Gibbs energy simulation

Sakane, S. Liu, W. B. Doren, D. J. Shock, E. L. Wood, R. H., Prediction of the Gibbs energies and an improved equation of state for water at extreme conditions from ab initio energies with classical simulations, Geochim. Cosmochim. Acta 2001, 65, 4067 1075... 

Smit et al. [19] used the partition function given by (10.4) and a free energy minimization procedure to show that, for a system with a first-order phase transition, the two regions in a Gibbs ensemble simulation are expected to reach the correct equilibrium densities. 

The Helmholtz and Gibbs energies on the other hand involve constant temperature and volume and constant temperature and pressure, respectively. Most experiments are done at constant Tandp, and most simulations at constant Tand V. Thus, we have now defined two functions of great practical use. In a spontaneous process at constant p and T or constant p and V, the Gibbs or Helmholtz energies, respectively, of the system decrease. These are, however, only other measures of the second law and imply that the total entropy of the system and the surroundings increases. 

Figs. 5.5 and 5.6 show the deviation in the activity coefficients predicted by COSMOSPACE and the BGY model from those obtained directly from the MC simulations using an addition to our MC code, which allows us to evaluate the activity coefficients of the components. We see from these results that COSMOSPACE is in much better agreement with the MC simulations than the BGY model. We have not calculated the activity coefficients for the AD model since it is not a model for the excess Gibbs energy. 

The local composition model (LCM) is an excess Gibbs energy model for electrolyte systems from which activity coefficients can be derived. Chen and co-workers (17-19) presented the original LCM activity coefficient equations for binary and multicomponent systems. The LCM equations were subsequently modified (1, 2) and used in the ASPEN process simulator (Aspen Technology Inc.) as a means of handling chemical processes with electrolytes. The LCM activity coefficient equations are explicit functions, and require computational methods. Due to length and complexity, only the salient features of the LCM equations will be reviewed in this paper. The Aspen Plus Electrolyte Manual (1) and Taylor (21) present the final form of the LCM binary and multicomponent equations used in this work. 

To finalize the development of the aqueous CO2 force field parameters, the C02 model was used in free energy perturbation Monte Carlo (FEP/MC) simulations to determine the solubility of C02 in water. The solubility of C02 in water is calculated as a function of temperature in the development process to maintain transferability of the C02 model to different simulation techniques and to quantify the robustness of the technique used in the solubility calculations. It is also noted that the calculated solubility is based upon the change in the Gibbs energy of the system and that parameter development must account for the entropy/enthalpy balance that contributes to the overall structure of the solute and solvent over the temperature range being modeled [17]. 

Figure 1.7. Gibbs energy of mixing for 1-propanol(1)-water(2) by the Aspen Plus simulator using the NRTL model.

In the theoretical treatment of diffusive reactions, one usually works with diffusion coefficients, which are evaluated from experimental measurements. In a multicomponent system, a large number of diffusion coefficients must be evaluated, and are generally interrelated functions of alloy composition. A database would, thus, be very complex. A superior alternative is to store atomic mobilities in the database, rather than diffusion coefficients. The number of parameters which need to be stored in a multicomponent system will then be substantially reduced, as the parameters are independent. The diffusion coefficients, which are used in the simulations, can then be obtained as a product of a thermodynamic and a kinetic factor. The thermodynamic factor is essentially the second derivative of the molar Gibbs energy with respect to the concentrations, and is known if the system has been assessed thermodynamically. The kinetic factor contains the atomic mobilities, which are stored in the kinetic database. 

The Gibbs energy of solvation is also accessible by models of statistical thermodynamics and can be directly calculated by molecular simulation using realistic intermolecular force fields for both the solvent and the solute. The link between the macroscopic properties and the microscopic interactions can then be established and the molecular mechanisms of solvation can be investigated following adequate and easily implemented in silico experiments. 

We end this long chapter with a brief discussion of a very important subject of intensive research. We present here only a few aspects of protein solvation. Since proteins do not have any measurable vapor pressure, their solvation Gibbs energy cannot be measured. It is also extremely difficult to compute it either theoretically or by simulation methods. However, owing to the utmost... 

Standard enthalpies of formation Ah and standard Gibbs energies of formation Agj are important for the calculation of enthalpies of reaction and chemical equilibria. For their estimation, the standard state at To = 298.15 K and Po = 101325 Pa in the ideal gas state is used. In process simulation programs, standard enthalpies and standard Gibbs energies of formation in the ideal gas state are usually taken as reference points for enthalpy calculation so that enthalpy and Gibbs energy differences are consistent with respect to chemical reactions. 

The following example shall illustrate the procedure of using the standard Gibbs energy of formation in a process simulator again, it should be pointed out that chemical reactions are explained in more detail in Chapter 12. 

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