Post on 28-Sep-2020
1
Mechanisms of retention in HPLCMechanisms of retention in HPLC
María Celia García-Álvarez-Coque
Department of Analytical Chemistry
University of Valencia
Valencia, Spain
https://sites.google.com/site/fuschrom/
HPLC’2013 (Amsterdam)
Part 7Part 7
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HPLC’2013 (Amsterdam)
1. Retention in reversed-phase, normal-phase and HILIC
2. Secondary equilibria in reversed-phase liquid chromatography: Part A
3. Secondary equilibria in reversed-phase liquid chromatography: Part B
4. Retention modelling (quantification or prediction): Part A
5. Retention modelling (quantification or prediction): Part B
6. Gradient elution
7. Peak profile and peak purity
8. Computer simulation
Index
Mechanisms of retention in HPLC
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HPLC’2013 (Amsterdam)
7.1. Introduction
7.2. Modified Gaussian models
7.3. Prediction of changes in peak profile
7.4. Peak purity
7.5. Recommended literature
7. Peak profile and peak purity
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HPLC’2013 (Amsterdam)
7.1. Introduction
7. Peak profile and peak purity
The main goal in method development is obtaining resolved peaks.
The optimisation of resolution is usually carried out using
information from simplified chromatograms, where only retention
times are taken into account. This treatment is supported by the
idea that the most relevant peak property affecting resolution is
retention. Realistic simulations of chromatograms require, however,
more elaborated treatments, where peak profiles are considered.
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HPLC’2013 (Amsterdam)
● A comprehensive prediction of resolution with mobile phase composition and other
factors requires a full simulation of chromatograms, built by adding the individual peaks.
Resolution criteria based solely on retention are less informative and reliable. This is
especially true for asymmetrical peaks.
● Accurate simulations allow checking the quality of predictions by comparison with the
corresponding experimental chromatograms.
● In most situations, normalised areas can be considered, but to take into account a minor
component, areas of individual peaks are needed to get a reliable optimisation.
7. Peak profile and peak purity
Therefore, there is a need to predict chromatographic peak profiles
as accurately as possible !!!
Advantages of considering peak profiles
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HPLC’2013 (Amsterdam)7. Peak profile and peak purity
0 5 10 15 20 25 30 35
Acebutolol
Celiprolol
Esmolol
Metoprolol
Oxprenolol
Pindolol
Propranolol
Timolol
Alprenolol
Ate
no
lol
Predicted
0 5 10 15 20 25 30 35
Propranolol
AlprenololCeliprolol
Oxprenolol
Esmolol
Acebutolol
Metoprolol
Timolol
Pin
dlo
l
Ate
no
lol
Experimental
Time, min
0 10 20 30 40 50 60 70
Alprenolol + Propranolol
OxprenololCeliprolol
Esmolol
Metoprolol
Acebutolol
Timolol
Pindolol
Atenolol Predicted
0 10 20 30 40 50 60 70
Alprenolol + Propranolol
Oxprenolol
Celiprolol
Esmolol
Metoprolol
Acebutolol
Tim
olo
lP
ind
olo
l
Atenolol
+
Time, min
Experimental
18.1% ACN 10.0% ACN
HMIM·BF4 0.0244 M
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HPLC’2013 (Amsterdam)
7.1. Introduction
7.2. Modified Gaussian models
7.3. Prediction of changes in peak profile
7.4. Peak purity
7.5. Recommended literature
7. Peak profile and peak purity
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HPLC’2013 (Amsterdam)
7.2. Modified Gaussian models: accurate models to describe peak profiles
7. Peak profile and peak purity
The elution profiles of symmetrical and non-overloaded chromatographic
peaks are well described by the Gaussian model. Non-ideal peaks (either
tailing or fronting) are, however, quite common in practice.
More than a hundred theoretical and empirical mathematical functions have
been reported for the description of peak profiles in different fields.
Time (min)
4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4
Non-Gaussiantailing peak
12.0 12.5 13.0 13.5 14.0 14.5 15.0
Time (min)
Gaussianpeak
2
02
1exp
Rtt
hh
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HPLC’2013 (Amsterdam)
● To be practical, the model should take advantage of the properties usually
monitored (retention time, width or efficiency, asymmetry, and area or height).
