High speed, high resolution capillary gas chromatography :
columns with a reduced inner diameter
Citation for published version (APA):
Schutjes, C. P. M. (1983). High speed, high resolution capillary gas chromatography : columns with a reduced inner diameter. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR67359
DOI:
10.6100/IR67359
Document status and date: Published: 01/01/1983
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' . ' ' . :
HIGH SPEED, HIGH RESOLUTION CAPI[lARY
·
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1 ·.
GAS CHROMATOGRAPHY
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.
,
. ' .
, . . ; I , . ' j
COLUMNS
•
WITH A REDUCED INNER DIAMETER
• ·
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•,··
. ·:.
•·
i I
DISSERTATIE DRUKKERIJ
10lbro
HELMOND
HIGH SPEED, HIGH RESOLUTION CAPILlARY
GAS CHROMATOGRAPHY
COLUMNS WITH A REDUCED INNER DIAMETER
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. DR. S. T. M. ACKERMANS, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAR TE VERDEDIGEN OP
DINSDAG 15 NOVEMBER 1983 TE 16.00 UUR DOOR
CORNELIS PIETER MAARTEN SCHUT JES
Dit proefschrift is goedgekeurd door de promotoren
Prof.Dr.Ir. C.A.M.G. Cramers en
a:a:n Netty
CHAPTER 1
CHAPTER 2
Contents
CONTENTS 5
GENERAL INTRODUCTION 9
FACTORS DETERMINING THE SPEED OF ANALYSIS
IN GAS CHROMATOGRAPHY 15
1.1 Introduction
1.2 The resolution concept
1.3 The minimum analysis time for a two 15 16
component mixture 19
1.4 A general approach for obtaining the
minimum analysis time 23
1.5 Optimisation of the analysis time for
multi-component mixtures 24
1.6 Comparison of the separation speed be-tween packed and capillary columns 27 1.7 The experimental conditions
for investigating the relationship between tR and d0
1.8 References
A STUDY OF THE RELATIONSHIP BETWEEN ANALYSIS TIME, COLUMN INNER DIAMETER AND THE PRESSURE GRADIENT
2,1 Introduction
2.2 The Golay-Giddings equation 2.3 The column pressure gradient 2.4 Factors affecting the optimum
carrier.gas velocity
2.5 The relationship between tR, d
0 and P
2.6 Instrumental contributions 2.7 Experimental
2.8 Results and discussion 2.9 References 28 30 33 33 34 38 40 44 45 47 49 62 5
CHAPTER 3 THE SPEED OF SEPARATION IN SOME IMPORTANT PRACTICAL CHROMATOGRAPHIC SITUATIONS 65
65 3.1 Introduction
3.2 Temperature progranuned conditions
(constant pressure mode} 66
3.3 Carrier gas velocities other than uopt 73 3.4 Columns with very high plate numbers 82
3.5 References 88
CHAPTER 4 THE DEACTIVATION AND COATING OF 50 UM I.D. CAPILLARY COLUMNS
4.1 Recent developments in column preparation
89 89
4.2 Equipment and methods 91
4.3 Coating without prior deactivation 95 4.4 Methods for the deactivation of
boro-silicate and fused-silica columns 97
4.5 References 105
CHAPTER 5 AN EVALUATION OF SAMPLING TECHNIQUES 109 5.1 Sample capacity and working range 109
~.2 Split mode injection 111
5.3 Splitless and on column injection 119
5.4 Fluidic logic injection 127
5.5 References, 133
CHAPTER 6 DETECTION AND DATA HANDLING WITH 50 UM
GC COLUMNS 135
6.1 The column working range with several different detectors
6.2 Flame ionization detection 6.3 Electron Capture detection 6.4 Mass Spectrometry 6.5 Data Handling 6.6 References 135 138 139 143 148 157
APPENDIX 1 LIST OF SYMBOLS
APPENDIX 2 THE DETERMINATION OF SOLUTE DIFFUSION COEFFICIENTS IN NORMAL AND CROSS-LINKED NON POLAR STATIONARY PHASES
APPENDIX 3 THE MIGRATION OF A COMPOUND IN THE CHROMATOGRAPHIC COLUMN AS A FUNCTION OF THE PRESSURE GRADIENT
APPENDIX 4 HIGH RESOLUTION CHROMATOGRAM (N=106) OF A NATURAL GAS CONDENSATE
159 163 175 back cover SUMMARY SAMENVATTING CURRICULUM VITAE ACKNOWLEDGEMENTS
AUTHOR'S PUBLICATIONS ON GAS CHROMATOGRAPHY 177 181 185 187 189 7
GENERAL INTRODUCTION
Gas chromatography (GC), first described in 1941 by Martin and Synge1
, has become a major tool for the separa-tion of samples containing volatile and volatilizable sub-stances. The technique is currently applied on a large scale in widely differing area's, e.g. for process deve-lopment and process control in chemical plants, for moni-toring environmental pollution, for studying complex meta-bolic patterns in clinical chemistry and for quality con-trol in the food and perfume industries.
Most of the basic theory of gas chromatography has been published between 1950 and 1970. Comparatively few new contributions to theory have been made since. Instead, the technological.enhancement of gas chromatography has become a major goal. Much research has been conducted in this fi.eld during the past decade. This includes our group
(Laboratory of Instrumental Analysis, Eindhoven University of Technology, Eindhoven, The Netherlands), participating
i.n the development of high resolution capillary GC.
Unquestionably, a substantial progress has been made in recent years2
' 3'4• The performance of both columns and of chromatographic equipment has been considerably improved. These developments have been particularly favourable to-wards capillary gas chromatography. Consequently, packed columns are steadily being replaced by capillary columns,
which have the additional advantage of a much higher per-meability5, and which now have a major share of the market.
In the domain of capillary column technology, outstan-ding deactivation methods have become available which provide an excellent inertness of the column inner wall6' 7• These enable the analysis of a vast range of substances, including very polar ones. Organic peroxides and azo com-pounds have successfully been employed for the immobiliza-tion of non polar and weakly polar staimmobiliza-tionary phases8
• The non extractable films obtained are remarkably stable and even allow the direct injection of microliter amounts of liquid samples.
The introduction of fused silica columns by Dandeneau and Zerenner9 in 1979 has greatly enhanced the acceptance of capillary columns in daily routine. The flexible, yet strong, fused silica columns are very easily mounted in the gas chromatograph, contrary to glass columns, which are considered to be too fragile and too difficult to handle by-many chromatographers working in a routine en-vironment.
