Interaction parameters between model calculations

In this equation, all molecules are divided into four groups paraffins (P), olefins (O), naphthenics (N), and aromatics (A). The v values represent the volume fractions of each component used, while the fa values are the blending values, which were calculated for each of the molecular lumps shown in Table 2. Pure component octane numbers used are designated as ON/, but one should note that in the development of the model, 57 molecular lumps were made based on GC analysis, and pure component ONs were assigned to each lump, and not necessarily each pure component. The kt values are calculated interaction parameters between paraffins, olefins, and naphthenics, and are also shown in Table 2. Based on this equation, and knowing the composition and pure octane numbers of a fuel mixture, an estimation of the blending ON may then be made. 

Chapter 18 - The determination region of solubility of methanol with gasoline of high aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquid-liquid phase diagram was obtained for this ternary system. These results were correlated simultaneously by the UNIQUAC model. By application of this model and the experimental data the values of the interaction parameters between each pair of components in the system were determined. This revealed that the root mean square deviation (RMSD) between the observed and calculated mole percents was 3.57% for methylcyclohexane + methanol + ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol at 288.2 K. 

The optimum UNIQUAC interaction parameters between methyl cyclohexane, methanol and ethylbenzene were determined using the experimental liquid-liquid data. The average RMSD value between the observed and calculated mole percents with a reasonable error for these system were methylcyclohexane + methanol + ethylbenzene, in the UNIQUAC model. 

Just a few years ago, the limitations of solubility parameter calculations and measurements discussed above were serious impediments to modeling the phasic and interfacial behaviors of polymeric systems. The coming of age of atomistic simulation methods over the last few years has improved this situation dramatically. As discussed in Section 5.A.3, whenever accuracy is important in calculating the phasic or the interfacial behavior of a system, it is nowadays strongly preferable to use atomistic simulations employing modem force fields of the highest available quality instead of solubility parameters in order to estimate the Flory-Huggins interaction parameters (%) between the system components as input for further calculations. 

Table IV. Binary Interaction Parameters (Ay and /,) and Standard Deviations (s/cm3 mol 1) between Model Calculations and the...

The LLE data of the ternary system composed of water + ethanol + cyclohexane were measmed at different temperatures of 298.2, 303.2, 308.2, and 313.2 K. The UNIQUAC model was used to correlate the experimental LLE data. The optimum UNIQUAC interaction parameters between water, ethanol, and 2-etyl-l-hexanol were determined using the experimental (liquid + liquid) data. The average rmsd value between the observed and calculated mole fractions with a reasonable error was 1.70% for the UNIQUAC model. The solubility of water in cyclohexane increases with amoimts of ethanol added to water + 2-ethyl-hexanol mixtore. 

Typical behaviour of osmotic and activity coefficients as calculated using Eqs. (5.36) and (5.37), is illustrated for trisodium citrate and tripotassium citrate in Fig. 5.15. It can be observed, that values of the (/w) and y+(/w) coefficients after a strong fall in very dilute solutions depend rather weakly on the citrate concentration. Since a T-,m) values are nearly temperature independent, the same is observed in the case osmotic and activity coefficients. It is worthwhile to mention that the Pitzer model was also used by Schunk and Maurer [163] when they determined water activities at 25 °C in ternary systems (citric acid + inorganic salt). The interactions parameters between ions, which were applied to represent activities in ternary systems, were calculated by taking into account the dissociation steps of citric acid and the formation of bisulfate ions for solutions with sodium sulfate. 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

A comparison between the Eg values listed in tables I and II with theoretical Gg values is not possible at present, since for calculation of Gg one needs to know the polymer-solvent interaction parameter as a function of Na2S04 concentration. Moreover, an assumption must be made about the segment distribution of the adsorbed layer. In the absence of such information, it is not possible to calculate Gg. However, the values of Eg obtained from rheology (tables I and II) are reasonable, considering the approximation made and the crude model used for calculating Es. 

The optimum UNIQUAC interaction parameters u, between methylcyclohexane, methanol, and ethylbenzene were determined using the observed liquid-liquid data, where the interaction parameters describe the interaction energy between molecules i and j or between each pair of compounds. Table 4 show the calculated value of the UNIQUAC binary interaction parameters for the mixture methanol + ethylbenzene using universal values for the UNIQUAC structural parameters. The equilibrium model was optimized using an objective function, which was developed by Sorensen [15],... 

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