Vibrational Heat Capacity Research Articles

Vibrational dynamics and heat capacity in syndiotactic poly(propylene) form II

Normal modes and their dispersion are obtained for planar-zigzag form II ( tttt) of syndiotactic polypropylene (sPP) in the reduced zone scheme using Urey–Bradley force field and Wilson's GF matrix method as modified by Higgs. It is observed that this all trans backbone conformation can be characteristized by a band at 1233 cm −1 (calculated at 1239 cm −1). A comparison is made with the spectra of its isotactic and helical form. Characteristic features of the dispersion curves such as crossing, repulsion and von Hove type singularities (regions of high density-of-states) have been explained. Heat capacity obtained from the density-of-states agrees with the experimental data up to 250 K at which the glass transition sets in and the experimental curve exhibits a marked change in slope.

Calorimetric Study of Dynamical Heterogeneity in Blends of Polyisoprene and Poly(vinylethylene)

The specific heat capacities Cp of blends consisting of cis-polyisoprene (PI) and poly(vinylethylene) (PVE) were measured in the temperature range from 80 to 320 K by using an adiabatic calorimeter. The configurational heat capacities Cconf of blends around the glass transition temperature Tg have been determined by subtracting the vibrational heat capacities estimated with the Einstein and Debye theories. The Cconf vs temperature T curves of the blends exhibit double sigmoidal increase at two glass transition temperatures Tg1 and Tg2 and can be resolved into two empirical sigmoidal curves. For each sigmoidal curve with the index j = 1 or 2, we have also determined the magnitude of the jump ΔCj and the broadness parameter Bj of the sigmoidal curves. The dielectric relaxation spectrum for the primary process of PI/PVE blends is known to be bimodal due to dynamical heterogeneity. The relationship between the bimodal dielectric segmental relaxation and the double glass transition processes has been analyzed.

Heat capacity of poly(butylene terephthalate)

AbstractThe 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

Vibrational dynamics and heat capacity of poly(glycolic acid)

Polyglycolic acid (PGA) (–CH 2–COO–) n is the first bioresorbable synthetic polymer which is used to make biomedical and pharmaceutical devices. It has a planar zigzag conformation. A comprehensive study of the normal modes and their dispersion in PGA using Urey Bradley force field is being reported. Characteristic features of the dispersion curves have been reported. The heat capacity derived from the dispersion curves via the density-of-states, is in good agreement with the experimental data of Lebedev and Yevstropov.

Isotopic dependence of the heat capacity of c-C, Si, and Ge: an ab initio calculation

The vibrational spectra of crystalline diamond, silicon, and germanium are calculated with a first-principles local density functional scheme using 64 as well as 128 atoms supercells. The (harmonic) dynamical matrices are obtained from linear response theory. The phonon density of states, calculated for various isotopic masses M, are used to evaluate the vibrational heat capacities C v and their dependence on M at low temperatures. Simple rules obeyed by the isotope effect of C v are discussed. The results are compared with recent experimental data for Ge. It is hoped that this work will encourage and help to interpret analogous measurements in diamond and silicon with different isotopic compositions.

Potential energy, relaxation, vibrational dynamics and the boson peak, ofhyperquenched glasses

