Lattice cluster theory of associating polymers. II. Enthalpy and entropy of self-assembly and Flory-Huggins interaction parameter χ for solutions of telechelic molecules

The lattice cluster theory for solutions of telechelic polymer chains, developed in paper I, is applied to determine the enthalpy Δh(p) and entropy Δs(p) of self-assembly of linear telechelics and to evaluate the Flory-Huggins (FH) interaction parameter χ governing the phase behavior of these systems. Particular focus is placed on examining how these interaction variables depend on the composition of the solution, temperature, van der Waals and local "sticky" interaction energies, and the length of the individual telechelic chains. The FH interaction parameter χ is found to exhibit an entropy-enthalpy compensation effect between the "entropic" and "enthalpic" portions as either the composition or mass of the telechelic species is varied, providing unique theoretical insights into this commonly reported, yet, enigmatic phenomenon.     

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.     

Liquid-liquid equilibria of polymer solutions: a closed miscibility loop phase behavior

In the phase behavior of binary polymer/solvent mixtures, a lower critical solution temperature (LCST) and hour-glass shaped and closed miscibility loop phase behavior are encountered. The closed miscibility loop phase behavior may be mainly due to highly oriented interactions such as hydrogen bonding. The purpose of this study is to describe closed miscibility loop phase behavior in the liquid-liquid equilibria of polymer solutions. To consider highly oriented interactions (or specific interactions), we employed a secondary lattice concept as a perturbation term.     

Phase behavior predictions for polymer blends containing reversibly associating endgroups

A mean field model is developed to predict how polymer–polymer miscibility changes if polymers are functionalized with noncovalent, reversibly binding endgroups. The free-energy model is based on the Flory–Huggins mixing theory and has been modified using Painter's association model to account for equilibrium self-association of endgroups. Model input parameters include the length of polymer chains, a temperature-dependent interaction parameter, and a temperature-dependent equilibrium constant for each type of associating endgroup. The analysis is applied to 12 possible blend combinations involving self-complementary interactions and seven combinations involving hetero-complementary [i.e. donor–acceptor (DA)] interactions. Combinations involve both monofunctional and telechelic associating chains. Predicted phase diagrams illustrate how self-complementary interactions can stabilize two-phase regions and how DA interactions can stabilize single phase regions. The model is a useful tool in understanding the delicate balance between the combinatorial entropy of mixing polymer chains, the repulsive interactions between dissimilar polymers, and the additional enthalpic and entropic changes due to end-group association of chain ends. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3285–3299, 2007     

Behavior of a polymer chain immersed in a binary mixture of solvents

The behavior of a polymer chain immersed in a binary solvent mixture is investigated via a single-polymer simulation using an effective Hamiltonian, where the solvent effects are taken into account through a density-functional theory for polymer-solvent admixtures. The liquid-liquid phase separation of the binary solvent mixture is modeled as that of a Lennard-Jones binary fluid mixture with weakly attractive interactions between the different components. Two types of energetic preferences of the polymer chain for the better solvent-(A) no preferential solvophilicity and (B) strong preferential solvophilicity-are employed as polymer-solvent interaction models. The radius of gyration and the polymer-solvent radial distribution functions are determined from the simulations of various molar fractions along an isotherm slightly above the critical temperature of the liquid-liquid phase separation. These quantities near the critical point conspicuously depend on the strength of the preferential solvophilicity. In the case where the polymer exhibits a strong preferential solvophilicity, a remarkable expansion of the polymer chain is observed near the critical point. On the other hand, in the case where the polymer has no preferential solvophilicity, no characteristic variation of the polymer conformation is observed even near the critical point. These results indicate that the expansion of a polymer chain enhances the local phase separation around it, acting as a nucleus of demixing in the vicinity of the critical point. This phenomenon in binary solvents near the liquid-liquid critical point is similar to the expansion of the polymer chain in one-component supercritical solvents near the liquid-vapor critical point, which we have reported [T. Sumi and H. Sekino J. Chem. Phys. 122, 194910 (2005)].     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

