A Simple Model of GC x GC Separations

John V. SeeleyOakland 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”– 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

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

A 3-Step Solvation Model

Conclusions Based on the 3-Step Solvation Model

Retention Order –Go

Retention Order (Solvent Cohes. – Constant) (Solute Size)+ (Solvent Polarity) (Solute

Polarity)

Retention Order (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 Polarityand Solvent Cohes.

The “Logic” Behind a 2-D Chromatogram

• GC x GC Chromatograms generate separations in two dimensionsone 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

Group Name Structure of Z

Alkanes

1-Alkenes

Aromatics

Cyclohexanes

1-Chloros

1-Fluoros

H

H2C CH

Cl

F

Group Name Structure of Z

1-Alcohols

2-Alcohols

tert-Alcohols

Aldehydes

2-Ketones

Acetates

HO

CH2

OH

C

H3C

H3C

H3C

CH

OH

C

O

H

C

O

H3C

C

O

OH3C

Z–(CH2)n–H Homologous Groups

A GC x GC Chromatogram of Several Series of Homologous Compounds

DB-624 x DB-Wax

1.90

2.10

2.30

2.50

2.70

2.90

0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0

primary retention time (s)

seco

nd

ary

rete

nti

on

tim

e (s

)

alkanes

acetates

ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

A GC x GC Chromatogram of Several Series of Homologous Compounds

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

Increasing n

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.0

2

Z

R

n

t

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-programmed 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 m x 1.4 m) – DB-Wax (30m x 250 m x 0.25 m)– DB-210 (30m x 250 m x 0.5 m)

• 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.

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.

Determination of rZ

Class rZ

Alkanes 0Alkenes 0Cyclohexanes 02-ketones 0Aromatics 0Acetates 0Aldehydes 01-chloros 01-alcohols 02-alcohols 0tert-alcohols 0

DB-624 from GCMS

0

5

10

15

20

25

30

35

0 5 10 15

rz + n

t R (

s)

alkanes

alkenes

cyclohexanes

chloro

acetates

2-ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

fit

Determination of rZ

Class rZ

Alkanes 0Alkenes 1.97Cyclohexanes 6.272-ketones 4.35Aromatics 6.85Acetates 4.45Aldehydes3.401-chloros 2.721-alcohols 4.172-alcohols 4.46tert-alcohols 4.81

DB-624 from GCMS

0

5

10

15

20

25

30

35

0 5 10 15

rz + n

t R (

s)

alkanes

alkenes

cyclohexanes

chloro

acetates

2-ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

fit

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

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+

rZ & n – Relationship to 2D Chromatogram

DB-624 x DB-Wax

1.85

2.05

2.25

2.45

2.65

2.85

50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.01tR(s)

2 t R (

s)

alkanes

alkenes

cyclohexanes

1-chloros

acetates

2-ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

Initial study focused on determining the rz values of 11 different compound

classes.

rZ & n – Relationship to 2D Chromatogram

The primary retention time is essentially linearly related to n + rZ.

1tR (rZ + n)

GC x GC 1tR vs. (rz + n) from GC-MS

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

3 5 7 9 11 13

rz + n

1 t R (

s)

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

aldehydes

rZ & n – Relationship to 2D Chromatogram

DB-624 x DB-Wax

1.85

2.05

2.25

2.45

2.65

2.85

50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.01tR(s)

2 t R (

s)

alkanes

alkenes

cyclohexanes

1-chloros

acetates

2-ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

Examine the secondary retention of a small region of the 2D chromatogram

rZ & n – Relationship to 2D Chromatogram

The secondary retention time is exponentially related to rZ.2tR (exp rZ) where rz = 2rz – 1rz

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

0 1 2 3 4

rZ

2 t Rexponential fit

octane

octene

methylcyclohexane

pentanone

toluene

propylacetate

pentanal

chloropentane

1-pentanol

2-pentanol

t-hexanol

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: Arz

rz = 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).

DB-624 x DB-Wax

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

4 5 6 7 8 9 10 11 12 13 14rz + n

A

rz

alkanes

alkenes

cyclohexanes

1-chloros

acetates

2-ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

DB-624 x DB-Wax

1.85

2.05

2.25

2.45

2.65

2.85

50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0

1tR(s)

2t R

(s)

alkanes

alkenes

cyclohexanes

1-chloros

acetates

2-ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

DB-624 x DB-210

0.6

1.1

1.6

2.1

2.6

3.1

3.6

4 6 8 10 12 14rz + n

A^

rz

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

aldehydes

DB-624 x210

2.05

2.25

2.45

2.65

2.85

50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0

1tr

tR (

s)alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

aldehydes

An Application of the Simplified Chromatogram: Changing Stationary Phase Order

HP-5 x DB-Wax Measured

1.7

1.9

2.1

2.3

2.5

2.7

2.9

3.1

150 250 350 450 550 650Primary Retention Time (s)

Se

co

nd

ary

Re

ten

tio

n T

ime

(s

)

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

fluoro

HP-5 x DB-Wax

0

2

4

6

8

10

12

14

4 6 8 10 12 14rz + n

A^

de

lta

R

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

fluoros

An Application of the Simplified Chromatogram: Changing Stationary Phase Order

DB-Wax X HP-5 Simulation

0

0.2

0.4

0.6

0.8

1

5 7 9 11 13 15rz + n

A^

del

taR

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

fluoros

DB-Wax X HP-5 Measured

1.6

2.1

2.6

3.1

100 200 300 400 500Primary Retention Time (s)

Sec

on

dar

y R

eten

tio

n T

ime

(s)

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

fluoro

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 timeinversion of secondary retention time

Comparable results are obtained with the DB-1 & HP-50+ column set.