In capillary GC, the introduction of the sample has always been a weak point. With a split-mode injector, discrimina-tion of the sample components is hard to avoid10
' 11 , especially when these compounds have a wide boiling point range. Newly developed injection techniques, in particular liquid on column injection10' 12 and programmed temperature injection13
' 14, offer an improved quantitative precision, and sample discrimination is almost eliminated, Concentra-tions of substances down to the ppm level can be detected and quantified without preconcentration. However, when employing the advanced injection techniques, peak broade-ning and peak deformation are sometimes hard to avoid15
•
Recent developments in electronics have had a great im-pact on instrument technology. In a modern gas
chromate-graph, the oven temperature is very well controlled. Tem-perature gradients inside the oven are small and short term temperature fluctuations are kept below O.l°C. Elec-trometer amplifiers with time constants below 50 msec, displaying a very low noise level, are now part of any modern gas chromatograph.
Microprocessor based data acquisition and processing equipment have become widely used, eliminating the tedious task of evaluating the chromatograms by hand. These low cost devices enable fast and reasonably accurate integra-tion and reporting, and also facilitate the automaintegra-tion of the analytical process.
To have full benefit of the separation power of the column, the standard deviation of the chromatographic peaks must remain well above the time constants arising from the chromatographic equipment. Hence, these time constants determine the maximum allowable analysis speed. Until 5 years ago, the time constants of the electrometer ampli-fiers usually had a value between 0,2-0.6 sec, and were the main limiting factor with respect to speed. Then, gas chromatographs with an electrometer time constant below 50 msec were introduced on the market. These enabled, at least in principle, a five to tenfold increase in the ana-lysis speed. In our philosophy, such a large increase in speed would be particularly beneficial to the separation of samples containing a large number of substances. Nor-mally, 30 to 90 minutes are required for analysing such a complex sample by conventional capillary gas chromatogra-phy.
In view of the high complexity of the sample, it is re-quired that the separation efficiency is preserved when increasing the analysis speed. Due to this restriction, reduction of the inner diameter of the capillary column is the only correct approach for the improvement of the analysis speed. The objective of this thesis is to investi-gate the practical usefulness of this approach.
In chapter 1 of this thesis, the factors determining the analysis time in gas chromatography are discussed. Crite-ria are derived which indicate how to obtain the minimum analysis time for a given separation.
In chapter 2, the Golay-Giddings "plate height" equation is discussed. The stationary phase contribution to the column plate height is investigated for normal non polar phases and for chemically immobilized phases. Experimen-tal results are given in appendix 2. The relationship be-tween the retention time, tR, and the column inner diame-ter, d0 , is studied, for columns .which are operated iso-thermally at the optimum carrier gas velocity. The gain in analysis time that can be obtained is shown to depend upon the column pressure gradient. When the ratio of the column inlet to outlet pressure is low, the retention time will decrease proportional to d
02 • In situations of high
pres-sure drop, tR decreases only proportional to d
0• Equations
for temperature-programmed conditions are derived in chap-ter 3, and lead to the same conclusions. When the carrier gas velocity is set above its optimum value, the decrease of tR with d0 is shown to be somewhat less pronounced, however, without being essentially changed.
In the last section of chapter 3, columns generating dver 5.105 theoretical plates are discussed. Chromatograms ob-tained on such a column are illustrated.
Methods for the preparation of well deactivated, non polar glass and fused silica columns of 50 ~m inner diameter are given in chapter 4.
In chapter S, the introduction of the sample into these very narrow bore columns is investigated. It is demonstra-ted that split, splitless and on-column injection techni-ques in principle can be employed. The compatibility of narrow bore columns with a split-mode injection system is discussed in more detail.
The fast "fluidic logic" injection system developed by Gaspar and co-workers16~18 is evaluated. When correctly
obta~ned, at pressures between 4 and 25 bar.
In chapter 6, the successful coupling of 50 pm diameter columns to an electron capture detector and to a mass spectrometer are described. The relationship between the signal-to-noise ratio and the quantitative precision of a microprocessor-based computing integrator are studied. The applicability of the integrator to narrow bore columns
is discussed.
REFERENCES
1. A.J.P. Martin and R.L.M. Synge, BioahemiaaL Journal, 35 (1941) 1358.
2. S.P. Cram and T.H. Risby, Anal. Chem., 50 (1978) 213R. 3. S.P. Cram, T.H. Risby, L.R. Field and Wei-Lu Yu, Anal.
Chem. , 52 (1980) 324R.
4. T.H. Risby, L.R. Field, F.J. Yang and S.P. Cram, Anal.
Chem., 54 (1982) 410R.
5. C.A. Cramers, J.A. Rtj~s and C.P.M. Schutjes,
Chroma-tographia,
!!
(1981) 439.6. K. Grob, G. Grob, W. Blum and W. Walther, J.
Chroma-togr., 244 (1982) 197.
7. G. Schomburg, H. Husmann and H. Borwitzky,
Chromato-graphia, (1979) 651.
8. B.W. Wright, P.A. Peaden, M.L. Lee and T.J. Stark, J.
Chromatogr., 248 (1982) 17.
9. R. Dandeneau and E.H. Zerenner, J. High Res.
Chroma-togr. ChromaChroma-togr. Commun., ~ (1979) 351.
10. G. Schomburg, H. Behlau, R. Dielmann, F. Weeke and H. Husmann, J. Chromatogr., 142 (1977) 87.
11. K. Grob Jr. and H.P. Neukom, J. High Res. Chromatogr.
Chromatogr. Commun., ~ (1979) 563.
12. K. Grob and K. Grob Jr., J. Chromatogr., 151 (1978) 311.
13. F. Poy, S. Visani and F, Terrosi, J. Chromatogr., (1981) 81.
14. G. Schomburg, H. Husmann, H. Behlau and F. Schulz, in
J. Rijks (Editor), 5th Symp. Capillary Chromatography, Riva del Garda, 1983, Elsevier, Amsterdam, 1983, p. 280 and p. 290.
15. K. Grob Jr., J. Chromatogr., 251 (1982) 235.
16. G. Gaspar, P. Arpino and G. Guiochon, J. Chromatogr. Sai., 15 (1977) 256.
17. G. Gaspar, J. Olivo and G. Guiochon, Chromatographia,
l!.
(1978) 321.18. G. Gaspar, R. Annino, C. Vidal-Madjar and G. Guiochon,
CHAPTER 1
FACTORS DETERMINING THE
SPEED OF ANALYSIS IN GAS
CHROMATOGRAPHY
1.1 INTRODUCTION
Theo~y reveals only one sensible approach to improve the speed of analysis without simultaneously impairing the resolution. For packed columns~ this can be rea-lised by reduction of the partiale diameter. For capillary aoZumns~
the inner diameter should be de-creased.
