Excess Heat Capacity Research Articles

Generalized Rosenfeld–Tarazona scaling and high-density specific heat of simple liquids

The original Rosenfeld–Tarazona (RT) scaling of the excess energy in simple dense fluids predicts a ∝T3/5 thermal correction to the fluid Madelung energy. This implies that the excess isochoric heat capacity scales as Cvex∝T−2/5. Careful examination performed in this paper demonstrates that the exponent −2/5 is not always optimal. For instance, in the Lennard-Jones fluid in some vicinity of the triple point, the exponent −1/3 turns out to be more appropriate. The analysis of the specific heat data in neon, argon, krypton, xenon, and liquid mercury reveals that no single value of the exponent exists, describing all the data simultaneously. Therefore, we propose a generalized RT scaling in the form Cvex∝T−α, where α is a density- and material-dependent adjustable parameter. The question concerning which material properties and parameters affect the exponent α and whether it can be predicted from general physical arguments requires further investigation.

Heat capacities and thermodynamic properties of urea phosphate and its aqueous solutions at various temperatures

Urea phosphate was produced through a complexation reaction of phosphoric acid and urea and subsequent cooling crystallization. The elemental composition analysis, XRD, and FTIR all confirmed that the prepared urea phosphate had high purity and good crystallinity, and showed a clear onset melting temperature of 118.12℃ and corresponding enthalpy change of 222.10 J∙g−1 in TG/DSC measurement. Meanwhile, the heat capacities of urea phosphate and its aqueous solution were carefully measured using microcalorimetry with an expanded relative uncertainty better than 2 %. The experimental results revealed that the heat capacity of urea phosphate rises rapidly with temperature, with an increase of 41 % from −20 to 100℃. The experimental heat capacity data were correlated with semi-empirical models of Maier-Kelley equation, Khodakovsky equation and Debye-Einstein equation which all give excellent reproduction of the measured data with very close average deviation around 0.5 %. The enthalpy, entropy, and Gibbs free energy of solid urea phosphate were estimated at various temperatures by integrating heat capacity against temperature with Maier-Kelley equation and the results confirmed urea phosphate is thermally quite stable below 100℃. The heat capacity of urea phosphate aqueous solution increases with concentration and temperature, and there is a strong linear relationship between the solution’s heat capacity and temperature when the composition remains constant. The apparent molar heat capacity of urea phosphate in solution is positive and increases with concentration and temperature. The extrapolated partial molal heat capacity of urea phosphate is temperature independent and shows an average value of −709.4 J·K−1·mol−1. Due to the partial dissociation and partial ionization of urea phosphate in solution, the excess molar heat capacities show positive deviation from that of ideal solution, which also increases with the increase of concentration and temperature.

Quantum migration and its local heat impact: Understanding local heat capacity of confined systems.

For noninteracting particles confined in a constant volume, the temperature derivative of the local energy assumes negative values in thermodynamic equilibrium at low temperatures. This peculiar behavior may entail the misleading unphysical conclusion that the local heat capacity is negative. However, we show that temperature-dependent density variations of confined particles induce an energy selective particle transport within the domain, here called temperature-induced quantum migration. This macroscopic quantum phenomenon causes a redistribution of local heat and ensures a non-negative local heat capacity. Moreover, it induces local heating and cooling effects and a massive overshoot in local heat capacity. The quantum migration also builds up the thermal part of confinement energy, manifesting in an excess global heat capacity. Analyzing the local energy fluctuations shows that the linear relationship between heat capacity and fluctuations is broken at the local scale.

Phase behaviour and heat capacities of DBN and DBU based protic ionic liquids – Insights into the ionic character and nanostructuration

Herein, we report the thermal behavior and high-precision heat capacity values, at T = 298.15 K, and in the range from 283 to 363 K, for several protic ionic liquids (PILs), derived from the 1:1 liquid mixtures of the organic superbases 1,5-diazabicyclo[4.3.0]non-5-ene (DBN) and 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) with some carboxylic acids (propionic, butyric, hexanoic and octanoic). Glass transition, Tg, crystallization, Tc, cold-crystallization, Tcc, and melting, Tm, temperatures were determined for the PILs studied, showing marked differences with the base – Tg is lower for all DBN PILs, and no Tm, Tc, and Tcc could be obtained for the DBU PILs. The standard molar heat capacities, Cp,m0, were obtained with an uncertainty of less than ±0.3 % and their dependence on the base and on the acid’s chain length was studied in detail. The Cp,m0 of the DBU PILs were found to be significantly higher than those of the corresponding DBN PILs, which corroborates the greater ionic character of DBU PILs. The heat capacity data suggested the existence of a trend-shift with the chain length of the carboxylic acid. Similar to aprotic ionic liquids, the shift occurs around n = 5 (pentanoic acid) and suggests the existence of some degree of nanostructuration into polar and non-polar domains in PILs with larger acids. Moreover, PILs can display abnormally high excess heat capacities, resulting from the formation of an ionic mixture from neutral species. Analysis of the calculated excess heat capacities indicates that PILs tend to become less ionic as the temperature increases, which goes in accordance with the acid-base equilibrium shift.