Dispersions of polymer ionomers: I

The principal subject discussed in the current paper is the effect of ionic functional groups in polymers on the formation of nontraditional polymer materials, polymer blends or polymer dispersions. Ionomers are polymers that have a small amount of ionic groups distributed along a nonionic hydrocarbon chain. Specific interactions between components in a polymer blend can induce miscibility of two or more otherwise immiscible polymers. Such interactions include hydrogen bonding, ion-dipole interactions, acid-base interactions or transition metal complexation. Ion-containing polymers provide a means of modifying properties of polymer dispersions by controlling molecular structure through the utilization of ionic interactions. Ionomers having a relatively small number of ionic groups distributed usually along nonionic organic backbone chains can agglomerate into the following structures: (1) multiplets, consisting of a small number of tightly packed ion pairs; and (2) ionic clusters, larger aggregates than multiplets. Ionomers exhibit unique solid-state properties as a result of strong associations among ionic groups attached to the polymer chains. An important potential application of ionomers is in the area of thermoplastic elastomers, where the associations constitute thermally reversible cross-links. The ionic (anionic, cationic or polar) groups are spaced more or less randomly along the polymer chain. Because in this type of ionomer an anionic group falls along the interior of the chain, it trails two hydrocarbon chain segments, and these must be accommodated sterically within any domain structure into which the ionic group enters. The primary effects of ionic functionalization of a polymer are to increase the glass transition temperature, the melt viscosity and the characteristic relaxation times. The polymer microstructure is also affected, and it is generally agreed that in most ionomers, microphase-separated, ion-rich aggregates form as a result of strong ion-dipole attractions. As a consequence of this new phase, additional relaxation processes are often observed in the viscoelastic behavior of ionomers. Light functionalization of polymers can increase the glass transition temperature and gives rise to two new features in viscoelastic behavior: (1) a rubbery plateau above T(g) and (2) a second loss process at elevated temperatures. The rubbery plateau was due to the formation of a physical network. The major effect of the ionic aggregate was to increase the longer time relaxation processes. This in turn increases the melt viscosity and is responsible for the network-like behavior of ionomers above the glass transition temperature. Ionomers rich in polar groups can fulfill the criteria for the self-assembly formation. The reported phenomenon of surface micelle formation has been found to be very general for these materials.     

Unified model of association-induced lower critical solution temperature phase separation and its application to solutions of telechelic poly(ethylene oxide) and of telechelic poly(N-isopropylacrylamide) in water

The authors present a model describing the coexistence of hydrophobic association and phase separation with lower critical solution temperature (LCST) in aqueous solutions of polymers carrying short hydrophobic chains at both chain ends (telechelic associating polymers). The LCST of these solutions is found to decrease along the sol/gel transition curve as a result of both end-chain association (association-induced phase separation) and direct hydrophobic interaction of the end chains with water. The authors relate the magnitude of the LCST decrease to a hydration cooperativity parameter sigma. The LCST decreases substantially (approximately 100 K) in the case of random hydration (sigma=1), whereas only a small shift (approximately 5-10 K) occurs in the case of cooperative hydration (sigma=0.3). The molecular weight dependence of the LCST drop is studied in detail in each case. The results are compared with experimental observations of the cloud points of telechelic poly(ethylene oxide) solutions, in which random hydration predominates, and of telechelic poly(N-isopropylacrylamide) solutions, in which cooperative hydration prevails.     

