Isothermal fits, interaction parameters

Figure 6. Dimensionless interaction parameters as determined from isothermal fits at various temperatures ((- -) KBr-water ( ) NaCl—water)...

The interaction parameters are weak, linear functions of temperature, as shown in Table 5, Table 6 and Figure 6. These tables and figure show the results of isothermal fits for activity coefficient data of aqueous NaCl and KBr at various temperatures. The Pitzer equation parameters are, however, strongly dependent on temperature (Silvester and Pitzer, (23)). 

The standard deviation has been determined as ct = j where v is the number of degrees of freedom in the fit. The parameters for the molecular interaction /3, the maximum adsorption Too, the equilibrium constant for adsorption of surfactant ions Ki, and the equilibrium constant for adsorption of counterions K2, are thus obtained. The non-linear equations for the Frumkin adsorption isotherm have been numerically solved by the bisection method. 

Monte Carlo isotherms of interacting and noninteracting dimers on a square lattice have been interpreted in terms of the new isotherm proposed in eq. (8). w and g were assumed as fitting parameters of our analysis and k=2 since data correspond to dimer adsorption. 

We have examined whether a simple non-bonded potential can be developed to be (i) transferable from one zeolite to another and (ii) to simulate without parameter adjustment isosteric heats at different temperatures and sorption uptake isotherms. The sorption of methane into Na- and K- zeolite X, and Na-and K-clinoptilolites was considered. Models for Na-X and K-X were constructed based on the averaged crystallographic results. The non-bonded parameters in a Lennard-Jones potential were iteratively adjusted so as to best reproduce the experimental isosteric heats in Na-X and K-X over a small temperature range. Methane-methane interaction parameters were taken from earlier work [89] and a final iteration was made so as to better fit the experimental sorption isotherms in clinoptilolite. This single and simple non-bonded potential parameter set then reproduces to a reasonable degree... 

The simulation adsorption isotherms for 1/2 adsorption on a square lattice at different values of the interaction parameter co are shown in Fig. 8.4. The interaction energy, V Meads-Mcads evaluated using a fit of experimental isotherm data of a... 

The goal is to obtain the unknown parameters for a selected isotherm equation. Special parameters of nearly all types of isotherms are the Henry coefficient as well as the saturation capacities for large concentrations. It is advisable to check the validity of the single-component isotherm equation before determining the component interaction parameters. In general the decision on a certain isotherm equation should be made on the basis of the ability to predict the experimental overloaded concentration profiles rather than fitting the experimental isotherm data. In any case, consistency with the Henry coefficient determined from initial pulse experiments with very low sample amounts must be fulfilled. 

At Tj = 180 °C for NFBN-DPEDC and at T = 200 °C for NFBN-DCBA (isothermal polymerization), the conversions, xcp, where blends with different fractions of additive became cloudy, were measured. Figure 3 shows that the evolution of xcp with the additive fraction is weak, and xcp is always lower than the gel conversion of the cyanates, about 0.6. For a polymer blend with two components, the free energy of mixing per unit volume of blend can be expressed by the Flory-Huggins equation. Elsewhere (30), we estimate the Flory-Huggins interaction parameter x by fitting the experimental points. 

Figure 6.18. Interfacial tension between polystyrene and poly(vinyl pyridine) in the presence of styrene-2-vinyl pyridine block copolymer, as calculated by self-consistent field theory for the system whose interfacial excess is shown in figure 6.17. The value of the Flory-Huggins interaction parameter Xps-pvp was taken as 0.11, which provides a good fit to the adsorption isotherm below the CMC. After Shull et al. (1990).

The isothermal miscibility map as shown in Table 3.7 delineates the miscibility from the immiscibility regions. Develop the binary interaction energy for the binary blend between two copolymers without any common monomers. Use linear regression and obtain the best-fit parameters for the six binary interaction parameter B,-, pairs using the information provided. Interpolate the isothermal miscibility map if necessary. 

In Figure 2.15 [66] experimental isothermal cloud-point curves of the linear low density polyethylene + hexane system are compared with the results of a fit of these data using the Sanchez-Lacombe equation of state. The pure component parameters of hexane were calculated from the critical point of hexane and its acentric factor [67]. The pure component parameters of the polymer were obtained from a simultaneous fit of PVT data and the data presented in Figure 2.15. The equations solved were those described by Koak and Heidemann [68]. The binary interaction parameter was linearly dependent on temperature. The polymer was... 

Solubility data for the systems PCL/CO2 and PCL/nanoclays/COa were then predicted by means of the equations 5-7 and they are reported in Figure 6. The amount of gas absorbed in the polymeric matrix was reduced by the presence of nanoclay particles and this effect was more pronounced in nanocomposites that showed complete clay exfoliation. As a matter of fact, the highest reduction of solubility was observed in samples containing 5% of nanoclay. In this case, the reduction of the solubility of CO2 in PCL was about 12%. The calculated sorption isotherms in this work were sensitive to the value of the interaction parameter tjf, contained in The best fitting was obtained by using a value of 0.98 for the interaction parameter = 1... 

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