The prime objective of gas chromatography is the com-plete separation of two or more compounds which are ini~ tially present as a mixture. To achieve this goal, the mixture is injected into a chroma~ographic column. Each sample component is distributed between the carrier gas and the stationary phase in a characteristic way, and, by consequence, is transported through the column at its own characteristic speed. Compounds which travel at a diffe-rent velocity will therefore elute from the column at dif-ferent times and thus in principle can be separated. The retention time, tR, of a compound on the chromatogra-phic column is given by:
(1.1) where k is the capacity ratio, which is partly related to
the thermodynamic parameters governing the distribution process, and t
0 is the time required for the elution of an unretained compound. Hence:
(1.2)
-where L is the column length and u is the average linear carrier gas velocity. The particle diameter dp (packed column) and the column inner diameter d
0 (capillary column) do not appear in the equations. Obviously, they can be ne-glected when short retention times are strived for per s~.
However, in practical situations, the chromatographer is primarily interested in the fastest possible separation of the sample, and not in the shortest possible retention time of one compound. The optimisation of the analysis speed is then subject to a serious constraint. Examples are given in figure 1.1, where chromatograms of equal ana-lysis time are compared. The'differences observed are due to dispersive processes which cause broadening of the com-pound zones during their transport through the chromato-graphic column.
It is known from theory1 • 2 that peak dispersion is hea-vily dependent on dp (or d~), on k, and on the diffusion coefficients of the compound in the carrier gas and in the stationary phase.
In the following sections, criteria for the optimisation of the analysis speed will be derived.
1.2 THE RESOLUTION CONCEPT
A property called the resolution, R5, is customarily employed to quantitatively describe the separation be-tween two adjacent chromatographic peaks. By definition,
10
5
8 9
6 7
4 I I I I I 1020
18/9
0
1020
1112
I13
14 I30
30
ISEC
SEC
Fig. 1.1. Two chromatograms obtained within the same
analysis time~ but with two different capillary columns of 3 m x 30 vm I.D. (upper chromatogram) and of 30 m re
0.3 mm (lower chromatog~am). Carrier gas: helium. Peaks: (1) methane, (2) n-pentane, (3) 2-me-butene-2,
(4) 4-me-pentene-1, (5) 2;3 di-me-butane, (6)
2-me-pentene-1, (7) n-hexane, (8) me-cyalopentane~ {9) 2,4-di-me-pentane, (10) benzene, (11) ayalohexane, (12) 2-me-hexane, (13) 3-me-2-me-hexane, (14) n-heptane.
(1. 3)
-where cr is the average standard deviation of the two peaks. Two components are usually considered to be completely separated when their retention times differ by more than 4 cr. So, when a complete separation is demanded, then the
constraint Rs '> 1 is implicitly made.
For two closely adjacent peaks, cr is nearly equal to the true standard deviation, cr, of both eluting peaks. Further-more cr is related to the theoretical plate height, H, and to the number of theoretical plates, N, by:
N (1.4)
N = L/H (1. 5)
Substitution of equations 1.1 and 1.4 into equation 1.3 leads to the well known expression:
1
4
a - 1
(1. 6)
where a
=
k2/k1 is the relative retention of the two
solu-tes. When the value of k2 is appropriately chosen, then
k
2/(1 + k2) approaches the maximum value of 1. Conditions
in which k
2 assumes a value close to zero must clearly be
avoided. Ignorance of this fact has caused a great deal of confusion regarding the separating power of chromatogra-phic columns, especially in early publications on gas
chromatography3
•
The relative retention a is primarily dependent on the vapour pressures of the two compounds. When these com-pounds belong to different chemical classes, a strong
de-pendence of a on the phase polarity is usually also
~'5 and by McReynolds6 can be helpful guide for selecting the most suitable stationary phase.
A second factor influencing ~ is the column temperature. The well known temperature dependence of Kovats indices for instance reflects this effect7' 8•
It can be calculated from equation 1.6 that a complete se-paration (R
=
1 at k=
2) requires a value of a > 1.10s '
for a conventional packed column (N ~ 4000 theoretical plates} and of ~ > 1.02 for a conventional capillary
co-lumn (N ~ 100,000 theoretical plates). Thus, the capacity ratio's of two successive peaks must differ by at least1~ with the packed column, and by 2% with the capillary
co-lumn. This large discrepancy in the minimum required value of ~ explains why the selection of the stationary phase is generally c?nsidered a minor problem in capillary GC, but
is often of major importance in packed gas chromatography. Once the stationary phase and Rs have been chosen, then the required number of theoretical plates is fixed and can be calculated from equation 1.6.
1.3 THE MINIMUM ANALYSIS TIME FOR A TWO COMPONENT MIXTURE Equation 1.1 can easily be adapted to include the ad-ditional factors which arise from the constraint made with respect to the resolution of the chromatographic peaks. In this paragraph, only a two component mixture will be con-sidered. The analysis time, tR, is assumed to be equal to the retention time of the second peak.
Combination of equations 1.1, 1.5 and 1.6 leads to:
~]
(1. 7)This expression is obviously an extended form of equation
~.1. Using equation 1.2, t
0 can be eliminated and equation 1.7 can be rewritten as:
t =
[16(-a-)2 (1
+ k)3 R2]
R a - 1 k2 s H {1. 8) -uAlthough the factors on the right hand side of this equa-tion are not completely independent, some interesting con-clusions can be drawn from them.
Firstly, the carrier gas velocity must apparently be set to the value at~hich (H/u) attains a minimum. Real GC columns in practice exhibit such a minimum. See chapter
3.3.
Secondly, it appears necessary to optimize the chromato-gram.
By differentiation of equation 1.8, an optimum value of k
=
2 is calculated, assuming that H is independent of k, which is only approximately true.The factor a/(a - 1) approaches a minimum value of 1 for large values of a. When a > 10, nothing can be gained by changing the stationary phase. In practice, only compounds with widely different boiling points may give such a high a. Then it becomes important to select the best available stationary phase.
Rs, k and a prescribe the optimal position of both peaks and also the optimal peak width. This leaves the user no freedom with respect to the appearance of the fastest possible chromatogram.
