Development of a comprehensive, three-dimensional gas chromatograph (GC3) instrument is described. The instrument utilizes two six-port diaphragm valves as the interfaces between three, in-series capillary columns housed in a standard Agilent 6890 gas chromatograph fitted with a high data acquisition rate flame ionization detector. The modulation periods for sampling column one by column two and column two by column three are set so that a minimum of three slices (more commonly four or five) are acquired by the subsequent dimension resulting in both comprehensive and quantitative data. A 26-component test mixture and quantitative standards are analyzed using the GC3 instrument. A useful methodology for three-dimensional (3D) data analysis is evaluated, based on the chemometric technique parallel factor analysis (PARAFAC). Since the GC3 instrument produces trilinear data, we are able to use this powerful chemometric technique, which is better known for the analysis of two-dimensional (2D) separations with multichannel detection (e.g., GC x GC-TOFMS) or multiple samples (or replicates) of 2D data. Using PARAFAC, we mathematically separate (deconvolute) the 3D data "volume" for overlapped analytes (i.e., ellipsoids), provided there is sufficient chromatographic resolution in each of the three separation dimensions. Additionally, PARAFAC is applied to quantify analyte standards. For the quantitative analysis, it is demonstrated that PARAFAC may provide a 10-fold improvement in the signal-to-noise ratio relative to a traditional integration method applied to the raw, baseline-corrected data. The GC3 instrument obtains a 3D peak capacity of 3500 at a chromatographic resolution of one in each separation dimension. Furthermore, PARAFAC deconvolution provides a considerable enhancement in the effective 3D peak capacity.

The concept and definition of orthogonality in the context of comprehensive two-dimensional (2D) separations are interesting topics of active discussion. Over the years, several approaches have been taken to quantify the degree of orthogonality, primarily to serve as a metric to optimize (and compare) comprehensive 2D separations. Recently, a mathematical function was reported that is qualitatively instructive for the purpose of providing such a metric. However, the mathematical function has some quantitative shortcomings. Herein, we both explore and partially correct this function. The orthogonality metric, referred to previously and herein as the orthogonality, O, was mathematically related to the fraction of the 2D separation space occupied by compounds (i.e., fractional coverage) and the peak capacity, P, for one dimension of the 2D separation. The fractional coverage, f, is simply related to the percentage coverage, which is equal to 100%(f). Our main finding was that the values for O as a function of P for a given percentage coverage achieve a constant value at large P but deviate severely to lower O values at small P. For comprehensive 2D separations operated such that the second dimension is at small P, the findings we report have consequences for those who consider applying the O metric. Finally, it is discussed that the percentage coverage may be a better metric to gauge the extent to which the compounds in a given sample mixture have been disseminated in the 2D separation space.