Thermophysical properties of Ni-Ti melts measured by electromagnetic levitation method using static magnetic field

The normal spectral emissivity, molar heat capacity at constant pressure, and thermal conductivity of Ni-Ti melts were measured during electromagnetic levitation under a static magnetic field. The emissivity and heat capacity of the Ni-Ti melts were measured under a 3 T static magnetic field. The temperature range for the emissivity measurements was 1240–1839 K, and the temperature range for the heat capacity measurements ranged was 1223–1851 K. The emissivity and heat capacity of the Ni-Ti melts, except for the Ni mole fractions (xNi) of 0 and 0.25, showed without temperature dependence within the experimental temperature range. Furthermore, the heat capacity was larger than the ideal solution over the whole range of compositions. The emissivity of the Ni-Ti melts was discussed based on the Drude model. The temperature dependence of thermodynamic functions, such as enthalpy of mixing, excess entropy, and excess Gibbs energy, were calculated using excess heat capacity. The thermal conductivity of Ni-Ti melts was measured under a static magnetic field of 10 T. The temperature range for the thermal conductivity measurements was 1177–1900 K. The thermal conductivities of the Ni-Ti melts increased with increasing temperature, exhibited a local minimum for xNi = 0.75, and were higher than those calculated using the Wiedemann–Franz laws. This difference in thermal conductivity was discussed by considering the contribution of atomic vibrations.

A simple model for density anomaly and excess thermodynamic properties of alcohol-like in water-like mixture

ABSTRACT Molecular dynamics simulations were employed to gain insights into the density anomaly and excess thermodynamic properties of a binary mixture composed of a solvent resembling water and a solute resembling alcohol. In our model, both fluids were represented by spherical particles interacting through effective potentials: a two-length scale potential for the solvent–solvent interaction while purely repulsive potentials were used for the solute–solute and solute–solvent interactions. The temperature of maximum density (TMD) present in the pure solvent system is also observed in our mixture. The TMD exhibits a positive deviation in the mixture when compared to the pure solvent fluid under high-pressure conditions, while it shows a negative deviation under low-pressure conditions what is consistent with experiments. The excess volume, enthalpy and isobaric heat capacity show extreme values at x ≈ 0.4 . Using the radial distribution function and the translational order parameter we suggest that this behaviour can be explained in terms of solute particles caged in solvent network.

Specific heat and excess heat capacity of grout with phase change materials using heat conduction microcalorimetry

Microencapsulated phase-change-materials (PCMs) incorporated in cementitious grout can be used as a source of energy in an underground thermal energy storage system. Differential scanning calorimetry (DSC) is a widely used technique to measure the latent heat or specific heat of PCM-embedded cementitious materials. However, using milligram sample sizes (as required by DSC) of a cementitious material fails to represent the actual scale of cementitious components. This is the reason why, in the present paper, non-isothermal heat conduction microcalorimetry (MC) was evaluated as a tool for determining the thermal properties of PCM-embedded grout as well as pure PCM (three PCMs were used). An MC experimental protocol (using both single and 5–6 temperature cycles) was developed and used to measure latent heat and melting and crystallization temperatures, which were in good agreement with those reported for pure PCMs by the producers. In addition, the specific heats of the PCM-containing grout also agreed with measurements using the hot disk technique. Overall, the results show that the MC technique can be used as a potential standard method in determining thermal processes in complex systems, such as in PCM-embedded cementitious systems, where a large sample size is needed to represent the material.

