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.     

Calculation of the heat capacity of linear macromolecules from theta-temperatures and group vibrations

An automated computer program is presented for the calculation of heat capacity of macromolecules from skeletal vibration frequencies described by the Tarasov equation and group vibration frequencies. The heat capacities calculated for crystalline polyethylene and polytetrafluoroethylene fit well with the experimental data from our ATHAS data bank. The program will be part of the planned ATHAS Computation Center.     

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     

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     

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.     

Computation of heat capacities of solid state benzene,p-oligophenylenes and poly-p-phenylene

Heat capacities (C_p) of solid benzene, biphenyl,p-terphenyl,p-quaterphenyl, and poly-p-phenylene were analyzed using the ATHAS Scheme of computation. The calculated heat capacities based on approximate vibrational spectra of solid benzene and the series of oligomers containing additional phenylene groups were compared to experimental data newly measured and from the literature to identify possible additional large-amplitude motion. The skeletal heat capacity was fitted to the Tarasov equation to obtain the one- and three-dimensional vibration frequencies ₁ and ₃ using a new optimization approach. Their relationship to the number of phenylene groupsn is: ₁=426.0–150.3/n; and ₃=55.4+81.8/n. Except for benzene, the quantitative thermal analyses do not show significant contributions from large-amplitude motion below the melting temperatures.This work was financially supported by the Div. of Materials Res., NSF, Polymers Program, Grant # DMR 90-00520 and Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U. S. Department of Energy, under contract number DE-AC05-96OR22464.     

Heat capacity of poly(vinylidene fluoride) and polytetrafluoroethylene between 5 and 200°K

Heat capacities of poly(vinylidene fluoride) (PVF₂) and polytetrafluoroethylene (PTFE) have been measured between 5 and 100°K with an accuracy of (1–5)% by adiabatic calorimetry. Calculations based on contributions from known optical lines and the Tarasov continuum model are in good agreement with experimental results down to 30°K for PVF₂ and 10°K for PTFE, and yield characteristic temperatures θ₁ and θ₃ which are consistent with previous values determined from high-temperature (100—350°K) data. At lower temperature the measured heat capacity is significantly higher [(30–100)%] than the model prediction, and can be satisfactorily accounted for by the introduction of localized vibrators at a concentration of about 1% as compared to acoustical oscillators and at a characteristic temperature of about 20°K. Using established data on polyethylene for comparison, the principle of additivity for heat capacities is found to be valid down to at least 20°K, convering the region (<60°K) where interchain vibrations contribute significantly to the heat capacity. Possible reasons for this unexpected behavior are discussed.     

吡啶-2,6-二甲酸氢钾的合成、结构表征及热化学性质

合成了吡啶-2,6-二甲酸氢钾(KHDPC). 利用X射线单晶衍射仪确定了化合物的晶体结构. 用精密自动绝热热量计测量了其在78~360 K温度区间的低温热容. 利用最小二乘法对配合物的实验热容进行拟合, 得到热容随温度变化的多项式方程. 利用此方程计算出温度区间内的舒平热容值及相对于298.15 K时的热力学函数值. 利用Hess定律设计合理的热化学循环, 在等温环境下利用溶解-反应热量计分别测定所设计热化学反应的反应物和产物在所选溶剂中的溶解焓并计算出反应的反应焓. 最后, 计算出该化合物的标准摩尔生成焓为-(1052.69±1.52) kJ/mol.     

Heat capacities and entropies of linear,aliphatic polyesters

New measurements of the heat capacity in the melt of poly(trimethylene succinate) (PTMS), poly(trimethylene adipate) (PTMA), and poly(hexamethylene sebacate) (PHMS) from 310 to 400 K are presented. Based on these data and literature data on eight other molten polylactones and poly(ethylene sebacate) (PES), an addition scheme is developed for linear, aliphatic polyesters that leads to the equation: which represents the ATHAS-recommended melt heat capacities for all linear polyesters. Combining previously discussed solid heat capacities, derived from an approximate frequency spectrum, with the new liquid heat capacities, the various thermodynamic functions (enthalpy, entropy, and Gibbs function) could be derived using the ATHAS computation scheme. The average value of residual entropy at zero kelvin of 5.3 ± 1.8 J/(K mol) per mobile bead for glassy linear polysters was found to be somewhat higher than for many other polymers in the data bank, but closer to that observed for linear, aliphatic polyamides. The phase transitions of PTMS, PTMA, and PHMS are also analyzed using the quantitative baselines available from the heat capacity study.     

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.     

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.     

