16 INTRODUCTION
13. L. S. Ettre, LCGC, 25 (2007) 640.
14. L. S. Ettre, LCGC, 19 (2001) 506.
15. L. S. Ettre, LCGC, 243 (2006) 390.
16. L. S. Ettre, LCGC, 23 (2005) 752.
17. J. G. Kirchner, Thin-layer Chromatography, Wiley-Interscience, New York, 1978, pp.
5–8.
18. J. C. Moore, J. Polymer Sci. Part A, 2 (1964) 835.
19. L. S. Ettre and A. Zlatkis, eds., 75 years of Chromatography—A Historical Dialog,
Elsevier, Amsterdam, 1979.
20. L. S. Ettre, LCGC, 23 (2005) 486.
21. J. F. K. Huber and J. A. R. Hulsman, J. Anal. Chim. Acta, 38 (1967) 305.
22. J. J. Kirkland, Anal. Chem., 40 (1968) 218.
23. L. R. Snyder, Anal. Chem., 39 (1967) 698, 705.
24. R. P. W. Scott, W. J. Blackburn, and T. J. Wilkens, J. Gas Chrommatogr., 5 (1967) 183.
25. J. J. Kirkland, ed., Modern Practice of Liquid Chromatography, Wiley-Interscience, New
York, 1971.
26. T. Braumann, G. Weber, and L. H. Grimme, J. Chromatogr., 261 (1983) 329.
27. A. J. P. Martin and R. L. M. Synge, Biochem. J., 35 (1941) 1358.
28. A. T. James and A. J. P. Martin, Biochem. J., 50 (1952) 679.
29. L. S. Ettre, LCGC, 19 (2001) 120.
30. J. C. Giddings, Dynamics of Chromatography. Principles and Theory, Dekker, New
York, 1965.
31. L. R. Snyder, J. Chem. Ed., 74 (1997) 37.
32. L. S. Ettre, LCGC Europe, 1 (2001) 314.
33. L. R. Snyder, Anal. Chem., 72 (2000) 412A.
34. C. W. Gehrke, ed., Chromatography—A Century of Discovery 1900–2000, Elsevier,
Amsterdam, 2001.
35. R. L. Grob and E. F. Barry, Modern Practice of Gas Chromatography,4thed.,
Wiley-Interscience, NewYork, 2004.
36. B. Fried and J. Sherma, Thin-Layer Chromatography (Chromatographic Science, Vol.

New York, 2000.

CHAPTER TW O
BASIC CONCEPTS AND THE
CONTROL OF SEPARATION
2.1 INTRODUCTION, 20
2.2 THE CHROMATOGRAPHIC PROCESS, 20
2.3 RETENTION, 24
2.3.1 Retention Factor k and Column Dead-Time t
0
,25
2.3.2 Role of Separation Conditions and Sample Composition, 28
2.4 PEAK WIDTH AND THE COLUMN PLATE NUMBER
N
,35
2.4.1 Dependence of N on Separation Conditions, 37
2.4.2 Peak Shape, 50
2.5 RESOLUTION AND METHOD DEVELOPMENT, 54
2.5.1 Optimizing the Retention Factor k,57
2.5.2 Optimizing Selectivity α,59
2.5.3 Optimizing the Column Plate Number N,61
2.5.4 Method Development, 65
2.6 SAMPLE SIZE EFFECTS, 69
2.6.1 Volume Overload: Effect of Sample Volume on Separation, 70
2.6.2 Mass Overload: Effect of Sample Weight on Separation, 71
2.6.3 Avoiding Problems due to Too Large a Sample, 73
2.7 RELATED TOPICS, 74
2.7.1 Column Equilibration, 74
2.7.2 Gradient Elution, 75
2.7.3 Peak Capacity and Two-dimensional Separation, 76

summarized in Table 2.1. For sample analysis, the predominant HPLC mode in use
today is reversed-phase chromatography (RPC), which features a nonpolar column
in combination with a (polar) mixture of water plus an organic solvent as mobile
phase. Unless noted otherwise, RPC separation will be assumed in this book. Other
HPLC modes are described in later sections of the book, as noted in Table 2.1. In
Chapters 2 through 8 we will assume that the composition of the solvent remains
the same throughout separation, which is called isocratic elution, as opposed to
Samples
Column Detecto
r
Pump
Injection
valve
Solvent
reservoir
Figure 2.1 Schematic of an HPLC system.
2.2 THE CHROMATOGRAPHIC PROCESS 21
gradient elution where the solvent composition is deliberately changed during the
separation (Section 2.7.2, Chapter 9).
The column consists of a cylindrical tube that is typically filled with small
(usually 1.5- to 5-μm diameter) spherical particles (Fig. 2.2a). These particles are
in most cases porous silica, with an individual pore portrayed in Figure 2.2b
as a cylinder of some specified diameter (typically about 10 nm for use with
‘‘small-molecule’’ samples i.e., molecular weights <1000 Da). The inside of each
pore is covered with the stationary phase—in this example, C
18
groups that are
attached to the silica particle. Figure 2.2c shows a more realistic representation of
present-day porous particles for HPLC. The particle is formed by aggregating small,
spherical, subparticles as shown. The actual pores are formed by the spaces between