Equation 1.8 initially appears to give no information regarding the selection of the most useful column and car-rier gas. In several excellent papers9
' 10' 11' 12 dealing with the optimisation of the analysis time in gas
chroma-tography it is however shown, that this information can be obtained in an explicit form when in equation 1.8 H and
u
are expressed in more basic physical properties. Unfortu-nately, plate height depends onu
in a complicated manner 1' 2 and is in addition a complex function of the column pressure drop. Some approximations are commonly made, which simplify the problem, but which also restrict thevalidity of the final equations derived. Assuming that the column is operated at the minimum value of H/u, that the inlet pressure, pi' is at least three times the outlet pressure, p
0, and neglecting the stationary phase contri-bution to dispersion, Guiochon11 obtained, for a capilla-ry column:
(I. 9)
were d
0 is the column diameter, n the dynamic viscosity of the carrier gas and D g,o the diffusion coefficient of the solute in the carrier gas at the column outlet pressure. For gases behaving ideally, the product p0 Dg,o is equal to p1 Dg,l
=
Dg' which is constant over a wide pressure range. Dg,l is the diffusion coefficient at atmospheric pressure,J::\,
and is listed in handbooks.Differentiation of equation 1.9 yields an optimum value of k = 1.76, which is slightly below the tentative value of k 2, obtained by differentiation of equation 1.8. Equation 1.9 reveals a third power dependence of tR on ci/{a- 1) and on Rs. Thus, when a fast analysis is requi-red the stationary phase should be carefully selected and an unnecessarily large resolution should neither be accep-ted nor strived for. Unfortunately, many practical chroma-tographers are not aware of these important rules. Chroma-tographic columns are very often operated under conditions which produce nearly the maximum resolution possible. Par-ticularly in capillary gas chromatography, a tremendous amount of time is wasted in this way.
According to equation 1.9 the inner diameter, d
0 , is the only dimension of a capillary column which is allowed to
be chosen freely once a constraint with respect to the resolution has been made. For packed columns, an expres-sion similar to equation 1.9 can be derived, with the par-ticle diameter, dp' instead of de.
The relationship between tR' de' pi and p0 is extensively
discussed in chapter 2. The linear dependence suggested
by equation 1.9 only exists when pi > 3 p0 •
For both packed an capillary GC columns, the best carrier
gas employed is the one with the lowest value of
(n/Dg)~.
According to the kinetic-molecular theory of gases13, n is
proportional to M~/o2, where M is the molecular weight of
the gas and
o
is the diameter of the molecule. Forhydro-gen and helium, cis about 2.5 Angstrom. For heavier gases
like N2,
co
2 and argon,o
is about 3.5A.
The diffusioncoefficient is to a first approximation proportional to
~14
(1/M) , so the dependence of the analysis time on the
carrier gas can be estimated from the value of
M~/o.
Forseveral gases, values of
M~/o
are given in table 1.I.Table 1.I. Values of
M~/o,
aalaulated for several aarriergases. M~/o gas (X 109 g ~ m -1 ) hydrogen 5.7 helium 8.0 nitrogen 15.1 argon 18.1 carbon dioxide 19.0
Hydrogen is obviously the best choice. With helium, the analysis time will be prolonged by about 40%. The other gases are approximately three times slower than hydrogen, and preferably should not be used in fast chromatography.
1.4 A GENERAL APPROACH FOR OBTAINING THE MINIMUM ANALYSIS TIME
Equation 1.9, a~d a similar expression for packed
co-lumns are functions of independent factors only, and there-fore clearly illustrate the approach which has to be fol-lowed to obtain the minimum analysis time. Three indepen-dent criteria can be formulated:
1. The shape of the chromatogram has to be optimized. The required appearance of the chromatogram is
descri-bed by the factors k, ~ and Rs' which occur in the
bracke-ted part of equation 1.9.
Summarising, the last eluting peak should have a capacity ratio of about 2 and a stationary phase should be selected which provides the largest possible value of a. The value of Rs' which is a measure of the "quality" of the separa-tion, is assumed to be selected by the chromatographer. Since tR is proportional to the third power of the
resolu-tion, the value demanded for Rs should be minimal (Rs ~ 1).
Once ~, k and Rs have been selected, the number of
theore-tical plates required for the separation can be calculated from equation 1.6.
2. Hydrogen should be employed as the carrier gas.
When the use of hydrogen is prevented by safety require-ments, helium can be considered a good alternative. The velocity of the carrier gas should be set at the value for which the function H/u attains its minimum.
3. The smallest possible column diameter (capillary GC) or particle diameter (packed GC) should be used. At this point, a drawback of capillary columns should be mentioned. Their sample capacity is known to decrease strongly with a decrease in de. Although a low sample ca-pacity is regarded acceptable in many instances, i t may occasionally prevent a further reduction of de.
Equation 1.9 is valid for a two component mixture only. The first criterion, concerning the optimal shape of the chromatogram, will have to be altered when optimisation of the analysis time for a multi-component mixture is requi-red. On the other hand, the second and the third criterion are in no way related to the appearance of the chromato-gram. It seems reasonable to postulate that these criteria are valid in optimising any separation with respect to time. This assumption has been confirmed for temperature programmed gas chromatography. See section 3.2.
1.5 OPTIMISATION OF THE ANALYSIS TIME FOR MULTI-COMPONENT MIXTURES
Theories dealing with the analysis time of a multi-com-ponent mixture usually begin with the assumption that a "critical pair" of peaks will be present in the chromato-gram. When the critical pair are satisfactorily separated, then so too are all other peaks in the chromatogram.
An elegant treatment of the retention time in multi-compo-nent analysis has been presented by Guiochon11
• For capil-lary columns he obtained an expression which greatly re-sembles equation 1.9:
where n is the ratio of the k value of the last peak in the chromatogram and the k value of the second peak of the critical pair. The differences observed between equation 1.9 and 1.10 only affect the factors describing the shape of the chromatogram.
Differentiation of equation 1.10 shows that the optimum value fork has become a function of n. If n = 1, kopt
=
1.76. When increasing n, kopt decreases to about 1. How-ever, values obtained for tR differ by only 10% when k =1.76 is entered in equation 1.10 instead of of the true value of kopt11• The dependence of kopt on n is therefore not of practical importance.
The value of n, and thus the capacity ratio of the last eluting peak, should be kept low. This fact should be con-sidered when selecting the stationary phase, as will be discussed later.
Summarising, it can be concluded that the minimum sis time for a multi-component sample which is analy-sed isothermally can be obtained by applying the criteria outlined in section 1. 4 to the "critical pair" of peaks in the chromatogram. The analysis time can be decreased even further when temperature programming and pressure program-ming are applied. In the optimal situation, each pair of adjacent peaks in the chromatogram should have the same resolution as the "critical pair".