乙二胺盐酸盐的低温热容和热化学性质

合成了乙二胺盐酸盐, 并表征了其晶体结构. 测定了其在78~370 K温度区间的低温热容, 通过最小二乘法拟合得到热容对温度的多项式方程. 设计了合理的热化学循环, 测定了所设计反应的反应物和产物的溶解焓, 得到反应焓. 利用Hess定律计算出乙二胺盐酸盐的标准摩尔生成焓为-(540.74±1.33) kJ/mol. 利用紫外-可见光谱和折光指数的结果检验了所设计热化学循环的可靠性.     

2-吡嗪羧酸银的合成、晶体结构及热化学性质

以二次蒸馏水为溶剂,合成了2-吡嗪羧酸银(Ag(pyza)(s)),并利用X-射线单晶衍射法表征了其晶体结构.根据晶体结构数据计算得到2-吡嗪羧酸银的晶格能为554.10 kJ/mol.利用TG/DSC热分析技术研究了该化合物的热分解过程;用精密自动绝热热量计测量了其在78~378 K温区的低温热容;通过最小二乘法拟合得到了摩尔热容随折合温度变化的多项式方程,利用此方程计算出该化合物的舒平热容和各种热力学函数.通过设计合理的热化学循环,利用等温环境溶解-反应热量计分别测定了所设计热化学反应的反应物和产物在选定溶剂中的溶解焓,通过计算得到反应的反应焓为:?(31.919±0.526)kJ/mol.利用Hess定律计算出2-吡嗪羧酸银的标准摩尔生成焓为:?(243.659±1.298)kJ/mol.利用紫外-可见光谱仪对反应物和产物溶解所得溶液分别进行测量,从而证实了所设计热化学循环的可靠性.     

Analysis of a symmetric neopolyol ester

Quantitative thermal analysis was carried out for tetra[methyleneoxycarbonyl(2,4,4-trimethyl)pentyl]methane. The ester has a glass transition temperature of 219 K and a melting temperature of 304 K. The heat of fusion is 51.3 kJ mol^?1, and the increase in heat capacity at the glass transition is 250 J K^?1 mol^?1. The measured and calculated heat capacities of the solid and liquid states from 130 to 420 K are reported and a discussion of the glass and melting transitions is presented. The computation of the heat capacity made use of the Advanced Thermal Analysis System, ATHAS, using an approximate group-vibration spectrum and a Tarasov treatment of the skeletal vibrations. The experimental and calculated heat capacities of the solid ester were compared over the whole temperature range to detect changes in order and the presence of large-amplitude motion. An addition scheme for heat capacities of this and related esters was developed and used for the extrapolation of the heat capacity of the liquid state for this ester. The liquid heat capacity for the title ester is well represented by 691.1+1.668T [J K^?1 mol^?1]. A deficit in the entropy and enthalpy of fusion was observed relative to values estimated from empirical addition schemes, but no gradual disordering was noted outside the transition region. The final interpretation of this deficit of conformational entropy needs structure and mobility analysis by solid state¹³C NMR and X-ray diffraction. These analyses are reported in part II of this investigation.     

Analysis of the contribution of skeletal vibrations to the heat capacity of linear macromolecules in the solid state

Automatic computer programs are developed to calculate one- two-, and three-dimensional Debye functions. Prior tables of these functions are critically reviewed. Also, strategies are derived to calculate Debye temperatures from heat capacities. Both, simple three-dimensional Debye analyses and Tarasov analyses were carried out on 35 linear macromolecules. The experimental heat capacities for these analyses were collected in the ATHAS data bank. It is shown that the skeletal heat capacity of linear macromolecules is often best represented by only two vibrations per chain atom. For most of the all-carbon chain macromolecules the intramolecular skeletal heat capacity can be given by C_vs=D₁[520 (28/MW)^1/2] whereMW is the molecular mass andD ₁ represents the one-dimensional Debye function. Polyoxides show a higher intramolecular theta temperature, but a lower intermolecular theta temperature. Double bonds and phenylene groups in the chain increase the intramolecular theta temperature.Dedicated to Prof. Dr. F. H. Müller.On leave from the Lumumba Peoples' Friendship University, Moscow, USSR.     

