A new method of fitting approximate vibrational spectra to heat capacities of solids with Tarasov functions

A new, least-squares optimization method with interpolation is devised to fit skeletal vibrational heat capacities to the two parameters θ₁ and θ₃ in the Tarasov function used for heat capacity calculations of linear macromolecules. When heat capacities are available in the proper temperature range, θ₁ and θ₃ can be determined uniquely in a single computer run. Appended to our Advanced THermal Analysis System (ATHAS), this new method offers an improvement in analyzing heat capacity data and facilitates the systematic study of the physical significance of θ₁ and θ₃ values for all polymers and related molecules of the ATHAS data bank.     

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 capacity measurements of SnSe and SnSe2

The heat capacities of SnSe and SnSe₂ were measured in the temperature range 230–580 K using a computer interfaced differential scanning calorimeter. From these measurements, the Debye temperatures of SnSe and SnSe₂ were calculated as a function of temperature. An estimated Debye temperature of 220 K for SnSe was used to calculate the absolute entropy of SnSe at 298 K to be 85.2 ± 6.0 J K^?1 mole^?1. In the light of other work, the suitability of Debye temperatures for estimating low temperature heat capacities of SnSe₂ is questioned.     

Low-temperature heat capacity of β-glycine and a phase transition at 252 K

Low-temperature heat capacity of unstable -glycine was measured in a temperature range 5.5 to 295 K, and thermodynamic functions were calculated. At very low temperatures, heat capacity fits a sum of cubic (Debye) and linear terms: C_p=aT+bT ³. The linear contribution increases with temperature and disappears at the second-order phase transition near 252 K which was observed for the first time.     

Thermodynamic properties of pyridine-containing polyphenylene dendrimers of the first-fourth generations

The temperature dependence of the heat capacity C _p° = f(T) of hard pyridine-containing polyphenylene dendrimers of the first, third, and fourth generations was studied for the first time in an adiabatic calorimeter at 6–300 K. Using the experimental data obtained, the standard thermodynamic functions, viz., heat capacity, enthalpy, entropy, and Gibbs energy in the range from T → 0 to 300 K, were calculated for these dendrimers and the value of standard entropy of formation of the studied compounds at T = 298.15 K was estimated. The low-temperature heat capacity of the dendrimers was analyzed on the basis of the Tarasov and Debye theories of heat capacity of solids and by the multifractal method. The characteristic temperatures and fractal dimensionality D were determined, and some conclusions about the type of structure topology were drawn. The isotherms of the dependence of thermodynamic functions of the dendrimers on the molecular weight were obtained.     

Low-temperature heat capacity of diglycylglycine

Heat capacity of tripeptide diglycylglycine was measured in a temperature range from 6.5 to 304 K. The results were compared with those for glycine and glycylglycine. Peptide bonding was found not to change C _P(T) virtually above 70 K, where heat capacity does not obey the Debye model. Comparison with literature data allows one to expect a significant difference in the heat capacity for enantiomorph and racemic species of valine and leucine, like it was found recently for D-and DL-serine.     

The heat capacity of solid poly(p-xylylene) and polystyrene

The constant-pressure heat capacity C_p of poly(p-xylylene) (PPX) has been measured from 220 to 625 K by differential scanning calorimetry. The constant-volume heat capacities C_v of both, PPX and its isomer polystyrene (PS) have been interpreted in the light of literature data on full normal-mode calculations for PS and estimates from low-molecular-weight analogs for PPX for the 39 group vibrations. Nine skeletal vibrations were used in this discussion with characteristic temperatures θ₁ and θ₃ of 534.5 and 43.1 K for PS. It was also possible to calculate a heat capacity contribution of a phenylene group within a polymer chain. Single 48-vibration θ₁ temperatures of 3230 K for PS and 2960 K for PPX are sufficient to describe C_v above 220 K. Below 140 K, PS heat capacity shows deviations from the Tarasov treatment.     

