The heat capacity of lead from 300 to 850°k: conversion of cp to cv for liquid lead

Abstract

Recent measurements of the heat capacity at constant pressure C_p for lead from 300 to 850°K have shown that C_p for liquid lead decreases continuously from the melting point to 850°K. Using data in the literature of density and velocity of sound, the dilation correction has been applied to C_p to obtain the heat capacity at constant volume C_v for liquid lead. Application of the dilation correction to solid lead gives a C_v curve which uncreases only about one joule/gm-atom-°K from 300 to 600°K, whereas the C_v curve for liquid lead decreases almost 5 joules/gm-atom-°K from 600 to 850°K. A careful assessment of the uncertainty in the quantities used in the dilation correction leads to an uncertainty in C_v of ± 2.5% (about one joule/gm-atom-°K), and thus the decrease in C_v for liquid lead is quite real.     

Melting behavior of highly stretched isotactic polypropylene film

Isotactic polypropylene film was stretched in poly(ethylene glycol) at 140°C and its melting behavior was investigated by using a differential scanning calorimeter (DSC-1B). The shape of the melting curve depends largely on the stretching ratio, v. A sample stretched to moderate extension (1 < v < 3.5–4) has only a single melting peak (163°C) in the thermogram. When the sample is stretched beyond v = 3.5–4, the thermogram becomes more and more complex with increase of v, and some peaks appear when stretched to 10 < v < 13. The lowest peak which is considered to be the melting peak of the intermolecular crystals produced by the unfolding of chain molecules in the lamellae develops gradually with increase of v. In the thermogram for v = 18 the lowest temperature peak is most pronounced, in contrast to the highest temperature peak which decreases markedly in intensity. The phenomenon shows that large amounts of lamellar crystals are converted to intermolecular crystals in this region. On further stretching (v > 20) a very sharp high temperature peak appears, whose half-width is about 1°C. Qualitatively similar results were obtained for the samples stretched in poly(ethylene glycol) at 150°C and in air at 140 and 150°C.     

Time and temperature-based study for the production of high T C phase by sol-gel technique in Pb-bscco system

The high T_C superconducting phase Bi₂Sr₂Ca₂Cu₃Ox (2223) in the Pb-BSCCO system has been produced by EDTA-gel processing using nitrate solutions. The precursor has heated in two stages, at 300 and 800°C each for 2 h, to avoid the burning of the important species involved in the final product. The effects of time (6 to 48 h) and temperature (845 and 855°C) on the formation of the 2223 phase have been studied by sintering the samples in air. Thermal analysis (TG/DTA), X-ray diffraction (XRD), scanning electron microscopy (SEM) and a vibrating sample magnetometer (VSM) have been employed to investigate the powder produced at different stages of decomposition, oxidation and formation of sintered materials from the powders. The volume-fraction of the 2223 phase at 845°C increases with time, the maximum value of the 2223 phase was obtained at 120 h. It has been observed that the formation of the high T_C phase is remarkably enhanced at the temperature of the endothermic peak of the DTA curve. The best result has been obtained in the sample sintered for 24 h at the temperature 855°C (endothermic peak). This also indicated that at 855°C, the large volume-fraction of 2223 phase with T_C 113 K grew in short time and as the sintering time increased, it decomposed into the Bi₂Sr₂CaCu₂Ox (2212) phase and other phases.     

The low‐temperature phase of 1,3‐di­bromo‐2,4,6‐tri­methyl­benzene: a single‐crystal neutron diffraction study at 120 and 14 K

