Leonid M. Blumberg

Comparison of one-dimensional and comprehensive two-dimensional separations by gas chromatography

Comprehensive two-dimensional gas chromatography (GC x GC) can reveal information on the composition of a sample in a way that cannot be done by one-dimensional GC (1D-GC). GC x GC also offers much greater control of chromatographic selectivity based on molecular structure. However, in spite of more than 15 years of claims of the ability of GC x GC to resolve an overwhelmingly larger number of peaks than 1D-GC, and in spite of the theoretically proven potential of GC x GC to have an order of magnitude larger peak capacity than 1D-GC, the peak capacity of currently practiced GC x GC does not generally exceed the peak capacity attainable from 1D-GC with the same analysis time and the same minimal detectable concentration (MDC). The methodology for comparing the peak capacity of GC x GC to 1D-GC is described. The comparison of the performance of GC x GC to 1D-GC shows that the modulator is the key bottleneck limiting the performance of existing GC x GC. To realize the full potential of GC x GC, duration of injection from a modulator into the second-dimension column should be reduced by an order of magnitude or more. Use of powerful data analysis techniques such as peak deconvolution in both dimensions can further increase resolving power of GC x GC.

Quantitative comparison of performance of isothermal and temperature-programmed gas chromatography

As a basic metric of separation for comparing isothermal and temperature-programmed GC (gas chromatography), we used the separation measure. S (defined elsewhere). We used this metric as both a measure of separation of any two peaks, and a measure of separation capacity of arbitrary intervals where peaks can potentially exist. We derived several formulae for calculation of S for any pair of peaks regardless of their shape and the distance from each other in isothermal and temperature-programmed GC. The formulae for isothermal GC can be viewed as generalizations of previously known expressions while, in the case of temperature-programmed GC, no equivalents for the new formulae were previously known from the literature. In all formulae for S. we identified similar key component-metrics (solute separability, intrinsic efficiency of separation, specific separation measure, separation power) that helped us to identify and better understand the key factors affecting the separation process. These metrics also facilitated the quantitative comparison of separation capacities and analysis times in isothermal and temperature-programmed GC. Some of these metrics can be useful beyond GC. In the case of GC, we have shown that, if the same complex mixture was analyzed by the same column, and the same separation requirements were used then isothermal analysis can separate more peaks than its temperature-programmed counterpart can. Unfortunately, this advantage comes at the cost of prohibitively longer isothermal analysis time. The latter is a well know fact. Here, however, we provided a quantitative comparison. In a specific example, we have shown that a single-ramp temperature program with a typical heating rate yields about 25% fewer peaks than the number of peaks available from isothermal analysis of the same mixture using the same column. However, that isothermal analysis would last 1000 times longer than its temperature-programmed counterpart. Using twice as longer column in the case of a temperature-programmed analysis, allows one to recover the 25% disadvantage in the number of separated peaks, while still retaining a 500-fold advantage in the speed of analysis.

Metrics of separation in chromatography

A new metric, separation measure, S, for chromatographic separation is proposed. Unlike other metrics such as resolution, separation number, and some versions of peak capacity, the new metric provides a consistent, additive measure of the separation of pairs of peaks as well as the separation capacities of arbitrary intervals within the analysis time. The attribute of additivity means that the separation measure of any separation interval is equal to the sum of the separation measures of its subintervals. Practical aspects of the measurement of S are also addressed. In addition to definition of S, a definition of peak capacity, n, that is consistent with S, and includes useful features of other known definitions of n is proposed for an arbitrary time interval.

Elution parameters in constant-pressure, single-ramp temperature-programmed gas chromatography.

The dependence of the degree of interaction of a solute with the stationary phase at the time of its elution from the column in temperature-programmed GC is best described by interaction level of the solute. The latter represents the fraction of a solute residing in the stationary phase relative to the total amount of the solute. A simple approach to the evaluation of interaction levels of eluting solutes in a single-ramp temperature program is proposed. In a single-ramp temperature program having no preceding temperature plateau, all solutes that elute at temperatures that are about 60 degrees C higher than the initial temperature of the heating ramp elute with nearly the same interaction levels that can be found as exp(-r), where r is dimensionless heating rate. A specially designed temperature plateau preceding the ramp causes all solutes eluting during the entire time of the ramp to elute with nearly the same interaction levels equal to exp(-r). A transformation of the interaction level of a solute into its retention factor or mobility factor (a fraction of a solute in a mobile phase in relation to the total amount of the solute) and vice versa is also described.

Evaluation of conditions of comprehensive two-dimensional gas chromatography that yield a near-theoretical maximum in peak capacity gain☆

The peak capacity gain (Gn) of a GC×GC system is the ratio of the system peak capacity to that of an optimized one-dimensional GC analysis lasting the same time and providing the same detection limit. A near-theoretical maximum in Gn has been experimentally demonstrated in GC×GC-TOF based on a 60m×0.25mm primary column. It was found that Gn was close to 9 compared to the theoretical maximum of about 11 for this system. A six-sigma peak capacity of 4500 was obtained during an 80min heating ramp from 50°C to 320°C. Using peak deconvolution, 2242 individual peaks were determined in a Las Vegas runoff water sample. This is the first definitive experimental demonstration known to us of an order-of-magnitude Gn. The key factors enabling this gain were: relatively sharp (about 20ms at half height) reinjection pulses into the secondary column, relatively long (60m) primary column, the same diameters in primary and secondary columns, relatively low retention factor at the end of the secondary analysis (k≅5 instead of 15, optimal for ideal conditions), optimum flow rate in both columns, and helium (rather than hydrogen) used as the carrier gas. The latter, while making the analysis 65% longer than if using H2, was a better match to the reinjection bandwidth and cycle time.

