A new and reliable calibration method for vibrating tube densimeters over wide ranges of temperature and pressure

A new method for accurately converting vibrating tube periods of oscillation in density values is presented. This method is based on the fundamental requirement of the non-dependence on pressure of the vibration period of the cell under vacuum. An analytical method permits to correctly evaluate the evacuated vibrating tube periods of the Anton Paar cells namely the high pressure cells, 512 and 512P, as a function of temperature. It is further shown that the previously experimental method for the determination of this parameter is not suitable for obtaining reliable density values. A new simple calibration procedure is described and tested over wide ranges of temperature, T = (283.15 to 323.15) K and pressure, P = (0.1 to 60) MPa. New recommended density values for n-alkanes (C₆, C₇, C₈, and C₁₀) and tetrachloromethane, calculated by the proposed method, are given and compared with literature values in terms of mutual uncertainties.     

New calibration methodology for calorimetric determination of isobaric thermal expansivity of liquids as a function of temperature and pressure

A new method for determining isobaric thermal expansivity of liquids as a function of temperature and pressure through calorimetric measurements against pressure is described. It is based on a previously reported measurement technique, but due to the different kind of calorimeter and experimental set up, a new calibration procedure was developed. Two isobaric thermal expansivity standards are needed; in this work, with a view on the quality of the available literature data, hexane and water are chosen. The measurements were carried out in the temperature and pressure intervals (278.15 to 348.15) K and (0.5 to 55) MPa for a set of liquids, and experimental values are compared with the available literature data in order to evaluate the precision of the experimental procedure. The analysis of the results reveals that the proposed methodology is highly accurate for isobaric thermal expansivity determination, and it allows obtaining a precise characterisation of the temperature and pressure dependence of this thermodynamic coefficient.     

Rotational viscosity γ1 of nematic liquid crystals as a function of temperature,pressure and density

Abstract

Measurements of the rotational viscosity γ₁ and the density are presented for a mixture of 4′-methoxybenzylidenebutylaniline (MBBA) and its ethoxy homologue EBBA and a mixture of cyclohexylphenylnitriles (ZLI 2413 from Merck AG) as a function of temperature and pressure. A new set-up for the measurement of densities under pressures of up to 3kbar is described. It is shown that the pressure dependence of the kinematic rotational viscosity γ₁/ρ and the temperature dependence of γ₁ under isobaric and isochoric conditions have common features with that of the shear viscosity of isotropic liquids. Furthermore, it is found that the curves γ₁ = f(1/T) for constant p and γ₁ = g(ρ) for constant T can be shifted one onto another by an appropriate shift of the scale of the independent variable.     

Compressed liquid density measurements of dimethyl ether with a vibrating tube densimeter

A measurement system for compressed liquid densities over the temperature range of (293 to 373) K with pressures up to 70 MPa has been developed in this work. The core component of the system is a commercial vibrating tube densimeter (DMA-HPM) and the system was calibrated by water and vacuum via the method of Lagourette et al. Compressed liquid densities of dimethyl ether have been measured along nine isotherms between (293.84 and 372.94) K up to 70 MPa with the densimeter system as a function of temperature and pressure. The experimental data obtained in this work were correlated to the Tait equation with an average absolute percentage deviation of 0.014%. Also, the Tait equation was compared with the literature data.     

Specific volume of polymers as a function of temperature and pressure

Summary The specific volume of pure and plasticized polyvinylchloride and of polymethylmethacrylate was studied with a dilatometer as function of temperature (–80 to +150 °C) and hydrostatic pressure (1 to 1000 at.). Beside the glass transition also two types of secondary transitions are observed with PVC and PMMA which correspond to dynamic secondary dispersion ranges.Below the glass transition the specific volumina depend on how they were reached.The transition temperatures of the samples were determined at elevated pressures with decreasing temperatures. Glass transition and secondary transitions cause stepwise increases of the thermal expansivities and the isothermal compressibilities. Above the glass transition the compressibilities are rising in proportion to the temperature.With PVC all transition temperatures are shifted by about 0,013 to 0,015 °C/at as the pressure is raised. With PMMA the transitions at –7 °C and at +62 °C are not affected by hydrostatic pressure while the glass transition is shifted by 0,018 °C/at.Addition of plasticizer to PVC shifts the glass transition to lower and the secondary transition to higher temperatures.There is no agreement between the measured shifting factorsdT _g/dp and those calculated according toEhrenfest's law/=dT _g/dp.

