Thermal Pressure Coefficient Research Articles

Water's Thermal Pressure Drives the Temperature Dependence of Hydrophobic Hydration.

With the aid of literature experimental data and reported results from molecular simulation, two thermodynamic relations are found to provide a theoretical basis for the understanding of a variety of characteristic features associated with the solvation of small nonpolar molecules in water. Thus, the large and positive solvation heat capacity, enthalpy-entropy compensation, the solubility minimum and solvation free energy maximum with respect to temperature, enthalpy convergence, and entropy convergence are rationalized in a unified way. Our key finding is that all of these phenomena are driven by the thermal pressure coefficient of pure water, which, via the isobaric thermal expansivity and the isothermal compressibility, reflects its unusual thermodynamics. Remarkably, the solubility minimum is found to be a direct consequence of water's density maximum.

Volumetric properties of 2,5-dimethylfuran in mixtures with octane or dodecane from 293 K to 393 K and pressures up to 70 MPa

We report isothermal volumetric properties for two binary systems constituted by 2,5-dimethylfuran (x)+a linear alkane (1−x); octane and dodecane are the representative alkanes. Compressed liquid densities were obtained via oscillating period measurements in two commercial vibrating U-shaped tube densimeters. The experiments were performed within the pressure and temperature intervals from 0.1MPa to 70MPa and from 293K to 393K, respectively. Properties for these binary systems were measured at x=(0.1154, 0.2999, 0.4967, 0.6962, 0.8924) for 2,5-dimethylfuran+octane mixtures; whereas, compositions measured for 2,5-dimethylfuran+dodecane mixtures were x=(0.1995, 0.4067, 0.4972, 0.6053, 0.8045). Experimental density data were correlated by using the Tammann-Tait equation. Thermodynamic derived properties were calculated from the same equation, and their dependence on pressure, temperature and composition was discussed. These properties were isobaric thermal expansivity, isothermal compressibility, thermal pressure coefficient, internal pressure and mixing molar volume.

Effect of temperature on compressibility properties of 0.1, 0.5 and 1.0 molal solutions of alkali metal halides. Part 1. Aqueous solutions of sodium chloride, sodium bromide, sodium iodide, potassium chloride, potassium bromide, potassium iodide, rubidium chloride and rubidium iodide in the 278.15 K to 353.15 K temperature range

Sound velocities in aqueous 0.1mol·kg−1, 0.5mol·kg−1 and 1.0mol·kg−1 solutions of NaCl, NaBr, NaI, KCl, KBr, KI, RbCl and RbI were measured at 1K intervals from T=(278.15 to 353.15) K. Determined sound velocities and densities served to determine the isentropic and isothermal compressibility coefficients, the apparent molar compressibilities, the apparent molar volumes, the isochoric thermal pressure coefficients, cubic expansion coefficients, changes of heat capacities with volume and with pressure, and the hydration numbers. In addition were evaluated the ultrasonic relaxation times and corresponding thermodynamic functions of the activation of the viscous process. Determined parameters are qualitatively correlated with changes in the structure of water when alkali metal halides are dissolved in it.

Effect of temperature on compressibility properties of 0.1, 0.5 and 1.0 molal solutions of alkali metal nitrates. Part 2. Aqueous solutions of lithium nitrate, sodium nitrate and potassium nitrate in the 278.15 K to 353.15 K temperature range

Sound velocities in aqueous solutions of LiNO3, NaNO3 and KNO3 were measured at 1K intervals from T=(278.15 to 353.15)K, in the 0.1mol·kg−1 0.5mol·kg−1 and 1.0mol·kg−1 solutions. Determined sound velocities and densities served to determine the isentropic and isothermal compressibilities, the apparent molar compressibilities, the apparent molar volumes, the isochoric thermal pressure coefficients, cubic expansion coefficients, changes of heat capacities with volume and with pressure, and the hydration numbers. In addition were evaluated the ultrasonic relaxation times and corresponding thermodynamic functions of the activation of the viscous process. Determined parameters are qualitatively correlated with changes in the structure of water when alkali metal nitrates are dissolved in it.