Modelling of skewed peaks
7. Peak profile and peak purity
An adequate and handy mathematical peak model is needed to describe
each peak in a chromatogram.
tR
4.0 4.4 4.8 5.2
BA
Time (min)
w = A + B
h0
f = B/A
ABBA
tN
/25.1)(
7.412
2R
Foley and Dorsey
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HPLC’2013 (Amsterdam)
h(t) : height at time t h0 : maximal peak height
tR : solute retention time
s0 : measurement of the peak width at the peak maximum assuming a Gaussian
s1 and higher order terms : account for peak distortion
Polynomially modified Gaussian model
7. Peak profile and peak purity
One of these handy equations consists of a modification of the Gaussian
equation, where the standard deviation varies with the distance to the peak
maximum, which has been called polynomially modified Gaussian (PMG).
(7.1)
2
2R2R10
R0
...)()(2
1exp)(
ttsttss
tthth
In spite of the apparent complexity, implementing the PMG model in a
programming language is straightforward, and the degree of realism that it
confers to the optimisation system is worthwhile.
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HPLC’2013 (Amsterdam)
● The higher the degree, the more flexible the model, and the more the chances to fit
the experimental data.
● No limit to the polynomial degree, but in practice, parabolic (PMG2) or cubic (PMG3)
functions are enough to account for most chromatographic signals.
● The chromatogram of a sample may contain a large number of peaks that should be
modelled or predicted individually: optimisation of chromatographic resolution.
a PMG model with a linear standard deviation term (PMG1) is the most
convenient to reduce the computation time.
7. Peak profile and peak purity
The equation represents a family of models, since the polynomial degree within
the standard deviation term can be changed.
2
R10
R0
)(2
1exp)(
ttss
tthth
2
2R2R10
R0
...)()(2
1exp)(
ttsttss
tthth
PMG1
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HPLC’2013 (Amsterdam)
B: right halfwidth A : left halfwidth
f = B/A : asymmetry factor measured at 10% peak height
7. Peak profile and peak purity
2
R10
R0
)(2
1exp)(
ttss
tthth
(7.2)
1/
1/466.01
AB
ABs
1/
1/1
/
11
466.02
0AB
AB
AB
BAs
(7.3)
10% peak height
Time (min)
4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4
BA
this accounts for the peak
asymmetry and avoids
the base-line noise
PMG1
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HPLC’2013 (Amsterdam)
● The base-line increase is troublesome in optimisation, where the signal of individual peaks
should be added to give composite signals.
● The artefacts are more prominent for strongly asymmetrical signals (B/A > 2.5), and for
simulations involving long time windows.
Base-line increase
7. Peak profile and peak purity
It has been said that the PMG model can fit almost any peak. However,
it gives problematic baseline increases out of the peak region.
Time (min)
PMG1 - - - -
PMG2
the peaks should be restored
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HPLC’2013 (Amsterdam)
● Setting the height at each side of the peak region to the respective minimal value.
● Using a modified Gaussian function with a parabolic variance.
7. Peak profile and peak purity
2RR
20
2R
0)()(
)(
2
1exp)(
ttbttas
tthth
20s
AB
ABa
AB
sb
201
(7.5)
(7.6)
(7.4)
10.8 11.2 11.6 12.0
Time, min1 2 3 4 5 6 7 8 9
ALT
CHL
BEN XIPETH
SPI
Time, min
Solutions to the PMG base-line increase
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HPLC’2013 (Amsterdam)
Replaces the outer regions by exponential decays at
each side of the PMG peak at 10% peak height, hold to
the restriction that the slopes of the modified Gaussian
and exponential functions at the respective connecting
points should coincide.
7. Peak profile and peak purity
Bttttkkh
Attttkkh
RRright2,right1,
RRleft2,left1,
for)}({exp
for)}({exp(7.7)
310
0left2,
)( Ass
Ask
)(exp1.0 left,20left1, Akhk
310
0right2,
)( Bss
Bsk
)(exp1.0 right,20right1, Bkhk
(7.8)
(7.9)
(7.10)
(7.11)
Time (min)
4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4
exponentialdecays
10% peakheight
Mixed exponential-PMG function
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HPLC’2013 (Amsterdam)
7.1. Introduction
7.2. Modified Gaussian models
7.3. Prediction of changes in peak profile
7.4. Peak purity
7.5. Recommended literature
7. Peak profile and peak purity
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HPLC’2013 (Amsterdam)
7.3. Prediction of changes in peak profile
7. Peak profile and peak purity
Band profiles are the result of partitioning and adsorption/desorption
processes within the column and extra-column effects.
