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CALIBRATION METHODS NOMENCLATURE AND CLASSIFICATION
Pawe Kocielniak
Department of Analytical ChemistryFaculty of Chemistry, Jagiellonian University
Poland
PROBLEMS
In analytical chemistry: there is inevitable necessity of carrying out calibration, but
there is a lack of clearly defined, current nomenclature
relating to the domain of analytical calibration
Such a situation can become a source of misunderstandings and obscurities,which
can cause improper or wrong analytical proceeding,
can create didactic difficulties,
ANALYTICAL PROCEDURE
SAMPLING
DIGESTION
SAMPLE PREPARATION
ANALYTICAL CALIBRATION
GENESIS OF CALIBRATION
R = F ( ca )
R = f (ca; cd1, cd2, , cdn; pa1, pa2, , pam; pc1, pc2, , pck)
INTERFERENTSINSTRUMENTAL
PARAMETERS
PHYSICOCHEMICAL
PARAMETERS
R = F ( ca )
GENESIS OF CALIBRATION
R = f (ca; cd1, cd2, , cdn; pa1, pa2, , pam; pc1, pc2, , pck)
INTERFERENTS INSTRUMENTALPARAMETERS PHYSICOCHEMICALPARAMETERS
R = F ( ca )
R = f (K; ca; cd1, cd2, , cdn)
GENESIS OF CALIBRATION
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CALIBRATION
reconstruction of the calibration dependence, R=F(ca),to the empirical form (i.e. to the calibration graph)with the use of the standard solution(s) and
transformation of the measurement data obtained for the sampleto the analyte concentration
Three steps of a calibration procedure:- laboratory treatment,
- measurement,- mathematical and statistical calculations.
RECONSTRUCTION
R
ca
calibration dependence
RECONSTRUCTION
R
ca
calibration dependence
calibration graph
TRANSFORMATION
R
ca
Rx
cax
calibration dependence
calibration graph
TERMINOLOGY
Calibration procedure A detailed mode of performing particular stages
(laboratory, measurement and mathematical) of the calibration
Calibration method specific way of realization of the calibration procedure,
characteristic in terms of both the transformation and reconstruction ways,leading not only to main calibration purposes
but additionally to a special analytical aim
CALIBRATION METHODS
Batch analysiscalibration curve methodset of standards methodstandard addition method
dilution methoddilution and successive addition methodinternal standard method
Flow analysisinterpolative standard addition methodgradient ratio calibration method
exponential dilution flask calibration methodmix and match method
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NEW CLASSIFICATION
New classification is based on:- how the calibration dependence is reconstructed, and
- how the measurement data are transformed
NEW CLASSIFICATION
New classification is based on:- how the calibration dependence is reconstructed, and
- how the measurement data are transformed
All calibration methods used in chemical analysiscan be divided to three categories:- interpolative-extrapolative
-indicative
R
ca
Rx
R
ca
Rx
cax cax
R
ca
Rx
cax
INTERPOLATIVE EXTRAPOLATIVE INDICATIVE
CALIBRATION METHODS IN NEW CLASSIFICATION
(Ra/Rs)N
Ra/Rs
ca
0 ca1 ca2 ca3 caN
(Ra/Rs)1
(Ra/Rs)0
(Ra/Rs)x
(Ra/Rs)2
(Ra/Rs)3
RaN
Ra
ca
0 ca1 ca2 ca3 caN
Ra1
Ra0
Rax
Ra2
Ra3
A
C
Ra1
Ra
ca
0 ca1
RaN
R0
Rax1
Ra3
Ra2
D
Rbx
Rb3
Rb
ca
0 ca1 ca2 ca3 caN
B
RbN
Rb0
Rb1
Rb2
cax
Rax2
RaxN
Rax3
cax
cax cax
~
~ ~
~
~
~
BIndirect
InterapolativeMethod (IIM)
AConventionalInterpolativeMethod (CIM)
CInterpolative
Internal StandardMethod (IISM)
DInterpolative
DilutionMethod (IDM)
RaN
Ra
ca0 ca1 ca2 ca3 caN
Ra1
Ra0
Rax
Ra2
Ra3
cax~
~
CONVENTIONAL INTERPOLATIVE METHOD (CIM)
easy, convenient, fast
most popularRbx
Rb3
Rb
0 ca1 ca2 ca3 caN
RbN
Rb0
Rb1
Rb2
cax
~
~ca
INDIRECT INTERPOLATIVE METHOD (IIM)
gives a chance to determinenew analytes
application of an analyticalmethod is expanded
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(Ra/Rs)N