Development of fast enantioselective gas-chromatographic analysis using gas-chromatographic method-translation software in routine essential oil analysis (lavender essential oil).

The study aimed to find the best trade-off between separation of the most critical peak pair and analysis time, in enantioselective GC-FID and GC-MS analysis of lavender essential oil, using the GC method-translation approach. Analysis conditions were first optimized for conventional 25 m x 0.25 mm inner diameter (dc) column coated with 6(I-VII)-O-tert-butyldimethylsilyl-2(I-VII)-3(I-VII)-O-ethyl-beta-cyclodextrin (CD) as chiral stationary phase (CSP) diluted at 30% in PS086 (polymethylphenylpolysiloxane, 15% phenyl), starting from routine analysis. The optimal multi-rate temperature program for a pre-set column pressure was determined and then used to find the pressures producing the efficiency-optimized flow (EOF) and speed-optimized flow (SOF). This method was transferred to a shorter narrow-bore (NB) column (11 m x 0.10 mm) using method-translation software, keeping peak elution order and separation. Optimization of the enantioselective GC method with the translation approach markedly reduced the analysis time of the lavender essential oil, from about 87 min with the routine method to 40 min with an optimal multi-rate temperature program and initial flow with a conventional inner diameter column, and to 15 min with FID as detector or 13.5 min with MS with a corresponding narrow-bore column, while keeping enantiomer separation and efficiency.

Evaluation of column performance in constant pressure and constant flow capillary gas chromatography

It has been demonstrated that there is no significant difference between the maximum peak capacity and analysis time at the same peak capacity in constant pressure (isobaric) and constant flow (isorheic) modes of temperature programmed GC. In view of that, the choice between the two pneumatic modes should be based on considerations other than the speed-separation performance of the column.

Metrics of separation performance in chromatography. Part 1. Definitions and application to static analyses.

Earlier introduced metrics of separation performance are described in a systematic way. After providing the definitions of the metrics suitable for a broad variety of applications, the study focuses on static analyses (isothermal GC, isocratic LC, etc.) and their general separation performance. Statistically expected number of resolved (adequately separated) single-component peaks is treated as the ultimate metric of general separation performance of chromatographic analysis. That number depends on the peak capacity of the analysis and the number of components in a test mixture. The peak capacity, in turn, depends on the separation capacity of a column and the lowest separation required by the data-analysis system for resolving poorly separated peaks. The separation capacity is a special case of a broader metric of the separation measure which is a function of column efficiency, solute separability, and the level of the solute interaction with a column stationary phase. The formulae for theoretical prediction of all these metrics for arbitrary pairs of peaks in static analyses are derived. To provide a better insight into the basic metrics of the separation performance, additional metrics such as the solute discrimination (relative difference in solute velocities), utilization of separability (solute discrimination per unit of their separability), specific separation (the separation per unit of separability), and others are defined and found for static analyses.

Metrics of separation performance in chromatography: Part 2. Separation performance of a heating ramp in temperature-programmed gas chromatography

Metrics of separation performance described in Part 1 of this series were applied here to theoretical evaluation of performance of a heating ramp in temperature-programmed GC. As in Part 1, the dependence of the separation (Δs) of two arbitrarily spaced peaks (the number of σ-slots between them) on operational parameters of GC analysis was treated here as the main building block for construction of other performance metrics. Simple expressions describing Δs of two peaks eluting during isobaric linear heating ramp and dependence of Δs on the heating rate, on column efficiency and on the peak spacing were derived. The use of dimensionless heating rate and other dimensionless operational parameters made these expressions universally suitable for different column dimensions, heating rates, carrier gas types, flow rates, etc. The use of dimensionless parameters also made it possible to express Δs as a simple function of the earlier introduced chromatographically meaningful characteristic parameters of thermodynamics of solute-column interactions. The expressions for Δs developed here, together with the ones described in Part 1 were used for theoretical prediction of total separation capacity (s(c)), total peak capacity (n(c)), and total number of resolved peaks in temperature-programmed analysis controlled by a balanced temperature program consisting of a linear heating ramp preceded by specially designed balanced temperature plateau. A numerical example of these parameters for a particular column, heating rate, carrier gas, and its flow rate is also provided. It has been shown that n(c) obtainable in temperature-programmed analysis is 2-3 times larger than that obtainable in equally long isothermal analysis using the same column and gas. Comparison of this improvement with potentially more than an order of magnitude larger peak capacity of GC×GC has been discussed. Also described are the speed of analysis (the number of σ-slots per unit of time), and other characteristics of the separation performance of a heating ramp. In many respects, metric Δs is similar to the widely known metric of resolution (R(s)). Advantages of Δs over R(s) as a metric of the separation performance, as well as the advantages of other metrics utilized here over their widely known counterparts are discussed.

Metrics of separation performance in chromatography: Part 3: General separation performance of linear solvent strength gradient liquid chromatography

The separation performance metrics defined in Part 1 of this series are applied to the evaluation of general separation performance of linear solvent strength (LSS) gradient LC. Among the evaluated metrics was the peak capacity of an arbitrary segment of a chromatogram. Also evaluated were the peak width, the separability of two solutes, the utilization of separability, and the speed of analysis-all at an arbitrary point of a chromatogram. The means are provided to express all these metrics as functions of an arbitrary time during LC analysis, as functions of an arbitrary outlet solvent strength changing during the analysis, as functions of parameters of the solutes eluting during the analysis, and as functions of several other factors. The separation performance of gradient LC is compared with the separation performance of temperature-programmed GC evaluated in Part 2.