The phonon heat capacity of diborides: The approximation of interacting sublattices

The temperature dependence of the heat capacity of structures formed by alternating layers with different atomic compositions is described using the model of interacting three- and two-dimensional Debye sublattices. The parameters of the model are the characteristic temperatures Θ₁ and Θ₃ of the sublattices and the characteristic temperature Θ₂ corresponding to vibrations between the sublattices. (In the accepted approximation, Θ₂ equals the characteristic Debye temperature of the substance at absolute zero.) The model was used to analyze the temperature dependences of the lattice (phonon) heat capacities of transition and rare-earth metal diborides MB₂. This allowed the characteristic temperatures Θ _i and trends of their variations depending on metal atomic numbers to be determined.     

Heat capacity of poly(butylene terephthalate)

The low‐temperature heat capacity of poly(butylene terephthalate) (PBT) was measured from 5 to 330 K. The experimental heat capacity of solid PBT, below the glass transition, was linked to its approximate group and skeletal vibrational spectrum. The 21 skeletal vibrations were estimated with a general Tarasov equation with the parameters Θ₁ = 530 K and Θ₂ = Θ₃ = 55 K. The calculated and experimental heat capacities of solid PBT agreed within better than ±3% between 5 and 200 K. The newly calculated vibrational heat capacity of the solid from this study and the liquid heat capacity from the ATHAS Data Bank were applied as reference values for a quantitative thermal analysis of the apparent heat capacity of semicrystalline PBT between the glass and melting transitions as obtained by differential scanning calorimetry. From these results, the integral thermodynamic functions (enthalpy, entropy, and Gibbs function) of crystalline and amorphous PBT were calculated. Finally, the changes in the crystallinity with the temperature were analyzed. With the crystallinity, a baseline was constructed that separated the thermodynamic heat capacity from cold crystallization, reorganization, annealing, and melting effects contained in the apparent heat capacity. For semicrystalline PBT samples, the mobile‐amorphous and rigid‐amorphous fractions were estimated to complete the thermal analysis. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4401–4411, 2004     

Conformational contribution to the heat capacity of the starch and water system

The heat capacities of starch and starch—water have been measured with adiabatic calorimetry and standard differential scanning calorimetry and are reported from 8 to 490 K. The amorphous starch containing 11–26 wt % (53–76 mol %) water shows a partial glass transition decreasing from 372 to 270 K, respectively. Even the dry amorphous starch gradually increases in heat capacity above 270 K beyond that set by the vibrational density of states. This gradual increase in the heat capacity is identified as part of the glass transition of dry starch that is, however, not completed at the decomposition temperature. The heat capacities of the glassy, dry starch are linked to an approximate group vibrational spectrum with 44 degrees of freedom. The Tarasov equation is used to estimate the heat capacity contribution due to skeletal vibrations with the parameters Θ₁ = 795.5 K, Θ₂ = 159 K, and Θ₃ = 58 K for 19 degrees of freedom. The calculated and experimental heat capacities agree better than ±3% between 8 and 250 K. Similarly, the vibrational heat capacity has been estimated for glassy water by being linked to an approximate group vibrational spectrum and the Tarasov equation (Θ₁ = 1105.5 K and Θ₃ = 72.4 K, with 6 degrees of freedom). Below the glass transition, the heat capacity of the solid starch—water system has been estimated from the appropriate sum of its components and also from a direct fitting to skeletal vibrations. Above the glass transition, the differences are interpreted as contributions of different conformational heat capacities from chains of the carbohydrates interacting with water. The conformational parts are estimated from the experimental heat capacities of dry starch and starch—water, decreased by the vibrational and external contributions to the heat capacity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3038–3054, 2001     

Heat capacity of poly(vinyl methyl ether)

