Vibrational Heat Capacity Research Articles

Heat capacity of poly(trimethylene terephthalate)

Thermal analysis of poly(trimethylene terephthalate) (PTT) has been carried out using standard differential scanning calorimetry and temperature-modulated differential scanning calorimetry. Heat capacities of the solid and liquid states of semicrystalline PTT are reported from 190 K to 570 K. The semicrystalline PTT has a glass transition temperature of about 331 K. Between 460 K and 480 K, PTT shows an exothermic ordering. The melting endotherm occurs between 480 K and 505 K with an onset temperature of 489.15 K (216 C). The heat of fusion of typical semicrystalline samples is 13.8 kJ/mol. For 100% crystalline PTT the heat of fusion is estimated to be 28--30 kJ/mol. The heat capacity of solid PTT is linked to an approximate group vibrational spectrum, and the Tarasov equation is used to estimate the skeletal vibrational heat capacity ({Theta}{sub 1} = 542 K and {Theta}{sub 3} = 42 K). A comparison of calculation and experimental heat capacities show agreement of better than {+-}2% between 190--300 K. The experimental heat capacity of liquid PTT can be expressed as a linear function of temperature: C{sub p} {sup L}(exp) = 211.6 + 0.434 T J/(K mol) and compares well with estimations from the ATHAS data bank using groupmore » contributions of other polymers with the same constituent groups ({+-} 0.5%). The change of heat capacity at T{sub g} of amorphous PTT has been estimated from the heat capacities of liquid and solid to be 86.4 J/(K mol). Knowing C{sub p} of the solid, liquid, and the transition parameters, the thermodynamic functions: enthalpy, entropy and Gibbs function were obtained.« less

Calorimetric Study of Glassy and Liquid Toluene and Ethylbenzene: Thermodynamic Approach to Spatial Heterogeneity in Glass-Forming Molecular Liquids

The heat capacities of glassy and liquid toluene and ethylbenzene were measured with an adiabatic calorimeter. Both samples were doped with about 10% of benzene to suppress crystallization. The effects of the doping were corrected for by assuming the additivity of the heat capacities of toluene (or ethylbenzene) and benzene. The configurational entropies of several glass-forming liquids, including toluene and ethylbenzene, were calculated as functions of temperature from their heat-capacity data. For these calculations, the vibrational heat capacities were determined by the least-squares fitting of the Debye and Einstein functions to the experimental values using auxiliary spectroscopic data from the literature. The size of cooperative rearranging region (CRR), which was first conceived by Adam and Gibbs, was calculated from the configurational entropy in a simplifying approximation that neglects distribution of CRR size and internal entropy of CRR. For all of the systems examined, the size of CRR increas...

Vibrational frequencies and ideal-gas heat capacities as calculated by a modified Urey-Bradley force field. Fluorochloroderivatives of methane

Ideal-gas heat capacities are required to estimate caloric properties of fluids. Relationships between ideal-gas and molecular properties are given by statistical thermodynamics. For many molecules the required molecular data, i.e. vibrational frequencies, or heat capacity data from different references are contradictory or still lacking. Here a method is applied, which is able to predict the vibrational frequencies for many molecules from known data of few molecules with an accuracy sufficient for the calculation of heat capacities. A brief description of the method, based on a mechanical model of the molecules, is given. The application to all fluorochloro-substituted methanes will demonstrate its reliability. Reliable experimental heat capacity data indicate, that an accuracy of ± 0.8% is achieved.

Vibrational Dynamics and Heat Capacity of Poly(L-lysine)

Poly(L-lysine) is a polypeptide having a bulky hydrophobic side chain. A systematic study of the full vibrational dynamics, including phonon dispersion, for the α-helical form of this biopolymer has been reported using Wilson’s GF matrix method as modified by Higgs for an infinite polymeric chain. The calculated frequencies explain well the IR and Raman spectra. A comparison of the amide modes with other α-helical polypeptides is reported here. Spectral frequencies have been obtained for the N-deuterated species to check the validity of force field and correctness of assignments. Heat capacity has also been calculated from dispersion curves via density-of-states using Debye relation in the temperature range 50–500 K. The calculated values are found to be in close agreement with the recent experimental data of Roles et al. [Biopolymers, 33, 753 (1993)].

