MULTIDIMENSIONAL
CHROMATOGRAPHY
Jiří ŠEVČÍK
Prague, the Czech Republic
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MDCH-GENERAL
ABOUT
UNCERTAINTY
MULTIDIMENSIONALITY
INFORMATION CONTENT
MULTIDIMENSIONAL HW
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MDCH-GENERAL
PROBLEMS of measurements
residual error of a complex
response model
n
Y  a   (bi  X i )   i
1
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MDCH-GENERAL
PROBLEMS of measurements
extremly high
number of
isomers
low concentration
levels
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missing
- standards
- generally valid
QSPR models
limited hardware
possibilities
DESCRIPTORS of measurement
MEASUREMENT
LIMITED
QUANTIFIED
BY
residual error of response model
standards
BY
ultimate uncertainty
reproducibility
QSPR models
additivity of probability
hardware
information content
information based instrumentation
identification
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MDCH-GENERAL
what is ULTIMATE UNCERTAINTY
causality
ultimate
uncertainty
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MDCH-GENERAL
EXPRESSING UU
for one-dimensional system
UU  1  Pn   Zn  1/ N
1 rij  1
Rij  
 n
4
rij
 1 rij  1 1

UU  Zn   
4
 Rij
r
ij


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EXPRESSING UU
/
/
t j  ti  t
Zn
UU 
2


w j  4  ti /  t  1/ n
 2t /  t  1

 i
 t /  t 
n
 i

UU is determined by system efficiency
(for one-dimensional system)
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PROBABILITY
of the retention position
x position
l mean component density
P x   l  e
lx
x
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PROBABILITY
of the difference in the retention position
x0 difference
a saturation factor of sep space X
x0
P x  x0   l  e lx dx  1  e lx0  1  e a
0
x0
t1 t2
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MDCH-GENERAL
PEAK CAPACITY
nc peak capacity
a saturation factor of sep space X
x0
1
a  lx0 
m
m
X
nc
x0
t1 t2
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MDCH-GENERAL
PEAK CAPACITY
in isothermal mode
peak width = (a+btx)
t
 a  b  t2 
n 21
1

nc  1 
dt  1 
 ln

4R t t
bR
 a  b  t1 
1
x0
t1 t2
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PEAK CAPACITY
in a linear temperature program mode
peak width = (a)
t2
1 1
1
nc  1   dt  1 
 t2  t1
Rt w
w R
1
x0
t1 t2
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PEAK CAPACITY
comparison of operation modes
peak capacity
The effect of the chromatografic conditions
on the peak capacity in a one-dimensional system
(for R=1 and k<1;10>)
1 000
500
0
0
80 000
plate number
isothermal
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temp.program
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160 000
PROBABILITY
of peak overlapping
n
compounds
Pn  e
2a
in

 1 e
x0
t1 t2
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MDCH-GENERAL
x0

a n 1
PROBABILITY
of peak clusters overlapping
pn number of clusters with the same
number of compounds
pn  m  Pn
p  m  e 2a 
a


1

e

n

n 1
x0
t1 t2
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MDCH-GENERAL
 m  e a
CLUSTERS (n-tets) in
one-dimensional chromatography
Počet singletů v n-tetech
35
30
1
2
25
3
20
4
5
15
6
10
7
5
8
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100000
90000
80000
Počet teoretických pater
10
70000
60000
50000
40000
30000
9
20000
10000
0
n-tet
WHAT is
the chromatographic
dimension
chromatography
(a constant value of KD)
switching
(a straight inlet-separation-detector)
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MDCH-GENERAL
WHAT is
multidimensional
chromatography
(within one run
changes of KD for the same analyte)
switching
(within one run
multiplication of any part of trajectory
inlet-separation-detector)
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WHAT is
hyphenation
can be multi-d-chromatography
(HPLC-GC)
can be multi-d-switching
(FID-MS)
interface of different techniques
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MDCH-GENERAL
PEAK CLUSTERS
in multidimesional chromatography
pn
number of clusters with the same number of compounds
2d a d 
2d a d 

d m
pn
 e
 1  e


n
pd   2d ad  m 
e

 2d a d
1 e
KD2
 2d a d
KD1
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MDCH-GENERAL
n 1
KD3
PEAK CAPACITY
in multidimesional chromatography
nc(d)
maximum number of separated peaks
2d
d
d


