detectors in gas chromatography

Journal of Chromatography Library - Volume 4

DETECTORS IN GAS CHROMATOGRAPHY


JOURNAL OF CHROMATOGRAPHY LIBRARY
Volume 1 Chromatography of Antibiotics
by G. H. Wagman and M. J. Weinstein
Volume 2 Extraction Chromatography
edited by T. Braun and G. Ghersini
Volume 3 Liquid Column Chromatography. A Survey of Modern Techniques
and Applications
edited by Z. Deyl, K. Macek and J. Janak
Volume 4 Detectors in Gas Chromatography
by J. SevCik


Journal of Chromatography Library - Volume 4

DETECTORS
IN GAS CHROMATOGRAPHY
JIkf SEVcfK
Department of Analytical Ciieunistrj., Ciiarles University, Prague

ELSEVIER SCIENTIFIC PUBLISHING COMPANY
AMSTERDAM - OXFORD - NEW YORK 1976


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Library of Congress Cataioging in Publication Data

“

4’

.(’

Sevcik, Jiri.
Detectors i n gas chromatography.
(Journal of c h r m t c g r a p h y l i b r a r y ; v. 4 )
Includes b i b l i o g r a p h i c a l referenees and index.
1. Gas chranatography. I. T i t l e .
11. Series.
0 7 9 . C45548
544’ .926
75-30850
ISBN 0-444-9985 7 -8

Q JIRI SEVCfK 1975
Translation 0 KAREL STULfK 1976

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PRINTED IN CZECHOSLOVAKIA


CONTENTS

List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

9

.

1.1 Concentration distribution of the eluted substance at the column outlet .
1.2 Detector signal . . . . . . . . . . . . . . . . . . . . . . . . .
.
1.2.1 Detector response . . . . . . . . . . . . . . . . . . . . .
.
1.3 Effect of the measuring device on signal changes . . . . . . . . . . .
1.4 Sample injection . . . . . . . . . . . . . . . . . . . . . . . .
.
1.5 Parameters characterizing detectors . . . . . . . . . . . . . . . . .
1.5.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . .
.
1.5.2 Detector linearity . . . . . . . . . . . . . . . . . . . . .
.
1.5.3 Linear dynamic range . . . . . . . . . . . . . . . . . . . .
.
1.5.4 Lowest detectable amount . . . . . . . . . . . . . . . . . .
1.5.5 Detector selectivity . . . . . . . . . . . . . . . . . . . . .
.
1.6 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . .
.

. The Thermal Conductivity Detector (TCD)

2

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2.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 TCD signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 TCD background current . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 TCD response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Effect of experimental parameters on the magnitude.and shape of the TCD signal . . .
2.3.1 Carrier gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Construction of the TCD . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2.1 Sensor heating voltage . . . . . . . . . . . . . . . . . . . . . . .
2.3.2.2 Sensor parameters . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2.3 Cell geometric constant . . . . . . . . . . . . . . . . . . . . . . .
2.3.2.4 Temperatures of the sensor and the cell walls . . . . . . . . . . . .
2.3.2.5 Time constant of the TCD . . . . . . . . . . . . . . . . . . . . . .
2.3.2.6 Measuring circuits . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Applications of the TCD . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. Ionization Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

3.1 Physical principles of the detection . . . . . . . . . . . . .
3.1.1 The collision . . . . . . . . . . . . . . . . . . . .
3.1.2 Effect of the electric field intensity . . . . . . . . . . .

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17
22
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24
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30
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34
36
37
39

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42

43
43
46
46
47
49
49
51

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52
52
55

56
57
59
59
60
62


3.2 Ionization energy sources . . . . . . . . . . . . . . .
3.3 Reactions in the ionization detector . . . . . . . . . . .
3.3.1 The slow-down mechanism . . . . . . . . . . . .
3.3.2 Recombination . . . . . . . . . . . . . . . . .
3.3.3 Background current of the ionization detector . . .
3.4 Literature . . . . . . . . . . . . . . . . . . . . . .

