Configurational splitting

Lubricant seals must be in good condition and properly fitted into place. Coupling covers contain the lubricant and prevent contaminants from entering the coupling interior. The covers are designed in two configurations, split either horizontally or vertically. Holes are provided in the covers to allow lubricant to be added without coupling disassembly. 

Hi > H2 this is the L-S (or Russell-Saunders) couphng. In this case, only Hi is taken into account in first order perturbation theory. It commutes with L and S where L = li -I- I2 and S = Si -I- S2, so that each configuration splits into terms being (2L -I- 1)(2S -I- l)-fold degenerate. 

In the weak-field limit due to electron repulsion the d configuration splits into a couple of states F< D< P< G< S, as shown before. The energy of the state relative to the F ground state, expressed by means of the Racah parameters, is 15B according to Eq. (10). Switching on octahedral (Oh) field interaction, due to group theoretical considerations the F state correlates with Ti-h T2-h A2 and the P state with i under conservation of the multiplicity. 

Due to the spin-orbit interaction of the inner electron and the direct electrostatic interaction, each configuration splits into levels,j characterized by the quantum numbers yj[K these levels are 2 2K + l)-fold degenerate. On account of the S2-dependent interactions, each of these levels splits into two adjacent levels having the consecutive / values... 

Hence all except s configurations split into two levels having the following properties ... 

Sum Square Splitting and Root Mean Square Splitting as Measures of Configurational Splitting... 

Randall [48] and other workers [49, 50] studied amorphous polystyrene. Randall [48] concluded that nine methylene resonances could be resolved. A high-field strong methane resonance is also present, but shows no apparent configurational splitting. The observation of nine resonances is interesting because a C-NMR sensitivity to just tetrad sequences would have produced six resonances, whereas a complete hexad sensitivity would have produced 20 resonances. 

In the central part (Sect. 3), the simulation technique will be explained in detail and illustrated by the example of atactic poly(propylene) (Sects. 3.1-3.3). Special sections are devoted to the simulation of the solid state spectrum (Sect. 3.4), the correlation of chemical shift and geometry (Sect. 3.5), a molecular orbital (MO) analysis (Sect. 3.6), the configurational splitting in solution (Sect. 3.7) and the role of the anisotropy of the chemical shift as a source of structural information (Sect. 3.8). 

The presence of various configurations in a sample gives rise to a configurational splitting in the solution NMR spectrum. This aspect will be discussed in some more detail in Sect. 3.7. 

Fig. 13. Experimental solid state spectrum of atactic poly(propylene) (top) and solution spectrum of configurational splitting in the methylene region (bottom). The broadening in the solid state spectrum is appreciably larger than the configurational splitting. Reprinted with minor changes from [63]...

For the simulation both of the solid state NMR spectrum and the configurational splitting [10] in solution we adopt the 5-state RIS model of Suter and Flory [86]. This model correctly reproduces the experimental radii of gyration some difficulties have been reported for various temperature coefficients [87]. For amorphous isotactic poly(propylene) the radii of gyration in solution and in the melt nearly coincide [88, 18]. Thus, the model [86] is apparently a valid description of poly(propylene) both in solution and in bulk on the longer length scale (> 10 A) of scattering experiments. 

In the same spirit, the configurational splitting in solution can be calculated. The position of the configuration (xi,X2,X3) is simply the conforma-tionally averaged shift. 

In Eq. (3.17), the sum extends only over those geometries with the correct configuration (xi, X2, X3). It should be noted, that by Eq. (3.17), the configurational splitting in solution may be computed without special assumptions on the geometry dependence of the chemical shift. Only if a simple functional dependence for ok G ) is postulated, the phenomenological parametrisation of the YS uche effect is recovered (Sect. 2.5). 

The ab initio IGLO calculations can be used to calculate the configurational splitting in solution by simply calculating the conformational average for a given configuration (xi,X2,X3). For the reader s convenience, the formula Eq. (3.17) derived in Sect. 3.3.3 is adopted to the special case of the methylene unit A of the model molecule... 

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