Pressure-induced formation of diblock copolymer "micelles" in supercritical fluids. A combined study by small angle scattering experiments and mean-field theory. I. The critical micellization density concept

We developed a simple mean-field theory to describe polymer and AB diblock copolymer phase separation in supercritical (SC) fluids. The highly compressible SC fluid has been described by using a phenomenological hole theory, properly extended to consider the solvent/polymer/vacancy pseudoternary mixture. The model has been applied to describe the phase behavior of AB-diblock copolymers under the assumption of a strong solvent selectivity for just one copolymer chain. In our model the solvent selectivity is a strong function of the external pressure because in compressible fluids vacancies reduce the number of favorable solvent-polymer contacts. The combined effect of the pressure on the average solvent quality and selectivity for a single polymer chain makes the phase behavior of a diblock copolymer in SC fluids quite complex. Small angle neutron and x-ray scattering (SANS and SAXS) measurements have been performed on SC-CO2 solutions of different AB-diblock copolymers containing a perfluorinated chain. The data obtained over a wide range of pressure and temperature confirm our theoretical predictions.     

Phase behavior and self-organized structures of diglycerol monolaurate in different nonpolar organic solvents

Nonaqueous phase behavior and reverse micellar structures of diglycerol monolaurate (DGL) in different nonpolar organic solvents, such as n-decane, n-tetradecane, and n-hexadecane, have been studied over a wide range of compositions and temperatures. The equilibrium phases are identified by means of visual observation and small-angle X-ray scattering (SAXS). A solid phase present at lower temperature swells small amount of oils and transforms into a lamellar liquid crystalline structure at higher temperature. The melting temperature of the solid phase is virtually constant at all mixing ratios of the surfactant and oil. With the further increase of temperature, the liquid crystal transforms into an isotropic single-liquid phase near the surfactant axis, whereas there is a coexistence region of two isotropic phases near the solvent axis. The area of the two-liquid (II) phase region depends largely on the hydrocarbon chain length of the oils, the longer chain leading to the wider II area. Accordingly, the DGL surfactant is most miscible with decane, exhibiting a reduced miscibility with increasing solvent hydrocarbon chain length. Increasing temperature enhances the dissolution tendency of the surfactant in oil, where the two-liquid phase transforms into an isotropic single phase. SAXS analysis based on the GIFT technique is used to characterize the structure of the reverse micellar aggregates in the isotropic single-phase liquids. We have demonstrated that instead of changing polarity or a functional group of the solvent molecules, if we optimize the hydrophilic nature of the surfactant head group, the alkyl chain length of the solvent oils can serve as a tunable parameter of the micellar geometry. The hydrophilic surfactant DGL interestingly forms cylindrical micelles in nonpolar oils, decane, and tetradecane in the dilute region above the II phase region. The micellar size shows temperature dependence behavior, and the micellar length goes on increasing with decreasing temperature; eventually we found a signature of the onset of critical fluctuations in the deduced pair-distance distribution function near the phase separation line. The signature of the attractive interaction between the cylindrical reverse aggregates when a phase separation line is approached is likely to be a precursor of critical phenomenon. Doping with a trace of water results in a similar but more pronounced structural enhancement. The transfer free energy of diglycerol moiety from a hydrophilic environment to different hydrocarbon oils may account for these phenomena.     

Polymer chain conformation in the phase separation process of a binary liquid mixture

A polymer chain conformation change near the critical point of liquid-liquid phase separation was investigated. Poly(N-isopropylacrylamide) labeled with a small amount of carbazolyl group for a fluorophore (P(NIPA-Cz)) was prepared. A ternary system of P(NIPA-Cz)+cyclohexane+methanol was investigated by the fluorescence spectroscopic technique. A mixed solvent of cyclohexane+methanol (CH/MeOH) shows phase separation at the upper critical solution temperature. Light scattering intensity, fluorescence emission intensity and fluorescence anisotropy ratio, as a function of temperature, were measured with quasi statically approaching to the critical demixing point. The fluorescence intensity of the carbazolyl groups attached to the polymer chain decreases with approaching to the critical temperature. This result suggests that the radius of gyration of the polymer decreases upon approaching to the critical demixing point of the solvent. We discuss the collapse and aggregation processes of the polymer based on the fluorescence quenching method. The rotational diffusion coefficient of carbazolyl groups attached to the polymer chain was estimated by the fluorescence depolarization technique. The rotational motion of carbazolyl groups is slowed down upon approaching the critical point.     