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65
68
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68
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69
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71

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4 The Electron Capture Detector ( E C D ) . . . . . . . . . . . . . . . . . . . . . .

72

4.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 ECD signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 ECD background current . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 ECD response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2.1 Linearity and linear dynamic range . . . . . . . . . . . . . . . . .
4.2.2.2 Sensitivity and selectivity of the ECD . . . . . . . . . . . . . . . . .
4.3 Experimental conditions affecting the ECD signal . . . . . . . . . . . . . . . . .

4.3.1 Carrier gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Construction of the ECD . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Applications of the ECD . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72
74
74
76
77
77
79
79
80
82
85

. The Flame Ionization Detector (FID) . . . . . . . . . . . . . . . . . . . . . . .

5

87

5.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 FID signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 FID background current . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 FID response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2.1 Linear dynamic range and linearity of the FID . . . . . . . . . . . . .
5.2.2.2 Sensitivity and selectivity of the FID . . . . . . . . . . . . . . . . .
5.3 Experimental conditions affecting the magnitude and character of the FID signal . . .

5.3.1 Gas flow-rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Geometry of the FID . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 FID applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87
91
92
92
94
95
95
95
97

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6

101
102

The Thermionic Detector Using an Alkali Metal Salt (TIDAj . . . . . . . . . . . . . 105

6.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
106
6.2 TlDA signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
109
6.2.1 TlDA background current . . . . . . . . . . . . . . . . . . . . . . . . .
110

6.2.2 TIDA response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
112
6.2.2.1 Linearity and linear dynamic range of the TlDA . . . . . . . . . . . . 115
6.2.2.2 Sensitivity and selectivity of the TIDA . . . . . . . . . . . . . . . . . 116
6.3 Effect of the experimental conditions on the magnitude and character of the TIDA signal . 117
117
6.3.1 Gas flow-rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Detector geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . .
118
6.4 TIDA applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
120
121
6.5 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 The Photoionization Detector (PID) . . . . . . . . . . . . . . . . . . . . . . .

123

7.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123


7
7.2 PID signal . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 PID background current . . . . . . . . . . . . . .
7.2.2 PID response . . . . . . . . . . . . . . . . . . .
7.3 Effect of the experimental conditions on the PID signal . .

7.3.1 Carrier gas . . . . . . . . . . . . . . . . . . . .
7.3.2 Geometric arrangement of the PID . . . . . . . . . .
7.3.2.1 Discharge compartment . . . . . . . . . . .
7.3.2.2 Detection compartment . . . . . . . . . . .
7.4 PID applications . . . . . . . . . . . . . . . . . . . .
7.5 Literature . . . . . . . . . . . . . . . . . . . . . . .

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131
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133

The Helium Detector (HeD) . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.1 Detection mechanism . . . . . . . . . . . . . . . . .
8.2 HeD signal . . . . . . . . . . . . . . . . . . . . . .
8.2.1 HeD background current . . . . . . . . . . . . .
8.2.2 HeD response . . . . . . . . . . . . . . . . . .

8.2.2.1 Linearity and linear dynamic range of the HeD
8.2.2.2 Sensitivity and selectivity of the HeD . . . . .
8.3 Effect of experimental conditions on the HeD signal . . . .
8.3.1 Carrier gas . . . . . . . . . . . . . . . . . . .
8.3.2 Construction of the helium and argon detectors . . .
8.4 HeD applications . . . . . . . . . . . . . . . . . . .
8.5 Literature . . . . . . . . . . . . . . . . . . . . . .

. The Flame Photometric Detector (FPD) .

9

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133

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9.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 FPD signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1 FPD background current . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.2 FPD response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.2.1 Linearity and linear dynamic range of the FPD . . . . . . . . . . . . .
9.2.2.2 Sensitivity and selectivity of the FPD . . . . . . . . . . . . . . . . .
9.3 Effect of experimental conditions on the magnitude of the FPD signal . . . . . . . .
9.3.1 Composition of the gases and their flow-rates . . . . . . . . . . . . . . . .
9.3.2 Detector temperature . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.3 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4 Use of the flame photometric detector . . . . . . . . . . . . . . . . . . . . . .
9.5 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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10 The Coulometric Detector ( C D ) . . . . . . . . . . . . . . . . . . . . . . . . .

