Interfacial thermodynamics of compressible polymer solutions

A variational model is developed to compute the coupled density and concentration fields that define the structure of planar interface between equilibrium phases of a compressible polymer solution. The solution of the model in conjunction with the modified Sanchez-Lacombe, with parametric data relevant to real polymer solutions, quantifies the role of compressibility on interfacial thermodynamics and interfacial tension. In particular, it is found that pressure pulses originating from density changes compensate chemical stresses. The interfacial tension, based on Bakker's equation, between equilibrium polymer solution phases and corresponding interfacial thickness exhibits pressure scaling behavior analogous to that predicted with temperature for incompressible polymer solutions.     

Acousto-spinodal decomposition of compressible polymer solutions: early stage analysis

The structure and dynamics of early stage kinetics of pressure-induced phase separation of compressible polymer solutions via spinodal decomposition is analyzed using a linear Euler-Cahn-Hilliard model and the modified Sanchez Lacombe equation of state. The integrated density wave and Cahn-Hilliard equations combine the kinetic and structural characteristics of spinodal decomposition with density waves arising from pressure-induced couplings. When mass transfer rate is slower that acoustic waves, concentration gradients generate density waves that cycle back into the spinodal decomposition dynamics, resulting in oscillatory demixing. The wave attenuation increases with increasing mass transfer rates eventually leading to nonoscillatory spinodal demixing. The novel aspects of acousto-spinodal decomposition arise from the coexistence of stable oscillatory density dynamics and the unstable monotonic concentration dynamics. Scaling laws for structure and dynamics indicate deviations from incompressible behavior, with a significant slowing down of demixing due to couplings with density waves. Partial structure factors for density and density-concentration reflect the oscillatory nature of acousto-spinodal modes at lower wave vectors, while the single maximum at a constant wave vector reflects the presence of a dominant mode in the linear regime. The computed total structure factor is in qualitative agreement with experimental data for a similar polymer solution.     

The Fast Relaxation Process between Hydrophobically Modified Associating Polyacrylamide and Different Surfactants at the Water‐Octane Interface

In our previous work (Macromolecules 2004, 37:2930), we found that the hydrophobic blocks of polyacrylamide modified with 2‐phenoxylethyl acrylate (POEA) and anionic surfactant sodium dodecyl sulfate (SDS) may form mixed associations at octane/water interface. However, the process involving the exchange of surfactant molecules between monomers and mixed associations in interface is so fast that we cannot obtain its characteristic time. In this article, the interfacial dilational viscoelastic properties of another hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2‐ethylhexyl acrylate (EHA) (<1.0 mol%) at the octane‐water interfaces were investigated by means of oscillating barriers method and interfacial tension relaxation method respectively. The influences of anionic surfactant SDS and nonionic surfactant Triton X‐100 on the dilational viscoelastic properties of 7000 ppm polymer solutions were studied. The results showed that the interaction between P(AM/2‐EHA) and SDS was similar to that of P(AM/POEA) and SDS. Moreover, we got the relaxation characteristic time of the fast process involving the exchange of s Triton X‐100 molecules between monomers and mixed associations.

We also found that the interfacial tension response of hydrophobically associating water‐soluble copolymers to the sinusoidal oscillation of interfacial area at low bulk concentration is as same as that of the typical surfactants: the interfacial tension decreases with the decrease of interfacial area because of the increase of interfacial active components. However, the interfacial tension increases with the decrease of interfacial area at 7000 ppm P(AM/2‐EHA), which is believed to be correlative with the structure of absorbed film. The results of another hydrophobically associating polymer P(AM/POEA) and polyelectrolyte polystyrene sulfonate (PSS) enhanced our supposition. The phase difference between area oscillation and tension oscillation has also been discussed considering the apparent negative value.     