Some features of heat capacity changes in aqueous solutions of low molecular weight alkanols at T = 298.15 K and ambient pressure

The specific (cp) and molar (Cp) heat capacities of dilute aqueous solutions of methanol (MeOH), ethanol (EtOH), 1-propanol (n-PrOH) and 2-propanol (i-PrOH) were measured using an adiabatic calorimetry at T = 298.15 K and ambient pressure. Based on the obtained results, the excess molar heat capacities, CpE, as well as the apparent molar heat capacities of each of components, Cp,∅,12, of the system {water (1) + alkanol (2)} were calculated. The standard (at infinite dilution) Cp,2o values were also estimated. All the CpE values are positive and pass through maxima, which shift to the range of a lower mole fraction of alcohol, x2, when the molecular weight of the latter increases. The same goes for the Cp,∅,1max values, too. In turn, the order of changing Cp,∅,2max within the narrow high-diluted range of (∼0.01 <x2 < 0.035) m.f. is oppositely directed. It is established that the x2 value at dCpE/dx2 = 0 is approximately half of the sum of the x2 values at Cp,∅,1max and Cp,∅,2max, a fact indicating the parity contribution of both interacting components of the solution to the structure-energy transformations occurring in it.

Heat Capacity of Various (Solvent + Terpene) Mixtures as Function of Composition and Temperature

The heat capacity of different mixtures of terpenes (α-pinene, β-pinene, limonene oxide) and solvents (acetone, toluene, ethyl acetate) at atmospheric pressure (85.1 kPa atm in Medellin, Colombia) were measured using a microcalorimeter at several terpene molar fractions and from room temperature to a value close to the solvent boiling point. The mixtures analyzed were acetone + α-pinene from 298.15 to 323.15 K, toluene + limonene oxide and toluene + β-pinene from 298.15 to 358.15 K, and ethyl acetate + β-pinene between 298.15 and 338.15 K. These mixtures, at the selected temperature ranges, are used in fine chemical catalytic reactions. The experimental heat capacity values were fitted to polynomials as a function of temperature. Excess heat capacity was calculated with the measured molar heat capacity for all the mixtures, it decreased with temperature. Experimental uncertainty was less than 1.5% with a confidence level of 95% using k = 2. The experimental results were consistent, for example the heat capacity of ethyl acetate + β-pinene mixture increased as the temperature increased and decreased with the composition of the solvent; at 308.15 K the heat capacity decreased from 252.73 to 245.17 J mol−1 K−1 when solvent composition increased from 0.1546 to 0.2797 and at a solvent composition of 0.1546, heat capacity increased from 237.26 to 252.73 J·mol−1·K−1 when temperature increased from 298.15 to 308.15 K.

Analysis of excess molar heat capacities of three component mixtures comprising of cyclic organic solvents: Graph and Flory theories

The present work reports measurement and estimation of heat capacities, CP and excess heat capacities, (CPE)ijk (using CP data) of 1-methylpiperidine (i) + pyrrolidin-2-one (j) + cycloheptanone or cyclohexanone or cyclopentanone (k) mixtures at several temperatures. (CPE)ijk data have been correlated with the mole fraction of the constitutional molecule (via Redlich-Kister polynomial) to commute standard deviations and ternary coefficients. (CPE)ijkdata have also been examined in terms of Graph and Flory's theories. It has been perceived that (CPE)ijkvalues computed using Graph theory compare well with their corresponding experimental values. Further, (CPE)ijk data obtained by Flory's theory for 1-methylpiperidine (i) + pyrrolidin-2-one (j) + cyclopentanone (k) mixtures are of the same sign.

Viscosity, heat capacity and refractive index studies for binary liquid mixtures containing 1,3-diaminopropane and alkyl acetates: Experimental and theoretical interpretation

The viscosity (η), heat capacity (CP) and refractive index (nD) of 1,3-DAP (1,3-Diaminopropane) (1) + AAc (MAc(methyl acetate), EAc(ethyl acetate), PAc(propyl acetate) and BAc(butyl acetate)) (2) binary mixture were measured at standard ambient temperature i.e. 298.15 K under the atmospheric pressure 0.1 MPa. The data of η, CP and nD were further used to determine deviation in viscosity (Δη), excess molar heat capacity (CPE), excess Gibbs free energy of activation (G∗E), and deviation in refractive index (ΔnD). η were analyzed by Bloomfield and Dewan model (BFD). The η values were further correlated by various correlations like Kendall, Bingham, Kendall-Monroe, Arrhenius, Katti-Chaudhari, Tamura-Kurata, Grunberg-Nissan, Frenkel, Hind-McLaughlin-Ubbelohde, Heric, McAllister, Lulian, Krishnan-Laddha and Heric-Brewer. Further various correlations like Heller, Lorentz-Lorenz, Arago-Biot, Newton, Gladstone-Dale, Erying and Weiner were used to correlate nD data. The derived thermo-physical properties were also interpreted in terms of molecular interactions and correlated with Redlich- Kister polynomial equation (R.K.).