10.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . .
10.2 CD signal . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.1 CD background current . . . . . . . . . . . . . . . . . .
10.2.2 CD response . . . . . . . . . . . . . . . . . . . . . . .
10.2.2.1 Linearity and linear dynamic range of the CD . . . .

10.2.2.2 Sensitivity and selectivity of the CD . . . . . . . .
10.3 Effect of experimental conditions on the magnitude of the CD signal .
10.3.1 Gas flow-rate . . . . . . . . . . . . . . . . . . . . . .

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145
149
151

152
153
155
155

155
156
157
159
162
165

165
169
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170
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170
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172

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145


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10.3.2Construction of the detector . . . . . . . . . . . . . . . . . . . . . . .
10.3.2.1 Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.3 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4 Applications of the CD . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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11 The Electrolytic Conductance Detector ( E l C D )

. . . . . . . . . . . . . . . . . .

172
175
175
175
179
181

11.1 Detection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2 ElCD signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.1 ElCD background current . . . . . . . . . . . . . . . . . . . . . . . .
11.2.2 ElCD response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3 Construction of the ElCD . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.4 Applications of the ElCD . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181
183

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189

Index

185

185
186
187

188


LIST OF SYMBOLS

A

A
A
A
a

- atom
- radioactive source activity
-

experimental constant

- radiative transition probability
- geometric constant

a
aa

- probability ratio for two processes

b
B
B

- optical path length
- atom

bc

bci
C

- analytical property of a
- constant
- background current
- ionization background current
- carrier gas

C

- instantaneous concentration

co

- initial concentration

p i n

CmaX

c'

C,
Cy

D
e

E
EP
E,
F
G
H
I
I
ic

ic,
i
ic,,,

minimum instantaneous concentration
- maximum instantaneous concentration
- instantaneous concentration in the effective volume of the detector
- heat capacity at constant pressure
- heat capacity at constant volume
- diffusion coefficient
- secondary electron, slow electron
- voltage
- excitation potential
- excitation energy of the eluted substance
- Faraday constant
- mass

- height equivalent to a theoretical plate
- current
- atom or molecule of impurity
- ionization current
- ionization current of alkali metal
~ - ionization
~
~
current
.
~ of ~de-excited atomic states
- ionization current due to electron capture
-


10
ic,,,

- ionization current of impurities in the carrier gas

icHe - ionization current of the carrier gas due to direct ionization
ic,,
- ionization current of carbonaceous substances due to the FID mechanism
- intensity of emitted light
I,
- intensity of fluorescence emitted light
1,
- initial intensity of emitted light
Z:
ZP

- ionization potential
J
- Joule's constant
k
- constant
k 1 , 2 , ,3, , . - rate constant of reaction 1, 2, 3, . . .
kd.i - rate constant of dissociation, ionization
- statistical constant dependent on the number of measurements, n
k,
K
- absolute temperature, Kelvin
K
- thermal conductivity
Ka,b - dissociation constant of acid, base
1
- electron free path
1
- length of heated filament
I
- detector linearity
L
- column length
M
- atom
M
- molecular weight
M"
- metastable atomic state
M*
- excited atomic state

n
- number of electrons
- number of theoretical plates
n
n
- number of measurements
N
- number of moles
N'
- number of moles in the effective volume of the detector
ORG - polyatomic molecule of organic compound
CI(0RG) - chlorine-containing ployatomic organic molecule
p
- pressure
pc,s - partial pressures of the carrier gas, the eluted substance
ppb - part per billion (American billion = lo9)
Q
- electric charge
Q
- conductivity cell constant
Q
- amount of heat
Q E - cross-section for electron capture ionization
Qc,s - cross-section of direct ionization of carrier gas, eluted substance
r
- column radius
r
- radius of the sensor
R
universal gas constant