配合物Zn(Phe)(NO3)2·H2O(s)的低温热容和标准摩尔生成焓

利用精密自动绝热热量计直接测定了配合物Zn(Phe)(NO3)2·H2O(s) (Phe:苯丙氨酸)在78-370 K温区的摩尔热容. 通过热容曲线的解析得到该配合物的起始脱水温度为, T0=(324.27±0.37) K. 将该温区的摩尔热容实验值用最小二乘法拟合得到摩尔热容(Cp, m)对温度(T)的多项式方程, 并且在此基础上计算出了它的舒平热容值和各种热力学函数值. 依据Hess定律, 通过设计热化学循环, 选择体积为100 mL浓度为2 mol·L-1 的盐酸作为量热溶剂, 利用等温环境溶解-反应热量计分别测定混合物{ZnSO4·7H2O(s)+2NaNO3(s)+L-Phe(s)}和{Zn(Phe)(NO3)2·H2O(s)+Na2SO4(s)}的溶解焓为, ⊿dH0m,1 =(69.42±0.05) kJ·mol-1, ⊿dH0 m,2 =(48.14±0.04) kJ·mol-1, 进而计算出该配合物的标准摩尔生成焓为, ⊿fH0m =-(1363.10±3.52) kJ·mol-1. 另外, 利用紫外-可见(UV-Vis)光谱和折光指数(refractiveindex)的测量结果检验了所设计的热化学循环的可靠性.     

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 poly(trimethylene terephthalate)

The heat capacity of poly(trimethylene terephthalate) (PTT) has been measured using adiabatic calorimetry, standard differential scanning calorimetry (DSC), and temperature-modulated differential scanning calorimetry (TMDSC). The heat capacities of the solid and liquid states of semicrystalline PTT are reported from 5 to 570 K. The semicrystalline PTT has a glass transition temperature of 331 K. Between 340 and 480 K, PTT can show exothermic ordering depending on the prior degree of crystallization. The melting endotherm of semicrystalline samples occurs between 480 and 505 K, with a typical onset temperature of 489 K (216°C). The heat of fusion of the semicrystalline samples is about 15 kJ mol⁻¹. For 100% crystalline PTT the heat of fusion is estimated to be 30 ± 2 kJ mol⁻¹. The heat capacity of solid PTT is linked to an approximate group vibrational spectrum and the Tarasov equation is used to estimate the heat capacity contribution due to skeletal vibrations (θ₁ = 550.5 K and θ₂ = θ₃ = 51 K, N_skeletal = 19). The calculated and experimental heat capacities agree to better than ±3% between 5 and 300 K. The experimental heat capacities of liquid PTT can be expressed by: $ C^L_p(exp) $ = 211.6 + 0.434 T J K⁻¹ mol⁻¹ and compare to ±0.5% with estimates from the ATHAS data bank using contributions of other polymers with the same constituent groups. The glass transition temperature of the completely amorphous polymer is estimated to be 310–315 K with a ΔC_p of about 94 J K⁻¹ mol⁻¹. Knowing C_p of the solid, liquid, and the transition parameters, the thermodynamic functions enthalpy, entropy, and Gibbs function were obtained. With these data one can compute for semicrystalline samples crystallinity changes with temperature, mobile amorphous fractions, and resolve the question of rigid-amorphous fractions.© 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2499–2511, 1998     

Effect of rapid solidification on heat capacities of Al-Sr alloys

Heat capacities of both the ingot-like and melt-spun Al-Sr alloys have been measured through the temperature range 373 to 1060 K using differential scanning calorimetry. The experimental results show that rapid solidification has a slight effect on the temperature dependence of the heat capacities of the Al-Sr alloys. The heat capacities of the melt-spun Al-Sr alloys increase more slowly than those of the ingot-like alloys with increasing temperature from 373 to 900 K. Furthermore, the effect of rapid solidification on the heat capacities becomes more obvious with increasing Sr concentration in the Al-Sr alloys. The data of the heat capacities between 373 and 900 K have been fitted with the least square method and a linear dependence on temperature was assumed for that temperature range. This revised version was published online in July 2006 with corrections to the Cover Date.     

吡啶-2,6-二甲酸氢锂的合成、结构及热化学性质

以甲醇和水的混合溶液为溶剂, 合成了吡啶-2,6-二甲酸氢锂Li(HDPC)(H₂O)(s), 利用X射线单晶衍射法表征了其晶体结构. 用精密自动绝热热量计测量了其在78～378 K温区的低温热容. 通过最小二乘法拟合得到摩尔热容随折合温度变化的多项式方程, 利用此方程计算出了化合物的舒平热容和各种热力学函数. 设计合理的热化学循环, 利用等温环境溶解-反应热量计分别测定所设计热化学反应的反应物和产物在选定溶剂中的溶解焓, 通过计算得到反应焓为-(46.83 ±0.16) kJ/mol. 利用Hess定律计算出吡啶-2,6-二甲酸氢锂的标准摩尔生成焓为-(747.90 ±1.46) kJ/mol. 利用紫外-可见光谱仪对反应物和产物溶液的测量证实所设计热化学循环的可靠性.