Pressure dependence of dielectric properties of chlorinated polyethylene vulcanizate. III. β relaxation

The effects of temperature and pressure on the shift factor and the dielectric increment of the β relaxation process were measured for vulcanized chlorinated polyethylene. The isobaric and isochoric activation enthalpies, H^*_P and H^*_V, the activation volume V^*, the pressure dependence of the glass–glass transition temperature, T_gβ/dP, and the apparent extinction temperature T_0β were obtained. The pressure dependences of both V^* and the dielectric increment would reach very small values near the liquid–glass transition temperature T_g, and the β process seems to be affected by the transition near T_g. The value of H^*v/H^*p for the β process is larger than that for the α process, and it is suggested that the molecular motions pertaining to the β process are more strongly restricted than those pertaining to the α process. The ratio T_0β/T₀, where T₀ is the characteristic temperature in the Vogel–Fulcher–Tammann–Hesse equation for the α process, follows the empirical relation of Matsuoka and Ishida, T_gβ/T_g ～0.75. The value of dT_gβ/dP estimated from T_g and T_0β/T₀ is consistent with the experimental value.     

The dependence of dielectric response of an elastomer on hydrostatic pressure

Dielectric methods have been employed to study the high-pressure behavior of a polyurethane elastomer (Solithane 113) in the vicinity of its α transition. The α-loss peak is shifted to higher temperatures and broadened somewhat with the application of hydrostatic pressure up to 6.4 kbars. The slope of T_α vs. P, or dT_α/dP, obtained at low frequencies was found to be equal to dT_g/dP obtained by a volumetric method. Moreover, it attained a nonzero limiting value at high pressures for each frequency tested (3—30,000 Hz) and the limiting value itself increased with increasing frequency from 10.5°C/kbar at 3 Hz to 18°C/kbar at 30,000 Hz. The activation enthalpy ΔH* was found to be nearly constant over the pressure range tested, but the activation volume ΔV* decreased with increasing pressure. The relation dT_α/dP = T (ΔV*/ΔH*) was shown to hold for the elastomer.     

Equations of state for polyamide‐6 and its nanocomposites. II. Effects of clay

The pressure‐volume‐temperature (PVT) dependencies of polyamide‐6 and its nanocomposites (polymeric nanocomposites) were measured at temperatures T = 300–600 K and pressures P = 0.1–190 MPa, thus spanning the range of molten and “solid” phases. The Simha‐Somcynsky (S‐S) cell‐hole equation of state (EOS) was used for describing the molten region. At T_g(P) ≤ T ≤ T_m(P), the “solid” phase is a mixture of the liquid polyamide‐6 with dispersion of crystals. Accordingly, the PVT behavior in this region was described as a combination of the S‐S EOS for the liquid phase and the Midha‐Nanda‐Simha‐Jain (MNSJ) EOS for the crystalline one. These two theories based on different models yielded two sets of the characteristic reducing parameters, P^*, T^*, V^* and the segmental molecular weight, M_s. Incorporation of 2 and 5 wt % clay increased P^* and reduced T^* and V^*, but the effects were small. Fitting the combination of S‐S and MNSJ EOS' to isobaric “solid” phase data yielded the total crystallinity, X_cryst, and the correcting excess specific volume, ΔV_m,c. Both parameters were sensitive to pressure, P, and the clay content, w—the former increased with P and w, whereas the latter decreased. The raw PVT data were numerically differentiated to obtain the thermal expansion and compressibility coefficients, α and κ, respectively. At T < T_m, addition of clay reduced their relative magnitude, whereas at T > T_m, the opposite effect was observed, most likely owing to the excess of intercalant in the polymeric nanocomposites samples. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 966–980, 2009     

Estimation of Physico-chemical Properties of Ionic Liquid EPReO_4 Using Surface Tension and Density

An ionic liquid (IL) EPReO₄ (N‐ethylpyridinium rheniumate) was prepared. The density and surface tension values of the IL were determined in the temperature range of 293.15–343.15 K. The ionic volume and surface entropy of the IL were estimated by extrapolation, respectively. In terms of Glasser's theory, the standard molar entropy and lattice energy of the IL were estimated, respectively. Using Kabo's and Rebelo's methods, the molar enthalpy values of vaporization of the IL, Δ^g_lH⁰_m (298 K), at 298 K and, Δ^g_lH⁰_m (T_b), at hypothetical normal boiling point were estimated, respectively. According to the interstice model, the thermal expansion coefficient of IL EPReO₄ (α) was calculated and compared with experimental value, finding their magnitude order is in good agreement by 8.98%.     