R
- amplifier resistance

-


11
- heated filament resistance
- detector response to property a

- estimated standard deviation
- eluted substance
-

signal of analytical probcrty a, of eluted substance S

- time
-

the Student distribution

- time of the beginning and the end of elution
-

time corresponding to the inflection points of the elution curve

- elution time

- elution curve width
- time of passage of gas through the effective volume of the detector

- temperature

temperature of the detector walls
temperature of the heated filament
linear flow-rate of gas
volume flow-rate of gas
flow-rate expressed in moles
- mean molecular velocity
- velocity of electrons
v1 , 2 . 3 . ._.- rate of reaction 1 , 2, 3, . . .
I/
- volume
- effective volume of detector
I/,,,
X
- molar fraction
Z
- constant
Z i - ionic charge
Z
- the third particle in a three-body collision
z,, za - number of non-elastic collisions
-

a
c!
c1

6

r
A

q,,
1"

e
T

@

recombination coefficient
temperature coefficient
degree of dissociation
thermistor material constance
selectivity
- change in parameter
- photoionization efficiency
- mean free path, mobility
- density
- time constant
- fluorescence yield
-


PREFACE

Much attention has been paid to the theoretical aspects of gas chromatographic
separation processes. Considerably less theoretical work has been devoted to elucidating the function of the detection part of the instrument, the “black box” that
yields the actual results for interpretation. This leads to a situation in which, for

example, experimenters are prepared to calculate Kovfits retention index values to
hundredths of a unit without considering the time constant of the measuring device
and recorder employed.
An ever increasing demand for high-precision measurements has evolved as
a result of rapidly developing research techniques. Thermostats maintaining the
temperature constant to within a few hundredths of a degree have been constructed
and gas flow-rates are controlled with a precision of kO.1 cm3/min. Simultaneously,
detectors are regarded as ideal measuring devices; this assumption is obviously false
and has been the cause of many erroneous conclusions.
The principle aim of this book is to draw attention to a number of experimental
conditions that exert a considerable effect on the magnitude and character of the
detector response. At present, there are only two bboks on gas chromatographic
detectors. The treatment in German by Jentzsch and Otte appeared in 1970; that by
D.J. David in English was published just as the manuscript of this book was submitted to the publishers in the beginning of 1974. These two books survey experimental work carried out up to 1969 and 1970 respectively.
This book brings the subject up to date (papers published up to May 1974 are
covered) but, in contrast to the above two books, is not intended to give an exhaustive
survey of the literature on gas chromatographic detectors. Attention is centred rather
on the clarification of detection mechanisms and explanation of the dependences of
the detector response on experimental conditions.
General conclusions which are intended to serve as criteria in designing new
detectors are drawn whenever possible.
In the Introduction, response formation is considered in general terms and relationships that characterize all detectors are derived; although some of these relationships differ from those commonly used, it is felt that they represent a closer
approximation to the actual situation that obtains because of the consistent general
approach followed in their derivation. The formation of such a general theory is
based on the large amount of published data and the author wishes to acknowledge
the important role played by these data. The literature cited is by no means exhaustive;


13
only those references which have a direct bearing have been included. There is no

doubt that much of what has been written here will have to be considerably modified as
a result of further research; it is the author’s hope that this book will prove a stimulus for such work.
The author is grateful to a1 those who assisted him during the preparation of the
book, to all the authors and publishers who gave permission to reproduce original
figures and tables, to Dr. J. Novik for critical discussions and to Dr. M. Stulikovi
and Dr. K. Stulik for translating the manuscript into English and for comments on
the text.


This Page Intentionally Left Blank


1.