We describe a combination of laboratory and simulation studies that givequantitative information on the energy landscape for glass-forming liquids. Bothtypes of study focus on the idea of suddenly extracting the thermal energy, so thatthe system obtained for subsequent study has the structure, and hence potentialenergy, of a liquid at a much higher temperature than the normal glass temperatureTg.One type of study gives information on the energy that can be trapped inexperimental glasses by hyperquenching, relative to the normal glass,and on the magnitude of barriers separating basins of attraction on thelandscape. Stepwise annealing studies also give information on the matter ofenergy heterogeneity and the question of ‘nanogranularity’ in liquids nearTg.The other type of study gives information on the vibrational properties of asystem confined to a given basin, and particularly on how that vibrationalstructure changes with the state of configurational excitation of the liquid. Afeature in the low frequency (‘boson peak’) region of the density of vibrationalstates of the normal glass becomes much stronger in the hyperquenched glass.Qualitatively similar observations are made on heating fragile glass-formers intothe supercooled and stable liquid states. The vibrational dynamics findings aresupported and elucidated by constant pressure molecular dynamics/normalmode MD/NM simulations/analysis of the densities of states of differentinherent structures of a model fragile liquid (orthoterphenyl (OTP) in theLewis–Wahnstrom approximation). These show that, when the temperature israised at constant pressure, the total density of states changes in a mannerthat can be well represented by a two-Gaussian ‘excitation across thecentroid’, leaving a third and major Gaussian component unchanging.The low frequency Gaussian component, which grows with increasingtemperature, has a constant peak frequency of 18 cm−1and is identified with the Boson peak. It is suggested that the latter can serve as asignature for configurational excitations of the ideal glass structure, i.e. thetopologically diverse defects of the glassy solid state. The excess vibrational heatcapacity associated with this generation of low frequency modes with structuralexcitation is shown to be responsible for about 60% of the jump in heat capacityat Tg,most of the remainder coming from configurational excitation.

Specific heats Cp, Cv, Cconf and energy landscapes of glassforming liquids

In pursuit of understanding of the paradoxical success of the Adam–Gibbs equation in both experiment and computer simulation studies, we examine the relation between liquid behavior at constant pressure and constant volume and compare the inherent structures excitation profiles for the two cases. This allows us to extend qualitatively the recent correlation of kinetic and thermodynamic measures of fragility to constant volume systems. The decreased fragility at constant volume is understood in terms of the relation C p > C c(cp)> C c(cv)> C v . In the process, we find a parallel between the range of volumes, relative to the total excess volume, that are explored in the first few orders of magnitude of relaxation time increase, and the range of amorphous state inherent structure energies, relative to the total range, that are explored in ergodic computer simulations, which also cover only this limited range of relaxation time change. The interesting question of whether or not fragile behavior is determined in the configurational or vibrational manifold of states is left unanswered in this work. However, the approximate proportionality of the configurational and total excess entropies that is needed to interpret the success of the Adam–Gibbs equation (which has been questioned by other authors) is confirmed within the needed limits, using data from three different types of investigation: experiments (on Se), simulation (of water in the SPC-E model), and analytical models of both defect crystals and configurationally excited liquids. Some consequences of the abrupt increases in vibrational heat capacity at T g implied by this proportionality, are discussed.

Atomic dynamics of icosahedral Zn 63Mg 26.3Y 10.7 studied by neutron inelastic scattering

The dynamic structure factor of ZnMgY has been determined using neutron inelastic scattering techniques. From the time-of-flight spectra also the generalized vibrational density of states (GVDOS) was determined, which was used to calculate the temperature dependence of some of the thermodynamic properties like the vibrational heat capacity. The GVDOS of icosahedral ZnMgY consists of two main bands. The main dominant band at lower energies is composed of three subbands. This is characteristically different from the GVDOS of the Mackay type of icosahedral alloys investigated so far. The more pronounced separation of the subbands seems to be characteristic for the GVDOS of Frank–Kasper type of icosahedral quasicrystals.

Conformational contribution to the heat capacity of the starch and water system

AbstractThe 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

Vibrational dynamics and heat capacity of syndiotactic poly(4-methyl-1-pentene)

The normal modes and their dispersion are obtained for syndiotactic poly(4-methyl-1-pentene) in the reduced zone scheme using Wilson’s GF matrix method as modified by Higgs. Urey–Bradley force field has been used. A comparison is made with the spectra of its isotactic form to identify conformational sensitive modes and other spectral differences. Heat capacity has been calculated via density-of-states using Debye relation in the temperature range 50–330 K and compared with the experimental measurements.

