Low-temperature Adiabatic Calorimetry Research Articles

Heat capacity and thermodynamic properties of PbS: Optimization based on calorimetric and electrochemical data

Heat capacity of PbS (galena) has been measured in the temperature range from 12 to 338 K using adiabatic calorimetry. Results of the measurements are consistent with previous adiabatic calorimetric data measurements but differ notably from those obtained by relaxation calorimetry. Using experimental data on adiabatic heat capacity measurements in the range of 12–338 K (including our data), results of EMF measurements, and literature data on H0(T) – H0(298.15 K) as inputs, we have optimized the thermodynamic properties of lead sulfide (PbS, galena) based on the quasi-harmonic model vibrational spectrum proposed by Kieffer and advanced to consider intrinsic anharmonicity. In this approach, the volume and temperature dependence of vibrational frequencies are considered, and the enthalpy of formation of PbS, ΔfH0(298.15 K), is treated as an optimized model parameter. The thermodynamic properties of PbS are described with a single set of model parameters over the entire range of its stability (0–1374 K) at a pressure of 1 bar. The model can be optimized based on either the reduced (Cp0 and ΔfG0(T)) or full (Cp0, H0(T) – H0(298.15 K), ΔfG0(T)) datasets. The both variants of the optimization predict the similar thermodynamic properties of PbS, in particular, values of the enthalpies of formation differ less than 0.1 kJ mol−1 and are consistent with ΔfH0(298.15 K) obtained experimentally by oxide melt solution calorimetry. The low-temperature adiabatic calorimetry data and high-temperature results of EMF experiments (or other reliable experimental data on ΔfG0(T)) represent a minimal sufficient set of input data providing optimization of thermodynamic properties at ambient pressure by the technique established in present study.

Excess heat capacity and entropy of mixing along the hydroxyapatite-chlorapatite and hydroxyapatite-fluorapatite binaries

The heat capacity, Cp, of synthetic hydroxyapatite [Ca5(PO4)3OH–OH-Ap], as well as of ten compositions along the OH-Ap-chlorapatite (Cl-Ap) join and 12 compositions along the OH-Ap-fluorapatite (F-Ap) join have been measured using relaxation calorimetry (heat capacity option of the Physical Properties Measurement System—PPMS) and differential scanning calorimetry (DSC) in the temperature range of 5–764 K. Apatites along the Cl-OH and F-OH joins were synthesized at 1100 °C and 300 MPa in an internally heated gas pressure vessel via an exchange process between synthetic fluorapatite or chlorapatite crystals (200–500 μm size) and a series of Ca(OH)2-H2O solutions with specific compositions and amounts relative to the starting apatite. The standard third-law entropy of OH-Ap, derived from the low-temperature heat capacity measurements, is S° = 386.3 ± 2.5 J mol−1 K−1, which is ~ 1% lower than that resulting from low-temperature adiabatic calorimetry data on OH-Ap from the 1950’s. The heat capacity of OH-Ap above 298.15 K shows a hump-shaped anomaly centred around 442 K. Based on published structural and calorimetric work, this feature is interpreted to result from a monoclinic to hexagonal phase transition. Super ambient Cp up to this transition can be represented by the polynomial: C_{p}^{{text{OH - Ap}}} {}_{{298K - 442K}}left( {{text{J mol}}^{ - 1} {text{K}}^{- 1}} right) = {1013.7-13735.5T^{{ - 0.5}}} + 2.616718,10^{7} T^{{ - 2}} - 3.551381,10^{9} T^{{ - 3}} .. The DSC data above this transition were combined with heat capacities computed using density functional theory and can be given by the Cp polynomial: C_{p}^{{text{OH - Ap}}} {}_{{ >,442K}}left( {{text{J mol}}^{ - 1} {text{K}}^{- 1}} right) = {877.2-11393.7 T^{ - 0.5}} + {5.452030,10^{7}} ,T^{- {2}} - {1.394125,10^{10}} ,T^{- {3}}. Positive excess heat capacities of mixing, ∆Cpex, in the order of 1–2 J mol−1 K−1, occur in both solid solutions at around 70 K. They are significant at these conditions exceeding the 2σ-uncertainty of the data. This positive ∆Cpex is compensated by a negative ∆Cpex of the same order at around 250 K in both binaries. At higher temperatures (up to 1200 K), ∆Cpex is zero within error for all solid solution members. As a consequence, the calorimetric entropies, Scal, show no deviation from ideal mixing behaviour within a 2σ-uncertainty for both joins. Excess entropies of mixing, ∆Sex, are thus zero for the OH-Ap–F-Ap, as well as for the OH-Ap–Cl-Ap join. The Cp–T behaviour of the OH-Ap endmember is discussed in relation to that of the F- and Cl-endmembers.

