Heat Capacity Of Solids Research Articles

Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space

This article considers a variant of the heat conduction theory of thermal conductivity, in which the heat flux pseudovector has a weight of 1. The pseudoinvariants associated to the heat flux pseudovector are sensitive to mirror reflections and inversions of threedimensional space. The primary purpose of the study was to find a heat flux vector that is algebraically equivalent to the microrotation pseudovector and to measure elementary volumes and areas using pseudoinvariants that are sensitive to mirror reflections. To represent spinor displacements, a contravariant microrotation pseudovector with a weight of +1 was selected. Thus, the heat flux and mass density were expressed as odd-weight pseudotensors. The Helmholtz free energy per unit doublet pseudoinvariant volume was employed as the thermodynamic state potential of the following functional arguments: absolute temperature, symmetric parts, and accompanying vectors for the linear asymmetric strain tensor and the wryness pseudotensor. The results obtained show that the thermal conductivity coefficient and heat capacity of elastic micropolar solids are pseudoscalars of odd weight, indicating their sensitivity to mirror reflections.

Major and minor hysteresis loops in the enthalpy-temperature and phase fraction-temperature diagrams of solid/liquid phase change materials

A rate-independent hysteresis model originally proposed by Ivshin and Pence (1994) is extended to describe thermal hysteresis in enthalpy, specific heat capacity and phase fraction of solid/liquid phase transitions. It turns out that, even for smooth cyclic temperature variations, major and minor loops in the enthalpy-temperature diagram are not necessarily closed. Jump discontinuities may occur upon switches between heating and cooling. This issue is highly problematic: the model does not obey the law of conservation of energy. This problem particularly concerns the frequently found setting that solid and liquid heat capacities do not coincide and the phase transition enthalpy is assumed constant, i.e. independent of temperature. Two possible solutions are proposed. They follow the idea of Kirchhoff’s Law and relate temperature variations of the phase transition enthalpy to the difference in specific heat capacities of the distinct phases. Conditions for path reversibility and for the existence of closed major and minor loops (limit cycles) are given. The models show good agreement with experimental data generated by differential scanning calorimetry (DSC) of three types of paraffin-based solid/liquid phase change materials (PCM). These materials are increasingly adopted for storing thermal energy in building applications and show thermal hysteresis for complete and partial melting/solidification cycles.

The cytisine-enriched poly(3-hydroxybutyrate) fibers for sustained-release dosage form

The polymeric cytisine-enriched fibers based on poly(3-hydroxybutyrate) were obtained using electrospinning method. The biocompatibility study, advanced thermal analysis and release of cytisine from the poly(3-hydroxybutyrate) fibers were carried out. The nanofibers' morphology was evaluated by scanning electron microscopy. The formation and description of phases during the thermal processes of fibers by the advanced thermal analysis were examined. The new quantitative thermal analysis of polymeric fibers with cytisine phases based on vibrational, solid and liquid heat capacities was presented. The apparent heat capacity of fibers was measured using the standard differential scanning calorimetry. The quantitative analysis allowed for the study of the glass transition and melting/crystallization process. The mobile amorphous fraction, degree of crystallinity and rigid amorphous fraction were determined depending on the thermal history of semicrystalline polymeric fibers. Furthermore, the cytisine dissolution behaviour was studied. It was observed that the kinetic of the release from polymeric nanofiber is delayed than for the marketed product. The immunosafety of the tested polymeric nanofibers with cytisine was confirmed by the Food and Drug Agency Guidance as well as the European Medicines Agency. The polymeric matrix with cytisine seems to be a promising candidate for the prolonged release formulation.

Features of Ca1-xYxF2+x solid solution heat capacity behavior: diffuse phase transition

Features of Ca1-xYxF2+x solid solution heat capacity behavior: diffuse phase transition

A generalized thermophysical model for materials from molecular clusters to bulk crystals

Evolution of properties of bulk materials from its molecular clusters has been a relatively unexplored topic. In this article, we present a generalized model for total thermal energy and heat capacity of solids by considering that a bulk solid is evolved from zero-dimensional molecular clusters through one-dimensional wires and two-dimensionalquantum sheets . The basic difference among these structures is shown to be the phonon density of states, which is continuous (unconfined) in a bulk solid, whereas it is confined in one, two, and three dimensions in QSs, QWs, and QDs, respectively. Considering a semi-empirically derived phonon density of states and the total unconfined and quantum confined dimensions in these structures, we arrived at a generalized equation. The generalized equation fits well to many experimental heat capacities including palladium and nickel nanoparticles, single-walled carbon nanotubes, and cadmium selenide quantum dots with high degree of accuracy (R2 > 0.99). This close agreement between experiments and the generalized equation derived herewith provide promising directions to understand the evolution of bulk properties of materials.

