is the surface potential dependant growth law. Subsequently, the growth law is the typical Lifshitz-Slyozov (LS) growth law. The results indicate that the surface potential can result in the mutual transformation between completely wetting and partially wetting for the substrate interface. It can be found that the higher surface potential leads to the faster and stronger transmission of the effect of the substrate on the spinodal decomposition in the bulk.     

Novel phase inversion process for symmetric membrane formation through thermal quenching of polymer solution in same solvent

A new and useful form of phase inversion for the formation of porous polymeric membranes is presented herein. As in the case of thermally induced phase separation (TIPS), this new form involves only two components (polymer and solvent) and a thermal quench; here the quench is accomplished via immersion in a cold bath of the micromolecular component (solvent) of the dope. Ιn terms of a fixed‐pressure two‐component phase diagram the quench is a non‐vertical one. We will refer to the new method as cold‐solvent induced phase separation (CIPS). In the present work we study mainly the poly(ethylene‐co‐vinyl alcohol)/1,3‐propanediol system which leads to bi‐continuous structures stemming from a combination of liquid‐liquid demixing and crystallization. In addition, we compare with the case of the Nylon‐l2/formic acid system that we have briefly considered before and study further herein; the consequences of the TIPS to CIPS shift of method are different for the two systems, and the two situations are representative of two general possibilities. We also report general properties such as porosity, tensile strength, water permeation flux, and crystallinity of the produced poly(ethylene‐co‐vinyl alcohol) membranes. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42282.     

Soapless emulsion polymerization of methyl methacrylate. II. Simulation of polymer particle formation

In this work, a generalized mathematical model was developed to estimate the variation of particle concentration during the entire course of soapless emulsion polymerization of methylmethacrylate (MMA). All of the factors, such as oligomeric radical absorption or desorption by polymer particles, coagulation between polymer particles, and the termination effect on the formation mechanism of polymer particles, were considered and included in this model. When appropriate parameters were selected, this model could be successfully used to interpret the experimental behavior of particle concentration during the entire reaction. Under different conditions, the rate of polymerization, the number of radicals in each particle, the instantaneous average molecular weight of polymers, and the rate constant of termination were also calculated. All of them coincided with the experimental results quite well. © 1996 John Wiley & Sons, Inc.     

Effect of polymer density on polyethylene hollow fiber membrane formation via thermally induced phase separation

Microporous high‐density polyethylene (HDPE) and low‐density polyethylene (LDPE) hollow fiber membranes were prepared from polyethylene–diisodecyl phthalate solution via thermally induced phase separation. Effect of the polyethylene density on the membrane structure and performance was investigated. The HDPE membrane showed about five times higher water permeability than the LDPE membrane because it had the larger pore and the higher porosity at the outer membrane surface. The formation of the larger pore was owing to both the initial larger structure formed by spinodal decomposition and the suppression of the diluent evaporation from the outer membrane surface due to the higher solution viscosity. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 471–474, 2004     

Modeling of asymmetric membrane formation. II. The effects of surface boundary conditions

An analysis is carried out to evaluate the effects of alternate surface boundary conditions on the predictions of our previously developed (Part I) pseudobinary diffusion model for membrane formation by the phase inversion process. Attention is addressed to a comparison of concentration profiles in the quenched film for a constant flux interface (CF) condition and a mass transfer rate (MT) interface condition. A numerical algorithm is developed to handle the MT condition based on an explicit, finite difference marching method. Comparison of concentration profiles with those obtained earlier for the CF boundary condition show that since results for both cases are very similar, either condition can be used in concentration profile calculations. Changes in bath conditions will mainly affect membrane formation through the changed solvent/nonsolvent flux ratio during quenching.     

Membrane transport of organics. III. Permeation of some carboxylic acids through bipolar polymer membrane