Stacked-cup multiwall carbon nanotubes as components of energy-intensive suspension jet fuels

Objectives. The addition of high-density carbon materials to jet fuels can lead to a significant increase in the volumetric energy of the fuel combustion. The purpose of the current study was to thermodynamically analyze the possibility of obtaining model hydrocarbon fuels from toluene and T-1 using stacked-cup multiwall carbon nanotubes (MWCNTs). Methods. Bomb combustion calorimetry was used to define the combustion energy of the MWCNTs in the crystalline state. The temperature dependence of the MWCNTs’ heat capacity in the range 5–370 K and the fusion parameters were estimated using low-temperature adiabatic calorimetry. The physical density of MWCNTs was measured using the pycnometric method. The sedimentation stability of the mixtures of MWCNTs with liquids was determined using centrifugation at 7000 g. The calculations were carried out in MS Excel. Results. The energy and enthalpy of combustion of a technical sample of MWCNTs in the crystalline state were determined. Based on the smoothed heat capacity values, the standard thermodynamic functions (enthalpy, entropy, and Gibbs reduced energy) of MWCNTs in the crystalline state were obtained in a temperature range of 0–2000 K. The extrapolation of the MWCNTs’ heat capacity was carried out at a temperature of up to 2000 K using the heat capacity of crystalline graphite. It has been established that mixtures of MWCNTs with liquids containing more than 33 mass % of MWCNTs are stable during centrifugal sedimentation at 7000 g. For the toluene–MWCNTs and fuel T-1–MWCNTs model systems, the specific and volumetric combustion energies, the adiabatic combustion temperatures, and the conditional final maximum speed of the model rockets with fuel of various compositions were also calculated. Conclusions. The thermodynamic analysis showed that the addition of MWCNTs can significantly increase the volumetric energy intensity of traditional jet fuels, which can in turn improve the operational characteristics of drones and rockets.

Thermodynamic properties of CaMoO4 at high temperatures

We studied the thermodynamic properties of calcium molybdate (CaMoO4) single crystal sample. Heat capacity was measured by DSC in the 255–766 K range. Isobaric thermodynamic functions (entropy, enthalpy, and Gibbs free energy) were calculated in the 298.15–766 K range. Melting point and enthalpy of melting were determined experimentally. We calculated isochoric heat capacity and thermodynamic functions up to the melting temperature of 1750 K by using low-temperature adiabatic calorimetry data within the framework of the effective sum method. We obtained the characteristic temperatures associated with the moments of the phonon density of states and its effective cutoff frequency. We estimated accuracy of the obtained results and compared the results with the known data.

Low-temperature heat capacity and thermodynamic functions of natural chalcanthite

The heat capacity of natural chalcanthite (copper sulfate pentahydrate, CuSO4·5H2O) from the deposit Kosmurun has been measured by the method of low-temperature adiabatic calorimetry over the temperature range of (4.3–320)K. The identity of the mineral was proved by methods of XRD, EMPA, IR and Raman spectroscopy. The thermodynamic functions have been calculated based on the experimental data on the heat capacity. The lattice component of heat capacity below 20K was extracted. The standard values of the heat capacity and entropy for natural chalcanthite are as follows: C°p,m=288.0±0.4J·mol−1K−1, S°m=295.2±0.8Jmol−1K−1.