Introduction

Progress in gas chromatography very frequently depends on the development of
measuring techniques that are capable of monitoring substances after their separation.
While the separation process has often been treated in detail, less attention has been
devoted to the accuracy of results and the stability of various measuring devices,
The latter are termed ‘‘detectors” and form an independent part of the gas chromatograph. Their use is based on the various physical and chemical properties of the
eluted substances or products formed by their reaction inside the detector.
The method first employed for the monitoring of substances separated gas chromatographically was titration [35]. Later, gas volumes were measured [36] or the
eluted substances were weighed after deposition on active charcoal placed on the pan
of a balance [5]. None of these methods required calibration or electronic circuitry
and thus contributed to the development of gas chromatography in the 1950s. However, simple detection methods are still employed, such as visual observations [74].
The progress of gas chromatography has led to the application of numerous physical detection principles. Changes in the electrical properties of materials are utilized
in the thermal conductivity detector, in which changes in the resistance of a heated
wire, thermistor or transistor are measured. The piezoelectric detector [37, 39, 431
with a quartz crystal, the pyroelectric detector [68] containing lithium tantalate and

semiconductor detectors employing the p-n junction of a silicon diode [18,28, 51, 711
or tunnel junction supra conductivity [131 have also been used in gas chromatography
[17]. A detector utilizing variations in the electric conductivity of a TiO, layer [27]
is based on an analogous principle. In the literature can also be found descriptions of
catalytic detectors [2] and detectors that measure differences in the dielectric constants
of substances [ 5 5 , SO]; the sorptiothermal detector [16] and thermal flux meters [64]
respond to heat changes in the system being studied, in a similar manner to the thermal conductivity detector.
Detectors based on the measurement of variations in the gas density utilize the
inverse proportionality between the flow-rates of gases and their molecular weights
[25, 531. These detectors are among the oldest gas chromatographic detectors;
they have been modified in various ways, e.g., the measurement of changes in the gas
density has been performed on a diaphragm [59] or combined with other detectors [22].
Changes in electronic energy states and in rotafional and vibrational energies of
niolecules have also been utilized for the construction of detectors [12]. Atomic
emission spectra [76], atomic absorption [3, 321, chemiluminescence [75,77] and


16
fluorescence [8] of molecules or quenching of excited states in very sensitive measurements [lo] have been employed.
The sensitivity of measurements increased considerably when the measurement of
ionization currents was introduced. In the ionization current detection mechanism,
various processes are involved, are mutually combined and cannot be separated, as
follows from the additivity of ionization cross-sections [41]. In addition to the ionization detectors discussed below (ECD, FID, TIDA, PID, HeD), an electron mobility
detector [52]: a cross-section detector [14, 661 and a surface ionization detector
[ll, 231 have been described. The function of these detectors is based on collisions
of particles of the eluted substances with high-energy particles. The latter are obtained
from radioisotopes or from an electric discharge. However, such a discharge causes
not only ionization but also excitation of molecules and atoms, resulting in emission
of light. Thus detectors employing an electric discharge as a source of energy are
often called emission detectors [63]. In addition to measuring the intensity of the

emitted light, it is possible to measure the voltage at which the discharge begins [61],
the discharge current [30, 501 or the ionization current [47-491. The ionization is
affected by the space charge [56] and by the intensity of the electric field in which the
ions move [69]. All of the above quantities have been employed in the design of GC
detectors.
For the elucidation of the ionization mechanism, plasma chromatography [40] has
great importance for monitoring the fragments formed during ionization processes
under conditions identical with those in the detector. Mass spectrometry combined
with gas chromatography has made possible the identification of components in
complex mixtures.
Emitted radiation is also measured in gas chromatography. These detectors are
termed radiogas detectors [79] and they measure the number of radioactive particles
or pulses [38] with proportional counters [17, 731 or scintillators [34]. Detectors
utilizing neutron activation analysis [9] can also be included in this group.
In addition to the above-mentioned detectors, gas chromatography has employed
the monitoring of differences in the magnetic properties of substances (paramagnetism
or diamagnetism) in the magnetic detector [21], changes in the velocity of sound in
the ultrasonic detector [24, 60, 821 and changes in the temperature of a flame [70],
in surface potential [26] and in a number of other physical properties.
The chemical properties of the eluted substances are utilized less frequently [67, 72,
831. Coulometry and conductimetry are used, as are polarography [65] and potentiometry with ion-selective electrodes [44 - 461. In analyses of the atmosphere,
microbiological detectors [15] have been used. In Martin’s opinion [54], the reactions
that will find the greatest use in the future are those in which the eluted substances
are converted into CO, or H,O. The calibration will then be simple and, moreover,
chemical amplification will be possible.
It follows from this brief introduction that a very wide variety of physical principles
are utilized for measuring purposes in gas chromatography. The following chapters


17

are devoted to discussion of selected detectors which are the most frequently used
and/or bear promise for future development. The main attention is centred on
clarification of the detection mechanism and of the dependence of the signal on the
experimental conditions. Familiarity with these principles is essential for' correct
interpretation of the results obtained and for optimization of the design of the
measuring device.