Measurement of heat capacity to gain information about time scales of molecular motion from pico to megaseconds

Molecular motion has primarily a time scale of picoseconds. Quantum mechanical models of small-amplitude vibrations and local, large-amplitude motions can be fitted quantitatively to equilibrium heat capacities. Macroscopic calorimetry, thus yields indirectly the characteristic frequencies of molecular motion in the range of 10 11–10 13 Hz. At lower temperature, much of the large-amplitude molecular motion is restricted to cooperative movements and slows to macroscopic times so that calorimetry can directly measure the kinetics of these changes which may extend the time scales to megaseconds and beyond. In this light, instrumentation and interpretation of differential scanning temperature-modulated calorimetry (DSTMC) are discussed. Six basic thermal effects govern the thermal analysis of linear macromolecules: (1) the vibrational heat capacity; (2) heat capacities arising from large amplitude molecular motion; (3) reversible transitions; (4) annealing; (5) secondary crystallization and (6) primary crystallization. Of these only (1)–(3) are reversible. To these six thermal effects that do not change the molecular integrity, chemical reactions, evaporation, and condensation have to be added for a full thermal analysis. The latter effects have not been treated in this paper.

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

AbstractThe 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

A thermodynamic connection to the fragility of glass-forming liquids.

Although liquids normally crystallize on cooling, there are members of all liquid types (including molecular, ionic and metallic) that supercool and then solidify at their glass transition temperature, Tg. This continuous solidification process exhibits great diversity within each class of liquid-both in the steepness of the viscosity-temperature profile, and in the rate at which the excess entropy of the liquid over the crystalline phase changes as Tg is approached. However, the source of the diversity is unknown. The viscosity and associated relaxation time behaviour have been classified between 'strong' and 'fragile' extremes, using Tg as a scaling parameter, but attempts to correlate such kinetic properties with the thermodynamic behaviour have been controversial. Here we show that the kinetic fragility can be correlated with a scaled quantity representing excess entropy, using data over the entire fragility range and embracing liquids of all classes. The excess entropy used in our correlation contains both configurational and vibration-related contributions. In order to reconcile our correlation with existing theory and simulations, we propose that variations in the fragility of liquids originate in differences between their vibrational heat capacities, harmonic and anharmonic, which we interpret in terms of an energy landscape. The differences evidently relate to behaviour of low-energy modes near and below the boson peak.

Vibrational Spectra and Heat Capacity of Methane, and the Speed of Sound

Vibrational Spectra and Heat Capacity of Methane, and the Speed of Sound

Vibrational Dynamics and Heat Capacity of Polyacetylene

Phonon dispersion studies have been made on the cis-transoid form of polyacetylene (PA) chain. Unlike the trans-transoid form reported earlier, this conformation shows crossover and repulsion characteristics in the optical modes. Detailed assignments of modes are given, and the predictive value of the heat capacity obtained via the density of states as a function of temperature is reported.

A high-temperature and high-pressure Raman spectroscopic study of CaGeO 3 garnet

High-pressure and high-temperature Raman spectra of CaGeO3 tetragonal garnet have been collected to 11.5 GPa and 1225 K, respectively, in order to investigate possible intrinsic anharmonic behaviour in this phase. The Raman peak positions were observed to vary linearly with pressure and temperature within the ranges studied, with the higher-energy peaks showing larger P- and T-induced shifts than the low energy modes. The observed T-induced shifts are similar to those reported for grossular and andradite, while the observed P-induced shifts are generally larger than those of aluminosilicate and MgSiO3 majorite garnets (Gillet et al. 1992; Rauch et al. 1996) due to the larger bulk modulus of CaGeO3 garnet. The observed mode shifts of CaGeO3 garnet were used to determine the isothermal and isobaric mode Gruneisen parameters for this phase. These parameters are similar in value to those reported previously for grossular and andradite (Gillet et al. 1992). The calculated intrinsic anharmonic parameters, a i , for CaGeO3 garnet were determined to be nonzero, indicating significant anharmonic behaviour for this phase. These values, which range from −3.8 × 10−5 K−1 to −1.3 × 10−5 K−1, are also similar to those reported for andradite and grossular, but smaller than those determined for pyrope (Gillet et al. 1992). Hence, we expect MgSiO3 majorite to show greater anharmonicity than the germanate analogue studied by us. The anharmonic parameters determined for CaGeO3 tetragonal garnet may now be introduced into quasiharmonic vibrational heat capacity models to account for the observed anharmonic behaviour.

