Pressure–volume–temperature properties and free volume parameters of PEO/PMMA blends

Melt-miscible polymer blends of poly(ethylene oxide)/atactic poly(methyl methacrylate (PEO/a-PMMA)) were prepared by melt-mixing and characterized by pressure–volume–temperature (PVT) dilatometry in the pressure and temperature range of 0 to 200 MPa and 20 to 200°C, respectively. The PVT data were analyzed in terms of two equations of state (EOS). The empirical Tait EOS was applied in the glassy, semicrystalline, and equilibrium melt state, and the Simha-Somcynsky EOS theory was applied in the equilibrium melt and glassy state. The Simha-Somcynsky EOS theory contains a free volume function. The temperature, pressure, and composition dependence of the free volume fraction h calculated from the Simha-Somcynsky EOS theory was studied. As a function of blend composition we observe that the free volume fraction, thermal expansivity, and compressibility all deviate mainly positively from linearity while the specific volume deviates mainly negatively from linearity. These findings are reconciled with composition-dependent free volume parameters, the free volume and cell volume as well as with self- and cross-interaction parameters derived from the Simha-Somcynsky EOS theory as applied to polymer mixtures. Moreover, the pressure dependence of glass and melting transitions as well as crystallization kinetics have been investigated. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1061–1080, 1998     

Equation of state for high density solid and melt polyethylene

Pressure‐volume‐temperature (PVT) measurements for high‐density linear polyethylene (LPE) are studied experimentally over a temperature range of 290 to 470 K and pressures up to 3.1 kbar. For melt, the results can be represented by the Tait equation within the precision of the data. It is noticed that for each isotherm, an abrupt departure from the Tait representation occurs at a particular pressure. This is ascribed to onset of solidification due to pressure. Further, variation of the degree of crystallinity with pressure at various temperatures has been investigated. Finally, the PVT data has been analyzed in terms of the LJD cell theory in its original form without any modifications or simplifications of the cell potential. Satisfactory agreement is obtained between experiment and theory over the entire range of PVT data both in solids and melt states. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1618–1623, 2005     

Temperature and concentration dependence of diffusion coefficients in ethylene–propylene-diene copolymers

Self-diffusion and partition coefficients were measured for two commercial ethylene–propylene-diene copolymers (EPDM) and five solvents at infinite dilution using inverse gas chromatography. Mutual diffusion coefficients for solvents in EPDM also were measured for finite concentration using gravimetric sorption for three of the solvents. From the inverse gas chromatography experimental values for self-diffusion coefficients were obtained. Free-volume parameters were obtained through regression of the self-diffusion coefficient as a function of temperature. Mutual diffusion coefficients as a function of concentration were predicted using free volume theory and compared with experimental data obtained using gravimetric sorption. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1713–1719, 1998     

Volume dependence of thermal conductivity and isothermal bulk modulus up to 1 GPa for poly(vinyl acetate)

The thermal conductivity λ and heat capacity per unit volume of poly(vinyl acetate) (260 kg mol⁻¹ in weight average molecular weight) have been measured in the temperature range 150–450 K at pressures up to 1 GPa using the transient hot-wire method, which yielded λ = 0.19 W m⁻¹ K⁻¹ at atmospheric pressure and room temperature. The bulk modulus K has been measured in the temperature range 150–353 K up to 1 GPa. At atmospheric pressure and room temperature, K = 4.0 GPa and (∂K/∂p)_T = 8.3. The volume data were used to calculate the volume dependence of λ, $g = - \left( {\frac{{\partial \lambda /\lambda }}{{\partial V/V}}} \right)_T .$ The values for g of the liquid and glassy states were 3.0 and 2.7, respectively, and g of the latter was almost independent of volume and temperature. Theoretical models can predict the value for g of the glassy state to within 25%. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1451–1463, 1998     

Carbon dioxide–poly(vinylidene fluoride) interactions at high pressure

The article reports on the behaviour of poly(vinylidene fluoride) in carbon dioxide at 42°C and 80°C and in a pressure range of 0.1–30 MPa. Experimental techniques for the measurement of gas mass uptake and polymer dilatation are described and the corresponding data are reported as mass sorption and dilatation isotherms, respectively. The mass uptake experiment was also used to follow the evolution of the coefficient of diffusion of carbon dioxide into the polymer as a function of pressure or concentration. An analysis for the calculation of the partial molar volume of carbon dioxide as a function of pressure is also given, which shows that the ‘apparent’ partial molar volume of the carbon dioxide decreases with pressure to very low values, at high pressure. The computed values are significantly less than those for either the liquid or the solid phases of pure carbon dioxide, and also lower than some data previously reported for silicone elastomers. A consideration of the origins of this apparent anomaly is given in the conclusions. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2435–2447, 1998     

Molecular mobility of substituted poly(p-phenylenes) characterized by a range of polymer relaxation techniques