Plasticization of cellulose and its derivatives

The relaxation transitions in binary blends of cotton cellulose nitrate with castor oil and of chitosan and wood cellulose with betulin were studied by low-temperature adiabatic calorimetry in the range 80–320 K and by differential thermal analysis in the range 80–620 K. The solubility of these “structural” plasticizers in the above polysaccharides was determined. The phase diagrams of the polymer-plasticizer systems were constructed and analyzed.

Chirality-related interactions and a mirror symmetry violation in handed nano structures.

Hindering of inversion transitions and a violation of mirror symmetry of the right- and left-handed configurations of diazabizyclooctane (dabco, N2C6H12) enantiomers has been studied with low-temperature adiabatic calorimetry. The dabco molecules were sandwiched in a high-porous layered structure of a metal organic framework (MOF) compound. We show from the data of low-temperature adiabatic calorimetry and (1)H NMR spin relaxation method that hindering of inversion transitions of dabco molecules cannot be associated with the influence of the intracrystalline self-consistent molecular field as a continuously monitoring environment within the quantum Zeno effect. In addition, lack of another manifestation of this effect associated with the collisional suppression of the inversion transitions in MOF samples impregnated by helium has been shown. These results lead to the conclusion that chiral polarization is related to the fundamental effect of parity nonconservation.

Thermodynamic properties of chlorite and berthierine derived from calorimetric measurements

In the context of the deep waste disposal, we have investigated the respective stabilities of two iron-bearing clay minerals: berthierine ISGS from Illinois [USA; (Al0.975FeIII0.182FeII1.422Mg0.157Li0.035Mn0.002)(Si1.332Al0.668)O5(OH)4] and chlorite CCa-2 from Flagstaff Hill, California [USA; (Si2.633Al1.367)(Al1.116FeIII0.215Mg2.952FeII1.712Mn0.012Ca0.011)O10(OH)8]. For berthierine, the complete thermodynamic dataset was determined at 1 bar and from 2 to 310 K, using calorimetric methods. The standard enthalpies of formation were obtained by solution-reaction calorimetry at 298.15 K, and the heat capacities were measured by heat-pulse calorimetry. For chlorite, the standard enthalpy of formation is measured by solution-reaction calorimetry at 298.15 K. This is completing the entropy and heat capacity obtained previously by Gailhanou et al. (Geochim Cosmochim Acta 73:4738–4749, 2009) between 2 and 520 K, by using low-temperature adiabatic calorimetry and differential scanning calorimetry. For both minerals, the standard entropies and the Gibbs free energies of formation at 298.15 K were then calculated. An assessment of the measured properties could be carried out with respect to literature data. Eventually, the thermodynamic dataset allowed realizing theoretical calculations concerning the berthierine to chlorite transition. The latter showed that, from a thermodynamic viewpoint, the main factor controlling this transition is probably the composition of the berthierine and chlorite minerals and the nature of the secondary minerals rather than temperature.

Thermodynamic properties of saponite, nontronite, and vermiculite derived from calorimetric measurements