An analytical study on transient thermal behavior of a packed-bed molten salt thermocline thermal storage

A volume averaged set of the governing equations for local thermal non-equilibrium fluid saturated porous media was applied to study transient thermal behavior of convection and conduction within a packed-bed thermocline thermal storage tank. General analytical expressions, which agree well with numerical results, were derived for the prediction of transient temperature fields of molten salt and granulated material. Three important dimensionless parameters, namely, the solid fluid heat capacity ratio, interstitial Stanton number and Peclet number based on the effective thermal diffusivity, are identified to investigate their effects on the thermal response of the packed-bed thermocline thermal storage tank. An explicit analytical expression for the effective discharging efficiency has been derived as a function of the three important dimensionless parameters. The expression may serve as a powerful tool to design a packed-bed thermocline thermal storage tank according to required operational conditions.

An update on liquid heat capacity estimations of cyclic organic compounds by group additivity and their application in estimations of complex molecules by synthetic and retrosynthetic analysis

Group additivity is very useful technique for estimating heat capacities of organic substances. This contribution examines a concern regarding the use of this technique when estimating the heat capacities of large molecules. The concern addresses the observation of a tendency of group values, particularly liquids, to overestimate heat capacities of large cyclic or highly branched liquid compounds of a commonly used group method. Group values for estimating cyclic liquids have been updated. In addition, a protocol is also described for the estimations of both liquid and solid heat capacities of large complex molecules at T = 298.15 K that takes advantage of currently available experimental data of potential precursors. The materials estimated using this protocol include several natural products, a statin and a number of steroids. Results are compared to available experimental data.

Heat capacity of cytisine – the drug for smoking cessation

The characterization of cytisine (CYT) and its blends with poly(lactic acid) was performed using thermal analysis, elemental analysis, infrared spectroscopy, and powder X-ray diffractometry. The heat capacities, total enthalpy, and phase transitions of CYT were established from 1.8 to 448.15 K (−271.35 – 175 °C) by advanced thermal analysis. Data were obtained using a Quantum Design Physical Property Measurement System (PPMS) and a differential scanning calorimetry (DSC). The low-temperature heat capacity of the crystalline CYT in the range of 1.8 to 300 K (−271.35 – 26.86 °C) was measured by PPMS and fitted to a theoretical model in the low temperature region below 11 K (−262.15 °C), to orthogonal polynomials in the middle range 5 K <T < 60 K (−268.15 °C < t < −213.15 °C) and to the Debye and Einstein functions in the high range of temperature above 60 K (−213.15 °C). The liquid heat capacity was calculated based on the approximated linear regression data above the molten state of the experimental heat capacity of CYT obtained by the standard DSC measurements, and it was expressed as Cpliquid = 0.0838T + 346.78 J·K−1·mol−1. The calculated heat capacity in the solid state was extended to a higher temperature and was used, together with liquid heat capacity, as the reference baselines for the advanced thermal analysis of CYT. The PPMS and DSC/TMDSC methods are complementary methods for thermal analysis of cytisine. The PPMS method allowed determination of the equilibrium heat capacity in the solid state, which together with the equilibrium heat capacity in the liquid state allowed to analyze of the experimental apparent heat capacity of cytisine obtained based on DSC. The melting temperature and the total heat of fusion of crystalline material were established as 431.8 K (158.65 °C) and 26.5 kJ·mol−1, respectively. The solid and liquid heat capacities and transition parameters of CYT were applied to calculate total enthalpies for fully amorphous and crystalline states. Analyses of DSC and X-ray confirmed the presence of the solid-solid transition linking with not so far described a polymorphism phenomenon of CYT. Based on the thermogravimetric analysis the temperature of degradation of CYT was determined as 460.5 K (187.35 °C). Also, a preliminary thermal analysis of the blends of cytisine and poly(lactic acid) as a new candidate for drug delivery system was presented.

