Determination from interaction parameter

Second, using the fully relativistic version of the TB-LMTO-CPA method within the atomic sphere approximation (ASA) we have calculated the total energies for random alloys AiBi i at five concentrations, x — 0,0.25,0.5,0.75 and 1, and using the CW method modified for disordered alloys we have determined five interaction parameters Eq, D,V,T, and Q as before (superscript RA). Finally, the electronic structure of random alloys calculated by the TB-LMTO-CPA method served as an input of the GPM from which the pair interactions v(c) (superscript GPM) were determined. In order to eliminate the charge transfer effects in these calculations, the atomic radii were adjusted in such a way that atoms were charge neutral while preserving the total volume of the alloy. The quantity (c) used for comparisons is a sum of properly... 

Thus, if the saturated vapor pressure is known at the azeotropic composition, the activity coefficient can be calculated. If the composition of the azeotrope is known, then the compositions and activity of the coefficients at the azeotrope can be substituted into the Wilson equation to determine the interaction parameters. For the 2-propanol-water system, the azeotropic composition of 2-propanol can be assumed to be at a mole fraction of 0.69 and temperature of 353.4 K at 1 atm. By combining Equation 4.93 with the Wilson equation for a binary system, set up two simultaneous equations and solve Au and A21. Vapor pressure data can be taken from Table 4.11 and the universal gas constant can be taken to be 8.3145 kJ-kmol 1-K 1. Then, using the values of molar volume in Table 4.12, calculate the interaction parameters for the Wilson equation and compare with the values in Table 4.12. 

Carbon Dioxide - Water System, The data of Wiebe and Gaddy (4, 5, 6) were used exclusively in this study to determine the interaction parameters for the carbon dioxide - water binary system. These data cover the temperature and pressure range from 12°C to 100°C and from 25 atm to 700 atm respectively. As with the HzS - H2O system, a constant interaction parameter has been obtained for the gaseous phase and the carbon dioxide - rich... 

Peppas N, Merrill E. Determination of interaction parameter for poly(vinyl alcohol) in gels crosslinked from solution. Journal of Polymer Science 1976, 14, 459 464. 

In the case of MAS, the spectra typically display a number of spinning sidebands spaced by the spinning frequency. The intensities of the spinning sidebands approximately represent the intensity of the static powder spectrum and hence the overall envelope of the sideband intensities represents the powder line shape. While analytical solutions have also been derived for the intensity of the sidebands as a function of the spinning frequency and anisotropic shielding parameters, it is typically much easier to determine these interaction parameters from numerical simulations - again considering that this method directly takes the experimental errors and spectral noise into account. 

As discussed in Chapter 2 of this Handbook, the osmotic pressure can provide one of the most direct methods of determination of interaction parameter. The estimation of these interaction parameters is applied to PS/PVME blends in toluene and ethyl benzene respectively [Shiomi et al., 1985]. It is observed that in toluene varied with composition from -0.044 to h-0.0093, while in ethyl benzene it increased with PVME content from -0.06 to 0.027. 

The absolute melting temperature for the polymer (M = 12,200) was reported to be 501K. From these data, determine the interaction parameter and the heat of fusion (density of m-cresol = 1.03 g cm and density of nylon 6 = 1.12 g cm- ). 

The activit of toluene in a toluene/polyphenyleneoxide (PPO) solution has been determined from vapour pressure measurements. At a volume ftaction of toluene of < = 0.75 the activity El = 0.99. Determine the interaction parameter % uwpo- The molecular weight of PPO is 10 g/mol. 

From a, b, c one can also determine the interaction parameters such as repulsive energy J between oil and... 

In terms of interaction parameters J and L within the spin-lattice model, Gompper and Schick have calculated the structure function of bicontinuous microemulsion systems. Comparing the structure functions obtainable from SANS with those calculated ones by Gompper and Schick, we could determine the interaction parameters in right order of magnitude. 

In the next step, we have determined microscopic interaction parameters. We adopted an approximation, which was successfully used in calculating the interaction parameters of the water/AOT/decane system [13]. We calculated the parameters a, b and c of Gompper and Schick s scattering formula (5) in terms of the fitting parameters A, B and C of Teubner-Strey s scattering formula (1) for variable values of d and subsequently the interaction parameters JjT, L jT and 0s from Eq. (7). Figure 4 is an example of the result of JjT, L /T and 0s as a function of d for the LTM phase. In order to determine the interaction parameters we need a proper value of lattice parameter d, which is related to the molecular length of the surfactant. We have chosen d = 15 A for all three phases, which was found to be suitable in this system for the reason described... 

Binary interaction parameters are determined for each pq pair p q) from experimental data. Note that = k and k = k = 0. Since the quantity on the left-hand side of Eq. (4-305) represents the second virial coefficient as predicted by Eq. (4-231), the basis for Eq. (4-305) lies in Eq. (4-183), which expresses the quadratic dependence of the mixture second virial coefficient on mole fraction. 

Another problem of atomic charges determined by fitting is related to the absolute accuracy. Although inclusion of charges on all atoms does not significantly improve the results over those determined from a reduced set of parameters, the absolute deviation between the true and fitted electrostatic potentials can be quite large. Interaction... 

Due to the linear Independence of occupation indices Tji the concentration-dependent parameters can be determined from the concentration-independent ones. In the special case of interactions limited to the fourth order and nearest neighbors one finds for fcc-based alloys... 

The term pt is a binary interaction parameter which must be determined from phase equilibrium data. We will discuss determination of p 9 values in more detail later. 

The algorithm we used for solvent/polydisperse polymer equilibria calls for only one solvent/polymer interaction parameter. The interaction parameter (pto) i ed in the algorithm can be determined from essentially any type of ethylene/polyethylene phase equilibrium data. Cloud-point data have been used (18). while Cheng (16) and Harmony ( ) have done so from gas sorption data. 

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