Molecular Dynamics Simulation Study of Eucommiaulmoides GUM/AG Nanoparticle Composites

A study of eucommia ulmoides gum (EUG)/Ag nanoparticle (NP) composites by molecular dynamics (MD) simulations to understand their structure, polarizability, thermodynamic properties, and mechanical properties is proposed. The effects of simulation temperature and Ag NPs size on these parameters were also studied. The results revealed that the composites exhibited an isotropic amorphous structure, and the distribution uniformity of the Ag NPs was enhanced by changing the simulation temperature. Several atoms of the Ag NPs were in an amorphous state, and a polarized layer was observed on the interface between the Ag NPs and the eucommia ulmoide matrix. The interface size increased as the temperature increased and nanoparticles size decreased. The isochoric heat capacity and thermal pressure coefficient of the EUG/Ag-NP composites exhibited significant size effects and improved thermal interferences, which indicated that the presence of the Ag NPs had a positive effect on the mechanical properties of the EUG.

Communication: Enthalpy relaxation in a metal-organic zeolite imidazole framework (ZIF-4) glass-former.

Amorphization in metal-organic framework materials initiated by the collapsed crystal offers new access to glasses; however, the understanding of such glasses remains to be clarified. Here, we studied the glass transition thermodynamics and kinetics in a zeolitic imidazolate framework ZIF-4 utilizing enthalpy relaxation measurements. The calorimetric glass transition profile and relaxation behaviors in ZIF-4 are found to reproduce the basic features and correlations manifested by conventional melt-quenched glasses. A comparison with various melt-quenched glasses suggests that the low fragility of ZIF-4 is ascribed to the low thermal-pressure coefficient due to the directional tetrahedral bond, partly leading to the low vibrational entropy in the melt-crystal entropy difference.

Effect of high pressure and temperature on volumetric properties of {water (1) + ethylenediamine (2)} mixtures

For {water (1)+ethylenediamine (2)} binary mixture the densities at atmospheric pressure and compressions, k=ΔV/Vo, at pressures from 10 to 100MPa of have been measured over the whole concentration range and temperatures from 278.15 to 323.15K. The molar isothermal compressions and molar isobaric expansions, the thermal pressure coefficients and the internal pressure of water+ethylenediamine mixture have been calculated at all state parameters examined. It was shown that the values of molar isothermal compression and molar isobaric expansion of the mixtures rich in water varied insignificantly whereas the thermal pressure coefficients changed strongly within that concentration range. The magnitude of the extreme on the concentration dependence of the thermal pressure coefficient was unusually large that was probably connected with the influence of 2H2O-EDA hydrate complex.

Evaluation of High-Pressure Thermophysical Parameters of the Diacylglycerol (DAG) Oil Using Ultrasonic Waves

Modeling of high-pressure technological processes in the food industry requires knowledge of thermophysical parameters of processed foodstuffs in a broad range of pressures and temperatures. However, the high-pressure thermophysical parameters of foodstuffs are very rarely published in the literature. Therefore, further research is necessary to achieve a deeper insight into the biophysical and thermophysical phenomena under pressure to provide better control of technological processes and optimize the effects of pressure. The essential goal of this work is to evaluate the impact of high pressure and temperature on the thermophysical parameters of liquid foodstuffs on the example of diacylglycerol (DAG) oil (which attracted recently a considerable attention from research and industrial communities due to its remarkable benefits for health), using ultrasonic wave velocity and density measurements. Isotherms of adiabatic and isothermal compressibility, isobaric thermal expansion coefficient, internal pressure, and thermal pressure coefficient versus pressure were evaluated, based on the measurement of the compressional ultrasonic wave velocity and density of DAG oil at high pressures (up to 500 MPa) and at various temperatures. The adiabatic compressibility is affected mostly by the changes of pressure, i.e., it grows about four times when the pressure increases from the atmospheric pressure (0.1 MPa) to 400 MPa at a temperature of 50 °C. By contrast, the internal pressure is a pronounced function of the temperature, i.e., it increases six times when the temperature rises from 20 to 50 °C at a pressure of a 200 MPa. To perform numerical calculations, it was convenient to introduce a Tammann–Tait type equation of state to approximate the measured density isotherms of the investigated DAG oil. The results obtained in this paper can be applied in modeling and optimization of high-pressure technological processes and processing of foodstuffs. Evaluation of high-pressure isotherms of the considered thermophysical parameters of the DAG oil is an original authors’ contribution to the state-of-the-art.