Surface tension of polystyrene blends: Theory and experiment

Surface tension of linear–linear and star/linear polystyrene blends were measured using a modified Wilhelmy method. Our results show that for both polystyrene blend systems, the surface tension‐composition profile is convex, indicating a strong surface excess of the component with lower surface energy. Star/linear blends display more convex surface tension profiles than their linear–linear counterparts, indicative of stronger surface segregation of the branched‐component relative to linear chains. As a first step toward understanding the physical origin of enhanced‐surface segregation of star polymers, self‐consistent field (SCF) lattice simulations (both incompressible and compressible models) and Cahn‐Hilliard theory were used to predict surface tension‐composition profiles. Results from the lattice simulations indicate that the highly convex surface tension profiles observed in the star/linear blend systems are only possible if an architecture‐dependent, Flory interaction parameter (χ = 0.004) is assumed. This conclusion is inconsistent with results from bulk differential scanning calorimetry (DSC) measurements, which indicate sharp glass transitions in both the star/linear and linear/linear homopolymer blends and a simple linear relationship between the bulk glass transition temperature and blend composition. To implement the Cahn‐Hilliard theory, pressure‐volume‐temperature (PVT) data for each of the pure components in the blends were first measured and the data used as input for the theory. Consistent with the experimental data, Cahn‐Hilliard theory predicts a larger surface excess of star molecules in linear hosts over a wide composition range. Significantly, this result is obtained assuming a nearly neutral interaction parameter between the linear and star components, indicating that the surface enrichment of the stars is not a consequence of complex phase behavior in the bulk. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1666–1685, 2009     

Liquid–liquid equilibria of polymer solutions: Flory‐huggins with specific interaction

We have developed a new Flory‐Huggins model by adding a specific interaction parameter derived from a modified double‐lattice model for the Helmholtz energy of mixing for binary liquid mixtures. This model is very simple and could be easily integrated into engineering applications. Using this revised model, we can successfully describe the phase behavior of polymer solutions with an upper critical solution temperature (UCST), a lower critical solution temperature (LCST), both UCST and LCST, and a closed miscibility loop. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 162–167, 2010     

Interfacial tension in a lower critical solution temperature blend: Effect of temperature,blend composition,and deformation of the interphase

Interfacial tension is a very important material parameter in two‐phase polymer blends. It determines the morphology development during processing, which is crucial for the end‐use properties of the material. Although different techniques for interfacial tension measurement give comparable results for immiscible polymers, the determination of the interfacial tension in lower critical solution temperature blends is not straightforward. This is illustrated for poly(α‐methyl styrene acrylonitrile)/poly(methyl methacrylate)(PαMSAN/PMMA), a slightly incompatible polymer pair. Interfacial tension has been measured with three different techniques: small‐amplitude oscillatory shear, recovery after elongation, and elongation of a multilayer sample. The large differences in these results can be attributed to the fact that most experimental techniques determine an apparent value, rather than the thermodynamic equilibrium value, of the interfacial tension. The latter is only obtained if the measurement is performed under quiescent conditions on a system that is composed of the coexisting PαMSAN‐rich and PMMA‐rich phases. The apparent interfacial tension depends on the actual composition of the phases and on the deformation of the interface. An order of magnitude approximation for such effects has been derived from theoretical considerations. Finally, each of these apparent values can be of practical importance. If a blend is prepared by melt mixing of the pure polymers, a high apparent value of interfacial tension should be considered. If, however, a blend is prepared by phase separation of a homogeneous mixture, the thermodynamic value is important. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 679–690, 2002     

Interactions between Hydrophobically Modified Associating Polyacrylamide and Cationic Surfactant at the Water‐Octane Interface: Interfacial Dilational Viscoelasticity and Relaxation Processes

The interfacial dilational viscoelastic properties of hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2‐ethylhexyl acrylate (EHA) (<1.0 mol%) with a hydrolyzed degree of about 1.5–2.0% at the octane‐water interfaces were investigated by means of two methods: the interfacial tension response to sinusoidal area variations (oscillating barriers method) and the relaxation of an applied stress (interfacial tension relaxation method) respectively. The influence of cationic surfactant cetyl trimethylammonium bromide (CTAB) on the dilational viscoelastic properties was studied. The results obtained by oscillating barriers method showed that dilational modulus decreased moderately with the increase of CTAB concentration. The results obtained by interfacial tension relaxation measurements showed that two main relaxation processes exist in the interface at 7,000 ppm polymer concentration: one is the fast process involving the exchange of hydrophobic blocks between the proximal region and distal region in the interface; the other is the slow relaxation process involving conformational changes of polymer chain in the interface. By adding CTAB, the slow process changed obviously due to the strong electrostatic interaction between oppositely charged surfactant and hydrolyzed part of polymer chain. Only when the CTAB concentration was close to the “equal charge point,” the associations formed mainly by the hydrophobic interaction like that in SDS/polymer system appeared and the characteristic time of fast process decreased obviously. The information of relaxation processes obtained from interfacial tension relaxation measurements can explain the results from dilational viscoelasticity measurements very well.     