The permeation of acetic (AA), propionic (PA), lactic (LA), oxalic (OA), citric (CA), and tartaric (TA) acids through the bipolar ion‐exchange membrane Neosepta BP‐1 (Tokuyama Corp.) was studied. It was found that the fluxes (J, mol cm^?2 s^?1) and mass‐transfer coefficients (k, cm s^?1) increase in the following order: CA < OA < LA < TA < PA ≤ AA. The transport processes in the Neosepta BP‐1 membrane are concentration‐dependent and can be described phenomenologically using I‐Fick's law for diffusion. The permeation phenomena correspond to the solution–diffusion model similarly as to the permeation of carboxylic acids through strongly acidic cation‐exchange membranes. However, in competitive AA–PA transport experiments, typically for strongly basic membranes, the separation ability of the BP‐1 membrane with a preference toward AA was observed. The selectivity coefficients α calculated as the ratio of the respective mass‐transfer coefficients vary in the range from 1.31 ± 0.2 to 2.1 ± 0.6. These values depend on the feed composition and the system arrangement, which means that α is always higher for the system with the anion‐exchange layer is in contact with a feed solution. Rather low fluxes of PA, AA, and other acids, as compared to some monopolar membranes (Neosepta AFN‐7, Nafion‐120, Flemion), are promising for the application of the bipolar membrane in an electrodialytic separation of carboxylic acids from their aqueous solutions or mixtures. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2705–2717, 2001     

Enthalpic and entropic origins of nucleation barriers during polymer crystallization: the Hoffman-Lauritzen theory and beyond

In the search for a greater understanding of polymer crystallization, numerous experimental observations with regards to microscopic structures and macroscopic properties have been reported in the past half-century. There are generally two types of experimental results to provide information about the mechanisms of polymer crystal growth, i.e. molecular dynamic/scattering and structural/morphological. Since we cannot follow the trajectory of individual chain molecules when they undergo the transition from liquid to solid state during the crystallization process, structural/morphological analysis of polymer crystals reveal information recorded during this process. Namely, the final structure and morphology of polymer crystals have atomic, stem and global chain conformation information embedded in them during crystallization which provides evidence which can be used to deduce molecular aspects of the polymer crystallization process. It is commonly understood that polymer crystallization, from the thermodynamic perspective, is a first-order transition involving the relaxation of a metastable undercooled melt towards the equilibrium state which is rarely reached in polymer crystals. This process is controlled by a free energy barrier. A molecular model is required to describe the landscape of the free energy barriers and to provide an analytical explanation concerning and predictions about polymer crystallization. The Hoffman-Lauritzen (HL) theory, which was put forward more than 40 years ago, was one of the first analytical theories to illustrate how polymers crystallize. Since then, modifications to the HL theory and suggestions for new approaches have been reported, but the core physical picture of the HL theory has largely remained intact. This article consists of four major parts: (1) we will compare the crystallization of small molecules and long chain molecules, and the relationship between crystallization and crystal habits. The diversity of crystalline structures and morphologies of semi-crystalline polymers must be taken into account when studying the crystallization mechanism of polymers (2) this article also serves as a brief review of the HL theory and its importance in our understanding of polymer crystallization (3) we have tried to answer the question: what is the nucleation barrier? Specifically, we will illustrate that the nucleation barrier in polymer crystallization consists of both enthalpic and entropic components as deduced from experimental results. This barrier, from our perspective, consists of selection processes taking place in different length- and time-scales (4) finally, there is a brief discussion on what issues remain, in particular, in the areas of undercooled liquid structures and the initial stages of crystallization.     

Later-stage spinodal decomposition in polymer solution under high pressure—analyses of qm and Im

Later-stage spinodal decomposition (SD) of polymer solutions (polypropylene/trichlorofluoromethane) induced by pressure-jump was examined in situ as a function of pressure P by using time-resolved light scattering method with the cell designed for high pressure and high temperature. The time-evolution of the magnitude of scattering vector q_m(t,P) at maximum scattered intensity and the maximum scattered intensity I_m(t,P) were analyzed in order to characterize the coarsening processes of the later-stage SD, where t refers to time after the onset of pressure-jump. The changes in q_m(t,P) and I_m(t,P) with t at different P's were found to fall onto the respective master curves on the reduced plots, indicating that the scaling postulate is valid not only for the coarsening behaviors at different temperatures but for those at different P's.     

Thermal decomposition of cellulose/synthetic polymer blends containing grafted products. II. Cellulose/polyacrylonitrile blends

The homogeneous grafting of acrylonitrile onto cellulose was carried out in a dimethyl sulfoxide/paraformaldehyde solvent system. The grafted products were added to cellulose/polyacrylonitrile (PAN) blends as compatibilizers. The thermal decomposition behavior of the blends was investigated by thermogravimetry. The thermal stability of the blends with higher grafted product content was lower by more than 100°C than that of the blends without grafted product. The accessibility values of the former blends were larger than those of the latter. The microphase-separated structures of the grafted product blends were finer than those without the product. Dynamic mechanical measurements and differential scanning calorimetry were performed to estimate the glass transition temperatures, T_g, of the blends. The variation in T_g was smaller than that in characteristic temperatures determined by thermogravimetry. The difference in thermal decomposition behavior was correlated to that in compatibility. Thermogravimetry was found to be effective for estimating the compatibility in cellulose/PAN blends containing grafted products. © 1996 John Wiley & Sons, Inc.     