Molecular simulation of the thermodynamic, structural, and vapor-liquid equilibrium properties of neon.

The thermodynamic, structural, and vapor-liquid equilibrium properties of neon are comprehensively studied using ab initio, empirical, and semi-classical intermolecular potentials and classical Monte Carlo simulations. Path integral Monte Carlo simulations for isochoric heat capacity and structural properties are also reported for two empirical potentials and one ab initio potential. The isobaric and isochoric heat capacities, thermal expansion coefficient, thermal pressure coefficient, isothermal and adiabatic compressibilities, Joule-Thomson coefficient, and the speed of sound are reported and compared with experimental data for the entire range of liquid densities from the triple point to the critical point. Lustig's thermodynamic approach is formally extended for temperature-dependent intermolecular potentials. Quantum effects are incorporated using the Feynman-Hibbs quantum correction, which results in significant improvement in the accuracy of predicted thermodynamic properties. The new Feynman-Hibbs version of the Hellmann-Bich-Vogel potential predicts the isochoric heat capacity to an accuracy of 1.4% over the entire range of liquid densities. It also predicts other thermodynamic properties more accurately than alternative intermolecular potentials.

PρT measurement and PC-SAFT modeling of N,N-dimethyl formamide, N -methyl formamide, N,N-dimethyl acetamide, and ethylenediamine from T = (293.15–423.15) K and pressures up to 35 MPa

The PρT data of N,N -dimethylformamide (DMF) and N,N-dimethylacetamide (DMA) were measured at temperature range of (293.15–413.15) K and pressures up to 30 MPa. The same properties also were measured for N-methylformamide (NMF) and ethylenediamine (EDA) over the temperature range within (293.15 to 423.15) K and (293.15–383.15) K and at pressures up to 35 MPa and 30 MPa, respectively. The measurements at 10 K intervals and along eight isobars were done. The experimental density values were correlated with the Tait equation. Based on the obtained result, other thermodynamic properties, such as, isothermal compressibility, κT, thermal expansion coefficient, αP, and thermal pressure coefficient, γV, were calculated. Also, the PC-SAFT model was used to correlate the densities of the pure solvents at the above-mentioned temperature and pressure range. In general, both models yield comparable and satisfactorily good correlation of the high pressure and temperature density.

Accuracy of temperature-derivative of radial distribution function calculated under approximations in Ornstein-Zernike theory for one-component Lennard-Jones fluid

The accuracy of the temperature derivative of radial distribution function obtained under hypernetted chain (HNC), Kovalenko-Hirata (KH), Percus-Yevick (PY) and Verlet-modified (VM) closure approximations is examined for one-component Lennard-Jones fluid. As relevant thermodynamic quantities, constant-volume heat capacity and thermal pressure coefficient are investigated in terms of their accuracy under the above four approximations. It is found that HNC and KH closures overestimate these quantities, whereas PY closure tends to underestimate them. VM closure predicts rather accurately the quantities. A significant cancellation is observed along the integration for the above quantities under HNC and KH closures, especially at high density state.

ChemInform Abstract: Entropic Phase Transitions and Accompanying Anomalous Thermodynamics of Matter

