Table Of Content-
JOURNAL OF CHROMATOGRAPHY LIBRARY volume 37
gradient elution
in column liquid
chromatography
theory and practice
t? Jandera and J Chura’Cek
Department of Analytical Chemistry, University of Chemical Technology,
Pardubice, Czechoslovakia
E LSEVl ER
Amsterdam - Oxford - New York - Tokyo 1985
ELSEVIER SCIENCE PUBLISHERS B.V.
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Library of Congress Cataloging in Publication Data
Jmdera, P. (Pavel), 1944-
Gradient elution in column liquid chromatography.
(Journal of chromatography library ; v. 3)
Bibliograpw: p.
Includes index.
1. Liquid chrometography. I. Churlrek, Jamslav.
11. Title. 111. Series.
~~79.~454~19386s 543'.0894 85-1498
ISBN 0-444-42124-6
ISBN 044442124-6 (Vol. 31 1
ISBN 044441616-1 (Series)
0 Elsevier Science Publishers B.V., 1985
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xv
JOURNAL OF CHROMATOGRAPHY LIBRARY
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Volume 1 Chromatography of Antibiotics (see also Volume 26)
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Volume 5 Instrumental Liquid Chromatography. A Practical Manual on High-Per-
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Volume 6 Isotachophoresis. Theory, Instrumentation and Applications
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Volume 7 Chemical Derivatization in Liquid Chromatography
by J.F. Lawrence and R.W. Frei
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hy E. Heftmann
Volume 9 HPTLC - High Performance Thin-Layer Chromatography
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Volume 15 Antibiotics. Isolation, Separation and Purification
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Volume 16 Porous Silica. Its Properties and Use as Support in Column Liquid Chro-
matography
by K.K. Unger
Volume 17 75 Years of Chromatography - A Historical Dialogue
edited by L.S. Ettre and A. Zlatkis
xv I
Volume 18A Electrophoresis. A Survey of Techniques and Applications.
Part A: Techniques
edited by Z. Deyl
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edited by Z. Deyl
Volume 19 Chemical Derivatization in Gas Chromatography
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Volume 20 Electron Capture. Theory and Practice in chromatography
edited by A. Zlatkis and C.F. Poole
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Volume 24 Chemical Methods in Gas Chromatography
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Volume 25 Modern Liquid chromatography of Macromolecules
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Volume 26 Chromatography of Antibiotics
Second, Completely Revised Edition
by G.H. Wagman and M.J. Weinstein
Volume 27 Instrumental Liquid Chromatography. A Practical Manual on High-Per-
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Second, Completely Revised Edition
by N.A. Parris
Volume 28 Microcolumn High-Performance Liquid Chromatography
by P. Kucera
Volume 29 Quantitative Column Liquid Chromatography. A Survey of Chemometric
Methods
by S.T. Balke
Volume 30 Microcolumn Separations. Columns, Instrumentation and Ancillary
Techniques
edited by M.V. Novotny and D. Ishii
Volume 31 Gradient Elution in Column Liquid Chromatography. Theory and Practice
by P. Jandera and J. ChurGiek
Volume 32 The Science of Chromatography. Lectures Presented at the A.J.P. Martin
Honorary Symposium, Urbino, May 27-31, 1986
edited by F. Bruner
XVII
PREFACE
In the last 15 years, high-performance 1 iquid chromatography (HPLC) has become
one of the most widely used analytical methods with a rapid increase in the num-
Der of applications to the analysis of various compounds. This increase was mainly
due to the advent of sophisticated instrumentation and to the development of
new working techniques. It is not surprising that many books on HPLC have been
(and are still being) published. In addition to works concerning the general
aspects of HPLC, several books appeared treating special fields of application,
such as instrumentation or special detection techniques. It is understandable
that the main concern of these books was instrumentation and the development of
efficient columns, which made possible the success of HPLC.
We wanted to write a book on gradient elution in HPLC. Gradient elution means
programming the composition of the mobile phase during the separation, in con-
trast to isocratic elution, in which the composition of the mobile phase is
held constant. This is the reason why the primary concern of this book is the
influence of the mobile phase and its composition on separation. The correct
selection of the mobile phase for a given separation problem gives to the
practising chromatographer a powerful tool for achieving successful separations
of a wide variety of complex samples, and this is further increased by the
possibility of changing the composition of the mobile phase during the elution.
In virtually all fields of application gradient elution has been applied with
the aim of improving resolution and shortening the time of separation. The
utility of this technique increases with increasing complexity of samples that
have to be analysed using HPLC.