Effect of temperature on polymer migration II: Concentration equation

Polymer migration is a generally well-known phenomenon in a flow field, and it has been verified that the sources of such phenomena are nonhomogeneity of the flow, concentration effects and hydrodynamic interactions between the polymer molecules. In addition, temperature effects were found to be another source of polymer migration. The Langevin equation for a polymer molecule was first derived from single chain dynamics using a kinetic theory for the bead-spring elastic harmonic dumbbell model, as described in part I (reference [1]). In this paper the diffusion equation and concentration profile of the polymer molecules induced by a temperature gradient are obtained from the Fokker-Planck equation. A new differential operator is also introduced to calculate the concentration profile. From the concentration equation obtained in the general flow geometry, we find that in dilute polymer solution there are significant effects on the polymer migration not only due to the nonhomogeneity of the flow field but also due to temperature gradients.     

Study on morphology of ternary polymer blends. II. Effect of composition

The composition effect on morphology of polypropylene/ethylene–propylene–diene terpolymer/polyethylene (PP/EPDM/PE) and polypropylene/ethylene–propylene–diene terpolymer/polystyrene (PP/EPDM/PS) ternary blends has been investigated. In all of the blends, polypropylene as the major phase was blended with two minor phases, that is, EPDM and PE or PS. From morphological studies using the SEM technique a core–shell morphology for PP/EPDM/PE and separated dispersed morphology for PP/EPDM/PS were observed. These results were found to be in agreement with the theoretical predictions. The composition of components affected only the size of dispersed phases and had no appreciable effect on the type of morphology. The size of each dispersed phase, whether it forms core or shell or disperses separately in matrix, can be related directly to its composition in the blend. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1138–1146, 2001     

Effect of fatty acid positional distribution and triacylglycerol composition on lipid by-products formation during heat treatment: I. polymer formation

Effects of the fatty acid positional distribution and of the triacylglycerol (TG) composition on polymerization of TG during heat treatment were studied. Diacid TG molecules, acylated only with linoleic acid or linolenic acid along with palmitic acid, and positioned either in the central position (PLP and PLnP, respectively) or in one of the two outer positions (PPL and PPLn, respectively) were synthesized. Monoacid TG, i.e., trilinolein and trilinolenin, were also synthesized and mixed with tripalmitin in a 1:2 ratio. These model TG were also compared to TG models that consisted of a canola oil and its randomized counterpart, whose fatty acid positional distribution and TG composition were determined by means of high-performance liquid chromatography (HPLC). After heating, the polymer content and composition were evaluated by HPLC-size exclusion chromatography. Both pure TG and the canola oil models showed that acylation of polyunsaturated acids in the central position was protective against polymerization, although the effect was mainly observed with linolenic acid. The synthetic-TG study showed that the monoacid TG species exhibited higher sensitivity toward polymerization than the diacid species. The slight differences in the TG species between both canola oils did not allow observation of such a relationship with regard to TG composition.     

Analysis of nonsolvent–solvent–polymer phase diagrams and their relevance to membrane formation modeling

Calculations have been carried out, based on Flory–Huggins solution theory, to analyze the behavior of the ternary nonsolvent–solvent–polymer phase diagram for typical membrane-forming systems. Consideration is given to the behavior of the spinodal as well as binodal curves, tie-line slopes, and critical points as a function of various parameters, most especially those related to the concentration dependency of the interaction parameters. Implications regarding membrane structure formation are discussed, and the suitability of different functional forms for the interaction parameter concentration dependence is also analyzed. The net result of these calculations is to demonstrate the importance of the various parameters in controlling the phase-diagram behavior and particularly to show the critical role of the concentration dependence of the solvent–polymer interaction parameter in affecting the nature of the miscibility gap.     

热诱导相分离法制备高分子微孔膜的原理与进展

简述了热诱导相分离 (TIPS)法制备高分子微孔膜的相平衡热力学及相分离动力学原理 ,并对国内外研究进展进行了评述