Synergistic use of Knudsen effusion quadrupole mass spectrometry, solid-state galvanic cell and differential scanning calorimetry for thermodynamic studies on lithium aluminates

Three ternary oxides LiAl₅O₈(s), LiAlO₂(s) and Li₅AlO₄(s) in the system Li-Al-O were prepared by solid-state reaction route and characterized by X-ray powder diffraction method. Equilibrium partial pressure of CO₂(g) over the three-phase mixtures {LiAl₅O₈(s)+Li₂CO₃(s)+5Al₂O₃(s)}, {LiAl₅O₈(s)+5LiAlO₂(s)+2Li₂CO₃(s)} and {LiAlO₂(s)+Li₅AlO₄(s)+2Li₂CO₃(s)} were measured using Knudsen effusion quadrupole mass spectrometry (KEQMS). Solid-state galvanic cell technique based on calcium fluoride electrolyte was used to determine the standard molar Gibbs energies of formations of these aluminates. The standard molar Gibbs energies of formation of these three aluminates calculated from KEQMS and galvanic cell measurements were in good agreement. Heat capacities of individual ternary oxides were measured from 127 to 868 K using differential scanning calorimetry. Thermodynamic tables representing the values of Δ_fH⁰(298.15 K), S⁰(298.15 K) S⁰(T), C_p⁰(T), H⁰(T), {H⁰(T)-H⁰(298.15 K)}, G⁰(T), Δ_fH⁰(T), Δ_fG⁰(T) and free energy function (fef) were constructed using second law analysis and FACTSAGE thermo-chemical database software.     

Heat capacity and thermodynamic functions of manganite ferrites NdMIMnFeO5 (MI = Li, Na) in the range of 298–673 K

The heat capacities of the new manganite ferrites NdM^IMnFeO₅ (M^I = Li, Na) are investigated in the range of 298.15–673 K by dynamic calorimetry. It is found that in the investigated temperature range, C _p ^○ ～ f(T) curves exhibit λ-shaped effects at 348 and 473 K for NdLiMnFeO₅, and at 423 K for NdNaMnFeO₅, corresponding probably to phase transitions of the second kind. Equations describing the experimentally obtained C _p ^○ ～ f(T) curves are derived, and the temperature dependences of the investigated compounds’ thermodynamic functions, S○(T), H○(T) ? H○(298.15), and Φ ^xx (T), are calculated.     

Thermodynamic studies on SrFe12O19(s), SrFe2O4(s), Sr2Fe2O5(s) and Sr3Fe2O6(s)

The citrate-nitrate gel combustion route was used to prepare SrFe₂O₄(s), Sr₂Fe₂O₅(s) and Sr₃Fe₂O₆(s) powders and the compounds were characterized by X-ray diffraction analysis. Different solid-state electrochemical cells were used for the measurement of emf as a function of temperature from 970 to 1151 K. The standard molar Gibbs energies of formation of these ternary oxides were calculated as a function of temperature from the emf data and are represented as (SrFe₂O₄, s, T)/kJ mol⁻¹ (±1.7)=−1494.8+0.3754 (T/K) (970?T/K?1151). (Sr₂Fe₂O₅, s, T)/kJ mol⁻¹ (±3.0)=−2119.3+0.4461 (T/K) (970?T/K?1149). (Sr₃Fe₂O₆, s, T)/kJ mol⁻¹ (±7.3)=−2719.8+0.4974 (T/K) (969?T/K?1150).Standard molar heat capacities of these ternary oxides were determined from 310 to 820 K using a heat flux type differential scanning calorimeter (DSC). Based on second law analysis and using the thermodynamic database FactSage software, thermodynamic functions such as Δ_fH°(298.15 K), S°(298.15 K) S°(T), C_p°(T), H°(T), {H°(T)-H°(298.15 K)}, G°(T), free energy function (fef), Δ_fH°(T) and Δ_fG°(T) for these ternary oxides were also calculated from 298 to 1000 K.     