Structural and thermodynamic effects of hydration in Na-zeolite A (LTA) from low-temperature heat capacity

Zeolite A (Linde Type A; LTA) is an industrially important porous mineral that has recently been shown to exhibit framework flexibility upon changes in hydration level. To investigate the flexibility transition from a thermodynamic perspective, we have performed heat capacity measurements on sodium zeolite A at seven incremental hydration levels ranging from zero to equilibrium with ambient air. Excess low-frequency vibrations beyond the predictions of the Debye model are found in all samples, and the frequency of these vibrations increases as a function of hydration level. This suggests that an increase in hydration causes a decrease in at least one type of framework flexibility for sodium zeolite A. In addition, a subtle excess heat capacity contribution from 150 to 280 K is observed only for low and intermediate hydration levels, which may arise from a transformation tied to framework flexibility previously observed in zeolite A via gas absorption calorimetry. Values of the standard thermodynamic functions Cp,m°, Δ0TSm°, Δ0THm°, andΦm° are also reported.

Anti-sigmoidal Composition Dependence of Glass Transition Temperature and Excess Heat Capacity Across It in a Binary System of Globular Alcohols

Anti-sigmoidal Composition Dependence of Glass Transition Temperature and Excess Heat Capacity Across It in a Binary System of Globular Alcohols

Understanding the emergence of the boson peak in molecular glasses

A common feature of glasses is the “boson peak”, observed as an excess in the heat capacity over the crystal or as an additional peak in the terahertz vibrational spectrum. The microscopic origins of this peak are not well understood; the emergence of locally ordered structures has been put forward as a possible candidate. Here, we show that depolarised Raman scattering in liquids consisting of highly symmetric molecules can be used to isolate the boson peak, allowing its detailed observation from the liquid into the glass. The boson peak in the vibrational spectrum matches the excess heat capacity. As the boson peak intensifies on cooling, wide-angle x-ray scattering shows the simultaneous appearance of a pre-peak due to molecular clusters consisting of circa 20 molecules. Atomistic molecular dynamics simulations indicate that these are caused by over-coordinated molecules. These findings represent an essential step toward our understanding of the physics of vitrification.

Normal spectral emissivity and heat capacity of Pd–Fe melts measured at constant pressure under electromagnetic levitation with a static magnetic field

The normal spectral emissivity at 807 and 940 nm and heat capacity at constant pressure of Pd–Fe melts were measured under electromagnetic levitation with a static magnetic field. The samples were made of Fe of mass purity 99.9985%. The present emissivity of Fe melts was relatively low compared with previously reported data using Fe with purity lower than 99.95% mass purity. The spectral emission of the Fe melts was analyzed using their normal spectral emissivity obtained from the Drude model. The excess heat capacity of Pd–Fe melts was evaluated from the measured heat capacity of Pd–Fe melts. Applying the Lupis–Elliot rule, we concluded from the obtained excess heat capacity that the enthalpy of mixing and excess entropy of the Pd–Fe melts should be negative. The composition dependence of the enthalpy of mixing, excess entropy, and excess Gibbs energy of Pd–Fe melts were evaluated using data obtained in this study and the literature.

Sub-nL thin-film differential scanning calorimetry chip for rapid thermal analysis of liquid samples.

Differential scanning calorimetry (DSC) is a popular thermal analysis technique. The miniaturization of DSC on chip as thin-film DSC (tfDSC) has been pioneered for the analysis of ultrathin polymer films at temperature scan rates and sensitivities far superior to those attainable with DSC instruments. The adoption of tfDSC chips for the analysis of liquid samples is, however, confronted with various issues including sample evaporation due to the lack of sealed enclosures. Although the subsequent integration of enclosures has been demonstrated in various designs, rarely did those designs exceed the scan rates of DSC instruments mainly because of their bulky features and requirement for exterior heating. Here, we present a tfDSC chip featuring sub-nL thin-film enclosures integrated with resistance temperature detectors (RTDs) and heaters. The chip attains an unprecedented sensitivity of 11 V W-1 and a rapid time constant of 600 ms owing to its low-addenda design and residual heat conduction (∼6 μW K-1). We present results on the phase transition of common liquid crystals which we leverage to calibrate the RTDs and characterize the thermal lag with scan rates up to 900 °C min-1. We then present results on the heat denaturation of lysozyme at various pH values, concentrations, and scan rates. The chip can provide excess heat capacity peaks and enthalpy change steps without much alteration induced by the thermal lag at elevated scan rates up to 100 °C min-1, which is an order of magnitude faster than those of many chip counterparts.

