Modeling of thermodynamic behavior of PVT properties and cloud point temperatures of polymer blends and polymer blend + carbon dioxide systems using non-cubic equations of state

In recent years, many factors influencing phase behavior of polymer blends have been studied because of their widely technological importance, as a simple method of formulating new materials with tailored properties which make them suitable for a variety of applications. This work has three main goals which were reached by using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS), which in previous works have shown their ability to handle long chain and associating interactions. First, both equations of state were tested with the correlation of the specific volumes of pure blends (PBD/PS, PPO/PS, PVME/PS, PEO/PES) and the prediction of the specific volumes for blends; second, the modeling of blend miscibilities in the liquid–liquid equilibria (LLE) of PBD/PS, PPG/PEGE, PVME/PS, PEO/PES, and PnPMA/PS blends; third, the modeling of the phase behavior of PS/PVME blends at various compositions in the presence of CO₂. PC-SAFT and SL pure-component parameters were regressed by fitting pure-component data of real substances (liquid pressure–volume–temperature, PVT, data for polymers and vapor pressure and saturated liquid molar volume for CO₂) and the fluid phase behavior of blend systems were simulated fitting one binary interaction parameter (k_ij) by regression of experimental data using the modified likelihood maximum method. Results were compared with experimental data obtained from literature and an excellent agreement was obtained with both EoS, which were also capable of predicting the fluid phase behavior corresponding to the critical solution temperatures (LCST: lower critical solution temperature, UCST: upper critical solution temperature) of blends.     

Molecular weight dependence of polystyrene segmental dynamics in dilute blends with poly(vinyl methyl ether)

The segmental dynamics of backbone‐deuterated polystyrenes (d₃PS) with varying molecular weights (1.7–67 kg/mol) have been measured in blends with poly(vinyl methyl ether) (PVME). ²H NMR T₁ values at 15 and 77 MHz are reported for the pure d₃PS and for the dilute d₃PS component in PVME matrices. The temperature shift that is needed to superpose the NMR T₁ data for the pure d₃PS and the d₃PS as a dilute component in the blend ranges from 45 to 70 K. In the framework of Lodge/McLeish model, the self‐concentration value for d₃PS in these dilute blends with PVME is found to be independent of molecular weight. We thus establish for this system that the substantial influence of molecular weight on the blend segmental dynamics can be explained by homopolymer T_g differences. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2252–2262, 2007     

Gas sorption and transport in miscible blends of tetramethyl bisphenol-A polycarbonate and polystyrene

The permeability coefficients for He, O₂, N₂, CH₄, and CO₂ in miscible blends of polystyrene (PS) and tetramethyl bisphenol-A polycarbonate (TMPC) at 35°C and 1 atm driving pressure are reported. Sorption isotherms for CO₂ and CH₄ are also presented. The isotherms were fitted to the dual sorption model. The Langmuir capacity factor was found to follow an earlier correlation based on unrelaxed volume. For each gas, the permeability was found to go through a minimum when plotted against blend composition. This behavior is primarily the result of the volume change on mixing observed for this system. The attractive interaction between TMPC and PS is relatively strong as indicated by density and solubility data. The value of the binary interaction parameter was found to be of the same magnitude as that for poly(phenylene oxide) (PPO)-polystyrene (PS) blends. Considering the similarity of structure between PPO and TMPC, it is concluded that similar phenyl-phenyl interactions and conformational changes on blending may prevail in TMPC/PS blends.     

Comparison of glass transition and interpretation on miscibility in blends of amorphous poly(vinyl methyl ether) with highly crystallizable versus less‐crystallizable polyesters

Various phase behavior of blends of poly(vinyl ether)s with polyesters of two types (highly crystalline and less crystalline with different main‐chains) were examined using differential scanning calorimetry (DSC) and optical microscopy (OM). Effects of varying the main‐chain polarity of the constituent polyesters on the phase behavior of the blends were analyzed. Miscibility in PVME/polyester blends was found only in polyesters with backbone CH₂/CO ratio = 3.5 to 7.0). T_g‐composition relationships for blends of PVME with highly crystalline polyesters (PBA, PHS) were found to differ significantly from those for PVME blends with less‐crystalline polyesters (PTA, PEAz). Crystallinity of highly crystalline polyester constituents in blends caused significant asymmetry in the T_g‐composition relationships, and induced positive deviation of blends' T_g above linearity; on the other hand, blends of PVME with less crystalline polyesters exhibit typical Fox or Gordon‐Taylor types of relationships. The χ parameters for the miscible blends were found to range from ?0.17 to ?0.33, reflecting generally weak interactions. Phase behavior was analyzed and compared among blends of PVME with rapidly crystallizing vs. less‐crystallizing polyesters, respectively. Effects of polyesters' crystallinity and structures on phase behavior of PVME/polyester blends are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2899–2911, 2007     