Interfacial nematodynamics of heterogeneous curved isotropic-nematic moving fronts

The early stages of liquid crystal phase ordering upon thermal quenches of isotropic phases into unstable and metastable temperature ranges is studied using two-dimensional (2D) computational solutions of the governing Landau-de Gennes (L-dG) equations for low molar mass nematic liquid crystals and analysis based on the corresponding interfacial nematodynamic model. The early phase ordering stage, for both unstable and metastable quenches of the isotropic phase, is shown to lead to highly textured nematic spherulites through a mechanism of interfacial defect nucleation. The underlying mechanisms of interface-driven texturing are elucidated using complementary 2D computational parametric studies of the bulk L-dG equation and analysis of the IN model. It is shown that for highly curved nanodomains and realistic elastic anisotropy, sharp interfacial transitions between uniaxial and biaxial states arise and are resolved by interfacial defect nucleation, which upon subsequent migration into the spherulite's interior leads to strong texturing. This paper shows that texture formation in the early stages of phase ordering is interface driven, and due to low interface tension, elastic anisotropy, and large curvature. Interfacial defect shedding in highly curved, low tension, anisotropic interfaces is a significant defect nucleation mechanism that needs to be taken into account when considering texturing processes.     

Interfacial effects in organophilic montmorillonite–poly(ϵ‐caprolactone) nanocomposites

In the last few years much progress has been made in the development of hybrid polymer–inorganic filler nanocomposites. Nevertheless, many questions remain. The comprehension of the structure and the interactions at the polymer–nanofiller interface are crucial to foresee and control the properties of nanocomposites. Because of the high surface ratio of the inorganic nanofiller, the interface is expected to have a prevailing role in determining the nanocomposite properties. In this study we use X‐ray photoelectron spectroscopy (XPS) as a tool for the surface characterization of an organophilic montmorillonite/poly(ε‐caprolactone) exfoliated nanocomposite. The XPS core levels of the nanocomposite have been compared with those obtained from its precursors, and analyzed as reference compounds to evaluate eventual differences attributable to the polymer–nanofiller interfacial interactions. The XPS investigation has allowed us to propose a qualitative model of possible interface interactions between poly(ε‐caprolactone) and the organo‐modified montmorillonite. The model is substantiated by Fourier transform infrared spectroscopy (FTIR). © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3907–3919, 2004     

Molecular weight dependence of phase behavior of PEO/P(EO‐b‐DMS) blends: Application of Sanchez‐Lacombe lattice fluid theory

Molecular weight dependence of phase separation behavior of the Poly (ethylene oxide) (PEO)/Poly(ethylene oxide‐block‐dimethylsiloxane) (P(EO‐b‐DMS)) blends was investigated by both experimental and theoretical methods. The cloud point curves of PEO/P(EO‐b‐DMS) blends were obtained by turbidity method. Based on Sanchez‐Lacombe lattice fluid theory (SLLFT), the adjustable parameter, (quantifying the interaction energy between different components), was evaluated by fitting the experimental data in phase diagrams. To calculate the spinodals, binodals, and the volume changes of mixing for these blends, three modified combining rules of the scaling parameters for the block copolymer were introduced. The calculated binodals with those modified combining rules show good agreement with the experimental data. Furthermore, the calculated volume changes during mixing decrease with increasing molecular weight of PEO, and the relationship between the volume changes and temperature is quite different for the mixtures with different molecular weight of PEO. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 452–459, 2008     

Models for adhesion at weak polymer interfaces

The weak interfaces between immiscible polymer pairs typically fail through chain scission. The critical facture toughness for such interfaces is closely related to the density of intermolecular entanglements at the interface. From scaling analysis, a simple correlation between facture toughness and chain entanglement was developed. It predicts well the interfacial adhesion for many immiscible polymer pairs found in the literature. For an interface with block copolymer reinforcement, its critical fracture toughness comes from both intermolecular entanglements of homopolymers and copolymer bridges. In the chain scission regime (low copolymer coverage), the block copolymer contribution is found proportional to copolymer interfacial coverage, with the coefficient being the energy to stretch and break a copolymer chain. The chain‐breaking energy for different copolymers was evaluated and compared to literature data. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2313–2319, 2009     