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 Capacities and Relaxation Effects of Se-Te-Cd Glasses

Heat capacity measurements were made by using differential scanning calorimetry in the glass transition region for Se70Te30-xCdx (x = 2, 4, 6, 8, and 10) amorphous alloys which were a couple of weeks old. Specific heat values showed an extremely large increase at the transition temperature. A rescan of the samples, heated just beyond the temperature at which the endothermic spike has been obtained, revealed a normal behaviour. This indicates that these glasses relax to equilibrium within a short span of time and the huge maximum in specific heat, Cp, is a complete artifact of the thermal history of the samples. Below the glass transition the Cp values are in the classical limits of Dulong and Petit for the vibrational heat capacity of solids. The glass transition temperatures, Tg, for these compositions are decreasing with increasing Cd content and ΔCp, the difference between liquid and glass heat capacities, also shows a similar trend.

High-temperature Raman spectroscopic and X-ray diffraction study of beta -Mg2SiO4; insights into its high-temperature thermodynamic properties and the beta - to alpha -phase-transition mechanism and kinetics

Other| June 01, 1996 High-temperature Raman spectroscopic and X-ray diffraction study of beta -Mg 2 SiO 4 ; insights into its high-temperature thermodynamic properties and the beta - to alpha -phase-transition mechanism and kinetics Bruno Reynard; Bruno Reynard Universite de Rennes, Institut de Geologie, Rennes, France Search for other works by this author on: GSW Google Scholar Fouzia Takir; Fouzia Takir Search for other works by this author on: GSW Google Scholar Francois Guyot; Francois Guyot Search for other works by this author on: GSW Google Scholar Gabriel D. Gwanmesia; Gabriel D. Gwanmesia Search for other works by this author on: GSW Google Scholar Robert C. Liebermann; Robert C. Liebermann Search for other works by this author on: GSW Google Scholar Philippe Gillet Philippe Gillet Search for other works by this author on: GSW Google Scholar Author and Article Information Bruno Reynard Universite de Rennes, Institut de Geologie, Rennes, France Fouzia Takir Francois Guyot Gabriel D. Gwanmesia Robert C. Liebermann Philippe Gillet Publisher: Mineralogical Society of America First Online: 02 Mar 2017 Online Issn: 1945-3027 Print Issn: 0003-004X Copyright © 1996 by the Mineralogical Society of America American Mineralogist (1996) 81 (5-6): 585–594. https://doi.org/10.2138/am-1996-5-605 Article history First Online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Bruno Reynard, Fouzia Takir, Francois Guyot, Gabriel D. Gwanmesia, Robert C. Liebermann, Philippe Gillet; High-temperature Raman spectroscopic and X-ray diffraction study of beta -Mg 2 SiO 4 ; insights into its high-temperature thermodynamic properties and the beta - to alpha -phase-transition mechanism and kinetics. American Mineralogist 1996;; 81 (5-6): 585–594. doi: https://doi.org/10.2138/am-1996-5-605 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyAmerican Mineralogist Search Advanced Search Abstract We performed in-situ Raman spectroscopy and X-ray diffraction experiments at high temperature and ambient pressure to investigate the intrinsic anharmonic properties of β-Mg2SiO4 and the mechanism and kinetics of its back-transformation to forsterite. High-temperature Raman spectra of β-Mg2SiO4 and its back-transformed products were recorded up to 1200 K. β-Mg2SiO4 persists metastably up to 800-900 K, and the Raman frequency shifts with temperature were determined. Between 800 and 1000 K, new peaks are observed at about 670 and 1020 cm-1. Above 1000 K,a direct transformation to forsterite occurs. The peaks that appear between 800 and 1000 K are attributed to a defective spinelloid that forms as an intermediate phase during the back-transformation of β-Mg2SiO4 to forsterite. Similar features are observed in the Raman spectrum of partially transformed γ-Ni2SiO4 heated at 1073 K and ambient pressure for 10 min. These results indicate that a two-step mechanism, possibly martensitic, is operative in the backtransformation of the β- and γ-phases to olivine at low to moderate temperatures and for a large overstepping of the equilibrium conditions.The kinetics of the β- to α-Mg2Si04 back-transformation were monitored between 1023 and 1120 K at ambient pressure using X-ray powder diffraction. For the kinetic data obtained in air, two regimes are evident from an Avrami analysis. The first regime is characterized by an exponent n ≈ 2 for a low transformed fraction (X < 0.5); the second has n ≈ 1 for higher transformed fractions. For this second regime, an activation energy of 432 ± 64 kJ/mol is derived for the growth process from the kinetic data. A smaller data set collected in vacuum indicates much slower transformation rates and suggests a significant effect of the O2 or H2O partial pressures on the kinetics.Intrinsic mode anharmonic parameters can be calculated from the Raman frequency shifts with temperature and used to correct vibrational heat capacity models for intrinsic anharmonic effects. These corrections are slightly higher for the β-phase than for forsterite but the difference is within the experimental error. This indicates that, within the resolution of our experiments, no significant effect of intrinsic anharmonicity on the location and slope of the α-β phase transition can be predicted. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Deuteration effect on the specific heat of nickel hexammine nitrate