The stability of clay minerals is an important factor in assessing the durability of containment barriers for deep waste storage. In that context, the complete thermodynamic data set of three 2:1 ferro-magnesian clay minerals have been determined at 1 bar and from 2 to 520 K, using calorimetric methods. The studied clay samples were, respectively, the Na-saturated saponite Sap-Ca-1, Na 0.394 K 0.021 Ca 0.038 (Si 3.569 Al 0.397 Fe 3+ 0.034 )(Mg 2.948 Fe 2+ 0.021 Mn 0.001 )O 10 (OH) 2 , the Ca-saturated nontronite NAu-1, Ca 0.247 K 0.020 (Si 3.458 Al 0.542 )(Mg 0.066 Fe 3+ 1.688 Al 0.268 Ti 0.007 )O 10 (OH) 2 , and the Ca-saturated Santa Olalla vermiculite, Ca 0.445 (Si 2.778 Al 1.222 )(Al 0.192 Mg 2.468 Fe 3+ 0.226 Fe 2+ 0.028 Ti 0.018 Mn 0.007 )O 10 (OH) 2 . The standard enthalpies of formation were obtained by solution-reaction calorimetry at 298.15 K. The heat capacities were measured between 2 and 520 K, using low-temperature adiabatic calorimetry, heat-pulse calorimetry, and differential scanning calorimetry. The standard entropies and the Gibbs free energies of formation at 298.15 K have been calculated from these values. Finally, the equilibrium constants at 298.15 K have been determined. A comparison between these experimental data and estimated values obtained from prediction models available in the literature enabled the most usual calculation methods available to date to be assessed for each thermodynamic property.

Thermodynamic properties of synthetic calcium-free carbonate cancrinite

Calcium-free carbonate cancrinite with formula unit Na8.28[Al5.93Si6.07O24](CO3)0.93(OH)0.49·3.64H2O (CAN) has been synthesized under hydrothermal conditions. The product has been characterized by the methods of scanning electronic microscopy and energy dispersive X-ray analysis, Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis with FTIR of evolved gases (TGA–FTIR), and X-ray powder diffraction. The heat capacity of CAN has been measured from 6 to 259 K via low-temperature adiabatic calorimetry. A linear combination of Einstein functions has been used to approximate the obtained data on the heat capacity. The thermal contributions to the entropy and enthalpy of CAN in the temperature range 0–300 K have been calculated from these data. The heat capacity and third-law absolute entropy of CAN at 298.15 K are 1,047 ± 30 and 1,057 ± 35 J mol−1 K−1, respectively. High-temperature oxide-melt solution calorimetry has been used to determine the enthalpy of formation from elements of CAN at 298.15 K; the value equals −14,684 ± 50 kJ mol−1. The Gibbs energy of formation from elements at 298.15 K has been calculated and totaled −13,690 ± 51 kJ mol−1.

Heat capacity and thermodynamic functions of 2-methylbiphenyl and 3,3′-dimethylbiphenyl in the range of 6 to 372 K

The heat capacities of 2-methylbiphenyl and 3,3′-dimethylbiphenyl are measured by means of low-temperature adiabatic calorimetry in the temperature range of 6 to 372 K. The thermodynamic characteristics of fusion and the glass transition of the investigated compounds are determined. The saturation vapor pressure and enthalpy of vaporization of 3,3′-dimethylbiphenyl are determined according to the dynamic method based on the transfer of a substance vapor in a helium flow. The absolute entropies and changes in Gibbs energies of biphenyl derivatives are calculated from the data obtained in the condensed and ideal gas states. The contribution of the Cb-(Cb) group is determined using the Benson additive method for calculating the absolute entropies of biphenyl derivatives in the liquid state (where Cb is the carbon atom in a benzene ring).

Thermodynamic properties of illite, smectite and beidellite by calorimetric methods: Enthalpies of formation, heat capacities, entropies and Gibbs free energies of formation

