P. M. Owens and D. W. Loehle
Center for Molecular Sciences
United States Military Academy
West Point, NY 10996

Injector
Monitor
Detector
Analytical
Detector
Precolumn
Dean's
Switch
Nonpolar SP
Semipolar SP
Polar SP
Analytical
Columns
GC OVEN
Figure 1. Multidimensional parallel column GC system using nonpolar, semipolar and polar stationary phases (SP).

System 1 System 2
5m, 0.53mm HP1
Precolumns
15m, 0.50mm UAC-1
Analytical Columns
10m, 0.53mm HP1 15m, 0.25mm UAC-1
10m, 0.53mm HP17 15m, 0.25mm UAC-17
10m, 0.53mm HP20M 15m, 0.25mm UAC-CW

t r
= t m
+ t m k t m
= mobile phase hold-up time k = partition ratio t’ r
= t r
- t m t’ r
= adjusted retention time k = (t r
- t m
) / t m
= t’ r
/ t m

Parallel Column Retention Equations
Single analyte & 3 columns w / diff. stationary phases (SP) t r
(SP1) = t m
+ t m k (SP1) t r
(SP2) = t m
+ t m k (SP2) t r
(SP3) = t m
+ t m k (SP3)
• The k’s result from specific solutestationary phase interactions and can therefore be used for solute identification

Day 1
Day 1
t
IS
(1) = t m1
+ t m1 k
IS t
AN
(1) = t m1
+ t m1 k
AN
Day 2
Day 2 t
IS
(2) = t m2
+ F * t m2 k
IS t
AN
(2) = t m2
+ F * t m2 k
AN
F corrects for changes in k

t’
AN
(2) / t’
IS
(2) = t’
AN
(1) / t’
IS
(1)
( t’ = t r
- t m
)
Accounts for variations in t m
’s
Accounts for linear variations in k (F factor)

a
a
A, IS
= t’
A
(2) / t’
IS
(2) = t’
A
(1) / t’
IS
(1)
• Generate GC library to tabulate a ’s for each compound on all stationary phases
• Run int. std. with all analyte & library runs
• Since a ’s are T-dependent, run all samples with identical temperature programs

• Sum of a differences
Hit Metric =
S
( a
AN
SP
- a
LIB
)
• Euclidean distance
Hit Metric = [1-
S
( a
N, AN
SP
* a
N, LIB
)] a
N, AN and a
N, LIB are normalized vectors from set of a ’s for each compound

HP17 HP20M
• Sum of a differences
Cyclooctane 1.85
Cyclooctadiene 1.93
1-Heptanol 1.84
1.77
1.93
1.84
• Euclidean Search
Cyclooctane 1.85
Nonanoic Acid 3.05
Octanoic Acid 2.71
1.77
2.87
2.57
1.46
2.46
2.19
HP1
1.46
1.49
1.58

K
D
= k b
K
D
= Distribution constant k = Partition ratio b
= Phase ratio (Vg / Vs )
K
D depends on three variables: 1) temperature,
2) solute, & 3) stationary phase

K
D
= k b t r
= t m
+ t m k
D
D
G = -RT ln K
G =
D
H - T ln k + ln b
= -
D
H / R T +
D
S / R
D
D
S ln k = -
D
H / R (1 / T) +
D
S / R - ln b

ERRORS IN PREDICTED RETENTION TIMES
T PROG OF 12/MIN FROM 15/MIN & 8/MIN
0.1
0.05
0
-0.05
-0.1
C8 C10 C12 C14 C16
COMPOUND
HP20M HP17 HP1

ERRORS IN PREDICTED RETENTION TIMES
T PROG OF 20/MIN FROM 15/MIN & 8/MIN
0.1
0.05
0
-0.05
-0.1
C8 C10 C12 C14 C16
COMPOUND
HP20M HP17 HP1

Retention Prediction Errors (CV)
Prediction Used T-progs of 8 o C/min & 15 o C/min
Sample (C7-C11) 12 C/min 20 C/min
Alkanes (C8-C16) 0.27%
Halogenated
Ketones
0.38%
0.56%
Aldehydes 0.61%
Alkanes (C9-C15) 0.33%
0.51%
0.87%
0.59%
0.62%
0.45%

ERRORS IN PREDICTED RETENTION TIM ES
T PROG OF 12/MIN FROM 15/MIN & 8/MIN
0.2
0
-0.2
C8 C7CL C8CL C9CLC10 CL
COM POUND
HP20M HP17 HP1

ERRORS IN PREDICTED RETENTION TIMES
T PROG OF 20/MIN FROM 15/MIN & 8/MIN
0.2
0
-0.2
C8 C7AL C8AL C9AL C10AL C16
COMPOUND

0.1
Tr Variation on GC Stationary Phases
FOR GC RUNS 30 DAYS APART
-0.1
6 8 10 12 14 16 18 20

1500
RETENTION INDICES FROM 2 INSTRUMENTS
WITH .25mm & .53mm DB1/17/20M COLUMNS
1400
1300
1200
1100
1000
900
C7CL C8CL C9CL C10CL
GC1-20M GC1-DB17 GC1-DB1
GC2-20M GC2-DB17 GC2-DB1
C11BR

Library
Compounds
Predict Retention for Analyte
GC conditions
Predict Analyte
Retention under
Lib. GC Conditions
X Single Analyte
Chromatogram

• Measures interaction on multiple stationary phases
- a separate dimension of analyte information
• Requires the use of internal standards to characterize GC operating conditions
• Thermodynamic modeling allows adjustment of library retentions to current operating conditions

• Interinstrument variability assessment
• Development of calibration procedures to minimize retention prediction errors
• Optimization of stationary phase selection
• Evaluation of an increased number of parallel columns
• Application for complex mixture analysis

• Association of Graduates and Army
Research Office
• Beverly S. Scott & Rodney S. Gonzalez
• Tony Weaver
• Department of Chemistry, USMA