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 and Thermodynamic Properties of Hydrated Sodium Cupric Arsenate [NaCuAsO4·1.5H2O（s）]

Low-temperature heat capacities of the solid compound NaCuAsO4·1.5H2O(s)were measured using a precision automated adiabatic calorimeter over a temperature range of T=78 K to T=390 K.A dehydration process occurred in the temperature range of T=368-374 K.The peak temperature of the dehydration was observed to be TD=(371.828±0.146)K by means of the heat-capacity measurement.The molar enthalpy and entropy of the dehydration were ΔDHm=(18.571±0.142)kJ/mol and ΔDSm=(49.946±0.415)J/(K·mol),respectively.The experimental values of heat capacities for the solid(Ⅰ)and the solid-liquid mixture(Ⅱ)were respectively fitted to two polynomial equations by the least square method.The smoothed values of the molar heat capacities and the fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K were tabulated at an interval of 5 K.     

Computation of Heat Capacities of Solids Using a General Tarasov Equation

The general Tarasov function is fitted to the skeletal heat capacities of materials with widely different crystal structures. Examples are chosen from flexible macromolecules (polyethylene, polypropylene, poly(ethylene terephthalate), selenium, rigid macromolecules (diamond and graphite), and a small molecule (fullerene, C60). A new optimization approach using the MathematicaTM software is developed. It results in one-, two-, and three-dimensional Debye temperatures, Θ1, Θ2 and Θ3 the fitting parameters of the Tarasov function. In addition to the Tarasov function, the evaluation of the heat capacities makes use of approximate group-vibrational spectra. The results support the earlier assumption that Θ2=Θ3 for simple, solid, linear macromolecules. In more complicated bonding situations, Θ1, Θ2 and Θ3 are used as averaging fitting parameters. This general approach provides an improvement in the quantitative thermal analyses of polymers and other substances included in the ATHAS Data Bank. Sufficient programming information is provided to enable anyone the computation with a copy of the popular MathematicaTM software. The programming file is also downloadable from the WWW. This revised version was published online in July 2006 with corrections to the Cover Date.     

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     

水合烟酸铜Cu(Nic)2•H2O(s)(Nic＝烟酸)的合成、表征及热力学性质

近几十年来,烟酸盐类化合物或配合物由于优越的吸收率高和无毒副作用等特点使其在化妆品、药品和食品等领域作为营养添加剂具有重要应用前景。然而,这类化合物的基础热力学数据极其缺乏,从而限制了这类化合物的理论研究和应用开发的深入开展。为此,本论文利用室温固相合成方法和球磨技术合成了一种新化合物Cu(Nic)2•H2O(s),利用化学分析、元素分析、FTIR和X-射线粉末衍射技术表征了它的结构和组成,利用精密自动绝热热量计准确地测量了它在78-400 K温区的摩尔热容。在热容曲线的T ＝ 326-346 K温区观察到一个明显的固-液相变过程。利用相变温区三次重复实验热容的测量结果确定了此相变过程的峰温、相变焓和相变熵分别为：Tfus＝(341.290 ±0.873) K, DfusHm＝(13.582±0.012) kJ×mol-1, DfusSm＝(39.797±0.067) J×K-1×mol-1。通过最小二乘法将相变前和相变后的热容实验值分别拟合成了热容对温度的两个多项式方程。通过热容多项式方程的数值积分,得到了这个化合物的舒平热容值和相对于298.15 K的各种热力学函数值,并且将每隔5 K的热力学函数值列成了表格。     

Heat capacity and thermodynamic functions of MnBr2 · 4D2O and MnCl2 · 4D2O

The heat capacities of MnBr₂ · 4D₂O and MnCl₂ · 4D₂O have been experimentally determined from 1.4 to 300 K. The smoothed heat capacity and thermodynamic functions (H°_TH°₀) and S°_T are reported for the two compounds over the temperature range 10 to 300 K. The error in the thermodynamic functions at 10 K is estimated to be 3%. Additional error in the tabulated values arising from the heat capacity data above 10 K is thought to be less than 1%. A λ-shaped heat capacity anomaly was observed for MnCl₂ · 4D₂O at 48 K. The entropy associated with the anomaly is 1.2 ± 0.2 J/mole K.     