Free volumes in simple and polymeric liquids

Values of ε₀ν₀ the vaporization energy and volume in the hypothetical liquid state at 0°K., are derived for some simple polar and nonpolar molecules used as models for vinyl polymers. The following empirical relationship between the free volume fraction, f = (v ? v₀)/v, and the liquid compressibility coefficient β is demonstrated: ?f² ∝? This is applied to several vinyl polymer liquids near their glass transition temperatures, T_g, giving. f_g ? 0.17, if the “hard-core” volume v^* is considered to be independent of pressure and temperature, (i.e., v^* = v₀); or, f_g ?0.12, if the P,T dependence of v^* is considered to be the same as that of the glass. These agree with f_g values derived by Simha and Boyer from thermal expansion coefficients for the two analogous cases. An empirical viscosity-free volume equation of the Doolittle form: η = ATⁿe^b/f is applied to the glass transition, on assuming that this is an isoviscosity state and with the use of reported values for the expansion and compressibility coefficients and dT_g/dP for three polymers: polystyrene, poly(methyl methacrylate), and poly(vinyl acetate). Reasonable values of b/n are thus obtained. This viscosity equation is critically examined in the light of molecular theories of liquid viscosity.     

Analysis of the melt viscosity and glass transition of polystyrene

The melt viscosity, the glass transition, and the effect of pressure on these are analyzed for polystyrene on the basis of the Tammann-Hesse viscosity equation: log η = log A + B/(T ? T₀). Evidence that the glass transition is an isoviscosity state (log η_g ? 13) for lower molecular weight fractions (M < M_c) is reviewed. For a polystyrene fraction of intermediate molecular weight (M ? 19,000; t_g = 89°C.), it is shown that B is independent of the p–v–T state of the polymer liquid and that dT₀/dP = dT_g/dP. This is consistent with the postulate that B is determined by the internal barriers to rotation in the isolated polymer chain. Relationships are derived for flow “activation energies” at constant pressure and at constant volume, and for the “activation volume.” Values for polystyrene along the zero-pressure isobar and along the constant viscosity, glasstransition line are reported. For the latter, ΔV_g* is constant and corresponds to about 10 styrene units. The “free volume” viscosity equation: log η = log A + b/2.3?, is reexamined. For polystyrene and polyisobutylene, ?_g/b = 0.03, but ?_g and b themselves differ appreciably in these polymers. The parameter b is the product of an equilibrium term Δα and the kinetic term B, and none of these is a “universal” constant for different polymers. The physical significance of the free volume parameter ?, particularly with regard to the “excess” liquid volume, remains undefined. Two new relationships for dT_g/dP, one an exact derivation and the other an empirical correlation, are presented.     

Effects of diluent on molecular motion and glass transitions in polymers. II. The system polyvinylchloride–tetrahydrofuran

Dielectric measurements, differential thermal analyses, and density measurements are reported on concentrated solutions of polyvinylchloride in tetrahydrofuran. The relaxation processes observed between 80 and 400°K have been classified into four types. From the analysis of experimental data, the primary process at the highest temperature and the process at the lowest temperature are assigned, respectively, to segmental motion of the polymer and motion of the solvent. Activation plots for the primary process conform to the Vogel–Tamman equation. The dielectric glass-transition temperature T'_g (defined as the temperature at which the dielectric relaxation time is 100 sec) determined with this equation agrees well with the glass-transition temperature T_g from thermal analysis. Therefore, T_g can be represented by an expression of the form The parameters of the Vogel–Tamman equation A and B are nearly independent of concentration, whereas T_o depends strongly on concentration. The dipole moment per monomeric unit calculated from the experimental data changes with concentration and exhibits steep increments around 30% and 90% by weight. The width of the distribution of the relaxation time also increases with the concentration. The results were compared with those for the system polystyrene–toluene studies in the same way.     