Thermodynamic consequences of subdivision for all first-order phase transitions (PT) into enthalpy- and entropy-driven ones (H-PT and S-PT), proposed previously [arXiv:1403.8053], are under discussions. Key-value for proposed discrimination is main benefit (decreasing) in enthalpy or (nega)entropy in spontaneous phase decomposition, i.e. the sign of latent heat of PT and consequent slope of its P(T)-dependence. The main driving mechanism for many isostructural S-PT is the decay (delocalization) of some kind of bound complexes, e.g. atoms, molecules etc. Thermodynamic features of H-PT and S-PT differ significantly. Entropic PT are always the part of more general thermodynamic anomaly—domain where great number of usually positive second cross derivatives (e.g. Gruneisen parameter, thermal pressure coefficient etc.) became negative simultaneously. This domain is restricted (in the case of isostructural S-PT) by remarkable bound, where all mentioned second derivatives are equal to zero. Isostructural S-PT has more complicated topology of stable, metastable and unstable states and their boundaries—binodals and spinodals in comparison with ordinary enthalpic PTs. Two new thermodynamic objects accompany isostructural S-PT: (i) appearance of third (additional) region of metastable states with positive compressibility, isolated from the regions of stable states; (ii) appearance of new additional spinodal, topped with a new singular point, separating metastable and unstable states. These additional spinodal and singular point obey to relation (∂P/∂V)T = ∞. All thermodynamic anomalies of entropic PTs correspond to conclusive and transparent geometrical feature of such PTs: multilayered structure of thermodynamic surfaces for temperature, entropy and internal energy as pressure- density functions U(P, V), S(P, V) and T(P, V).

Measurements of the density, speed of sound, viscosity and derived thermodynamic properties of geothermal fluids from south Russia Geothermal Field. Part II

Density, (ρ), speed of sound, (W), and viscosity, (η) of natural geothermal fluids from south Russia Geothermal Fields (Dagestan, Caspian seashore) have been measured over the temperature range from (277–353) K at atmospheric pressure. The measurements were made using the Anton Paar DMA4500 densimeter and Stabinger SVM3000 viscodensimeter for four geothermal fluid samples from the various hot-wells Izberbas (No. 68 and 129), Ternair (No. 27T and No. 38T). A sound-speed analyzer (Anton Paar DSA 5000) was used for simultaneously measurement of the speed of sound and density of the same geothermal fluid samples. The average differences between the measured geothermal fluids densities and viscosities and pure water values (IAPWS formulation) are within (0.1–1.77) % and (0.13–2.1) %, respectively, which are considerably higher than their experimental uncertainties. This differences are caused by the high concentrations of some type of ion species, such as (Na+: 7.7 g/l (#38T); Cl−1:7.7 g/l (#38T); SO4−2: 0.75 g/l (#68); S+: 0.24 g/l (#68); K+:0.15 g/l (# 27T); Ca+2: 0.074 g/l (#27T); B+:0.06 g/l (#38T); and Mg +2: 0.033 g/l (#38T)), in the geothermal fluids, which strongly effect on salt concentration dependence of the measured properties. Measured values of density and speed of sound were used to calculate other derived thermodynamic properties such as adiabatic coefficient of bulk compressibility (βS), coefficient of thermal expansion (αP), thermal pressure coefficient (γV), isothermal coefficient of bulk compressibility (βT), isochoric heat capacity (CV), isobaric heat capacity (CP), enthalpy difference (ΔH), partial pressure derivative of enthalpy (∂H∂P)T, and partial derivatives of internal energy (internal pressure) (∂U∂V)T, of the geothermal fluid samples. Measured values of density, viscosity, and speed of sound were used to develop correlation models for the temperature and ion species concentration dependences, which reproduced the measured values within 0.03% (density), 2.47% (viscosity), and 0.20% (speed of sound). To confirm the accuracy and predictive capability of the developed correlation models for density, speed of sound, and viscosity, we have applied the models to well-studied binary aqueous salt solutions (H2O + NaCl). The prediction of the density and viscosity of aqueous sodium chloride solutions based on the developed models were very close to their experimental uncertainties (within 0.03% for density and 1.56% for viscosity). The measured properties at atmospheric pressure have been used as a reference data for prediction of the high-pressure thermodynamic behavior. The predictive capability of the model has been checked on reliable experimental data for binary aqueous NaCl solutions at high pressures reported by Kestin and Shankland (1984) and Rogers and Pitzer (1982). The prediction for density and viscosity is within 0.03% and 1.57%, respectively.