In the low‐temperature phase of di­bromo­mesityl­ene (1,3‐di­bromo‐2,4,6‐tri­methyl­benzene), C₉H₁₀Br₂, the mol­ecule deviates significantly from the C_3h molecular symmetry encountered in tri­bromo­mesityl­ene (1,3,5‐tri­bromo‐2,4,6‐tri­methyl­benzene), even for the endocyclic bond angles. An apparent C_2v molecular symmetry is observed. The angle between the normal to the molecular plane and the normal to the (100) plane is ∼20°. The overall displacement was analysed at 120 K with rigid‐body‐motion tensor analysis. The methyl group located intermediate between the two Br atoms is rotationally disordered at both temperatures. This disorder was treated using two different approaches at 14 K, viz. the conventional split‐atom model and a model using the special annular shapes of the atomic displacement parameters that are available in CRYSTALS [Watkin, Prout, Carruthers & Betteridge (1999). Issue 11. Chemical Crystallography Laboratory, Oxford, England], but only through the latter approach at 120 K. The disorder locally breaks the C_2v molecular symmetry at 14 K only. Intra‐ and intermolecular contacts are described and discussed in relation to this methyl‐group disorder. The bidimensional pseudo‐hexagonal structural topology of tri­halogeno­mesityl­enes is altered in di­bromo­mesityl­ene insofar as the (100) molecular layers are undulated and are not coplanar as a result of an alternating tilt angle of ∼34° propagating along the [011] and [01] directions between successive antiferroelectric molecular columns oriented roughly along the a axis.     

The thermodynamic properties of polytetrafluoroethylene

Polytetrafluoroethylenes of different crystallinity were analyzed between 220 and 700 K by differential scanning calorimetry. A new computer coupling of the standard DSC is described. The measured heat capacity data were combined with all literature data into a recommended set of thermodynamic properties for the crystalline polymer and a preliminary set for the amorphous polymer (heat capacity, enthalpy, entropy, and Gibbs energy; range 0–700 K). The crystal heat capacities have been linked to the vibrational spectrum with a θ₃ of 54 K, and θ₁ of 250 K, and a full set of group vibrations. C_v to C_p conversion was possible with a Nernst–Lindemann constant of A = 1.6 × 10^?3 mol K/J. The glass transition was identified as a broad transition between 160 and 240 K with a ΔC_p of 9.4 J/K mol. The room-temperature transitions at 292 and 303 K have a combined heat of transition of 850 J/mol and an entropy of transition of 2.90 J/K mol. The equilibrium melting temperature is 605 K with transition enthalpy and entropy of 4.10 kj/mol and 6.78 J/K mol, respectively. The high-temperature crystal from is shown to be a condis crystal (conformationally disordered), and for the samples discussed, the crystallinity model holds.     

IR matrix spectra of CsNO2, RbNO2, KNO2, and NaNO2. The structure of CsNO2

The IR spectra of alkali nitrites were studied in Ar matrices at the temperature of 7 K. The spectra of CsNO₂ were investigated with the aid of ¹⁵N and ¹⁸O isotopes in order to determine the structure of the gaseous molecules. The IR spectra of ¹⁸O-enriched CsNO₂ samples were recorded and the results interpreted by means of normal coordinate calculations. CsNO₂ has a planar ring structure of C_2v, symmetry. The bond angle ONO of this molecule was calculated to be 116 ± 5°. NaNO₂ as well as the remaining alkali nitrites have C_2v, symmetry structures. Far-IR spectra of alkali nitries were recorded in order to measure the interionic stretching vibrations; in some case low-frequency bands were observed and assigned to the A₁ and B₁ interionic stretching modes.     

Thermodynamic properties of α-platinum dichloride

The heat capacity of crystalline α-platinum dichloride was measured for the first time in the temperature intervals from 11 to 300 K (vacuum adiabatic microcalorimeter) and from 300 to 620 K (differential scanning calorimetry). In the 300–620 K temperature interval, the C° _p values for α-PtCl₂ (cr) coincide with the heat capacity of CrCl₂ (cr) within the limits of experimental error, which made it possible to estimate the heat capacity of α-PtCl₂ (cr) at higher temperatures. The approximating equation of the temperature dependence of the heat capacity in the interval from 298 to 900 K C° _p (±0.8) = 63.5 + 21.4·10⁻³ T + 0.883·10⁵/T ² (J mol⁻¹ K⁻¹) was derived using the experimental values, as well as the literature data on the heat capacity of CrCl₂ (cr). For the standard conditions, the C° _p,298.15 and S°_298.15 values are 70.92±0.08 and 100.9±0.33 J mol⁻¹ K, respectively; H°_298.15 − H°₀ = 14 120±42 J mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1136–1138, June, 2008.     