The kinetics of the solvolysis of chloropentacyanocobaltate(III) ions in water containing 2-methoxyethanol or diethylene glycol: A contrast with the effect of more hydrophobic cosolvents

The kinetics of the solvolysis of [Co(CN)₅Cl]^3– have been investigated in water +2-methoxyethanol and water + diethylene glycol mixtures. Although the addition of these linear hydrophilic cosolvent molecules to water produces curvature in the variation of log(rate constant) with the reciprocal of the dielectric constant, their effect on the enthalpy and entropy of activation is minimal, unlike the effect of hydrophobic cosolvents. The application of a Gibbs energy cycle to the solvolysis in water and in the mixtures using either solvent-sorting or TATB values for the Gibbs energy of transfer of the chloride ion between water and the mixture shows that the relative stability of the emergent solvated Co(III) ion in the transition state compared to that of Co(CN)₅Cl^3– in the initial state increases with increasing content of cosolvent in the mixture. By comparing the effects of other cosolvents on the solvolysis, this differential increase in the relative stabilities of the two species increases with the degree of hydrophobicity of the cosolvent.List of Symbols v₂ partial molar volume of the cosolvent in water + cosolvent mixtures - V ₂ ^o molar volume of the pure cosolvent - H _mix ^E excess enthalpy of mixing water and cosolvent - S _mix ^E excess entropy of mixing water and cosolvent - G _t ^o (i)_n the Gibbs energy of transfer of speciesi from water into the water + cosolvent mixture excluding electrostatic contributions - k _s first order rate constant for the solvolysis in water + cosolvent mixtures - D _s dielectric constant of the water + cosolvent mixture - H ^* the enthalpy of activation for the solvolysis - S ^* the entropy of activation for the solvolysis - G ^* the Gibbs energy of activation for the solvolysis - V ^* the volume of activation for the solvolysis - i ^* speciesi in the transition state for the solvolysis - H _o Hammett Acidity Function - TATB method for estimating the Gibbs energy of transfer for single ions assuming those for Ph₄As⁺ and BPh ₄ ^– are equal     

Volumes of mixing and theP * effect: Part I. Hexane isomers with normal and branched hexadecane

The Prigogine-Flory theory of solution thermodynamics has been used to interpret molar excess volume data, V ^E , for two series of alkane mixtures: the five isomers of hexane mixed with normal hexadecane (Data from Reeder, et al.) and the five hexane isomers mixed with a highly branched hexadecane isomer, 2,2,4,4,6,8,8-heptamethylnonane (this work). Values of V ^E are negative and similar for both series, but vary considerably with the hexane within a series. According to the theory, V ^E contains a P^* contribution not found in the excess enthalpy and entropy, which depends strongly on the internal pressures and the derived P^* parameters of the components. Values of V ^E are well predicted for both series, the variation of V ^E corresponding to the different internal pressures or P^* parameters of the hexanes.     

Dominant factors affecting the pressure dependence of melting temperatures in homologous series of aliphatic polyesters

The pressure dependence of the melting temperature of six aliphatic polyesters belonging to two different homologous series, poly(x-succinate) and poly(x-adipate) having even number of methylene groups (2,4,6) in the alkylene segment (x) was investigated by high pressure differential thermal analysis (HP-DTA) up to 500 MPa. The phase diagrams of these polyesters were newly determined except for poly(ethylene adipate). The dT_m/dp_o at atmospheric pressure was obtained from the quadratic equation and the trend of dT_m/dp_o with respect to the number of methylene groups in the monomer unit in each homologous series is discussed. Amorphous densities at 25 °C, expansion and compressibility coefficients in the melt of these polyesters are also reported. The entropy of fusion (ΔS_m), enthalpy of fusion (ΔH_m), volume change on melting (ΔV_m), conformational entropy (ΔS^or) and volume entropy (ΔS^v) were correlated with respect to the number of methylene groups in the alkylene segment. ΔV_m and ΔS^v displayed a similar trend as that of dT_m/dp_o while ΔS_m, ΔS^or and ΔH_m showed an increasing trend. The influence of these parameters on dT_m/dp_o is discussed in the context of the Clapeyron equation.     