A dielectric study of secondary relaxations and the “memory effect” in two compatible polystyrene blends

Dielectric permittivities and loss tangents of 10 and 30% poly(2,6-dimethyl-1,4-phenylene oxide) (PPO)–polystyrene (PS) blends and 10 and 25% poly(vinyl methyl ether) (PVME)–polystyrene blends have been measured from 80 to 360 K at 1 and 10 kHz. The PPO-PS blends have two secondary relaxations below T_g and the PVME-PS blends have three regions. All blends have a β process which appears near 290 K, is independent of PPO or PVME concentration, and is associated with the local modes of motions of PS chains. It is suggested that the β process of PS allows a dipolar reorientation of the PPO or PS chain segments by creating more favorable surroundings for the motions of the latter. The effect of physical aging in the PPO-PS blend is substantial but the “memory effect” is significantly less. This is due to the lower contribution to tanδ from the β process of the blend.     

Preparation of microcellular polypropylene/polystyrene blend foams with tunable cell structure

By using supercritical carbon dioxide (sc‐CO₂) as the physical foaming agent, microcellular foaming was carried out in a batch process from a wide range of immiscible polypropylene/polystyrene (PP/PS) blends with 10–70 wt% PS. The blends were prepared via melt processing in a twin‐screw extruder. The cell structure, cell size, and cell density of foamed PP/PS blends were investigated and explained by combining the blend phase morphology and morphological parameters with the foaming principle. It was demonstrated that all PP/PS blends exhibit much dramatically improved foamability than the PP, and significantly decreased cell size and obviously increased cell density than the PS. Moreover, the cell structure can be tunable via changing the blend composition. Foamed PP/PS blends with up to 30 wt% PS exhibit a closed‐cell structure. Among them, foamed PP/PS 90:10 and 80:20 blends have very small mean cell diameter (0.4 and 0.7 µm) and high cell density (8.3 × 10¹¹ and 6.4 × 10¹¹ cells/cm³). Both of blends exhibit nonuniform cell structure, in which most of small cells spread as “a string of beads.” Foamed PP/PS 70:30 blend shows the most uniform cell structure. Increase in the PS content to 50 wt% and especially 70 wt% transforms it to an irregular open‐cell structure. The cell structure of foamed PP/PS blends is strongly related to the blend phase morphology and the solubility of CO₂ in PP more than that in PS, which makes the PP serve as a CO₂ reservoir. Copyright © 2009 John Wiley & Sons, Ltd.     

Preparation and characterization of microcellular polystyrene/polystyrene ionomer blends with supercritical carbon dioxide

The preparation of microcellular polystyrene (PS), lightly sulfonated polystyrene (SPS), zinc‐neutralized lightly sulfonated polystyrene (ZnSPS), and blends of PS/SPS and PS/ZnSPS via supercritical CO₂ was carried out with the pressure‐quench process. Both higher foaming temperature and lower pressure result in larger cell sizes, lower cell densities, and lower relative density for microcellular ionomers and blends as for microcellular PS. The difference among various microcellular samples is the change of cell size with the sample composition. The cell size decreases in the sequence from SPS, through PS/SPS blends, PS and PS/ZnSPS blends, to ZnSPS. The diffusivity of CO₂ in samples also decreases in the sequence from SPS, through PS/SPS blends, PS and PS/ZnSPS blends, to ZnSPS. For this series of samples with similar structure and identical solubility of CO₂, the varying diffusivity is responsible for the difference of cell sizes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 368–377, 2003     

Phase behavior in mixtures of a homopolymer and a block copolymer 1. FTIR and DSC studies

Miscibility in blends of three styrene-butadiene-styrene and one styrene-isoprene-styrene triblock copolymers containing 28%, 30%, 48%, and 14% by weight of polystyrene, respectively, with poly(vinyl methyl ether) (PVME) were investigated by FTIR spectroscopy and differential scanning calorimetry (DSC). It was found from the optical clarity and the glass transition temperature behavior that the blends show miscibility for each kind of triblock copolymers below a certain concentration of PVME. The concentration range to show miscibility becomes wider as the polystyrene content and molecular weight of PS segment in the triblock copolymers increase. From the FTIR results, the relative peak intensity of the 1100 cm^-1 region due to COCH₃ band of PVME and peak position of 698 cm^-1 region due to phenyl ring are sensitive to the miscibility of SBS(SIS)/PVME blends. The results show that the miscibility in SBS(SIS)/PVME blends is greatly affected by the composition of the copolymers and the polystyrene content in the triblock copolymers. Molecular weights of polystyrene segments have also affected the miscibility of the blends. ©1995 John Wiley & Sons, Inc.     