In this paper the behaviour of the specific heat on NH3 deuteration in nickel hexammine nitrate is determined from the analysis of different contributions of the crystal lattice. For a non-deuterated crystal the experimental specific heat outside the phase transition regions was reproduced well by the sum of harmonic oscillator specific-heat functions plus a correction for thermal dilatation. In calculating the specific heat, maximum use has been made of frequencies derived from spectroscopy. NH3 deuteration provides a good test of the analysis procedure. Since deuteration generally shifts the frequencies of some of the vibrations, a hydrogenous compound and its deuterated analogue have different vibrational heat capacities. One would expect a larger heat capacity for a deuterated crystal; this is indeed observed by calorimetry. Hence, this model has to be verified by calculating and comparing with experiment how NH3 deuteration affects the specific heat. The difference between the experimental NiDNO3 and NiHNO3 specific-heat values, referred to as Delta cexpD-H, is expressed as the sum of the contributions from the frequency shifts in the vibrational spectrum of the deuterated crystal compared with that of the non-deuterated crystal. The results of the analysis show that the calculated Delta cD-H is very close to the experimental values. This result strongly supports the simple Debye plus Einstein model.

The ATHAS database on heat capacities of polymers

Abstract

Thermodynamic Characterization of the Plastic Crystal and Non-Plastic Crystal Phases of C70

Abstract Heat capacity measurements were performed on chromatographically purified C70 from 120 to 560 K by DSC. The experimental values were linked to the vibrational heat capacity, calculated based on normal-mode vibration frequencies available from the literature. Good agreement is found, as prior for C60 Major orientational disorder is introduced in two closely spaced transitions, reflecting the change to the phase that displays anisotropic rotation of the rugby-ball shaped molecules. The total entropy of the disordering transitions is 22.4 J/(Kmol), slightly lower than that of C60, but additional entropy is gradually acquired between 120 K and the transition temperature, making the total entropy gain higher than that of C60, as expected for a less symmetric molecule. The Debye temperature for the six lattice vibrations of C70 was calculated to be 45 K, compared to 53 K for C60 No melting temperature could be detected for C70 up to 950 K, but the entropy of fusion is estimated to be 12 J/(K mol). Enth...

Heat capacity of actinide dioxides

We analyse available experimental information on the vibrational heat capacity of ThO 2, with particular emphasis on anharmonic effects, and on the similarities in the vibrational properties of actinide dioxides of the CaF 2 type structure. The result is then used in a discussion of the heat capacity of UO 2. The contribution from crystal-field split 5f-electron states is calculated from published spectral data, which allows remaining nonvibrational and controversial contributions to the heat capacity to be separated out. An important aim of the paper is also to demonstrate a method of analysing high-temperature thermodynamic data.

Heat capacity and enthalpy of sublimation of sulfur hexafluoride

The heat capacity of sulfur hexafluoride (SF 6) was measured in the temperature range T = 5 K to T = 250 K with an adiabatic calorimeter. The enthalpy of sublimation was measured at T = 186.00 K with a newly constructed apparatus. A first-order solid-to-solid phase transition appeared at T = (95.02±0.02) K and fusion at T = (223.72 ± 0.01) K. The vibrational heat capacity (baseline) was determined in terms of a least-squares method using Debye and Einstein functions. The molar entropies of the solid-to-solid transition and the fusion were determined to be (23.37±0.01) J · K −1 · mol −1 and (23.36 ± 0.01) J · K −1 · mol −1, respectively. The molar enthalpy and molar entropy of sublimation at T = 186.00 K were (23.22 ± 0.01) kJ · mol −1 and (124.8 ± 0.1) J · K −1 · mol −1, respectively. The third-law entropy at T = 298.15 K and pressure p = 10 5 Pa was calculated from the present results to be (291.2 ± 0.5) J · K −1 · mol −1. This value agreed well with the statistical value calculated from the most reliable spectroscopic data, indicating that SF 6 becomes completely ordered at T → 0.