Pressure dependence of dielectric properties of chlorinated polyethylene vulcanizate. I. α relaxation and shift factors

The complex dielectric constant was measured under elevated pressure for the α relaxation of vulcanized chlorinated polyethylene. Both temperature and pressure effects on the static dielectric constants, the activation enthalpy, and volume, and the pressure dependence of the glass-transition temperature were obtained. The dependence of shift factors on temperature was expressed by the Vogel–Fulcher–Tamman–Hesse (VFTH) equation: ?log a_T = A ? B/(T ? T₀). The parameters A, B, and T₀ for each pressure applied were calculated by minimizing the standard deviation between log a_T and experiments. The values of the parameters in the Williams–Landel–Ferry (WLF) equation: ?log a_T = C₁(T ? T_g)/[C₂ + (T ? T_g)], were also estimated from the resulting values of the VFTH parameters. All these parameters depended on pressure. The activation volume plotted against T ? T_g decreased with increasing pressure.     

Effect of pressure and temperature on chromophore reorientation in a new syndioregic main‐chain hydrazone nonlinear optical polymer

Second harmonic generation (SHG) was used to measure the temperature dependence of the reorientation activation volume (ΔV*) of a syndioregic main‐chain hydrazone (SMCH) nonlinear optical polymer. The decay of the SHG signal from poled films of SMCH was recorded at hydrostatic pressures up to 2924 atm and at temperatures between 25 °C below the glass‐transition temperature (T_g) to 20 °C above it. ΔV* for pressures less than 500–1000 atm and T > T_g decreased as the temperature was increased. For pressures greater than 1000 atm, ΔV* was essentially constant for all temperatures. In addition, the size of ΔV* indicated that the chromophore in this main chain was internally flexible. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 895–900, 2001     

Analysis of the equations of state of polyolefin melts in terms of the simha-somcynsky hole theory

Pressure–volume–temperature data on melts of low-density polyethylene, polypropylene (PP), poly(butene-1) (PBT), and poly(4-methylpentene-1) (PMP) previously reported by us have been evaluated in terms of the Simha–Somcynsky hole theory of polymeric liquids by a determination of the reducing parameters P^*, V^*, and T^* for each system. Literature data on the reducing parameters of linear polyethylene and of a branched polyethylene of intermediate density are also considered. Agreement with theory is best for the polyethylenes and deteriorates markedly in the series PBT:PP:PMP. These higher polyolefins have very low values of P^*, thus suggesting a deficiency of the Simha–Somcynsky theory at high reduced pressures P? = P/P^*. In these polyolefins, systematic variations of the reducing parameters (and molecular parameters derived therefrom) are noted and discussed. Correlations found previously between T^* and the moleculer weight M₀ of the effective segment of the theory or its hard-core volume M₀V^* are obeyed by the polyethylenes only. The higher polyolefins show serious deviations from these correlations.     

Kinetics of the solvolysis of trans-dichlorotetra(4-t-butylpyridine)-cobalt(III) ions in mixtures of water with methanol and with ethanol

For the solvolysis of Co(4-t-Bupy)₄Cl₂^? ions in water + methanol and water + ethanol, log (rate constant) does not vary linearly with the reciprocal of the dielectric constant. The Gibbs free energy, the enthalpy, and the entropy of activation are insensitive to changes in the solvent composition in these mixtures, although a slight broad maximum in ΔH* and ΔS* probably exists at mole fractions of about 0.2 in water + ethanol. This contrasts with the extrema in ΔH* and ΔS* found with more hydrophobic alcohols used as cosolvents. However, the application of a Gibbs energy cycle to the solvolysis in water and in the mixtures shows that there is a differential effect of changes in solvent structure on the emergent solvated Co^III cation in the transition state and on Co(4-t-Bupy)₄Cl₂⁺ in the initial state. The stability of the former increases relative to that of the latter as the cosolvent content of the mixture rises. © 1995 John Wiley & Sons, Inc.     

