Resolution requirements

Likewise, efficient interface reconstruction algorithms and mixed cell thermodynamics routines have been developed to make three-dimensional Eulerian calculations much more affordable. In general, however, computer speed and memory limitations still prevent the analyst from doing routine three-dimensional calculations with the resolution required to be assured of numerically converged solutions. As an example. Fig. 9.29 shows the setup for a test involving the oblique impact of a copper ball on a hardened steel target... 

The choice of mass spectrometer for a particular analysis depends on the namre of the sample and the desired results. For low detection limits, high mass resolution, or stigmatic imaging, a magnetic sector-based instrument should be used. The analysis of dielectric materials (in many cases) or a need for ultrahigh depth resolution requires the use of a quadrupole instrument. 

The resolution required in any analytical SEC procedure, e.g., to detect sample impurities, is primarily based on the nature of the sample components with respect to their shape, the relative size differences of species contained in the sample, and the minimal size difference to be resolved. These sample attributes, in addition to the range of sizes to be examined, determine the required selectivity. Earlier work has shown that the limit of resolvability in SEC of molecules [i.e., the ability to completely resolve solutes of different sizes as a function of (1) plate number, (2) different solute shapes, and (3) media pore volumes] ranges from close to 20% for the molecular mass difference required to resolve spherical solutes down to near a 10% difference in molecular mass required for the separation of rod-shaped molecules (Hagel, 1993). To approach these limits, a SEC medium and a system with appropriate selectivity and efficiency must be employed. 

A greater disparity is found in terms of the resolution requirements that are placed by various organizations on GPC column sets. A common resolution requirement is to measure the resolution R, as defined in Eq. (1) ... 

Having defined that the resolution required to separate the critical pair in a specific sample is 4a it is now possible to calculate the number of theoretical plates that are necessary to provide adequate quantitative accuracy. This can be easily carried out using the information provided by the Plate Theory in the chapter 2. Restating figure 10 from chapter 2 as figure 8, it is seen that the retention volume difference between the peaks (Av) is... 

What multiple charging does not do, however, is to provide an equivalent increase in the resolution of the mass spectrometer and the resolution required to separate the individual isotopic contributions from a multiply charged species is identical to that required for the corresponding singly charged species. Figures 4.16 and 4.17 show the ions from the 7- - charge state of aprotin at resolutions of 1500 and 5000, respectively. 

You have calculated the resolution required to separate the molecular ion of atomio oomposition C284H432N84O79S7 from the isotopic peak containing one atom. Carry out a similar exerolse to oaloulate the resolution required to separate the equivalent Ions when they eaoh have (a) 5 charges, (b) 7 charges, and (c) 10 charges. Compare the values obtained. 

For higher-molecular-weight materials, the resolution required to observe the individual isotopic contributions increases proportionally. 

Calculate the resolution required to separate ions occurring at 280.0596 and... 

These figures clearly demonstrate that the number of charges on the ion does not affect the resolution required to separate the ions in the molecular ion region. 

TOF-SIMS has important potentials in many areas of life science, in fundamental and applied research as well as in product development and control. This holds for the characterization of biological cells and tissues, of sensor and microplate arrays, of drug delivery systems, of implants, etc. In all these areas, relevant surfaces feature a very complex composition and structure, requiring the parallel detect ion of many different molecular species as well as metal and other elements, with high sensitivity and spatial resolution requirements, which are exactly met by TOF-SIMS. 

In general, the mass resolution required for most analyses is such that the singly charged isotope patterns of the detected ions are readily discernible. For applications involving molecular weights up to about 1500 Da, this can be provided by magnetic sector, quadrupole, and time-of-flight mass spectrometers. 

The choice of columns used for 2DLC is based upon experience with the sample and resolution required. The HPLC column descriptors of selectivity, resolution, peak capacity, sample capacity, degree of sample recovery, and speed of separation have been discussed previously (Unger et al., 2000). Columns with higher peak capacity and sample capacity (IEC, HIC, NPLC, and RPLC) are preferred in the first dimension, and higher speed columns (SEC and RPLC) are better in the second dimension. This is discussed in detail in Chapters 2 and 6. 

It was the development of the rotating glassy carbon electrode with a preplated or co-plated mercury film that gave this technique the sensitivity and resolution required for use in seawater. 

Figure 2. Resolution required to resolve molecular impurities around mass 88 on...

The modes of addition shown in Figure 6.3 are similar to those shown in Figure 6.2 and are consistent with extant mechanistic work [6,9] they accurately predict the identity of the slower reacting enantiomer. It should be noted, however, that variations in the observed levels of selectivity as a function of the steric and electronic nature of substituents and the ring size cannot be predicted based on these models alone more subtle factors are clearly at work. In spite of such mechanistic questions, the metal-catalyzed resolution protocol provides an attractive option in asymmetric synthesis. This is because, although the maximum possible yield is 40 %, catalytic resolution requires easily accessible racemic starting materials and conversion levels can be manipulated so that truly pure samples of substrate enantiomers are obtained. 

Scheme 6.11. Tandem Zr-catalyzed kinetic resolution and Ru-catalyzed conversion of the resulting optically pure ethers in the enantioselective synthesis of dihydrofurans. The efficiency of the catalytic resolution requires the presence of the pendant acyclic alkene and depends on its substitution.

J.A. Yergey, R.J. Cotter, D. Heller and C. Fenselau, Resolution requirements for middle molecule mass spectrometry, Anal. Chem., 56 (1984) 2262-2263. 

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