Kinetic Study of the Degradation of PAC-1 and Identification of a Degradation Product in Alkaline Condition

A selective and validated stability-indicating LC method was developed for the kinetic study of the degradation of PAC-1, which was carried out in aqueous solutions at 37, 60, 80 and 100 °C with pH 1.5–9.0. Separation was performed on a Kromasil C₁₈ column with acetonitrile–water–fomic acid (30:70:0.1, v/v/v) as mobile phase with a flow rate of 1.0 mL min⁻¹ at 281 nm. The degradation rate obtained indicated a first-order reaction law and the activation energy (E _a) was calculated. The results showed that temperature and pH values were significant factors affecting the degradation of PAC-1. An unknown degradation product in alkaline condition was isolated using a reverse-phase semi-preparative LC system. The structure of the degradation product is identified as 2-hydroxy-3-(2-propenyl)-[[2-hydroxy-3-(2-propenyl)phenyl]methylene]hydrazone utilizing the ¹H NMR, ¹³C NMR, IR and Q-TOF-MS techniques.

     

Influence of temperature on sage seed gum (Salvia macrosiphon) rheology in dilute and concentrated regimes

Herein, the influence of temperature (10°C, 30°C, 50°C, 70°C, and 90°C) on the dynamic (using amplitude sweep, frequency sweep, and temperature sweep tests), steady-shear, thixotropy (using hysteresis loop, single shear decay, and in-shear structural recovery tests), yield stress (static and dynamic yield stresses), and dilute solution (intrinsic viscosity ([η]), voluminosity (v_s), shape factor (v), Berry number (C[η]), and chain flexibility) properties of sage seed gum (SSG) have been studied. In this way, the effect of type of thermal procedure (iso-thermal and non-isothermal), temperature program (temperature gradient and temperature profile sweeps), and the rate of thermal program (1, 5, and 10°C/min) on the structural changes during heating and cooling stages were also investigated. Furthermore, the time–temperature superposition and Cox–Merz rules were tested on dynamic and steady shear rheological data.     

Relaxation of DF(v = 1) by various polyatomic molecules

By means of the technique of laser-induced fluorescence, the room-temperature vibrational relaxation of DF(v = 1) has been studied in the presence of several polyatomic chaperones. The rate coefficients obtained [in units of (μ;sec·torr)^?1] are CH₄, 0.22; C₂H₆, 0.61; C₄H₁₀, 1.26; C₂H₂, 4.0 × 10^?2; C₂H₂F₂, 1.86 × 10^?2; C₂H₄, 0.175; CH₃F, 0.36; CF₃H, 1.95 × 10^?2; CF₄, 1.0 × 10^?3; CBrF₃, 5.6 × 10^?4; NF₃, 5.1 × 10^?4; SO₂, 1.27 × 10^?2; and BF₃, 7.1 × 10^?3. Results are also reported for vibrational relaxation rate coefficients for HF(v = 1) in the presence of the following chaperones: CH₄, 2.6 × 10^?2; C₂H₆, 5.9 × 10^?2; C₃H₈, 8.4 × 10^?2; and C₄H₁₀, 0.128. A comparison of DF and HF results indicates that for deactivation by C_nH_n+2, rate coefficients for DF are approximately an order of magnitude larger than for HF. The deactivation rate coefficient of DF(v = 1) by CH₄ was found to decrease with increasing temperature between 300 and 740°K.     

Lateral thermal expansion of cellulose Iβ and IIII polymorphs

Measurements of the thermal expansion coefficients (TECs) of cellulose crystals in the lateral direction are reported. Oriented films of highly crystalline cellulose I_β and III_I were prepared and then investigated with X‐ray diffraction at specific temperatures from room temperature to 250 °C during the heating process. Cellulose I_β underwent a transition into the high‐temperature phase with the temperature increasing above 220–230 °C; cellulose III_I was transformed into cellulose I_β when the sample was heated above 200 °C. Therefore, the TECs of I_β and III_I below 200 °C were measured. For cellulose I_β, the TEC of the a axis increased linearly from room temperature at α_a = 4.3 × 10^?5 °C^?1 to 200 °C at α_a = 17.0 × 10^?5 °C^?1, but the TEC of the b axis was constant at α_b = 0.5 × 10^?5 °C^?1. Like cellulose I_β, cellulose III_I also showed an anisotropic thermal expansion in the lateral direction. The TECs of the a and b axes were α_a = 7.6 × 10^?5 °C^?1 and α_b = 0.8 × 10^?5 °C^?1. The anisotropic thermal expansion behaviors in the lateral direction for I_β and III_I were closely related to the intermolecular hydrogen‐bonding systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1095–1102, 2002     

