Second-dimension

Advantages. Compared to DOR, a small rotor can be used allowing relatively fast spiiming speeds high RF powers can be attained and if the coil is moved with the rotor a good filling factor can be obtained. In the isotropic dimension high-resolution spectra are produced and the second dimension retains the anisotropic information. 

Thus, a mass spectrum records ion abundances in one dimension. In the second dimension, it records m/z ratios. The mass spectrum is a record of m/z values of ions and their abundances. 

For the extension to two dimensions we consider a square lattice with nearest-neighbor interactions on a strip with sites in one direction and M sites in the second so that, with cyclic boundary conditions in the second dimension as well, we get a toroidal lattice with of microstates. The occupation numbers at site i in the 1-D case now become a set = ( ,i, /25 5 /m) of occupation numbers of M sites along the second dimension, and the transfer matrix elements are generalized to... 

Efforts have been made, however, to extend the range or extent of samples that can be analysed by using a two-dimensional separation when used in heart-cut mode. This has been reported to include the use of numerous parallel micro-traps to essentially store the primary column eluent fractions ready for second-column separation, and the use of parallel second-dimension columns. 

Figure 3.8 Second-dimension chiral cyclodextrin capillary column separation of a non-racemic pair of nonachlorobomane compounds extracted from dolphin blubber, shown with expanded attenuation in the inset. The primary separation (not shown) was performed on an apolar primary capillary column. Reproduced from H.-J. de Geus et al. J. High Resol. Chromatogr. 1998, 21, 39 (59).

The ability of a GC column to theoretically separate a multitude of components is normally defined by the capacity of the column. Component boiling point will be an initial property that determines relative component retention. Superimposed on this primary consideration is then the phase selectivity, which allows solutes of similar boiling point or volatility to be differentiated. In GC X GC, capacity is now defined in terms of the separation space available (11). As shown below, this space is an area determined by (a) the time of the modulation period (defined further below), which corresponds to an elution property on the second column, and (b) the elution time on the first column. In the normal experiment, the fast elution on the second column is conducted almost instantaneously, so will be essentially carried out under isothermal conditions, although the oven is temperature programmed. Thus, compounds will have an approximately constant peak width in the first dimension, but their widths in the second dimension will depend on how long they take to elute on the second column (isothermal conditions mean that later-eluting peaks on 2D are broader). In addition, peaks will have a variance (distribution) in each dimension depending on... 

Each of these is a separate second-dimension chromatogram of slices of the first dimension... 

Figure 4.9 The peaks produced in the second dimension (see Figure 4.8) can be plotted as a contour shape in the retention or separation space, with characteristic retentions in each dimension. It can be seen that such peaks are now well resolved.

With comprehensive GC, we can now choose a rational set of columns that should be able to tune the separation. If we accept that each column has an approximate isovolatility property at the time when solutes are transferred from one column to the other, then separation on the second column will largely arise due to the selective phase interactions. We need only then select a second column that is able to resolve the compound classes of interest, such as a phase that separates aromatic from aliphatic compounds. If it can also separate normal and isoalkanes from cyclic alkanes, then we should be able to achieve second-dimension resolution of all major classes of compounds in petroleum samples. A useful column set is a low polarity 5 % phenyl polysiloxane first column, coupled to a higher phenyl-substituted polysiloxane, such as a 50 % phenyl-type phase. The latter column has the ability to selectively retain aromatic components. 

A properly tuned comprehensive 2-dimensional gas chromatograph distributes substances in the first dimension according to the strength of their dispersive interactions. .. and in the second dimension according to their specific non-dispersive... 

Figure 8.13 Schematic diagram of 2-D planar cliromatographic separation using "D. In the first dimension (a and b) the total solvent strength was reduced stepwise at constant selectivity (Sx, Svi Sx Syi) to acliieve differences in polarity. In the second dimension (c and d), the...

Another means of realizing multidimensional separation is combination of two complementary separation techniques which use different methods of separation. In such multi-modal separation, different techniques can be coupled in which PC is used as the second dimension and another separation method, as the first. Some possible variations are as follows ... 