Reversible and irreversible heat capacity of poly(trimethylene terephthalate) analyzed by temperature-modulated differential scanning calorimetry

The heat capacity of poly(trimethylene terephthalate) (PTT) has been analyzed using temperature-modulated differential scanning calorimetry (TMDSC) and compared with results obtained earlier from adiabatic calorimetry and standard differential scanning calorimetry (DSC). Using quasi-isothermal TMDSC, the apparent reversing and nonreversing heat capacities were determined from 220 to 540 K, including glass and melting transitions. Truly reversible and time-dependent irreversible heat effects were separated. The extrapolated vibrational heat capacity of the solid and the total heat capacity of the liquid served as baselines for the analysis. As one approaches the melting region from lower temperature, semicrystalline PTT shows a reversing heat capacity, which is larger than that of the liquid, an observation that is common also for other polymers. This higher heat capacity is interpreted as a reversible surface or bulk melting and crystallization, which does not need to undergo molecular nucleation. Additional time-dependent, reversing contributions, dominating at temperatures even closer to the melting peak, are linked to reorganization and recrystallization (annealing), while the major melting is fully irreversible (nonreversing contribution). © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 622–631, 2000

Vibrational Frequencies and Ideal Gas Heat Capacities of Fluorochloro-Derivatives of Methane as Calculated from Quantum Mechanical Methods

In a previous paper various quantum mechanical methods were applied to difluoromethane in order to find a suitable path to accurate ideal gas heat capacities. Now, these calculations are extended to all fluorochloro-derivatives of methane. Reliable experimental heat capacity data reveal that the combination of quantum mechanics and statistical thermodynamics facilitates a prediction of ideal gas heat capacities with an accuracy of ±1% and better. This is very close to the range of accuracy, which is observed for the best experimental zero pressure heat capacity data from different sources of the literature.

Heat capacity of solid-state biopolymers by thermal analysis

Heat capacities in the solid state of four globular proteins (bovine β-lactoglobulin, chicken lysozyme, ovalbumine, and horse myoglobin) and of the poly(amino acid) poly(L-tryptophan) have been determined using the Advanced THermal Analysis System (ATHAS). The experimental measurements were performed with adiabatic and differential scanning calorimetry over wide temperature ranges. The heat capacities were linked to an approximate vibrational spectrum by making use of known group vibrations and of a set of parameters, Θ1 and Θ3, of the Tarasov function for the skeletal vibrations. Good agreement was found between experiments and calculations with root mean square errors mostly within ±3%. The experimental data were analyzed also with an empirical addition scheme using the known data for poly(amino acid)s measured earlier. Based on this study, vibrational heat capacities can now be predicted for all proteins with an accuracy comparable to common experiments. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2093–2102, 1999

Application of the Advanced Thermal Analysis System (ATHAS) to Differential Scanning Calorimetry (DSC) and Temperature-Modulated DSC of Polymers

The Advanced THermal Analysis System (ATHAS) involves the establishment of the link between heat capacity at low temperatures and molecular, vibrational motion. This description is then used to extrapolate the vibrational heat capacities to high temperatures. Next, the measured data can be analyzed in terms of conformational mobility, of importance to assess sample properties. Broad melting and glass transitions can thus be analyzed. Modem differential scanning calorimetry, DSC, and temperature-modulated DSC, TMDSC, are used to separate reversible and irreversible processes. An effort will be made to suggest when it is possible to apply quick DSC, and when it is necessary to use the slower, but more precise and informative TMDSC.