Precision Calorimeter Model Development: Generative Design Approach

In a wide range of applications, heating or cooling systems provide not only temperature changes, but also small temperature gradients in a sample or industrial facility. Although a conventional proportional-integral-derivative (PID) controller usually solves the problem, it is not optimal because it does not use information about the main sources of change—the current power of the heater or cooler. The quality of control can be significantly improved by including a model of thermal processes in the control algorithm. Although the temperature distribution in the device can be calculated from a full-fledged 3D model based on partial differential equations, this approach has at least two drawbacks: the presence of many difficult-to-determine parameters and excessive complexity for control tasks. The development of a simplified mathematical model, free from these shortcomings, makes it possible to significantly improve the quality of control. The development of such a model using generative design techniques is considered as an example for a precision adiabatic calorimeter designed to measure the specific heat capacity of solids. The proposed approach, which preserves the physical meaning of the equations, allows for not only significantly improving the consistency between the calculation and experimental data, but also improving the understanding of real processes in the installation.

(Invited) The Chemistry of the Sulfuric Acid Molten Salt Catalyst

The most successful molten salt catalyst is undoubtedly the SO2 oxidation catalyst used for the production of sulfuric acid. Sulfuric acid is by far the most produced inorganic commodity chemical, with a world yearly production in 2021 of 250 Mtons, corresponding to a value of around 20 Billion USD.The typical catalyst composition is reported as about 6.5% (w/w) V2O5 promoted by M2SO4 (with M being an alkali metal, mainly K, containing also Na and sometimes Cs) and supported on diatomaceous earth. BASF issued the first patent for this type of catalyst in 1914. For long time it was considered as a heterogeneous solid catalyst for the key proces of oxidation of SO2 to SO3 by air which by reaction with H2O forms sulfuric acid .However, within the last 80 years evidence was found that the catalyst by uptake of the reaction product SO3 during operation at 400 - 600 °C became a molten salt mixture of alkali pyro- and hydrogen-sulfates wherein V2O5 dissolved. Thus, in the early 1980s it was recognized that the complex chemistry and compound formation of vanadium in the V2O5-M2S2O7-M2SO4-MHSO4 (M=alkali) molten salt system was key to the mechanistic understanding and systematic improvement of the working industrial catalyst.The multiinstrumental research on the chemistry of the catalyst model system and operando investigations of the industrial catalyst, including thermal, spectroscopic and electrochemical methods, that have been applied for the last 40 years, will be reviewed here.Of this the joint research with Marcelle Gaune-Escard and her group in Marseille, France has been concerned with the molten salts M2S2O7 and MHSO4, the binary molten salt systems M2S2O7–MHSO4, and the molten salt-gas systems M2S2O7–V2O5 and M2S2O7–M2SO4–V2O5 (M=Na, K, Rb, Cs) in O2, SO2, and Ar atmospheres. These catalyst model systems have been investigated by thermal methods such as calorimetry, differential enthalpic analysis, and differential scanning calorimetry. Fundamental thermodynamic data such as temperatures and molar heats of solid–solid transition and fusion, phase diagrams, heat capacities of solids and liquids, heat of mixing and heats of complex formation have been obtained.Based on this accumulated research effort the mechanism of the catalytic reaction has been proposed around 20 years ago and it seems to be the state-of-the-art even today.References :1. Lapina, O., Balzhinimaev, B.S., Boghosian, S., Eriksen, K.M., Fehrmann, R. (1999). Progress on the mechanistic understanding of SO2 oxidation catalysts. Catal. Today, 51, 469–479.2. Hatem, G., Eriksen, K.M., Gaune-Escard, M., Fehrmann, R. (2002). SO2 oxidation catalyst model systems characterized by thermal methods. Topics Catal., 19, 323–331.3. Boghosian, S., Fehrmann, R., Bjerrum, N.J., Papatheodorou, G.N. (1989). Formation of crystalline compounds and catalyst deactivation during SO2 oxidation in V2O5-M2S2O7 (M=K, Na, Cs) melts. J. Catal., 119, 121–134.4. Folkmann, G.E., Hatem, G., Fehrmann, R., Gaune-Escard, M., Bjerrum, N.J. (1991). Conductivity, thermal analysis, and phase diagram of the system Cs2S2O7-V2O5: Spectroscopic characterization of CS4(VO2)2(SO4)2S2O7. Inorg. Chem., 30, 4057–4061.5. Rasmussen, S.B., Hama, H., Lapina, O., Khabibulin, D.F., Eriksen, K.M., Berg, R.W., Hatem, G., Fehrmann, R. (2003). Thermal conductivity, NMR, and Raman spectroscopic measurements and phase diagram of the Cs2S2O7-CsHSO4 system. J. Phys. Chem. B, 107, 13823–13830.6. Folkmann, G.E., Hatem, G., Fehrmann, R., Gaune-Escard, M., Bjerrum, N.J. (1993). Complex formation in pyrosulfate melts. 4. Density, potentiometry, calorimetry, and conductivity of the systems Cs2S2O7–V2O5, Cs2S2O7–Cs2SO4, and Cs2S2O7–Cs2SO4–V2O5 in the temperature range 340-550 °C. Inorg. Chem., 32, 1559–1565.

