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     

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.     

The heat capacity and thermodynamic functions of pyromorphite over the temperature range 5–320 K

The heat capacity of natural mineral, pyromorphite Pb₅(PO₄)₃Cl, was measured over the temperature range 4.2–320 K using low-temperature adiabatic calorimetry. An anomalous temperature dependence of heat capacity with a maximum at 273.24 K was observed between 250 and 290 K. The heat capacity, entropy, enthalpy, and reduced thermodynamic potential of pyromorphite were calculated and tabulated over the temperature range 5–320 K. The standard thermodynamic functions of the mineral are C _p298.15^o = 414.98 ± 0.44 J/(mol K), S _298.15^o = 585.31 ± 0.99 J/(mol K), H _298.15^o − H ₀^o = 80.90 ± 0.08 kJ/mol, and Φ_298.15^o = 313.97 ± 0.84 J/(mol K).     

Phase transitions in mesophase macromolecules. VI. The transitions in poly(oxy-2,2′-dimethylazoxybenzene-4,4′-diyloxydodecanedioyl)

The transitions of poly(oxy-2,2′-dimethylazoxybenzene-4,4′-diyloxydodecanedioyl) (PDAD) have been analyzed by differential scanning calorimetry, optical microscopy, and light scattering. The mesophase glass devitrifies at 288 K [ΔC_p = 220 J/K mol]. Crystallization from the liquid mesophase can be described between 322 and 362 K by an Avrami expression with an exponent between 3 and 4. Results of light scattering and optical microscopy are in accord with a spherulitic morphology grown after athermal nucleation. Melting of the semicrystalline samples (crystallinity up to 58%) occurs at about 391 K. The heat of fusion of the completely crystalline sample is calculated to be only 13.55 kJ/mol. The mesophase to isotropic phase transition occurs at 418 K with a heat of transition of 4.1 kJ/mol. A general discussion of these transitions is given.     

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     

Phase transition in V5O9

Electrical resistivity, magnetic susceptibility, and heat capacity of V₅O₉ have been measured through its phase transition temperature (T_t) around 129 K. The associated changes in enthalpy and entropy were found to be 2095 J/mole and 19.24 J/mole · deg., respectively. A qualitative thermodynamic analysis has been attempted to correlate the crystal symmetry, electrical, magnetic, and heat capacity behavior at T_t. The metal-semiconductor transition appears as a consequence of the crystallographic order-disorder process, since the electrical and magnetic contributions to configurational entropy change are relatively small.     

Heat capacity and magnetic phase transition of two-dimensional metal-assembled complex (NEt<Subscript>4</Subscript>)[{Mn<Superscript>III</Superscript>(salen)}<Subscript>2</Subscript>Fe<Superscript>III</Superscript>(CN)<Subscript>6</Subscript>]

Summary Heat capacity measurements of the two-dimensional metal-assembled complex, (NEt₄)[{Mn^III(salen)}₂Fe^III(CN)₆] [Et=ethyl, salen= N,N’-ethylenebis(salicylideneaminato) dianion], were performed in the temperature range between 0.2 and 300 K by adiabatic calorimetry. A ferrimagnetic phase transition was observed at T_c1=7.51 K. Furthermore, another small magnetic phase transition appeared at T_c2=0.78 K. Above T_c1, a heat capacity tail arising from the short-range ordering of the spins characteristic of two-dimensional magnets was found. The magnetic enthalpy and entropy were evaluated to be ΔH=291 J mol^-1 and ΔS=27.4 J K^-1 mol^-1, respectively. The experimental magnetic entropy agrees roughly with ΔS=Rln(5·5·2) (=32.5 J K^-1 mol^-1; R being the gas constant), which is expected for the metal complex with two Mn(III) ions in high-spin state (spin quantum number S=2) and one Fe(III) ion in low-spin state (S=1/2). The heat capacity tail above T_c1 became small by grinding and pressing the crystal. This mechanochemical effect would be attributed to the increase of lattice defects and imperfections in the crystal lattice, leading not only to formation of the crystal with a different magnetic phase transition temperature but also to decrease of the magnetic heat capacity and thus the magnetic enthalpy and entropy.     

