Internal thermodynamic modeling

Futerko and Hsing presented a thermodynamic model for water vapor uptake in perfluorosulfonic acid membranes.The following expression was used for the membrane—internal water activity, a, which was borrowed from the standard Flory—Huggins theory of concentrated polymer solutions ... 

It is therefore essential that thermodynamic modeling be applied to obtain a simultaneous quantitative fit to the phase diagram and thermodynamic data in order to evaluate the internal consistency of the various published data. Then a reliable framework can be established for smoothing, interpolating, and extrapolating experimental data that are costly and laborious to obtain. In Chapter 3 an associated solution model is presented. This model provides a good fit to the data for the Hg-Cd-Te system as well as for the Ga-In-Sb system, which is closer to the simpler picture of an ideal solution. 

Studies on thermodynamic restrictions on turbulence modeling show that the kinetic energy equation in a turbulent flow is a direct consequence of the first law of thermodynamics, and the turbulent dissipation rate is a thermodynamic internal variable. The principle of entropy generation, expressed in terms of the Clausius-Duhem and the Clausius-Planck inequalities, imposes restrictions on turbulence modeling. On the other hand, the turbulent dissipation rate as a thermodynamic internal variable ensmes that the mean internal dissipation will be positive and the thermodynamic modeling will be meaningful. 

When studying the surface acid-base properties of montmorillonite, it is essential to understand that hydrogen ions and cations of the support electrolyte can also participate in cation-exchange processes. The processes on the internal and external surfaces have to be taken into consideration simultaneously, and they both have to be included into the equilibrium thermodynamical models. 

Ghiorso M. S. and Sack R. O. (1995) Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-soUd equiUbria in magmatic systems at elevated temperatures and pressures. Contrib. Mineral. Petrol. 119, 197-212. 

Roth WL (1964) Magnetic properties of normal spinels with only A-A interactions. J Physique 25 507-515 Sack RO, Ghiorso MS (1991) An internally consistant model for the thermodynamic properties of Fe-Mg-titanomagnetite-aluminate spinels. Contrib Mineral Petrol 106 474-505 Salje EKH (1990) Phase Transitions in Ferroelastic and Co-elastic Crystals. Cambridge University Press, Cambridge, UK... 

Hejna, B. Thermodynamic Model of Noise Information Transfer. In AIP Conference Proceedings, Computing Anticipatory Systems CASYS 07 - Eighth International Conference Dubois, D., Ed. American Institute of Physics Melville, New York, 2008 pp 67-75. ISBN 978-0-7354-0579-0. ISSN 0094-243X. 

Three different approaches have been used. Firstly, the distribution of the major elements between mineral phases and a coexisting silicate melt may be calculated from experimental phase equilibrium data using regression techniques. Secondly, mineral-melt equilibria can be determined from mineral-melt distribution coefficients. A third, less empirical and more complex, approach is to use equilibrium thermodynamic models for magmatic systems. These require a thermodynamically valid mixing model for the liquid and an internally consistent set of solid-liquid thermodiemical data. 

The purpose of this chapter is to present the experimental results for the full-scale LAD outflow tests in liquid hydrogen. Test conditions were taken over a wide range of liquid temperatures (20.3-24.2 K), tank pressures (100-350 kPa), and outflow rates (0.010-0.055 kg/s) thermally and operationally representative of an in-space propellant transfer from a depot storage tank or to a smaller scale in-space engine. Horizontal LAD tests were conducted to measure independently the frictional and dynamic losses down the channel. Flow-through-screen tests were performed to measure independently the dominate pressure loss in LEO, the FTS resistance. Meanwhile, 1-g inverted vertical LAD outflow tests were conducted to obtain performance data for two full-scale 325 x 2300 LAD channels. One of the channels had a perforated plate and a custom-built internal thermodynamic vent system to enhance performance. Model predictions from Chapter 3 are compared to each set of experimental data. 

Kohler, S. Saadat, A., 2003. Thermodynamic Modeling of Binary Cycles Looking for Best Case Scenarios. International Geothermal Conference, 2003 Reykjavik, Island. 

Thermodynamic Modeling of the Internal Circulation Gasifier 347 Thermodynamic maxima for coid gas efficiency (---) and syngas yield (---)... 

By means of this thermodynamic model the internal friction for an isotropic ferromagnet near Tq was calculated by Belov et al. (1960) and Peqioular (1965). The internal friction characterizes the damping of the sample s sound vibrations with time and is defined as a ratio of the mechanical energy dissipated over a period of time to the fill mechanical energy of the sample. It is related to the sound attenuation coefficient as... 