In practice, it may be very difficult to decide which peaks in the chromatogram should be considered as the "critical pair". One is often confronted with a situation, in which i t is impossible to obtain a satisfactory degree of resolution between all pairs of adjacent peaks simul-taneously. This problem was recently studied by Davis and Giddings15, who stated that
"a chromatogram must be appro~imately 951 vacant in order to provide a 901 probability that a given compound of in-terest will appear aa an isolated peak."
This statement is based on the assumption, that the peaks are spread randomly on the chromatogram. Apparently, the compounds present in a mixture can only be fully separated
during a single chromatographic run when their number is well below the peak capacity of the chromatogram. The peak capacity is defined as the maximum number of peaks that can be accomodated without overlap, and has been dis-cussed in more detail by Giddings16•
For mixtures of limited complexity in practice a satis-factory resolution between all peaks can be obtained. The two peaks with the lowest resolution can then be conside-red as the "critical pair". However, to achieve this goal, a very careful selection of the stationary phase may be required. Due to the number of components involved, the selection of the phase may be a very cumbersome task, un-less mathematic optimisation strategies17118 are employed. If the number of compounds in the sample approaches the peak capacity of the column, then peak overlap will be very common15
• Also, peaks resulting from three or more overlapping compounds will be present in the chromatogram 15• Under such circumstances, the assignment of a "criti-cal pair" is a very difficult task. It is also doubtful whether the "critical pair" approach can still make a
re-levant contribution to the optimisation of the analysis
time. Instead, it appears that the "optimal" chromatogram
has to be established experimentally by the chromatogra-pher. Alternatively, the difference between the peak ca-pacity and the number of sample components can be increa-sed. This approach will reduce the peak overlap and makes the critical pair concept useful again, however at the cost of analysis time. This can be realized in several ways. Obviously, the peak capacity itself can be increased, by employing a column with a larger number of theoretical plates16• Also, the complexity of the chromatogram can be reduced, either by fractionation of the sample before or during the injection, or by performing multi-dimensional gas chromatography19' 20• The employment of specific detec-tors:should be considered when only a limited number of
sam-ple compounds, buried in a comsam-plex matrix, are of interest. 1.6 COMPARISON OF THE SEPARATION SPEED BETWEEN PACKED
AND CAPILLARY COLUMNS
To our knowledge, the fastest separation published to date is by Jonker and co-workers21- 22, and shows the reso-lution of methane, ethane, propane and n-butane in 0.15 sec. This was achieved with a 3.2 em long column packed with LiChrosorb Si-60 particles with an average particle diameter of 10 pm, which gave 650 theoretical plates for n-butane at k
=
2.From this example i t should not be concluded that a packed column offers a superior speed of separation compared to a capillary column. In fact, the reverse is often true, as can be derived from theory.
The operating characteristics of chromatographic columns are customarily specified using the reduced plate height h and the reduced velocity v0 .For packed columns, h = H/dp and v0
=
u d /D • For capillary columns, h=
H/d and v ==o p g,o c o
uo dc/Dg,o·
Normally, packed columns are operated11 near to h
=
3, v0
=
3, whereas capillary columns are operated near to h=
1.5, v0=
5. Assuming dp and d0 to be equal, the plate height of the packed column, and thus the column length needed to obtain a given number of theoretical plates, is larger by a factor 2. The carrier gas velocity of the ca-pillary column is higher by about the same amount. Capil-lary columns have the additional advantage of an approxi-mately 30 times lower pressure drop.Rewriting equations 1.1~ 1.2 and 1.5 in reduced quantities, and neglecting the compressibility of the carrier gas, yields:
h N d2 (1 + k)
V o g,o D (1.11)
where d is either the particle diameter or the column in-ner diameter.
For the same plate number, capillary columns thus are superior to packed columns from the viewpoint of analysis speed. Neglecting some special applications, capillary columns are apparently preferable for separations which are critical with respect to time.
1.7 THE EXPERIMENTAL CONDITIONS FOR INVESTIGATING THE RELATIONSHIP BETWEEN tR AND de
Once the diameter of the capillary column has been chosen, the analysis time of the sample cannot be decrea-sed below a certain minimum, tR i , without at the same ,m n time decreasing the resolution below the minimum value re-quired (see eq. 1.10). Conventional 25m x 0.25 mm columns often need a minimum analysis time of 20-90 minutes for complex samples such as urinary steroids or crude oil fractions.
The only possible way to decrease tR m· , ~n without sacrifi-cing resolution, is to decrease the inner diameter of the column. Hence, it is of obvious interest to study the pro-perties of columns with a diameter below 0.25 mm I.D. in more detail. The conclusions obtained from such a study of course must be experimentally verified.
The comparison of columns of different inner diameter re-quires a very careful experimental setup. Identical chro-matograms should be obtained with all columns, except for a proportionality factor on the time axis. According to the criteria indicated in section 1.4, this implies that amongst other factors the capacity ratio and the column plate number should be kept constant.
The.capacity ratio is related to the partition coefficient K, describing the distribution of the solute between the carrier gas and the stationary phase:
k
=
K/B (1.12) where B is the phase ratio of the column, which is defined by:(1.13) Vg and Vs are the volumes occupied by the carrier gas and by the stationary phase respectively.
k k
•
3.2 1 0. 0•
•
•
I ••
i ••
3.0~
9.6 2.8 9.0-r.
I' II
I II
t.
II
I II
0 1 0 20 0 1 0 Pj(atm)Fig. 1.2. The capacity ratio as a function of the column
inlet pressure for n-undecane (left) and n-trideaane
(right)~ with helium (•) or nitrogen (®), at 120°C,
measured with a 8 m x 50 pm I.D. capillary column.
In practice, the dependence of B on temperature and pres-sure can be ignored.
K is inversely related to the vapour pressure of the so-lute, and thus is strongly dependent on temperature. The influence of pressure on K is usually described using the second cross virial coefficient23• The pressure effect can almost be neglected when hydrogen or helium are used as the carrier gas, but can become quite prominent when ni-trogen or carbon dioxide are employed21• See figure 1.2.
Summarising, with an investigation of the relationship be-tween the column inner diameter and the analysis time, the following factors should be kept constant:
- the theoretical plate number, which determines the co-lumn length.
- the stationary phase. - the phase ratio
e.
- the column temperature.- the capacity ratio. This implies the use of hydrogen or helium as the carrier gas.
- in addition, for linear temperature programmed condi-tions, the product r.t
0 should be kept constant. Here,
r is the programming rate. see chapter 3.2.
