Equation of state of poly(dimethylsiloxane) melts

The pressure–volume–temperature (PVT) properties of three commercial samples of poly(dimethylsiloxane) are studied experimentally and theoretically in the temperature range 25–150°C and for pressure to ∼ 3 kbar. The Tait equation is employed to represent the data at elevated pressure. Isothermal compressibilities are computed for the three samples. The melt data are analyzed in terms of the Simha–Somcynsky hole theory, and scaling parameters of pressure, volume, and temperature are obtained. Satisfactory agreement between theory and experiment is found over the entire range of experimental pressures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 841–850, 1998     

Pressure–volume–temperature of molten and glassy polymers

The pressure–volume–temperature (PVT) dependencies of several amorphous polymers (PS, PC, PPE, and PPE/PS 1:1 blend) in the glassy and molten state were studied. The Simha–Somcynsky (S–S) lattice‐hole equation of state (EOS) was used. Fitting the PVT data in the molten state to the EOS yielded the free volume quantity, h = h(T, P), and the characteristic reducing parameters, P*, V*, and T*. The data within the glassy region were interpreted assuming that the latter parameters are valid in the molten and vitreous state, than calculating h = h(T, P) from the experimental values of V = V(T, P). Next, the frozen free volume fraction in the glass was computed as FF = FF(P). The FF values of polystyrene (PS) resins at ambient pressure showed little scattering (FF_P=1 = 0.691 ± 0.008), while their P‐dependencies varied, reflecting the thermodynamic history of the glass formation as well as the PVT measurements protocol. The pressure gradient of T_g was compared with the Ehrenfest relation for the second‐order transition; here also agreement depended on the method of vitrification. The experimental values of FF at ambient pressure decreased with increasing values of the characteristic temperature reducing parameter, T*. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 270–285, 2007.     

A predictive approach based on the Simha–Somcynsky free‐volume theory for the effect of dissolved gas on viscosity and glass transition temperature of polymeric mixtures

The gas concentration and pressure effects on the shear viscosity of molten polymers were modeled by using a unified approach based on a free volume theory. A concentration and pressure dependent “shift factor,” which accounts for free volume changes associated with polymer‐gas mixing and with variation of absolute pressure as well as for dilution effects, has been herein used to scale the pure polymer viscosity, as evaluated at the same temperature and atmospheric pressure. The expression of the free volume of the polymer/gas mixture was obtained by using the Simha and Somcynsky equation of state for multicomponent fluids. Experimental shear viscosity data, obtained for poly(ε‐caprolactone) with nitrogen and carbon dioxide were successfully predicted by using this approach. Good agreement with predictions was also found in the case of viscosity data reported in the literature for polystyrene and poly(dimethylsiloxane) with carbon dioxide. Free volume arguments have also been used to predict the T_g depression for polystyrene/carbon dioxide and for poly(methyl methacrylate)/carbon dioxide mixtures, based on calculations performed, again, with the Simha and Somcynsky theory. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1863–1873, 2006     

Prediction of solvent diffusion coefficient in amorphous polymers based on an equation‐of‐state

This study develops a modified free‐volume model to predict solvent diffusion coefficients in amorphous polymers by combining the Vrentas–Duda model with the Simha–Somcynsky (S‐S) equation‐of‐state (EOS), and all the original parameters can be used in the modified model. The free volume of the polymer is estimated from the S‐S EOS together with the Williams‐Landel‐Ferry fractional free volume, and the complex process of determining polymer free‐volume parameters in the Vrentas–Duda model and measuring polymer viscoelasticity can be avoided. Moreover, the modified model includes the influence of not only temperature but also pressure on solvent diffusivity. Three common polymers and four solvents are employed to demonstrate the predictions of the modified model. The calculation results are generally consistent with the experimental values. It is reasonable to expect that the modified free‐volume model will become a useful tool in polymer process development. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1000–1009, 2006     