1.1

CONCENTRATION DISTRIBUTION OF THE ELUTED
SUBSTANCE AT THE COLUMN OUTLET

A substance S passes through the column and, as a result of the establishment of
multiple equilibria, its concentration in the gaseous phase varies. If N , is the number
of moles of substance S, then its instantaneous concentration at the column outlet can
be expressed by the equation

where :1' is the retention volume, V o is the volume of gas passed during the elution of
concentration cs and n is the number of theoretical plates.
The volume of the eluted gas can be replaced by an expression containing the gas
volume flow-rate, u , the elution time, t , and the retention time, r:,

The number of theoretical plates, n, can be expressed as the ratio of the column
length, L, to the height equivalent to a theoretical plate, H:

n

= L/H

(1.4)

On substitution of expressions (1.2) - (1.4) into equation (l.l), the relationship for
the instantaneous concentration of the eluted substance assumes the form
cs

=

3
JL
exp
u . t , 2nH

[&
-

(1 -

3'1

For the maximum concentration of the eluted substance, t = t , and hence

L

(1.6)


18

The integral time function of the concentration distribution of the eluted substance
fulfils the condition of Gaussian random distribution

/')s.di

=

Y

and has a maximum, c;Ipx, at time t = t , and two inflection points at times tinf
located symmetrically on both sides of t,:
tinf = t

L
+
R - H

The time interval between the inflection points corresponds to the width of the
elution curve, 2 x A t , and is given by

At

=

J(L/H)

It follows from the Gaussian distribution law that the value of function Y equals
unity within the integrated time interval, (- co, 00). When the integration
limits are given by multiples of A t , the value of integral Y is always smaller than the

+

-f

FIG. 1.1. An ideal elution curve: t~
f 4 A? - elution time limits.

-

elution time, A?

-

the elution curve width,

value corresponding to the oveiall amount of eluted substance (Fig. 1.1). When the
multiple, 4(+At), is used, the error is as little as + 3 x
which is satisfactory
when considering the experimental conditions.
The actual separation of the eluted substance in the column is affected by the
siinultaneous processes of dissolution and adsorption, by shifts in the equilibria in
the presence of inert substances, by the amount of eluate [33] and especially by the
amount of eluted substance, N , [31]. The above relationships describing the theoretical
separation must then be modified by introducing correcting terms [29, 841 in order
to satisfy better the experimental conditions. With a change in the concentration of
the eluted substance, a change in the concentration of the carrier gas occurs. These


19
changes can be expressed in terms of changes in the partial pressures, as the overall
pressure is constant in the open column separating system.
If no other substance is present in the colun~n,then it contains only the carrier
gas, C, the instantaneous concentration of which, c,, is constant along the whole
column; its partial volume, V,, equals the overall column volume and its partial

pressure, p , at the column outlet. On introduction of a substance S into the column,
the partial pressure of the carrier gas changes: the overall pressure is unchanged, so
that

+ Ps

P

=

Pc

p

=

(N,

As

+ N s + ...) RT
V

-

where N,, N,, etc., are the numbers of moles of substances C, S, etc., respectively.
For p s , the relationship

is obtained and the partial volume of the eluted substance is given by
V,

=

N,RT
~

P
TABLE 1 . 1
THE AVERAGE VALUES OF THE CARRIER GAS A N D THE ELUTED
SUBSTANCE PARTIAL PRESSURES IN VARIOUS COLUMNS
Column

V

diameter
[mml

[mljmin]

