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.     

Ginzburg number and phase behavior of binary polymer blends in pressure fields

In some polymer blends the temperature and pressure dependence of thermal composition fluctuations have been measured with small angle neutron scattering. The Ginzburg number Gi, the Flory‐Huggins parameter Γ, and the phase boundaries were determined for pressure fields up to 150 MPa. In polymer blends the compressibility leads to a strongly increased Gi which could be appreciably larger than in low molecular liquids and which decreases with increasing pressure fields. Usually, the phase boundaries of UCST as well as of LCST blends shift with pressure to higher temperatures. One blend having PDMS as one component, however, shows an abnormal decrease of the phase boundaries with increasing pressure. The Clausius‐Clapeyron equation correctly predict from the experimentally determined Γ and Gi the observed pressure dependence of the phase boundaries.     

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.     

Predicting mixture phase equilibria and critical behavior using the SAFT-VRX approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.     

Ion-induced multiply reentrant liquid-liquid transitions and the nature of criticality in ethanol-water mixture

We report a quite unusual feature of four liquid-liquid reentrant transitions in ethanol (E)+water (W)+ammonium sulfate mixture by meticulous tuning of the ammonium sulfate concentration in a narrow range, as a function of temperature, at atmospheric pressure. Detailed exploration of the intricate phase behavior in terms of E/W sections shows that the range of triple reentrance shrinks with increasing E/W. The behavior of osmotic susceptibility is investigated by light scattering, near the critical point, in the one-phase region by varying the temperature at fixed concentration of the components, in a particular E/W section. The critical exponent of susceptibility (gamma) and correlation length (nu) are observed to have Fisher renormalized Ising values [Phys. Rev. 176, 237 (1968)], with gamma(r)=1.41 and nu(r)=0.718. The effective susceptibility exponent, gamma(eff), exhibits a sharp, nonmonotonic crossover from Ising to mean-field critical behavior, which is completed outside the critical regime. The amplitude of the correlation length, xi(o)(=21.2+/-0.4 A), deduced from light scattering experiment, is an order of magnitude larger than the typical values in usual aqueous electrolyte systems. This value of xi(o) is further verified from small-angle x-ray scattering (SAXS) experiments and found to be consistent. SAXS experiments on the critical sample reveal the presence of long-ranged intermolecular correlations, leading to supramolecular structuring, at a temperature far away from the critical point. These results convincingly demonstrate that the finite length scale arising due to the structuring competes with the diverging correlation length of critical concentration fluctuations, which influences the nonasymptotic critical behavior in this aqueous electrolyte system. The sulphate ions play a dominant role in both structuring and the complex phase behavior.     

The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.     

Composition fluctuations in a homopolymer-diblock copolymer mixture covering the three-dimensional Ising, isotropic Lifshitz, and Brasovskiĭ classes of critical universality

The phase behavior of a three-component polymer blend consisting of a critical mixture of polybutadiene and polystyrene (PB/PS) with varying amount of a symmetric PB-PS diblock copolymer was explored with small-angle neutron scattering. Our focus were thermal composition fluctuations which we discuss in terms of mean field, three-dimensional Ising, isotropic Lifshitz, and Brasovski? classes of critical universality. Particular attention is spent to the observation of a narrow reentrant two-phase regime and double critical point in the Lifshitz critical regime as well as the Lifshitz line. Critical exponents of the isotropic Lifshitz case are proposed in spite of the demonstrated nonexistence of the isotropic Lifshitz critical point. The Ginzburg number (Gi) and Flory-Huggins parameter were determined over the whole diblock concentration range; Gi changes by three orders of magnitude, two orders of magnitude of that change over a 0.03 diblock concentration interval within the isotropic Lifshitz regime.     

Simulation and theory of flexible equilibrium polymers under poor solvent conditions

Grand canonical Monte Carlo simulation and simple statistical thermodynamic theory are used to model the aggregation and phase separation of systems of reversibly polymerizing monomers, capable of forming chains with or without the ability to cyclize into rings, with isotropic square-well attractions between nonbonded pairs of monomers. The general trend observed in simulation of chain-only systems, as predicted in a number of published theoretical works, is that the critical temperature for phase separation increases and the critical monomer density decreases with rising polymer bond strength. Introduction of the equilibrium between chains and rings into the theory lowers the predicted critical temperature and increases the predicted critical density. While the chain-only theories predict a vanishing critical density in the limit of complete polymerization, when ring formation is taken into account the predicted critical density in the same limit approaches the density of the onset of the ring-chain transition. The theoretically predicted effect of cyclization on chemical potential is in good qualitative agreement with a subset of simulation results in which chain-only systems were compared with equilibrium mixtures of rings and chains. The influence of attractions on the aggregation number and radius of gyration of chains and rings observed in simulations is also discussed.     

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     

Phase behavior of self-associating fluids with weaker dispersion interactions between bonded particles

In this study, we explore the global phase behavior of a simple model for self-associating fluids where association reduces the strength of the dispersion interactions between bonded particles. Recent research shows that this type of behavior likely explains the thermodynamic properties of strongly polar fluids and certain micellar solutions. Based on Wertheim's theory of associating liquids [M. S. Wertheim, J. Stat. Phys. 42, 459 (1986); 42, 477 (1986)], our model takes into account the effect that dissimilar particle interactions have on the equilibrium constant for self-association in the system. We find that weaker interactions between bonded molecules tend to favor the dissociation of chains at any temperature and density. This effect stabilizes a monomeric liquid phase at high densities, enriching the global phase behavior of the system. In particular, for systems in which the energy of mixing between bonded and unbonded species is positive, we find a triple point involving a vapor, a dense phase of chain aggregates, and a monomeric liquid. Phase coexistence between the vapor and the monomeric fluid is always more stable at temperatures above the triple point, but a highly associated fluid may exist as a metastable phase under these conditions. The presence of this metastable phase may explain the characteristic nucleation behavior of the liquid phase in strongly dipolar fluids.     