Yamamoto et al. also coupled gel permeation HPLC and CE in an on-line fashion in 1990, where capillary isotachophoresis was again used in the second dimension. This technique was also not comprehensive due to the loss of resolution between the techniques. It was also not particularly fast, with a 23 min CE cycle, which was repeated 90 times throughout the HPLC run (14). Volume incompatibility between HPLC and CE was one problem not addressed in this study, in which a large HPLC column was coupled to an electrophoresis capillary. 

An example of the results obtained in the form of a chromatoelectropherogram can be seen in Figure 9.6. The contour type data display showed the three variables that were studied, namely chromatographic elution time, electrophoretic migration time, and relative absorbance intensity. Peptides were cleanly resolved by using this two-dimensional method. Neither method alone could have separated the analytes under the same conditions. The most notable feature of this early system was that (presumably) all of the sample components from the first dimension were analyzed by the second dimension, which made this a truly comprehensive multidimensional technique. 

A six-port valve was first used to interface the SEC microcolumn to the CZE capillary in a valve-loop design. UV-VIS detection was employed in this experiment. The overall run time was 2 h, with the CZE runs requiring 9 min. As in the reverse phase HPLC-CZE technique, runs were overlapped in the second dimension to reduce the apparent run time. The main disadvantage of this yu-SEC-CZE method was the valve that was used for interfacing. The six-port valve contributed a substantial extracolumn volume, and required a fixed volume of 900 nL of effluent from the chromatographic column for each CZE run. The large fixed volume imposed restrictions on the operating conditions of both of the separation methods. Specifically, to fill the 900 nL volume, the SEC flow rate had to be far above the optimum level and therefore the SEC efficiency was decreased (22). 

In GC X GC, a sample is separated into a large number of small fractions and each of these is subsequently quantitatively transferred to a secondary column to be further separated. The second separation is very much faster than the first separation, so that the fractions can be narrow and the separation obtained on the first column can be maintained. The collection of the fractions from the first column is achieved by focusing, rather than by valve switching, and the entire sample reaches the detector. The consequence is a chromatogram, with a two-dimensional plane, rather than a one-dimensional axis, as the time domain. One dimension of this plane represents the retention time on the first column, while the second dimension represents the retention time on the second column. Every separated peak can be presented as a... 

These authors also analysed marine diesel fuel with GC X GC, connected to a quadrupole mass spectrometer for identification purposes, although the scan speed of the spectrometer was not quite suited for the fast second-dimension peaks... 

The aim of the second dimension depth is to consider protein 3D-stmctures to uncover structure-function relationships. Starting from the protein sequences, the steps in the depth dimension are structure prediction, homology modeling of protein structures, and the simulation of protein-protein interactions and ligand-complexes. 

Two-dimensional gel electrophoresis (2DE) is a two-dimensional technique for protein separation, which combines isoelectric focusing and sodium dodecyl sulphate (SDS) electrophoresis. The high resolving power results from separation according to charge (isoelectric point) in the first dimension and size (mobility in a porous gel) in the second dimension. Depending on the gel size, from several hundred to more than 5,000 proteins can be separated. 

Scheme 5-14 may be called a two-dimensional system of reactions, in contrast to Scheme 5-1 which consists of a one-dimensional sequence of two acid-base equilibria. In Scheme 5-14 the (Z/E) configurational isomerism is added to the acid-base reactions as a second dimension . The real situation, however, is yet more complex, as the TV-nitrosoamines may be involved as constitutional isomers of the diazohydroxide. In order not to make Scheme 5-14 too complex the nitrosoamines are not included, but are shown instead in Scheme 5-15. The latter also includes the addition reactions of the (Z)- and ( )-diazoates (5.4 and 5.5) to the diazonium ion to form the (Z,Z)-, (Z,E)- and (2 2i)-diazoanhydrides (5.6, 5.7 and 5.8) as well as proto-de-nitrosation reactions (steps 10, 11 and 12). This pathway corresponds to the reverse reaction of diazotization, as amine and nitrosating reagent (nitrosyl ion) are formed in this reaction sequence.

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