An Application of the Simplified Chromatogram: Predicting the Retention Position of Non-

Homologous CompoundsThe 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: Ar

DB-624 from GCMS

0

5

10

15

20

25

30

35

3 8 13

rz + n

t R (

s)

alkanes

alkenes

cyclohexanes

chloro

acetates

2-ketones

1-alcohols

2-alcohols

aromatics

tert-alcohols

aldehydes

fit

Asymmetric Sigmoid of DB-624 GC-MS Data

DB-Wax from GCMS

0

5

10

15

20

25

3 8 13 18

rz + n

t R (

s)

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

aldehydes

fit

Asymmetric Sigmoid of DB-Wax GC-MS Data

DB-624 vs. DB-Wax Alcohols

2.25

2.45

2.65

2.85

3.05

50.0 100.0 150.0 200.0 250.0 300.0

primary retention time (s)

sec.

ret

. tim

es (

s)DB-624 vs. DB-Wax Alcohols

3.5

4.5

5.5

6.5

7.5

8.5

9.5

4 6 8 10 12

1r

A

r2-methyl-1-propanol

3,3-dimethyl-2-butanol

3-methyl-1-butanol

4-methyl-2-pentanol

4-methyl-1-pentanol

5-methyl-1-hexanol

2-methyl-2-propen-1-ol

4-penten-1-ol

cis-3-hexen-1-ol

trans-2-hexen-1-ol

DB-624 vs. DB-Wax Alcohols

2.25

2.45

2.65

2.85

3.05

50.0 100.0 150.0 200.0 250.0 300.0

3.5

4.5

5.5

6.5

7.5

8.5

9.5

4 6 8 10 12

Alcohol Mixture

r values are calculatedfrom the curve fits.

Excellent prediction of peak position

DB-624 vs. DB-Wax

2.3

2.5

2.7

2.9

3.1

3.3

3.5

3.7

6 7 8 9 10 11 12

1r

A

r

DB-624 vs. DB-Wax

2.2

2.3

2.4

2.5

100 150 200 250 300 350

Primary Retention Time (s)

Sec

on

dar

y R

et. T

ime

(s)

m-xylene

p-xylene

o-xylene

isopropyl benzene

m-ethyl toluene

p-ethyl toluene

1,3,5-trimethyl benzene

o-ethyl toluene

tertbutyl benzene

1,2,4-trimethyl benzene

isobutyl benzene

p-isopropyl toluene

1,2,3-trimethyl benzene

m-diethyl benzene

p-diethyl benzene

o-diethyl benzene

1,2,4,5-tetramethyl benzene

1,2,3,5-tetramethyl benzene

1,2,3,4-tetramethyl benzene

Aromatic Mixture

Excellent prediction of relative retention of non-homologous compounds

DB-624 vs. DB-Wax

2.2

2.4

2.6

2.8

3.0

3.2

50.0 100.0 150.0 200.0 250.0 300.0 350.0

primary retention time (s)

sec.

ret

. tim

es (

s)DB-624 vs. DB-Wax

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

4 6 8 10 12

1r

A

r

Aromatic/Alcohol Mixture

Great intra-group predictions

Poor inter-group predictions.

This is due to the extreme structural differences between the two groups.

A Linear Free Energy Model ofGC x GC SeparationsSimple 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.

Columns s' e' a'

DB-1 0.814 0.000 0.727

HP-5 1.182 0.000 0.784

DB-624 1.772 -0.325 1.582

HP-50+ 2.604 0.669 1.175

DB-1701 2.413 0.000 2.588

DB-210 5.768 -1.548 0.348

AT-Wax 5.935 1.013 8.506

Z nz S E A

alkanes 0.00 0.00 0.00 0

1-alkenes 1.75 0.08 0.09 0

cyclohexanes 6.35 0.10 0.24 0

2-ketones 3.20 0.68 0.13 0

aromatics 6.15 0.51 0.61 0

acetates 3.35 0.60 0.06 0

aldehydes 2.38 0.65 0.15 0

1-fluoros 0.50 0.35 -0.01 0

1-chloros 2.20 0.40 0.20 0

1-alcohols 1.85 0.42 0.22 0.37

2-alcohols 3.20 0.36 0.21 0.33

tert-alcohols 3.85 0.30 0.19 0.31

r = n + nz + s’S + e’E + a’ACompound size

Polarity of Functional Group

Definition of the LFER Simplified Chromatogram

• 1tR proxy: 1r = n + nz + 1s’ S + 1e’ E + 1a’ A

• 2tR proxy: Ar r = 2r - 1r = s’ S + e’ E + a’ AA 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.

DB-624 x DB-Wax Experimental

1.85

2.05

2.25

2.45

2.65

2.85

50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0Primary Retention Time (s)

Se

co

nd

ary

Re

ten

tio

n T

ime

(s)

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

aldehydes

DB-624 x AT-Wax LFER

0

2

4

6

8

10

4 6 8 10 12 14

LFER 1r

A

r

alkanes

alkenes

cyclos

chloro

acetates

ketones

p alcs

salcs

aro

talcs

aldehydes

Evaluation of LFER Simplified Chromatogram

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.

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 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.