The heat capacity of poly(vinyl methyl ether) (PVME) has been measured using adiabatic calorimetry and temperature‐modulated differential scanning calorimetry (TMDSC). The heat capacity of the solid and liquid states of amorphous PVME is reported from 5 to 360 K. The amorphous PVME has a glass transition at 248 K (?25 °C). Below the glass transition, the low‐temperature, experimental heat capacity of solid PVME is linked to the vibrational molecular motion. It can be approximated by a group vibration spectrum and a skeletal vibration spectrum. The skeletal vibrations were described by a general Tarasov equation with three Debye temperatures Θ₁ = 647 K, Θ₂ = Θ₃ = 70 K, and nine skeletal modes. The calculated and experimental heat capacities agree to better than ±1.8% in the temperature range from 5 to 200 K. The experimental heat capacity of the liquid rubbery state of PVME is represented by C_p(liquid) = 72.36 + 0.136 T in J K^?1 mol^?1 and compared to estimated results from contributions of the same constituent groups of other polymers using the Advanced Thermal AnalysiS (ATHAS) Data Bank. The calculated solid and liquid heat capacities serve as baselines for the quantitative thermal analysis of amorphous PVME with different thermal histories. Also, knowing C_p of the solid and liquid, the integral thermodynamic functions of enthalpy, entropy, and free enthalpy of glassy and amorphous PVME are calculated with help of estimated parameters for the crystal. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2141–2153, 2005     

Heat capacities of poly(amino acid)s and proteins

In an ongoing effort to understand the thermodynamic properties of proteins, solid-state heat capacities of poly(amino acid)s of all 20 naturally occurring amino acids and 4 copoly(amino acid)s have been previously reported on and were analyzed using our Advanced THermal Analysis System (ATHAS). We extend the heat capacities of poly(L-methionine) (PLMFT) and poly(L-phenylalanine) (PLPHEA) with new low temperature measurements from 10 to 340 K. In addition, analyses were performed on literature data of a first protein, zinc bovine insulin dimer C₅₀₈H₇₅₂O₁₅₀N₁₃₀S₁₂Zn, using both the ATHAS empirical addition scheme and computation with an approximate vibrational spectrum for the protein. For the solid state, agreement with the measurement could be accomplished to ±1.6% for PLMET, ±3.5% for PLPHEA, and ±3.2% for insulin, linking the macroscopic heat capacity to its microscopic cause, the group and skeletal vibrational motion. For each polymer, one set of parameters, Θ₁ and Θ₃, of the Tarasov function representing the skeletal vibrational contribution to the heat capacity are obtained from a new optimization procedure [PLMET: 542 K and 83 K (number of skeletal vibrations N_s = 15); PLPHEA: 396 K and 67 K (N_s = 11); and insulin monomer: 599 K and 79 K (N_s = 628), respectively]. Enthalpy, entropy, and Gibbs free energy have been derived for the solid state. © 1995 John Wiley & Sons, Inc.     

Heat capacity of solid state proteins

In an ongoing effort to understand the thermodynamic properties of proteins, ovalbumin, lactoglobulin, lysozyme are studied by adiabatic and differential scanning calorimetry over wide temperature ranges. The heat capacities of the samples in their pure, solid states are linked to an approximate vibrational spectrum with the ATHAS analysis that makes use of known group vibrations and a set of parameters, Θ₁ and Θ₃, of the Tarasov function for the skeletal vibrations. Good agreement is found between experiment and calculation with rms errors mostly within ±3%. The analyses were also carried out with an empirical addition scheme using data from polypeptides of naturally occurring amino acids. Due to space limitation, only selected results are reported.     

Magnetic structure of Ni(DCOO)2(D2O)2

Ni(HCOO)(2)(H(2)O)(2) is a structurally simple coordination polymer showing interesting magnetic phase transitions at low temperature (<16K). Previously published studies of these phase transitions have yielded inconsistent results, questioning the correctness of the published magnetic structure. Here heat capacity and magnetic susceptibility of a fully, a partly and a non-deuterated sample were measured, and they all exhibit magnetic phase transitions around 3 and 15 K. Neutron powder diffraction data was collected on the fully deuterated sample at various temperatures between 1.5 and 25 K. A magnetic model was refined against the neutron diffraction data using a spin system composed of two canted antiferromagnetic sublattices. The magnetic moments of the two sublattices show different magnitude, 1.7 μ(B) and 1.3 μ(B), and the temperature dependence of the magnetic sublattices is quite different. One of the sublattices shows the expected temperature behavior of an antiferromagnetic compound whereas the other sublattice follows a Brillouin like function with a slowly increasing magnetization below the Ne?el temperature.     