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Zusammenfassung Das spezifische Volumen von reinem und weichgemachtem Polyvinylchlorid und von Polymethylmethacrylat wurde mit Hilfe eines Dilatometers als Funktion der Temperatur (–80 bis +150 °C) und des hydrostatischen Drucks (1 bis 1000 at) gemessen. Außer dem Glasübergang wurden bei PVC und PMMA noch weitere sekundäre Übergangsbereiche gefunden, die dynamischen Nebendispersionsgebieten entsprechen.Unterhalb der Glastemperatur hängen die spezifischen Volumina stark von dem Wege ab, auf dem sie erreicht wurden.Die Übergangstemperaturen der Proben wurden bei erhöhtem Druck mit fallender Temperatur bestimmt. Der Glasübergang und die sekundären Übergänge sind von stufenweisen Änderungen der thermischen Ausdehnungskoeffizienten und der isothermen Kompressibilitäten begleitet. Oberhalb des Glasübergangs steigen die Kompressibilitäten proportional zur Temperatur an.Bei PVC werden alle Übergangstemperaturen durch steigenden Druck um etwa 0,013 bis 0,015 °C/at verschoben. Bei PMMA werden die Übergangsgebiete bei –7 °C und bei +62 °C durch hydrostatischen Druck nicht beeinflußt, während der Glasübergang um etwa 0,018 °C/at verschoben wird.Der Zusatz von Weichmacher zu PVC verschiebt den Glasübergang zu tieferen und den sekundären Übergang zu höheren Temperaturen.Die gemessenen VerschiebungsfaktorendT _g/dp stimmen nicht mit den nach derEhrenfestschen Beziehung berechneten überein.

     

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.     

Polymer thin film properties as a function of temperature and pressure

We report on evanescent wave optical measurements of the glass transition temperature, T_g, of spin-cast PMMA films as a function of film thickness and molecular weight. It was found that for films of high molecular weight PMMA (M_n > 100,000 g mol⁻¹) a strong T_g depression occurs for films that are thinner than 100 nm in case they are deposited on hydrophobic substrates. This strong T_g depression of up to 25°C decreases if similarly thick films of PMMA of low molecular weights are investigated and vanishes completely for PMMA with M_n < 12,000 g mol⁻¹. For films made of these materials T_g is found to be identical to that of the bulk even for films as thin as 5 nm. The results might be interpreted in terms of free volume considerations. To check this assumption we also designed and built a pressure cell that can be used together with the evanscent wave optical techniques for similar measurement, but with the additional option to do the measurements at different pressures up to ca. 100 MPa to further vary the free volume of these polymer films in constrained geometry. Some first results obtained with this setup are also described.     

Electron mobility in supercritical pentanes as a function of density and temperature

The excess electron mobility in supercritical n-, iso- and neopentane was measured isothermally as a function of density. The density-normalized mobility μN in all three isomers goes through a minimum at a density below the respective critical densities, and the mobility is quite temperature-dependent in this region, then goes through a minimum. The μN behavior around the minimum in n-pentane is well accounted for by the Cohen-Lekner model with the structure factor S(K) estimated from the speed of sound, while that in iso- and neopentane is not.     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

Rotational viscosity γ1 of nematic liquid crystals as a function of temperature, pressure and density

Measurements of the rotational viscosity γ₁ and the density are presented for a mixture of 4'-methoxybenzylidenebutylaniline (MBBA) and its ethoxy homologue EBBA and a mixture of cyclohexylphenylnitriles (ZLI 2413 from Merck AG) as a function of temperature and pressure. A new set-up for the measurement of densities under pressures of up to 3kbar is described. It is shown that the pressure dependence of the kinematic rotational viscosity γ₁/ρ and the temperature dependence of γ₁ under isobaric and isochoric conditions have common features with that of the shear viscosity of isotropic liquids. Furthermore, it is found that the curves γ₁ = f(1/T) for constant p and γ₁ = g(ρ) for constant T can be shifted one onto another by an appropriate shift of the scale of the independent variable.     

