Predictions Based upon Theoretical Equations

Comparison of predictions based upon the theoretical equations with experimental data. The specific systems considered are ... 

Figure 11 shows the theoretical permeabilities that are expected for a two-phase blend of polymers. The two solid curves represent calculations based upon Maxwell s equation (24) for an aspect ratio of 1 for the discontinuous phase. The dotted line is a prediction of the permeability using Nielsen s model (25) when a barrier polymer with an aspect ratio of 8 is discontinuous in a nonbarrier matrix. Figure 12 shows the expected result of a phase inversion for a two-polymer blend. The discontinuous phase is assumed to have an aspect ratio of 1. At some critical composition, the composite switches from being continuous in one polymer to being continuous in the other. Figure 12 is really a special case of Figure 11. Selar RB is a blend of polyethylene and nylon-6. Polyethylene is the majority constituent and forms the continuous phase. The product has its best barrier when it can be used in processes that impart orientation to the product. This gives a high aspect ratio to the nylon-6 and enhanced barrier to the article. Blends of polyethylene and EVOH are being developed.

The most appropriate form of the theoretical equations for predictive purposes is that based upon the Hirschfelder-Eucken result of equation (4.127) in which all of the various diffusion coefficients for internal energy are replaced by binary diffusion coefficients. That is, equation (4.127) is rewritten as... 

Theoretical equations, based upon extended Debye-Huckel parameters or equations of state, have been advanced by Pitzer [78] and Helgeson [79] to predict the behavior of electrolyte solutions over a wide range of temperature, concentration, and pressure. Experimental heat-capadty data are still needed for trivalent and tetravalent ions. Nevertheless, databases have been established that use the scarce experimental measurements and the tenuous theoretical formalisms to predict high-temperature equilibria [80]. 

The TEC model developed by Teo also has been successfully applied to rationalize the geometries of a large number of cluster compounds. The TEC model combines Lauher s rule with Euler s theorem and adds an adjustable parameter This parameter X is equal to the number of electron pairs present in excess of that predicted by the 18-electron rule. " X has also been interpreted in terms of the number of missing antibonding orbitals. Given a value for X, determined by the shape of the cluster, an equation predicts the electron count for a cluster. Theoretical justification of the parameter X is based largely upon the classical molecular orbital calculations performed by Hoffmann and Lipscomb via the extended Hiickel method on the corresponding polyhedral boron hydride clusters The values... 

The objective of the work reported in this paper was to compare the results of two journal orbit prediction methods with experimental data obtained from a test rig (1). Theoretical Method A is of the rigorous type thus using numerical film pressure solutions at each time step (2), whilst Method B, referred to as the Reaction Method, achieves a fast orbit solution by the use of pre-computed velocity coefficients. Method A has been previously described in reference (3), and the development of the oil film force equations upon which the Reaction Method is based is outlined in reference (4). 

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