A Simple Model of GC x GC Separations

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A Simple Model of GC x GC Separations

• John V. Seeley
• Oakland University
• 3/6/07

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Model Goals

• Generation of a Simplified Chromatogram from
• 1-D retention times
• Linear free energy relationship parameters
• Retention indices
• Utility of the Simplified Chromatogram
• Demonstrates the underlying mechanisms of a GC x
  GC separation
• Approximate representation of relative peak
  position
• Quick screening new column sets
• Demonstrates the influence of stationary phase
  order on chromatogram structure
• Demonstrates the concept of orthogonality in GC
  x GC

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Model Goals

• The model does not attempt to
• Predict absolute retention times (just relative
  retention position)
• Predict peak widths
• Find optimal flow, temperature, modulation
  conditions, and/or column dimensions
• Generate accuracy at the cost of convenience

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A 3-Step Solvation Model
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Conclusions Based on the 3-Step Solvation Model
Retention Order a DGo Retention Order a
(Solvent Cohes. Constant) (Solute Size)
(Solvent Polarity) (Solute Polarity) Retention
Order a (Solute Size) (Solvent
Polarity)/(Solvent Cohes. Constant) (Solute
Polarity) Big Conclusions 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.
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The Logic Behind a 2-D Chromatogram

• GC x GC Chromatograms generate separations in two
  dimensions
• one dimension is primarily a size separation
• one dimension is primarily a polarity
  separation
• Mixtures of monofunctional homologous organic
  compounds of the type
• 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

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Z(CH2)nH Homologous Groups
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A GC x GC Chromatogram of Several Series of
Homologous Compounds
DB-624 x DB-Wax
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A GC x GC Chromatogram of Several Series of
Homologous Compounds
Increasing n

• Fairly flat bands
• Uniform vertical structure for different values
  of n

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Observations of Chromatogram Structure

• Each homolgous group (i.e., each Z) has a
  different starting primary retention time.
  Changing the value of n leads to a shift in
  primary retention time that is independent of Z.
  This suggests the use of a retention index, r,
  that is linearly related to n and has a
  Z-dependent offset, rz.
• r n rz
• rZ is a unique constant for each functional class
  and each column
• 1tR f (r)
• f monotonically increasing function
• Compounds of the same functional class generate
  peaks in a horizontal band. This means secondary
  retention time is independent of n and most
  likely determined by the rz factors on the
  primary and secondary column.

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Determination of rZ

• We would like to be able to determine the values
  of rz for a wide variety of functional groups on
  a wide range of columns.
• There are many possible sources of data that can
  be used to determine rz, but temperature-programme
  d 1-D GC data is probably the most plentiful.
• For this study we primarily use 1-D GC-MS Data
• DB-624 (30m x 250 mm x 1.4 mm)
• DB-Wax (30m x 250 mm x 0.25 mm)
• DB-210 (30m x 250 mm x 0.5 mm)
• Experimental Conditions
• Constant flow 1 mL/min He
• Temp. Program 35 oC for 4 min 5 oC/min to 200
  oC Hold for 10 min.

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Determination of rZ

• rz provides information on the significance of
  dispersive and polar interactions between the
  stationary phase and the functional group Z.
• We define rZ 0 for n-alkanes.
• Plot tR vs. n for several homologous sets
  including alkanes and horizontally shift the
  homologous sets achieve maximum alignment. The
  value of the shift is defined to be rz.
• Once rz is determined. The value of the
  retention index r is known for each member of the
  homologous set using r n rz .
• The retention index r is essentially a
  nonparametric, diversely defined, divided by 100,
  temperature-programmed Kovats retention index.

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Determination of rZ
Class rZ Alkanes 0 Alkenes 0 Cyclohexanes
0 2-ketones 0 Aromatics 0 Acetates 0 Aldehydes
0 1-chloros 0 1-alcohols 0 2-alcohols 0 tert-a
lcohols 0
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Determination of rZ
Class rZ Alkanes 0 Alkenes 1.97 Cyclohexan
es 6.27 2-ketones 4.35 Aromatics 6.85 Acetates
4.45 Aldehydes 3.40 1-chloros 2.72 1-alcohols 4
.17 2-alcohols 4.46 tert-alcohols 4.81
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Determination of rZ
Classes DB-624 rZ DB-Wax rZ DB-210 rZ
Alkanes 0.00 0.00 0.00
Alkenes 1.97 2.35 2.17
Cyclohexanes 6.27 6.65 6.49
2-ketones 4.35 6.89 6.81
Aromatics 6.85 9.20 7.78
Acetates 4.45 6.85 6.40
Aldehydes 3.40 5.87 5.58
1-chloros 2.72 4.38 3.79
1-alcohols 4.17 8.53 5.19
2-alcohols 4.46 8.23 5.51
Tert-alcohols 4.81 8.12 5.92
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Determination of rZ

• Alignment analysis was repeated with data from
• catalog retention times
• columns with different dimensions (same
  stationary phase)
• diverse temperature programs
• variability rz values was on the order of /- 0.1
• alignment analysis generates comparable fits for
  other commonly used stationary phases including
  DB-1, DB-1701, HP-5, and HP-50

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rZ n Relationship to 2D Chromatogram
Initial study focused on determining the rz
values of 11 different compound classes.
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rZ n Relationship to 2D Chromatogram

• The primary retention time is essentially
  linearly related to n rZ.
• 1tR a (rZ n)

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rZ n Relationship to 2D Chromatogram
Examine the secondary retention of a small region
of the 2D chromatogram
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rZ n Relationship to 2D Chromatogram

• The secondary retention time is exponentially
  related to DrZ.
• 2tR a (exp DrZ) where Drz 2rz 1rz

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Definition of the Simplified Chromatogram

• Our goal is to generate a 2D retention time plot
  with structure that is similar to the real GC x
  GC chromatogram.
• 1tR proxy 1r 1rz n
• 2tR proxy ADrz
• 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).

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An Application of the Simplified Chromatogram
Changing Stationary Phase Order
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An Application of the Simplified Chromatogram
Changing Stationary Phase Order
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An Application of the Simplified Chromatogram
Changing Stationary Phase Order
Key Results 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.
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An Application of the Simplified Chromatogram
Predicting the Retention Position of
Non-Homologous Compounds
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
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Asymmetric Sigmoid of DB-624 GC-MS Data
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Asymmetric Sigmoid of DB-Wax GC-MS Data
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Alcohol Mixture r values are calculated from the
curve fits. Excellent prediction of peak position
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Aromatic Mixture Excellent prediction of
relative retention of non-homologous compounds
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Aromatic/Alcohol Mixture Great intra-group
predictions Poor inter-group predictions. This
is due to the extreme structural differences
between the two groups.
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A Linear Free Energy Model of 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.
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Polarity of Functional Group
r n nz sS eE aA
Compound size
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Definition of the LFER Simplified Chromatogram

• 1tR proxy 1r n nz 1s S 1e E 1a A
• 2tR proxy ADr
• 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.

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Evaluation of LFER Simplified Chromatogram
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LFER Studies 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.
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Main Conclusions 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 wont 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.