Heat capacity of a polydiacetylene single crystal from 3 to 300 K

Heat capacities C_p of a polydiacetylene-bis(toluene sulfonate) single crystal and its monomer have been measured in the temperature range from 3 to 300 K. The temperature dependence of C_p for both monomer and polymer crystals differs from that for monoatomic solids. By applying a chain lattice model for a polymer crystal, the temperature dependence of the heat capacity can be described assuming a phonon density of states given by bending and stretching modes of the polymer backbone. With a combination of one-dimensional and three-dimensional elastic continuum approximations, the heat capacity has been calculated and a good fit to the data has been obtained. A small peak in C_p was detected at 161 K for the monomer and at 198 K for the polymer. This may be ascribed to a lower-temperature phase transition in the polydiacetylene crystals evidenced by previous x-ray and spectroscopic measurements.     

Low-temperature thermal properties of Pb2P2Se6 and Pb1.424Sn0.576P2Se6

The heat capacities of Pb₂P₂Se₆ and Pb_1.424Sn_0.576P₂Se₆ were measured at temperatures between 10 and 320 K for the former and between 10 and 330 K for the latter. The heat capacities values were analyzed by harmonic approximation using the Debye and Einstein functions. They were calculated using 3 Debye and 7, 7, 7, 6 Einstein sets. The calculated heat capacities were in good agreement with the observed ones.     

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.     

The thermodynamic properties of crystalline Sr<Subscript>0.5</Subscript>Zr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> phosphate from <Emphasis Type="Italic">T</Emphasis> → 0 to 665 K

The temperature dependence of the heat capacity of crystalline Sr_0.5Zr₂(PO₄)₃ phosphate was studied by precision adiabatic vacuum and dynamic scanning calorimetry over the temperature range 7–665 K. The low-temperature dependence of the heat capacity was analyzed using the Debye theory of the heat capacity of solids and its multifractal generalization, which allowed conclusions to be drawn about the heterodynamic characteristics of the structure. The experimental data obtained were used to calculate the standard thermodynamic functions of Sr_0.5Zr₂(PO₄)₃ from T → 0 to 665 K. The standard absolute entropy of Sr_0.5Zr₂(PO₄)₃ was in turn used to calculate the standard entropy of its formation from simple substances at 298.15 K.     

Heat capacities of solid copoly(amino acid)s

Recently heat capacities C_p of poly(amino acid)s of all naturally occurring amino acids have been determined. In a second step the heat capacities of four copoly(amino acid) s are studied in this research. Poly(L -lysine · HBr-alanine), poly(L -Lysine · HBr-phenylalanine), poly(sodium-L -glutamate-tyrosine), and poly(L -proline-glycine-proline) heat capacities are measured by differential scanning calorimetry in the temperature range 230–390 K. This is followed by an analysis using approximate group vibrations and fitting the C_p contributions of the skeletal vibrations of the corresponding homopolymers to a two-parameter Tarasov function. Good agreement is found between experiment and calculation. Predictions of heat capacities based on homopoly(amino acid)s are thus expected to be possible for all polypeptides, and enthalpies, entropies, and Gibbs functions for the solid state can be derived.     

The thermodynamic properties of (2,2′-dipyridyl)bis(4-chloro-3,6-di-tert-butyl-<Emphasis Type="Italic">o</Emphasis>-benzosemiquinone)cobalt

The heat capacity of paramagnetic (2,2′-dipyridyl)bis(4-chloro-3,6-di-tert-butyl-o-benzosemi-quinone)cobalt was studied over the temperature range 8–390 K by precision adiabatic vacuum and high-accuracy dynamic calorimetry. The physical transformation observed at 309–388 K was caused by the transition of the semiquinone-catecholate to bis-semiquinone form of the complex. Above 388 K, thermal destruction was superimposed on the physical transition. 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 300 K. An analysis of the low-temperature heat capacity of the complex in terms of the Debye theory of the heat capacity of solids and its multifractal generalization led us to conclude that the complex had a predominantly chain structure.