Structural phase transitions in La2-x(Ba,Sr)xCuO4-y and related physical properties.

A Landau free energy for the ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$(Ba,Sr${)}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathit{y}}$ family is constructed, including the coupling energy between the order parameter and strain tensor. Using group theory, it is demonstrated that the coupling energy can be expressed as a sum of terms linear in the strain and quadratic in the order parameter and should contain a coupling term bilinear in the two order-parameter components. The structural phase transitions (SPT's) in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$(Ba,Sr${)}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathit{y}}$ are discussed on this basis. It is shown that several SPT's may occur in this system under different conditions. The observations of the influences of applied pressure, doping concentration x, and oxygen deficiency y on the SPT temperature are interpreted quantitatively. Relations connecting spontaneous strain, soft-mode vibrational frequencies, heat capacity, and elastic constants of the lower-temperature phases are derived. The mean-field results of the elastic properties and the results of the scaling analysis are also given. The results of ultrasonic measurements on a ${\mathrm{La}}_{1.88}$${\mathrm{Sr}}_{0.12}$${\mathrm{CuO}}_{4}$ single crystal are reported. The present and other relevant experimental observations are compared with the obtained theoretical results. The possible effects of structural phase transitions or structural instabilities on the superconductivity of the system are discussed.

Thermal behavior of epoxy resins

A series of epoxy resins has been analyzed by measuring their heat capacities from 140 K up to decomposition using differential scanning calorimetry. The data for the solids were compared to the vibrational heat capacities computed using an approximate vibrational spectrum consisting of skeletal heat capacities (based on a Tarasov analysis) and group vibrations (obtained from IR and Raman data). The heat capacities for the liquid were used to construct an addition scheme for the molecules with similar groups in their repeating unit. The glass transition and the melting transition are discussed by analyzing the fast-cooled and well crystallized samples.

Thermodynamic characterization of fullerene (C60) by differential scanning calorimetry

Heat capacity measurements on C 60 were carried out by differential scanning calorimetry from 120 to 560 K. This heat capacity was linked based on existing normal-mode and lattice calculation, to the vibrational heat capacities. In this way the thermodynamc functions are available from absolute zero of temperature. The phase transition at 256 K could be intified as a crystal-to-plastic crystal transition with an increase in entropy of 27.3 J/(K mol)

Investigation of the thermophysical properties of polymers by the temperature wave technique

The technique of temperature waves to measure the complex thermophysical characteristics of materials has been proposed. The relations for the moduli and arguments of these characteristics for the case of plane temperature waves have been calculated. The temperature dependences of the moduli and arguments of complex thermophysical characteristics of polyvinylacetate (PVAc) at different frequencies and also the temperature dependences of its vibrational and configurational heat capacities have been determined. It has been shown that the vibrational heat capacity of PVAc in the region of softening grows sharply and its configurational heat capacity goes through a peak. The segmental mobility has been found to affect the heat transfer in the polymer in an ambivalent way causing both a decrease and increase of thermal conductivity.

Effect of nonequilibrium solvation on chemical reaction rates. Variational transition-state-theory studies of the microsolvated reaction Cl-(H2O)n + CH3Cl

The authors present a potential energy surface for the microhydrated S{sub N}2 reaction of a chloride ion with methyl chloride in the presence of one or two water molecules. All degrees of freedom are included. The authors analyze the stationary points corresponding to reactant, ion-dipole complex, and transition state for the monohydrated and the dihydrated reactions, and they use generalized transition-state theory to evaluate the rate constants for these reactions. A noteworthy feature of the dynamics calculations is that vibrational zero point effects are included, as are effects of quantization on vibrational heat capacities and entropies, and water molecules are treated as nonrigid. The authors find that the rate constant at 300 K decreases from the gas-phase value of 3.5 {times} 10{sup {minus}14} cm{sup 3} molecule {sup {minus}1} s{sup {minus}1} to a value of 1.1 {times} 10{sup {minus}17} cm{sup 3} molecule{sup {minus}1} s{sup {minus}1} for the monohydrated reaction and to a value of 3.7 {times} 10{sup {minus}20} cm{sup 3} molecule{sup {minus}1} s{sup {minus}1} for the dihydrated reaction.

