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Aristotle University of Thessaloniki
RETENTION PREDICTION AND
SEPARATION OPTIMIZATION UNDER
MULTILINEAR GRADIENT ELUTION IN
HPLC WITH MICROSOFT EXCEL
MACROS
S.Fasoula A,*, H. Gika B, A. Pappa-LouisiA, P.
NikitasA
S
Department of Chemistry, Aristotle University of Thessaloniki
B Department of Chemical Engineering, Aristotle University of Thessaloniki
A
The aim
The exploration of Excel 2010 or 2013 capabilities in the
whole procedure of separation optimizations under
multilinear gradient elution in HPLC
Microsoft Excel :
friendly computational
environment
application of systematic
optimization strategies much easier
for the majority of chromatographers
The Excel versions up to 2007 did not equip with the proper optimization
tool.
In the new versions, 2010 and 2013, the Solver add-in provides
optimization capabilities when the cost function is not differential, like
those adopted in liquid chromatography.
2
The steps…
of a computer-assisted separation optimization under multilinear
organic modifier gradient elution based on gradient retention data
Fitting initial gradient data of each solute
to a retention model
1
2
3
Test the capability of the above by
prediction under different conditions
Determination of the optimal gradient
conditions
3
The retention models examined
1.
ln k ( )  c0  c1
3. ln k ( )  c0  c1 ln 
2. ln k ( )  c0  c1  c2 2
k solute retention factor, k=(tR-t0)/t0
tR solute retention time
t0 column dead time
φ is the organic modifier volume fraction
c0, c1, c2 are the adjustable parameters
4. ln k ( )  c0  c1 ln( 1  c2 )
6. ln k ( )  c0 
5. ln k ( )  c0  2 ln( 1  c1 ) 
c2
1  c1
4
c2
1  c1
Determination of retention
by initial gradient data … model
The optimization procedure demands the solution of the fundamental
gradient elution equation
has an analytical solution only in case of
multilinear organic modifier gradient occurs
AND
P.Nikitas, A. Pappa-Louisi,
A. Papageorgiou,
J. Chromatogr. A
1157(2007)178-186
The solute retention is described by
 Retention models 1-5
 Retention model 6 -Nikitas-Pappa's (NP)
approach was adopted for the solution of the
fundamental equation.
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Our approach…
The multilinear gradient profile is divided
into subsections, so that at each φ range the
dependence of ln k vs. φ to be linear,
although the total retention model is not
linear

c2
ln k ( )  c0 
1  c1
6
5
4
2
3

2
1
in
1
0
t1
t2
t3
t4
t5
t6
6
t
Example of the whole
optimization procedure
Step 1
Fitting procedure
Retention data
12 solutes (purines, pyrimidines, nucleosides)
Under 5 different gradient conditions
7
Results…
No
model
1
lnk=c0-c1φ
2
lnk=c0-c1φ+c2φ^2
3
lnk=c0-c1*lnφ
4
lnk=c0-c1*ln(1+c2*φ)
5
lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ)
6
lnk=c0-c2*φ/(1+c1*φ)
method
A-M1
NP-M1
A-M2
NP-M2
fitting
aver % error
2.4
2.6
1.5
1.5
NP-M3
1.6
1.6
A-M4
2.4
A-M5
NP-M5
1.4
1.4
NP-M6
1.4
A-M3
o Even in case an analytical solution exists, sometimes the solver is trapped
M5
Our
andapproach
M6 the
exhibit
istheabest
very
fitting
satisfactory
performance
method
among
the
to 4solve
models
the
with
oo oM3
exhibits
best
between
the 2 models
withthen
two
in local
minima
andfitting
gives performance
unreliable adjustable
parameters,
and
our
three
fundamental
adjustable
gradient
parameters.
elution
equation,
especially
in
case
there
is
no
adjustable
approach parameters
to solve the fundamental gradient elution equation is a good
analytical solution.
alternative method.
8
Step 2
The prediction ability of the retention models derived in
the fitting procedure is detected on the prediction
spreadsheets using the experimental retention data
obtained under 7 mono-linear and 4 bilinear gradient
profiles
Prediction procedure
9
Results…
No
model
1
lnk=c0-c1φ
2
lnk=c0-c1φ+c2φ^2
3
lnk=c0-c1*lnφ
4
lnk=c0-c1*ln(1+c2*φ)
5
lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ)
6
lnk=c0-c2*φ/(1+c1*φ)
fitting
aver % error
2.4
2.6
1.5
1.5
prediction
aver % error
5.2
5.3
3.7
3.7
NP-M3
1.6
1.6
3.6
3.6
A-M4
2.4
5.2
A-M5
NP-M5
1.4
1.4
3.3
3.3
NP-M6
1.4
3.1
method
A-M1
NP-M1
A-M2
NP-M2
A-M3
the M6 model seems to be the proper choice to be used in the
optimization procedure.
10
Step 3
Once the proper retention model is adopted the optimal
gradient profile is determined on the proper optimization
spreadsheet using the corresponding adjustable parameters
Optimization procedure
11
Conclusions
 We created Excel spreadsheets that can be adopted both
for a computer-assisted optimization of
chromatographic separations and for metabolite
identification by the majority of chromatographers
without some experience or knowledge of programming
 Microsoft Excel is a user-friendly environment due to its
unique features in organizing, storing and manipulating
data using basic and complex mathematical operations,
graphing tools, and programming.
12
Acknowledgement
The project is implemented under the Operational
Program “Education and Lifelong learning" and is
co-funded by the European Union (European Social
Fund) and National Resources
(Excellence II: Metabostandards 5204)
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