On the interpretation of the unusual behavior of aqueous-organic mixtures in concentration regions with intersecting isotherms of heat capacity properties

Based on our own and some literature results, we have carried out a detailed analysis of concentration regions of the aqueous-organic mixture in which the temperature dependences of both excess molar heat capacity, CpE, and apparent molar heat capacity of each component, Cp,ϕ,i, are intersected. It is established that the ∂CpE/∂T and ∂Cp,ϕ,w/∂Tderivatives (W is water) for the {(W + hexamethylphosphoramide (HMPA)} and {(W + tert‑butanol (t-BuOH)} mixtures intersect in a rather narrow concentration interval between (0.30 and 0.35) and (0.35 and 0.40) mole fractions of the organic component, respectively. This fact we have interpreted as evidence that the decisive role in the mutually overlapping heat-capacity contributions to CpEresulting in such a situation plays the abnormal change in the isobaric molar heat capacity of W (Cp,w), which has a minimum at T ≈ 308 K, when the temperature increases.

Molecular interactions in multicomponent liquid mixtures: Excess molar heat capacities

Molar heat capacities, CP for 1-methylpiperidine (1) + pyrrolidin-2-one (2) + pyridine, α-, β-, γ-picoline (3) mixtures have been assessed at 293.15, 298.15, 303.15, 308.15 K temperatures and same have been employed to compute excess molar heat capacities, CPE. The CPE data have been allied with the composition of the component molecules (Redlich–Kister expansion) and ternary adjustable parameters calculated along with standard deviations. CPE have been verified in terms of Graph theory. Obtained results inferred that commuted CPE values compare favorably well with measured data. Agreement between experimental and calculated CPE values suggest that several assumptions made in driving CPE data are valid.

Molar heat capacities and excess molar heat capacities of mixtures containing ionic liquids and cyclic amides

• The C p , ( C p ) 123 have been assessed for binary and ternary mixtures at several temperatures. • C P E , ( C P E ) 123 have been evaluated using assessed data. • C P E , ( C P E ) 123 data have been analyzed in terms of Graph theory. • Graph theory precisely predicts C P E , ( C P E ) 123 data at the studied mole fractions. Current analysis pertains with the measurement of molar heat capacities, ( C P ) 123 for 1-butyl-2,3-dimethylimidazolium tetrafluoroborate [Bdmim][BF 4 ] or 1-ethyl-3-methylimidazolium tetrafluoroborate [Emim][BF 4 ] (1) + 1-methylpyrrolidin-2-one (NMP) (2) + pyrrolidin-2-one (2-PY) (3) ternary and C P for [Bdmim][BF 4 ] (1) + NMP (2) or 2-PY (3) binary mixtures within temperature series 293.15–308.15 K in a gap of 5 K. Excess heat capacities, ( C P E ) 123 , C P E have been determined using measured data. ( C P E ) 123 , C P E are positive at studied compositions for the ternary and binary mixtures, respectively. ( C P E ) 123 , C P E data have been tested in terms of Graph theory. A reasonable agreement has been perceived between experimental and calculated ( C P E ) 123 , C P E data.

Including state-of-the-art physical understanding of thermal vacancies in Calphad models

A physically sound thermochemical model accounting for explicit thermal vacancies in elements and alloys is presented. The model transfers the latest theoretical understanding of vacancy formation into the Calphad formalism where it can extend currently available thermodynamic databases to cover vacancy concentrations without a complete re-assessment. The parametrization of the model is based on ab initio-calculated enthalpy of vacancy formation and two model parameters describing the excess heat capacity of vacancy formation. Excellent agreement is obtained with temperature-dependent vacancy concentrations and elemental heat capacities while reasonable extrapolation of phase stability to high temperatures is ensured. Extrapolation to multicomponent systems is reasonable and the long-standing Neumann–Kopp related problem in the Calphad community is solved since multicomponent solid solutions will no longer show fingerprints of elemental heat capacity peaks at their melting points. FCC-Ag, FCC-Al and FCC-Cu, FCC-Zn, FCC-Ni, BCC-Ti, and BCC-W are used as a demonstration, along with the Cu–Zn binary system.