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     

Dynamic modeling of the morphology of latex particles with in situ formation of graft copolymer

Modification of the polymer–polymer interfacial tension is a way to tailor‐make particle morphology of waterborne polymer–polymer hybrids. This allows achieving a broader spectrum of application properties and maximizing the synergy of the positive properties of both polymers, avoiding their drawbacks. In situ formation of graft copolymer during polymerization is an efficient way to modify the polymer–polymer interfacial tension. Currently, no dynamic model is available for polymer–polymer hybrids in which a graft copolymer is generated during polymerization. In this article, a novel model based on stochastic dynamics is developed for predicting the dynamics of the development of particle morphology for composite waterborne systems in which a graft copolymer is produced in situ during the process. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

The influence of partial emulsification on coalescence suppression and interfacial tension reduction in PP/PET blends

This study examines how the relative role of coalescence suppression and interfacial tension reduction influence the particle size at various levels of in situ compatibilization. The polymers studied are polyethylene terephthalate (PET) as matrix and a polypropylene (PP) as dispersed phase compatibilized by a triblock copolymer of poly(styrene–hydrogenated butadiene–styrene) (SEBS) grafted with maleic anhydride. The interfacial tension was studied by the breaking‐thread method, and it was used along with the morphology to characterize the emulsification efficacy of the copolymers. By modifying the concentration of MA grafted on the SEBS, different levels of emulsification of the blends were obtained. A comparison of 1/99 and 10/90 PP/PET blends compatibilized by SEBS‐g‐MA allows one to distinguish the relative role of interfacial tension and coalescence suppression in diminishing particle size. It is shown that varying degrees of residual coalescence remain, depending on the level of %MA in the copolymer. A detailed study of the 2%MA system below interfacial saturation was carried out to shed further light on the dependence of coalescence suppression on emulsification level and interfacial coverage. After separating out the contribution of interfacial tension on particle size reduction, it is shown that coalescence suppression for this system increases gradually with areal density of modifier at the interface right up to the region of interfacial saturation. Finally, the interfacial and morphological data were used to test the ability of the Lee and Park model to describe coalescence in polymer blends. Reasonable agreement was found between the parameter c₁, describing the coalescence in that model, and the trends related to residual coalescence from this study. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 939–951, 1999     

Physical aging and structural relaxation in polymer nanocomposites

Molecular dynamics simulations of a coarse‐grained polymer nanocomposite model are used to study the impact of nanoparticles on physical aging. The physical aging rate of the composites is obtained from measurements of the per‐particle pair energy, while the (segmental) mean‐squared displacement and creep compliance are used to probe simultaneously the dependence of structural relaxation times on waiting time elapsed since the glass was formed. Although bulk regions behave similarly to a neat polymer glass, interfacial regions exhibit a reduction in the physical aging rate for attractive polymer–nanoparticle interactions. Repulsive interactions lead instead to a significant increase. This change in physical aging rate is found to be proportional to the local mobility of the polymer atoms. By contrast, aging exponents obtained from time‐waiting time superposition of mean‐squared displacements or compliance curves are much less affected by the nanoinclusions. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1789–1798, 2009     

The brittle–ductile transition induced by thermal ageing of toluene cast poly(2,6‐dimethyl‐1,4‐phenylene oxide) as observed by interfacial friction

The interfacial shear stress of toluene cast poly(2,6‐dimethyl‐1,4‐phenylene oxide) films has been studied as a function of annealing temperature. The surface topography of these films was studied by scanning probe microscopy following a single sliding pass. Casting from toluene results in a semicrystalline film with a rigid amorphous phase and containing a small amount of residual solvent that exhibits a higher interfacial shear stress than a high temperature annealed solvent‐free amorphous film. Films containing small amounts of toluene exhibit a wear pattern consisting of ripples oriented perpendicular to the sliding direction following a single sliding pass. These results support the notion that the interfacial shear stress is a function of the shear yield stress, and, that during sliding friction tensile stresses must form at the polymer surface. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1637–1643, 2009     

