Phase separation kinetics in unentangled polymer solutions under high‐rate extension

Phase separation processes following high‐rate extension in unentangled polymer solutions are studied theoretically. The flow‐induced demixing is associated with the coil–stretch transition predicted in high‐molecular‐weight polymer solutions at high‐enough Weissenberg numbers. The developed mean‐field theory is valid in the dilute/semidilute solution regime, where the stretched coils overlap strongly. We elucidate and discuss the main kinetic stages of the polymer/solvent separation process including (i) growth of concentration fluctuations and formation of oriented protofibrils by anisotropic spinodal decomposition; (ii) development of well‐defined highly oriented and stiff fibrils forming an anisotropic network (cross‐linked fiber); (iii) microphase separation and lateral collapse of the network yielding dense oriented fiber. These novel predictions are in qualitative agreement with the experimental data. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 623–637     

On the nature of phase separation of polymer solutions at high extension rates

Experiments with stretching moderately concentrated polymer solutions have been carried out. Model experiments were carried out for poly(acrylonitrile) solutions in dimethyl siloxane. Just the choice of concentrated solutions allowed for a clear demonstration of a demixing effect with the formation of two separate phases—an oriented polymer fiber and solvent drops sitting on its surface. An original experimental device for following all subsequent stages in the demixing process was built. It combined two light beams, one transverse to the fiber and a second directed along (inside) the fiber, the latter played the role of an optical line. This gives a unique opportunity to observe processes occurring inside a fiber. The process of demixing starts from the volume phase separation across the whole cross section of a fiber at some critical deformation and the propagation of the front of demixing along the fiber. Then a solvent cylindrical skin appears which transforms into a system of separate droplets. New experimental data are discussed based on a comparison of the current different points of view on the phenomenon of deformation‐induced phase separation: thermodynamic shift of the equilibrium phase transition temperature, growth of stress‐induced concentration fluctuations in two‐component fluids, and mechanically pressing a solvent out from a polymer network. The general belief is that a rather specific (so‐called “beads‐on‐a‐string”) structure of a filament is realized in stretching dilute solutions: beads of a polymer solution connected by oriented polymer bridges forming a single object. The situation in stretching moderately concentrated solutions appears quite different: real phase separation was observed. So, the alternative phenomenon to the formation of the “beads‐on‐a‐string” structure has been experimentally proven. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 559–565     

Phase diagram for microphase separation transition in poor solvent polymer solutions

In the present paper, we consider the possibility of microphase separation transition in poor solvent polymer solutions. It is shown that this phenomenon can take place if the following two conditions are fulfilled: i) there is a large entropic contribution to the entropy of polymer/solvent mixing, i.e., solvent acts like a plastisizer; ii) this entropic contribution is nonlocal. Both conditions are met below the glass transition temperature for the pure polymer near the so-called Berghmans point when the glass transition curve intersects the liquid-liquid phase separation curve for polymer solutions. The phase diagram for the microphase separation transition is calculated within the framework of weak segregation approximation first proposed by Leibler for block-copolymer systems. The regions of stability of different microdomain structures (lamellar, triangular, body-centered-cubic) are obtained. It is shown that under certain conditions the phase diagram can have two critical points related to the macro- and microphase separation respectively.This paper is dedicated to Prof. E. W. Fischer on the occasion of his 65th Birthday.This work was done in the course of the Humboldt Research Award stay of A.R. Khokhlov at the Max-Planck-Institute for Polymer Research in Mainz. During this stay A.R.K. greatly benefited from numerous discussions with Professor E.W. Fischer who introduced him to the fascinating field of glass transition in polymer systems and formulated several new directions for future research.     

Phase separation of micellar solutions at extreme dilution: A study of polystyrene-b-poly(sodium acrylate) micelles in aqueous NaCl solutions

Micellar solutions of polystyrene-b-poly(sodium acrylate) copolymers in aqueous NaCl were studied by static light scattering (SLS). It was found that micellar solutions of the copolymer, at concentrations of NaCl at, or above, 2.0 mol dm⁻³, became turbid on dilution at constant salt concentration and at constant temperature. Turbidity arose from highly dilute solutions (typically at a concentration three orders of magnitude lower than the overlap concentration of the micelle, C*), but at concentrations above the expected critical micellization concentrations (c.m.c.s). The observed turbidity was attributed to the phase separation of the micellar phase. A systematic investigation of the phase separation phenomenon was performed. The effects of various parameters on the solution behavior of the micellar solutions were studied, including the effect of the concentration of NaCl, the effect of temperature, and the effect of the length of the hydrophilic, corona-forming poly(sodium acrylate) block. Phase separation was attributed to the presence of a very large excess of NaCl in the dilute micellar solutions. It was proposed that phase separation arose because of the reduced hydration of the polyion, the decreased electrostatic repulsion between the micelles, and the increase in the amount of ion binding, which occur in highly dilute salt solutions. © 1996 John Wiley & Sons, Inc.     