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     

Temperature dependence of the thermodynamic parameters of cobalt(II) clathrochelate: X-ray diffraction and calorimetric characteristics of the low temperature structural phase transition

The temperature dependence of heat capacity of the polycrystalline sample of cobalt(II) clathrochelate in a range of 6–300 K is studied. Based on the smoothed dependence C _p(T), the entropy and enthalpy values in a temperature range of 8–300 K and their standard values at 298.15 K are calculated. In the C _p(T) curve in a range of 50–70 K, a process is recorded whose entropy and enthalpy are 1.2 J·(K·mol⁻¹) and 68 J·mol⁻¹ respectively. A comparison of the results with the data of a multitemperature X-ray diffraction study makes it possible to attribute this process to the structural phase transition.     

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     

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。     

Low-temperature heat capacity and high-temperature thermal behavior of sodium lutetium molybdate phosphate Na<Subscript>2</Subscript>Lu(MoO<Subscript>4</Subscript>)(PO<Subscript>4</Subscript>)

The low-temperature heat capacity of Na₂Lu (MoO₄)(PO₄) was measured by adiabatic calorimetry in the range of 7.47–345.74 K. The experimental data were used to calculate the thermodynamic functions of Na₂Lu (MoO₄)(PO₄). At 298.15 K, the following values were obtained: C _p ⁰ (298.15 K) = 237.7 ± 0.1 J/(K mol), S ⁰(298.15 K) = 278.1 ± 0.8 J/(K mol), H ⁰(298.15 K) ? H ⁰ (0 K) = 42330 ± 20 J/mol, and Φ⁰(298.15 K) = 136.1 ± 0. 3 J/(K mol). A heat capacity anomaly was found in the range of 10-67 K with a maximum at T _tr = 39.18 K. The entropy and enthalpy of transition are ΔS = 12.39 ± 0.75 J/(K mol) and ΔH = 403 ± 16 J/mol. The thermal investigation of sodium lutetium molybdate phosphate in the high-temperature range (623–1223 K) was performed using differential scanning calorimetry. It was found that during melting in the range of 1030–1200 K, Na₂Lu(MoO₄)(PO₄) degrades to simpler compounds; the degradation scenario is verified by X-ray powder diffraction.     

Low-temperature heat capacity of L- and DL-phenylglycines

Heat capacity of crystalline L- and DL-phenylglycines was measured in the temperature range from 6 to 305?K. For L-phenylglycine, no anomalies in the C _p (T) dependence were observed. For DL-phenylglycine, however, an anomaly in the temperature range 50?C75?K with a maximum at about 60?K was registered. The enthalpy and the entropy changes corresponding to this anomaly were estimated as 20?J?mol^?1 and 0.33?J?K^?1 mol^?1, respectively. In the temperature range 205?C225?K, an unusually large dispersion of the experimental points and a small change in the slope of the C _p (T) curve were noticed. Thermodynamic functions for L- and DL-phenylglycines in the temperature range 0?C305?K were calculated. At 298.15?K, the values of heat capacity, entropy, and enthalpy are equal to 179.1, 195.3?J?K^?1 mol^?1, and 28590?J?mol^?1 for L-phenylglycine and 177.7, 196.3?J?K^?1 mol^?1 and 28570?J?mol^?1 for DL-phenylglycine. For both L- and DL-phenylglycine, the C _p (T) at very low temperatures does not follow the Debye law C ?C T ³ . The heat capacity C _p (T) is slightly higher for L-phenylglycine, than for the racemic DL-crystal, with the exception of the phase transition region. The difference is smaller than was observed previously for the L-/DL-cysteines, and considerably smaller, than that for L-/DL- serines.     

