Line splitting

Of spectroscopic teclmiques, nuclear magnetic resonance (NMR) has been most widely used to measure orientational ordering in liquid crystals [M, 57 and ]. Most commonly, changes of line splittings in the spectra of... 

Triplet (Section 13.1 I) A symmetrical three-line splitting pattern observed in the 11 NMR spectrum when a proton has two equivalent neighbor protons. 

The H NMR spectrum of Rh(SH)(CO)(PPh3)2 in the mercaptide region (Figure 2.24) shows a 1 2 1 triplet owing to coupling to two equivalent (mutually trans) phosphines (/(P-H) 18.1 Hz), each line split into a doublet by a weaker coupling to 103Rh (/(Rh-H) 1.6 Hz). 

These modes show a line splitting in crystals of natural isotopic composition. [109]... 

Fig. 13 Isotopic line splitting of the V3 stretching vibration in single crystalline (see also Fig. 12(a)), after [108, 109], The origin of each absorption band is indicated by an isotopomer present in crystals of natural composition. While the absorption could be fitted by a Lorentzian band profile, the remaining peaks were dominated by the Gaussian contribution in the Voigt band shapes (solid lines below the spectrum). The sum result of fitting the isotopic absorption bands is inserted in the measured spectrum as a solid line...

Fig. 15 Energy level scheme of the isotopic line splitting of V9 in terms of the free molecules ( Sg and 81 87 as the main contributions) and of the orthorhombic crystal with natural abundance of isotopomers, after [109], Numerical values are observed wavenumbers (in cm ), values in brackets came from MD simulations on free rings [131] and in the case of au from LD calculations [116, 117]...

Figure 3.7 Frequency and cumulative frequency distributions of 3D-optimal sampling times for the Gompertz model, given the observations for subject 4. Vertical lines split the cumulative empirical distribution into equal probability regions.

The last quantum number was proposed to solve a mystery. Some spectral lines split into two lines when theory predicted that only one should exist. Several physicists had a hand in trying to solve this problem. By 1924, a consensus was reached. A new quantum property and number were needed to explain spectral splitting. At the time, the electron was considered to be a particle, and scientists called this new property spin, usually designated as mg. The spin quantum number has only two possible values -1-1/2 or -1/2. It is usually depicted as an arrow pointing up or down. 

A remarkable splitting of the two signals in the F-spectra of P2O3F4 is observed, when traces of difluorophosphoric acid are carefully excluded and the spectrum is scanned at very slow speed (777). The doublet is split into two triplets symmetrical to each other with the intensity ratio 1 2 5, which is in accordance with the AA XX A" a" expectation spectrum (777). The F-spectra of F2P(S)- 0—P(S)p2 can be interpreted in the same way the normally appearing doublet of lines splits into two symmetrical nonets at very slow scan speeds (777). 

We can now use a homodecoupling experiment to show that in the methyl signal (triplet, with each line split into a doublet) at 1.33 ppm, the distances between lines 1 and 3, 2 and 4, 3 and 5 or 4 and 6 are equal to (3JH-c-c-h) we irradiate the methylene protons and observe the methyl protons. The result of this experiment is shown in Fig. 3. 

Flilbert, J. D., Multiple In-Line Splitting of Pneumatic Conveying Pipelines, J. Pipelines, 3 161-172 (1982)... 

Selves, T. P., and Barnes, R. N., A Review of In-Line Splitting Techniques used in Pneumatic Conveying, 4 th Int. Conf. on Bulk Materials Storage, Handling and Transportation, 2 353-358, IEAust. Proc, Wollongong (1993)... 

FIGURE 2.2 Resolution may increase with increasing frequency. A two-line EPR absorption spectrum is given at three different microwave frequencies. The line splitting (and also the line position) is caused by an interaction that is linear in the frequency the linewidth is independent of the frequency. This is a theoretical limit of maximal resolution enhancement by frequency increase. In practical cases the enhancement is usually less in some cases there is no enhancement at all. 

Equation 10.2 affords a single, isotropic line split into a triplet by the 14N nucleus and a further splitting into doublets by the II nucleus, altogether resulting in a pattern of six-lines of equal width and intensity. For particular magnitudes of AN and AH the lines may partly, or completely overlap as is the case for the HO adduct of DMPO, which has AN AH, resulting in a four-line pattern with 1 2 2 1 intensities (Figure 10.2). 

The line splittings together with the relative line intensities allowed us to position the organic cations in their respective frameworks. 

Fig. 34. Comparison between spectra of skeletal muscle recorded from TA (left row) and SOL (right row) at 1.5 T (a) and 3.0 T (b). IMCL and EMCL as well as Cr3 and TMA are better separated in both muscles at 3.0 T. TMA signal shows line splitting in TA which are not shown in SOL spectra.

Fig. 35. Part of the spectrum recorded at 3.0 T from TA (shown in Fig. 33b) demonstrating the line splitting caused by dipolar coupling. Triplet structure of Cr3 is resolved, Tau/TMA lead to 4 signal components. The frequency difference between the two Ct2 signals centred at 3.95 ppm is smaller compared to 1.5 T, but these signals are of higher amplitude than in Cr3.

The IL is mainly located in the upper phases of the ATPS. The lower phases contain the phosphate salt. Water is partitioning almost evenly between the two-liquid phases. By definition, all initial compositions belonging to the same tie-line split into two liquid phases of identical composition only the volume amounts (and the phase ratios) change. Since the tie-lines are, by chance, almost parallel to the water hypotenuse, the phase diagram clearly shows that the chemical composition of the two liquid phases crucially depends on the water content of the system. 

A closed-form result involving only matrix solution and substitution operations was obtained. Under certain circumstances, particularly in the low-noise case, application of the Burg method results in spurious resolution or spontaneous line splitting (Fougere et al., 1976). One solution to this problem (Fougere, 1977) introduces iteration. 

Iron-containing superoxide dismutases are present in many species of bacteria (Hassan and Fridovitch, 1978). These nonheme iron proteins have a characteristic set of EPR lines split about g = 4.2 in the ferric state, arising from the middle Kramers doublet of a rhombic high-spin site. Ferrous iron superoxide dismutase forms an S = I complex with NO that resembles the lipoxygenase-NO adduct by EPR criteria (I. Fridovich, T. Kirby, and J. C. Salerno, (1978) unpublished observations). 

In the spin-correlated RP the two radicals interact via electron-electron dipolar and exchange interaction which leads to line splitting. The ET process creates the RP in a strongly spin-polarized state with a characteristic intensity pattern of the lines that occur either in enhanced absorption (A) or emission (E).144 145 The spectrum is therefore very intense and can directly be observed with cw EPR (transient EPR) or by pulse methods (field-swept ESE).14 To study the RPs high field EPR with its increased Zeeman resolution proved to be very useful the first experiment on an RP was performed by Prisner et al. in 1995146. From the analysis of the RP structure detailed information about the relative orientation of the two radicals can be extracted from the interaction parameters. In addition kinetic information about the formation and decay of the RP and the polarization are available (see references 145,147). 

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