Prediction Of Heat Capacity Research Articles

A new coordination number model and heat capacity of square-well fluids of variable width

A new coordination number model for square-well fluid is proposed in this work. The model modifies the theory previously developed for the coordination number of square-well fluids derived on the basis of the generalized van der Waals theory by Largo and Solana. In the present work, we have calculated the co-ordination number of a square-well fluid on the basis of high temperature expansion (HTE) approach along with the modified formula of the maximum reduced density and a novel approach to derive the coordination number of hard sphere fluids. We have also performed the theoretical predictions of constant-volume excess heat capacity of the square-well fluids. It is shown that the theoretical predictions of the constant-volume excess heat capacity determined by second-order perturbation term are in much better agreement with simulation data than to the values of C V E / N K obtained by other workers due to the better description of the second-order term.

Estimation of the Differential Molar Heat Capacities of Organic Compounds at Their Melting Point

Methods for the estimation of the differential molar heat capacity, the difference between the heat capacity of the solid and the liquid form of organic compounds at their melting point Δcp(Tm), are presented. Three schemes are considered: the first involves use of group contribution methods for the prediction of solid heat capacity (cpS) and liquid heat capacity (cpL); the other two, empirical correlations through the entropy of fusion at the melting point ΔSf(Tm). Recommendations for the different categories of organic compounds are made that provide substantial improvement over the commonly used assumption of Δcp = 0, in the prediction of ideal solid solubility and solid vapor pressure.

A flexible approach for understanding protein stability

A distance constraint model (DCM) is presented that identifies flexible regions within protein structure consistent with specified thermodynamic condition. The DCM is based on a rigorous free energy decomposition scheme representing structure as fluctuating constraint topologies. Entropy non-additivity is problematic for naive decompositions, limiting the success of heat capacity predictions. The DCM resolves non-additivity by summing over independent entropic components determined by an efficient network-rigidity algorithm. A minimal 3-parameter DCM is demonstrated to accurately reproduce experimental heat capacity curves. Free energy landscapes and quantitative stability-flexibility relationships are obtained in terms of global flexibility. Several connections to experiment are made.

Support Vector Machines‐Based Quantitative Structure—Property Relationship for the Prediction of Heat Capacity.

The support vector machine (SVM), as a novel type of learning machine, for the first time, was used to develop a Quantitative Structure-Property Relationship (QSPR) model of the heat capacity of a diverse set of 182 compounds based on the molecular descriptors calculated from the structure alone. Multiple linear regression (MLR) and radial basis function networks (RBFNNs) were also utilized to construct quantitative linear and nonlinear models to compare with the results obtained by SVM. The root-mean-square (rms) errors in heat capacity predictions for the whole data set given by MLR, RBFNNs, and SVM were 4.648, 4.337, and 2.931 heat capacity units, respectively. The prediction results are in good agreement with the experimental value of heat capacity; also, the results reveal the superiority of the SVM over MLR and RBFNNs models.

Support vector machines-based quantitative structure-property relationship for the prediction of heat capacity.

The support vector machine (SVM), as a novel type of learning machine, for the first time, was used to develop a Quantitative Structure-Property Relationship (QSPR) model of the heat capacity of a diverse set of 182 compounds based on the molecular descriptors calculated from the structure alone. Multiple linear regression (MLR) and radial basis function networks (RBFNNs) were also utilized to construct quantitative linear and nonlinear models to compare with the results obtained by SVM. The root-mean-square (rms) errors in heat capacity predictions for the whole data set given by MLR, RBFNNs, and SVM were 4.648, 4.337, and 2.931 heat capacity units, respectively. The prediction results are in good agreement with the experimental value of heat capacity; also, the results reveal the superiority of the SVM over MLR and RBFNNs models.

QSPR: Application to Heat Capacity Calculation

Within the framework of QSPR simulation methodology the practicality was demonstrated of fragment approach for forecasting heat capacity of various class organic compounds. An equation was advanced permitting reliable prediction of organic compounds heat capacity proceeding from Vx, parameter characterizing the molecule volume, and from fragment descriptors.

Quantitative structure property relationship models for the prediction of liquid heat capacity

AbstractQuantitative Structure‐Property Relationship (QSPR) models based on molecular descriptors derived from molecular structures have been developed for the prediction of liquid heat capacity at 25 °C using a diverse set of 871 organic compounds. The molecular descriptors used to represent molecular structures include constitutional and topological indices and quantum chemical parameters. Forward stepwise regression and radial basis function neural networks (RBFNNs) were used to construct the QSPR models. The root mean square errors in liquid heat capacity predictions for the training, test and overall data sets are 16.857, 18.744 and 17.141 heat capacity units, respectively. The prediction results are in agreement with the experimental values, but the RBFNN model seems to be better than stepwise regression method.