Porous particle (detail)
particle
Figure 2.2 The HPLC column. (a) Column packed with spherical particles; (b) schematic of
an individual particle, showing an idealized pore with attached C
18
groups; (c) more realistic
picture of a spherical, porous particle, showing detail (10× expansion).
22 BASIC CONCEPTS AND THE CONTROL OF SEPARATION
Table 2.1
HPLC Separation Modes
Chromatographic Mode Comment Details In
Reversed-phase
chromatography (RPC)
The column is nonpolar (e.g., C
18
), and the
mobile phase is a polar mixture of water
plus organic solvent (e.g., acetonitrile);
RPC is the most widely used mode,
especially for water-soluble samples.
Chapter 6, Section
7.3
Normal-phase
chromatography (NPC)
The column is polar (e.g., unbonded silica),
and the mobile phase is a mixture of
less-polar organic solvents (e.g., hexane
plus methylene chloride); NPC is used
mainly for water-insoluble samples,
preparative HPLC, and the separation of

for separating ionizable samples such as
acids or bases, and especially for the
separation of large biomolecules (e.g.,
proteins and nucleic acids).
Sections 7.5, 13.4.2
Ion-pair chromatography
(IPC)
RPC conditions are used, except that an
ion-pair reagent is added to the mobile
phase for interaction with sample ions of
opposite charge; IPC is useful for the
separation of acids or bases that are weakly
retained in RPC.
Section 7.4
Size-exclusion
chromatography (SEC)
An inert column is used with either an
aqueous or organic mobile phase; SEC
provides separation on the basis of
molecular weight and is used mainly for
large biomolecules or synthetic polymers.
Section 13.8
2.2 THE CHROMATOGRAPHIC PROCESS 23
it flows through the column, and sample molecules can enter the particle pores by
diffusion (there is normally no significant flow of mobile phase through the particle).
Figure 2.3 illustrates a hypothetical separation of a sample that contains three
sample compounds (or solutes), with individual sample molecules represented by
•
for solute X,  for solute Y,and for solute Z. For clarity, molecules of
the mobile phase are not shown, and molecules of the solvent that the sample is

5
inlet
outlet
Z
Y
X
+ + + +
+ + + +
sample
solvent
column
Figure 2.3 Illustration of the separation process in HPLC. (a–d) Sequential separation within
the column (i.e., as a function of time); (e) the final chromatogram; (f ) estimating values of
k from the chromatogram (e). Solute molecules X, Y,andZ are represented by
•
, ,and,
respectively; sample solvent molecules are shown by +.
24 BASIC CONCEPTS AND THE CONTROL OF SEPARATION
Differential migration (different average speeds at which solute molecules of
X, Y,andZ move, or migrate, through the column) forms the basis of chromato-
graphic separation. Without a difference in migration rates for two compounds,
their separation cannot occur. In this example molecules of X (
•
) move fastest, and
molecules of Z () move slowest; molecules of the sample solvent or mobile phase
are not retained by the column-packing, pass through the column quickest of all,
and leave the column first. Solvent molecules that form part of the injected sample
are represented in Figure 2.3b–e by +.
As a given solute moves through the column, its molecules become increasingly
spread out, so as to occupy a larger volume within the column. The volume that

x
at which solute X moves through the column is
determined by the fraction R of its molecules that are present in the flowing mobile
phase at any time. On average, u
x
will be equal to R times the migration rate or
velocity u of solvent molecules:
u
x
= Ru (2.1)
For example, if half of the molecules of X are in the mobile phase (R = 0.5) and half
are in the stationary phase, only half of the molecules are moving at any given time,
so the average migration rate of X will be one half as fast as that of the solvent.
As illustrated in Figure 2.4, the fraction R of molecules X in the mobile
(moving) phase is determined by an equilibrium process:
X (mobile phase) ⇔ X (stationary phase) (2.2)
Molecules of X in Figure 2.4 are found equally in the mobile and stationary phase
at any time, while molecules of Z predominate in the stationary phase; that is, Z
2.3 RETENTION 25
mobile
phase
stationary
phase
particl
e
XZ
pore
mobile phase
X
Z

V
s
C
m
V
m
=
C
s
/C
m
V
s
/V
m
= K (2.3)