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     

Theoretical simulation of thermally induced phase separation in a main‐chain liquid‐crystalline polymer solution

Phase diagrams of main‐chain liquid‐crystalline polymer (MCLCP) solutions have been calculated self‐consistently on the basis of a simple addition of the Flory–Huggins free energy for isotropic mixing, the Maier–Saupe free energy for nematic ordering, and the Flory free energy for chain rigidity of the MCLCP backbone. The calculated phase diagram is an upper critical solution type overlapping with the nematic–isotropic transition. The phase diagram consists of liquid–liquid, liquid–nematic, and pure nematic regions. Subsequently, the dynamics of thermally induced phase separation and morphology development have been investigated by the incorporation of the combined free energy density into the coupled time‐dependent Ginzburg–Landau (model C) equations, which involve conserved compositional and nonconserved orientational order parameters. The numerical calculations reveal a variety of the morphological patterns arising from the competition between liquid–liquid phase separation and nematic ordering of the liquid‐crystalline polymer. Of particular interest is the observation of an inflection in the growth dynamic curve, which may be attributed to the nematic ordering of the MCLCP component, which leads to the breakdown of the interconnected domains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 913–926, 2003     

Phase separation behavior of aqueous solutions of a thermoresponsive polymer

Cloud‐point and binodal curves of the LCST type were obtained for aqueous solutions of a thermoresponsive polymer, poly [2‐(2‐ethoxy)ethoxyethyl vinyl ether], poly(EOEOVE). The cloud‐point curve obtained was very flat except in a dilute region, that is the cloud‐point temperature was insensitive to the polymer concentration, resembling the cloud‐point curve for aqueous solutions of poly(N‐isopropylacrylamide). On the other hand, the binodal curve obtained was parabolic, and located within the two‐phase region of the cloud‐point curve. Accompanied with the phase separation, a sharp endothermic peak was observed in a region including the cloud‐point and binodal temperatures. The reciprocal of the osmotic compressibility ?Π/?c obtained by sedimentation equilibrium indicated that water changes from a good to poor solvent for poly(EOEOVE) with increasing temperature. Analyzing the ?Π/?c data by a thermodynamic perturbation theory, we determined the interchain interaction parameters, the hard‐core diameter d and the depth ε of the square‐well potential. Theoretical binodal and endothermic curves calculated by the perturbation theory using the estimated interaction parameters reproduced experimental ones semiquantitatively, but the theoretical binodal disagreed with the experimental flat cloud‐point curve. The disagreement at high concentrations was in the opposite direction to that expected from the sample polydispersity in the molecular weight. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2937–2949, 2005     

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).     

Chain conformations and phase separation in polymer solutions with varying solvent quality

Molecular dynamics simulations are used to investigate the conformations of a single polymer chain, represented by the Kremer-Grest bead-spring model, in a solution with a Lennard-Jones liquid as the solvent when the interaction strength between the polymer and solvent is varied. Results show that when the polymer-solvent interaction is unfavorable, the chain collapses as one would expect in a poor solvent. For more attractive polymer-solvent interactions, the solvent quality improves and the chain is increasingly solvated and exhibits ideal and then swollen conformations. However, as the polymer-solvent interaction strength is increased further to be more than about twice the strength of the polymer-polymer and solvent-solvent interactions, the chain exhibits an unexpected collapsing behavior. Correspondingly, for strong polymer-solvent attractions, phase separation is observed in the solutions of multiple chains. These results indicate that the solvent becomes effectively poor again at very attractive polymer-solvent interactions. Nonetheless, the mechanism of chain collapsing and phase separation in this limit differs from the case with a poor solvent rendered by unfavorable polymer-solvent interactions. In the latter, the solvent is excluded from the domain of the collapsed chains while in the former, the solvent is still present in the pervaded volume of a collapsed chain or in the polymer-rich domain that phase separates from the pure solvent. In the limit of strong polymer-solvent attractions, the solvent behaves as a glue to stick monomers together, causing a single chain to collapse and multiple chains to aggregate and phase separate.     