Heat capacity and index of refraction of polyzwitterions

Specific heat capacities and indices of refraction were measured for a series of six sulfobetaine zwitterionic polymers and compared to topological and group contribution models. Poly(sulfobetaine methacrylate) (PSBMA), poly(sulfobetaine acrylate) (PSBA), poly(ethyl sulfobetaine methacrylate) (PESBMA), poly(sulfobetaine methacrylamide) (PSBMAm), poly(sulfobetaine 2-vinylpyridine) (PSB2VP) and poly(sulfobetaine 4-vinylpyridine) (PSB4VP) were specially synthesized with changes of chemical structure in order to study effects of either the polymer backbone or the side group on their properties. Temperature modulated differential scanning calorimetry (TMDSC) as well as quasi-isothermal TMDSC were used to determine the temperature dependent specific heat capacity, cp(T) from 30 to 200 °C. The solid state specific heat capacities were measured for all the polyzwitterions, while liquid state heat capacity measurements were limited to PSBA and PESBMA. Ellipsometry at wavelengths from 300 nm to 3000 nm was used to measure the index of refraction for polyzwitterion thin films at room temperature. Theoretical room temperature values of cp and n were calculated for the polyzwitterions using topological and group contribution methods and compared to the measured values. The measured index of refraction values agree well with predictions for the polyzwitterions. However, for the solid state heat capacity, the model produces accurate prediction only for PSB2VP and PSB4VP. The discrepancy between the measured and predicted cp values is most likely due to the reduction of vibrational degrees of motion in the solid state for some of the polyzwitterions due to physical crosslinking.

A Hill Equation for Solid Specific Heat Capacity Calculation

The Hill Equation and Hill Coefficient have been used extensively in biochemistry for the description of noncovalent binding. Previously, the Hill Coefficient was correlated with the Gibbs free energy, which suggests that the Hill Equation might be extensible to covalent binding phenomena. To evaluate this possibility, the Hill Equation was compared to the Debye Model and Einstein Solid in the calculation of heat capacity for 53 covalent solids, which included stainless steels and refractory ceramics. Hill Equation specific heat predictions showed a standard error of 0.37 J/(mole⋅Kelvin), whereas errors from the Debye Model and Einstein Solid were higher at 0.45 J/(mole⋅Kelvin) and 0.81 J/(mole⋅Kelvin), respectively. Furthermore, the Hill Equation is computationally efficient, a feature that can accelerate industrial chemical process simulation(s). Given its speed, simplicity, and accuracy, the Hill Equation likely offers an alternative means of specific heat calculation in chemical process models.

Analytic Expressions for Debye Functions and the Heat Capacity of a Solid

Analytic expressions for the N-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the study of heat capacity of solids and the analysis of the asymptotic behavior of this function, both in the high and low temperature limits.