0.25

0.5
1.o

0.5

2.7
4.6
8.0

1.5
5
10
20
50
100
75
150

N c / l 5 sec
[mole/secl

5

Y 10-6

1 1 i: 1 0 - 5
2 8 Y 10-5
5 6 :< lo-’
1 I >:
2.2 x
55
10-4
1.1 x 1 0 - ~
83 x
1.6 X

pc
[torr]

632
395
698
646
691
730
745
698
752
71 3

Ns/15 sec
[mole/sec]

10-6
I O - ~
10-6
lo-’
10-~
10-5

10-~
10-4
10-5
10-4

PS
[torr]

128

265
62
114
69
30
15
62
8
47


20
On introduction of substance S into the column, the volume of the gaseous phase
changes. The overall volume of the gaseous mixture equals the sum of the partial
volumes of the individual components. As the column volume cannot be increased in
the gas chromatographic system, the volume changes occur as changes in the volume
flow-rate of the gaseous mixture. With a constant column cross-section, nr2, the
changes in the volume flow-rate appear as changes in the linear flow-rate, u. The
dependence of the height equivalent to a theoretical plate on the linear flow-rate is
generally hyperbolic; it is evident that the maximum concentration of the eluted
substance is also dependent on the flow-rate (equation (1.6)).
2

4

5

J

I

wyn w -

FIG. 1.2. The flame ionization detector response to CS, as a function of the amount of
sample; traces 1 , 2 , 3 , 4 and 5 corresponds to injection of 1,2, 3, 4 and 5 PI, respectively.

In order to determine the magnitude of these changes, the variations in the partial
pressures of the carrier gas and the eluted substance were calculated for various
amounts of sample, replacing the concentration distribution (equation 1.5) by the
average concentration of the substance eluted for 15 sec; the values are given in
Table 1.1. Under the actual conditions in a separating column, the changes in the
partial pressures are even more pronounced because of the Gaussian distribution,
being of the order of tens of a per cent. These facts can be illustrated by the response
of the flame ionization detector (FID) to 1-5 P I of carbon disulphide (Fig. 1.2).


21
As CS, is only slightly ionized in the FID (see Chapter 5), the ionization current
decreases with an increase in the partial pressure. The minimum ionization current
corresponds to the maximum concentration of CS2; the greater the amount of
sample injected, the more pronounced is the minimum in the ionization current.

-t
FIG. 1.3. The dependence of the instantaneous concentration of the eluted substance
on the overall amount, N,, the linear flow-rate, ri, and the elution time, t.

Therefore, the instantaneous concentration of the eluted substance is a function of
the overall amount of substance, N , , the linear flow-rate of the gaseous mixture and
the elution time, as depicted schematically in Fig. 1.3. From the general equations,
(1.6) and (1.8), it follows that the maximum concentration of the eluted substance at

the column outlet (the maximum on the elution curve):
- increases with the square root of the number of theoretical plates at a constant

flow-rate and elution time;
- decreases with increasing flow-rate at constant elution time and number

of theo-

retical plates;
- decreases with increasing elution time at a constant number of theoretical plates

and flow-rate.
The elution curve width:
- increases with increasing retention time at a constant number of theoretical

plates;

- decreases with an increasing number of theoretical plates at a constant retention
time.
The separated eluted substance is monitored by a detector at the column outlet.


22

The basic requirement placed on the detector is that the recording should give a true
picture of the concentration distribution in the column. Therefore, the detector
should not affect
the number of theoretical plates, i.e. should not participate in' the separation
process;
the retention time of the substance, i.e., should be placed at the last theoretical

plate of the column:
the gas flow-rate, i.e., its internal diameter and hydrodynamic resistance should
be identical with those of the column.
these theoretical requirements cannot be met completely in practice, the measured
values deviate from the actual separation results.

