mechanisms of retention in hplc · hplc’2013 (amsterdam) replaces the outer regions by...

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

2


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

3


7.1. Introduction

7.2. Modified Gaussian models

7.3. Prediction of changes in peak profile

7.4. Peak purity

7.5. Recommended literature


4


7.1. Introduction


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.

5


● 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.


Therefore, there is a need to predict chromatographic peak profiles

as accurately as possible !!!

Advantages of considering peak profiles

6

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

7


7.1. Introduction



7.4. Peak purity



8


7.2. Modified Gaussian models: accurate models to describe peak profiles


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

9


● 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


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

10


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


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.

11


● 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.


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

12


B: right halfwidth A : left halfwidth

f = B/A : asymmetry factor measured at 10% peak height


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

13


● 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


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

14


● Setting the height at each side of the peak region to the respective minimal value.

● Using a modified Gaussian function with a parabolic variance.


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

15


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.


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

16


7.1. Introduction



7.4. Peak purity



17




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

18


Peak parameters


● 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

19


Accuracy in the predictions


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

20


Mean peak shape parameters


M.J. Ruiz-Angel et al. / Analytica Chimica Acta 454 (2002) 109–123

21


● 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.


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

22


● … 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


RA02R11R10 tmAtataaA

RB02R11R10 tmBtbtbbB

(7.12)

(7.13)

Rw02

11R10 Rtmwtmtmmw (7.14) symmetrical peaks

Oral communication OR33


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


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.

24


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


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

25


Gradient elution


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)


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.

26


7.1. Introduction



7.4. Peak purity



27


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


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

28


● 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.


tR

4.0 4.4 4.8 5.2

BA

Time (min)

h0

2

R10

R0

)(2

1exp)(

ttss

tthth

29


Peak purity grants a particularly good performance in

optimisation, owing to several interesting advantages in

comparison with other resolution criteria.


30


● 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


0 pi 1

31




32


● 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:



what the chromatographer actually wishes: peaks free of interferences

33


● 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


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


● Problems related to peak crossing are also avoided, since any other peak in

the chromatogram is considered as interference.



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


● It is possible to optimise the separation of particular compounds (one or several).



36


● 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


n

iipP

1

Globalpeak purity

Elementarypeak purity

s

si

o

op

'1

37


● 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


n

iipP

1lim,lim

38


Comparison of chromatographic systems


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


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


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


Complementary mobile phases


We can also find complementary columns or separation techniques !!!

Poster CMTR26-TU

mechanisms of retention in hplc · hplc’2013 (amsterdam) replaces the outer regions by...

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