A methodology to define the Cubic Equation of State of a simple fluid

A method to define the Cubic Equation of State (CES) of a simple substance is presented in this work. CES is constructed with only three parameters of the fluid, namely, the critical compressibility Z_c≡P_cv_c/RT_c, the acentric factor ω ≡ − log  (P^(sat)/P_c) − 1 (where P^(sat) is the saturated vapor pressure), and the saturated vapor volume v^(sat) at the temperature T^(sat)/T_c = 0.7 (where T_c is the critical temperature, v_c is the critical volume, and P_c is the critical pressure). The resulting CES is unique for each substance and, in general, it is different from other known CES in the literature.     

Application of the modified van der waals equation for unsaturated vapour and liquid states

The Law-Lielmezs (L-L) modification of the Van der Waals equation of state: P = RT/(V-b)-a(T)/V² where: a(T) = a(T_c)·a(T_c·a(T¹) and: a(T¹) = 1 + pT^1q has been extended to include unsaturated states in terms of a correcting function C_f(such that the α(T¹) term becomes: a(T¹) = 1 + _pC_fT^1q The proposed extension has been compared with the results obtained by the use of the original Van der Waals equation of state.     

Critical parameters for isobutane determined by the image analysis

(p, ρ, T) Measurements and visual observations of the meniscus for isobutane were carried out carefully in the critical region over the range of temperatures: −15 mK ? (T − T_c) ? 35 mK, and of densities: −7.5 kg · m⁻³ ? (ρ − ρ_c) ? 7.5 kg · m⁻³ by a metal-bellows volumometer with an optical cell. Vapor pressures were also measured at T = (310, 405, 406, 407, and 407.5) K. The critical point of T_c and ρ_c was determined by the image analysis of the critical opalescence which is proposed in this study. The critical pressure p_c was determined to be the pressure measurement at the critical point. Comparisons of the critical parameters with values given in the literature are presented.     

Coexistence curve of 2,6-lutidine + water,near its lower critical point

Measurements of the refractive index of both phases of the mixture 2,6-lutidina + water, near the lower critical point, are reported. For T-T_c < 0.5 K, a simple power law, Δn = (0.0471±0.001)(T-T_c)^{(0.338±0.003)}, describes the data. For 0.5 K <T-T_c < 15 K, a decorated lattice model better describes the data.     

The kerr effect in the vicinity of the transition from the isotropic to smectic a phase

The equilibrium electrooptical effect in the isotropic phase of seven liquid crystalline substances (4-n-decyloxy-4′-cyanobiphenyl, carbosilane dendrimer of the fourth generation with cyanobiphenyl terminal fragments, and the fourth, fifth, sixth, seventh, and tenth members of the homologous series of 4-n-acylphenylene 4′-n-alkoxybenzoates) was studied. The smectic A phases were found to exhibit weaker divergence of the Kerr constant in the vicinity of the T _c isotropic melt-liquid crystal phase transition temperature compared with the nematic phases. The difference between T _c and the temperature T* of the virtual second-order phase transition varied from 3.2 to 19.0 K for the smectic A phases, which substantially exceeded the value (T _c-T*) ≤ 1 K for the nematic phases. A theory of the electrooptical properties of isotropic melts in the vicinity of the T _c temperature of the phase transition from the isotropic to smectic A phase is developed. An equation relating the T _c-T* difference to the phenomenological coefficients of the expansion of the Helmholtz energy of an isotropic melt into a series in powers of the coordination and orientational order parameters is obtained.     

A neutron diffraction and 170Yb Mössbauer investigation of the perovskite ytterbium titanium oxide

A phase with the perovskite structure (Pbnm) and a composition YbTiO_2.95 has been prepared by a high-temperature carbothermic method. Neutron diffraction shows a colinear ferrimagnetic structure at 7 K with Yb and Ti moments antiparallel along the c-axis of the orthorhombic cell and an Yb moment of 1.8(3)μ_B. ¹⁷⁰Yb Mössbauer measurements find a more precise and accurate value of 2.0(1)μ_B from the maximum hyperfine field. From the temperature dependence of the hyperfine field a T_c = 42(1) K is found. The Yb sublattice magnetization below T_c follows a Brillouin function. At low temperature a distribution of hyperfine fields is observed which is attributed to a random distribution of defects surrounding the Yb sites. The magnetic structure is discussed in relation to possible values for the crystal field parameters, especially B²₀.     