1.2

DETECTOR SIGNAL

The detector measures variations in the magnitude of an analytical property, a', of
the entering substance. The detector records a measurable change after a molecule
(radical, atom, ion) of the eluted substance collides with the detector sensor. Therefore, it is evident that reactions which occur outside the range of the sensor do not
contribute to the measured change. The space in which the measurement takes place
is denoted as the detector effective space. The measured change dependes only on
those molecules present in this space which possess the required analytical property.
The measured change, denoted as the signal, is proportional to the magnitude
of the given analytical property (thermal conductivity, ionization cross-section, etc.)
and to the number of molecules capable of reacting with the sensor. The signal is thus
proportional to the instantaneous concentration of the eluted substance and can be
described by the equation
St = k x at x N;'

(1.10)

where S: is the signal due to eluted substance S in a device measuring analytical
property a, k and I are constant characteristic of the experimental arrangement and
N ; is the number of moles of the eluted substance in the effective volume of the
detector. Signal Sz follows the concentration distribution of the eluted substance at
the column outlet.

At a given time, other substances that possess the same analytical property as the
eluted substance may be present in the effective volume of the detector. The overall
measured signal is then given by the sum of the signals for the eluted substance, the
carrier gas and impurities:

so = s.,

=

s; + s; + sp

(1.11)


23
Before the eluted substance enters the detector, only the molecules of the carrier gas
and of impurities present in the carrier gas are present in the effective volume of the
detector. Stationary conditions are established in the detector and the measured
signal is given by the equation

bc

=

S:

+ Sp

(1.12)

The signal measured in the absence of an eluted substance (equation (1.12)) is called
the detector background current.
As already mentioned, the gas chromatographic system is an open one, i.e., the
partial pressures in the effective volume of the detector change during the elution of
the studies substance. It is evident that the measured signal, S", is positive if
A S ; > d(S;

+ Sp)

(1.13a)

and negative when the opposite inequality holds, i.e.,

A s ; < d(s:

+ sp)

(1.13b)

From these two inequalities, it follows that the greater the absolute value of the
difference / A S : - d(Sg + Sp)l, the more the measured signal corresponds to the
change caused by the eluted substance. Therefore, for successful measurement, it is
necessary that the magnitude of the analytical property of the eluted substance
should be larger than that of the carrier gas and of any impurity which might be
present:
a:

< a: > a:

If these values are comparable, the measured signal is very small [42]. An ideal

measuring arrangement would involve a carrier gas that does not possess the measured
property; nitrogen is not ionized in the FID system.
During elution of the studied substance, the partial pressures of the carrier gas and
of the impurities present decrease. Therefore, the detector background current
decreases during the elution, attains a minimum at the maximum concentration of
the eluted substance, again increases on the further elution and finally reaches its
original value.
1.2.1

Detector response

The integral of the signal, s",over the interval ( t l , t z > , where f I and t , correspond
to the beginning and the end of the elution, respectively, is called the detector response. R":
(1.14)


24

The detector response thus consists of the sum of the background current and the
signal of the eluted substance, as shown in Fig. 1.4. It is thus obvious that the detector
response is proportional to the overall number of moles of the substance introduced
0

1

P

2

sa

.A
I

A

'.

R

0

'.

- \\ '\",/

#

/.

)r
-f

bc

I
?

at the column inlet and that the agreement between the response time-dependence
and the distribution in time of the concentration of the substance at the column

outlet improves with increasing values of inequalities (1.13a) and (1.1 3)b.

1.3

EFFECT OF THE MEASURING DEVICE ON SIGNAL CHANGES

The effective volume of the detector in which the measurement takes place can be
expressed in terms of the gas flow-rate and the time, fder, required for the passage of
the gaseous mixture through a volume I/,,,:

v,,, = u . tdet = ii . TI . r2 . tder

(1.15)

The time tdercan be calculated from the values following from the time distribution
of the concentration of the eluted substance; the substance concentration distribution
is characterized by values t , and A t (see Fig. 1.1). If the limits, + 4 x A t , are applied
to function Y, the following relationship can be written for tder:
(tL

- tl)

td,,/dt =

= +4dr = z . tdet

(1.16)

8/z

(1.17)

Equation (1.17) expresses the relationship between the separation conditions and the
effective volume of the detector; it is evident that the fraction equals zero for an ideal
detector. If t,,,/At 4 0, then the concentration distribution in the detector changes in
comparison with the conditions at the column outlet, described by equation (1.5).