Effect of carbon dioxide sorption on the phase behavior of weakly interacting polymer mixtures: Solvent‐induced segregation in deuterated polybutadiene/polyisoprene blends

The effect of carbon dioxide (CO₂) sorption on the lower critical solution temperatures of deuterated polybutadiene/polyisoprene blends was determined with in situ small‐angle neutron scattering. CO₂ was a poor solvent for both polymers and exhibited very weak selectivity between the blend components. The sorption of modest concentrations of CO₂, at pressures up to 160 bar, induced phase segregation at temperatures well below the binary‐phase‐separation temperature and caused an increased asymmetry in the lower critical solution temperature curve. The origin of solvent‐induced phase segregation in this weakly interacting polymer blend system was attributed predominantly to an exacerbation of the existing disparity in the compressibility of the components upon CO₂ sorption. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3114–3126, 2003     

Dilation of polyethylene by sorption of carbon dioxide

The dilation of low-density polyethylene accompanied by the sorption of CO₂ was measured by microscopy under pressures up to 50 atm at temperatures from 25 to 55°C. The dilatometry measurement, which is also applied to the determination of the thermal expansion coefficient, is directly performed by a cathetometer. The dilation of LDPE by sorbed CO₂ is linear with concentration. The buoyancy correction is described for the CO₂ sorption isotherms in LDPE. The partial molar volume of CO₂ in LDPE, calculated from the dilation and the sorption isotherms, is almost independent of temperature.     

Small-angle neutron scattering of polymer blends of polyvinylmethylether at dilute concentration in deuterated polystyrene

Small-angle neutron scattering was used to measure the radius of gyration and thermodynamics of blends of poly(vinylmethylether) (PVME) at dilute concentration in deuterated polystyrene (PSD). The data were analyzed using the Zimm equation and the random phase approximation theory. For PVME with a weight-average molecular weight of 38,400 the value of the radius of gyration, R_g, was found to be 47 Å in the limit of the concentration of PVME extrapolated to zero. Analysis of the temperature dependence of the Flory interaction parameter, χ/v₀, indicates that phase separation should occur at approximately 300°C for a sample with ϕ_PVME ≅ 9%. No significant temperature dependence of R_g was found over the experimental range studied. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 1–9, 1998     

In situ preparation of cross‐linked polystyrene/poly(methyl methacrylate) blend foams with a bimodal cellular structure

In situ preparation of a cross‐linked poly(methyl methacrylate) (PMMA) and polystyrene (PS) blend and its foaming were investigated for creating a bimodal cellular structure in the foam. Methyl methacrylate (MMA) monomer was dissolved in PS under supercritical CO₂ at a temperature of 60 °C and a pressure of 8 MPa, and the polymerization of MMA was conducted at 100 °C and 8 MPa CO₂, with a cross‐linking agent in PS. The blend was successively foamed by depressurizing the CO₂. CO₂ played the roles of plasticizing the PS and enhancing the monomer dispersion in PS during the sorption process and as a physical blowing agent in the foaming process. The cross‐linking agent was used for controlling the elasticity of polymerized PMMA domains and differentiating their elasticity from that of the PS matrix. The difference in elasticity delayed the bubble nucleation in the PMMA domains from that in the PS and made the cell size bimodal distribution, in which the smaller cells ranging from 10 to 30 µm in diameter were located in the wall of large cells of 200–400 µm in diameter. The effects of the initial MMA content, the concentration of cross‐linking agent, and the depressurization rate on the bimodal cell structure and bulk foam density were investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamics of Poly(vinylmethyl ether) Blends with a Strongly Interassociating Copolymer

We apply broadband dielectric relaxation spectroscopy to probe the dynamics of hydrogen bonded polymer blends. A copolymer consisting of 2,3-dimethylbutadiene (DMB) [86%] and p-(hexafluoro-2-hydroxyl-2-propyl)styrene (HFS) [14%] was synthesized and blended with poly(vinylmethyl ether) (PVME). The copolymer is capable of forming strong intermolecular hydrogen bonds, while minimizing the degree of intramolecular associations, and its blends with PVME are predicted to be miscible over the entire composition range. Two segmental processes, α and α₁, are present in blends containing 26, 50, and 76 weight percent copolymer. The slower process (α₁) is assigned to the segmental motion of the intermolecularly associated copolymer, and the faster process (α) to segmental motions of PVME modified by the HFS:DMB copolymer. A relaxation associated with residual water is present in the glassy state. A local process due to motions of the PVME ether groups (β) is also present in the glassy state, and does not change with blend composition.     