The thermodynamic properties of star-shaped fullerene-containing poly-N-vinylpyrrolidone

The temperature dependence of the heat capacity of star-shaped fullerene-containing poly-N-vinylpyrrolidone was studied over the temperature range 6–390 K by precision adiabatic vacuum and dynamic scanning calorimetry. The temperature intervals and thermodynamic characteristics of phase transitions were determined. The low-temperature dependence of the heat capacity of the substance was analyzed according to the Debye theory of the heat capacity of solids and its multifractal generalization. The data obtained were used to calculate the standard thermodynamic functions C _p ^o (T),H ^o(T)-H ^o(0), S ^o(T), and G ^o(T)-H ^o(0) of fullerene-containing poly-N-vinylpyrrolidone from T → 0 to 390 K. The standard entropy of formation of the polymer from simple substances and the entropy of its synthesis from poly-N-vinylpyrrolidone and fullerite C₆₀ at 298.15 K were calculated. The thermodynamic characteristics of fullerene-containing poly-N-vinylpyrrolidone are compared with those of the polymer-analogue without C₆₀.     

Heat capacity and thermodynamic functions of new nanostructured cuprate-manganite NdCa2CuMnO6

Heat capacities of nanostructured NdCa₂CuMnO₆ cuprate-manganite are measured by means of dynamic calorimetry on an IT-C-400 unit in the temperature interval of 298.15–673 K. It is established that a λ-shaped phase transition of the second kind is revealed at 348 K on the curve of the dependence C° _p ～ f(T) of NdCa₂CuMnO₆. Equations for the temperature dependence of the heat capacity of NdCa₂CuMnO₆ cuprate-manganite are derived from experimental data including the temperature of phase transition. Thermodynamic functions H°(T)-H°(298.15), S°(T), and Φ**(T) are calculated in the interval of 298.15–675 K.     

Thermodynamics of fluorinated derivatives of carbosilane dendrimers of high generations

The temperature dependences of the heat capacities of fluorinated derivatives of carbosilane dendrimers of high (4.5 and 7.5) generations were studied by adiabatic vacuum calorimetry in the range from 6 to 340 K for the first time. The standard thermodynamic characteristics of devitrification were estimated. The experimental results were used to calculate the standard thermodynamic functions C _p °(T), H°(T)?H°(0), S°(T)?S°(0), and G°(T)-H°(0) over the range from T??0 to 340 K and standard entropies of formation of dendrimers at T = 298.15 K. The low-temperature (T ?? 50 K) heat capacity was analyzed by using Debye??s heat capacity theory of solids and the multifractal model. The values of fractal dimensionality D were determined, and some conclusions about topology of the studied structures were made. The standard thermodynamic characteristics of the studied fluorinated derivatives of carbosilane dendrimers were compared.     

Low-Temperature Heat Capacities of Terbium Molybdate Phosphates M 2 I Tb(MoO4)(PO4) (MI = Na or K)

The heat capacities of Na₂Tb(MoO₄)(PO₄) and K₂Tb(MoO₄)(PO₄) were measured by adiabatic calorimetry at low temperatures (6.34–333.74 and 7.20–341.17 K, respectively). Smoothed thermal-capacities values were used to calculate the entropy, enthalpy increments, and reduced Gibbs energy. The respective values at 298.15 K are as follows: for Na₂Tb(MoO₄)(PO₄), C _p ⁰ (298.15 K) = 240.1 ± 0.2 J/(K mol), ⁰ (298.15 K) = 307.4 ± 0.4 J/(K mol), H ⁰(298.15 K) ? H ⁰(0) = 44.95 ± 0.03 kJ/mol, and Φ⁰(298.15 K) = 156.6 ± 0.5 J/(K mol); and for K₂Tb(MoO₄)(PO₄): C _p ⁰ (298.15 K) = 245.1 ± 0.1 J/(K mol), S ⁰(298.15 K) = 322.9 ± 0.1 J/(K mol), H ⁰(298.15 K) ? H ⁰(0) = 46.58 ± 0.02 kJ/mol, and Φ⁰(298.15 K) = 166.6 ± 0.2 J/(K mol). The noncooperative magnetic component of the heat capacity was estimated.     