Quasi-isothermal measurement by TMDSC in isotactic polypropylene

We measure the frequency dependences of complex heat flows for isothermally crystallized isotactic polypropylene (iPP) by the quasi-isothermal TMDSC. Regarding the quasi-isothermal melting processes as a kind of the single relaxation process, we analyze them by the Debye model. The resultant heat capacity of iPP is larger (about 11%) than usual thermodynamic heat capacity. We also found that the excess of the heat capacity, C _p (excess), has non-monotonous temperature dependence. A simple model introducing some kinetic modes into amorphous producing after and during temperature modulation can reproduce the temperature dependence of C _p (excess) very well.     

Heat capacity of solid‐state biopolymers by thermal analysis

Heat capacities in the solid state of four globular proteins (bovine β‐lactoglobulin, chicken lysozyme, ovalbumine, and horse myoglobin) and of the poly(amino acid) poly(L ‐tryptophan) have been determined using the Advanced THermal Analysis System (ATHAS). The experimental measurements were performed with adiabatic and differential scanning calorimetry over wide temperature ranges. The heat capacities were linked to an approximate vibrational spectrum by making use of known group vibrations and of a set of parameters, Θ₁ and Θ₃, of the Tarasov function for the skeletal vibrations. Good agreement was found between experiments and calculations with root mean square errors mostly within ±3%. The experimental data were analyzed also with an empirical addition scheme using the known data for poly(amino acid)s measured earlier. Based on this study, vibrational heat capacities can now be predicted for all proteins with an accuracy comparable to common experiments. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2093–2102, 1999     

Structure and Specific Heat of Disordered and Ordered Titanium Monoxide TiOy

The structure of disordered and ordered titanium monoxide containing structural vacancies in both sublattices was studied by Xray diffraction. The symmetry of the monoclinic Ti₅O₅ superstructure (space group C2/m) was analyzed. The type and channel of the TiO_y–Ti₅O₅ disorder–order transition was determined. The distribution functions of Ti and O atoms in the metal and nonmetal sublattices of titanium monoxide were calculated. The specific heats of TiO_y titanium monoxides (0.8< y< 1.27) were measured by differential scanning calorimetry for the disordered and ordered states in the range from 340 to 600 K. The dependences of the specific heat, enthalpy, and entropy on the composition and structure of TiO_y were found for the first time. A notable effect of the structural state on the specific heat was detected. In the indicated temperature range, the C _p (T) dependence is adequately described by a function that accounts for the Debye effect and the electronic specific heat.     

The low-temperature heat capacity of CaUO4 and SrUO4

The heat capacity of calcium monouranate CaUO₄ and strontium monouranate SrUO₄ have been measured over the temperature range (2 to 300) K. The results are significantly different from earlier measurements, confirming the conclusions from our previous study on BaUO₄. The standard entropy at T = 298.15 K of orthorhombic α-SrUO₄ is consistent with the values for the isostructural BaUO₄ as well as the alkali uranates Na₂UO₄ and Cs₂UO₄. The standard entropy of the rhombohedral CaUO₄ is appreciably different, which is attributed to the different structures of the uranium sublattices.     

