Mixing-time dependence

The frequency dependence is taken into accoimt through a mixed time-dependent method which introduces a dipole-moment factor (i.e. a polynomial of first degree in the electronic coordinates ) in a SCF-CI (Self Consistent Field with Configuration Interaction) method (3). The dipolar factor, ensuring the gauge invariance, partly simulates the molecular basis set effects and the influence of the continuum states. A part of these effects is explicitly taken into account in an extrapolation procedure which permits to circumvent the sequels of the truncation of the infinite sum-over- states. 

It must be observed again that the mixing times depend on the particular experimental techniques used to evaluate them. It is probably the different definitions of mixing time that are responsible for the differences in scale relations seen in Table V, although the limited range of some of the studies can also be a factor. The engineer faced with the problem of scale-up must decide if any of the studies outlined above are based on a mixing time definition which is especially appropriate to the situation with which he is concerned. 

Homonuclear and heteronuclear coupling constants can be determined from the mixing-time dependence of Hartmann-Hahn transfer (see Sections II and VI). For example, for two heteronuclear spins 1 /2, the ideal polarization-transfer frequency under planar Hartmann-Hahn mbdng is 7,5/2 (see Section VI). Heteronuclear H- Si coupling constants have been determined in IS, I2S, and I S spin systems by Fourier analysis of the cross-polarization intensity as a function of the mbdng time (Bertrand et al., 1978a) and by an iterative fitting procedure (Murphy et al., 1979). 

Vezin, W.R. Khan, K.A. Pang, H.M. Adjustment of precompression force to reduce mixing-time dependence of tablet tensile strength. J. Pharm. Pharmacol. 1983, 35, 555-558. 

Johansson ME. Investigations of the mixing time dependence of the lubricating properties of granular and powdered magnesium stearate. Acta Pharm Suec 1985 22 343-350. 

Mixing times depend on geometry, speed, and rheology, in the general form of Equation (9.18)... 

Injection mixers are similar to flow focusing mixers in that they also dilute one stream into another stream however, they differ from focusing mixers in that a small aperture is used to inject a thin stream into another stream. These mixers enable multiple flow streams to be injected and may be more desirable when flow rates or pressures cannot be controlled. Mixing time depends on the method of injection and device geometry. However, construction of small apertures or the... 

Figure 1.11 C-detected CODEX spectra of the protein hydrogel. (A) control, fn,=0.2 ms, tz = 150 ms. (B) Exchange, = 150 ms, —0.2 ms. (C) Difference, indicating the presence of motion. (D) Mixing-time dependence of the normalized exchange intensity Sq/S for the 55-ppm Ala peak. Reprinted from [123]. Copyright 2000 Elsevier.

Here D is diffusivity of the species under consideration, and varies from approximately 10 m /s for small molecules and ions to 10 m /s for large biomolecules. Therefore, an isolated system with non-uniform concentrations ultimately achieves a state of uniform concentration, i. e., it will be completely mixed. The mixing time depends on the diffusivity (D) and length scale over which diffusion must act in order to homogenize the concentration, known as the striation length (1st). The mixing time is then given by... 

Figure 10 Mixing-time dependence of covariance spectra in C-labeled samples of Ap42 fibril mixed with curcumin. (A) and (B) were obtained with a mixing time of 50 ms in Ap42 labeled at the 17-21 residues and at the N-terminus (see Fig. 8). (C) and (D) were obtained with a mixing time of 500 ms. Reprinted with permission from Ref. [76], Copyright 2011 Elsevier.

For structural analysis, one often needs to perform correlation experiments for various mixing times, since the mixing-time dependence of the cross-peak intensities provides important distance restrictions. Unfortunately, the cross-peaks of the DTD spectrum build up with the mixing time in a somewhat different way from those in the FT spectrum. To retain the quantitative feature of the buildup curves, Kaiser et al. proposed a template DTD scheme [93]. In template DTD, covariance processing is performed only on the data acquired with the longest mixing time. Then, the individual FT spectra obtained with various mixing times are multiplied by this common covariance spectrum (Fig. 21). As demonstrated in Fig. 22, the buildup curves of the template DTD spectra show similar behavior to those of the FT spectra. 

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