The free volume and related mobility properties of substituted poly(p-phenylene) polymers are examined. The techniques used range from positron annihilation, dielectric relaxation, and dynamic mechanical spectroscopy to thermally stimulated currents. Fractional free volume is determined for the samples with different substituted side groups and related to the glass transition temperature. Bulkier groups lead to a greater fractional free volume and lower glass transition temperatures. Comparison of molecular relaxation times using the different characterization techniques demonstrates that there is strong coupling between motion of the main chain and the side groups, on which the dipoles reside. Intermolecular coupling between the main chains at the primary relaxation is shown in this work to be related to the nature of the side chains and resultant free volume, as are the temperature locations of local, secondary relaxations. A qualitative model describing the effect of regiochemistry on the motions and packing of these materials is also proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1465–1481, 1998     

Pressure–volume–temperature data and surface tension of blends of poly(ethylene oxide) and poly(methyl acrylate) in the melt

The pressure–volume–temperature behavior of miscible blends of poly(ethylene oxide) (PEO) and poly(methyl acrylate) (PMA) was studied over extended ranges of temperature and pressure. From pressure–volume–temperature data, the reduction parameters for the Flory‐Orwoll‐Vrij equation‐of‐state were determined. It was found that reduction parameters as well as density, thermal expansion coefficient, and isothermal compressibility vary with composition in a nonlinear manner. The surface tension of the blends in the molten state was measured over the whole composition range using the sessile drop method. The surface tension was found to display negative deviation from additivity pointing toward a remarkable surface excess of PMA. Moreover, surface tension displays a minimum in the range of low PEO content at weight fraction of ～0.19. In addition, the temperature coefficient of surface tension shows negative deviation from linearity. It stays constant when PMA is in excess. Results are discussed in terms of equation‐of‐state thermodynamics. The minimum of surface tension can be well explained by weak self‐association of PEO in the bulk. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1893–1900, 2010     

Comparison of ultrasonic shear wave and dynamic-mechanical measurements in acrylic-type copolymers

An ultrasonic shear wave reflection method was applied to study film formation and temperature dependence of the complex shear modulus (G^*G′ + iG″) in different amorphous films made of aqueous dispersions of acrylic-type copolymers. The data are compared with dynamic-mechanical measurements in the low frequency range. It is shown that the temperature dependence of the storage (G′) and the loss modulus (G″) for both methods can be fitted by the same set of parameters using the Havriliak–Negami function incorporating the Vogel–Fulcher–Tamman–Hesse equation for the temperature dependence of relaxation times. The temperature dependence of the relaxation times obtained from the fits to the ultrasonic shear modulus is compared to the shift factors of the dynamic-mechanical measurements. The agreement between both methods is good. This suggests an almost thermorheological simplicity of the samples for the main glass–rubber relaxation and demonstrates the capacity of the ultrasonic rheometer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1703–1711, 1998     

Temperature and molecular weight dependence of interfacial tension between immiscible polymer pairs by the square gradient theory combined with the Flory–Orwoll–Vrij equation-of-state theory

Interfacial tension between immiscible polymer pairs was predicted by using a square gradient theory in conjunction with the Flory–Orwoll–Vrij equation-of-state expression for the free energy of mixing. The contact interaction parameter was determined by fitting the equation-of-state theory to experimental cloud points taken from the literature, and the square gradient coefficient was estimated from the relation derived from a scattering function. The modified square gradient theory could successfully predict both the magnitude and temperature dependence of interfacial tension between polystyrene and poly(methyl methacrylate), although no adjustable parameters were used in calculating interfacial tension. The molecular weight dependence of interfacial tension was also successfully predicted. The contribution of free volume on interfacial tension is analyzed for two systems: polystyrene/poly(methyl methacrylate) and polystyrene/poly(dimethyl siloxane) blends. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2683–2689, 1998     

Pressure–volume–temperature behavior of two polycyanurate networks

The pressure–volume–temperature (PVT) behavior was studied for two polycyanurate networks having different crosslink densities using a pressurizable dilatometer. The samples were studied at temperatures ranging from 60 to 180 °C and at pressures up to 170 MPa to yield PVT data in both rubbery and glassy states. The Tait equation is found to well describe the isobaric temperature scan and isothermal pressure scan data. The thermal expansion coefficients, instantaneous bulk moduli, and thermal pressure coefficients are extracted from the data and their dependence on crosslink density is examined. The time‐dependent viscoelastic bulk modulus (K(t)) is also calculated in the vicinity of the α‐relaxation from previously published pressure relaxation experimental data, and the strength and shape of the dispersion are found to be independent of crosslink density. The limiting bulk moduli depend strongly on temperature with those of the more loosely crosslinked sample being lower at a given temperature and pressure, although at T_g(P), the limiting moduli of the more loosely crosslinked sample are slightly higher than those of the more highly crosslinked sample. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Effect of molecular weight and temperature on physical aging of thin glassy poly(2,6-dimethyl-1,4-phenylene oxide) films

