Separation-shifted scaling

W. Zacharias, T. P. Straatsma, and J. A. McCammon, Separation-shifted scaling, a new scaling method for lennard-jones interactions in thermodynamic integration, J. Chem. Phys. 100 9025 (1994). 

Another solution to the problem is to modify the interaction potential. The interaction can be modified at very small distances, for example.- - This would not influence the dynamics of full particles, for which very small distances never occur. A more practical solution is the use of separation-shifted scaling. Rather than using the conventional nonbonded Lennard-Jones interaction... 

Separation-Shifted Scaling, a New Scaling Method for Lennard-Jones Interactions in... 

The separation of resonance frequencies resulting from the different electronic environments of the nucleus of the isotope is called the chemical shift. It is expressed in dimensionless terms, as parts per million (ppm), against an internal standard, usually retramethyLvilane (TMS). By convention, the chemical shift is positive if the sample nucleus is less shielded (lower electron density in the surrounding bonds) than the nucleus in the reference and negative if it is more shielded (greater electron density in the surrounding bonds). The chemical shift scale ((5) for a nucleus is defined as ... 

Figure 7. The Gay-Berne pair potential as a function of interparticle separation for side-by-side, cross, T-shaped, and end-to-end configurations of the pair corresponding to three members of the GB family (a) GB(3, 5, 2, 1), (b) GB(3.6, 5, 2, 1), and (c) GB(3, 5, 1, 1). The interparticle separation is scaled by ggb and the potential by cgb The potential is cut at 4gqb and shifted to zero at the cutoff. (Reproduced from Ref. 97.)...

Figure 3. Si NMR spectra of aqueous alkaline sodium silicate solutions with atomic ratios Na Si = LO and concentrations 0.65 M in Si (8). Only bands B, C, D and E are shown, although bands D and E are not well separated for this solution. Key natural abundance Si, 49.7 MHz spectrum (a) Si enriched to 95.3%, 15.7 MHz spectrum (b). Conditions peaks unsplit for enriched sample ( ), assignments are given peak is spurious (f) chemical shift scale given with respect to signal for monomer, Q high-frequency-positive convention is used. Irradiation frequency increases to the left.

The least expensive process NMR option is a small 10-20 MHz (0.2-0.4 T) magnet with a desktop computer containing most of the necessary electronics for a complete pulsed NMR experiment. This is commonly referred to as broadline NMR. With a low field strength, the linewidth of any peak is large compared to the chemical shift scale. Separating peaks into meaningful chemical shifts and the appropriate chemical structures is not attempted. The time domain is used exclusively to provide information on the sample. 

Cd(C10 )2 Positive values indicate deshielding of the cadmium nucleus. The vertical separation of scales emphasizes the chemical shift ranges expected for each ligand type, indicated at right. Abbreviations used include ... 

As an example the use of ceramic membranes for ethane dehydrogenation has been discussed (91). The constmction of a commercial reactor, however, is difficult, and a sweep gas is requited to shift the product composition away from equiUbrium values. The achievable conversion also depends on the permeabihty of the membrane. Figure 7 shows the equiUbrium conversion and the conversion that can be obtained from a membrane reactor by selectively removing 80% of the hydrogen produced. Another way to use membranes is only for separation and not for reaction. In this method, a conventional, multiple, fixed-bed catalytic reactor is used for the dehydrogenation. After each bed, the hydrogen is partially separated using membranes to shift the equihbrium. Since separation is independent of reaction, reaction temperature can be optimized for superior performance. Both concepts have been proven in bench-scale units, but are yet to be demonstrated in commercial reactors. 

Subsequently, it was appreciated that there are two major difficulties with this model potential. One was the observation that the width of the attractive well varied with the molecular orientations which is unrealistic [12]. Equally unrealistic is the prediction that the well depth depends only on the relative orientation of the two particles and not on their orientation with respect to the intermolecular vector (see Eq. 4). These difficulties were addressed by several groups [13] and culminated in the proposals by Gay and Berne [8] which are essentially ad hoc in character. To remove the angular variation of the width of the attractive well they changed the functional form from a dependence on the scaled distance (r/cr) (see Eq. 1) to a shifted and scaled separation R where... 

There have been several simulations of discotic liquid crystals based on hard ellipsoids [41], infinitely thin platelets [59, 60] and cut-spheres [40]. The Gay-Berne potential model was then used to simulate the behaviour of discotic systems by Emerson et al. [16] in order to introduce anisotropic attractive forces. In this model the scaled and shifted separation R (see Eq. 5) was given by... 

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