Model calculations, thermodynamic

Models for Thermodynamic and Phase EquHibha Calculations, edited by Stanley I. Sandler... 

It had already been pointed out that there is not a single interface for which the Galvani potential can be either measured experimentally or calculated thermodynamically from indirect experimental data. The only way of determining it is through theoretical calculations based on nonthermodynamic models. 

Needless to say, an analysis which will finally allow one to nail down all rates, activation parameters, and equilibrium constants requires a large amount of precise and reliable kinetic data from appropriate experiments, including the determination of isotope effects and the like, as well as a rather sophisticated treatment and solution of the complete kinetic scheme. Then a comparison is necessary between various organosilanes with different types of C-H and C-Si bonds as well as the comparison between the dtbpm and the dcpm ligand systems, not to speak of model calculations in order to understand the molecular origin of the kinetic and thermodynamic numbers. We are presently in the process of solving these problems. 

It has been observed that cobalt may undergo large-scale reconstruction under a synthesis gas environment.27 Reconstruction is a thermodynamically driven process that results in the stabilization of less reactive surfaces. Recent molecular modeling calculations have shown that atomic carbon can induce the clock reconstruction of an fee cobalt (100) surface.28 It has also been postulated and shown with in situ x-ray adsorption spectroscopy (XAS) on cobalt supported on carbon nanofibers that small particles (<6 nm) undergo a reconstruction during FTS that can result in decreased activity.29... 

Considerable use has been made of the thermodynamic perturbation and thermodynamic integration methods in biochemical modelling, calculating the relative Gibbs energies of binding of inhibitors of biological macromolecules (e.g. proteins) with the aid of suitable thermodynamic cycles. Some applications to materials are described by Alfe et al. [11]. 

Self-consistent approaches in molecular modeling have to strike a balance of appropriate representation of the primary polymer chemistry, adequate treatment of molecular interactions, sufficient system size, and sufficient statistical sampling of structural configurations or elementary transport processes. They should account for nanoscale confinement and random network morphology and they should allow calculating thermodynamic properties and transport parameters. 

It is tempting to relate the thermodynamics of electron-transfer between metal atoms or ions and organic substrates directly to the relevant ionization potentials and electron affinities. These quantities certainly play a role in ET-thermo-dynamics but the dominant factor in inner sphere processes in which the product of electron transfer is an ion pair is the electrostatic interaction between the product ions. Model calculations on the reduction of ethylene by alkali metal atoms, for instance [69], showed that the energy difference between the M C2H4 ground state and the electron-transfer state can be... 

The constraint in Eq. (38) that enables the direct computation of Tg is obtained by the extension of the Lindemann criterion to the softening transformation in glass-forming liquids [42, 56, 129, 130], and the details of this relation are explained in Section VI. Within the schematic model for glass formation (with specified e, Es, and monomer structure), all calculated thermodynamic properties depend only on temperamre T, on pressure P, and on molar mass Mmoi (which is proportional to the number M of united atom groups in single chains). The present section summarizes the calculations for To, Tg, Ti, and Ta as functions of M for a constant pressure of P = 0.101325 MPa (1 atm). 

Thermodynamic model calculations, which take into account the current temperature gradient in the Rhine graben and the composition of the altered granite, have shown that the hydrothermal fluids present in the granite cause a new stage of alteration (Komninou Yardley 1997). Model calculations have been performed in order to predict the formation of new... 

Next, we used an in-house library design software (see details in Chapter 15) to enumerate the virtual libraries and then calculated various physical properties. Products were removed from consideration if MW is > 300, number of rotatable bonds > 3, and ClogP > 3. For solubility, two in-house model calculations were applied as filters turbidimetric >10 mg/mL and thermodynamic solubility >100 xM. The resulting cherry-picked library was then reviewed by NMR spectroscopists to remove compounds with possible artifacts, likely to be insoluble, or likely to be false positive. These included some conjugated systems and compounds with likelihood of indistinct NMR spectra. 

I. C. Sanchez and C. G. Panayiotou, Equation of State Thermodynamics of Polymer and Related Solutions, chapt. 3 in "Models for Thermodynamic and Phase equilibria Calculations, S. L. Sandler ed., M. Dekker, New York, 1994. 

From a Solution Model. Calculation of the difference in reduced standard-state chemical potentials by methods I or III in the absence of experimental thermodynamic properties for the liquid phase necessitates the imposition of a solution model to represent the activity coefficients of the stoichiometric liquid. Method I is equivalent to the equation of Vieland (106) and has been used almost exclusively in the literature. The principal difference between methods I and III is in the evaluation of the activity coefficients... 

As often is the case (see Chapter 2, Sections 2.2.6 and 2.7), the molecular mechanics analysis above does not include any electrostatic interaction energies. To include these, the charge distribution and the charge compensation by ion-pairing to counter ions (perchlorate) have to be known. Model calculations indicate that an effective charge of around +1.6 per copper site, a value that is expected from thermodynamic considerations, leads to electrostatic repulsion energies of ca. 17 kJ mol-1 and 10 kJ mol-1, respectively, for the folded and stretched conformers. In agreement with the experiment (EPR spectra), this qualitative analysis indicates a preference for the folded structure of A, and for the stretched structure of B1 201. 

Rafal et al. (Chapter 7, "Models for Electrolyte Solutions, in Models for Thermodynamic and Phase Equilibria Calculations, S. I. Sandler, ed., Marcel Dekker, New York, 1994, p. 686) have provided a comprehensive discussion of speciation and thermodynamic models. 

The p0 dependence of oxygen nonstoichiometry (8) was determined by using coulometric titration. The data were analyzed using a simple point defect model and thermodynamic quantities were calculated. From this model, the standard enthalpy for oxidation (AH0f) and disproportionation (A77D) were determined to be -140.7 and 228.7 kJ/mol, respectively. The mobilities of the electron holes, electrons, and oxygen ions were calculated from the conductivity data using the defect concentrations determined from the stoichiometry and point defect model. 

Under natural conditions, these organisms derive little energy from nitrate reduction so the total biomass increase is small and slow in comparison to the turnover of reactants. Equilibrium models from thermodynamic calculations can often provide a useful first approximation for a real system. These models are limited by the accuracy and availability of thermodynamic data including temperature, pressure and activity dependencies, knowledge of all pertinent chemical species and related equilibria. 

The algorithm used to equilibrate ice, COy-bHoO, and CH4 6H2O with the solution phase uses aspects of several of the above techniques. First, the model calculates the fugacity coefficients for CC>2(g) and CH4(g) using the approach outlined in Eqs. 3.36 to 3.48 and 3.72 to 3.74. Then the model calculates which of the phases - ice, C02-6H20, or CH4-6H20 - is thermodynamically most stable by selecting the phase that minimizes the activity of water (aw). The reaction,... 

The FREZCHEM model was designed to characterize aqueous electrolyte solutions. To work properly, there must always be ions in solution, even if only hypothetical. To simulate pure water, pure gas hydrate, pure ice, or other nonion equilibria, you need to add minor concentrations of ions (e.g., Na = Cl = 1 x 10 6m). Such minor concentrations do not significantly affect the thermodynamic properties, but they do allow for proper model calculations. 

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