Novel correlations between the critical constants of the noble gases

For any particular fluid, the set of three critical constants (CC) – pressure P_c, temperature T_c and molar volume V_c – has a central importance in defining the physical behaviour of the fluid in the gas and liquid states. However, little attention seems to have been paid in the past to the relations between the CC of different substances. In the present paper, some simple and apparently novel relations have been found between the three CC for the set of four noble gases: Ne, Ar, Kr, Xe. Defining the critical quotient Q_c ≡ RT_c/P_c (where R is the Gas Constant) the correlations may be summarised by the dual equation: (V_c/cm³ mol⁻¹) = 27 + 0.31 (T_c/K) = 3.3 + 0.280 (Q_c/cm³ mol⁻¹), which describes the CC data for the quartet Ne–Xe with an average uncertainty of 0.5%. Regarding the other two noble gases, the two isotopes of the lightest member, ³He and ⁴He, show the deviations from these relations that are expected from quantal effects and their low molar masses; while for the heaviest member, Rn, the correlations enable a value of 145(5) cm³ mol⁻¹ to be estimated for V_c that is not otherwise well defined in the literature. By contrast, and contrary to the general assumption, the second lightest member, Ne, apparently does not show appreciable quantal effects in the area, so that Ne–Xe may be considered together as a group. These correlations are compared with the behaviour of a selection of polyatomic fluids; in these comparisons, the NG dual correlation equation provides a reference line defining the presumed simplest behaviour. This and related areas show a “Residual Volume Effect”, in that extrapolating the equivalent temperature and energy parameters to zero for the state of zero-mass point particles, referred to here as the hypothetical element zeronium (Ze), the system in each case still has a finite intercept; this intercept amounts to essentially 34% of the average volume for the present quartet Ne–Xe, rather than the zero volume expected for this condition.     

Validation of a recent generalized expression of Tc/Pc vs. the van der Waals surface area according to recent measurements

Recently, Kontogeorgis et al. [G.M. Kontogeorsis, I.V. Yakoumis, P. Coustikos, D.P. Tassios, Fluid Phase Equilibria, 140 (1–2) (1997) 145–146] developed a generalized expression for the ratio of the critical temperature to the critical pressure (T_c/P_c) with the van der Waals surface area (Q_w). Despite the extensive database involved in the development of this equation, the heaviest compounds involved were n-tetracosane in terms of T_c/P_c ratio and PEG-400 in terms of highest T_c. The maximum T_c/P_c value was below 100. The correlation is further validated in light of recent critical data appearing in the literature for heavy compounds with T_c/P_c ratio up to 185. The satisfactory agreement between experimental and predicted T_c/P_c ratios justifies its application to high molecular weight compounds other than those employed for its development.     

Electrical conductivity investigation of diluted potassium chloride solutions in binary mixture triethylamine-water near its consolute point

The binary liquid mixture of triethylamine + water (TEA-W) has a lower consolute point at a critical composition of 32.27 mass % triethylamine. Starting at a temperature within the one-phase region, the electrical conductivity of a sample of this mixture with addition of (K⁺, Cl⁻) ions was measured and found to be accurately described by the Vogel-Fulcher-Tammann (VFT) law. Before that, for the pure system, in a temperature range ΔT = T_c − T < 2 °C where T_c is the critical temperature, the electrical conductivity (σ) exhibits a monotonous deviation from the VFT behaviour. This anomaly is finite at T_c. The asymptotic behaviour of the electrical conductivity anomaly is described by a power law t^1−α, where t is the reduced temperature |(T−Tc)/Tc| and α is the critical exponent of the specific heat anomaly at constant pressure. For the electrolyte mixtures, by combining the viscosity and the electrical conductivity data, the value of the computed Walden product has been determined and the salt dissociation degrees as well as the Debye screening length have been estimated.     