Predictions of Conformational Enthalpy and Heat Capacity from the Zimm−Bragg Theory

Statistical mechanical calculations are presented of the conformational enthalpy and heat capacity of a solution of poly-γ-benzyl-l-glutamate using the partition function of Zimm and Bragg for helix−coil transitions. We determine the temperature dependence of the statistical parameter s from optical data and treat the parameter σ as a fitting parameter. We note, however, that consistency with the Zimm−Bragg theory requires that σ not be less than the square of the reciprocal of the number of residues per molecule. We utilize that data given by Ackermann and Ruterjans [Ackermann, Th.; Ruterjans, H. Ber. Bunsen-Ges. Phys. Chem. 1964, 68, 850] and find the same value for σ as they, σ = 2.5 × 10-5 for their solution of 0.257 mol of residue per liter in a solvent of dichloracetic acid and 1,2-dichlorethane. We consider our calculation to be in satisfactory agreement with that of the experiment but point out some problems associated with the determination of the temperature dependence of s.

New Perturbation Theory Model for Chainlike Molecule Fluid and the Predicted Heat Capacity

New Perturbation Theory Model for Chainlike Molecule Fluid and the Predicted Heat Capacity

Determination of the Fundamental Frequencies of Fluorochloro-Derivatives of Ethane and Its Application to Calculate Ideal Gas Heat Capacities

Quantum mechanical calculations for all fluorochloro-derivatives of ethane were performed. It was shown that the B3LYP/cc-pVDZ density functional method and single-point MP2/cc-pVTZ calculations lead to an accuracy of the molecular data that is sufficient for prediction of ideal gas heat capacities. Finally, reliable experimental heat capacity data reveal that an uncertainty of the heat capacity calculations of ±1.5% or less is achieved.

Equation of State of UO2

An international project supported by INTAS (International Association for Promotion of Cooperation with Scientists from the New Independent States of the former Soviet Union) was started in 1994 with the intent of constructing an equation of state (EOS) for liquid and gaseous UO2, which fully reproduces the comprehensive thermodynamic database for this compound. The new equation of state was devised for applications encompassing hypo- and hyper-stoichiometric compositions. A so-called “chemical model” was used for the theoretical description of liquid urania. This model is based on the thermodynamic perturbation theory (TPT) modified in order to account for the specific properties of the system investigated. It describes, in a unified formalism, a multicomponent mixture of chemically reactive, strongly interacting neutral and charged molecules and atoms. Comparisons of the predicted equilibrium vapor pressures with literature data provided an initial validation of the model up to temperatures of the order of 5500 K. A further, positive result is the fairly good agreement of the predicted heat capacity with experimental values, which extend up to 8000 K. A characteristic feature of non-congruentvaporization in UO2±x is the production of a very high maximum vapor pressure (P max∼1 GPa) as well as a substantial oxygen enrichment of the vapor phase over boiling UO2 ((O/U)max∼7). The critical point of a truly non-congruent phase transition in UO2 was also calculated. This point essentially differs from that defined for a gas–liquid phase transition in simple liquids; in particular, the equation (∂P/∂V) c ∼(P/V)≠0 applies here. The predicted critical parameters are: T c≈10120 K, P c≈965 MPa, ρ c≈2.61 g·cm−3.

Theoretical Prediction of Ideal Gas Heat Capacities of HCFCs

The ideal gas heat capacities of halogenated hydrocarbons are only partly known from experiments with the necessary accuracy. In an earlier approach to improve the knowledge of heat capacity data a method was applied which combined statistical thermodynamics and an intramolecular force field parameterized to experimental data. As outlined here, this method is further improved by combining quantum-mechanical calculations and statistical thermodynamics.

A Model for the Lipid Pretransition: Coupling of Ripple Formation with the Chain-Melting Transition

Below the thermotropic chain-melting transition, lipid membrane c P traces display a transition of low enthalpy called the lipid pretransition. It is linked to the formation of periodic membrane ripples. In the literature, these two transitions are usually regarded as independent events. Here, we present a model that is based on the assumption that both pretransition and main transition are caused by the same physical effect, namely chain melting. The splitting of the melting process into two peaks is found to be a consequence of the coupling of structural changes and chain-melting events. On the basis of this concept, we performed Monte Carlo simulations using two coupled monolayer lattices. In this calculation, ripples are considered to be one-dimensional defects of fluid lipid molecules. Because lipids change their area by ∼24% upon melting, line defects are the only ones that are topologically possible in a triangular lattice. The formation of a fluid line defect on one monolayer leads to a local bending of the membrane. Geometric constraints result in the formation of periodic patterns of gel and fluid domains. This model, for the first time, is able to predict heat capacity profiles, which are comparable to the experimental c P traces that we obtained using calorimetry. The basic assumptions are in agreement with a large number of experimental observations.

