Rotating Frame Model

The rotating frame model solves the momentum equations for the entire domain in a rotating frame. The Coriolis force is included in the process. Problems solved in a rotating frame typically use the angular velocity of the primary rotating component, Q, as the angular velocity of the frame. In stirred tanks, the impeller serves this purpose, so the frame is assumed to rotate with the impeller. Thus, the impeller is at rest in the rotating frame. The tank, however, rotates in the opposite direction, so must have a rotational boundary condition of — 

If baffles exist, they would need to rotate into the fluid with the same angular velocity, Unfortunately, this simple steady-state model is not equipped to handle the motion of elements such as baffles into or through the fluid. The approach is therefore only useful for unbaffled tanks with smooth tank walls that are geometrically equivalent to a perfect surface of revolution. Thus an unbaffled cylindrical tank with an axisymmetric bottom shape and no angular-dependent internals could be simulated in this manner. Vessels with baffles, dip tubes, or inflow-outflow ports could not. 

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Laboratory frame model A means of visualising the processes taking place in an NMR experiment by observing these processes at a distance, i.e., with a static coordinate system. See Rotating frame model. 

ROESY Rotating-frame Overhauser effect spectroscopy. A variation (one and two dimensional) on the nuclear Overhauser experiment (NOE). The techniques have the advantage of being applicable for all sizes of molecule. See Laboratory frame model. 

Another rotational diffusion model known as the anisotropic viscosity model156,157 is very similar to the above model, and its main feature is to diagonalize the rotational diffusion tensor in the L frame defined by the director. A similar (but not the same) expression as Eq. (71) is J R(r)co)... 

The precipitates of PVPh/PDMA from methanol and acetone solutions were examined by CPMAS NMR [51], and evidence for specific interaction was obtained with a 3 ppm shift in the phenolic carbon resonance peak. The proton spin-lattice relaxation times Tj were shorter than those predicted by a linear model, though the rotating frame spin-lattice relaxation times Tjp of the com-... 

Cross-link density and parameters relating to the network structure can be measured by NMR by analysis of the transverse relaxation decay (cf. Section 1.3) and the longitudinal relaxation in the rotating frame [67]. Combined with spatial resolution, the model-based analysis of relaxation yields maps of cross-link density and related parameters [68]. Often the statistical distribution of relaxation parameters over all pixels provides a reduced data set with sufficient information for sample characterization and discrimination [68]. 

For a spin whose chemical shift is exactly at the center of the spectral window, we call the pulse an on-resonance pulse because the pulse (or carrier ) frequency is exactly equal to the resonant frequency (precession frequency or Larmor frequency vG) of the spin. During the pulse, we can use the vector model to show the B field (the pulse) as stationary in the rotating frame of reference, because the x and y axes are rotating about the z axis at exactly the frequency of the pulse. The position of the B field in the x -y plane depends on the phase of the pulse, which is just the place in the sine function (0-360°) where the radio frequency oscillation starts at the beginning of the pulse. This can be controlled by the spectrometer and is written into the pulse sequence by the user ... 

Time period of forward CP in DCP - see text and Fig. 14 Depolarisation time period in DCP - see text and Fig. 14 P spin-lattice relaxation time in the laboratory frame Cross-polarization time constant for the I-P-S model H spin-lattice relaxation time in the rotation frame H spin-spin relaxation time in the laboratory frame Recycle delay... 

Assessment of Multiple Rotating Reference Frame Model Simulations... 

This section summarizes primarily the classical description of NMR based on the vector model of the Bloch equations. Important concepts like the rotating frame, the effect of rf pulses, and the free precession of transverse magnetization are introduced. More detailed accounts, still on an elementary level, are provided in textbooks [Deri, Farl, Fukl]. 

Most approaches to describe spin diffusion are based on a perturbation treatment [11]. Abragam [4] applied Fermi s Golden Rule while Suter and Ernst [12] used the perturbation theory in the rotating frame to obtain an estimate for the rate constant. Henrichs and Linder [13] and Kubo and McDowell [14] used the memory-function theory to model the system. The model of fluctuating local fields can also be applied in a Liouville-space description [15],... 

Polyesters derived from maleic anhydride and 2,2-di(4-hydroxyphenyl)pro-pane were copolymerised with styrene and then studied by CP/MAS NMR [39] spectroscopy. The three dimensional-crosslinked network formed by the polymerisation was examined using spin-lattice relaxation times in the rotating frame. A correlation between reaction conditions and the structure of the resulting material was found. The degree of residual unsaturation was determined by subtraction of two relaxation times from a linear additivity model used for erosslinked polymer systems. 

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