calibration method

7/29/2019 calibration method

1/5

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 )


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)



2/5

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 graph

TRANSFORMATION

R

ca

Rx

cax


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


3/5

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


4/5

(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


5/5

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

calibration method

Documents