The thermodynamic model stated above gives the following internal friction behavior for second-order magnetic phase transitions ... 

In this study, ab initio calculations have been performed to evaluate firstly, the influence of cationic disorder on internal energy variation (U) and excess of heat capacity evolution and secondly, the relative density behavior. The cationic disorder parameter versus temperature curve is deduced as a by product, according to an effective thermodynamic model using both a regular solution and a quadratic form of the internal energy [22]. Results are compared to available experimental data. 

The overall simulation of high-temperature corrosion processes under near-service conditions requires both a thermodynamic model to predict phase stabilities for given conditions and a mathematical description of the process kinetics, i.e. solid state diffusion. Such a simulation has been developed by integrating the thermodynamic program library, ChemApp, into a numerical finite-difference diffusion calculation, InCorr, to treat internal oxidation and nitridation of Ni-base alloys [10]. This simulation was intended to serve as a basis for an advanced computer model for internal oxidation and sulfidation of low-alloy boiler steels. 

The chemical composition, dimensions and the molecular parameters of four dental acrylic polymer materials and two polyacrylic acids of different molec.wt. used as model compounds were studied by NMR and IR spectroscopies, GPC, intrinsic viscosity and light scattering measurements. Two of the dental polymers were shown to be mainly polyacrylic acid, while one showed the peak pattern for an acrylic acid/methyl acrylate copolymer of about 2 1 composition and one was an oligomer derived from 2-hydroxyethyl methacrylate. The steric hindrance parameter, molecular stiffness and second virial coefficient were calculated using different thermodynamic models. The Flory-Fox-Shafgagen and the Stockmayer-Fixman models fitted the experimental data reasonably well and could be use to describe the molecular parameters of the acrylic polymers. 18 refs. (7th International Conference on Polymer Characterization (POLYCHAR-7), Denton, Texas, USA, Jan. 1999)... 

Figure IL8 Calculated changes using thermodynamic modelling as a function of metakaolin content. 70 wt.% portland cement +30 wt.% (metakaolin + limestone) based on the data from Steenberg et al. (2011) assuming complete reaction of metakaolin and A/S = 0.09 in C-S-H. (From Steenberg, M. et al., Composite cement based on portland cement clinker, limestone and calcined clay. Proceedings of the 13th International Congress on the Chemistry of Cement, Madrid, Spain, 97-104, 2011.)...

The explicit definition of water molecules seems to be the best way to represent the bulk properties of the solvent correctly. If only a thin layer of explicitly defined solvent molecules is used (due to hmited computational resources), difficulties may rise to reproduce the bulk behavior of water, especially near the border with the vacuum. Even with the definition of a full solvent environment the results depend on the model used for this purpose. In the relative simple case of TIP3P and SPC, which are widely and successfully used, the atoms of the water molecule have fixed charges and fixed relative orientation. Even without internal motions and the charge polarization ability, TIP3P reproduces the bulk properties of water quite well. For a further discussion of other available solvent models, readers are referred to Chapter VII, Section 1.3.2 of the Handbook. Unfortunately, the more sophisticated the water models are (to reproduce the physical properties and thermodynamics of this outstanding solvent correctly), the more impractical they are for being used within molecular dynamics simulations. 

Mathematical Consistency Requirements. Theoretical equations provide a method by which a data set s internal consistency can be tested or missing data can be derived from known values of related properties. The abiUty of data to fit a proven model may also provide insight into whether that data behaves correctiy and follows expected trends. For example, poor fit of vapor pressure versus temperature data to a generally accepted correlating equation could indicate systematic data error or bias. A simple sermlogarithmic form, (eg, the Antoine equation, eq. 8), has been shown to apply to most organic Hquids, so substantial deviation from this model might indicate a problem. Many other simple thermodynamics relations can provide useful data tests (1—5,18,21). 

It is reasonable to expeet that models in ehemistry should be capable of giving thermodynamic quantities to chemical accuracy. In this text, the phrase thermodynamic quantities means enthalpy changes A//, internal energy changes AU, heat capacities C, and so on, for gas-phase reactions. Where necessary, the gases are assumed ideal. The calculation of equilibrium constants and transport properties is also of great interest, but I don t have the space to deal with them in this text. Also, the term chemical accuracy means that we should be able to calculate the usual thermodynamic quantities to the same accuracy that an experimentalist would measure them ( 10kJmol ). 

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