1
Liteanu and Gocan wrote a book on gradient liquid chromatography 10 years
ago. However, it was necessarily concerned mainly with classical column (and
thin-layer) chromatography and could not take full account either of specific
problems of gradient elution in HPLC or of recent advances in the understanding
of the role of the mobile phase in the chromatographic process. Therefore, we
felt that there is a need for another book on this topic.
The theory of gradient elution chromatography has been developed to such an
extent that relatively precise calculations of the retention data and the
establishment of optimum conditions with respect to the separations required
are possible in many useful gradient elution systems. Unfortunately, the bene-
fits of the theory for the better identification of compounds and the faster
XVIII
selection of optimum separation conditions have not yet become widely known
and accepted among practising chromatographers, in spite of the increasing
number of papers devoted to the theory of gradient elution published in recent
years. We wanted to write a book that might be helpful in this respect.
We have divided the book into four parts. To obtain an idea of the theoret-
ical basis of gradient elution separations, it is necessary to become acquainted
with the fundamentals of the phenomena that control the influence of the mobile
phase and its composition on retention behaviour in various liquid chromato-
graphic systems under isocratic conditions. Therefore, it was felt necessary
to devote one part to this topic. In this first part, several models are
discussed that allow descriptions of the interrelationships between the composi-
tion of the mobile phase and retention, as characterized by capacity factors,
in chromatography on polar adsorbents, on polar bonded phases and on ion
exchangers, in reversed-phase systems and in ion-pair chromatography. The
quantitative description of these relationships is essential for developing any
theory of gradient elution 1 iquid chromatography.
Part I1 is concerned with the theory of gradient elution chromatography. We
have attempted to bring together different theories developed by several groups
of workers in the field rather than to give a simple survey of various approaches
The prediction of retention behaviour (retention volumes and times, bandwidths,
resolution, peak capacity, etc.) by calculation is treated in detail and pos-
sibilities are outlined for the rational optimization of gradient elution
conditions,
In Part 111, the instrumentation for the formation of mobile phase gradients
is described and possible sources of instrumental errors are discussed. Most
attention i s paid to commercially available gradient elution systems for HPLC,
and the "classical" laboratory-made gradient formers are only briefly mentioned,
because detailed descriptions of the various types and the methods for the
calculation of gradient profiles formed in these devices have been presented
by other workers'-3. Other instrumental aspects are discussed as far as they
concern specific problems connected with the practical use of the gradient
elu t ion technique.
Part IV gives examples of the application of gradient elution techniques
to separations of different classes of compounds in various chromatographic
systems. The number of published applications clearly shows the increasing use
of gradient elution in chromatography on non-polar chemically bonded phases
(which is by far the most frequently used method in contemporary HPLC). However,
these examples can by no means cover all of the published applications of gra-
dient elution and are intended rather as illustrations of the potential power
XIX
of this technique. Therefore, the examples of applications are presented mainly
with respect to the type of mobile phase gradient used.
Hydrophobic or hydrophilic gels are occasionally used in the gradient elution
technique for certain separation problems. However, these applications cannot
be considered as the application of gel chromatography in the sense of steric
exclusion chromatography, because the compounds are eluted later than would
correspond to the column dead volume and therefore the sample compounds interact
with the column packing materials. In real steric exclusion chromatography,
these interactions are absent and the mobile phase cannot influence the separa-
tion other than by improving or impairing the solubility of sample compounds
(or, possibly, by solvating them). Therefore, gel chromatography is not con-
sidered in this book and the applications of gels are classified among other
reversed-phase or normal-phase chromatographic systems, according to the nature
of the predominating interactions.
Because we did not intend just to write another book on column liquid chro-
matography, the reader is referred to some of the outstanding books dealing
with HPLC in general for information on the general aspects of HPLC. Only those
topics are treated which concern the theory, practice or applications of the
gradient elution technique and the book does not cover areas such as column
efficiency, general instrumentation and techniques.
We thank the many companies who supplied technical information. Dipl. Ing.
Zden6k DuZek is thanked for his assistance with the literature search, dipl.
Ing. Blanka Wankovd for careful drawing of the diagrams and Mrs. Marie ValdSkovd
for technical assistance during the preparation of.the manuscript.
Pardubice, 1984
Pave1 Jandera
Jaroslav ChurdEek
REFERENCES
1. C. Liteanu and S. Gocan, Gradient Liquid Chromatography, Wiley,NewYork, 1974.
2. L.P. Snyder, Ckromutogr. Rev., 7 (1965) 1.
3. 0. MikeS and R. Vespalec, in Z.-Deyl, K. Macek and J. Jandk (Editors), Liquid
CoZmn Chromatography, Elsevier, Amsterdam, 1975, Ch. 10.
