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.     

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.     

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.     

Thermal properties of ionic systems near the liquid-liquid critical point

Isobaric heat capacity per unit volume, C(p), and excess molar enthalpy, h(E), were determined in the vicinity of the critical point for a set of binary systems formed by an ionic liquid and a molecular solvent. Moreover, and, since critical composition had to be accurately determined, liquid-liquid equilibrium curves were also obtained using a calorimetric method. The systems were selected with a view on representing, near room temperature, examples from clearly solvophobic to clearly coulombic behavior, which traditionally was related with the electric permittivity of the solvent. The chosen molecular compounds are: ethanol, 1-butanol, 1-hexanol, 1,3-dichloropropane, and diethylcarbonate, whereas ionic liquids are formed by imidazolium-based cations and tetrafluoroborate or bis-(trifluromethylsulfonyl)amide anions. The results reveal that solvophobic critical behavior-systems with molecular solvents of high dielectric permittivity-is very similar to that found for molecular binary systems. However, coulombic systems-those with low permittivity molecular solvents-show strong deviations from the results usually found for these magnitudes near the liquid-liquid phase transition. They present an extremely small critical anomaly in C(p)-several orders of magnitude lower than those typically obtained for binary mixtures-and extremely low h(E)-for one system even negative, fact not observed, up to date, for any liquid-liquid transition in the nearness of an upper critical solution temperature.     

Lattice cluster theory of associating polymers. IV. Phase behavior of telechelic polymer solutions

The newly developed lattice cluster theory (in Paper I) for the thermodynamics of solutions of telechelic polymers is used to examine the phase behavior of these complex fluids when effective polymer-solvent interactions are unfavorable. The telechelics are modeled as linear, fully flexible, polymer chains with mono-functional stickers at the two chain ends, and these chains are assumed to self-assemble upon cooling. Phase separation is generated through the interplay of self-assembly and polymer/solvent interactions that leads to an upper critical solution temperature phase separation. The variations of the boundaries for phase stability and the critical temperature and composition are analyzed in detail as functions of the number M of united atom groups in a telechelic chain and the microscopic nearest neighbor interaction energy ε(s) driving the self-assembly. The coupling between self-assembly and unfavorable polymer/solvent interactions produces a wide variety of nontrivial patterns of phase behavior, including an enhancement of miscibility accompanying the increase of the molar mass of the telechelics under certain circumstances. Special attention is devoted to understanding this unusual trend in miscibility.     

Polymer modifies the critical region of the coexisting liquid phases

Several recent conceptual advances, which take advantage of the polymer conformation in the near critical point of coexisting liquid phases and practical techniques of some unique molecular interactions between polymer chain and the solvent molecules, have been made to allow the investigation of the effect of the well-defined polymer in phase separation of binary mixtures. The behavior of a flexible linear or branched chain polymer (polyethylene oxide, PEO, MW = 9 x 10(5), as an impurity) in the critical binary mixture of isobutyric acid (I) + water (W) was studied by the refractive index (n) measurements using a very accurate and sensitive refractometer. The refractive index in each phase of IW as well as three different PEO concentrations (C = 0.395, 0.796, and 1.605 mg/cm(3)) in the near critical composition of IW have been measured at temperatures below the system's upper critical point. We observed that the polymer was significantly affected in the critical region of IW and these various concentrations of PEO show an important behavior on the critical exponents (beta), the critical temperatures (T(c)), and critical composition (phi(c)), which are depicting the shape of the coexistence curve. The phase-transition region of coexisting phases of IW shifts down with the addition of PEO and T(c) decreases linearly with increasing PEO concentrations. This may indicate that the polymer chain entangles with each phase, thereby the polymer monomers strongly interact with neighbor solvent particles and also intrachain interaction between the polymer segments. At such conditions, the collapse of polymer chain is possible in the vicinity of the critical point. At temperatures T close enough to T(c), the critical exponent beta (defined by the relation (n(1) - n(2)) proportional, variant (T(c) - T)(beta), with n(1) and n(2) being the refractive indices of the coexisting phases) was found to decrease from 0.382 to 0.360 when the PEO concentration changes from 0.395 to 1.605 mg/cm(3). These values are higher than that of 0.326 +/- 0.005 of pure IW, which is compatible with the three-dimensional Ising value beta = 0.325. The observed critical exponents for the PEO in IW are fully renormalized Ising critical exponents. Besides, the phi(c) values decrease with increasing the C values in the mixture of IW. It appears that the shape of the PEO in IW coexistence curves is similar from that of pure IW.     