Foaming behavior of polypropylene/polystyrene blends enhanced by improved interfacial compatibility

A series of polypropylene (PP)/polystyrene (PS) blends were prepared by solvent blending with PS‐grafted PP copolymers (PP‐g‐PS) having different PS graft chain length as compatibilizers. The interfacial compatibility was significantly improved with increasing PS graft chain length until the interface was saturated at PS graft chain length being 3.29 × 10³ g/mol. The blends were foamed by using pressure‐quenching process and supercritical CO₂ as the blowing agent. The cell preferentially formed at compatibilized interface because of low energy barrier for nucleation. Combining with the increased interfacial area, the compatibilized interface lead to the foams with increased cell density compared to the uncompatibilized one. The increase in interfacial compatibility also decreased the escape of gas, held more gas for cell growth, and facilitated the increase in expansion ratio of PP/PS blend foams. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1641–1651, 2008     

Dilation and plasticization of polystyrene by carbon dioxide

We have used an optical interference technique to measure the dilation of polystyrene films in the presence of carbon dioxide or helium at pressures up to 20 atm. Dilation isotherms (plots of dilation versus gas pressure at constant temperature) were obtained for three samples of polystyrene which had widely differing molecular weights. The dilation isotherms have the same general shape as sorption isotherms, which means that all of the sorbed gas molecules contribute to volume dilation and non can be thought of as occupying molecular-sized voids in the polymer. Using sorption results from the literature we show that the partial molar volume of CO₂ at 35°C is about 39 cm³ mol^?1 and appears to be independent of polystyrene molecular weight. For a polystyrene sample with M_n = 3600, the partial molar volume of sorbed CO₂ increases to 44 and 50 cm³ mol^?1 at 45 and 55°C, respectively. The sorption of CO₂ in polystyrene is shown to depress the glass transition temperature of the mixture, consistent with theoretical predictions. The shape of the dilation and sorption isotherms are consistent with the depression of the glass transition temperature.     

The effect of phase‐separated morphology on the rheological properties of polystyrene/poly(vinyl methyl ether) blend

The effect of phase‐separated morphology on the rheological properties of polystyrene/poly(vinyl methyl ether) (PS/PVME) blend was investigated by optical microscopy (OM), light scattering (LS) method, and rheology. The blend had a lower critical solution temperature (LCST) of 112°C obtained by turbidity experiment using LS at a heating rate of 1°C/h. Three different blend compositions (critical 30/70 PS/PVME by weight) and two off‐critical (50/50 and 10/90)) were prepared. The rheological properties of each composition were monitored with phase‐separation time after a temperature jump from a homogeneous state to the preset phase‐separation temperature. For the 30/70 and 50/50 blends, it was found that with phase‐separation time, the storage and loss moduli (G′ and G″) increased at shorter times due to the formation of co‐continuous structures resulting from spinodal decomposition. Under small oscillatory shearing, shear moduli gradually decreased with time at longer phase‐separation times due to the alignment of co‐continuous structures toward the flow direction, as verified by scanning electron microscopy. However, for the 10/90 PS/PVME blend, the rheological properties did not change with phase‐separation times. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 889–906, 1999     

Gas sorption-induced dilation of poly(4-methyl-1-pentene)

Sorption and volume dilation isotherms of semicrystalline poly(4-methyl-1-pentene) (PMP) were measured using CO₂ and C₃H₈ as penetrants, which have sieving diameters of 3.3 and 4.3 Å, respectively. On the other hand, the PMP crystal has a void width of approximately 4 Å as estimated by X-ray diffraction, so it was anticipated that CO₂ would be able to sorb into the PMP crystal while C₃H₈ would not. The data show that C₃H₈ has a constant partial molar volume of approximately 87 cc/mol, just above the value reported in other rubbery polymers, and are consistent with the hypothesis that the C₃H₈ molecules are too large to sorb into the PMP crystals. The partial molar volume of CO₂ was found to be 39 cc/mol for CO₂ weight fractions of up to 0.03. Since the typical partial molar volume of CO₂ in rubbery materials is 46 cc/mol, the lower values in this study were attributed to CO₂ sorption into crystalline regions of the polymer, which provided no dilation. Application of a two-phase model using the assumption of Henry's law sorption showed that apparently all C₃H₈ sorption was occurring in the amorphous region but approximately 16% of CO₂ sorption occurred in the crystalline regions. © 1996 John Wiley & Sons, Inc.     