The thermodynamic properties of three aluminous 2:1 clay minerals were acquired at 1.013 bars and at temperatures between 5 and 500K using various calorimetric methods. Calorimetric measurements were performed on hydrated and dehydrated <2μm clay fractions of smectite MX-80 (Wyoming), illite IMt-2 (Silver Hill) and beidellite SBId-1 (Black Jack Mine). After purification, the mineralogical analyses gave the following structural formulae:Na0.409K0.024Ca0.009(Si3.738Al0.262)(Al1.598Mg0.214Fe0.1733+Fe0.0352+)O10(OH)2,K0.762Na0.044(Si3.387Al0.613)(Al1.427Mg0.241Fe0.2923+Fe0.0842+)O10(OH)2 and Ca0.185K0.104(Si3.574Al0.426)(Al1.812Mg0.09Fe0.1123+)O10(OH)2 for smectite MX-80, illite IMt-2 and beidellite SBId-1, respectively. Heat capacities were measured by low temperature adiabatic calorimetry and differential scanning calorimetry, from 5 to 500K. Standard enthalpies of formation were obtained from solution–reaction calorimetry at 298.15K. The standard Gibbs free energies of formation of the clay minerals were also calculated, together with the equilibrium constants at 25°C, for anhydrous and hydrated minerals. A comparison between these experimental data and estimated values obtained from prediction models available in the literature, enabled the calculation method that appears to be the most relevant to be selected, at least for aluminous 2:1 clay minerals.

Experimental determination of thermodynamic characteristics of smithsonite

The heat capacity of natural zinc carbonate (smithsonite, ZnCO3) has been measured by the method of low-temperature adiabatic calorimetry over the temperature range of (4.4 to 320)K. Its thermodynamic functions have been calculated based on the experimental data on the heat capacity. The standard values of the heat capacity and entropy for smithsonite are as follows: Cp,m=80.36±0.09J·mol−1·K−1, Sm=81.28±0.09J·mol−1·K−1.

The heat capacity and thermodynamic functions of cerussite

The heat capacity of natural lead carbonate (cerussite, PbCO 3) has been measured by means of the low-temperature adiabatic calorimetry over the temperature range of (4 to 320) K. Its thermodynamic functions С р ( Т), S( T) and H( T)– H(0) have been calculated over the whole temperature range from the experimental data on the heat capacity. The standard values of the heat capacity and entropy are equal to C p,m ∘ = 87.07 ± 0.09 J · mol −1 · K −1, S m ∘ = 125.45 ± 0.20 J · mol −1 · K −1, respectively. An anomalous deviation of the heat capacity has been registered in the range of (269 to 278) K.

Standard thermodynamic properties of Pd and Pt ditellurides

Platinumgroup elements (PGE) are transition metals of group VIII in the periodic table of chemical elements. Although similarities between PGE are emphasized in geochemistry, the types of their interac� tions with other elements and the specifics of their electron structure make it possible to classify PGE into three groups. Groups 1 and 2 include Ru with Os and Ir with Rh, respectively, and group 3 consists of Pt and Pd, which are the most chemically active PGE (this applies, first of all, to Pd) because of the structure of their electron shells. The most widely spread natu� rally occurring PGE tellurides are those of Pt and Pd, which usually contain Bi, and no pure binary com� pounds have ever been found. Pd and Pt ditellurides are typically contained in ores at Cu-Ni mineral deposits. An important problem is revealing the factors responsible for the different behavior of Pt and Pd in mineralforming processes, an issue that cannot be elucidated without knowing properties of the most widely spread minerals at these deposits. Our research was focused on the calorimetric determination of the enthalpy of formation of Pt and Pd ditellurides, with the use of literature data on lowtemperature adiabatic calorimetry and electrochemical measurements. Pt and Pd ditellurides can be easily synthesized by heating corresponding stoichiometric mixtures in ampoules of quartz glass evacuated to

The heat capacity and thermodynamic functions of pyromorphite over the temperature range 5–320 K

The heat capacity of natural mineral, pyromorphite Pb5(PO4)3Cl, was measured over the temperature range 4.2–320 K using low-temperature adiabatic calorimetry. An anomalous temperature dependence of heat capacity with a maximum at 273.24 K was observed between 250 and 290 K. The heat capacity, entropy, enthalpy, and reduced thermodynamic potential of pyromorphite were calculated and tabulated over the temperature range 5–320 K. The standard thermodynamic functions of the mineral are Cp298.15o = 414.98 ± 0.44 J/(mol K), S298.15o = 585.31 ± 0.99 J/(mol K), H298.15o − H0o = 80.90 ± 0.08 kJ/mol, and Φ298.15o = 313.97 ± 0.84 J/(mol K).

