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 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     

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     

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 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     

The equation of state of solid and molten poly (butylene terephthalate) to 300°C and 200 MPa

The volumetric behavior of poly (butylene terephthalate) (PBT) was studied from 30 to 303°C and pressures from atmospheric to 200 MPa. The pressure-volume-tempreature (PVT) data show behavior typical of other semicrystalline materials. The empirical Tait equation was used to fit the measured volumes in the solid and melt regions. The maximum deviations between the Tait fits and the measured volumes were 0.001 and 0.002 cm³/g in the semicrystalline and melt regions, respectively. The theoretical equation of Simha-Somcynsky was used to represent the PVT behavior of this material in the equilibrium melt. Fitting the theory to the data involves a determination of the reducing parameters of the theory. We find P* = 1139 MPa, V* = 0.7838 cm³/g, and T* = 11133 K. From these parameters we calculate that the chemical repeat unit of PBT has 6.37 external degrees of freedom, in comparison with 4.97 degrees of freedom to the closely related poly(ethylene terephthalate), with two less (? CH₂? ) units in the backbone. The difference of 1.4 degrees of freedom may be compared with the 0.88 degrees of freedom of the polyethylene (? C₂H₄? ) repeat unit itself.     

The size and number of local free volumes in polypropylenes: A positron lifetime and PVT study

The temperature dependence of the mean size of local free volumes in an amorphous atactic (aPP) and a semicrystalline syndiotactic polypropylene (sPP), and an amorphous ethylene‐propylene copolymer (E‐co‐P48) has been studied. Pressure‐volume‐temperature (PVT) experiments were performed for aPP, from which the hole fraction h of the Simha‐Somcynsky theory and the number density of holes were estimated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3089–3093, 2003     

Thermodynamic properties of dendrimers compared with linear polymers: General observations

The pressure‐volume‐temperature and thermal properties of dendrimers based on benzyl ether were measured and compared with literature values for monodisperse, linear polystyrenes. In addition, property measurements are presented for an exact linear analogue to the fifth‐generation dendrimer. The thermodynamic properties' molecular weight behavior for the dendrimers is unique when compared with that of linear polystyrene. All of the evidence presented in this work suggests that some form of structural transition occurs in the bulk at a molecular mass near that for the fourth‐generation dendrimer. No such transition is seen for polystyrene. Dendrimers exhibit an increased packing efficiency as evidenced by a decreased specific volume (increased density) as compared with an exact linear analogue of the fifth‐generation dendrimer analogue, and the dendrimer highlights the entropic differences between the two molecules. In addition, differences in the change in heat capacity with temperature for the two systems further allude to their entropic differences. A crystalline state can be formed for the lower generation dendrimer and linear analogue. This crystalline state is not seen in dendrimers above the third generation. These behaviors compiled with the difference in the glass‐transition temperature for the linear analogue suggest that the dendrimers' microstructure has a significant influence on the bulk thermodynamic state of the material. The Tait equation was fitted to the volume data for comparative purposes; the Tait equation has known limitations but was selected because of its widespread application. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1766–1777, 2001     

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     

Pressure-volume-temperature properties of blends of poly(2,6-dimethyl-1,4-phenylene ether) with polystyrene

The pressure-volume-temperature (PVT) properties of blends of poly(2,6-dimethyl-1,4-phenylene ether) (PPO) with polystyrene (PS) have been studied experimentally in both the glassy and melt states at 0, 20, 40, 50, 60, 80, and 100% PPO content. In all compositions a strong glass transition was observed varying linearly with composition. For all but the 40% PPO composition this was the only transition, indicating molecular compatibility of the components in these blends. The 40% PPO composition showed a very weak second transition near the glass transition of pure PS. A small amount of phase separation may have occurred in this blend. The data for the glassy and melt states were fitted to an empirical equation of state based on the Tait equation. The volume of the melts at constant pressure and temperature showed a virtually linear dependence on composition. Any negative excess volume of mixing compatible with the data would have to be very small, smaller than expected from previous measurements in the glassy state. Various properties relating to the glassy and melt states and to the glass transition were evaluated and are discussed as a function of composition. It was found that most properties of the glasses could not be modeled by simple functions of composition.     

