A Simple Model of GC x GC Separations John V. Seeley Oakland University 3/6/07 Model Goals Generation of a “Simplified Chromatogram” from: 1-D retention times Linear free energy relationship parameters Retention indices Utility of the “Simplified Chromatogram”
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John V. Seeley
Retention Ordera –DGo
Retention Ordera (Solvent Cohes. – Constant) (Solute Size)
+ (Solvent Polarity) (Solute Polarity)
Retention Ordera (Solute Size)
+ [(Solvent Polarity)/(Solvent Cohes. – Constant)] (Solute Polarity)
Solute Size should have a “universal” impact on retention order
Solute Polarity will have an impact that is separable from Solute Size
The impact of Solute Polarity will depend on Solvent Polarity
and Solvent Cohes.
one dimension is primarily a “size” separation
one dimension is primarily a “polarity” separation
Z – (CH2)n – H
are the simplest samples to demonstrate the nature of GC x GC separations.
Size determined by n and Z
Polarity determined by Z
DB-624 x DB-Wax
r = n + rz
rZ is a unique constant for each functional class and each column
1tR = f (r)
f = monotonically increasing function
Initial study focused on determining the rz values of 11 different compound classes.
The primary retention time is essentially linearly related to n + rZ.
1tRa (rZ + n)
Examine the secondary retention of a small region of the 2D chromatogram
The secondary retention time is exponentially related to DrZ.
2tRa (exp DrZ) where Drz = 2rz – 1rz
Drz = 2rz - 1rz
A is a constant between 1.5 and 1.8
Thus, the simplified chromatogram is generated from 1-D retention indices and a single, narrowly defined constant (A).
Simplified chromatograms for both column orders (i.e., non-polar x polar and polar x non-polar) are generated with the same sets of rz values.
The simplified chromatograms “capture the essence” of the retention positions in both configurations.
Thus, switching stationary phase order leads to a simple, predictable change in peak positions:
logarithmic warping of the primary retention time
inversion of secondary retention time
Comparable results are obtained with the DB-1 & HP-50+ column set.
The simplified chromatogram concept can be easily extended to non-homologous mixtures provided that the retention indices of the mixture compounds are known.
We have fit our plots of tR vs (rz + n) with an asymmetric sigmoid function.
This function can then be inverted to calculate the retention index of any compound (homologous or non-homologous) from its retention time.
Retention indices on primary and secondary columns can be combined to generate a simplified chromatogram.
1tR proxy: 1r
2tR proxy: ADr
r values are calculated
from the curve fits.
Excellent prediction of peak position
Excellent prediction of relative retention of non-homologous compounds
Great intra-group predictions
Poor inter-group predictions.
This is due to the extreme structural differences between the two groups.
GC x GC Separations
Simple models that predict retention from a linear combination of solute descriptors and corresponding stationary phase descriptors have been the subject of numerous studies over the past 40 years.
The linear free energy model originally developed by Abrahams et al. has been adopted by several research groups.
Descriptors are available for over 1000 solutes.
Poole et al. have published the descriptors of most of the commonly used capillary column stationary phases.
Poole et al. are currently revising the solute and stationary phase descriptors for improved accuracy.
r = n + nz + s’S + e’E + a’A
Dr = 2r - 1r = Ds’ S + De’ E + Da’ A
A is a constant between 1.5 and 1.8
Thus, the primary dimension is influenced by size and polarity, while the secondary dimension is only influenced by polarity.
LFER simplified chromatograms are surprisingly accurate.
Comparable results were obtained for HP-5 x DB-Wax, DB-Wax x HP-5, DB-1 x HP-50, and HP-50 x DB-1.
The LFER model shows that relative primary retention is dictated by compound size and column specific polarity.
The relative secondary retention is dictated by the difference in the column specific polarity between the primary column and the secondary column (compound size does not matter).
The notion of a non-polar x polar separation as being “orthogonal” is not entirely accurate. While the secondary dimension is orthogonal to compound size, the primary dimension is not orthogonal to compound polarity (I.e., compound polarity plays a role in the primary retention). Thus, the two dimensions are not orthogonal to one another. Actually, a lack of orthogonality is not a bad thing; especially, when trying to separate compounds with similar size.
The retention index of a compound can be expressed as a linear combination of a size descriptor and and a column-specific polarity descriptor.
The retention indices (and/or the size and polarity descriptors) of compounds can be determined from temperature-programmed, 1-D GC runs.
Such retention indices can be combined in a straightforward fashion to generate a simplified chromatogram.
The simplified 2-D chromatogram is a surprisingly accurate representation of the structure of the chromatogram.
Linear free energy parameters can be incorporated into the simplified chromatogram concept to generate a flexible tool for retention time prediction. The accuracy won’t be great, but it will be useful for screening column sets and stationary phase order.
The notion of “orthogonality” in GC x GC has been misused and over-hyped.