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.

A correction to Sandler–Wong mixing rules

Due to the temperature dependence of the covolume created by the use of Sandler–Wong mixing rules, thermodynamically inconsistent results will be predicted at very high pressures, including the prediction of negative heat capacities. In this paper, we propose a simple modification to the mixing rule, which prevents this problem and which performs slightly better in the prediction of the Gibbs excess energy.

Modeling lattice heat-capacity contributions by a single-parametric phonon dispersion approach

A new phonon distribution model was developed to provide a precise and reliable equation for lattice heat capacity at constant volume,e.g.for the resolution of excess thermophysical properties. Because this equation has a single characteristic temperature as a parameter determined after assignment of the other parameters available from chemical, crystallographical and/or elastic information, it is relatively easy to fit the model to the experimental heat-capacity data. It is based on the harmonic oscillator model and, therefore, may require adjustment at high sub-ambient temperatures or super-ambient regions. Three FORTRAN IV computer programs provide convenient devices to calculate the apparent characteristic temperatures from given heat-capacity values, to calculate lattice heat-capacity values for given characteristic temperatures, and to compare the (model) predicted heat capacity with experimental heat-capacity values.

Inorganic species in geologic fluids: Correlations among standard molal thermodynamic properties of aqueous ions and hydroxide complexes

Correlations among experimentally determined standard partial molal thermodynamic properties of inorganic aqueous species at 25°C and 1 bar allow estimates of these properties for numerous monatomic cations and anions, polyatomic anions, oxyanions, acid oxyanions, neutral oxy-acid species, dissolved gases, and hydroxide complexes of metal cations. Combined with correlations among parameters in the revised Helgeson-Kirkham-Flowers (HKF) equation of state (Shock et al., 1992), these estimates permit predictions of standard partial molal volumes ( V° ), heat capacities ( C° P ), and entropies ( S° ), as well as apparent standard partial molal enthalpies ( Δ H° P,T ) and Gibbs free energies (ΔḠ° P,T) of formation to 1000°C and 5 kb for hundreds of inorganic aqueous species of interest in geochemistry. Data and parameters for more than 300 inorganic aqueous species are presented. Close agreement between calculated and experimentally determined equilibrium constants for acid dissociation reactions and cation hydrolysis reactions supports the generality and validity of these predictive methods. These data facilitate the calculation of the speciation of major, minor, and trace elements in hydrothermal and metamorphic fluids throughout most of the crust of the Earth.

On the applicability of the Sandler-Wong mixing rules for the calculation of thermodynamic excess properties— VE, HE, SE, CpE

Investigation of derived thermodynamic properties using Sandler-Wong mixing rules shows that predicted excess properties can be unreliable since they are a complex function of the original Gibbs free energy model and the a and b terms. Sometimes the mixing rule will predict a different qualitative behaviour for the heat of mixing when compared to the one predicted by the original Gibbs excess model. Moreover the mixing rules can produce thermodynamic inconsistency at elavated pressures and lead to the prediction of negative heat capacities.

Thermodynamics of alkanol–alkane systems. New modifications of the ERAS model

A new modification of the ERAS model, which is widely used to describe thermodynamic properties of alcohol–alkane systems, has been proposed. Its necessity results mainly from the observation that the original model is not able to reproduce excess heat capacity data. It is based on a different formulation of the so-called chemical contribution to the model. The refined approach has been tested through correlation and prediction of excess heat capacities, excess enthalpies, excess volumes, excess Gibbs energies and also the spectroscopic properties, giving results better, or not worse, than the original ERAS model.

Prediction of Heat Capacities of Solid Inorganic Salts from Group Contributions

A group contribution technique is proposed to predict the coefficients in the heat capacity correlation, C p = a + bT + c/T 2 + dT 2 , for solid inorganic salts. The results from this work are compared with experimental data from the literature. The technique is shown to give good predictions for both simple and complex solid inorganic salts. Literature heat capacities for a large number (664) of solid inorganic salts covering a broad range of cations (129), anions (17), and ligands (2) have been used in regressions to obtain group contributions for the parameters in the heat capacity temperature function. A mean error of 3.18% is found when predicted values are compared with literature values for heat capacity at 298 K.