0 10 20 30 40 50 60
1
2
3
4 5
6
7 89
10
Time, min
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HPLC’2013 (Amsterdam)
Peak parameters
7. Peak profile and peak purity
● The within column processes are affected by the mobile phase composition and
chemical changes in the solute.
● Changes in organic solvent and additive concentration, pH, and other factors,
such as ionic strength, may alter the peak profiles.
Efficiency (N) and asymmetry degree (B/A), or the individual A and B values, summarise
the relative peak width and skewness. Thus, their prediction can be expected to allow,
together with retention and peak area, the required prediction of chromatographic bands
in an optimisation process.
ABBA
tN
/25.1)(
7.412
2R
tR
4.0 4.4 4.8 5.2
BA
Time (min)
w = A + B
h0
f = B/A
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HPLC’2013 (Amsterdam)
Accuracy in the predictions
7. Peak profile and peak purity
Models for the prediction of the peak profile parameters are less accurate than
those for the prediction of retention. In spite of the poorer accuracy, better
predictions will be achieved by considering variations in the peak profile
parameters with mobile phase composition for each solute, with regard to those
obtained using a common value for all solutes and mobile phases, or even,
particular mean values for each solute in the training set.
0
10
20
30
40
0 10 20 30 40
Experimental retention time (min)
Pre
dic
ted
rete
nti
on
tim
e (
min
)
0.0
0.4
0.8
1.2
1.6
0 0.5 1.0 1.5 2.0
Pre
dic
ted
wid
ths
(min
)
Experimental widths (min)
1.0
1.4
1.8
1.0 1.4 1.8 2.2
Pre
dic
ted
asym
metr
yExperimental asymmetry
15 sulphonamides
C18 / 17.1% acetonitrile
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HPLC’2013 (Amsterdam)
Mean peak shape parameters
7. Peak profile and peak purity
M.J. Ruiz-Angel et al. / Analytica Chimica Acta 454 (2002) 109–123
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HPLC’2013 (Amsterdam)
● Attend the variations in the neighbourhood of the predicted point.
● Experimental data obtained with the closest available mobile phases to that predicted are
used: the prediction of peak profile parameters can be as straightforward as a weighted
mean or a linear interpolation.
7. Peak profile and peak purity
Local or global models can be used to predict peak profile parameters.
Linear interpolation
A = a0 X + a1 Y + a2
B = b0 X + b1 Y + b2
X = Factor 1
Y = Factor 2
Local models
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HPLC’2013 (Amsterdam)
● … model the global trend of the training set or for each particular solute at varying
experimental conditions.
● If an adequate correlation can be established between the peak profile parameters
(A and B) and the retention time (which can be predicted with high accuracy), the
peak parameters will also be predicted with sufficient accuracy.
● The correlations are parabolic (almost linear):
A0 , B0 , w0 : related to the extra-column broadening
mA , mB , mw : rates of increase of the peak halfwidths or width with retention time
Global models
7. Peak profile and peak purity
RA02R11R10 tmAtataaA
RB02R11R10 tmBtbtbbB
(7.12)
(7.13)
Rw02
11R10 Rtmwtmtmmw (7.14) symmetrical peaks
Oral communication OR33
HPLC’2013 (Amsterdam)
23
2 4 6 8 10 12
0.1
0.2
0.3H
alf
wid
th(m
in)
Time (min)
Phenols / X-Terra
B
A
0.0
0.4
0.8
1.2
0 10 20 30 40
Time (min)
Phenols / Chromolith
B
A
7. Peak profile and peak purity
Halfwidths plots
All compounds eluted in a given RPLC column and experiencing similar kinetics have
been observed to follow a similar trend of variation of peak halfwidths with retention
time. The halfwidth plots allow characterising column performance using peak profile
parameters for compounds eluted at diverse retention times.