Thermodynamic investigation of several natural polyols (II)

The low-temperature heat capacity C _p,m of sorbitol was precisely measured in the temperature range from 80 to 390 K by means of a small sample automated adiabatic calorimeter. A solid-liquid phase transition was found at T=369.157 K from the experimental C _p-T curve. The dependence of heat capacity on the temperature was fitted to the following polynomial equations with least square method. In the temperature range of 80 to 355 K, C _p,m/J K⁻¹ mol⁻¹=170.17+157.75x+128.03x ²-146.44x ³-335.66x ⁴+177.71x ⁵+306.15x ⁶, x= [(T/K)−217.5]/137.5. In the temperature range of 375 to 390 K, C _p,m/J K⁻¹ mol⁻¹=518.13+3.2819x, x=[(T/K)-382.5]/7.5. The molar enthalpy and entropy of this transition were determined to be 30.35±0.15 kJ mol⁻¹ and 82.22±0.41 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 390 K with an interval of 5 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.     

Conductivity of some semiconducting polyazophenylenes

The electrical conductivity of a series of semiconducting polyazophenylenes was studied as a function of temperature and molecular weight in the temperature range 293–493°K and for molecular weights between 9500 and 62800. The compounds studied included poly-2,4-diminotoluene and poly-2,5-diaminotoluene. The temperature dependence of conductivity obeys the exponential law σ = σ₀ exp {–E_a/kT}. All of the compounds studied show a break in the conductivity curve at a temperature of about 380°K with the slope of the curve greater at temperatures above 380°K. The activation energies E_a determined from the higher slopes are in the range 0.63–0.89 eV, and the corresponding σ₀ values are in the range 10^?4-10° (ohm-cm)^?1. Both E_a and σ₀ show a tendency to increase with increasing molecular weight such that the compensation law was valid. Activation energies and σ₀ values determined from the (smaller) slope below the temperature of the break point showed a tendency to decrease with successive measurements on new samples. This indicates some kind of orientation effect, and conclusions concerning the properties of the material on basis of results below the break point are therefore difficult.     

Synthesis and structure analysis of (K[DB18 C6])4(C60)5·12THF containing C60 in three different bonding states

A new fulleride, (K[DB18C6])₄(C₆₀)₅?12 THF, was prepared in solution using the “break‐and‐seal” approach by reacting potassium, fullerene, and dibenzo[18]crown‐6 in tetrahydrofuran. Single crystals were grown from solution by the modified “temperature difference method”. X‐ray analysis was performed revealing a reversible phase transition occurring on cooling. Three different crystal structures of the title compound at different temperatures of data acquisition are addressed in detail: the “high‐temperature phase” at 225 K (C2, Z=2, a=49.055(1), b=15.075(3), c=18.312(4) Å, β=97.89(3)°), the “transitional phase” at 175 K (C2 m, Z=2, a=48.436(5), b=15.128(1), c=18.280(2) Å, β=97.90(1)°), and the “low‐temperature phase” at 125 K (Cc, Z=4, a=56.239(1), b=15.112(3), c=36.425(7) Å, β=121.99(1)°). On cooling, partial radical recombination of C₆₀^.? into the (C₆₀)₂^2? dimeric dianion occurs; this is first time that the fully ordered dimer has been observed. Further cooling leads to formation of a superstructure with doubled cell volume in a different space group. Below 125 K, C₆₀ exists in the structure in three different bonding states: in the form of C₆₀^.? radical ions, (C₆₀)₂^2? dianions, and neutral C₆₀, this being without precedent in the fullerene chemistry, as well. Experimental observations of one conformation exclusively of the fullerene dimer in the crystal structure are further explained on the basis of DFT calculations considering charge distribution patterns. Temperature‐dependent measurements of magnetic susceptibility at different magnetic fields confirm the phase transition occurring at about 220 K as observed crystallographically, and enable for unambiguous charge assignment to the different C₆₀ species in the title fulleride.     

