Sample dimensionality

J. C. Giddings, Sample dimensionality a predictor of order- disorder in component peak distribution in multidimensional separation , J. Chromatogr. 703 3-15 (1995). 

Figure 1 Match between separator and sample dimensionality in GCxGC...

Introduction Sample Dimensionality Group-Type Separation Target Analysis Quantification Fiona Analyses... 

Unlike most other samples that have to be analysed, petrochemical samples generally contain a limited number of classes of compounds, notably, alkanes, alkenes, cyclic alkanes, and aromatics with a different number of fused rings. The sample dimensionality therefore is rather limited (see below). The absolute number of compounds, however, is not only tremendous, but they all need to be analysed. In other words, the matrix itself is the goal of the analysis. So instead of looking for the needle in the haystack, the haystack itself needs to be characterised. In that respect, it is not too surprising that GCxGC from the conception of the technique on, has been developed using petrochemical samples as a subject [1,2]. 

In his paper on multidimensional analyses [3], Giddings explains sample dimensionality (s) as... 

To understand the origin of peak order and disorder in multidimensional analyses, let us extend the term sample dimensionality in the petrochemical sample. 

If the behaviour of a sample with a weakly expressed variable closely resembles that of a sample of lower dimensionality, this may be thought of as an apparent sample dimensionality s, equal to the number of variables strongly enough to produce suitable resolution. 

Required sample dimensionality s" number of sample variables that must be determined for the purpose of the analysis (see also discussion in Chapter 6). 

For the relationship between sample dimensionality and ordered or disordered chromatograms, see Table 1. 

An example of an ordered separation in which the required sample dimensionality fits the separation dimensionality is shown in Figure 1. And since the combination of the individual (orthogonal) selectivities toward the... 

Table 1 Relationship between sample dimensionality and chromatogram separation pattern...

Dimensionality is an important term, which can be used to describe the nature of the sample, or of the multidimensional system. System dimensionality simply refers to the number of coupled separation stages or dimensions used in the multidimensional system. For example, a single column liquid chromatograph would have a dimensionality of 1, whilst a LC-GC system described above has a dimensionality of 2. On the other hand, sample dimensionality, introduced by Giddings in 1995, is used to describe the intrinsic nature of the sample, and can be defined... 

Theoretically, optimum separation is achieved when the sample dimensionality and system dimensionality are equivalent, resulting in an ordered separation (Figure 3). In the above example, only one separation dimension would be required to analyze the alkane sample. If, however, the dimensionality of the sample exceeds that of the system, sample components will not be resolved in an orderly fashion, but rather a disordered or chaotic separation will result. In Figure 3, three descriptors are required to define the sample - shape, pattern, and size. In a chemical sense, these might be molar mass, polarity, and molecular shape. As more dimensions of separation are applied, greater definition of the mixture components is achieved. Unfortunately, for very complex samples, the sample dimensionality will be... 

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