Heat-Induced Gelation of Globular Protein Mixtures

Heat-induced conformational changes and heat-induced gels of whey and egg white albumen, and their major components were studied under physicochemical conditions that favour protein-protein interactions. We used differential scanning calorimetry (DSC) to compare their conformational heat stability, through the characteristic temperature (Θ_max) corresponding to the maximal heat flow and the overall calorimetric heat of reaction (Δ_r H _cal). Times needed to observe sol-gel state transitions at various temperatures were determined by a tilting test and the corresponding time-temperature experimental points were best fitted to two successive Arrhenius plots intersecting at Θ～Θ_max corresponding to the major protein component for whey proteins and to a minor protein component for egg white albumen. Observations of gel-networks by scanning electron microscopy indicated a wide range of stuctural patterns, depending on the composition of protein solutions. The results are discussed in terms of the temperature of maximal rate of heat-induced conformational changes and of sol-gel state transitions of protein molecules.     

AxMn1-xFe2O4铁氧体(A=Zn,Ni)中阳离子的占位有序化行为研究

基于尖晶石晶体结构信息,本文采用热力学三亚晶格模型,将材料热力学计算和第一性原理计算相结合,研究了Zn_xMn_1-x Fe₂O₄和Ni_xMn_1-xFe₂O₄立方相中的Zn²⁺、Ni²⁺、Mn²⁺以及Fe³⁺在8a和16d亚晶格上的占位有序化行为。结果表明:在锰铁氧体中,室温下Mn²⁺完全占据在8a亚晶格上,Fe³⁺完全占据在16d亚晶格上,属于正尖晶石结构;随着热处理温度升高,在1 273 K达到热处理平衡时的占位构型为(Fe_0.09³⁺Mn_0.91²⁺)[Fe_1.91³⁺Mn_0.09²⁺]O₄,在热处理温度升至1 473 K时,达到热处理平衡时的占位构型为(Fe_0.11³⁺ Mn_0.89²⁺)[Fe_1.89³⁺Mn_0.11²⁺]O₄,均与实验结果符合较好。在锌铁氧体中,室温下Zn²⁺完全占据在8a亚晶格上,Fe³⁺完全占据在16d亚晶格上,属于正尖晶石结构;在热处理温度较高时,Zn²⁺和Fe³⁺发生部分置换,符合实验结果。在镍铁氧体中,半数的Fe³⁺在室温下占据在8a亚晶格上,Ni²⁺与剩下另一半的Fe³⁺共同占据在16d亚晶格上,仅在热处理温度较高的时候发生微弱变化,亦与已有的实验结果吻合。在此基础上,本文进一步通过热力学预测建立了立方相尖晶石结构的Zn_xMn_1-xFe₂O₄、Ni_xMn_1-xFe₂O₄复合体系中阳离子占位行为与热处理温度对占位的影响。     

Heat capacity and thermodynamic properties of ramsdellite,Li2Ti3O7, and spinel,Li43Ti53O4

The heat capacity and heat content Li_{$\text{4}\text{3}$}Ti_{$\text{5}\text{3}$}O₄ and Li₂Ti₃O₇ have been measured in the temperature range 198—960 K. The lattice and dilation contributions to the heat capacity have been estimated. The standard thermodynamic functions and the high temperature enthalpy and entropy have been derived. The lattice heat capacity of Li_{$\text{4}\text{3}$}Ti_{$\text{5}\text{3}$}O₄ spinel appears to be consistent with the phonon model put forward by Grimes.     

Anomalies in Heat Capacity Measurements of RuO2-TiO2 System

DSC was used for heat capacity measurements of pure RuO₂ in the temperature range from 300 to 1170 K of solid solutions corresponding to the compositions of (Ti_1−x Ru_x )O₂ (x ≤0.15 and x ≥0.85) and in the temperature range from 300 to 1550 K of pure TiO2. The analysis of experimental data obtained within ±2% of accuracy has shown that the characteristic temperatures representing the harmonic lattice vibrations do not strongly depend on the chemical composition x . It was demonstrated that non-harmonic heat capacity is strongly correlated to x. The existence of additional excess heat capacity was observed with the mixed oxide solid solution samples of low Ru content and explained by the defect formation model. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dilute-solution properties of ring polystyrenes