Temperature dependence of the activation volume in a nonlinear optical polymer: Evidence for chromophore reorientation induced by sub-Tg relaxations

Second harmonic generation (SHG) was used to measure the temperature dependence of the reorientation activation volume of 4-(diethylamino)-4′-nitrotolane (DEANT) in poly(methyl methacrylate) (PMMA). The decay of the SHG signal from films of DEANT/PMMA was recorded at hydrostatic pressures up to 3060 atm and at different temperatures between 25°C below the glass transition temperature to 35°C above it. The activation volume, ΔV*_αβ associated with the long range α-type motion of the polymer remained constant at 213 ± 10 ų between T_g − 25°C and T_g + 10°C. At higher temperatures, ΔV*_αβ decreased linearly with increasing temperature. The activation volume, ΔV*_αβ, associated with short range secondary relaxations was constant over the entire temperature range with a value of 77 ± 10 ų. The data suggest that above T_g chromophore reorientation is coupled to both the long range and local motions of the polymer; whereas, well below T_g chromophore reorientation is closely coupled to the local relaxations of the polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 901–911, 1998     

Specific volume of polysulfone as a function of temperature and pressure

The pressure–volume–temperature (PVT) properties of a commercial polysulfone derived from bisphenol A and 4,4′-dichlorodiphenylsulfone are studied experimentally and theoretically in the temperature range 30–370°C and for pressures to 2000 kg/cm². PVT surfaces are determined for an annealed glass, formed under zero pressure, and for the melt. Two glass-transition lines must be distinguished: T(P) which is the intersection of the glass and melt PVT surfaces, and T_g(P), which is obtained by pressurizing the melt isothermally. The application of Ehrenfest-type equations to these transitions are discussed. The Prigogine–Defay ratio r = Δ_kΔC_p/TV(Δα)² at P = 0 is found to be equal to 0.95 (±20%), using ΔC_p data determined on identical samples. The melt data is compared with the Simha–Somcynski hole theory, using the reducing parameters V^* = 0.788 cm³/g, T^* = 12,560°K, P^* = 10,875 bar. The hole fraction appearing in the theory is found to be constant along T(P), but the glass PVT relationship cannot be reproduced by using the Simha–Somcynsky theory together with the assumption that the hole fraction remains constant in the glass. At P = 0 the hole fraction must be allowed to decrease with decreasing temperature, but at a slower rate than in the melt.     

Dielectric spectroscopy and calorimetry during postcuring of a linear chain polymer thermoset formed from a diepoxide and cyclohexylamine,and the nature of the products

The dielectric permittivity and loss spectra of an equimolar liquid mixture of diglycidyl ether of bisphenol-A and cyclohexylamine have been studied during the liquid's isothermal polymerization or curing in separate experiments at different temperatures and thereafter during the postcuring, both on rate-heating and isothermally. The spectra obtained during the growth of the linear chain polymer during the curing and postcuring show the evolution of an intermediate relaxation process whose position in the frequency plane remains relatively insensitive to the decrease in the configurational entropy during the postcuring, but whose strength increases. Postcuring ceases to occur once the calorimetric glass-liquid transition temperature of 345 K, corresponding to the ultimately formed polymeric state, has been reached. The increase in the number of covalent bonds, n, formed during curing and postcuring decreased the equilibrium dielectric permittivity, ε_s, and increased the characteristic relaxation time, τ₀, for all curing and postcuring conditions. For a fixed temperature and n, (dε_s/dT) and (dτ₀/dT), as well as the values ε_s and τ₀ of the ultimately formed state of the polymers differ significantly when the thermal history of polymerization differs. The slow dynamics in the glass-liquid transition region were analyzed in terms of the enthalpy relaxation and fictive temperature concepts. The distribution of relaxation times for these dynamics correspond to the stretched exponential parameter of 0.6, which is significantly greater than 0.39 determined for the dielectric α-relaxation spectra measured at a temperature 30 K higher. The enthalpy relaxation involves a narrower distribution of intermolecular barriers than dielectric relaxation. The results also show that the recently proposed method for determining the gelation time from the plots of the imaginary component of electrical impedance lacks scientific merit. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 303–318, 1998     