Molecular interactions in polystyrene cosolvent systems

Studied here are miscible binary cosolvents for polystyrene, for which polystyrene is insoluble in either of the individual solvents. Polymer-solvent interactions in solutions of atactic polystyrene in acetone/diethyl ether and in methylcyclopentane (MCP)/acetone binary cosolvents have been investigated using nuclear magnetic resonance (NMR) spectroscopy. Polystyrene ¹³C chemical shifts were measured as a function of miscible binary solvent compositions and temperature. The NMR data were used to calculate “association constants” as a measure of specific interactions of the solvent components with all sites on the polymer. In mixtures of acetone and diethyl ether, ¹³C-NMR indicates a weak interaction between the polystyrene phenyl ring and the diethylether solvent component. In the polystyrene/MCP/acetone system, present NMR data reveal no preferential interactions. Additional NMR measurements were performed on polystyrene in mixtures of CCl₄/acetone. From these results, it is concluded that although preferential polymer-solvent interactions are present in some cosolvent systems, they are not a prerequisite for such behavior.     

Depletion-induced surface alignment of asymmetric diblock copolymer in selective solvents

Phase separation of asymmetric diblock copolymer near surfaces in selective solvents is theoretically investigated by using the real-space version of self-consistent field theory (SCFT). Several morphologies are predicted and the phase diagram is constructed by varying the distance between two parallel hard surfaces (or the film thickness) W and the block copolymer concentration f(P). Morphologies of the diblock copolymer in dilute solution are found to change significantly with different film thicknesses. In confined systems, stable morphologies found in the bulk solution become unstable due to the loss of polymer conformation entropy. The vesicle phase region contracts when the repulsive interaction between the blocks is strong (strong segregation regime). The mixture of vesicles, rodlike and spherelike micelles and the mixture of vesicles and sphere-like micelles disappear in contrast to the weakly segregating regime. The walls strongly affect the phase separation of block copolymer in selective solvent, and the depletion layer near the surface contributes much to the micelle formation of the block copolymer. Interestingly, the self-assembled morphologies stay near the walls with the distance on the order of the radius of gyration of the block copolymer. The oscillation of the polymer distribution near the walls allows the surface phase separation to be observed due to the strong repulsion between the blocks A and B.     

Crystalline-amorphous interaction in relation to the phase diagrams of binary polymer blends containing a crystalline constituent

The present article describes an equilibrium theory for determining binary phase diagrams of various crystalline-amorphous polymer blends by taking into account the contributions from both liquid-liquid phase separation between the constituents and solid-liquid phase transition of the crystalline component. An analytical expression for determining a crystal-amorphous interaction parameter is deduced based on the solid-liquid transition, involving the solidus and liquidus lines in conjunction with the coexistence curve of an upper critical solution temperature type. Of particular importance is that the crystalline-amorphous interaction parameter can be determined directly from the melting point depression data. The present analysis is therefore different from the conventional Flory-Huggins interaction parameter, which is associated with the liquid-liquid phase separation. The validity of the present theory is tested with the experimental phase diagrams of blends of poly(ethylene oxide)/diacrylate and poly(vinyl alcohol)/cellulose.     

Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

Cloud point phenomena for POE-type nonionic surfactants in a model room temperature ionic liquid

The cloud point phenomenon has been investigated for the solutions of polyoxyethylene (POE)-type nonionic surfactants (C(12)E(5), C(12)E(6), C(12)E(7), C(10)E(6), and C(14)E(6)) in 1-butyl-3-methylimidazolium tetrafluoroborate (bmimBF(4)), a typical room temperature ionic liquid (RTIL). The cloud point, T(c), increases with the elongation of the POE chain, while decreases with the increase in the hydrocarbon chain length. This demonstrates that the solvophilicity/solvophobicity of the surfactants in RTIL comes from POE chain/hydrocarbon chain. When compared with an aqueous system, the chain length dependence of T(c) is larger for the RTIL system regarding both POE and hydrocarbon chains; in particular, hydrocarbon chain length affects T(c) much more strongly in the RTIL system than in equivalent aqueous systems. In a similar fashion to the much-studied aqueous systems, the micellar growth is also observed in this RTIL solvent as the temperature approaches T(c). The cloud point curves have been analyzed using a Flory-Huggins-type model based on phase separation in polymer solutions.     

Amphiphilic polymer brush in a mixture of incompatible liquids

An analogue of the Alexander‐DeGennes box model is used for theoretical investigation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory‐Huggins parameter χ_AB = 3.5). Thermodynamics of a polymer in the solvents A and B are described by parameters χ_B < χ_A ≤ 1/2. The equilibrium behavior of a brush is investigated in dependence on solvent composition, grafting density, polymer‐solvents and solvent‐solvent interactions. The possibility of a phase transition related with a strong preferential solvation of a brush by a minor solvent component with higher affinity to polymer is shown and examined. Microphase segregation inside a brush is also demonstrated despite overestimating of the brush homogeneity given by the box model. A further simplification of the model permits to obtain scaling formulas and to investigate main regularities in the brush behavior. This offers a clear physical picture of the phase segregation inside a brush in correlation with the phase state of a bulk solvent.     

Polymer solubility in mixed solvents

Modeling results indicate that polymer chains in mixtures of a good with a bad solvent exhibit preferential adsorption of the good solvent. That phenomenon is found to be strongly dependent on molecular weight and it increases with a decrease in chain length. These results have important consequences on polymer solubility. Thus, a low molecular weight chain in a solvent mixture behaves as if it were dissolved in the pure good solvent component, whereas the solubility of a longer chain is controlled by the average mixture composition. As a result, quenching a polydisperse system below the cloud point may induce molecular weight segregation between the two phases: the longer chains, which precipitate out first, tend to populate the polymer rich phase whereas the shorter chains, having greater solubility, remain in the solvent phase. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2782–2787, 1999     

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.     

EFFECT OF DILUENTS ON CRYSTALLIZATION OF POLY(VINYLIDENE FLUORIDE) AND PHASE SEPARATED STRUCTURE IN A TERNARY SYSTEM via THERMALLY INDUCED PHASE SEPARATION

The phase diagram of a ternary system of PVDF,dibutyl phthalate (DBP) and di(2-ethylhexyl) phthalate (DEHP) was determined in terms of a pseudo binary system with the same polymer concentration and different DBP content in diluent mixture.The experimental results showed that as the DBP content increased in diluent mixture,the phase separation changed from liquid-liquid phase separation to solid-liquid phase separation,and both the cloudy point for L-L phase separation and crystallization temperature shif...     

Dilute solution properties of anionic polystyrene in ternary mixture toluene-2-butanone-2-methyl-1-propanol

Several polystyrene samples with relatively narrow molecular weight distributions have been prepared by anionic polymerization. Dilute solution properties of these samples in binary and ternary liquid mixtures were investigated by light scattering and viscometry, using toluene and 2-butanone as solvents and 2-methyl-1-propanol as non-solvent. At 25° experiments were performed to find a set of compositions of the mixed solvent where the second virial coefficient of the osmotic pressure expansion equals zero for the polymer solution, and a set of compositions of the mixed solvent where the intrinsic viscosity of the polymer solution equals the value for polystyrene a theta solvent, such as cyclohexane at 34.5°. The results suggest that these sets of compositions are not identical. The specific effects of sorption and preferential sorption which give rise to the difference between the sets of compoisitions are qualitatively discussed in terms of the Flory-Huggins theory.     