The heat capacity and thermodynamic functions of Ca0.5Zr2(PO4)3 crystalline phosphate from T → 0 to 650 K

The temperature dependence of the heat capacity C _p ^o = f(T) of crystalline calcium-zirconium phosphate was studied over the temperature range 7–650 K by precision adiabatic vacuum and dynamic scanning calorimetry. The experimental data were used to calculate the standard thermodynamic functions C _p ^o (T), H ^o(T) ? H ^o(0), S ^o(T), and G ^o(T) ? H ^o(0) at temperatures from T → 0 to 650 K and the standard entropy of formation of Ca_0.5Zr₂(PO₄)₃ at T = 298.15 K. The data on low-temperature (30 K ≤ T ≤ 50 K) heat capacity were used to calculate fractal dimension D. Conclusions about the character of the topology of the structure of the phosphate were drawn.     

Thermodynamics of G-3(D4) and G-6(D4) carbosilanecyclosiloxane dendrimers

Temperature dependences of the heat capacity of G-3(D₄) and G-6(D₄) carbosilanecyclosiloxane dendrimers are studied for the first time by precision adiabatic vacuum and differential scanning calorimetry in the range of 6 to 350–450 K. Physical transformations in the investigated temperature range are observed and their standard thermodynamic characteristics are determined and discussed. Standard thermodynamic functions for a mole unit are calculated from the experimental data: C _p ^○ (T), H ^○(T), ? H ^○(0), S ^○(T) ? S ^○(0), and G ^○(T) ? H ^○(0) in the range of T → 0 to (350–449) K and standard entropies of formation at 298.15 K. Low-temperature (T ≤ 50 K) heat capacity is analyzed using the Debye theory of heat capacity of solids and the multifractal model. The values of fractal dimensionality D are determined and some conclusions on the topology of the investigated structures are drawn. The corresponding thermodynamic properties of the investigated carbosilanecyclosiloxane dendrimers under study are compared.     

Thermodynamic properties of carbosilane dendrimers of the third and sixth generations with ethyleneoxide terminal groups

The temperature dependences of the heat capacities of carbosilane dendrimers of the third and sixth generations with ethyleneoxide terminal groups are examined for the first time by means of precision adiabatic vacuum calorimetry at temperatures between 6.5 and 350 K. In this temperature range, physical transformations are observed and their standard thermodynamic characteristics are determined and discussed. The standard thermodynamic functions are calculated per nominal mole of a chosen unit using the obtained experimental data: C° _p (T), H°(T) - H°(0), S°(T) - S°(0), and G°(T) - H°(0) in the interval T → 0 to 350 K, and the standard entropies of formation at T = 298.15 K. The low-temperature (T ≤ 50 K) heat capacity is analyzed using the Debye theory of specific heat and a multifractal model. The values of fractal dimension D are also determined, and conclusions on the investigated structures’ topology are drawn. The corresponding thermodynamic properties of the studied dendrimers are compared as well.     

The thermodynamic properties of 5-vinyltetrazole and poly-5-vinyltetrazole over the temperature range from <Emphasis Type="Italic">T</Emphasis> → 0 to 350 K

The temperature dependences of the heat capacities of 5-vinyltetrazole and poly-5-vinyltetrazole were measured by adiabatic vacuum calorimetry over the temperature range 6-(350–370) K with errors of ～0.2%. The results were used to calculate the thermodynamic functions of the compounds, C _p ^° , H ^°(T) - H ^°(0), S ^°(T), and G ^°(T) - H ^°(0), over the temperature range from T → 0 to 350–370 K. The energy of combustion of 5-vinyltetrazole and poly-5-vinyltetrazole was measured in an isothermic-shell static bomb calorimeter. The standard enthalpies of combustion Δ _c H ^° and thermodynamic characteristics of formation Δ_f H ^°, Δ_f S ^°, and Δ_f G ^° at 298.15 K and p = 0.1 MPa were calculated. The results were used to determine the thermodynamic characteristics of polymerization of 5-vinyltetrazole over the temperature range from T → 0 to 350 K.     