Crystallization and melting of polyethylene copolymers: Differential scanning calorimetry and atomic force microscopy studies

The Hoffman–Lauritzen theory of secondary, surface nucleation and growth was primarily relied upon for about 40 years after its introduction in about 1960 to rationalize the crystallization of flexible chain polymers into lamellar crystals. However, in about 1998, Strobl and coworkers introduced a different model for crystallization, based on the stage‐wise formation of lamellae. Two major components of this model were as follows: (1) the concept of the formation of a mesomorphic melt as a precursor to crystallization and (2) the control of the melting temperature range of lamellar crystals of homogeneous polyolefin copolymers by an inner degree of order or perfection rather than on the crystal thickness. The first concept is in disagreement with the HL theory and the second with the Gibbs‐Thomson theory, which associates melting temperature with lamella thickness. In the present study, differential scanning calorimetry and atomic force microscopy were successfully employed to monitor the in situ quiescent crystallization of polyethylene homopolymer and copolymer. In the present study, evidence was not found to support the concept of lamellae with equal thickness melting over a broad temperature range. Some evidence was found that might be interpreted to support the concept of a mesomorphic melt as a precursor to crystallization. At present, the model promoted by Strobl and coworkers appears to be at an uncertain stage at which strong proof or disproof are not available. However, this alternative model has injected a new vitality into the study of crystallization of flexible chain polymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2369–2388, 2006     

Rheological characterization and microphase‐separated structure of a poly(ether‐block‐amide) segmented block copolymer

Melt of a segmented block copolymer having poly(lauryl lactam) as the hard segment and poly(tetramethylene oxide) as the soft segment was investigated by rheological techniques. Storage modulus of the polymer melt exhibits the nonterminal behavior resembling those of diblock and triblock copolymer melts, indicating the existence of a microphase‐separated structure. Contrary to block copolymers, the melt of the segmented block copolymer changes from a weak structure to a stiff one upon raising temperature. The storage modulus of the weak structure at low temperatures is inert to large‐amplitude oscillatory shear, while the oscillatory shear destroys the stiff structure at high temperatures and reduces its storage modulus to a value that is same as that of the weak structure. The tapping‐mode data of atomic force microscopy reveal that at low temperatures the polymer melt exhibits a biphasic structure consisted of small spherical soft domains dispersed in a slightly harder matrix; and at high temperatures the spherical domain structure preserves, though the domain coarsens and the hardness difference between the domain and the matrix enlarges. Infrared spectrum analysis shows that the temperature‐induced structural change is related to the dissociation of hydrogen bonding between the hard and soft segments. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2557–2567, 2005     

Kinetically controlled phase transitions in liquid‐crystalline polymers. II. Isothermal degradation of ferroelectric switching in a chiral side‐chain polysiloxane during slow smectic B phase formation

The kinetics of phase transformations in a chiral siloxane polymer has been studied with an Avrami analysis of the differential scanning calorimetry data. Ferroelectric switching has been measured as a function of the driving voltage and temperature. The evolution of the switching at a constant temperature has been studied within the temperature range of the kinetically governed smectic C*/smectic B phase transition. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1779–1784, 2005     

The pressure–volume–temperature relationship of cellulose

Pressure–volume–temperature (PVT) measurements of α-cellulose with different water contents, were performed at temperatures from 25 to 180 °C and pressures from 19.6 to 196 MPa. PVT measurements allowed observation of the combined effects of pressure and temperature on the specific volume during cellulose thermo-compression. All isobars showed a decrease in cellulose specific volume with temperature. This densification is associated with a transition process of the cellulose, occurring at a temperature defined by the inflection point T _t of the isobar curve. T _t decreases from 110 to 40 °C with pressure and is lower as moisture content increases. For isobars obtained at high pressures and high moisture contents, after attaining a minimum, an increase in volume is observed with temperature that may be related to free water evaporation. PVT α-cellulose experimental data was compared with predicted values from a regression analysis of the Tait equations of state, usually applied to synthetic polymers. Good correlations were observed at low temperatures and low pressures. The densification observed from the PVT experimental data, at a temperature that decreases with pressure, could result from a sintering phenomenon, but more research is needed to actually understand the cohesion mechanism under these conditions.     

