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     

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     

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     

Analysis of the residual entropy of amorphous polyethylene at 0 K*

The residual entropy of amorphous polyethylene (PE) at 0 K is discussed within the framework of the heat capacity (C_p). The measured C_p of the liquid was extended from the glass transition to low temperature by separately finding its three parts—the vibrational, conformational, and external contributions—and extrapolating each to low temperature. The vibrational C_p was calculated from the frequency distributions of the group vibrations on the basis of force constants obtained from experimental infrared and Raman spectra as well as the skeletal vibrations in the amorphous solid (glass) obtained from fitting of the appropriate experimental C_p to Debye functions in the form suggested by Tarasov. The conformational part of C_p was evaluated from a fit of the heat capacity of the liquid, decreased by the contributions of the vibrational and external parts, to a one‐dimensional Ising model that can be extrapolated to 0 K and requires two discrete states described by stiffness, cooperativity, and a degeneracy parameter. The external part was computed from the experimental data for expansivity and compressibility, fitted to an empirical equation of state, and modified at low temperatures in accordance with the Nernst–Lindemann approximation. The computed C_p of the liquid PE agreed with the experiment from 600 K to the beginning of the glass transition at about 260 K. Extending the heat capacity to 0 K, bypassing the freezing of the large‐amplitude conformational motion in the glass transition, led to a positive residual entropy and enthalpy and avoided the so‐called Kauzmann paradox. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1245–1253, 2002     

Reversible and irreversible heat capacity of poly[carbonyl(ethylene‐co‐propylene)] by temperature‐modulated calorimetry

The heat capacity of poly[carbonyl(ethylene‐co‐propylene)] with 95 mol % C₂H₄? CO? (Carilon EP®) was measured with standard differential scanning calorimetry (DSC) and temperature‐modulated DSC (TMDSC). The integral functions of enthalpy, entropy, and free enthalpy were derived. With quasi‐isothermal TMDSC, the apparent reversing heat capacity was determined from 220 to 570 K, including the glass‐ and melting‐transition regions. The vibrational heat capacity of the solid and the heat capacity of the liquid served as baselines for the quantitative analysis. A small amount of apparent reversing latent heat was found in the melting range, just as for other polymers similarly analyzed. With an analysis of the heat‐flow rates in the time domain, information was collected about latent heat contributions due to annealing, melting, and crystallization. The latent heat decreased with time to an even smaller but truly reversible latent heat contribution. The main melting was fully irreversible. All contributions are discussed in the framework of a suggested scheme of six physical contributions to the apparent heat capacity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1565–1577, 2001     

Enthalpies of Phase Transitions and Heat Capacity of TbCl3 and Compounds Formed in TbCl3–MCl Systems (M=K, Rb, Cs)

The molar enthalpies of the solid–solid and solid–liquid phase transitions were determined by differential scanning calorimetry for pure TbCl₃ and KTb₂Cl₇, RbTb₂Cl₇, CsTb₂Cl₇, K₃TbCl₆, Rb₃TbCl₆ and Cs₃TbCl₆ compounds. Both types of compounds, i.e. M₃TbCl₆ and MTb₂Cl₇ (M=K, Rb, Cs) melt congruently and show additionally a solid–solid phase transition with a corresponding enthalpy Δ_trs H ⁰ of 6.1, 7.6 and 7.0 kJ mol^–1 for potassium, rubidium and caesium M₃TbCl₆ compounds andΔ_trs H ⁰ of 17.1 (rubidium) and of 12.1 and 10.9 kJ mol^–1 (caesium) for MTb₂Cl₇ compounds, respectively. The enthalpies of fusion were measured for all the above compounds with the exception of Rb₃TbCl₆ and Cs₃TbCl₆. The heat capacities of the solid and liquid compounds have been determined by differential scanning calorimetry (DSC) in the temperature range 300–1100 K. The experimental heat capacity strongly increases in the vicinity of a phase transition, but varies smoothly in the temperature ranges excluding these transformations. C _p data were fitted by an equation, which provided a satisfactory representation up to the temperatures of C _p discontinuity. The measured heat capacities were checked for consistency by calculating the enthalpy of formation of the liquid phase, which had been previously measured. The results obtained agreed satisfactorily with these experimental data. This revised version was published online in August 2006 with corrections to the Cover Date.     