Liquid-liquid equilibria of polymer solutions: Applicability of extended Redlich-Kister expansion

We developed a simple and improved expression for the Helmholtz energy of mixing which uses a Taylor series of an exponential function based on extending the Redlich-Kister expansion. This model incorporates the chain-length dependence of polymers and specific interactions such as hydrogen bonds. The proposed model can accurately predict most phase diagrams of various binary polymer solutions including upper critical solution temperature (UCST), lower critical solution temperature (LSCT), both UCST and LCST, and closed miscibility loops. Our model fits experimental data of the complex phase behavior of polymer solutions well.     

二元阴离子型丙烯酰胺共聚物在二价金属离子存在下相分离行为的研究

水溶性丙烯酰胺类共聚物 ,作为粘度改性剂 ,在工业上已得到广泛应用 .特别近年来 ,它们大量应用于石油工业强化采油技术 ,引起了人们很大的重视[1] .目前 ,这类用途的聚合物 ,主要在聚丙烯酰胺结构中 ,引入阴离子组分和不断增高产物分子量的方法 ,以提高聚合物溶液粘度和增粘效果 ,然而 ,在二价金属离子 (如Ｃａ2 + ,Ｍｇ2 + 等 )存在下 ,羧酸阴离子型丙烯酰胺类共聚物很容易络合发生沉淀 ,从而失去增粘作用[2 ] .同时这类聚合物中酰胺基不稳定 ,易发生水解反应转化为羧酸基 ,并随温度升高而加剧[3 ] ,因此在温度较高的应用条件下 ,二价金属…     

Mean‐field‐theory for polymers in mixed solvents. Thermodynamic and structural properties

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the mixed solvent is near criticality without solute, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymer‐solvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes phase transition from a swollen state to an unperturbed state or even takes a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein‐Zernike series expansion.     

Self‐Assembly and Covalent Fixation for Topological Polymer Chemistry

A novel methodology (electrostatic self‐assembly and covalent fixation) has been proposed for designing various nonlinear polymer topologies, including monocyclic and polycyclic polymers, cyclic macromonomers and cyclic telechelics (kyklo‐telechelics), a‐ring‐with‐a‐branch topology polymers and polymeric topological isomers, as well as branched model polymers, such as star polymers and polymacromonomers. Thus, new telechelic polymer precursors having a moderately strained cyclic onium salt group as single or multiple end groups and carrying multifunctional carboxylates as the counterions were prepared through an ion‐exchange reaction. A variety of electrostatic self‐assemblies of these polymer precursors, formed particularly in dilute organic solution, was then subjected to heat in order to convert the ionic interactions into covalent linkages by ring‐opening reaction, and to produce topologically unique, nonlinear polymer architectures in high efficiency.     

Many body effects on the phase separation and structure of dense polymer-particle melts

Liquid state theory is employed to study phase transitions and structure of dense mixtures of hard nanoparticles and flexible chains (polymer nanocomposites). Calculations are performed for the first time over the entire compositional range from the polymer melt to the hard sphere fluid. The focus is on polymers that adsorb on nanoparticles. Many body correlation effects are fully accounted for in the determination of the spinodal phase separation instabilities. The nanoparticle volume fraction at demixing is determined as a function of interfacial cohesion strength (or inverse temperature) for several interaction ranges and nanoparticle sizes. Both upper and lower critical temperature demixing transitions are predicted, separated by a miscibility window. The phase diagrams are highly asymmetric, with the entropic depletion-like lower critical temperature occurring at a nanoparticle volume fraction of approximately 10%, and a bridging-induced upper critical temperature at approximately 95% filler loading. The phase boundaries are sensitive to both the spatial range of interfacial cohesion and nanoparticle size. Nonmonotonic variations of the bridging (polymer-particle complex formation) demixing boundary on attraction range are predicted. Moreover, phase separation due to many body bridging effects occurs for systems that are fully stable at a second order virial level. Real and Fourier space pair correlations are examined over the entire volume fraction regime with an emphasis on identifying strong correlation effects. Special attention is paid to the structure near phase separation and the minimum in the potential of mean force as the demixing boundaries are approached. The possibility that nonequilibrium kinetic gelation or nanoparticle cluster formation preempts equilibrium phase separation is discussed.     