When the above conditions are met, identical chromatograms will be obtained with columns of any diameter, except for
a proportionality factor on the time axis. 1 . 8 REFERENCES
1. J,j, van Deemter, F.J. Zuiderweg and A. Klinkenberg,
Chern. Eng. Sai.,
2
(1956) 271.2. M.J.E. Golay, in D.H. Desty (Editor), Gas
Chromato-graphy 1958, Butterworths, London, (1958), p.36.
3. J .H. Purnell, J. Chern •. Soc., (1960) 1268.
4. L. Rohrschneider, J. Chrornatogr., (1965) 1. 5. L. Rohrschneider, J. Chrornatogr., 22 (1966) 6.
6. W.O. McReynolds, J. Chrornatogr. Sci.,~ (1970) 685. 7. L.S. Ettre, Chrornatographia, ~ (1973) 489.
8. L.S. Ettre, Chrornatographia,
1
(1974) 39.9. J.H. Knox and M. Saleem, J. Chrornatogr. Sai., 7 (1969)
64.
10. G. Guiochon, Adv. Chrornatogr., ~ (1969) 179. 11. G. Guiochon, AnaL Chern., 50 (1978) 1812. 12. G. Guiochon, AnaZ. Chern., 52 (1980) 2002.
13. G.M. Barrow, PhysiaaZ Chemistry, McGraw-Hill, New York, 1966.
14. E.N. Fuller, P.O. Schettler and J.C. Giddings, Ind.
Eng. Chern. , 58 (1966) 19.
15. J .M. Davis and J.C. Giddings, AnaL Chern., 55 (1983)
418.
16. J.C. Giddings, Anal. Chern., 39 (1967) 1027.
17. R.J. Laub and J.H. Purnell, AnaZ. Chern., 48 (1976)
1720.
18. S.L. Morgan and S.N. Deming, J. Chromatogr., 112
(1975) 267.
19. D.R. Deans, J. Chromatogr., 203 (1981) 19.
20. G. Schomburg and F. Weeke, Chromatographia,
87.
(1982)
21. R.J. Jonker, Thesis, University of Amsterdam, Amsterdam, 1982.
22. R.J. Jonker, H. Poppe and J.F.K. Huber, Anal. Chern.,
54 (1982) 2447.
23. D.H. Desty, A. Goldup, G.R. Luckhurst and W.T. Swanton,
in M. van Swaay (Editor), Gas Chromatography 1962,
Butterworths, London, 1962, p. 79.
CHAPTER 2
A STUDY OF THE RELATIONSHIP
BETWEEN ANALYSIS TIME ,
COLUMN INNER DIAMETER
AND THE PRESSURE GRADIENT
2.1 INTRODUCTION
The reLationship bet~een
analysis time and inner ao-lumn diameter is sho~n to depend on the pressure gra-dient. At a Zo~ column inlet to outlet pressure ratio~ the analysis time is proportional
to the square of the coiumn diameter. For situations of a high pressure drop~ a li-near relationship is found.
Since the introduction of capillary gas chromatography 1'2 there has been a demand for an increased speed of ana-lysis. From a theoretical point of view, the reduction of the column inner diameter seems an obvious route towards shorter analysis times. The practical feasibility of this approach was convincingly demonstrated by Desty et al.3 in 1962, but surprisingiy since has received little atten-tion. In 1977, Gaspar and co-workers3'~ reported a novel
injection technique, based on a "fluidic logic" pneumatic device. With this system an injection bandwidth of about 10 msec could be realized. Both the Desty and Gaspar groups obtained analysis times of the order of a few
seconds on columns with inner diameters of 35 and 65 ~m, respectively. However, the samples analysed were simple mixtures of low boiling point hydrocarbons and the columns had low plate numbers (below 10 4 ).
In this chapter, the relationship between the column diameter and the speed of analysis is investigated with emphasis on columns having over 105 theoretical plates. 2.2 THE GOLAY-GIDDINGS EQUATION
A concept describing the relationship between the theo-retical plate height and the carrier gas velocity was pu-blished in 1958 by Golay1• Later, the theory.was extended
by Giddings and others6' 7, in order to account for the co-lumn pressure drop. The resulting equation, known as the "Golay-Giddings" equation, has become widely accepted, and is believed to represent an accurate estimation of the theoretical plate height of a column, as a function of the carrier gas speed:
[2 D 1 + 6 k + 11 k2
~~
"a]
H 2!0 + £1 + uo 96(1 + k)2 g,o + ~ k d2 uo f2 f ( 2. 1) 3 (1 + k)2 D swhere Ds is the diffusion coefficient of the solute in the stationary phase, df is the film thickness of the statio-nary phase and f1 and £
2 are pressure correction factors according to Giddings et al.6 and James and Martin8 res-pectively:
(2. 2)
(2. 4)
where P is the ratio of the column inlet to outlet pres-sure. When P approaches one, then f1 and f 2 also approach one. When P >> 1, then f1 will increase to its maximum value of 9/8. Thus, f
1 is hardly affected by the column pressure gradient, contrary to f2, which becomes very small for high values of P. In practice, the value of is often required. Mainly for the calculation of the car-rier gas velocity at the column outlet, u
0 , or the average linear carrier gas velocity, u, which are related8 by:
-u = uo f2 (2.5)
To facilitate the following discussion, a graphical repre-sentation of the relationship between P and f2 is given in
figure 2.1.
Approximate expressions for f2 can be employed instead of equation 2.3. Halasz and. Heine9 showed that f
2 can be ap-proximated by f2 ~
2 P3+ 1 with an accuracy of better than 8% over the entire pressure range. The approximation f2 ~
2 P 3~2
1
is correct to within 1.1% when 1.6 < P < 6.5. ForP > 6.5 f
2 is calculated with an accuracy of better than
2% using:
(2.6) The Golay-Giddings equation is often rewritten in a sim-plified form:
(2.7)
The B term describes longitudional diffusion, C and C
g,o s
a~count for resistance to mass transfer in the carrier gas and in the stationary phase respectively. The optimum car-rier gas velocity, uopt' for which the plate height is at
1
1\
\
\
R
I
\
•'
I
I
0.5
,,
f'..