水与正丁醇二元体系最低共沸混合物的热容

Molar heat capacities of n-butanol and the azeotropic mixture in the binary system [water （x=0.716） plus n-butanol （x=0.284）] were measured with an adiabatic calorimeter in a temperature range from 78 to 320 K. The functions of the heat capacity with respect to thermodynamic temperature were estabhshed for the azeotropic mixture. A glass transition was observed at （111.9±1.2） K. The phase transitions took place at （179.26±0.77） and （269.69±0.14） K corresponding to the solid-hquid phase transitions of n-butanol and water, respectively. The phase-transition enthalpy and entropy of water were calculated. A thermodynamic function of excess molar heat capacity with respect to temperature was estabhshed, which took account of physical mixing, destructions of self-association and cross-association for n-butanol and water, respectively. The thermodynamic functions and the excess thermodynamic ones of the binary systems relative to 298.15 K were derived based on the relationships of the thermodynamic functions and the function of the measured heat capacity and the calculated excess heat capacity with respect to temperature.     

Crystal Structure, Phase Transition, and Thermodynamic Properties of Bis-dodecylammonium Tetrachlorozincate (C12H25NH3)2ZnCl4(s)

The crystal structure and composition of (C₁₂H₂₅NH₃)₂ZnCl₄(s) were characterized by chemical and elemental analysis, X‐ray powder diffraction technique and X‐ray crystallography. The lattice energy of the title compound was calculated to be U_POT=888.82 kJ·mol^?1. Low temperature heat capacities of the title compound have been measured by a precision automated adiabatic calorimeter over the temperature range from 80 to 403 K. An obvious solid to solid phase transition occurred in the heat capacity curve, and the peak temperature, molar enthalpy and molar entropy of the phase transition of the compound were determined to be T_trs= (364.02±0.03) K, (_trsH_m= (77.567±0.341) kJ·mol^?1, and (_trsS_m= (213.77±1.17) J·K^?1·mol^?1, respectively. Experimental molar heat capacities before and after the phase transition were respectively fitted to two polynomial equations. The smoothed molar heat capacities and fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K were calculated and tabulated at an interval of 5 K.     

The thermal properties of poly(pivalolactone)

Quantitative thermal analysis was carried out for poly-(pivalolactone) (PPVL), including heat capacity determinations from 140 to 550 K. The experimental C_p below the glass transition temperature was fitted to an approximate vibrational spectrum and the ATHAS computation scheme was used to compute the “vibration only” heat capacities from 0.1 to 1000 K. The liquid C_p was derived from an empirical addition scheme and found to agree with the experimental C_p with an RMS of ±2.8% from 240 K to 550 K. A glass transition, T_g, could be detected at 260 K, and the change in heat capacity for 100% amorphous PPVL was calculated to be 38.8 J/(K mol). Above T_g, semicrystalline samples seem to show a rigid amorphous fraction that does not contribute to the increase in heat capacity at T_g. Using the ATHAS recommended heat capacities, the various thermodynamic functions (enthalpy, entropy, and Gibbs function) were derived. The residual entropy at 0 K for the amorphous PPVL was calculated to be 5.2 J/(K mol) per mobile bead, and was comparable to that obtained for a series of linear, aliphatic polyesters analyzed earlier.     

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.     

苏糖酸钾的低温热溶及标准摩尔生成焓测定

以苏糖酸与碳酸氢钾反应制得苏糖酸钾K(C₄H₇O₅)·H₂O，通过红外光谱、热重、化学分析及元素分析等对其进行了表征。用精密自动绝热热量计测量了该化合物在78K-395K温区的摩尔热容。实验结果表明，该化合物存在明显的脱水转变，其脱水浓度、摩尔脱水焓以及摩尔脱水熵分别为：(380.524 ± 0.093) K，(19.655 ± 0.012) kJ/mol 和 (51.618 ± 0.051) J/（K·mol）。将78K-362K和382K-395K两个温区的实验热容值用最小二乘法拟合，得到了两个表示热容随温度变化的多项式方程。以RBC-II型恒容转动弹热量计测定目标化合物的恒容燃烧能为(-1749.71 ± 0.91) kJ/mol，计算得到其标准摩尔生成焓为(-1292.56 ± 1.06) kJ/mol。     

Enthalpy of Phase Transitions and Heat Capacity of Stoichiometric Compounds in LaBr3-MBr Systems (M=K,Rb, Cs)

