Gordon parameter

The Gordon parameter, G, gives a measure of the eohesiveness of a solvent and, hence, a measure of the abihty of the PIL to be amphiphile self-assembly media. The Gordon valne is described by eq 1, where y is the snrface tension and Fm is the molar volnme, and can be considered to indicate the driving force of the PILs toward self-assembly. 

PILs with higher Gordon parameters are likely to have greater diversity and thermal stabihty of the liquid ciystalline... 

It is important to apply a first principles technique since an alternative ionic modelling approach based on the fom-Gordon formalism yields errors in the cell parameters as high as... 

Figure 3. Computer Simulations of the MSssbauer Spectra of Figure 1. A) Simulation of Figure lA B) Simulation of Figure IB C) Distribution of particle radii D) Relative volume fractions as a function of radius. For these simulations, the following parameters were used o 1.25, mean radius - 95X, k=8 x 105 ergs/cm3. The Klebsch-Gordon coefficients used were 3 3 1.

The second class of GGA exchange functionals use for F a rational function of the reduced density gradient. Prominent representatives are the early functionals by Becke, 1986 (B86) and Perdew, 1986 (P), the functional by Lacks and Gordon, 1993 (LG) or the recent implementation of Perdew, Burke, and Emzerhof, 1996 (PBE). As an example, we explicitly write down F of Perdew s 1986 exchange functional, which, just as for the more recent PBE functional, is free of semiempirical parameters ... 

An alternative approach to the calculation of accurate thermochemical data is to scale the computed correlation energy with multiplicative parameters determined by fitting to the experimental data. Pioneering methods using such an approach include the scaling all correlation (SAC) method of Gordon and Truhlar [32], the parameterized correlation (PCI-X) method of Siegbahn et al. [33], and the multi-coefficient correlation methods (MCCM) of Truhlar et al. [34-36]. Such methods can be used... 

Glass transition temperature is one of the most important parameters used to determine the application scope of a polymeric material. Properties of PVDF such as modulus, thermal expansion coefficient, dielectric constant and loss, heat capacity, refractive index, and hardness change drastically helow and above the glass transition temperature. A compatible polymer blend has properties intermediate between those of its constituents. The change of glass transition temperature has been a widely used method to study the compatibility of polymer blends. Normally, the glass transition temperatme of a compatible polymer blend can be predicted by the Gordon-Taylor relation ... 

Fig. 5. Interrelation between critical concentrations of crosslink forming (a) and ring forming (a) functionalities at the gel point calculated on the basis of random flight statistics for trifunctional polycondensation (/ = 3) and different values of parameters A and 91 [Gordon and Scantleburry (72)]...

On the other hand, parameters characterizing the structure of weakly crosslinked gels in the vicinity of the gel point can be obtained now quite precisely using Gordon s theory. 

More recently, Palais [17] showed that the generic cases of soliton—the Korteweg de Vries equation (KdV), the nonlinear Schrodinger equation (NLS), the sine-Gordon equation (SGE)—can be given an SU(2) formulation. In each of the three cases considered below, V is a one-dimensional space that is embedded in the space of off-diagonal complex matrices, ( ) and in each case L(u) at- I u, where u is a potential, i. is a complex parameter, and a is the constant, diagonal, trace zero matrix... 

In the case of a parabolic well the period is independent on the phase variables, the anharmonicity vanishes, and the bandwidth is nonzero only due to strong collisions. The more a potential profile differs from the parabolic one, the larger the anharmonicity and the wider the absorption band. The intensity of the absorption peak should then decrease since in accord with the Gordon rules (see, e.g., GT, Section III.G or see Section VIIA.4 in the present chapter) in an isotropic medium the integrated absorption does not depend on parameters of the model. 

Additional information on hydrodynamics of bubble columns and slurry bubble columns can be obtained from Deckwer (Bubble Column Reactors, Wiley, 1992), Nigam and Schumpe (Three-Phase Sparged Reactors, Gordon and Breach, 1996), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Gianetto and Silveston (Multiphase Chemical Reactors, Hemisphere, 1986). Computational fluid mechanics approaches have also been recently used to estimate mixing and mass-transfer parameters [e.g., see Gupta et al., Chem. Eng. Sci. 56(3) 1117-1125 (2001)]. 

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