Thermodynamic properties of aqueous polyacrylamide solutions as a function of pressure and temperature

The viscosities of dilute aqueous solutions of polyacrylamide were measured at temperatures from 20 to 60.4° and pressures up to 150 MPa using a falling-body viscometer. The viscosity coefficient, ν, increases exponentially with increasing pressure at a given temperature and concentration. The rate of increase of the apparent energy of activation. E≠, with pressure becomes more rapid as the concentration of the solutions increases. Intrinsic viscosity, [ν], increases with increasing pressure at a given temperature but almost levels off at pressures above 100 MPa while the Huggins constant, k_H, decreases. The Flory-Huggins interaction parameter, _X1, decreases at a greater rate with increasing pressure as the temperature decreases indicating that the effect of pressure on improving the compatability between the polymer and solvent is greater near the θ-temperature. The second virial coefficient, A₂, was calculated from the intrinsic viscosity data and compared with the results obtained by light scattering technique.     

Experimental determination of the electron tunneling probability as a function of distance for chemical reactions

The kinetics for the tunnelling reaction of trapped electrons with Cu(en)²⁺₃ in a rigid, glassy matrix at 77 K have been measured using pulse radiolysis. The distribution of the Cu(en)³⁺₃ ions was studied in the same system by measurements of ESR line widths, and found to be uniform (random). These measurements help to confirm the measured tunneling distances and the exponential dependence of the rates on the distance between the electron donor and acceptor.     

Potentiometric stripping determination of heavy metals using a graphite-reinforcement carbon vibrating electrode

Potentiometric stripping determination of Cd, Cu and Zn using a vibrating electrode (VE) is presented. A simple VE was constructed by using a piezoelectric bimorph oscillator and an inexpensive graphite-reinforcement carbon (GRC) rod (a mechanical pencil). Experimental results obtained with the simple VE follow the equation valid for quantitative application of potentiometric stripping analysis (PSA) in large solutions. It was found that the GRC vibrating electrode is suitable for multielement trace analysis of small samples of 0.05 mL. The relative standard deviations for divalent metals are better than 2%. Received: 3 February 1997 / Revised: 2 June 1997 / Accepted: 7 June 1997     

Potentiometric stripping determination of heavy metals using a graphite-reinforcement carbon vibrating electrode

Potentiometric stripping determination of Cd, Cu and Zn using a vibrating electrode (VE) is presented. A simple VE was constructed by using a piezoelectric bimorph oscillator and an inexpensive graphite-reinforcement carbon (GRC) rod (a mechanical pencil). Experimental results obtained with the simple VE follow the equation valid for quantitative application of potentiometric stripping analysis (PSA) in large solutions. It was found that the GRC vibrating electrode is suitable for multielement trace analysis of small samples of 0.05 mL. The relative standard deviations for divalent metals are better than 2%.     

Internal pressure and solubility parameter as a function of pressure

The main goal of this work was to measure the solubility parameter of a complex mixture, such as a crude oil, especially as a function of pressure. Thus, its definition is explained, as well as the main approximations generally used in literature. Then, the internal pressure is investigated, since it is presented as an alternative of the solubility parameter. In this work, the assumption that internal pressure is a measure of the physical solubility parameter was made, i.e. representing the dispersion and polar forces. As for the pressure influence, it was seen that internal pressure reaches a maximum contrary to solubility parameter.An indirect method was chosen to estimate internal pressure, using thermal expansivities (determined by microcalorimetry) and isothermal compressibilities (determined by density measurements). The uncertainty is within 2% for the expansivity and 0.1% for the density. Five pure compounds (four hydrocarbons and 1 alcohol) were investigated at 303.15 K and up to 30 MPa, as well as a dead crude oil. The “physical” solubility parameter is slightly increasing with pressure (up to 0.8 MPa^1/2 for cyclohexane) and, at 0.1 MPa, the difference with literature data is less than 1 MPa^1/2 for hydrocarbons. On the contrary, the difference reaches 9 MPa^1/2 for ethanol as expected, due to the presence of hydrogen bonding. A dead crude oil was also studied and its solubility parameter is within the expected range.Two cubic equations of states (Peng–Robinson and Soave–Redlich–Kwong) were able to approximate the “physical” solubility parameter of n-heptane (within 0.2 MPa^1/2), providing that the volumes were measured and used as input. The Peng–Robinson equation gave somewhat better results.     