Studies on temperature dependent kinetics of <Emphasis Type="Italic">Aspergillus awamori</Emphasis> feruloyl esterase in water solutions

The initial reaction rate (V ₀) for the esterification reaction of feruloyl esterase (FAE-II) at different temperatures (288, 298, 308, 318, 328, 338, 348, and 358 K) and various ethyl ferulate concentrations [(2, 4, 6, 8, 10, 12, 14, and 16) × 10⁻⁴ mol l⁻¹ of ethyl ferulate in water] were determined. The Lineweaver-Burk double reciprocal plot yielded the kinetic parameters (maximal velocity V _max, Michaelis constant K _m, and second order rate constant V/K). The effects of temperature on those 3 kinetic parameters were presented and discussed. The thermodynamic parameters ΔH* (enthalpy of activation), ΔG* (free energy of activation), ΔS* (entropy of activation), ΔG _E-S (free energy change of substrate binding), ΔG _E-T (free energy change of transition state formation), related to that biochemical process were determined and discussed from van’t Hoff plot, Arrhenius plot, and Eyring plot.     

Volume and enthalpy relaxation response after combined temperature history in polycarbonate

Summary Volume and enthalpy relaxation in polycarbonate subjected to double temperature jumps in the T_g region has been analysed. It concerns both initial T_down-jump from equilibrium above T_g to consolidation temperature below T_g and fina1 T_up-jump to relaxation temperature, also below T_g. The measured H and V data after T_up-jump were compared with respect to aging time calculating (dH/dV) ratio denoted as aging bulk modulus, K_a. According this new methodology H and V relaxation response after T_up-jump demonstrates differences in relaxation responses.     

Synthesis and Properties of [Ba(CHZ)(BT)(H2O)2]n as a New Energetic Coordination Compound

In order to enhance the thermal stability of the barium salt of 5,5′‐bistetrazole (H₂BT), carbohydrazide (CHZ) was used to build [Ba(CHZ)(BT)(H₂O)₂]_n as a new energetic coordination compound by using a simple aqueous solution method. It was characterized by FT‐IR spectroscopy, elemental analysis, and single‐crystal X‐ray diffraction. The crystal belongs to the monoclinic P2₁/c space group [a = 8.6827(18) Å, b = 17.945(4) Å, c = 7.2525 Å, β = 94.395(2)°, V = 1126.7(4) ų, and ρ = 2.356 g · cm^–3]. The Ba^II cation is ten‐coordinated with one BT^2–, two shared carbohydrazides, and four shared water molecules. The thermal stabilities were investigated by differential scanning calorimetry (DSC) and thermal gravity analysis (TGA). The dehyration temperature (T_dehydro) is at 187 °C, whereas the decomposition temperature (T_d) is 432 °C. Non‐isothermal reaction kinetics parameters were calculated by Kissinger's method and Ozawa's method to work out E_K = 155.2 kJ · mol^–1, lgA_K = 9.25, and E_O = 158.8 kJ · mol^–1. The values of thermodynamic parameters, the peak temperature (while β → 0) (T_p0 = 674.85 K), the critical temperature of thermal explosion (T_b = 700.5 K), the free energy of activation (ΔG^≠ = 194.6 kJ · mol^–1), the entropy of activation (ΔS^≠ = –66.7 J · mol^–1), and the enthalpy of activation (ΔH^≠ = 149.6 kJ · mol^–1) were obtained. Additionally, the enthalpy of formation was calculated with density functional theory (DFT), obtaining Δ_fH°₂₉₈ ≈ 1962.6 kJ · mol^–1. Finally, the sensitivities toward impact and friction were assessed according to relevant methods. The result indicates the compound as an insensitive energetic material.