Thermodynamic Properties of Tetraphenyltetrahydroxycyclotetrasiloxane,Octaphenyltetrahydroxytricyclooctasiloxane, Octaphenylpentacyclosilsesquioxane,and Polyphenylsilsesquioxane in the Range 0-300 K

The temperature dependences of the heat capacities of crystalline tetraphenyltetrahydroxycyclotetrasiloxane, octaphenyltetrahydroxytricyclooctasiloxane, and octaphenylpentacyclosilsesquioxane and of glassy polyphenylsilsesquioxane were measured in the range 6-300 K with an adiabatic vacuum calorimeter, with an accuracy of 0.3%. From these data, the thermodynamic functions C ⁰ _p (T), H ⁰(T) - H ⁰(0), S ⁰(T) - S ⁰(0), and G ⁰(T) - H ⁰(0) of these substances were calculated for the range 0-300 K. The standard entropies of their formation from elements at 298.15 K, _f S ⁰, and the entropies of mutual transformations of these substances in the range 0-298.15 K were calculated.     

Thermodynamic properties of second generation poly(phenylene-pyridyl) dendrimer

The temperature dependence of heat capacity C _p ^o = f (T) of second generation hard poly(phenylene-pyridyl) dendrimer (G2-24Py) was measured by a adiabatic vacuum calorimeter over the temperature range 6–320 K for the first time. The experimental results were used to calculate the standard thermodynamic functions: heat capacity C _p ^o (T), enthalpy H ^o(T)–H ^o(0), entropy S ^o(T)–S ^o(0) and Gibbs function G ^o(T)–H ^o(0) over the range from T → 0 K to 320 K. The standard entropy of formation at T = 298.15 K of G2-24Py was calculated. The low-temperature heat capacity was analyzed based on Debye’s heat capacity theory of solids. Fractal treatment of the heat capacity was performed and the values of the temperature characteristics and fractal dimension D were determined. Some conclusions regarding structure topology are given.     

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.     

Thermodynamic properties of crystalline phosphate Ba0.5Zr2(PO4)3 over the temperature range from T → 0 to 610 K

The temperature dependence of the heat capacity of crystalline barium zirconium phosphate C _p ^o  = f(T) was measured over the temperature range 6–612 K. The experimental data obtained were used to calculate the standard thermodynamic functions C _p ^o (T), H°(T) ? H°(0), S°(T), G°(T) ? H°(0) over the temperature range from T → 0 to 610 K and standard entropy of formation at 298.15 K. The data on the low-temperature (6 ≤ T/K ≤ 50) heat capacity were used to determine the fractal dimension of Ba_0.5Zr₂(PO₄)₃. Conclusions concerning the topology of the structure of phosphate were drawn. Thermodynamic properties of M_0.5Zr₂(PO₄)₃ (M = Ca, Sr, Ba) were compared.     

Low-Temperature Heat Capacities and Thermodynamic Properties of Hydrated Nickel L-Threonate Ni（C4H7O5）2·2H2O（S）

Low-temperature heat capacities of the compound Ni（C4H7O5）2·2H2O（S） have been measured with an auto- mated adiabatic calorimeter. A thermal decomposition or dehydration occurred in 350--369 K. The temperature, the enthalpy and entropy of the dehydration were determined to be （368.141 ±0.095） K, （18.809±0.088） kJ·mol ^-1 and （51.093±0.239） J·K^-1·mol^-1 respertively. The experimental values of the molar heat capacities in the temperature regions of 78-350 and 368-390 K were fitted to two polynomial equations of heat capacities （Cp,m） with the reduced temperatures （X）, [X=f（T）], by a least squares method, respectively. The smoothed molar heat capacities and thermodynamic functions of the compound were calculated on the basis of the fitted polynomials. The smoothed values of the molar heat capacities and fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K were tabulated with an interval of 5 K.     