Structural and vibrational characterization of the organic semiconductor tetracene as a function of pressure and temperature

Neutron powder diffraction and inelastic neutron scattering measurements were performed on crystalline tetracene, a molecular semiconductor of triclinic crystal structure that adopts a herringbone layered motif, as a function of pressure up to 358 MPa. In combination with theoretical and simulated computations, these measurements permit detailed characterization of the structural and vibrational changes of tetracene as a function of pressure. Powder diffraction at 295 K reveals anisotropic modification of the crystal structure with increasing pressure. Particularly, the unit cell parameters associated with the two-dimensional herringbone layers of the solid state structure displayed continuous change at all measured pressures, whereas perpendicular to the herringbone layers the structure remains relatively unchanged. The measured compressibilities along the [1 0 0], [0 1 0], and [0 0 1] crystal axes are −3.8 × 10⁻⁴, −1.9 × 10⁻⁴, and −3.4 × 10⁻⁴ Å/MPa, respectively. Inelastic neutron scattering spectra were collected at several pressures in the 25–75 and 0–25 meV energy ranges using a filter analyzer and a Fermi chopper time-of-flight spectrometer, respectively. Assignment of the spectral peaks to specific intramolecular vibrational modes has been accomplished using ab initio density functional theory calculations and the low energy lattice phonon modes were interpreted from the results of molecular dynamics simulations at 1 atm and 358 MPa. Anisotropic behavior parallel to that observed in the structural measurements is also apparent in both the intramolecular and lattice phonon vibrational dynamics. Intramolecular vibrations having atomic displacements entirely within the plane of the molecule’s aromatic ring remain unchanged with increasing pressure while vibrations with atomic displacements perpendicular to the molecular plane shift to higher energy. The lattice phonons display a similar anisotropy with increasing pressure. Phonon modes propagated within the herringbone layer are significantly shifted to higher energy with increasing pressure relative to the modes with displacements primarily perpendicular to the layers. Overall, both the planar internal geometry and the layered arrangement of the tetracene molecules significantly influence the observed structural and vibrational behavior with increasing pressure.     

Dielectric anisotropy in the nematic phase of 8PCH as a function of temperature and pressure

The dielectric permittivity components, ε_∥ and ε_⊥, in the nematic phase of 8PCH (trans-4-n-octyl(4-cyanophenyl)cyclohexane) were measured at 1 atm as a function of temperature (T), and at two temperatures as a function of pressure (p). A close similarity of the temperature and pressure behaviours of the dielectric anisotropy, δε = ε_∥ - ε_⊥, was established. It is argued that p and T are equivalent quantities in the formation of the nematic state. The well known Maier and Meier equations describe the dielectric parameters under both p = constant and T = constant conditions fairly well.     

Kinetic studies of the ClO + ClO association reaction as a function of temperature and pressure

The kinetics of the association reaction of ClO radicals: ClO + ClO + M --> Cl2O2+ M (1), have been investigated as a function of temperature T between 206.0-298.0 K and pressure p between 25-760 Torr using flash photolysis with time-resolved UV absorption spectroscopy. ClO radicals were generated following the photolysis of Br2/Cl2O mixtures in nitrogen diluent gas. Charge coupled device (CCD) detection of time resolved absorptions was used to monitor ClO radicals over a broad wavelength window covering the ClO (A 2Pi<-- X 2Pi) vibronic absorption bands. The high pass filtered ClO absorption cross sections were calibrated as a function of temperature between T = 206.0-320 K, and exhibit a negative temperature dependence. The ClO association kinetics were found to be more rapid than those reported in previous studies, with limiting low and high pressure rate coefficients, in nitrogen bath gas, k0 = (2.78 +/- 0.82) x 10(-32) x (T/300)(-3.99 +/- 0.94) molecule(-2) cm6 s(-1) and k(infinity) = (3.37 +/- 1.67) x 10(-12) x (T/300)(-1.49 +/- 1.81) molecule(-1) cm3 s(-1), respectively, (obtained with the broadening factor F(c) fixed at 0.6). Errors are 2sigma. The pressure dependent ClO association rate coefficients (falloff curves) exhibited some discrepancies at low pressures, with higher than expected rate coefficients on the basis of extrapolation from high pressures (p > 100 Torr). Reanalysis of data excluding kinetic data recorded below p = 100 Torr gave k0 = (2.79 +/- 0.85) x 10(-32) x (T/300)(-3.78 +/- 0.98) molecule(-2) cm6 s(-1) and k(infinity) = (3.44 +/- 1.83)x 10(-12) x (T/300)(-1.73 +/- 1.91) molecule(-1) cm3 s(-1). Potential sources of the low pressure discrepancies are discussed. The expression for k(0) in air bath gas is k0 = (2.62 +/- 0.80) x 10(-32) x (T/300)(-3.78 +/- 0.98) molecule(-2) cm6 s(-1). These results support upward revision of the ClO association rate coefficient recommended for use in stratospheric models, and the stratospheric implications of the results reported here are briefly discussed.