Ra/Rs
ca
0 ca1 ca2 ca3 caN
(Ra/Rs)1
(Ra/Rs)0
(Ra/Rs)x
(Ra/Rs)2
(Ra/Rs)3
cax~
~
INTERPOLATIVE INTERNAL STANDARD METHOD (IISM)
gives a chance to compensatethe random fluctuations of
analytical signals
precision of the analytical resultscan be improved
Ra1
Ra
ca
0 ca1
RaN
R0
Rax1
Ra3
Ra2
cax
Rax2
RaxN
Rax3
INTERPOLATIVE DILUTION METHOD (IDM)
gives a chance to eliminatethe interference effects
accuracy of the analytical resultscan be improved
RaN
Ra
ca
0 ca1 ca2 caN
~
Rax
Ra1
Ra2
A
Ra1
Ra
R0
Ra3
Ra2
D
Rbx
Rb2
Rb
ca
0 ca1 ca2 ca3
~
B
~RbN
Rb0
Rb1
-cax -cax
Ra0
(Ra/Rs)N
Ra/Rs
ca
0 ca1 ca2 caN
(Ra/Rs)x
(Ra/Rs)1
(Ra2/Rs)2
C
-cax
(Ra/Rs)0 ca
0 ca1-cax
Rax2
Rax1
RaxN
Rax3
RaN
~
~
~
BIndirect
ExtrapolativeMethod (IEM)
AConventionalExtrapolativeMethod (CEM)
CExtrapolative
Internal StandardMethod (EISM)
DExtrapolative
DilutionMethod (EDM)
INTERPOLATIVE VS. EXTRAPOLATIVE METHODSRa
ca0
Rax
-cax-cax
a
b
b
a
a
Ra
ca0
Rax
cax cax
a
a
a calibration dependence
a calibration dependence reconstructed appropriately by the calibration graph
b - calibration dependence reconstructed wrongly by the calibration graph
In contrast to the interpolative methods the extrapolative methodsgive a chance to compensate for the interfrence effect
0
Rb
ca
Rbx
cax
V
Vx0
INDICATIVE METHOD - TITRATION
- standard solution is added to thesample- analyte is not present in a sample
- a component of the standardsolution reacts selectively withan analyte
accuracy of the analytical results canbe considerably improved
GENERAL CHARACTERIZATIONOF THE CALIBRATION METHODS
with the aid of thecalibration graph takinginto account the locationof a characteristic
experimental point
on the basis of measurement dataobtained as a result of chemical reactionoccurring between an analyte containedin the sample solution and a component
of a single standard solution beingprogressively coupled with the sample
indicative
with the aid of thecalibration graph in theinterpolative way
on the basis of measurement data
obtained for a set of standard solution
(rarely for a single standard solution)
containing analyte being added the
sample solution
extrapolative
with the aid of thecalibration graph in theinterpolative way
on the basis of measurement dataobtained separately for a set of standardsolution (rarely for a single standardsolution) containing analyte and for thesample solution
interpolative
Transformation of themeasurement dataReconstruction of the calibrationdependenceethod
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CALIBRATION METHODS VS. INTERFERENCE EFFECT
+ + + + +indicative
- + + + +EDM- + + + +EISM- + + + +IEM- + + + +CEM
extrapolative
- - + + +IDM- - - + +IISM- - - - +IIM- - - - -CIM
interpolative
Resistance againstinterference effectsethod
EXTRAPOLATIVE / INTERPOLATIVE METHOD
Ra
ca0
(Rax)I
(-cax)III(-cax)I
(Rax
)III
(Rax)II
(-cax)II
INDICATIVE / INTERPOLATIVE METHOD
M
sample
WDet
P
titrant
V
Time(s)
10
10
10
s
0
0
0
20
20
20
30
30
30
40
40
40 50
50
50
60
60
70 80
T
r
a
n
s
m
i
ta
n
c
e
pH = 2.0
pH = 1.0
pH = 1.4
pHx
0 pH1 pH2 pH3 pH4
s
pH
sx
CONCLUSIONS
The classification allows the calibration procedures proposed in literature to be ordered andclarified
The classification is opened, i.e. the possibility is taken into consideration of developing ofnew calibration methods and introducing them to this classification
The classification inspires to develop new methods, e.g. by means of coupling of existingcalibration approaches
If titration is agreed to be considered as the calibration method, the common classificationof the analytical methods should be changed, e.g.
COULOMETRYDirect coulometry
Coulometric titrationCOULOMETRY
Calibration by the interpolative methodsCalibration by the extrapolative methods
Calibartion by the indicative method