The thermodynamics of perchlorates. I. Heat capacity of ND4ClO4 from 7 to 345 K and the analysis of heat capacities and related data of NH4ClO4 and ND4ClO4

The heat capacity of the orthorhombic salt: deuterated ammonium perchlorate, ND4 ClO4 , was measured from 7 to 345 K using adiabatic calorimetry. The heat capacity against temperature curve is smooth, continuous and without anomaly. Values of the standard molar thermodynamic quantities are presented up to 340 K. The heat capacities of ND4 ClO4 and NH4 ClO4 have been analyzed. The contributions to the vibrational heat capacity from the external optical modes of NH+4 or ND+4, ClO−4 and libration from the external modes of ClO−4 along with those of vibration from the internal optical modes of NH+4 or ND+4 and ClO−4, and the acoustic lattice modes for these ions have been calculated. The difference between the experimental and calculated heat capacity, called the residual heat capacity, equals the contribution from ammonium ion rotation and the thermal expansion of the lattice. With recent thermal expansion data, the correction from constant stress to constant strain has been applied and the derived rotational heat capacities of the NH+4 and ND+4 are determined to be in qualitative agreement with those derived from various rotational models.

Analysis of Thermodynamic Properties of the Hydrogen Solution in Amorphous Fe ‐ Ti Compounds

AbstractThe thermodynamic properties of the hydrogen solution in amorphous Fe ‐ Ti films (Ti: 43–60%) have been studied in the pressure range from 1 to 104 Pa and at temperatures from 293 to 623 K. It is shown that the observed pressure‐composition (PC) isotherms deviate positively from the Sievert's law, which is contrary to the negative deviation commonly observed in the hydrogen solution in crystalline compounds. In accordance with the positive deviation the relative partial molar enthalpies, ‐ Δ H̄, derived from the isotherms decrease with increasing the hydrogen concentration, and at very dilute concentration the value is about three times larger than that for the formation of monohydride of crystalline FeTi. These anomalously large ‐ Δ H̄ values for hydrogen dissolution in amorphous Fe‐Ti suggest that the local environment around the hydrogen atoms are quite different from that in crystalline FeTi. The relative partial molar entropy data are analyzed taking into account of the contribution from the vibrational and fromielectronic heat capacity and volume expansion terms. The results show that the number of interstitial sites available for hydrogen occupation at very dilute concentration is about five times smaller than the values observed in the V‐, Nb‐, Ta‐H systems.

Vaporization study on the niobium-oxygen solid solution by mass-spectrometric method

The vapor pressures over the niobium-oxygen solid solution were measured by mass-spectrometric method in the temperature range 2091–2379 K. The main vapor species were observed to be NbO(g) and NbO 2(g). The solidus line of the niobium-oxygen solid solution and the solubility limit of oxygen in niobium metal at high temperatures were determined from the vaporization behavior. The partial pressure of oxygen was calculated as a function of temperature and O/Nb composition from the partial pressures of NbO(g) and NbO 2(g), from which the partial molar enthalpy and entropy of oxygen in the niobium-oxygen solid solution were determined. The compositional dependence of the partial pressure of oxygen was observed to obey the Henry's law at low oxygen concentrations in niobium metal less than about 5 a/o. The partial molar enthalpy in the oxygen concentration range between 1 and 5 a/o was observed to be nearly independent of composition, suggesting the presence of very weak interaction between interstitial oxygens. The compositional dependence of the partial molar entropy of oxygen in this low oxygen concentration range was explained by assuming the occupation of the octahedral sites in b.c.c. niobium lattice by the interstitial oxygens. The partial excess entropy of oxygen was compared with the value derived from the sum of the contributions from the volume expansion, vibrational and electronic heat capacity terms.