Assessment by Monte Carlo simulation of thermodynamic correlation of retention times in dual‐column temperature programmed comprehensive two‐dimensional gas chromatography

Abstract

The correlation of retention times in comprehensive two-dimensional gas chromatography caused by correlation of enthalpy and entropy changes between two stationary phases, methylsilicone and poly(ethylene glycol), was examined using commercial GC software and in-house Monte Carlo simulation. The enthalpy change, deltaH0, and entropy change, deltaS0, of 93 compounds were predicted from isothermal one-dimensional gas chromatograms predicted by the software. These values then were mimicked by Monte Carlo simulation, which removed the strong correlation of deltaH0 and modest correlation of deltaS0 between the two phases. Retention times in a comprehensive two-dimensional gas chromatogram (GC x GC) and in simulations of it were predicted for typical dual-capillary temperature-programmed conditions using the actual, correlated values of deltaH0 and deltaS0 and their uncorrelated Monte Carlo counterparts, respectively. The uncorrelated deltaH0 and deltaS0 values caused the retention-time range of the simulations' second dimension to expand substantially beyond that in the GC x GC. Other simulations were developed using a restricted range of uncorrelated deltaH0 and deltaS0 values to mimic more closely the retention-time range of the GC x GC's second dimension. The intervals between nearest neighbor retention-time coordinates were calculated in both the latter simulations and the GC x GC. The intervals were larger in the simulations than in the GC x GC because the former contained uncorrelated coordinates and the latter contained correlated ones, which clustered along or near the diagonal. The retention times in the first dimension of the GC x GC were Poisson distributed, as assessed by statistical-overlap theory. In contrast, the two-dimensional reduced retention-time coordinates in the GC x GC were not Poisson distributed, because retention times were correlated. However, the reduced retention-time coordinates in the simulations were Poisson distributed.

Statistical‐overlap theory for elliptical zones of high aspect ratio in comprehensive two‐dimensional separations

“…Second, it is unclear how best to define the boundary; it must enclose the centers of all zones of interest but also intersect the profiles of zones near the boundary. Third, it is likely that a rectangular space is not always the ideal geometry to consider, especially for GC6GC, in which retention-time distributions spanning a large region may resemble a fan [9]. In spite of these issues, this work is a major step toward extending SOT to comprehensive separations.…”

“…These expressions are among ones used with point-process SOT in original [3,5] and modified [6,7,9] form. They are interpreted as predicting the average numbers of peaks containing 1, 2, 3, etc., zones in a large ensemble of 2-D separations…”

“…Various forms of SOT for these numbers were reported [1 -8] and applied [7] to 2-D separations several years ago. Recently, theory was used to quantify the reduction of intervals between retention times due to correlation in comprehensive two-dimensional gas chromatography (GC6GC) [9].…”

“…As discussed in ref. 9, it is not clear how well this theory applies to comprehensive 2-D separations for the following reasons.…”