Molar enthalpies of solid-solid and solid-liquid phase transitions of the LaBr₃, K₂LaBr₅, Rb₂LaBr₅, Rb₃LaBr₆ and Cs₃LaBr₆ compounds were determined by differential scanning calorimetry. K₂LaBr₅ and Rb₂LaBr₅ exist at ambient temperature and melt congruently at 875 and 864 K, respectively, with corresponding enthalpies of 81.5 and 77.2 kJ mol^-1. Rb₃LaBr₆ and Cs₃LaBr₆ are the only 3:1 compounds existing in the investigated systems. The first one forms from RbBr and Rb₂LaBr₅ at 700 K with an enthalpy of 44.0 kJ mol^-1 and melts congruently at 940 K with an enthalpy of 46.7 kJ mol^-1. The second one exists at room temperature, undergoes a solid-solid phase transition at 725 K with an enthalpy of 9.0 kJ mol^-1 and melts congruently at 1013 K with an enthalpy of 57.6 kJ mol^-1. Two other compounds existing in the CsBr-based systems (Cs₂LaBr₅ and CsLa₂Br₇) decompose peritectically at 765 and 828 K, respectively. The heat capacities of the above compounds in the solid as well as in the liquid phase were determined by differential scanning calorimetry. A special method - 'step method' developed by SETARAM was applied in these measurements. The heat capacity experimental data were fitted by a polynomial temperature dependence. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermodynamic investigation of room temperature ionic liquid

The molar heat capacities of the room temperature ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate (BMIBF₄) were measured by an adiabatic calorimeter in temperature range from 80 to 390 K. The dependence of the molar heat capacity on temperature is given as a function of the reduced temperature X by polynomial equations, C _P,m (J K^–1 mol^–1)= 195.55+47.230 X–3.1533 X ²+4.0733 X ³+3.9126 X ⁴ [X=(T–125.5)/45.5] for the solid phase (80~171 K), and C _P,m (J K^–1 mol^–1)= 378.62+43.929 X+16.456 X ²–4.6684 X ³–5.5876 X ⁴ [X=(T–285.5)/104.5] for the liquid phase (181~390 K), respectively. According to the polynomial equations and thermodynamic relationship, the values of thermodynamic function of the BMIBF₄ relative to 298.15 K were calculated in temperature range from 80 to 390 K with an interval of 5 K. The glass translation of BMIBF₄ was observed at 176.24 K. Using oxygen-bomb combustion calorimeter, the molar enthalpy of combustion of BMIBF₄ was determined to be Δ_c H _m ^o= – 5335±17 kJ mol^–1. The standard molar enthalpy of formation of BMIBF₄ was evaluated to be Δ_f H _m ^o= –1221.8±4.0 kJ mol^–1 at T=298.150±0.001 K.     

Low‐Temperature Heat Capacities and Standard Molar Enthalpy of Formation of Gramine (C11H14N2)

Low‐temperature heat capacities of gramine (C₁₁H₁₄N₂) were measured by a precision automated adiabatic calorimeter over the temperature range from 78 to 401 K. A polynomial equation of heat capacities as a function of temperature was fitted by least squares method. Based on the fitted polynomial, the smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15 K were calculated and tabulated at 5 K intervals. The constant‐volume energy of combustion of the compound at T=298.15 K was measured by a precision oxygen‐bomb combustion calorimeter as Δ_cU=−(35336.7±13.9) J·g⁻¹. The standard molar enthalpy of combustion of the compound was determined to be Δ_cH_m⁰=−(6163.2±2.4) kJ·mol⁻¹, according to the definition of combustion enthalpy. Finally, the standard molar enthalpy of formation of the compound was calculated to be Δ;_cH_m⁰=−(166.2±2.8) kJ·mol⁻¹ in accordance with Hess law.     

Thermal properties of seed proteins

The sample of LiCoO₂ was synthesized, and the heat capacity was measured by adiabatic calorimetry between 13 and 300 K. The smoothed values of the heat capacity were calculated from the data. The thermodynamic functions, standard enthalpy, entropy and Gibbs energy, of LiCoO₂ were calculated from the heat capacity and the numerical values are tabulated at selected temperatures from 15 to 300 K. The heat capacity, enthalpy, entropy, and Gibbs energy at T=298.15 K are 71.57 J K^–1mol^–1, 9.853 kJ mol^–1, 52.45 J K^–1 mol^–1, –5.786 kJ mol^–1, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Heat Capacities of Three Isomeric Chlorobenzenes and of Three Isomeric Chlorophenols

Isobaric heat capacities C _p in the liquid and in the solid phase of 1,2-dichlorobenzene, 1,3-dichlorobenzene, 1,2,4-trichlorobenzene, 3-chlorophenol and 4-chlorophenol and in the liquid phase of 2-chlorophenol were measured by commercial Setaram heat conduction and power compensated calorimeters. Results obtained cover the following temperature range (depending on the compound and state of aggregation): 1,2-dichlorobenzene 208 to 323 K,1,3-dichlorobenzene 183 to 323 K, 1,2,4-trichlorobenzene 133 to 323 K, 2-chlorophenol from293 to 353 K, 3-chlorophenol and 4-chlorophenol from 133 to 353 K. The heat capacity data obtained in this work were merged with available experimental data from literature, critically assessed and sets of recommended data were developed by correlating selected data as a function of temperature. Temperature and enthalpy of fusion of two isomeric chlorophenols and of 1,2,4-trichlorobenzene were also determined. This revised version was published online in August 2006 with corrections to the Cover Date.     