...r--
r---I I I
0
5
10
Fig. 2.1. The pressure correction faator f 2 as a function
of P.
a minimum, Hmin' can be found by differentiating equation 2.7 (or eq. 2.1) with respect to u0, giving:
c
g,o (f1 + y.l) +c
s (f 2 + (2.8)(2.9)
The importance of the individual factors in equation 2.8 and 2.9 has been discussed by Cramers and co-workers10' 11• Conditions under which simplified forms of these equations can be used were closely examined by the authors. For all practical purposes, y1 << f 110• Thus, y
The factor y2, having a negative value, is small compared to f2 when P < 1.25. At P >> 1, y2 is approximately equal to -0.5 £2•
For most capillary columns, the contribution of the sta-tionary phase to the theoretical plate height is small. From published values for the diffusion coefficients of n-alkanes in the gaseous phase12 and in the stationary phase13' 1" it is concluded, that the stationary phase con-tribution is normally less than 1%. For columns with a large pressure gradient the importance of the Cs term will be even less, due to the decreased value of £
2 • However, it can be questioned whether the data published by Millen and Hawkes13' 1
" is valid for capillary columns, because
their data was obtained with packed columns, the statio-nary phase being deposi.ted i.n pools near to the contact points of the glass beads.
Diffusion coefficients for immobilized (cross-linked) phases, which are now widely used in capillary GC, have not been reported to date. It has been suggested that the diffusion coefficients are smaller in immobilized phases. In order to establish the real importance of the Cs term in capillary gas chromatography, .diffusion coefficients of a homologous series of n-alkanes were measured for three different immobilized and three different non immobilized non polar phases. The methods used and results found are presented in appendix 2. Comparing columns of equal film thickness, it is evident that the diffusion coefficients are not significantly altered by immobilization of the stationary phase. However, accurate absolute values for the diffusion coefficients were not obtained, since all Ds values were observed.to decrease with the film thick-ness studied, for reasons which are not yet understood.
P;11 bar 100 . . 50 2 He 10 20 50 100 200 500 1000
Fig. 2.2. The optimum
aolumn inlet pressure as a funation of the inner column diameter and the theoretical plate number, for helium. Column outlet
pressure 1 bar. Pin bar 50
..
de 50 ..,m 20 10Fig. 2.3. The optimum inlet pressure for a 50 ~m I.D. capillary column as a func-tion of the theoretical plate number and the carrier gas. Column outlet pressure 1 bar.
2.3 THE COLUMN PRESSURE GRADIENT
Assuming laminar flow conditions, the local carrier gas velocity, ux, inside a capillary column is described by Darcy's law (slightly modified):
d2 - _c_ £2
32 n dx (2.10)
where n is the dynamic viscosity. For gases behaving ideally, integration of equation 2.10 leads to an expres-sion relating the carrier gas outlet velocity and the co-lumn pressure drop:
He H2 N2
d~
p0=
(P2 - 1)64
n
L (2.11)Using equations 2.8 and 2.11, and assuming an atmospheric outlet pressure, the optimum column inlet pressure can be calculated as a function of the column diameter and the plate number. Results are shown in figures 2.2 and 2.3. Obviously the required inlet pressure increases substan-tially when the column diameter is reduced. For example, an inlet pressure of about 10 bar is required for a 50 ~m I.D. column having 10 5 theoretical plates with helium as the carrier gas.
Expressions describing the shape of the pressure gradient and the velocity distribution along the column also can be derived15 from equation 2.10. Both distributions are a function of P. The local pressure, Px' is given:
px/po
t10
5
0.5
...
0
1
x/L
Fig. 2.4. The pressure
gradient over a aapillary
aolumn~ for several values of P.
ux/uo
10.5
0
(2.12)0.5 ...
x/L
Fig. 2.5. The aarrier gas
veloaity profile inside a aapillary aolumn, for several values of P.
39
For the local carrier gas velocity, ux:
X 2
- -(P -L (2 .13)
where x is the distance from the column inlet, measured along the longitudinal axis.
In figures 2.4 and 2.5, both distributions are shown as a function of the reduced length coordinate A
=
x/L, for several values of P.2.4 FACTORS AFFECTING THE OPTIMUM CARRIER GAS VELOCITY Assuming that the Cs term, describing the resistance to mass transfer in the stationary phase, can be neglected equations 2.8 and 2.9 can be simplified:
where: F(k) 1 + 6 k + 11 k 2 3(1 + k}2 (2.14) (2.15) (2.16) (2.17)
Combining equations 2.11, 2.14 and 2.15 leads to an expli-cit relationship between d
0 and the column inlet and out-let pressures:
p2 - 1 =
opt (2 .18)
From equation 2.14, the influence of the pressure gradient on Hmin is observed to be small. At large values of P, up
t
CM/SEC
Uopt
5
0
200
400
Fig. 2.6. The relationship between the aoZumn inner
dia-meter and the optimum aarrier gas veloaity for helium, aaZaulated for n-dodeaane at 100°C and k
=
5, assuming theoretiaa"l plate numbers of (1) 1000; (2) 10,000; (J) 20,000; {4) 100,000 and (5) 1,000,000.to 12.5% of the theoretical plates are lost, due to f1. In practice, the separation quality of a chromatographic column is usually judged from its coating efficiency CE11
, which is defined: CE 0.5 de
F(k)~
* 100% Hmin,exp (2. 19)This definition assumes that Cs is negligible and that
f
1 is equal to 1. Consequently, when P >> 1, a perfectly coated column will have a coating efficiency of only 87.5% instead of 100%, as is customarily found for conventional capillary columns operated at low P. Unawareness of this fact may lead to erroneous conclusions regarding the qua-lity of very narrow bore columns.
According to equations 2.15 and 2.16, the optimum linear carrier gas velocity, uopt' is highly dependent on the column pressure drop. Calculated curves, depicting the relationship between uopt and de for columns with the same number of theoretical plates, are illustrated in figure 2.6. These curves are generally sigmoid in shape. The op-timum velocity is observed to increase continuously as de decreases, and a heavy dependence on N is noted. Apparent-ly, two extreme situations can be discerned. At low plate
4
-numbers (e.g. N
=
10 ),in·which case P ~ 1 and u ~ u 0 , u t is seen to increase inversely to the column innerop 6
diameter. At very high plate numbers (e.g. N
=
10 ), where p is large, uopt is seen to become independent of de.In figure 2.6, at constant d , the highest valuesfor u c op t are observed for short, low plate number columns, working under a negligible pressure gradient. These columns there-fore display the highest separation speed, when defined in terms of theoretical plates per second. Therefore in theory at least, it is possible to realize a high separa-tion speed and a high plate number simultaneously by
performing recycling chromatography. The compounds leaving the column are then re-introduced several times into the inlet, using a switching valve. This approach has recent-ly been studied by several workers16' 17, who obtained some promising results. However, only a limited number of compounds can be subjected to recycling at one time.