The effects of polymer molecular weight and temperature on the physical aging of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) is examined. Gas permeability and refractive index were monitored during the aging process for PPO film samples at three aging temperatures below the glass transition temperature. Comparisons between the two samples of PPO that differ widely in molecular weight reveal an insignificant difference, which support the notion that above a critical molecular weight range there is little influence on aging rate. Increased temperature, over the limited range of 35–55 °C, results in higher aging rates for films made from both PPO materials. The rate of aging decreases strongly with increasing film thickness over the range examined, ∼0.4–25 μm. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1390–1398, 2007     

Direct observation of morphological differences as a function of reaction temperature in model systems for polyurethane foams

A series of polyurea urethanes was isothermally synthesized from toluene diisocyanate (TDI), water, and trifunctional poly(propylene oxide) in the temperature range of 50–150°C. Morphologies of the samples vary significantly as a function of reaction temperature. In this system, phase separation competes with polymerization and crosslinking. Both transmission electron microscopy and atomic force microscopy have shown a network type of structure for the 50°C samples, while the 150°C samples appear to be homogeneous. Infrared analysis shows that samples prepared at 150°C possess a morphology that is less strongly hydrogen bonded and has a broader distribution of hydrogen-bonded states compared to those prepared at lower temperatures. From this combination of techniques, it can be inferred that phase separation occurs faster than crosslinking at low temperatures; consequently, a phase-separated morphology forms. In contrast, crosslinking occurs faster than phase separation at higher reaction temperatures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3065–3077, 1998     

Isobaric cure shrinkage behaviors of epoxy molding compound in isothermal state

The warpage of plastic‐encapsulated IC packages after molding is believed to be induced by thermal and cure shrinkage of epoxy molding compound (EMC). To study the warpage behaviors of EMC, the amount of cure‐induced shrinkage needs to be understood. Volume shrinkage behaviors induced by cure reaction of EMC in isothermal and isobaric states were studied with a differential scanning calorimeter (DSC) and a pressure–temperature‐controlled dilatometer. The results show that higher pressure induce more volume shrinkage under fixed temperature but the difference of volume shrinkage under different pressure levels doesn't obey the principle of linearity. It is observed that the amount of chemical volume shrinkage at 145 °C is higher than those under three other temperatures: 160, 175, and 190 °C. The chemical volume shrinkage of EMC is found to be very process dependent. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2392–2398, 2005     

Effect of pressure and temperature on chromophore reorientation in a side-chain nonlinear optical polymer

Second harmonic generation (SHG) was used to measure the temperature dependence of the reorientation activation volume of the side-chain copolymer poly(disperse red 1 methacrylate-co-methyl methacrylate) (DR1-MMA). The decay of the SHG signal from poled films of DR1-MMA was recorded at hydrostatic pressures up to 3060 atm and at different temperatures between 25°C below the glass transition temperature (T_g) to 35°C above it. The activation volume, ΔV^*, decreased with increasing temperature. The data suggests that the coupling between chromophore reorientation and the long-range motion of the polymer is stronger for the DR1-MMA side-chain system than in previously measured guest–host systems. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2793–2803, 1998     

Polymer modification using difluoromethane (HFC 32) and carbon dioxide

The infusion of difluoromethane (HFC 32) and CO₂ into polystyrene and polyethylene has been characterized using a quartz crystal microbalance technique over a range of temperatures and pressures. The results were adequately modeled by Flory‐Huggins theory. Significant plasticization was observed in the polymeric materials and it is shown that manipulation of the experimental temperature, pressure, and rate of depressurisation can cause significant changes in the morphology of the samples. It is demonstrated for the first time how rate constant data for the kinetics of gas sorption can be extracted quickly and easily from in situ quartz crystal microbalance measurements. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1072–1083, 2006     

Cell theory and equation‐of‐state of chain molecular systems: Application to polymer solids

We use the Lennard‐Jones and Devonshire cell theory without any ad hoc simplification of the cell potential to obtain the equation‐of‐state (EOS) for chain molecular systems. The interactions of the central segment with second and third shells of neighbors are taken into account. Numerical values of the cell integrals are given in tabular form along with interpolation expressions that cover the range of PVT variables appropriate to polymers. Results of comparison with EOS based on square‐well form are also discussed. Application of the theory to polymer glasses of diverse structures is found to be quite successful in explaining the PVT behavior over a wide range of temperatures both at atmospheric and elevated pressures. Further, scaled volume at the glass‐transition temperature is discovered to be a corresponding state property. Turning to crystals, the theory is generally in good accordance with the PVT data of three well‐studied polymers both at atmospheric and elevated pressures. For linear polyethylene the agreement is good up to 42 kbar for the room‐temperature isotherm. On the other hand, at higher temperatures where the data are limited to 5 kbar, the agreement is determined to be satisfactory for the three polymers. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 515–530, 2001     