Segmental dynamics near the chain end of polystyrene in its ultrathin films: A study by single-molecule fluorescence de-focus microscopy

Rotational motion of fluorophores chemically attached to polystyrene chain-ends in ultra-thin films on solid substrates was studied by single-molecule fluorescence de-focus microscopy. The collective feature of the rotational motion was found and evidenced by the sharp change of the population of fluorophores undergoing rotational motion within a very narrow temperature range (named as the changing temperature, T _c). The T _c value was found to depend on film thickness and interfacial chemistry and the variation of the T _c value is also dependent on the molecular weight of the polymer. The results demonstrate that the spatial confinement effect enhances the segmental mobility near the polymer chain-ends while the interfacial attraction restricts the segmental motion inside the thin film.     

Critical resistivity in impurity doped binary liquid mixtures

The electrical resistance of the critical binary liquid system C₆H₁₂₊(CH₃CO)₂O is measured both in the pure form and when the system is doped with small amounts (≈ 100 ppm) of H₂O impurities. Near T_c, the resistance varies as dR/dT = A₁+A₂ (T-T_c)^-b with b ≈ 0.35. Neither the critical exponent b nor the amplitude ratio A₁/A₂ are affected by the impurities. A sign reversal of dR/dT is noticed at high temperatures T ? T_c.     

Anomalous octahedral distortion and multiple phase transitions in the metal-ordered manganite YBaMn2O6

By means of powder X-ray diffraction, powder neutron diffraction and transmission electron microscopy (TEM), we determined the crystal structures of a metal-ordered manganite YBaMn₂O₆ which undergoes successive phase transitions. A high-temperature metallic phase (T_c1=520 K<T) crystallizes in a triclinic P1 with the following unit cell: Z=2, a=5.4948(15) Å, b=5.4920(14) Å, c=7.7174(4) Å, α=89.804(20)°, β=90.173(20)°, γ=91.160(4)°. The MnO₆ octahedral tilting is approximately written as a⁰b⁻c⁻, leading to a significant structural anisotropy within the ab plane. The structure for T_c2<T<T_c1 is a monoclinic P2 (Z=2, a=5.5181(4) Å, b=5.5142(4) Å, c=7.6443(3) Å, β=90.267(4)°) with an a⁻b⁻c⁻ tilting. The structural features suggest a d_x²−y² orbital ordering (OO). Below T_c2=480 K, crystallographically inequivalent two octahedra show distinct volume difference, due to the Mn³⁺/Mn⁴⁺ charge ordering. The TEM study furthermore revealed a unique d_3x²−r²/d_3y²−r² OO with a modified CE structure. It was found that the obtained crystal structures are strongly correlated to the unusual physical properties. In particular, the extremely high temperature at which charge degree of freedom freezes, T_c2, should be caused by the absence of the structural disorder and by heavily distorted MnO₆ octahedra.     

Room temperature ferromagnetism in undoped and Fe doped ZnO nanorods: Microwave-assisted synthesis

One-dimensional (1D) undoped and Fe doped ZnO nanorods of average length ∼1 μm and diameter ∼50 nm have been obtained using a microwave-assisted synthesis. The magnetization (M) and coercivity (H_c) value obtained for undoped ZnO nanorods at room temperature is ∼5×10⁻³ emu/g and ∼150 Oe, respectively. The Fe doped ZnO samples show significant changes in M -H loop with increasing doping concentration. Both undoped and Fe doped ZnO nanorods exhibit a Curie transition temperature (T_c) above 390 K. Electron spin resonance and Mössbauer spectra indicate the presence of ferric ions. The origin of ferromagnetism in undoped ZnO nanorods is attributed to localized electron spin moments resulting from surface defects/vacancies, where as in Fe doped samples is explained by F center exchange mechanism.     

