Gradient shifts

Figure 8.2.7 Reference deconvolution applied to the methanol peak (a) original peak (b) methanol peak deconvolved to a 2 Hz Lorenzian lineshape (c) gradient-shifted methanol peak (d) gradient-shifted methanol peak deconvolved to the same 2 Hz Lorenzian lineshape (e) comparison of the sub-spectrum of the methanol sample using the subtraction algorithm with (sharp peak) and without (flattened peak) reference deconvolution. Reprinted from Hou, T., MacNamara, E. and Raftery, D., NMR analysis of multiple samples using parallel coils improved performance using reference deconvolution and multi-dimensional methods , Anal. Chem. Acta, 400, 297-305, copyright (1999), with permission of Elsevier Science...

Substantial gradient shift due to absorbance or refractive index changes of the mobile phase during broad gradients. This is particularly serious for running MS-compatible trifluoroacetic acid (TFA) or formic acid gradient at low UV. 

Gradient shifts can be reduced by reducing the concentrations of the mobile phase additives (i.e., from 0.5-01% TFA to 0.03-0.05%) and by balancing (matching) the absorbances of MPA and MPB. See example in Chapter 8, case study 2. This would also reduce the short-term baseline noise caused by pump blending. 

Figure 10.15. Chromatograms illustrating gradient shift problems at 230 nm encountered during method development of an impurity test method for a drug substance (Section 8.8.2). The UV spectrum of 0.05% TFA vs. water is shown in the inset, showing considerable absorbance at...

Figure 7.13. Tlvo-dimensional subspectra (A) 1-propanol and (B) ethanol generated from zero-gradient and gradient shifted 2D COSY spectra of four coils using the subtraction method. (Reproduced with permission from Anal. Chim. Acta, 400 297. Copyright Elsevier Press, 1999).

Use Equation VIII-1 to determine the effective mass of the cantilever if the cantilever has a spring constant C = 20 N/m, the minimum detectable force gradient is hF/dz = 4 X 10 N/m, and the frequency shift is 200 kHz. How does the frequency shift depend on distance from the surface if the force has a 1/z distance dependence ... 

In many instanees, it is important tiiat some fonn of ehemieal seleetivity be applied in magnetie resonanee imaging so as to distinguish nuelei m one or more speeifie moleeular enviromnent(s). There are many ways of doing this and we diseuss here just three. The first option is to ensure that one of the exeitation RF pulses is a narrow bandwidth, frequeney seleetive pulse applied in the absenee of any gradient [22]. Sueh a pulse ean be made speeifie to one partieular value of the ehemieal shift and thereby aflfeets only nuelei with that ehemieal shift. In praetiee this ean be a reasonable method for the speeifie seleetion of fat or oil or water in a mixed hydoearbon/water system. 

Figure Bl.14.7. Chemical shift imaging sequence [23], Bothx- andj -dimensions are phase encoded. Since line-broadening due to acquiring the echo in the presence of a magnetic field gradient is avoided, chemical shift infonnation is retained in tire echo.

The relationship between mean squared phase shift and mean squared displacement can be modelled in a simple way as follows This motion is mediated by small, random jumps in position occurring with a mean interval ij. If the jump size in the gradient direction is e, then after n jumps at time the displacement of a spin is... 

An alternative, and closely related, approach is the augmented Hessian method [25]. The basic idea is to interpolate between the steepest descent method far from the minimum, and the Newton-Raphson method close to the minimum. This is done by adding to the Hessian a constant shift matrix which depends on the magnitude of the gradient. Far from the solution the gradient is large and, consequently, so is the shift d. One... 

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