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HPLC’2013 (Amsterdam)7. Peak profile and peak purity
For compounds experiencing slow adsorption-desorption processes, the
slope of the straight-lines increases, especially for the right halfwidth.
Retention time (min)
0 5 10 15 20
Half
wid
th(m
in)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6Zorbax
no additive
Retention time (min)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Zorbax
HMIM·BF4
Half
wid
th(m
in)
Slow kinetics
Elution of basic compounds
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HPLC’2013 (Amsterdam)
Gradient elution
7. Peak profile and peak purity
2
g
gR
g
gR0
t
ttc
t
ttb
A
AA
(tR – tg) / tg
0 0.5 1 1.5 2 2.5
0
2
4
6
8
(A0 -
A)
/ A
(7.15)
A0 and tR : isocratic A and tg : gradient
0 20 40 60 80 100
0
0.4
0.8
1.2
1.6
2.0
Half
wid
th(A
, m
in)
Retention time (min)
m = 0
m = 0.8% (v/v)
compressioneffect
The concentration of organic modifier in isocratic conditions is assumed
to be the same as the concentration at the beginning of the gradient.
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HPLC’2013 (Amsterdam)
7.1. Introduction
7.2. Modified Gaussian models
7.3. Prediction of changes in peak profile
7.4. Peak purity
7.5. Recommended literature
7. Peak profile and peak purity
27
HPLC’2013 (Amsterdam)
oi : total area of the peak of interest
o’i : area under the peak overlapped by a
hypothetical chromatogram built with the
peaks of the accompanying compounds in
the sample (the possible interferences)
7.4. Peak purity
7. Peak profile and peak purity
Peak purity (peak area fraction free of interference or complement of
the overlapped fraction) is the ideal measurement to quantify peak
overlapping in a chromatogram.
i
ii
o
op
'1 (7.16)
tR
i
h0oi ’o’i
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HPLC’2013 (Amsterdam)
● The calculation of peak purities requires the prediction not only of the peak
position but also its profile, that is, the width and asymmetry for each peak in a
chromatogram.
● A resolution measurement based on the concept of peak purity was proposed
long time ago, but used marginally until the last decade, since its calculation is
only feasible through numerical computation. Fortunately, the state-of-the-art of
computers and the proposal of more practical peak models have revived its
interest.
7. Peak profile and peak purity
tR
4.0 4.4 4.8 5.2
BA
Time (min)
h0
2
R10
R0
)(2
1exp)(
ttss
tthth
29
HPLC’2013 (Amsterdam)
Peak purity grants a particularly good performance in
optimisation, owing to several interesting advantages in
comparison with other resolution criteria.
7. Peak profile and peak purity
30
HPLC’2013 (Amsterdam)
● It considers not only the peak position, but also its profile and size.
Therefore, the resolution diagrams provide a more realistic picture of the
system separation performance.
● It is a normalised measurement that ranges between zero for full overlapping
to one for full resolution, and depends on the relative peak areas. Its meaning
is therefore very intuitive:
peak purity p = 0.95 just means that
95% of the peak is free of interferences
(or 5% is overlapped)
Peak purity: realistic and intuitive
7. Peak profile and peak purity
0 pi 1
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HPLC’2013 (Amsterdam)
Peak purity: realistic and intuitive
7. Peak profile and peak purity
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HPLC’2013 (Amsterdam)
● Non-normalised measurements as RS grows indefinitely with peak separation,
even once the peaks are baseline resolved and a further separation is useless.
This forces the introduction of thresholds in RS that depend on peak asymmetry.
● With peak purities, weights or truncations in the function are not required to
delimit when baseline separation has been reached, and further resolution is
useless.
● Peak purity correlates particularly well with the appraisal of resolution of expert
analysts, even for peaks remarkably skewed and overlapped.
● The reason is that it is related to:
Peak purity: realistic and intuitive
7. Peak profile and peak purity
what the chromatographer actually wishes: peaks free of interferences
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HPLC’2013 (Amsterdam)
● It provides the separation quality for each individual peak, instead of each
peak pair. This provides an unambiguous relationship between compound
identities and numerical values.