Kinetics of thermally induced phase separation in ternary polymer solutions. II. Comparison of theory and experiment

Light‐scattering measurements and spinodal decomposition modeling have been used to quantify the kinetics of pore growth in thermally quenched polymer‐solvent–nonsolvent [poly(methyl methacrylate) (PMMA)/1‐methyl‐2‐pyrrolidinone (NMP)/glycerin] solutions. Solutions of fixed composition were quenched to a series of temperatures and light‐scattering measurements and model calculations were performed to determine the temperature dependence of the pore growth rate. Both the experimental results and the model calculations show that the growth rate exhibits a maximum at an intermediate quench temperature that is related to an interplay between the thermodynamic and transport effects that govern pore growth. A similar growth‐rate maximum is also observed when a series of solutions of varying nonsolvent composition are all quenched to the same temperature. The relevance of these experiments to the dynamics of pore growth and the eventual locking‐in of the two‐phase structure that forms during nonsolvent‐induced phase inversion is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1461–1467, 1999     

Apparent relaxation‐time spectrum cutoff in dilute polymer solutions: An effect of solvent dynamics

The apparent short time cutoff of the relaxation‐time spectrum at surprisingly long times for polymers in solution is a well known but not yet understood observation. To elucidate its origins we revisit viscoelastic and oscillatory flow birefringence data for solutions and melts of two linear polymers (polystyrene and polyisoprene) and present new measurements of oscillatory flow birefringence of the latter. Previous measurements have suggested that the “flexibility” of both polymers in solution is smaller than in the melt on the basis of the breadth of the relaxation‐time spectrum of the solution as compared with that of the melt. Our new measurements have explored a higher effective frequency range than was previously possible. This has allowed us to observe the effect of the rotational relaxation time of the solvent on the dynamics of the solution at high frequencies. To obtain the polymer global motion contribution, one now needs to subtract from the solution properties a frequency‐dependent complex solvating environment contribution. We show that the decrease in apparent “flexibility” for solutions arises from the presence of a solvent that exhibits a rotational relaxation time and thus simple viscoelastic behavior somewhat near the frequency window of the experiment. Although recent predictions of a model for a chain in a solvent with a single relaxation time are in qualitative agreement with our results, our data suggest that the solution results may reflect the influence of solvent on the development of the “entropic spring” forces at short times. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2860–2873, 2001     

Phase separation in thin films of end‐grafted block copolymers

An atomic force microscopy investigation was carried out on various thick (30–120 nm) polymethyl methacrylate‐b‐polystyrene and poly(2‐(dimethyl amino)ethyl methacrylate)‐b‐polystyrene films prepared via a grafting‐from method. The structure of the films was examined with both topographic and phase imaging. Several different morphologies were observed including a perforated lamellar phase with irregular perforations. In addition, complementary small‐angle X‐ray scattering and reflectometry results measurements on a non‐grafted polymer are presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Simulation of phase‐separated structures of liquid‐crystalline polymer/flexible polymer blends

The phase‐separation kinetics of liquid‐crystalline polymer/flexible polymer blends was studied by the coupled time‐dependent Ginzberg–Landau equations for compositional order parameter ? and orientational order parameter S_ij. The computer simulations of phase‐separated structures of the blends were performed by means of the cell dynamical system in two dimensions. The compositional ordering processes of phase separation are demonstrated by the time evolution of ?. The influence of orientational ordering on compositional ordering is discussed. The small‐angle light scattering patterns are numerically reproduced by means of the optical Fourier transformation of spatial variation of the polarizability tensor α_ij, and the azimuthal dependence of the scattering intensity distribution is interpreted. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2915–2921, 2001     

Phase separation and polymer crystallization in a poly(4‐methyl‐1‐pentene)–dioctylsebacate–dimethylphthalate system via thermally induced phase separation

The effects of the polymer concentration and quenching temperature on the phase separation, the membrane morphology and polymer crystallization behavior in a poly(4‐methyl‐1‐pentene) (TPX)‐dioctylsebacate (DOS)‐dimethylphthalate (DMP) system via thermally induced phase separation were studied with a pseudobinary phase diagram, with the weight ratio of DOS:DMP = 1:1. SEM was used to observe the membrane morphology and structure, whereas the TPX crystallization behavior was studied with DSC and WAXD. Liquid‐liquid phase separation occurred, although quenching under the crystallization temperature. As the quenching temperature decreased, the pore size decreased, with better connected pore structure formed. The membranes quenched at 333 and 363 K showed good cellular structures, with an average pore size of about 2.3μm, whereas the pores of the membranes quenched at 393 and 423 K were not well formed, with some lamellar crystals on the inner side. The diluent assisted the mobility of the polymer chain, which improved the polymer crystallization. Dual‐melting‐peak behavior occurred for all the samples studied here. As the quenching temperature increased, the first peak of the melting trace moved to a higher temperature, whereas the second one stayed almost the same. The flexibility of the TPX main chain was restricted by the side groups, which allowed liquid‐liquid phase separation to occur first when quenched below the equilibrium crystallization temperature. This allowed primary and secondary crystallization, which was responsible for the dual‐melting‐peak behavior. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 153–161, 2007     

A new instrument for measuring the viscoelastic properties of dilute polymer solutions