Systematic investigation of global phase behavior of polymer mixtures in the pressure-temperature plane

We investigate the critical lines of polymer mixtures in the presence of their vapor phase at the mathematical double point, where two critical lines meet and exchange branches, and its environment. The model used combines the lattice gas model of Schouten, ten Seldam and Trappeniers with the Flory-Huggins theory. The critical line structure is displayed for various combinations of the chain length and system parameters in the pressure (P)-temperature (T) plane, as is usually done with experimental results. This type of work sheds light on the essential transition mechanism involved in the phase diagram's change of character, such as multi-critical points and mathematical double points, which are of great practical importance in supercritical fluid extraction processes. The P, T diagrams are discussed in accordance with the Scott and van Konynenburg binary phase diagram classification. We found that our P, T plots were in agreement with type II, type III, or type IV phase diagram behaviors. We also found that some of our phase diagrams represent the liquid-liquid equilibria in polymer solutions and mixtures.     

Composition analysis of an ethylene–propylene block copolymer by fractionation and turbidity measurements at the lower critical solubility gap

The composition of an ethylene-propylene block copolymer with a nominal 15% content of ethylene by weight (EP?B15%) has been investigated through fractionation near the lower critical solution temperature (LCST). Observation of the solution heated above the boiling point of the solvent indicated that some polymer was phase separating, apparently continuously, between the LCSTs of polyethylene (PE) an polypropylene (PP) of similar molecular weight. IR and DSC analysis of three fractions obtained by twice separating the concentrated phase from the dilute phase gave the following result: EP?B15% consists of an ethylene-rich block copolymer (93% E), an EP copolymer of intermediate composition, and a propylene-rich copolymer (94% P). The three fractions constitute respectively 12%, 12%, and 76% of the total weights. In order to choose a suitable temperature for fractionation, a turbidity analysis of the solution of the initial polymer is made continuously during phase separation. The trace of turbidity against temperature shows three peaks of turbidity at temperatures T₀, T₁ and T₂, which can be associated with the above fractions. A mixture of PE, PP, and a 33% E random copolymer gives a turbidity trace with characteristic temperatures very similar to that of EP-B15% in the same solvent. Fractionation from several solvents or mixtures of solvents indicated that the composition of the fractions did not depend significantly on the nature of the solvent. Conditions for obtaining a quantitative analysis of a mixture from a thermogram are discussed. Turbidity analysis during phase separation and fractionation at the LCST can be a useful tool in analyzing and separating complex mixtures before use of powerful analytical techniques such as NMR or IR spectroscopy.     

Topological transformation of the phase diagram for the ternary system cesium nitrate-water-acetonitrile

In the ternary system cesium nitrate-water-acetonitrile, in which liquid-liquid phase separation with an upper critical solution point (UCSP) exists in the liquid binary subsystem, was studied in the range from ?5 to 120°C using visual polythermal analysis. Liquid-liquid phase separation in the ternary system is observed above 96.0°C and below 2.8°C. Acetonitrile distribution coefficients between the aqueous and organic phases of monotectic equilibrium were calculated for various temperatures. Phase isotherms of the system confirm the general scheme of the topological transformation of phase diagrams in salt-binary solvent ternary systems with salting out.     

A new theory for polymer/solvent mixtures based on hard-sphere limit

Based on hard-sphere limit of binary mixtures with different molecular size of components a theory has been developed for calculating activities of solvents in polymer/solvent mixtures. The theory considers various chain configurations for polymer molecules, varying from extended chain to the coiled chain. According to this theory the activity of solvent can be calculated from molecular weights (MWs) and densities as the only input data. The only adjustable parameter in the calculations, is the hard-sphere diameter of polymer, which provides useful criteria for the judgement on the chain configuration of polymer.The activity calculations have been performed for seven binary mixtures of polymer/solvent and compared with experimental data at various temperatures and for a varying range of MWs of polymers.The solvents in the mixtures were both of polar and nonpolar natures. The activity calculations for the same systems were performed by the well-known Flory-Huggins theory. Comparing the results of calculations with those of Flory-Huggins theory indicates that, the proposed theory is able to predict the activities of the solvent with good accuracy.The radius of gyration, excluded volume and interaction parameter for polymer chain have been calculated using the parameter obtained in the new theory. The calculated interaction parameter in the new theory, is interpreted in terms of attraction, repulsion and interchange energy of polymer and solvent in the mixture.