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     

Isochoric and isobaric glass formation: Similarities and differences

Pressure-volume-temperature (PVT) studies were performed on a glass-forming polymer, poly(carbonate) (PC), under both isobaric and isochoric (constant volume) conditions. An isochoric glass transition was observed and the formation points were found to be consistent with those obtained isobarically. Although the isobaric and isochoric responses were, as expected, the same in the rubbery state, the glassy state values were found to be different and dependent upon the glass formation history. The isobaric data exhibited larger changes in going from the rubber to the glass, hence a “stronger” glass transition, than did the isochoric data. Inserting the experimental values for the thermal expansion coefficient α and isothermal compressibility β, into appropriate thermodynamic relations, measures of the strength of each transition are defined. Strength estimates based on literature values of α and β are compared to the experimental measures of the isochoric and isobaric transitions. In addition, both the isobaric and isochoric PVT results were analyzed in terms of the Fox and Flory free volume theory which assumes that the glass transition is an iso-free volume state. While the isobaric results were consistent with the Fox and Flory theory, the isochoric results were not consistent with the idea of an iso-free volume glass transition. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1561–1573, 1997     

Pressure‐volume‐temperature and glass transition behavior of silica/polystyrene nanocomposite

The pressure‐volume‐temperature (PVT) behavior and glass transition behavior of a 10 wt % silica nanoparticle‐filled polystyrene (PS) nanocomposite sample are measured using a custom‐built pressurizable dilatometer. The PVT data are fitted to the Tait equation in both liquid and glassy states; the coefficient of thermal expansion α, bulk modulus K, and thermal pressure coefficient γ are examined as a function of pressure and compared to the values of neat PS. The glass transition temperature (T_g) is reported as a function of pressure, and the limiting fictive temperature (T_f′) from calorimetric measurements is reported as a function of cooling rate. Comparison with data for neat PS indicates that the nanocomposite has a slightly higher T_g at elevated pressures, higher bulk moduli at all pressures studied, and its relaxation dynamics are more sensitive to volume. The results for the glassy γ values suggest that thermal residual stresses would not be reduced for the nanocomposite sample studied. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1131–1138     

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     

Positron annihilation lifetime study of continuous volume phase transition of poly(N-isopropylacrylamide) gel induced in methanol–water mixed solvent

The macroscopic volume shrinkage and swelling of poly(N-isopropylacryl-amide) (PNIPA) gel induced by the compositional change in the methanol–water mixed solvent is correlated to the change in the nanoscopic free volume size and numerical concentration formed in the PNIPA gels. The free volume size and numerical concentration are estimated from the longest component appearing in the positron annihilation lifetime curves. The apparent free volume fraction calculated by the free volume size and numerical concentration, and dispersion of the free volume deduced by the size distribution are utilized to analyze the origin and location of the free volumes. The free volume parameters obtained by analysis of the positron annihilation data show various nanoscopic phases occuring within the PNIPA gels during the volume change, implying the variation of the strength of the interactions among the solvent molecules and the polymer chains of the PNIPA. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1141–1151, 1998     

Effect of thermal history on the free volume properties of semi‐crystalline poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) membranes by positron annihilation lifetime spectroscopy

Free volume properties of a series of poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) (PHBV) membranes, which were produced by various nonisothermal crystallization processes (rapid‐, step‐, and slow‐cooling processes), were investigated using positron annihilation lifetime (PAL) spectroscopy over a temperature range of 25–90 °C. From the annihilation lifetime parameters, the temperature dependence of free volume size, amount, size distribution, and fractional free volume and thermal expansion properties of free volume were discussed. A model which assumed that amorphous phase was subdivided into mobile and rigid amorphous fractions (MAF and RAF) in the semicrystalline polymer was considered to interpret the temperature dependence of those free volume properties. Morphological observation of the semicrystalline polymer by small‐angle X‐ray scattering (SAXS) indicated that the rapid‐cooled (cold‐crystallized) membranes showed a much thinner thickness of the repeating lamellar/amorphous layers and most likely higher amount of RAF, which restrained the chain motion, than the step‐ and slow‐cooled (melt‐crystallized) membranes. The difference of free volume properties among various PHBV membranes was created according to the crystalline structure of the polymer from different thermal history. The polymer crystallized with slower cooling rate induced higher crystallinity and resulted in less free volume amount and lower fractional free volume. In addition, the thermal expansion coefficients of free volume size were affected by the crystallization rate of PHBV polymer. Larger distribution of the free volume size of melt‐crystallized membranes was observed as a result of the bimodal distribution of the lamellar periodicity and less amount of RAF than that of the cold‐crystallized membranes. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 855–865, 2009     