● This makes certain operations, such as weighting or exclusion of peaks
easier.
Peak purity: individual measurement
7. Peak profile and peak purity
0 10 20
1
23
4
5
67
8
910
Time, min
Kromasil column
15% (v/v) acetonitrile
0.1125 M SDS
pH 3
34
HPLC’2013 (Amsterdam)
● Problems related to peak crossing are also avoided, since any other peak in
the chromatogram is considered as interference.
Peak purity: individual measurement
7. Peak profile and peak purity
1 45
0 10 20 30 40 50 60 0 1 2 3 4 5
2
3
4 5
6
7 8 9
10
1
2
3
6 78
910
Time, min Time, min
15% acetonitrile 30% acetonitrile
35
HPLC’2013 (Amsterdam)
● It is possible to optimise the separation of particular compounds (one or several).
Peak purity: individual measurement
7. Peak profile and peak purity
36
HPLC’2013 (Amsterdam)
● It is an intrinsically normalised measurement. Therefore, the combination of
elementary resolutions into a single global value is facilitated and, eventually,
the further combination with other quality criteria.
● However, the interpretation of the global resolution is less evident than for the
elementary values, since it includes other effects, such as the number of peaks
and the distribution of the individual values.
Peak purity: normalised measurement
7. Peak profile and peak purity
n
iipP
1
Globalpeak purity
Elementarypeak purity
s
si
o
op
'1
37
HPLC’2013 (Amsterdam)
● Limiting peak purity (the maximal elementary value found for each solute):
indicates the maximal expectancy of resolution for each solute in the experimental
domain.
● If the limiting value is small, no mobile phase will resolve the solute: the capability
of the system is already fully exploited, and a further enhancement will need a
drastic change in the separation system.
The combined limiting peak purity prospects the global capability of the
chromatographic system !!!
Peak purity: new resolution measurements
7. Peak profile and peak purity
n
iipP
1lim,lim
38
HPLC’2013 (Amsterdam)
Comparison of chromatographic systems
7. Peak profile and peak purity
0.9550.91295.5
0.5430.50993.7
0.2200.088540.2
Global%
1.0001.0000.8080.8080.9950.797Timolol
1.0001.0000.9780.9780.9880.988Sotalol
1.0001.0000.9950.9630.6170.600Propranolol
0.9770.9771.0001.0001.0001.000Pindolol
1.0001.0001.0001.0000.9980.969Oxprenolol
0.9780.9780.9390.9390.7690.740Nadolol
1.0001.0001.0001.0001.0000.988Labetalol
1.0001.0001.0001.0001.0000.879Esmolol
1.0001.0001.0001.0001.0000.874Celiprolol
1.0001.0000.9390.9390.7690.745Carteolol
1.0001.0001.0001.0001.0000.958Bisoprolol
1.0001.0000.9780.9780.9930.992Atenolol
1.0001.0000.9950.9630.6220.606Alprenolol
1.0001.0000.8070.8070.9950.801Acebutolol
plimpoptplimpoptplimpopt
C18 / SDS / propanolDeactivated C18 / acetonitrile
C18 / acetonitrile / TEACompound
39
HPLC’2013 (Amsterdam)7. Peak profile and peak purity
The fact that it is able to anticipate the maximal resolution
capability of the separation system is particularly useful
for tackling low resolution situations, where conventional
resolution criteria fail. This is made by counting the
resolved peaks (peak count).
Peak purity: new optimization strategies
40
HPLC’2013 (Amsterdam)7. Peak profile and peak purity
Compounds with p ≥ 0.90
0 10 20 30 40 50 60
2 4 6 8 10
pH = 3
1224
2023810111
14+25
9
2122
1516
19
27
4
3
75217
6
28
29
26+30+18+13 30% acetonitrile
Peak count = 12
0 10 20 30 40 50 60
2 4 6 8 10
Time, min
1724202319
2527
2221
1829
262810
30+168+12
15
14+7+1511
13+3+46+1+5+2pH = 12
Peak count = 8
41
HPLC’2013 (Amsterdam)
Complementary mobile phases
7. Peak profile and peak purity
We can also find complementary columns or separation techniques !!!
Poster CMTR26-TU