Heat Capacities and Thermodynamic Properties of a H2O + Li2B4O7 Solution in the Temperature Range from 80 to 356 K

The molar heat capacities of an aqueous Li₂B₄O₇ solution were measured with a precision automated adiabatic calorimeter in the temperature range from 80 to 356 K at a concentration of 0.3492 mol⋅kg⁻¹. The occurrence of a phase transition was determined based on the changes in the curve of the heat capacity with temperature. A phase transition was observed at 271.72 K corresponding to the solid-liquid phase transition; the enthalpy and entropy of the phase transition were evaluated to be Δ H _m = 4.110 kJ⋅mol⁻¹ and Δ S _m = 15.13 J⋅K⁻¹⋅mol⁻¹, respectively. Using polynomial equations and thermodynamic relationship, the thermodynamic functions [H _T −H _298.15] and [S _T −S _298.15] of the aqueous Li₂B₄O₇ solution relative to 298.15 K were calculated in temperature range 80 to 355 K at intervals of 5 K. Values of the relative apparent molar heat capacities of the aqueous Li₂B₄O₇ solution, C _p,φ, were calculated at every 5 K in temperature range from 80 to 355 K from the experimental heat capacities of the solution and the heat capacities of pure water.     

Thermodynamic investigation of several natural polyols

The low-temperature heat capacity C _p,m of erythritol (C₄H₁₀O₄, CAS 149-32-6) was precisely measured in the temperature range from 80 to 410 K by means of a small sample automated adiabatic calorimeter. A solid-liquid phase transition was found at T=390.254 K from the experimental C _p-T curve. The molar enthalpy and entropy of this transition were determined to be 37.92±0.19 kJ mol⁻¹ and 97.17±0.49 J K⁻¹ mol⁻¹, respectively. The thermodynamic functions [H _T-H _298.15] and [S _T-S _298.15], were derived from the heat capacity data in the temperature range of 80 to 410 K with an interval of 5 K. The standard molar enthalpy of combustion and the standard molar enthalpy of formation of the compound have been determined: Δ_c H _m⁰(C₄H₁₀O₄, cr)= −2102.90±1.56 kJ mol⁻¹ and Δ_f H _m⁰(C₄H₁₀O₄, cr)= − 900.29±0.84 kJ mol⁻¹, by means of a precision oxygen-bomb combustion calorimeter at T=298.15 K. DSC and TG measurements were performed to study the thermostability of the compound. The results were in agreement with those obtained from heat capacity measurements.     

无水烟酸钾的合成、表征及热化学

选择分析纯烟酸和无水醋酸钾为反应物, 利用室温固相合成方法, 合成了无水烟酸钾. 利用FTIR和X射线粉末衍射等方法表征了它的结构. 用精密自动绝热热量计测定了它在77～400 K温区的低温热容, 将该温区的摩尔热容实验值用最小二乘法拟合, 得到热容随温度变化的多项式方程. 用此方程进行数值积分, 得到此温区内每隔5 K的舒平热容值和相对于298.15 K时的各种热力学函数值. 在此基础上, 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固相反应的反应物和生成物在所选溶剂中的溶解焓, 从而得到该固相反应的反应焓为 (25.87±0.47) kJ•mol^－1. 最后, 依据Hess定律计算出烟酸钾的标准摩尔生成焓为 ＝－(560.57±1.09) kJ•mol^－1.     

Measurement of high temperature heat content of silicon by drop calorimetry

Heat content of silicon has been measured in a temperature range of 700-1820 K using a drop calorimeter. Boron nitride was used as a sample crucible. The enthalpy of fusion and the melting point of silicon determined from the heat content-temperature plots are 48.31±0.18 kJ mol^-1 and 1687±5 K, respectively. The heat content and heat capacity equations were derived using the Shomate function for the solid region and the least square method for the liquid region, respectively, and compared with the literature values. This revised version was published online in August 2006 with corrections to the Cover Date.