Thermodynamics of undecanolactone,tridecanolactone, and pentadecanolactone from 0 to 340 K

The heat capacities C_p^o of undercanolactone, tridecanolactone, and pentadecanolactone have been measured between 10 and 370 K in a vacuum adiabatic calorimetric cryostat within about 0.2 per cent. The temperatures and enthalpies of physical transitions have been also estimated. The enthalpies of combustion of the compounds have been measured in an isothermal calorimeter with an accuracy of 0.05 per cent. From the results the functions {H (T) ? H (0)}, S^o(T), and {G^o(T) ? H^o(0)} have been calculated over the range 0 to 340 K, and the values of ΔH_f^o, ΔG_f^o and ΔS_f^o have been evaluated at T = 298.15 K.     

Thermodynamic properties of first- and third-generation carbosilane dendrimers with terminal phenyldioxolane groups

The heat capacities of first- and third-generation carbosilane dendrimers with terminal phenyldioxolane groups are studied as a function of temperature via vacuum and differential scanning calorimetry in the range of 6 to 520 K. Physical transformations that occur in the above temperature range are detected and their standard thermodynamic characteristics are determined and analyzed. Standard thermodynamic functions C_p^ο(T), [H°(T) ? H°(0)], [S°(T) ? S°(0)], and [G°(T) ? H°(0)] in the temperature range of T → 0 to 520 K for different physical states and the standard entropies of formation of the studied dendrimers at T = 298.15 K are calculated, based on the obtained experimental data.     

Molar heat capacities and standard molar enthalpy of formation of 2-amino-5-methylpyridine

The heat capacities (C _p,m) of 2-amino-5-methylpyridine (AMP) were measured by a precision automated adiabatic calorimeter over the temperature range from 80 to 398 K. A solid-liquid phase transition was found in the range from 336 to 351 K with the peak heat capacity at 350.426 K. The melting temperature (T _m), the molar enthalpy (Δ_fus H _m⁰), and the molar entropy (Δ_fus S _m⁰) of fusion were determined to be 350.431±0.018 K, 18.108 kJ mol⁻¹ and 51.676 J K⁻¹ mol⁻¹, respectively. The mole fraction purity of the sample used was determined to be 0.99734 through the Van’t Hoff equation. The thermodynamic functions (H _T-H _298.15 and S _T-S _298.15) were calculated. The molar energy of combustion and the standard molar enthalpy of combustion were determined, ΔU _c(C₆H₈N₂,cr)= −3500.15±1.51 kJ mol⁻¹ and Δ_c H _m⁰ (C₆H₈N₂,cr)= −3502.64±1.51 kJ mol⁻¹, by means of a precision oxygen-bomb combustion calorimeter at T=298.15 K. The standard molar enthalpy of formation of the crystalline compound was derived, Δ_r H _m⁰ (C₆H₈N₂,cr)= −1.74±0.57 kJ mol⁻¹.     

Influence of the molecular weight of polystyrene on its thermodynamic properties

The thermodynamic properties of a series of polystyrene samples with different molecular weights (M _w was varied from 2.5·10³ to 6.57·10⁴) were studied by precision adiabatic vacuum, high-accuracy dynamic, and combustion calorimetry: temperature dependences of the heat capacity in a wide temperature range, thermodynamic characteristics of glass transition and glassy state under standard pressure, and energy of combustion. The thermodynamic functions C ^○ _p (T), H ^○(T) - H ^○(0), S ^○(T) - S ^○(0), and G ^○(T) - H ^○(0) of polystyrene with different molecular weights, enthalpies of combustion Δ_c H ^○, thermodynamic parameters of formation from simple substances Δ_f H ^○, Δ_f S ^○, and Δ_f G ^○ at T = 298.15 K, and parameters of their synthesis from monomers were calculated from the experimental data. The temperature dependences of the heat capacity for a region of 0–380 K, glass transition temperatures, and thermodynamic characteristics of formation and synthesis of polystyrene depending on its molecular weight were examined.