3
Chapter 1
THE MOBILE PHASE AND CHROMATOGRAPHIC BEHAVIOUR UNDER ISOCRATIC CONDITIONS
The quantitative theory of gradient elution chromatography is based on the
interrelationships between the composition of the mobile phase and retention
behaviour in isocratic elution chromatography, where the eluent composition is
held constant throughout the separation’ The theory of gradient elution
y2.
chromatography is much more complicated than that of isocratic elution, but a
number of phenomena in elution chromatography with programmed composition of
the mobile phase can be readily understood from analogies with isocratic elution
~hromatography~’~Th. erefore, it is necessary to become familiar at least with
the basic principles of the influence of the mobile phase composition on the
chromatographic behaviour of sample compounds under isocratic conditions before
dealing with the theory of gradient elution chromatography. A detailed discus-
sion of the theory of isocratic elution chromatography is beyond the scope of
this book, but it is useful to consider briefly several basic quantities that
are important for the description of the chromatographic process.
Separation in elution liquid column chromatography can be characterized by
several important parameters, which can be evaluated directly from the chro-
Vi;
matogram: retention volume, vR; corrected (net) retention volume, bandwidth,
w (in volume units); and resolution of compounds 1 and 2, RS. The retention in
liquid column chromatography can be characterized either by retention time, tR,
or by retention volume, VR, which are the time (or the volume of eluate from
the column) from the injection of the sample on to the column to the elution
of the maximum of the elution curve (peak) of a chromatographed compound (Fig.
1.1). The two quantities are interrelated by the equation
VR = tRFm (l.la)
V i = t’F (l.lb)
R m
where Fm is the volume flow-rate of the mobile phase (volume of eluate per unit
ti
time) and is the corrected (net) retention time.
From the retention volume, VR, (or retention time, tR)t he capacity factor
of a sample compound, k’, can be calculated, if the volume of the mobile phase
in the column (column void volume), Vm, is known:
References on p. 52.
4
-
t*V
Fig. 1.1. Interpretation of a chromatogram in liquid column chromatography. Re-
tention times (t , ti),r etention volumes (VR, Vi), column dead time (t )* dead
volume ), ,,v( and landwidths (w) in liquid column chromatography. I, SampTe in-
jection; t, time elapsed; V, volume of eluate.
The capacity factor is a dimensionless quantity that depends neither on the
dimensions of column nor on the flow-rate of the mobile phase. Essentially, it
is a quantity that gives the ratio of the total amount of sample compound in
the stationary phase to its amount in the mobile phase. Thus, k' is proportional
to the distribution coefficient, KD, which gives the ratio of the concentrations
of the sample compound in the two phases:
where $ is the phase ratio in the column, i.e., the ratio of the volume of the
stationary phase (Vs) to that of the mobile phase (V,). Of course, the mass of
the stationary phase can be used instead of vs, with a corresponding change i n
definition of KD.
Chromatography is used to separate sample compounds, and consequently a quan-
titative description of the separation is of major interest for both the prac-
tice and the theory of chromatography. Resolution, R,, is the quantity most
frequently and obviously most appropriately used to characterize the separation
5
of two sample compounds 1 and 2. This is the d,istance between the two elution
maxima (the difference in the elution volumes or elution times) divided by the
average bandwidth of the two compounds (in volume or time units). For the sake
of simplicity, the bandwidth of the later eluted compound (2) is often used
instead of the average bandwidth:
From eqn. 1.4 it follows that resolution increases with increasing difference
in retention volumes (difference in the retention of the two sample compounds)
and decreases with increasing bandwidth, which should be therefore kept as
narrow as possible. The sample is usually injected on the column as a very
narrow band (volumes of a few microlitres), but broadening of this band inevi-
tably occurs during migration along the column. The width of a band eluted from
the column is proportional to the retention volume of the sample compound and
it depends on the efficiency of the column under given conditions, which is
conveniently characterized by the number of theoretical plates, n:
-40 m‘
w = L * Vm(l t k’) =- * (1 t k’)
\I;i
where u is the standard deviation of the bandwidth at the end of the column in
length units.
The total number of theoretical plates in the column is proportional to the
column length, L:
v 2
n = H = ):16(
where H is the height equivalent to a theoretical plate, which depends on a
number of parameters (temperature, mobile phase viscosity and linear velocity,
sample compound diffusion coefficient, particle diameter and thickness of sta-
tionary phase layer of the packing material, e t ~ . ~Th.e linear velocity of
the mobile phase, U, is a very important parameter, which influences not only
bandwidth and resolution, but also the speed of analysis. It is related to
the volume flow-rate of the mobile phase, Fm, by the equation
References on p. 52