Entropic phase transitions and accompanying anomalous thermodynamics of matter

Thermodynamic consequences of subdivision for all first-order phase transitions (PT) into enthalpy- and entropy-driven ones (H-PT and S-PT), proposed previously [arXiv:1403.8053], are under discussions. Key-value for proposed discrimination is main benefit (decreasing) in enthalpy or (nega)entropy in spontaneous phase decomposition, i.e. the sign of latent heat of PT and consequent slope of its P(T)-dependence. The main driving mechanism for many isostructural S-PT is the decay (delocalization) of some kind of bound complexes, e.g. atoms, molecules etc. Thermodynamic features of H-PT and S-PT differ significantly. Entropic PT are always the part of more general thermodynamic anomaly—domain where great number of usually positive second cross derivatives (e.g. Grüneisen parameter, thermal pressure coefficient etc.) became negative simultaneously. This domain is restricted (in the case of isostructural S-PT) by remarkable bound, where all mentioned second derivatives are equal to zero. Isostructural S-PT has more complicated topology of stable, metastable and unstable states and their boundaries—binodals and spinodals in comparison with ordinary enthalpic PTs. Two new thermodynamic objects accompany isostructural S-PT: (i) appearance of third (additional) region of metastable states with positive compressibility, isolated from the regions of stable states; (ii) appearance of new additional spinodal, topped with a new singular point, separating metastable and unstable states. These additional spinodal and singular point obey to relation (∂P/∂V)T = ∞. All thermodynamic anomalies of entropic PTs correspond to conclusive and transparent geometrical feature of such PTs: multilayered structure of thermodynamic surfaces for temperature, entropy and internal energy as pressure- density functions U(P, V), S(P, V) and T(P, V).

Atomistic water models: Aqueous thermodynamic properties from ambient to supercritical conditions

Progress in obtaining an accurate atomistic model for water is reviewed and evaluated with particular attention to thermodynamic properties such as the thermal pressure coefficient, thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule–Thomson coefficient, speed of sound and vapor–liquid equlibria. The different multi-site models are categorised in terms of bond rigidity/flexibility and polarization. The models are assessed for their ability to reproduce experimental values at conditions ranging from ambient to supercritical conditions. In general, three or four sites are sufficient to obtain reasonable results with the addition of more sites not consistently yielding improvements. The addition of bond flexibility, while improving agreement with experiment for such properties as phase coexistence, dielectric constants, viscosity and diffusion, does not appear to significantly improve the prediction of thermodynamic properties in general. For the supercritical heat capacities and thermal expansion coefficient the flexible TIP4P/2005f model yields less accurate values than its rigid TIP4P/2005 counterpart. In contrast, accounting for polarizability consistently results in improved agreement with experiment. For properties such as the isochoric heat capacity and thermal expansion coefficient, the polarizable MCYna model yields values that are in very close agreement with experimental data in the temperature range of 300–600K. A quantitative ranking scheme is proposed and applied to ambient conditions. At or near ambient conditions, the overall ranking of models investigated is (iAMOEBA, MCYna)>(BKd3, TIP4P/FQ, GCPM, BK3)>(TIP4P/2005, SPC/Fw, SPC/E)>(SPC, TIP4P/2005f, NvdE, TIP5P)>(TIP4P, TIP3P)>(MCY, MCYL).

Modeling thermodynamic derivative properties of ionic liquids with ePC-SAFT

In this work, ePC-SAFT was extended to predict the second order thermodynamic derivative properties of pure ionic liquids (ILs), such as isothermal and isentropic compressibility coefficients, thermal pressure coefficient, heat capacities, speed of sound, thermal expansion coefficient and internal pressure. ePC-SAFT predictions were compared with available experimental data of imidazolium-based ILs. The pure-component ePC-SAFT parameters for the IL-cations [C2mim]+, [C4mim]+, [C6mim]+ and [C8mim]+, and IL-anions [BF4]−, [PF6]− and [Tf2N]− were taken from literature in order to predict the thermodynamic derivative properties. The pure-component ePC-SAFT parameters for the IL-cations [C3mim]+, [C5mim]+, [C7mim]+ and [C10mim]+ were predicted based on linear molecular-weight-dependent relations. These estimated ePC-SAFT parameters were verified by comparing so-predicted pure-IL density as well as predicted CO2 solubility in ILs with respective experimental data. Further, these parameters were used to predict the second order thermodynamic derivative properties. The comparison of model prediction with experimental data showed that ePC-SAFT predictions were reliable in a wide temperature and pressure range.