FT–IR spectroscopic and thermal studies of poly(styrene-co-1-vinyl naphthalene) and poly(vinyl methyl ether) blends

The FT–IR spectroscopic analysis and the thermal behavior of the blends of styrene-1-vinyl naphthalene copolymers [P(S-co-1VN)] and poly(vinyl methyl ether) (PVME) were investigated in this work. The copolymers containing 23, 50, and 80% by weight of styrene were synthesized by radical polymerization. The blend films of the P(S-co-1VN) and PVME were cast from the mixed solvent of benzene/trimethylbenzene [50/50 (v/v)]. It was found from the optical clarity and the glass transition temperature behavior that the blends of PVME with P(S-co-1VN) of 80 wt % styrene and 20 wt % 1-vinylnaphthalene (1VN) show miscibility below 50 wt % of the copolymer concentration and the concentration range to show miscibility becomes wider as the composition of 1VN decreases in the copolymers. From the FT–IR results, the relative peak intensity of the 1100 cm^?1 region due to COCH₃ bond of PVME and the peak position of 774 cm^?1 region due to the naphthyl ring of 1VN were sensitive to the miscibility of the P(S-co-1VN)/PVME blends. The frequency differences of the phenyl ring and the naphthyl ring in the P(S-co-1VN) from each frequency in the P(S-co-1VN)/PVME blends increase with increasing composition of styrene in the copolymers and with increasing concentration of PVME in the blends. A threshold energy exists to induce molecular interaction between the naphthyl ring of 1VN and the COCH₃ of PVME and to result in the miscible blends, regardless of the copolymer composition as well as the blend concentration. The threshold energy was estimated as about 3.689 × 10^?21 cal (779 cm^?1) for the P(S-co-1VN)/PVME blend system. It can be concluded that the miscibility in P(S-co-1VN)/PVME blends is largely affected by the composition of the copolymers, and the blends become more miscible as the composition of styrene in the copolymers increases.     

Phase separation dynamics of a poly(vinyl methyl ether)/polystyrene (PVME/PS) blend studied by ultrafast differential scanning calorimetry

In this work, ultrafast differential scanning calorimetry (UFDSC) is used to study the dynamics of phase separation. Taking poly(vinyl methyl ether)/polystyrene (PVME/PS) blend as the example, we firstly obtained the phase diagram that has lower critical solution temperature (LCST), together with the glass transition temperature (T_g) of the homogeneous blend with different composition. Then, the dynamics of the phase separation of the PVME/PS blend with a mass ratio of 7:3 was studied in the time range from milliseconds to hours, by the virtue of small time and spatial resolution that UFDSC offers. The time dependence of the glass transition temperature (T_g) of PVME‐rich phase, shows a distinct change when the annealing temperature (T_a) changes from below to above 385 K. This corresponds to the transition from the nucleation and growth (NG) mechanism to the spinodal decomposition (SD) mechanism, as was verified by morphological and rheometric investigations. For the SD mechanism, the temperature‐dependent composition evolution in PVME‐rich domain was found to follow the Williams–Landel–Ferry (WLF) laws. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1357–1364     

Sorption of CO2 in polymers observed by positron annihilation technique

Positron annihilation lifetimes were measured for several polymers in the atmosphere of high pressure CO₂ gas. At low CO₂ pressured both ₃ andI ₃ decreased due to the Langmuir-type sorption, and at higher pressures their values recovered because the Henry-type sorption takes over. The amount of sorbed CO₂ and dilation of the bulk volume were measured simultaneously, and the free volume fraction was determined at each CO₂ pressure. The free volume fraction became smaller (for polyimide and polycarbonate) or slightly larger (for polyethylene) with the progress of sorption. However, the size of the o-Ps hole estimated from the ₃ value increased regardless of the change of the free volume fraction. It appears that o-Ps is selectively looking at larger holes or expanding the holes in which it is accommodated. For polycarbonate, which remains to be glassy even at the largest CO₂ sorption attained in the experiment, the o-Ps hole size became larger than that before sorption. This implies that, even if the polymer is glassy as bulk, the sorption site is strongly prone to molecular displacement by the pressure of the penetrating Ps. Cautious consideration is evoked about directly correlating the o-Ps lifetime and intensity with the free volume in general.