Nucleation of self-associating fluids: free versus activated association

We use the density functional theory of statistical mechanics in a square gradient approximation to analyze the structure, size, and work of formation of critical nuclei in self-associating fluids where association reduces the strength of the interactions between bonded particles. This effect is expected in systems of strongly dipolar particles that associate into chains. In this work we analyze the nucleation behavior of two types of self-associating fluids: a system comprised of particles that can freely associate, and a system in which the association process involves a thermally activated initiation step. For the first case, we explore the properties of critical nuclei in fluids that exhibit a metastable critical point between a vapor phase and a highly associated liquid phase. In fluids where the association dynamics involves an initiation step, we investigate the nucleation behavior in the vicinity of the polymerization transition. In both cases critical nuclei undergo a structural transition that shares many of the features of the coil-globule transition reported in Monte Carlo simulations of strongly dipolar Stockmayer fluids. Our results suggest that the sharp structural transition observed in these simulations is evidence of the existence of a second-order or nearly second-order association transition in these model fluids.     

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.     

Theoretical analysis of polydispersity in the nematic phase of self-assembled semiflexible chains

In recent simulations of semiflexible equilibrium polymers [X. Lu and J. T. Kindt, J. Chem. Phys. 120, 10328 (2004)] a roughly biexponential distribution of chain lengths was observed in the nematic phase. In this study, we show that a theory representing the nematic phase as an equilibrium mixture of randomly oriented chains below a critical length Lc and chains above Lc obeying a Gaussian orientational distribution reproduces this distribution qualitatively. The agreement between predicted and simulated phase boundaries is improved, with a narrower isotropic-nematic coexistence region, compared with a monoexponential chain distribution. We find, furthermore, that the critical length Lc scales as the inverse of monomer concentration, irrespective of the bond strength of the chains, but that at the phase boundary, the fraction of monomers found in disordered chains peaks at a certain bond strength.     

Thermodynamic properties of Lennard-Jones chain molecules: renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.     

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.     

Rheological behavior of silica suspensions in aqueous solutions of associating polymer

Associating polymers are hydrophilic long-chain molecules containing a small amount of hydrophobic groups. The aqueous solutions show viscoelastic responses above some critical concentrations because a three-dimensional structure is formed by association of hydrophobic groups. When the associating polymers are added to silica suspensions at low concentrations, the flocculation is induced by bridging mechanisms, and the flow of suspensions become shear-thinning. For suspensions prepared with polymer solutions in which the associating network is developed, the viscosity decreases, shows a minimum, and then increases with increasing particle concentration. The viscosity decrease may arise from the breakdown of associating network due to adsorption of polymer chains onto the silica surfaces. As the particle concentration is increased, the polymer concentration in solution is decreased, and finally, all polymer chains are adsorbed on the surfaces. Beyond this point, the partial coverage of particle surfaces takes place and strong interactions are generated between particles by polymer bridging. Since the stable suspensions are converted to highly flocculated systems, the viscosity is increased and the flow becomes shear-thinning. The concentration effect of silica particles on the viscosity behavior of suspensions can be explained by a combination of viscosity decrease in solution due to polymer adsorption and viscosity increase due to flocculation.     

Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems containing associating compounds. In this work, a set of correlations was proposed to calculate the CPA model parameters for the narrow cuts in ill-defined C₇₊ fractions. The correlations were then combined with either the characterization method of Pedersen et al. or that of Whitson et al. to extend CPA to reservoir fluids in presence of water and polar chemical such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model multicomponent systems. In addition, modeling of mutual solubility between light hydrocarbons and water is also addressed.     

表面活性(可控)接枝聚合研究进展

表面是材料与外界接触的窗口,材料的众多性质,如耐磨性、耐腐蚀性、生物相容性等均在很大程度上取决于表面的构成.可通过在材料表面接枝不同的聚合物链使之满足不同的需要.表面引发的活性(可控)聚合可得到分布均匀、厚度可控的接枝层,因而成为表面改性中的重要方法.本文介绍了一系列表面引发的活性(可控)聚合技术及其应用举例,对这一领域所取得的研究进展及现状作一综述.     

Composition fluctuations, chemical exchange, and nuclear relaxation in membranes containing cholesterol

A thermodynamic model of cholesterol-phospholipid complexes is used as a starting point for calculating fluctuations in membranes containing cholesterol and phospholipids. The calculations describe fluctuations in the concentration of complexes formed between cholesterol and phospholipids with longer saturated fatty acid chains. The fluctuations in complex concentrations arise by two distinct mechanisms. In one, the chemical composition of the sample varies from point to point, and the concentration of the complexes varies according to local chemical equilibrium. In the second, the composition remains fixed, and the complexes form and dissociate according to chemical reaction kinetics. In both cases the nuclear resonance frequency of a deuterium labeled phospholipid undergoes fluctuations and line broadening as a consequence of the formation and dissociation of complexes. For a specific ternary lipid mixture at its critical composition, deuterium nuclear resonance line broadening of chain labeled phospholipids is calculated for temperatures up to 10 degrees -20 degrees above the miscibility critical temperature. This line broadening is associated with fluctuations in the degree of phospholipid chain ordering related to the formation and dissociation of complexes.