LCGC Europe published a paper in 2003 that sought to establish a nomenclature for comprehensive twodimensional gas chromatography (GC×GC).^{1} Recently a term called modulation ratio (M_{R}) was added to the lexicon of GC×GC. This defines the way a peak is sampled from a first dimension column into a second column. It is a rather simple definition in practice, which helps the analyst to understand the relative dimensions required of the two columns (in particular, those of the second column) to ensure that sampled solutes elute within the modulation period chosen. Using the modulation ratio, we can decide how many modulated peaks need to be measured to provide a suitable quantitative estimation of the peak area of a solute.
The M_{R} value requires an understanding of the concept of modulation phase because this affects how modulated peaks vary in size according to the manner in which the first dimension is sampled. This article will put into context the different interpretations that can be elucidated through ideas of the modulation ratio.
The Modulation Ratio Concept, M
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The modulation ratio is defined by Equation (1):^{2}
Figure 1

We have chosen this definition to quantify the relationship between the width of a peak at baseline that elutes from a first dimension column (^{1}w_{b}), to the selected modulation period, P_{M}, that we use to generate the modulation process in comprehensive twodimensional gas chromatography (GC×GC). Seeley used a term called the dimensionless sampling period, τ, to relate first and second dimension peak properties.^{3} Beens et al.^{4} employed a term called modulation criterion, where the ratio of maximum second dimension retention time to first dimension peak standard deviation (SD) is required to be ≤ 1.5.
Table 1: Relationship between first dimension peak width (^{1}w_{b})and standard deviation (^{1}σ), and the modulation period (P_{M}) for a given modulation ratio (M_{R}).

The modulation ratio essentially means that if the modulation period P_{M} is set the same as the peak standard deviation (SD), then we will have a M_{R} value of 4σ/σ (i.e., M_{R} = 4). It was proposed by Murphy et al.^{5} that ~ 4 modulated peaks should be generated if the first dimension resolution is to be preserved in the comprehensive experiment. The concept of M_{R} is an improved interpretation of this idea. Since the peak width is defined as 4σ, then in this instance we get "about" 4 modulations per peak. Let us put that into context. If a peak is about 10 s wide, then using a P_{M} of 2.5 s will give an M_{R} of 4. Refer to Figure 1 for a further definition of the M_{R} concept with respect to the sampling of the first dimension peak. Table 1 reports the interrelation between P_{M} and M_{R} for various peak widths at base.