multidimensional chromatography

020213GK MDCH-GENERAL

MULTIDIMENSIONAL

CHROMATOGRAPHY

Jiří ŠEVČÍKPrague, the Czech Republic


ABOUT

UNCERTAINTY

MULTIDIMENSIONALITY

INFORMATION CONTENT

MULTIDIMENSIONAL HW


PROBLEMS of measurements

residual error of a complex response model

n

iii XbaY1

)(


PROBLEMS of measurements

extremly high number of isomers

low concentration levels

missing - standards - generally valid QSPR models

limited hardware possibilities


DESCRIPTORS of measurement

residua l error o f response m odel

sta nda rds

Q SP R m odels

ha rdw a re

L I M I T E D B Y

reproducib ility

identif ica tion

inform a tion ba sed instrum enta tion

inform a tion content

a dd itivity of p roba bility

ultim a te uncerta inty

Q U A N T I F I E D B Y

M EASUREM ENT


what is ULTIMATE UNCERTAINTY

causality

ultimate uncertainty

complementarity

probability


EXPRESSING UU

for one-dimensional system NZPUU nn /11

nrr

Rij

ijij

141

ijij

ijn Rr

rZUU 11

41


EXPRESSING UU

UU is determined by system efficiency (for one-dimensional system)

ttt ij // nttw ij /14 /

nttttZUU

i

in 122 /

/


PROBABILITY of the retention position

x position mean component density

xexP

x


PROBABILITY of the difference in the retention position

x0 difference saturation factor of sep space X

eedxexxP xx

x 11 00

00

x0

t1 t2


PEAK CAPACITY

nc peak capacity saturation factor of sep space X

x0

t1 t2

mn

mXxx

c

100


PEAK CAPACITYin isothermal mode

peak width = (a+btx)

x0

t1 t2

1

2ln1114

12

1tbatba

RbdttR

nnt

tc


PEAK CAPACITYin a linear temperature program mode

peak width = (a)

x0

t1 t2

1211111

2

1

ttRw

dtwR

nt

tc


PEAK CAPACITYcomparison of operation modes

The effect of the chromatografic conditions on the peak capacity in a one-dimensional system

(for R=1 and k<1;10>)

0

500

1 000

0 80 000 160 000

plate number

peak

cap

acity

isothermal temp.program


PROBABILITY of peak overlapping

n compounds in x0

x0

t1 t2

12 1 n

n eeP


PROBABILITY of peak clusters overlapping

pn number of clusters with the same number of compounds

x0

t1 t2

nn Pmp

emeempn

n 1

2 1


CLUSTERS (n-tets) in one-dimensional chromatography

1000

0

2000

0

3000

0

4000

0

5000

0

6000

0

7000

0

8000

0

9000

0

1000

0010

9

8

76

54

32

1

0

5

10

15

20

25

30

35

Poče

t sin

glet

ů v

n-te

tech

Počet teoretických pater

n-tet


WHAT isthe chromatographic

dimension

chromatography (a constant value of KD)

switching (a straight inlet-separation-detector)


WHAT ismultidimensional

chromatography (within one run

changes of KD for the same analyte)

switching (within one run

multiplication of any part of trajectory inlet-separation-detector)


WHAT ishyphenation

can be multi-d-chromatography (HPLC-GC)

can be multi-d-switching (FID-MS)

interface of different techniques


PEAK CLUSTERS in multidimesional chromatography

pn number of clusters with the same number of compounds

KD1

122 1

nd

n dd

dd

eenmp

d

d

dd

e

emp ddd

2

2

12

KD2

KD3


PEAK CAPACITY in multidimesional chromatography

nc(d) maximum number of separated peaks

KD1

KD2

KD3

d

icd

dd

c indn

121

22


RELATIVE PEAK DENSITY in multidimensional chromatography

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5 6 7

log(m)

p/m

1-D 2-D 3-D 4-D

_

_


WHAT isthe information content

uncertainty (entropy) prior to an experiment

and after it

probability that some input and output events will happen


WHAT isthe 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


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

i

kikm

kkik

kikik IP

OIPOP

OIPOP

OIPOPIOP /

/

//

1


PROBABILITIES in chromatography

output/input relation

P(Ok/Ii)

P(Ii/Ok)

P(Ok)

m k 1

aposteriory probability

m k 1

1 i n

1 i n11

output prob

P(Ii)

apriori probability


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



a priori status H(I)prior to an analysis

in

ii IPldIPIH

1



a posteriori status H(I/Ok)after the signal Ok has been measured

kin

ikik OIPldOIPOIH ///

1



a posteriori status H(I/O)after the analysis has been performed

km

kk OIHOPOIH //

1


INFORMATION CONTENT

the difference between uncertaintiesbefore and after the analysis has been carried out

dIOIIIId

dd

//

1

OIHIHOII //

multidimensional


INFORMATION CONTENTways 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


QUANTIFICATIONusing peak capacity

separation system configuration (efficiency, selectivity, operational modes) sample composition (number of compounds, chromatographic similiarities and overlap)

nR

tt

ldnldI1log

logmin

max

max


INFORMATION CONTENTin multidimensional chromatography

mode expression [bit]

IXFR 3 to 8

IMON 5 to 11

2

122

2

22

2

1

11 100

1141 RI

AAn

AAnld

XFRIAAnld

1

11

141


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


multidimensional chromatographySYSTEMS

serialparallel

KD1 <> KD2 <> KDd


multidimensional chromatographySERIAL SYSTEMS

recycle comprehensive

tandem


SWITCHING MODESin multidimensional chromatography

SFL solvent-flushXFR transferMON monitoringBFL back-flushTRP trappingRJN re-injecton


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

ii

mii S

APSPAP1

1

reqobt

SISI


MS-SIM separation of GC non separated isomers


FUTURE INSTRUMENTATION

principle of additivity of partial probabilities

1lim1

iiP

),,( 2iji rPifUU


FUTURE INSTRUMENTATION

HW miniaturization

SW deconvolution routines multidimensional statistics


ABOUT

UNCERTAINTY

MULTIDIMENSIONALITY

INFORMATION CONTENT

MULTIDIMENSIONAL HW


MULTIDIMENSIONALchromatography

is the analytical approach to

the Bohr principle of complementarity.

.

multidimensional chromatography

Documents

ksheet1peak capacity

retention position x

multidchromatography

saturation factor

retention position x0

system efficiency

straight inletseparation

trajectory inletseparation