Exploration of the Crystal Structure and Thermal and Spectroscopic Properties of Monoclinic Praseodymium Sulfate Pr2(SO4)3

Praseodymium sulfate was obtained by the precipitation method and the crystal structure was determined by Rietveld analysis. Pr₂(SO₄)₃ is crystallized in the monoclinic structure, space group C2/c, with cell parameters a = 21.6052 (4), b = 6.7237 (1) and c = 6.9777 (1) Å, β = 107.9148 (7)°, Z = 4, V = 964.48 (3) ų (T = 150 °C). The thermal expansion of Pr₂(SO₄)₃ is strongly anisotropic. As was obtained by XRD measurements, all cell parameters are increased on heating. However, due to a strong increase of the monoclinic angle β, there is a direction of negative thermal expansion. In the argon atmosphere, Pr₂(SO₄)₃ is stable in the temperature range of T = 30–870 °C. The kinetics of the thermal decomposition process of praseodymium sulfate octahydrate Pr₂(SO₄)₃·8H₂O was studied as well. The vibrational properties of Pr₂(SO₄)₃ were examined by Raman and Fourier-transform infrared absorption spectroscopy methods. The band gap structure of Pr₂(SO₄)₃ was evaluated by ab initio calculations, and it was found that the valence band top is dominated by the p electrons of oxygen ions, while the conduction band bottom is formed by the d electrons of Pr³⁺ ions. The exact position of ZPL is determined via PL and PLE spectra at 77 K to be at 481 nm, and that enabled a correct assignment of luminescent bands. The maximum luminescent band in Pr₂(SO₄)₃ belongs to the ³P₀ → ³F₂ transition at 640 nm.     

The thermodynamic properties of bis(η6-o-xylene)chromium(I) fulleride over the temperature range from T → 0 to 340 K

The temperature dependence of the heat capacity of bis(η⁶-o-xylene)chromium(I) fulleride, [(η⁶-(o-xylene))₂Cr]^+?[C₆₀]^??, over the temperature range 6–340 K was measured on an adiabatic vacuum calorimeter. The low-temperature (20 K ≤ T ≤ 50 K) heat capacity was subjected to multifractal processing; conclusions about the heterodynamic character of the structure were drawn. The experimental data were used to calculate the standard thermodynamic functions C _p ^° (T), H ^°(T)-H ^°(0), S ^°(T), and G ^°(T)-H ^°(0) over the temperature range from T → 0 to 340 K and estimate the standard entropy of fulleride formation from simple substances at 298.15 K. The standard thermodynamic characteristics of [(η⁶-(o-xylene))₂Cr]^+?[C₆₀]^?? were compared with those of the initial fullerene C₆₀.     

Pilot Quality-Assurance Study of a Third-Generation Batch-Mode Clinical-Scale Automated Xenon-129 Hyperpolarizer

We present a pilot quality assurance (QA) study of a clinical-scale, automated, third-generation (GEN-3) ¹²⁹Xe hyperpolarizer employing batch-mode spin-exchange optical pumping (SEOP) with high-Xe densities (50% natural abundance Xe and 50% N₂ in ~2.6 atm total pressure sourced from Nova Gas Technologies) and rapid temperature ramping enabled by an aluminum heating jacket surrounding the 0.5 L SEOP cell. ¹²⁹Xe hyperpolarization was performed over the course of 700 gas loading cycles of the SEOP cell, simulating long-term hyperpolarized contrast agent production in a clinical lung imaging setting. High levels of ¹²⁹Xe polarization (avg. %P_Xe = 51.0% with standard deviation σ_PXe = 3.0%) were recorded with fast ¹²⁹Xe polarization build-up time constants (avg. T_b = 25.1 min with standard deviation σ_Tb = 3.1 min) across the first 500 SEOP cell refills, using moderate temperatures of 75 °C. These results demonstrate a more than 2-fold increase in build-up rate relative to previously demonstrated results in a comparable QA study on a second-generation (GEN-2) ¹²⁹Xe hyperpolarizer device, with only a minor reduction in maximum achievable %P_Xe and with greater consistency over a larger number of SEOP cell refill processes at a similar polarization lifetime duration (avg. T₁ = 82.4 min, standard deviation σ_T1 = 10.8 min). Additionally, the effects of varying SEOP jacket temperatures, distribution of Rb metal, and preparation and operation of the fluid path are quantified in the context of device installation, performance optimization and maintenance to consistently produce high ¹²⁹Xe polarization values, build-up rates (T_b as low as 6 min) and lifetimes over the course of a typical high-throughput ¹²⁹Xe polarization SEOP cell life cycle. The results presented further demonstrate the significant potential for hyperpolarized ¹²⁹Xe contrast agent in imaging and bio-sensing applications on a clinical scale.     