Low temperature measurements of the heat capacity and thermodynamic functions of pseudo-malachite Cu5(PO4)2(OH)4

The investigation of the heat capacity of a natural specimen of copper phosphate—pseudo-malachite Cu5(PO4)2(OH)4 in the temperature range between 4.2K and 320K has been carried out by the method of low-temperature adiabatic calorimetry. Tabulated values of the heat capacity and thermodynamic functions of the mineral including the changes of entropy and enthalpy and the Gibbs function of free energy have been calculated. The standard values of thermodynamic functions of pseudo-malachite at T=298.15K are Cp,m°=(385.43±0.41) J mole−1 K−1, Δ0TSm°=(412.16±0.61) J mole−1 K−1, Δ0THm°=(63681.5±57.0) J mole−1, Fm°=(198.57±0.47) J mole−1 K−1. In the low-temperature area 0<(T/K)<22.69 an anomaly has been registered in the variation of the heat capacity of the mineral, for which the lattice constituent has been determined. The contribution of anomalous component into entropy and enthalpy of the mineral is ΔStr=(5.772±0.081)Jmole−1K−1, ΔHtr=(29.94±0.42)Jmole−1.

Thermodynamic characteristics of a natural zinc silicate hemimorphite

The temperature dependence of heat capacity of a natural zinc silicate, hemimorphite Zn4Si2O7(OH)2·H2O, over the temperature range 5–320 K has been investigated by the method of low-temperature adiabatic calorimetry. On the basis of the experimental data on heat capacity over the whole temperature interval, its thermodynamic functions C p (T), S(T) and H(T) − H(0) have been calculated. The existence of a phase transition in the area of 90–105 K determined on the basis of vibrational spectra has been confirmed, and changes of entropy ΔS tr. and enthalpy ΔH tr. of the phase transition have been calculated. Hemimorphite heat capacity has also been determined by the calculation methods according to the valence force field model in LADY program. The values of force constants of valence bonds and angles have been calculated by semi-empirical method PM5. The calculated IR and Raman spectra concordant with the experimental spectra have been obtained. The heat capacity values calculated according to the found vibrational states satisfactorily agree with those experimentally obtained with an accuracy of ±1.7% in the area of 120–200 K, and not more than ±0.8% for the interval of 200–300 K. This fact testifies that the calculation of thermodynamic characteristics is correct.

Heat capacity and thermodynamic functions of 4,4′-dimethylbiphenyl and 4,4′-di-tert-butylbiphenyl

The heat capacity (C p m ) of 4,4′-dimethylbiphenyl and 4,4′-di-tert-butylbiphenyl in the temperature range of 8—373 K was measured by low-temperat ure adiabatic calorimetry, and thermodynamic characteristics of the solid-phase transitions of 4,4′-d i-tert-butylbiphenyl were determined. Temperatures, enthalpies, entropies of melting, and the purity of the samples of the tested substances were determined by means of differential scanning calorimetry. The main thermodynamic functions of the substances in the condensed state at 298 K were calculated.

Thermodynamic functions of buthylderivatives of ferrocene

The heat capacity of isobuthanoylferrocene, C5H5FeC5H4-COCH(CH3)2, was measured by low-temperature adiabatic calorimetry. The purity, temperature, and enthalpy of fusion were obtained. The ideal gas thermodynamic functions were derived at T = 298.15 K. The purity and thermodynamic functions of fusion of isobuthylferrocene, C5H5FeC5H4-CH2CH(CH3)2, were obtained by differential scanning calorimetry. The sample was synthesized by the reduction of isobuthanoylferrocene obtained by the direct acylation of ferrocene.