Parametric studies of interaction strengths in polymer/CO2 systems: discontinuous molecular dynamics simulations

Discontinuous molecular dynamics simulations are performed on homopolymer/solvent and surfactant/solvent systems. The homopolymer and surfactant molecules are modeled as freely jointed square-well chains. Solvent molecules are modeled as both hard spheres and square-well spheres. We explore how the various interaction parameters affect the types of phase behavior and micellization observed in the homopolymer/solvent and surfactant/solvent systems. Increasing the packing fraction of homopolymers in both hard-sphere solvents and square-well solvents increases the solvent's ability to dissolve homopolymers only when the segment-solvent interaction strength exceeds a critical value. Although only upper critical solution temperature (UCST) behavior is observed for homopolymers in hard-sphere solvents, both UCST and lower critical solution temperature (LCST) behavior are observed for homopolymers in square-well solvents, depending upon the interaction strengths and chain length. This indicates that it is necessary to account for the solvent-solvent attraction to model LCST behavior in supercritical CO2. Our simulation results on surfactants in hard-sphere solvents show that it is necessary to account for the interactions experienced by both the head and tail blocks in order to capture the essential features of surfactant/supercritical CO2 systems.     

Pressure-induced formation of diblock copolymer "micelles" in supercritical fluids. A combined study by small angle scattering experiments and mean-field theory. II. Kinetics of the unimer-aggregate transition

We developed a simple time-dependent mean-field theory to describe the phase separation kinetics of either homopolymers or AB-diblock copolymers in supercritical (SC) fluids. The model, previously used to describe the phase behavior of AB-block copolymers under the assumption of strong solvent selectivity for just one copolymer chain, has been extended to study the kinetics of the phase separation process. Time resolved small angle x-ray scattering (TR-SAXS) measurements have been performed on different AB-diblock copolymers containing a perfluorinated chain and dissolved in SC-CO2. The data obtained over a wide range of pressure and temperature confirm our theoretical predictions. Particularly interesting is the presence of two relaxation frequencies for the homogeneous solution --> spherical aggregate transition, where the two relaxation processes depend on the depth of the pressure jump and on temperature. The whole phenomenon could be explained as an initial SC solvent/polymer phase separation followed by a slow reorientation process to form spherical aggregates driven by the copolymer solvophilic moiety.     

Solution‐crystallization and related phenomena in 9,9‐dialkyl‐fluorene polymers. II. Influence of side‐chain structure

Solution‐crystallization is studied for two polyfluorene polymers possessing different side‐chain structures. Thermal analysis and temperature‐dependent optical spectroscopy are used to clarify the nature of the crystallization process, while X‐ray diffraction and scanning electron microscopy reveal important differences in the resulting microstructures. It is shown that the planar‐zigzag chain conformation termed the β‐phase, which is observed for certain linear‐side‐chain polyfluorenes, is necessary for the formation of so‐called polymer‐solvent compounds for these polymers. Introduction of alternating fluorene repeat units with branched side‐chains prevents formation of the β‐phase conformation and results in non‐solvated, i.e. melt‐crystallization‐type, polymer crystals. Unlike non‐solvated polymer crystals, for which the chain conformation is stabilized by its incorporation into a crystalline lattice, the β‐phase conformation is stabilized by complexation with solvent molecules and, therefore, its formation does not require specific inter‐chain interactions. The presented results clarify the fundamental differences between the β‐phase and other conformational/crystalline forms of polyfluorenes. © 2015 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1492–1506