Influence of deformation on irreversible and reversible crystallization of poly(ethylene‐co‐1‐octene)

The effect of uniaxial deformation and subsequent relaxation at ambient temperature on irreversible and reversible crystallization of homogeneous poly(ethylene‐co‐1‐octene) with 38 mol % 1‐octene melt‐crystallized at 10 K min was explored by calorimetry, X‐ray scattering, and Fourier transform infrared spectroscopy. At 298 K, the enthalpy‐based crystallinity of annealed specimens increased irreversibly by stress‐induced crystallization from initially 15% to a maximum of, at least, 19% when a permanent set of more than 200% was attained. The crystallinity increased by formation of crystals of pseudohexagonal structure at the expense of the amorphous polymer, and as a result of destruction of orthorhombic crystals. The stress‐induced increase of crystallinity was accompanied by an increase in the apparent specific heat capacity from 2.44 to about 2.59 J g^?1 K^?1, which corresponds to an increase of the total reversibility of crystallization from, at least, 0.10 to 0.17% K^?1. The specific reversibility calculated for 100% crystallinity increased from 0.67 to 0.89% K^?1 and points to a changed local equilibrium at the interface between the crystal and amorphous phases. The deformation resulted in typical changes of the phase structure and crystal morphology that involve orientation and destruction of crystals as well as the formation of fibrils. The effect of the decrease of the entropy of the strained melt on the reversibility of crystallization and melting is discussed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1223–1235, 2002     

The thermodynamic properties of Ba2SrUO6

The standard enthalpy of formation of crystalline Ba₂SrUO₆ at 298.15 K was determined by reaction calorimetry (-2940.0 ± 8.5 kJ/mol). The heat capacity of the compound was measured over the temperature range 8-330 K by adiabatic vacuum calorimetry. The thermodynamic functions of Ba₂SrUO₆ were calculated. The standard entropy (-558.6 ± 2.1 J/(mol K)) and Gibbs function of formation at 298.15 K (-2773.5 ± 9.0 kJ/mol) were determined.     

The thermodynamic properties of magnesium uranoborate tetrahydrate

The standard enthalpy of formation of crystalline Mg(BUO₅)₂ · 4H₂O at 298.15 K (?5563 ± 10 kJ/mol) was determined by reaction calorimetry. The heat capacity of the compound was studied over the temperature range 8–340 K by adiabatic vacuum calorimetry, and its thermodynamic functions were calculated. The standard entropy and Gibbs function of formation at 298.15 K (?1692.2 ± 3.4 J/(mol K) and ?5059 ± 11 kJ/mol, respectively) were determined.     

The thermodynamic properties of magnesium uranoborate

The standard enthalpy of formation of crystalline Mg(BUO₅)₂ at 298.15 K (?4347.5 ± 8.0 kJ/mol) was determined by reaction calorimetry. The heat capacity of magnesium uranoborate was studied by adiabatic vacuum calorimetry over the temperature range 8–330 K. The thermodynamic functions of the compound were calculated. The standard entropy and Gibbs energy of formation at 298.15 K were found to be ?903.0 ± 2.1 J/(mol K) and ?4078.5 ± 9.0 kJ/mol, respectively.     

Enthalpy-entropy compensation in ionic micelle formation

The enthalpy-entropy compensation in ionic surfactant micellization process over a large temperature range is examined. The surfactants SDS and C₁₆TAB are investigated experimentally, and the enthalpy and entropy changes are evaluated based on phase separation or mass action models together with the other three surfactant systems. The relationship between compensation temperature and the reference temperatures is discussed.Notations C _p heat capacity change, J/mol-K - CMC critical micelle concentration,M - CMC₀ critical micelle concentration atT=T ₀,M - G Gibbs free energy change, kJ/mol - H enthalpy chang, kJ/mol - h _c enthalpy change for transfer of a methylene group to water, kJ/mol - R gas constant, 8.314 J/mol-K - S entropy change, J/mol-K - S _c entropy change for transfer of a methylene group to water, J/mol-K - S ^* entropy change atT=T ^*, J/mol-K - T temperature,K - T _c compensation temperature, K - T _H temperature at which H=0, K - T ₀ temperature at the minimum point, K - T ^* 112°C Greek Letters degree of dissociation     

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.     

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.