A dynamic nuclear magnetic resonance spectroscopic study of conformational properties of 1,3-dioxepane and 4,4,7,7-tetramethyl-1,3-dioxepane

The 251 MHz ¹H and the natural abundance 63.1 MHz ¹³C NMR spectra of 1,3-dioxepane (1) and 4,4,7,7-tetramethyl-1,3-dioxepane (2) have been investigated over the temperature range of 5 to ?180 °C. While the spectra of 1 show no dynamic NMR effect, compound 2 exists in solution as a 1:1 mixture of a symmetrical (C₂) twist-chair and its mirror image conformation. The free energy barrier for the conformational racemization of 2 is 43 kJ mol^?1 (10.3 kcal mol^?1). Interconversion paths between various conformations of 2 are discussed. Compound 1 is suggested to have a symmetrical (C₂) twist-chair conformation which is rapidly pseudorotating via a chair conformation to achieve a time averaged symmetry of C_2v, even at ?180 °C.     

Crystal Transformation and Development of Tensile Properties upon Drawing of Poly(L-lactic acid) by Solid-State Coextrusion: Effects of Molecular Weight

Melt-crystallized films of poly(L -lactic acid) (PLLA) with M_v in the range of 3.8 ∼ 46 × 10⁴ consisting of α-form crystals were uniaxially drawn by solid-state coextrusion. The effects of M_v, extrusion draw ratio (EDR), and extrusion temperature (T_ext) on the crystal/crystal transformation from α- to β-form crystals and the resultant tensile properties of drawn products were studied. The crystal transformation proceeded with EDR and more rapidly for the higher M_v's. Furthermore, the crystal transformation proceeded most rapidly with EDR at a T_ext around 130 °C, independently of the M_v's. As a result of the optimum combination of processing variables influencing the the crystal transformation (M_v, T_ext, and drawability), highly oriented films consisting of β-form crystals alone were obtained by coextrusion of higher M_v samples at T_ext's slightly below the melting temperature (150 ∼ 170 °C) and at higher EDR's > 11. Both the tensile modulus and strength increased rapidly with EDR. The modulus at a given EDR was slightly higher for the samples with higher M_v's. In contrast, the strength at a given EDR was remarkably higher for the higher M _v's. The highest tensile modulus of 8.0 GPa and strength of 500 MPa were obtained with the sample of the highest M_v of 46 × 10⁴ coextruded at 170 °C to the highest EDR of 14.     

Creep behavior of amorphous ethylene–styrene interpolymers in the glass transition region

The viscoelastic behavior of amorphous ethylene–styrene interpolymers (ESIs) was studied in the glass transition region. The creep behavior at temperatures from 15°C below the glass transition temperature (T_g) to T_g was determined for three amorphous ESIs. These three copolymers with 62, 69, and 72 wt % styrene had glass transition temperatures of 11, 23, and 33°C, respectively, as determined by DMTA at 1 Hz. Time–temperature superposition master curves were constructed from creep curves for each polymer. The temperature dependence of the shift factors was well described by the WLF equation. Using the T_g determined by DMTA at 1 Hz as a reference temperature, C₁ and C₂ constants for the Williams, Landel, and Ferry (WLF) equation were calculated as approximately 7 and 40 K, respectively. The master curves were used to obtain the retardation time spectrum and the plateau compliance. The entanglement molecular weight obtained from the plateau compliance increased with increasing styrene content as 1,600, 1,870, and 2,040, respectively. The entanglement molecular weight of the ESIs was much closer to that of polyethylene (1,390) than to that of polystyrene (18,700); this was attributed to the unique chain microstructure of these ESIs with no styrene–styrene dyads. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2373–2382, 1999     

Molecular structure of dipivaloylmethane and the intramolecular hydrogen bond problem

Molecular structure of dipivaloylmethane was investigated by X-ray electron diffraction at 24°C. The C_2v and C_s geometrical models involving an intramolecular hydrogen bond are considered. The C_2v model with enol hydrogen lying symmetrically relative to the oxygen atoms has several advantages over the classical model of the enol tautomer. Translated from Zhumal Struktumoi Khimii, Vol. 41, No. 1, pp. 58-66, January–February, 2000     

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.     

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.