Sorption and swelling of poly(DL‐lactic acid) and poly(lactic‐co‐glycolic acid) in supercritical CO2: An experimental and modeling study

Tissue engineering scaffolds require a controlled pore size and structure to host tissue formation from cell populations. Supercritical carbon dioxide (scCO₂) processing can be used to form porous scaffolds in which the escape of CO₂ from a plasticized polymer melt generates gas bubbles that shape the pores. The process is difficult to control with respect to changes in final pore size, porosity, and interconnectivity, while the solubility of CO₂ in the polymers strongly affects the foaming process. An in‐depth understanding of polymer CO₂ interaction will enable a successful scaffold processing. Amorphous poly(DL ‐lactic acid) (P_DL LA) and poly(lactic acid‐co‐glycolic acid) (PLGA) polymers are attractive candidates for fabricating scaffolds. In this study, CO₂ sorption and swelling isotherms at 35 °C and up to 200 bar on a variety of homo‐ and copolymers of lactic acid and glycolic acids are presented. Sorption is measured through a gravimetric technique using a suspension microbalance and swelling by visualization. The obtained results are modeled using the Sanchez‐Lacombe equation of state. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 483–496, 2008     

Hydrocarbon and fluorocarbon solubility and dilation in poly(dimethylsiloxane): Comparison of experimental data with predictions of the Sanchez–Lacombe equation of state

Sorption and dilation isotherms are reported for a series of gases (N₂, O₂, CO₂), hydrocarbon vapors (CH₄, C₂H₆, C₃H₈), and their fluorocarbon analogs (CF₄, C₂F₆, C₃F₈) in poly(dimethylsiloxane) (PDMS) at 35°C and pressures up to 27 atmospheres. The hydrocarbons are significantly more soluble in hydrocarbon-based PDMS than their fluorocarbon analogs. Infinite dilution partial molar volumes of both hydrocarbons and fluorocarbons in PDMS were similar to their partial molar volumes in other hydrocarbon polymers and in organic liquids. Except for C₂H₆ and C₃H₈, partial molar volume was independent of penetrant concentration. For these penetrants, partial molar volume increased with increasing concentration. The Sanchez–Lacombe equation of state is used to predict gas solubility and polymer dilation. If the Sanchez–Lacombe model is used with no adjustable parameters, solubility is always overpredicted. The extent of overprediction is more substantial for fluorocarbon penetrants than for hydrocarbons. Very good fits of the model to the experimental sorption and dilation data are obtained when the mixture interaction parameter is treated as an adjustable parameter. For the hydrocarbons, the interaction parameter is approximately 0.96, and for the fluorocarbons, it is approximately 0.87. These values suggest less favorable interactions between the hydrocarbon-based PDMS matrix and the fluorocarbon penetrants than between PDMS and hydrocarbons. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3011–3026, 1999     

Thermodynamic Modeling of Polymer Solution Interface

A new method is presented to characterize the interfacial concentration field and interfacial tension between equilibrium polymer solution phases, using readily accessible equilibrium concentration data. The new method is tested and validated using experimental data from different polystyrene solutions and it consists of i) calculation of a universal expression for the concentration gradient coefficient based on the Cahn‐Hilliard model and the Wolf interfacial tension master equation, and ii) development of a highly accurate algebraic function (Kappa distribution) that, for a given equilibrium polymer concentration set, yields the essentially exact interfacial profile predicted by the classical gradient theory for polymer solutions.

     

Interfacial tension and acid‐base approaches to polymer interactions

A significant correlation has been shown to exist between the interfacial tension of polymer pairs and their acid‐base pair interaction. The relationship is inverse, with interfacial tensions decreasing as acid‐base interactions increase. Interfacial tensions, frequently used as an indicator of polymer compatibility, were measured by the breaking thread method at temperatures in the vicinity of 200 °C. Acid‐base pair interaction values were measured by inverse gas chromatography over wide temperature ranges. The observed correlation confirms the important contribution made by short‐range, acid‐base interactions to the observed value of interfacial tension and supports the prediction of equations based on fundamental definitions of surface forces. A collateral finding of this work is the decrease of acid‐base functionality with rising temperature for all polymers studied. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2096–2104, 2000