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     

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     

Effect of annealing temperature on interrelation between the microstructural evolution and plastic deformation in polymers

The mechanical loading induced flow of glassy polymers is triggered by the nucleation of shear transformation units, and strongly depends on the initial microstructural state of the material. Therefore, investigation of the possible relationship between the microstructural state variables and plastic deformation is required for a better understanding of the macroscopic response of this class of materials during large deformation. In this study, free volume content is considered as a state variable and thermal treatment is selected as a process through which the accelerated and forced evolution of the free volume can be imposed. For two well‐known glassy polymers, poly(methyl methacrylate) and polycarbonate, the free volume content alteration upon annealing is monitored via positron annihilation spectroscopy, and the changes of the micro‐ and macromechanical properties are also obtained by utilizing nanoindentation technique and employing the homogeneous amorphous flow theory. The correlation between the microstructural state variable, that is, free volume, and the micromechanical state variable, that is, shear activation volume, is then investigated. The results reveal opposite direction of alterations of free volume and shear activation volume with annealing temperature. Accordingly, the possibility of the existence of an interrelation between these two state variables is critically discussed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1286–1297     

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     

A quantitative model for the specific volume of polymer–diluent mixtures in the glassy state

A mathematical model to describe the specific volume of glassy mixtures of a polymer and a low molecular weight diluent or additive is presented. The model is based on understandable physical assumptions and relies on parameters that can be determined experimentally or estimated from methods available in the literature. The predictions of the model show good agreement with the experimental data for mixtures of four polymers with diluents that in the pure state are liquid, glassy, or crystalline. The observed negative departure from volume additivity, as defined by simple additivity of the specific volume of the pure glassy polymer and the pure amorphous diluent, is the result of the relaxation of the excess volume of the glassy mixture relative to the equilibrium state caused by mixing two components with different glass transition temperatures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1037–1050, 1998     

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Dilatometric behavior and glass transition in a styrene‐acrylonitrile copolymer

Equilibrium and glass transition behavior of a styrene‐acrylonitrile copolymer (SAN) under different thermobaric histories were studied by means of a PVT dilatometer. Equilibrium behavior, as determined by isothermal and isobaric measurements, could be satisfactorily described using the Simha‐Somcynsky and Tait equations of state. Glass transition behavior depended upon the applied transformation path from the liquid‐equilibrium state to the glassy state. From isobaric cooling ramps performed at constant rate and at several pressures, it was possible to determine the glass transition temperature and its dependence upon pressure; whereas from isothermal compressions at various temperatures, it was possible to determine a glass transition pressure and its temperature dependence. Both the dependences were linear, and a correlation was observed between the slopes of the fitting lines. A possible interpretation of this correlation is provided in terms of free volume determined at the glass transition point by applying the Simha‐Somcynsky theory. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1904–1913, 2005     

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     

PVT properties of linear and dendritic polymers

The aim of this article is to examine the limits of applicability of the Simha‐Somcynsky (S‐S) equation of state (EOS) by comparing the pressure‐volume‐temperature (PVT) data and the derivatives (compressibility, κ, and thermal expansion coefficient, α) of anionic linear polystyrene (PS) with poly(benzyl ether) dendrimers (PBED). Fitting the PVT of PBED data to the S‐S EOS was similarly satisfactory as that of PS and the computed Lennard‐Jones (L‐J) interaction parameters showed similar errors of ca. 1%. Next, the experimental derivatives, α and κ of PS and PBED were compared with these functions computed from the S‐S EOS—good agreement was obtained for α at ambient pressure, P, indicating validity of the S‐S theory at least up to the first derivative. While the predicted κ = κ(P) dependence for PS and a linear PBED homologue was correct, for dendrimers the compressibility was higher at low pressure and it was lower at high P than theory predicts. Also the extracted values of the L‐J repulsion volume, v*, between a segment pair was smaller than expected. The specific architecture of dendrimer molecules is responsible for this behavior, since their 3D configuration is significantly different from the S‐S model with uniform segmental density and oxygen bonds in the main and side chains add flexibility. © 2009 NRC Canada. J Polym Sci Part B: Polym Phys 48: 322–332, 2010     

Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

In the framework of the free‐volume (FV) theory, a new equation was derived for the evaluation of self‐diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas–Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self‐diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529–540, 2010