Apart from reduction of the column inner diameter, equa-tion 2.15 suggests a second way to increase the optimum carrier gas velocity. For an ideal gas, the product D g,o . p
0 is constant. Hence D g,o , and consequently u o, p 0 t ' may be increased by reducing the column outlet pressure. An extensive theoretical treatment on this subject has re-cently been published by Cramers et al. 18 and Leclercq et al.19• They observed a good agreement between theoretical and experimental data. Assuming vacuum outlet pressure, which implies a high value of P, the minimum plate height was predicted to increase by a factor of 9/8. The optimum carrier gas velocity was also predicted to increase. The gain in speed of analysi.s, G, as derived by both authors was: 3 G p -i,opt,atm (2.20) o?Lopt,atm
-where p. t t is the required inlet pressure when the
~,op ,a m
column is operated at atmospheric outlet pressure, P 1. G is seen to increase with decreasing values of p. ~,op t ,a m t . Thus, vacuum outlet gas chromatography will be of particu-lar interest for columns which have a high permeability, due to a large inner diameter or a short length. Vacuum outlet gas chromatography should be considered when a short analysis time and a large sample capacity are re-quired simultaneously. In addition, vacuum outlet condi-tions are most useful when performing GC-MS. Interfacing liners apparently are superfluous. The capillary column
can be inserted directly into the ion source of the mass spectrometer. A flame ionisation detector cannot be used at a very low pressure. The katharometer20 '21 and the electron capture detector22 have been shown to perform well.
2.5 THE RELATIONSHIP BETWEEN tR' d
0 AND P
Using equations 1.1, 1.2 and 1.5, the retention time of a compound can be rewritten:
(1 + k) (2.21)
u
In the following theory i t is assumed that the carrier gas velocity is maintained at the optimum value uopt' for which the plate height is at a minimum, Hmin· In addition, the Cs term is neglected. Under these conditions, a rela-tionship between the analysis time and the column diameter is found by combining equations 2.14, 2.15, 2.16 and 2.19:
{k + 1) F(k) N f d2
1 c
16 D q,o
f2
(2 .22)As indicated in chapter 1, section 1.7, i t is important to compare situations of identical resolution when studying the effect of the column diameter on the analysis time. This implies amongst others that k, N and D g,o must be constant for all columns studied. Equation 2.22 can then be further simplified:
{2. 23) where c is a constant.
Thus, the column pressure drop will have a considerable influence on the relationship between tR and d
0, mainly via £2.
By use of equations 2.2, 2.3 and 2.18 the factor f1/f 2
can be elaborated as a very complex function of de. Nume-rical evaluation of this function shows that equation 2.23 is of the general form tR = c 2 d~ where c 2 is a constant
and 1 < m < 2.
Two extreme situations can be discerned. At P ~ 1, f 1/f2
=
1 and m = 2. Here the retention time is seen to decrease as the square of de. This dependence is observed when co-lumns of limited plate number are studied~. At large va-lues of P, f1/f2 can be approximated by f 1/f2 ~i
P. Ac-cording to equation 2.18 Popt is then inversely propor-tional to de. Consequently, the retention time will now decrease only in proportion to the column diameter. Summarizing, i t is concluded from equation 2.23 that re-duction of the column diameter presents an attractive route for improving the speed of analysis in isothermal capillary gas chromatography, even for columns that are operated under a considerable pressure gradient.2.6 INSTRUMENTAL CONTRIBUTIONS
Often the variance, o~, that is actually measured for a peak leaving the column differs appreciably from
(2.24) where o; is the variance that will originate from the chromatographic processes taking place inside the column. The following rule of additivity of variances is generally valid:
(2.25)
where cr!c accounts for the extra-column contributions that may arise from injection bandwidth, detector cell volume, dead volumes and time constants of the electronic equip-ment, etc.
A thorough mathematical treatment on extra column contri-butions to chromatographic band broadening has been pu~ blished by Sternberg23
•
Gaspar and co-workers5 have shown that the extra column contributions can be accounted for by adding to the Golay-Giddings equation an extra term,
o,
which is proportional toii
2: H (2.26) where: D (1 + k)2 L (2.27)and a;c is assumed to be expressed in time units.
According to equations 2.23 and 2.24,
o;
will decrease when the column inner di.ameter is reduced while N is held con-stant. Thus, for very rapid analyses using short columns(tR proportional to
d~),
it can be expected (eq. 2.25} that the peak width values will be determined mainly by instrumental factors. To prevent this situation, a2 must. z ec
be lowered proportionally to a .Specially designed injection and
detec-tion equipment having low time constants are then required, as reported by Gaspar et al.
In our philosophy, the use of modern commercial instru-ments without modification in combination with columns of high plate number i.s of more practical interest. If the decrease in column di.ameter is accompanied by an appro-priate increase in the plate number, then a~ will approxi-mately remain unchanged. The gain in analysis speed is then traded for increased separating power and a!c need not to be lowered by complicated instrumental designs.
2.7 EXPERIMENTAL
Columna
Glass capillary columns of 50 ~m I.D •. x 0.6 - 1.0 mm O.D., and of 0.3 mm I.D. x 1.0 mm O.D. were drawn from bo-rosilicate tubing (Duran 50, Schott, Wertheim, G.F.R., or Hypersil, Corning, Corning, NY, U.S.A.) on a home-made precision drawing apparatus2~. Microscopic examination
re-vealed that the Lfiner diameter of the 50 vm I.D. columns obtained was constant within 4 to 10%, depending mainly on the precision of the borosilicate preforms used. Fused silica columns of 55 ~m I.D. x 0.3 mm O.D., and of
30 ~m I.D. x 0.2 mm O.D., were obtained from SGE (Melbourne, Australia).
The average inner diameters of the columns used for plate height studies were accurately measured by weighing the amount of mercury that could be introduced into a piece of column of known length.
Initially, due to lack of a suitable deactivation tech-nique, the empty columns were rinsed and directly coated. The deactivation problem has only recently been solved. The methods used for column preparation are described in detail in Chapter 4. The ends of the glass columns were straightened by gentle heating in an electrical device
(Pierce Eurochemie, Rotterdam, The Netherlands}.
Gas Chromatograph
All experiments, ex·cept the studies performed with the fluidic logic device (Chapter 5.5), were carried out on a Fractovap 2900 gas chromatograph (Carlo Erba, Milan, Italy), equipped with a split/splitless injector and a flame ioni-sation detector (FID). According to the specifications supplied, the time constant of the electrometer amplifier was 50 msec for the 1 V integrator output and about 150 msec for the 10 mV recorder output. The noise level was approximately at 10- 14 A.