The temperature Θ_A2 at which the second virial coefficient A₂ is zero for ring polystyrenes is 28.5°C in cyclohexane, independent of molecular weight in the range 2 × 10⁴ to 4.5 × 10⁵. This cannot be explained solely by the Candau–Rempp–Benoit theory, which takes into account the effect of segment density on Θ_A2 The radius of gyration of a ring is found to be approximately one-half that of a linear polymer with the same molecular weight. The intrinsic viscosities [η] and intrinsic translational friction coefficients [f] of ring polystyrenes with molecular weights ranging from 7 × 10³ to 4.5 × 10⁵ have been measured in cyclohexane at 34.5°C (Θ, the Flory theta temperature for linear polystyrenes) and in toluene (a good solvent). The results are compared with those for linear polystyrene. It is found that the Mark–Houwink exponent is less than one-half in cyclohexane at Θ. In toluene it is 0.67 compared to 0.73 for linear polystyrene. The hydrodynamic measurements suggest that large rings are less expanded than the linear polymers with the same molecular weight, contrary to many predictions.     

Hydration heat capacities of hydrophobic solutes at 248–373 K

A new equation is suggested to define the temperature dependence of the Gibbs energy of hydration of hydrophobic substances: ΔG ⁰ = b ₀ + b ₁ T + b ₂lnT. According to this equation, the hydration heat capacity is in inverse proportion to temperature. Consistent values of hydration heat capacity of nonpolar solutes have been obtained for different temperatures using data on solubility and dissolution enthalpy. The contributions of the hydrocarbon radicals and OH group to the heat capacity of hydration of the compounds were found for the temperature range 248–373 K. The hydration heat capacity of the hydroxyl group has a weak dependence on temperature and increases by only 12 J/(mol·K) in the specified temperature interval. Changes in the hydration entropy of hydrophobic and OH groups are calculated for the temperature increasing from 248 K to 373 K.     

Heats of solution of several freons in water from 5 to 45°C

An extensive set of measurements of the heats of solution of a number of fluorine-containing gases (CCl₂F₂, CClF₃, CBrF₃, CF₄) have been performed from 5 to 45°C. The temperature dependence allows accurate determination of the heat capacity change in the solution process as a function of temperature. To a first approximation these heat capacity results agree with the predictions of the simple two energy state model for water molecules in the first solvation shell. The further extension of the general applicability of this model, originally developed to account for the thermodynamic properties of solvation of hydrocarbon and other small apolar gases in water, suggests that the unique thermodynamic properties of hydrophobic solvation are largely determined by the water molecules in the first solvation shell.     

Excess Heat Capacity in Yttria Stabilized Zirconia

The heat capacity of 9.70 and 11.35 mol% yttria stabilized zirconia ((ZrO₂)_1–x(Y₂O₃)_x; x=0.0970, 0.1135) was measured by adiabatic calorimetry between 13 and 300 K, and some thermodynamic functions were calculated and given in a table. A large excess heat capacity extending from the lowest temperature to room temperature with a broad maximum at about 75 K was found in comparison with the heat capacity calculated from those of pure zirconia and yttria on the basis of simple additivity rule. The shape of the excess heat capacity is very similar to the Schottky anomaly, which may be attributed to a softening of lattice vibration. The amount of the excess heat capacity decreased with increasing yttria doping, while the maximum temperature did not vary. The relationships among the excess heat capacity, defect structure and interatomic force constants, and also the role of oxygen vacancy were discussed.This revised version was published online in November 2005 with corrections to the Cover Date.     

The heat capacity of NdPO4

The heat capacity of neodymium orthophosphate has been measured in the temperature range (0.6 to 1570) K. From the results the excess (electronic) heat capacity has been derived by subtracting the lattice heat capacity derived from the heat capacity of the isostructural LaPO₄ and GdPO₄, reported earlier. The calculated excess heat capacity thus obtained is in reasonable agreement with that calculated from the crystal field energies.