Thermophysical properties of 1-butanol over a wide range of temperatures and pressures up to 200 MPa

(p,ρ,T) Data of 1-butanol over a wide range of temperatures [T=(263.15 to 468.15) K] and pressures up to p= 140MPa are reported with an estimated experimental relative combined standard uncertainty in density of Δρ/ρ=±(0.01 to 0.03) %. The measurements were carried out with a newly constructed Anton Paar DMA HPM vibration tube densimeter. The system was calibrated using double-distilled water, aqueous NaCl solutions, methanol, toluene and acetone. An equation of state (EOS) for fitting of the (p,ρ,T) data of 1-butanol has been developed as a function of pressure and temperature. The experimental (p,ρ,T) data have been successfully extrapolated up to temperatures T=253.15K and pressures up to p=200MPa using the equation of state.After a thorough analysis of literature values and validity of the constructed equation of state, various thermophysical properties such as isothermal compressibility, isobaric thermal expansibility, differences in isobaric and isochoric heat capacities, thermal pressure coefficient, internal pressure at temperatures [T=(253.15 to 468.15) K] and pressures up to p= 200MPa were calculated. Additionally, heat capacity of 1-butanol at temperatures T=(253.15 to 468.70) K and at ambient pressure were measured using a differential scanning calorimeter. After these measurements some more calculations of further thermophysical properties at temperatures [T=(253.15 to 468.70) K] and pressures up to p= 200MPa, like specific heat capacities at constant pressure and volume, speed of sound and isentropic expansibility, have been executed.

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

ABSTRACTThe 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 (Tg) is reported as a function of pressure, and the limiting fictive temperature (Tf′) 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 Tg 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

THERMOPHYSICAL PROPERTIES OF 1-BUTYL-3-METHYLIMIDAZOLIUM BIS(TRIFLUOROMETHYLSULFONYL)IMIDE AT HIGH TEMPERATURES AND PRESSURES

Pressure-density-temperature (p, ρ ,T) data of the ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [BMIM][NTF2] at T = (273.15 to 413.15) K and pressures up to p =140 MPa are reported with an estimated experimental relative combined standard uncertainty of Δ ρ / ρ = ±(0.01 to 0.08)% in density. The measurements were carried out with a newly constructed Anton-Paar DMA HPM vibration-tube densimeter. The system was calibrated using double-distilled water, aqueous NaCl solution, methanol, toluene and acetone. An empirical equation of state for fitting the (p, ρ ,T) data of [BMIM][NTF2] has been developed as a function of pressure and temperature. This equation is used for the calculation of the thermophysical properties of the ionic liquid, such as isothermal compressibility, isobaric thermal expansibility, thermal pressure coefficient, internal pressure, isobaric and isochoric heat capacities, speed of sound and isentropic expansibility.

Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

An embedded-fragment ab initio second-order many-body perturbation (MP2) method is applied to an infinite three-dimensional crystal of carbon dioxide phase I (CO2-I), using the aug-cc-pVDZ and aug-cc-pVTZ basis sets, the latter in conjunction with a counterpoise correction for the basis-set superposition error. The equation of state, phonon frequencies, bulk modulus, heat capacity, Grüneisen parameter (including mode Grüneisen parameters for acoustic modes), thermal expansion coefficient (α), and thermal pressure coefficient (β) are computed. Of the factors that enter the expression of α, MP2 reproduces the experimental values of the heat capacity, Grüneisen parameter, and molar volume accurately. However, it proves to be exceedingly difficult to determine the remaining factor, the bulk modulus (B0), the computed value of which deviates from the observed value by 50-100%. As a result, α calculated by MP2 is systematically too low, while having the correct temperature dependence. The thermal pressure coefficient, β = αB0, which is independent of B0, is more accurately reproduced by theory up to 100 K.