Additive single atom values for thermodynamics I: Volumes, entropies, heat capacities of ionic solids

In an earlier simple “group contribution” method, molar volumes of organic and inorganic materials were predicted by summing optimised single atom values weighted according to the molecular formula. We here first revisit this procedure for volumes and then apply the method to entropies and heat capacities, providing updated predictive methods. The atom sum method has the unique advantage of working with an essentially complete parameter set because of the finite number of chemical elements but at the expense of omitting the nuance of special interactions as in other more sophisticated and complex group contribution methods. Thus, it does not distinguish among materials with the same chemical formula (that is, among phases or isomers).We here analyse data for nearly 3 500 inorganic materials, both anhydrous and hydrated. On analysing this wealth of data, we note that the optimised atom sum volume data follow the atomic sequence pattern of element volume data quite closely, but with relatively reduced values for the alkali metals and alkaline earths. The entropy atom sum values are similarly dispersed across the atomic sequence. Heat capacity atom sum values have a much reduced range, corresponding to the relatively small range of the ambient heat capacities of inorganic solids as implied by the Dulong-Petit upper limit of 3R per atom. We provide estimates of linear temperature effects for each of the three properties: volume, entropy and heat capacity.The properties of water in hydrates versus pure liquid water are compared for each thermodynamic property yielding information on the effects of incorporation of water into the solid.In summary, summations encompassing inorganic anhydrate and hydrate volumes, entropies and heat capacities over temperature ranges are available from this work, enabling simple first-order thermodynamic predictions and checks.

Molecular dynamics simulation of thermodynamic properties and local structure of Na2CO3-K2CO3 eutectic salt during phase transition

In this paper, the thermodynamic properties and local structure of Na2CO3-K2CO3 eutectic salt were simulated by using Born Mayer potential function. The phase transition temperature, solid specific heat capacity (Cp), liquid Cp and density of Na2CO3-K2CO3 eutectic salt were obtained by molecular dynamics calculation. Compared with the experimental results, the error of phase transition temperature, solid Cp(550K-650 K) were 6.32% and 1.61% respectively, which verified the accuracy and reliability of MD simulation method. Moreover, the local microstructure of Na2CO3-K2CO3 eutectic salt was characterized by radial distribution functions (RDF) and angular distribution functions (ADF), combined with the simulated results of the thermodynamic properties, revealed the variation of Cp, density, coefficient of thermal expansion and viscosity with the increasing temperature. Furthermore, the change of ions during the solid-liquid phase transition of Na2CO3-K2CO3 eutectic salt was analyzed from the microscopic point of view, and the microstructure of Na2CO3-K2CO3 eutectic salt in the solid-liquid phase was obtained.

Low temperature heat capacity of nanosize amorphous solids

Contrary to previous studies based on bulk materials, we analyze the behavior of the vibrational density of states (VDOS) and specific heat of an amorphous solid of nano-scales (∼3 nm) at low temperature. With Hamiltonian formulation based on the intermolecular dispersion forces, our analysis indicates a universal semi-circle form of the average VDOS in the bulk of the spectrum along with a super-exponentially increasing behavior in its edge. The latter in turn leads to a specific heat with a superlinear temperature (T) dependence below T < 1 K even at nano-scales, and, surprisingly agreeing with the experiments although the latter are carried out at macroscopic scales. The omnipresence of dispersion forces at microscopic scales indicates the application of our results to other disordered materials too.

