## Expanding System Capacity

Statistical methods have been employed to determine the ability of a column to resolve a complex mixture of compounds, assuming their distribution within the column to be entirely random. This theoretical analysis is informative, but typical complex mixtures must be treated on a case-by-case basis. The chromatographer must define the information required from an analysis; there may be no need to resolve every peak in a mixture if the required target solutes are only a small fraction of the total components. An optimized separation need focus only on those components which must be analysed. For example, the analysis of benzene and toluene in gasoline fractions, where only the resolution and quantification of these compounds are required, means that the measurement of all other components is of less or even of no concern.

The capacity of the total system (or the restricted region about the target solutes) will be expanded in the multidimensional analysis. Specific regions of the effluent from the first column must be isolated and these small fractions transferred to the second column. These two columns may be referred to as the pre-column or first dimension, and the analytical column or second dimension.

Consider the above GC column with a capacity of 540 peaks. If this is coupled to a second column with capacity of, for example, 280 peaks, and if the two columns represent completely orthogonal separations, we would have a theoretical capacity of 540 x 280 = 151 200 peaks. More generally:

«tot = (n )z where ntot is total peak capacity, n is the average capacity on each column and z is the number of coupled columns.

This can only be possible if the full capacity of each dimension can be achieved in the MDGC analysis. This is not normally so; it depends critically on the manner in which the column interfacing is performed, and how the transfer and subsequent second-dimension analysis is carried out. In fact, with selected heart-cut analysis, the total system capacity is better described as the summation, rather than the product, of the capacity of the two coupled columns:

= 2n or, more generally:

Consider a first column with a small unresolved group of, say, five peaks each of 10 s basewidth, eluting over a period of 35 s which is transferred to the second column. The peak capacity of the first column in the region of interest is only 3.5. If the second column has the ability to separate these peaks n

Figure 1 Multidimensional gas chromatography schematic diagram. Courtesy of SGE International.

just to basewidth, then its capacity towards the target solutes is 5. (If the peak separation is random, we will require a higher peak capacity in order to be assured that the five peaks will be separated.) In GC, solute boiling point plays a key part in the retention of compounds, and superposed on this primary retention parameter will be secondary properties such as polarity of the column and solutes, defining solute-

specific interactions. Since each column's retention depends in the first instance on the overall volatility of each component, then the heart-cut or transferred solutes cannot be distributed over the total elution space of the second column. Rather, it is restricted to the range that the combined effect of boiling point and polarity imposes on the compounds. A non-polar first column means close eluting solutes have similar boiling points. A polar second column will enhance solute polarity differences to achieve separation. Figure 2 shows examples of heart-cutting poorly resolved sections of one column to another column. If the solutes subsequently elute relatively close together, much of the theoretical capacity of the second column is not employed.

In many MDGC systems, a cryofocusing step is used at the start of the second column to collect heart-cut fractions as a narrow band, as shown in Figure 2B centre. When the cryogenic fluid is turned off, the solutes recommence their travel on the second column, starting at the same initial position and time. If unresolved compounds from the first column are separated, the aim of the experiment is achieved. The use of a second oven, in which the second column is located, may require a cold trap since just keeping the second oven at a low temperature may not be sufficient to immobilize the solutes. If trapping is not required, the second oven may track the temperature of the first oven.

The need for a cryogenic trapping procedure requires further consideration. Since it will focus solutes at the start of the second column, it will also remix partially resolved compounds. Depending on whether the solutes reverse their relative retention on the two phases, the action of focusing the solutes may either improve or worsen the separation.

Figure 2 (A) Heart-cutting the poorly resolved section of the top column to the bottom column improves separation, but the full capacity of the second dimension may not be fully used. A second-dimension analysis, which only requires the space shown by lines labelled b, would be preferable to that shown by lines labelled a, where excess analysis time would result. (B) Two heart-cuts are performed on the first dimension (top). Both heart-cuts enter one cryogenic trap with all components recombined into one band (centre). The second-dimension analysis (bottom) is then used to provide greater selectivity difference for the range of solutes and enhanced separation of the components.

Figure 2 (A) Heart-cutting the poorly resolved section of the top column to the bottom column improves separation, but the full capacity of the second dimension may not be fully used. A second-dimension analysis, which only requires the space shown by lines labelled b, would be preferable to that shown by lines labelled a, where excess analysis time would result. (B) Two heart-cuts are performed on the first dimension (top). Both heart-cuts enter one cryogenic trap with all components recombined into one band (centre). The second-dimension analysis (bottom) is then used to provide greater selectivity difference for the range of solutes and enhanced separation of the components.

In summary, MDGC may be used in the following arrangements:

• single oven, with or without a cryotrap

• dual oven, with or without a cryotrap

• single or dual oven with multiple sorption/collec-tion traps

• single oven with rapid second-dimension analysis and modulated transfer system - the so-called comprehensive 2D GC.

Figure 3 summarizes a number of different arrangements for performing multidimensional chromatography. Irrespective of the dimension types, the coupling must enable the flow stream to introduce solute into the second dimension. Direct coupling (or pressure tuning in GC) need only use a column connector, but other methods use multiple heart-cuts into one storage reservoir, as indicated by the circle shown in 3A (e.g. a single cryotrap in GC), or separate storage devices with discrete analysis of each, as shown in 3B, or a specially designed modulator to allow continual sampling/analysis of fractions from dimension 1, as in 3C (see later). In the case of method 3A, 2D will probably require a broad range of analysis conditions since collected fractions will have a wide volatility range. In 3B, each separate 2D analysis need only be performed over a limited range of conditions, selected according to volatility considerations.

Figure 3 Coupling two dimensions, transferring selected bands and completing the second-dimension analysis can involve a range of procedures. (A) The second separation dimension can be a single chromatographic analysis, with selected dimension 1 (D,) heart-cuts combined, e.g. in a cold trap, prior to dimension 2 (D2). (B) A series of second-dimension analyses, each for an individual D1 heart-cut, can be run with each heart-cut stored in a separate sample reservoir, e.g. sampling loops in HPLC or cold traps in GC. (C) By operating the second dimension in a rapid repetitive fashion, the comprehensive chromatograpy method is possible.

Figure 3 Coupling two dimensions, transferring selected bands and completing the second-dimension analysis can involve a range of procedures. (A) The second separation dimension can be a single chromatographic analysis, with selected dimension 1 (D,) heart-cuts combined, e.g. in a cold trap, prior to dimension 2 (D2). (B) A series of second-dimension analyses, each for an individual D1 heart-cut, can be run with each heart-cut stored in a separate sample reservoir, e.g. sampling loops in HPLC or cold traps in GC. (C) By operating the second dimension in a rapid repetitive fashion, the comprehensive chromatograpy method is possible.

In regular MDGC, there will be a limited number of second-dimension analyses, or a limited number of heart-cut events. Conventionally, both dimensions will employ columns of reasonably normal types in respect of lengths, diameters and carrier gas flow rates.

In an offline system, or where fractions are collected in a storage section prior to introduction into the second dimension, such as a sampling loop in HPLC, the time between collection of heart-cut and second-dimension analysis might not strictly represent a continuous coupled analysis.

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