A new oscillating capillary viscometer has been developed and used for measuring viscoelastic flow properties of dilute polymer solutions. These flow properties are determined from measurements of the pressure to volume flow relationships for sinusoidal flow in cylindrical glass capillaries. The theory for this measurement procedure is based upon the known theory for oscillatory flow of a viscoelastic fluid in circular tubes and which is presented with a few supplementations in this paper.The oscillatory flow is generated by a piezoelectric driver which is dipped directly into the aqueous solution. The advantage of this driver is that the excitation voltage for the piston is a direct measure of the motion of the piston. Changes in pressure are measured with a sensitive low-pressure quartz tranducer.The viscometer was tested with aqueous glycerol solutions and a gelatin gel. The viscoelastic flow properties of dilute polymer solutions (gelatin, gelatin/color-coupler, polyacrylamide) were then investigated in the frequency range 5 Hz to 150 Hz at very small volume flow amplitudes. The results presented illustrate the suitability of the method. The results are also evaluated with regard to the stabilizing action of slightly viscoelastic gelatinous coating liquids in the high-speed coating process in the manufacture of photographic materials.     

Micellar electrokinetic chromatography for high‐performance analytical separation

Capillary electrophoresis (CE) is a relatively new method of analytical separation having the advantages of high separation efficiency, requirement of a small sample amount, low operating cost, and fast separation time. CE is a separation method where the analyte migrates under an electric field due to a charge on the analyte. Hence, CE was unable to separate neutral analytes until the advent of micellar electrokinetic chromatography (MEKC). MEKC is performed with an addition of ionic micelles to an electrophoretic medium, where a portion of the analyte is incorporated into the micelle and has an apparent charge, which can be subject to electrophoretic separation. The migration velocity of the neutral analyte in MEKC depends on what portion of the analyte is incorporated into the micelle. Thus, the separation principle of MEKC is similar to that of chromatography, although the micelle corresponding to the stationary phase in chromatography is not stationary inside the capillary. The fundamental characteristics and theoretical treatments of the behavior of the analyte in MEKC were studied extensively by the author's group. MEKC has been established as one of the most popular separation modes in CE. This review describes how MEKC was developed and how it is useful as a method of analytical separation. © 2008 The Japan Chemical Journal Forum and Wiley Periodicals, Inc. Chem Rec 8: 291–301; 2008: Published online in Wiley InterScience ( www.interscience.wiley.com ) DOI 10.1002/tcr.20156     

Rheological measurements and light-scattering experiments of dilute solutions of high molecular polystyrene. Light-scattering of flowing polymer solutions

We describe the behavior of dilute polymer solutions by means of light-scattering under shear flow. Solution properties of polystyrene in benzene over a wide range of molecular weight has been studied to determine the coefficientsa andK of the Mark-Houwink relationship and to estimate the rheological conditions with regard to light-scattering experiments of flowing polymer solutions. The investigations were carried out to measure the shear-rate dependence of macromolecules in solution, e.g., to observe an orientation and changing of the mean-square radius of gyration.     

Small molecule self‐assembly in polymer matrices

Using small molecules in polymer matrices is common in applications such as (i) plasticizing polymers to modify the glass transition and mechanical properties and (ii) dispersion of photoactive or electroactive small molecules in polymer matrices in organic‐electronic devices Aggregation of these small molecules and phase separation leading to crystallization often cannot be morphologically controlled. If these are designed with self‐assembling codes such as hydrogen bonding or aromatic interactions, their phase separation behavior would be distinctly different. This review summarizes the studies on morphologies in such situations, such as (i) sub‐surface assembly in polymer matrices, (ii) controlled polymerization‐induced phase separation to create polymer blends, (iii) using the polymer to direct the assembly of small molecules in liquid crystalline devices, (iv) functionalizing a polymer with self‐assembling small molecules to cause organo‐gelation which the polymer itself would not by itself, and (v) using such systems as templates to create porous polymer structures. Organic–inorganic hybrids using polymers as templates for nanostructures and imprinted porous membranes is an emerging area. Since self‐assembly is one of the dominating area of research with respect to both small molecules, polymers as well as the combination of the two, this review summarizes the studies on the aforementioned topics. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 451–478     

New free‐volume‐related activity model for polymer solutions

A new activity model was developed with the use of the Gibbs–Helmholtz relation at constant pressure and composition. This model consists of combinatorial and residual terms. The residual term is the same as that in the UNIQUAC method, but the total area fraction of molecules is introduced on account of the hole effect. The combinatorial part takes into account the free volume (FV) effect, which plays a significant role in polymer systems. The validity of this model is demonstrated by calculating the solvent activities in 36 polymer solutions in comparison with Entropic‐FV (EFV) and UNIFAC‐FV methods. The total average absolute deviations (AAD) from the experimental observations are 8.27, 6.38, and 1.64 for EFV, UNIFAC‐FV, and the present method, respectively. It is found that the fit to these experimental data by the present model is quite good over a wide range of concentration. An estimation of the infinite dilution activity coefficients also proves the validity of the new method. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3299–3307, 2005