Efficient Debye Function Interpolation Formulae: Sample Applications to Diamond

The well-known classical heat capacity model developed by Debye proposed an approximate description of the temperature-dependence of heat capacities of solids in terms of a characteristic integral, the T-dependent values of which are parameterized by the Debye temperature, Θ D . However, numerous tests of this simple model have shown that within Debye’s original supposition of approximately constant, material-specific Debye temperature, it has little chance to be applicable to a larger variety of non-metals, except for a few wide-band-gap materials such as diamond or cubic boron nitride, which are characterized by an unusually low degree of phonon dispersion. In this study, we present a variety of structurally simple, unprecedented algebraic expressions for the high-temperature behavior of Debye’s conventional heat-capacity integral, which provide fine numerical descriptions of the isochoric (harmonic) heat capacity dependences parameterized by a fixed Debye temperature. The present sample application of an appropriate high-to-low temperature interpolation formula to the isobaric heat capacity data for diamond measured by Desnoyers and Morrison [17], Victor [24], and Dinsdale [25] provided a fine numerical simulation of data within a range of 200 to 600 K, involving a fixed Debye temperature of about 1855 K. Representing the monotonically increasing difference of the isobaric versus isochoric heat capacities by two associated anharmonicity coefficients, we were able to extend the accurate fit of the given heat capacity ( C p ( T ) ) data up to 5000 K. Furthermore, we have performed a high-accuracy fit of the whole C p ( T ) dataset, from approximately 20 K to 5000 K, on the basis of a previously developed hybrid model, which is based on two continuous low-T curve sections in combination with three discrete (Einstein) phonon energy peaks. The two theoretical alternative curves for the C p ( T ) dependence of diamond were found to be almost indistinguishable throughout the interval from 200 K to 5000 K.

Scaling Behavior between Heat Capacity and Thermal Expansion in SolidsSupported by the National Natural Science Foundation of China (Grant No. 51001113).

We experimentally analyze the heat capacity and thermal expansion of reference solids in a wide temperature range from several Kelvin to melting temperature, and establish a universal double-linear relation between the experimental heat capacity C p and thermal expansion β, which is different from the previous models. The universal behavior between heat capacity and thermal expansion is important to predict the thermodynamic parameters at constant pressure, and is helpful for understanding the nature of thermal properties in solids.

Thermodynamic properties, mechanical properties and interatomic potential in solids: a Shou-Shi-Ling ( ) game

Two formulae were developed to express sublimation enthalpy and Young’s modulus on a thermodynamic basis. The first formula reveals how the sublimation enthalpy is correlated with the thermal expansion coefficient and heat capacity of solids, whereas the second formula relates the Young’s modulus with sublimation enthalpy and equilibrium interatomic (intermolecular) distance. While the formulae themselves divulge the physical nature of the macroscopic properties such as sublimation enthalpy, coefficient of thermal expansion and Young’s modulus, these two formulae provide alternative ways to quantitatively estimate thermodynamic or mechanical properties of great importance in the development of new materials. Built upon these formulae, the effective connection among mechanical, thermodynamic properties along with the microscopic feature, the interatomic potential, was found fairly useful in the areas such as medicinal designing, environmental research, evaluation of the contamination in specific, and the development of lithium ion batteries, superconducting and even architectural materials, wherein either thermodynamic or mechanical properties or both are imperative.

Calculation of the fusion enthalpy temperature dependence of polyaromatic hydrocarbons from the molecular structure: Old and new approaches

Experimental determination of the phase transition enthalpies temperature dependences requires measurement of the transition enthalpies or the heat capacities of the final and initial states in the temperature range of interest. Both experiments are complicated and not always possible. Almost 30 years ago Chickos et al. proposed a scheme for adjustment of the sublimation, vaporization, fusion enthalpies of organic compounds to 298.15 K using readily available parameters – the heat capacities of the liquid and solid at 298.15 K, which could be calculated from the molecular structure. Since then, this scheme has been employed by most researchers in the field of thermodynamics of organic compounds and substantially facilitated the critical evaluation and comparative analysis of the phase transition enthalpies measured at different temperatures.Recently we employed solution calorimetry for the study of the sublimation, vaporization and fusion enthalpies at 298.15 K. In most cases the phase transition enthalpies adjusted to 298.15 K using Chickos et al. scheme were in agreement with the results obtained by solution calorimetry, but in some cases significant discrepancies were observed. Particularly, the fusion enthalpies of polyaromatic hydrocarbons at 298.15 K obtained using Chickos et al. scheme appeared to be systematically lower than determined by solution calorimetry, up to 10 kJ·mol−1. In the present work we analyzed the limitations of Chickos et al. scheme that could lead to the disagreement and proposed an alternative approach for adjustment of the fusion enthalpies of polyaromatic hydrocarbons to 298.15 K. During construction of this approach we refined the group contributions for the calculation of the heat capacities of liquid polycyclic aromatic hydrocarbons at 298.15 K and found a way to consider the effect of temperature on difference between the liquid and solid states heat capacities in the range of recalculation.