Pressure–Volume–Temperature properties of polyolefin liquids and their melt miscibility

The pressure–volume–temperature (P–V–T) properties of a number of metallocene-produced polyolefins were measured experimentally at 10 MPa ≤ P ≤ 200 MPa and 30°C ≤ T ≤ 220°C in a dilatometer-type P–V–T apparatus. These included ethylene copolymers typical of linear low density polyethylene, with several α-olefins as comonomers and a wide range of comonomer content. The experimental P–V–T data were correlated with the equations of state from the Sanchez–Lacombe and Flory–Orwoll–Vrij theories. The solubility parameter map of the polyolefins, at atmospheric pressure, was established on the basis of the thermodynamic data. As the temperature increases, the solubility parameter of the polyolefin decreases. The solubility parameters of copolymers of ethylene with propylene, butene, hexene, and octene under constant temperature are all more or less the same at equal weight percent of comonomer. As the incorporation of branches increases, the solubility parameter decreases. The melt miscibility of the polyolefin blends can be predicted to design various blend products for specific applications from this solubility parameter map. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2835–2844, 1999     

Chromatographic investigation of the effect of dissolved carbon dioxide on the glass transition temperature of a polymer and the solubility of a third component (additive)

The effect of dissolved carbon dioxide on the glass transition temperature of a polymer, PMMA, has been investigated using molecular probe chromatography. The probe solute was iso-octane, and the specific retention volumes of this solute in pure PMMA and mixtures of PMMA with CO₂ were measured over a temperature range of 0 to 180°C and CO₂ pressures from 1 to 75 atm. The amount of CO₂ dissolved in the polymer was calculated from a model fit to previously published solubility data determined chromatographically. Classical van't Hoff-type plots were used to determine the glass transition temperature of CO₂-impregnated PMMA from low pressure up to 46 atm of CO₂. Solvent-induced plasticization was observed with the glass transition temperature decreasing by about 40°C. At some pressures, glass transitions at low temperatures could not be determined from the van't Hoff plots because of the proximity of the polymer glass transition temperature to the gas–liquid transition temperature for CO₂. For these pressures, a new method was developed to determine the glass transition composition. The glass transition pressure was then calculated from the measured composition and temperature using an isotherm model. In every case, the glass transition temperature decreased linearly with increasing concentration of CO₂ in the polymer. However, at higher compositions, the glass transition pressure decreased with increasing composition and decreasing temperature. The observed retention volume of iso-octane with PMMA in a glassy state was correlated with an adsorption model developed from a theory for liquid–solid chromatography derived by Martire. This model accurately described the observed decrease in retention of iso-octane by adsorption on the surface of glassy PMMA with increasing concentration of CO₂ dissolved in the polymer. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2537–2549, 1998     

Statistical thermodynamics evaluation of polymer–polymer miscibility

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004     

Volume dependence of thermal conductivity and bulk modulus for poly(propylene glycol)

The thermal conductivity λ and heat capacity per unit volume of poly(propylene glycol) PPG (0.4 and 4.0 kg·mol⁻¹ in number-average molecular weight) have been measured in the temperature range 150–295 K at pressures up to 2 GPa using the transient hot-wire method. At 295 K and atmospheric pressure, λ = 0.147 W m⁻¹K⁻¹ for PPG (0.4 kg·mol⁻¹) and λ = 0.151 W m⁻¹K⁻¹ for PPG (4.0 kg·mol⁻¹). The temperature dependence of λ is less than 4 × 10⁻⁴ W m⁻¹K⁻² for both molecular weights. The bulk modulus has been measured in the temperature range 215–295 K up to 1.1 GPa. At atmospheric pressure, the room temperature bulk moduli are 1.97 GPa for PPG (0.4 kg·mol⁻¹) and 1.75 GPa for PPG (4.0 kg·mol⁻¹). These data were used to calculate the volume dependence of $ \lambda ,g\, = - \left( {\frac{{\partial \lambda /\lambda }}{{\partial V/V}}} \right)_T $. At room temperature and atmospheric pressure (liquid phase) we find g = 2.79 for PPG (0.4 kg·mol⁻¹) and g = 2.15 for PPG (4.0 kg·mol⁻¹). The volume dependence of g, (∂g/∂ log V)_T varies between −19 to −10 for both molecular weights. Under isochoric conditions, g is nearly independent of temperature. The difference in g between the glassy state and liquid phase is small and just outside the inaccuracy of g of about 8%. The theoretical model for λ by Horrocks and McLaughlin yields an overestimate of g by up to 120%. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 345–355, 1998