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     

Specific ionic conduction in poly[oligo (oxyethylene glycol) methacrylate] (PMEO)–Li salt complexes under high‐pressure CO2

We measured the ionic conductivity of amorphous poly[oligo (oxyethylene glycol) methacrylate] (PMEO)–lithium salt complexes under a CO₂ pressure varying from 0.1 to 20 MPa. The pressure dependence of the conductivity was positive, and the conductivity was higher than that under an inert gas such as N₂. The ion‐conductive behavior has been modeled using both the Vogel–Tammann–Fulcher (VTF) equation and activation volume theory. The calculated parameters of the VTF equation show that CO₂ that had permeated into the PMEO matrix acts as solvent molecules to dissolve ions and lower the glass transition temperature at high pressures. The ionic conduction in PMEO complexes under high‐pressure CO₂ was scarcely related to the VTF parameters and activation volume equations. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3151–3158, 2005     

Dielectric relaxation study in electron‐irradiated ferroelectric poly(vinylidene fluoride‐trifluoroethylene) (80/20 mol%) copolymer

The relaxor ferroelectric (RFE) behavior in high‐energy electron‐irradiated poly(vinylidene fluoride‐trifluoroethylene) [P(VDF‐TrFE)] 80/20 mol % copolymer system is characterized over a broad frequency and temperature range. The dielectric properties remarkably vary with the irradiated dose in terms of the change from normal ferroelectric (FE) to RFE phase. During the RFE–paraelectric (PE) transition, the dielectric constants, as a function of temperature, can be described by the Vogel–Fulcher (V–F) relation. It has been found that the relationship between the real and imaginary part of dielectric constant in irradiated copolymer can be well fitted with modified Cole–Cole equation and Debye relaxation equation, exhibiting similar features as inorganic RFEs. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2972–2980, 2005     

PP/POE共混物的P-V-T属性及压力对结晶温度的影响

采用PVT膨胀仪研究了PP/POE共混物的P-V-T属性, 利用Tait方程预测其比容和热膨胀系数(α), 研究了压力对结晶温度(Tc)的影响. 结果表明, Tait状态方程可用来预测部分相容的、半结晶PP/POE共混物的PVT行为. PP结晶前后的比容变化比POE的大得多, 随着POE含量的增加, PP/POE共混物结晶前后比容的变化均逐渐减小. PP在熔融状态下的α比固体状态的大, 而POE正好相反. PP/POE共混物的α随温度和压力的变化与其组成密切相关. 随着压力的增高, PP, POE及其PP/POE共混物的结晶温度均呈线性增高的趋势.     

Reversible melting and crystallization of high‐molar‐mass poly(oxyethylene)

The heat capacity of poly(oxyethylene) (POE) with a molar mass of 900,000 Da has been analyzed with differential scanning calorimetry and quasi‐isothermal, temperature‐modulated differential scanning calorimetry. The crystal structure, lattice parameters, and coherently scattering domain sizes have been measured with wide‐angle X‐ray diffraction as a function of temperature. The high‐molar‐mass POE crystals are in a folded‐chain macroconformation and show some locally reversible melting starting already at about 250 K. At 335 K, the thermodynamic heat capacity reaches the level of the melt. The reversible crystallinity depends on the modulation amplitude and has been varied in the melting range from ±0.2 to ±3.0 K. Before melting, there is neither a change in the crystal structure nor a change in the domain size, but the expansivity of the crystals increases at about 320 K. These observations support the interpretation that the monoclinic POE crystals possess a glass transition temperature with a midpoint at about 324 K, whereas the maximum melting temperature is 341 K. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 475–489, 2007