nc d  
   1   nci
d
2
 i 1
2

KD2
KD1
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MDCH-GENERAL
KD3
RELATIVE PEAK DENSITY
in multidimensional chromatography
_
p/m
1
0,9
0,8
0,7
0,6
4-D
3-D
2-D
1-D
0,5
0,4
0,3
0,2
0,1
0
0
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1
2
3
_
log(m)
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4
5
6
7
WHAT is
the information content
uncertainty (entropy)
prior to an experiment
and after it
probability that some input and
output events will happen
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WHAT is
the information content
input P(Ii)
prior to an experiment - there is an analyte i
output P(Ok)
after the experiment – there will be a measurable signal
(larger than LOD)
conditional probability
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CONDITIONAL PROBABILITIES
P(Ok/Ii)
there will be the output - measurable signal larger than LOD
when there will be the analyte i as the input
P(Ii/Ok)
there will be the analyte i as the input when there will be
the output - measurable signal larger than LOD
P Ok   P Ii / Ok 
P Ok   P Ii / Ok 
P Ok / Ii  

m
P Ii 
 P Ok   P Ii / Ok 
k 1
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PROBABILITIES
in chromatography
output/input relation
output prob
aposteriory probability
m
m
k
P(Ok/Ii)
P(Ii/Ok)
P(Ok)
k
1
1
apriori probability
1
1
P(Ii)
1
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i
n
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1
i
n
UNCERTAINTY (ENTROPY) of
a priori status H(I)
prior to an analysis
a posteriori status H(I/Ok)
after the signal Ok has been measured
a posteriori status H(I/O)
after the analysis has been performed
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UNCERTAINTY (ENTROPY) of
a priori status H(I)
prior to an analysis
n
H I     P Ii   ld P Ii 
i 1
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MDCH-GENERAL
UNCERTAINTY (ENTROPY) of
a posteriori status H(I/Ok)
after the signal Ok has been measured
n
H I / Ok     P Ii / Ok   ld P Ii / Ok 
i 1
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MDCH-GENERAL
UNCERTAINTY (ENTROPY) of
a posteriori status H(I/O)
after the analysis has been performed
H I / O  
m
 P Ok   H I / Ok 
k 1
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INFORMATION CONTENT
the difference between uncertainties
before and after the analysis has been carried out
I I / O  H I   H I / O
multidimensional
I I /  
d
 Id I / O  I d 
d 1
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INFORMATION CONTENT
ways of quantification
integration
assumption of the normal distribution of
the data and of the measuring error
a histogram
an approach based on maximum
peak capacity
an approach based on real peak
capacity
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QUANTIFICATION
using peak capacity
separation system configuration
(efficiency,
selectivity, operational modes)
sample composition
(number of compounds,
chromatographic similiarities and overlap)
tmax 

 log

tmin 

I  ld nmax   ld
 
R 

 log1 
n 
 
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MDCH-GENERAL
INFORMATION CONTENT
in multidimensional chromatography
mode
IXFR
IMON
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expression
[bit]
1 

2
2
2 2
1 
 A2  1
  A1  1
 RI   
  n2 
  
ld  n1
   3 to 8
4
A
A
100

  
 2 
 
  1 



1 
 A1  1
  I XFR
ld   n1
 4 
 A1 
MDCH-GENERAL
5 to 11
INFORMATION based
GC INSTRUMENTATION
multidimensional column systems
IF (RIA)i= a THEN (RIA)k= c AND (RIA)k= d
hyphenated techniques
P(SA)k <<>> P(SB)k
expert systems
lim Σ(ε)i= 0
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multidimensional chromatography
SYSTEMS
serial
parallel
KD1 <> KD2 <> KDd
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multidimensional chromatography
SERIAL SYSTEMS
recycle
comprehensive
tandem
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SWITCHING MODES
in multidimensional chromatography
SFL
solvent-flush
XFR
transfer
MON
monitoring
BFL
back-flush
TRP
trapping
RJN
re-injecton
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MDCH-GENERAL
PROCESS OF
IDENTIFICATION
matching actual found pattern with true one
- peak identification (noise reduction, integration,
deconvolution)
- peak correlation (similarity link)
- analyte identification (match with standards)
redundant information content
m
A
P Ai    P Si   P  i 
Si 

1
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MDCH-GENERAL
I S obt
I S req
1
MS-SIM separation of GC non
separated isomers
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MDCH-GENERAL
FUTURE INSTRUMENTATION
principle of additivity of partial
probabilities

lim  Pi  1
i 1
2
UU  f (i , Pi , r ij )
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FUTURE INSTRUMENTATION
HW
miniaturization
SW
deconvolution routines
multidimensional statistics
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MDCH-GENERAL
ABOUT
UNCERTAINTY
MULTIDIMENSIONALITY
INFORMATION CONTENT
MULTIDIMENSIONAL HW
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MDCH-GENERAL
MULTIDIMENSIONAL
chromatography
is the analytical approach to
the Bohr principle of
complementarity.
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.