Effect of conductive fillers on the cyclic stress-strain and nano-scale free volume properties of silicone rubber

The effect of carbon black(CB) and graphite(G) powders on the macroscopic and nano-scale free volume properties of silicone rubber based on poly(di-methylsiloxane)(PDMS) was studied through thermal and cyclic mechanical measurements, as well as with positron annihilation lifetime spectroscopy(PALS). The melting temperature of the composites(Tm) and the endothermic enthalpy of melting(?Hm) were estimated by differential scanning calorimetry(DSC). Tm and the degree of crystallinity(χc) of PDMS composites were found to decrease with increasing the CB content. This can be explained due to the increase in physical cross-linking which results in a decrease in the crystallite thickness. Besides, χc was found to be dependent on the filler type. Cyclic stress-strain behavior of PDMS loaded with different contents of filler has been studied. Mullins ratio(RM) was found to be dependent on the filler type and content. It was found that, RM increases with increasing the filler content due to the increase in physical cross-linking which results in a decrease in the size of free volume, as observed through a decrease of the o-Ps lifetime τ3 measured by PALS. Moreover, the hysteresis in PDMS-CB composites was more pronounced than in PDMS-G composites. Furthermore, a correlation was established between the free volume Vf and the mechanical properties of PDMS composites containing different fillers. A negative correlation was observed between Vf and RM.     

Pressure effects of a genuine organic crystalline ferromagnet dupeyredioxyl

We have revealed that the isothermal magnetization M of the genuine organic crystalline dupeyredioxyl (N,N′-dioxy-1,3,5,7-tetramethyl-2,6-diazaadamantane; T_c(0)=1.48 K) observed below 10 K converges on the S=1 Brillouin function B₁((H+λM)/k_BT) with λ=2.4±0.2 or 2zJ/k_B=3.6±0.3 K, where J and z are, respectively, the averaged exchange interactions and coordination numbers for the S=1 spin system. This fact suggests that S=1 is constructed within a molecule via a strong ferromagnetic coupling between two S=1/2 spins on each of the two NO moieties. The modified notation of the Rushbrooke and Wood theory, T_c=2AzJS(S+1)/k_B (A=0.23±0.02 for the three-dimensional Heisenberg systems), is found to quantitatively hold not only for this S=1 spin system but also for other S=1/2 ferromagnets β-phase p-NPNN (2zJ/k_B=3.6 K) and 2,5-DFPNN (2zJ/k_B=2.8 K). Pressure effects of this compound have been studied under the hydrostatic pressure (P) up to 15 kbar. T_c(P) is revealed to show a negative pressure effect with the initial gradient a=d(T_c(P))/dP=−0.047 kbar⁻¹, nearly the same value for other organic ferromagnets as β-phase p-NPNN (−0.048 kbar⁻¹) and p-Cl-TEMPO radical (−0.03 kbar⁻¹), in contrast to the positive pressure effect for genuine antiferromagnets such as TANOL (a=+0.15 kbar⁻¹). Microscopically, different from the above two ferromagnets, the pressure-induced destruction of the orthogonality of molecular orbitals associated with the two NO moieties plays an effective role in reducing the intramolecular ferromagnetic interaction J₀. The possible weaker intermolecular interactions other than J₀ and J are also expected to be more susceptible to the stress of pressure to result in the reduction of their values perhaps even changing their sign, just as in the case of β-phase NPNN or p-Cl-TEMPO.     

The study of phase transition of KHF2 doped with sodium ions with Raman intensities of the lattice modes as the order parameter

The phase transition of doped K_1-xNa_xHF₂ is studied with the K⁺ translatory mode and the HF⁻₂ librational mode, which are Raman active in the low temperature phase while inactive in the high temperature phase, as the order parameter. Particular attention is paid to the elucidation of the critical exponent β which is defined as the parameter relating the lattice Raman intensity to the temperature near T_c through (T_c - T)^β. β values for various dopings are interpreted to understand the dynamics of the phase transition in the critical region. The analysis shows that a very small amount of doping results in a drastically large effect in the critical region. Further doping does not induce further a critical effect in a proportional way. This enables one to define the undoped and doped systems with a very small amount of dopant as two distinct states.