Introduction to Isotope Dilution Analysis

Nacho García AlonsoUniversity of Oviedo

1. The concept of Isotope Dilution.2. The isotopic nature of the elements.3. The isotope dilution experiment: basic equations.4. Advantages and disadvantages.5. Measurement of isotope abundances by MS: Applications in elemental and organic analysis.6. On-line isotope dilution analysis.7. Conclusions.

The concept of Isotope Dilution

How many yellow marbles are in the box?

64 black marbles

+ =

For analysis we take an aliquot from the sample and measure the ratio of yellow to black marbles

From the measured ratio we can calculate the total number of yellow marbles in the box.

The concept of Isotope Dilution Analysis

BYX

=64 2568/32*64 ==X

Concept of Concept of ““ Isotope RatioIsotope Ratio ””

8 black marbles (B)

32 yellow marbles (Y)

Mass SpectrometerMass Spectrometer

The isotopic nature of the elements

Isotopes are different “manifestations” of the same chemical element (defined by its number of protons and electrons ) with a variable number of neutrons in their nucleus.

Carbon-12 Carbon-13

• Isotopes of one element possess different atomic masses .

• Isotopes can be stable or unstable (radioactive).

• The chemical behaviour of all isotopes of an element is almostindependent of its mass (isotopic effects).

Carbon-14X

The isotope composition of the elements in Nature

Isotope Exact mass Abundance1H 1.007825 0.999852H 2.014102 0.0001512C 12.000000 0.989313C 13.003355 0.010714N 14.003074 0.996315N 15.000109 0.003716O 15.994915 0.9976217O 16.999131 0.0003818O 17.999159 0.00200

Isotope Composition of the Elements, 2001. J. Phys. Chem. Ref. Data, 34(2005)57-67.

0

5

10

15

20

25

30

35

112 113 114 115 116 117 118 119 120 121 122 123 124 125

Mass

Abu

ndan

ce (

%)

The isotope composition of natural abundance tin

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1561 1562 1563 1564 1565 1566 1567

Nominal mass

Abu

ndan

ce

Mass isotopomer distribution of a peptide of formula C68H107N17O25

The isotope composition of chemical compounds

1313CC111212CC6767

11HH1071071414NN1717

1616OO2525 oror1212CC6868

22HH1111HH106106

1414NN17171616OO2525 oror

1212CC686811HH107107

1515NN111414NN1616

1616OO25 25 oror1212CC6868

11HH1071071414NN1717

1717OO111616OO2424

1212CC686811HH107107

1414NN17171616OO2525

Visual Basic macro for the calculation of massisotopomer distributions in Excel.

The isotope composition of bovine insulin (C 254H377O75N65S6)

Isotopically enriched atoms and compounds

Na213CO3 99%

enrichment

Isotope Se74 Se77 Se Nat74 0.9967 0.0011 0.008976 0.0006 0.0070 0.093777 0.0003 0.9455 0.076378 0.0007 0.0294 0.237780 0.0015 0.0149 0.496182 0.0003 0.0022 0.0873

Isotopically enriched forms of selenium

OH OHOH

Phenol 13C1-Phenol 13C6-Phenol

Isotopically labelled phenols

The black marbles

The Isotope Dilution experiment

An unknown number of atoms (molecules) of an element(compound) with natural isotope composition, sample , isspiked with a known number of atoms (molecules) of thesame element (compound) enriched in a minor isotope, spike . After isotope equilibration, the isotope composition in theblend is measured by Mass Spectrometry.

Natural abundance Isotopically enriched Blend

Basic equation

enrnatm NNN +=

ienr

inat

im NNN +=

ienrenr

inatnat

imm ANANAN ×+×=⋅

ienrenr

inatnat

im AxAxA ×+×=

Global molar balance:

Molar balance for the i isotope (-omer):

Molar balance using isotope abundances:

Dividing by the global molar balance we get:

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+⎥⎦

⎤⎢⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−−−−

n

n

enr

nat

nenr

nnat

nenr

nnat

enrnat

enrnat

enrnat

nm

nm

m

m

m

e

e

e

e

e

x

x

AA

AA

AA

AA

AA

A

A

A

A

A

1

3

2

1

11

33

22

11

1

3

2

1

....

.........

enrnat

natnat NN

Nx

+=

enrnat

enrenr NN

Nx

+=

enr

nat

enr

nat

xx

NN

=

Where:

are the molar fractions for the natural and enriched forms.

The molar fractions can be calculated by multiple least squares (n>2):

The final isotope dilution equation:

and

Calculation of molar fractions

Using the function “LINEST” in Excel

Abundances of pure components

Abundances in the blend

Molar fractions

Advantages of Isotope Dilution Analysis

Relative measurements (isotope abundances).

Ideal internal standard ( the same element/compound ) Correction for signal driftCorrection for matrix effects

Quantitative separation processes are not required.

Losses of substance are compensated.

Methodological calibration graphs are not needed.

Excellent precision and accuracy.

Blend

Certifiedweights

(CALIBRATION)

Standard Kg Sample

Samplepreparation

Spike

Mass Spectrometer

Measurementof isotope

abundances

Sample weightAnalyte weight

Conc =.“Instrumental calibration”

To ensure the accuracy of the measured isotope

abundances in the blend

Primary measurement method: Traceability chain

Isotope Dilution equation

Certified isotopic standard

Correction of systematic effects

Disadvantages of Isotope Dilution Analysis

The isotope composition of the natural abundance and isotopically labelled element or compound must be known in advance.

The concentration of the spike mu st be determined by reverse isotope dilution analysis.

Limited availability of isotop ically labelled compounds.

Isotopic effects on separation pr ocesses (e.g. fully deuterated compounds).

The measured isotope abundances must be accurate ( spectral interferences, mass bias, detector non-linearity, etc .)

Measurement of isotope abundances by MS

The information obtained depends on the ion source employed.

ICP Elemental isotope abundances

EI Mass isotopomer distributions in gaseous molecules and their molecular fragments

ESI Mass isotopomer distributions of ions in solution and their molecular fragments

The measurement procedure depends on the type of analyser (quadrupole, time of flight, MS/MS).

The ICP as ion source

Sample aerosol

DesolvationH2O(l) H2O(g)

VaporisationMX(s) MX(g)

AtomisationMX(g) M + X

IonisationM M+

RecombinationM+ + e- M

J. Anal. At. J. Anal. At. SpectromSpectrom., 18(2003)11., 18(2003)11

J. Anal. At. J. Anal. At. SpectromSpectrom., 14(1999)1505., 14(1999)1505

0

2000

4000

6000

8000

10000

12000

14000

75 76 77 78 79 80 81 82 83

m/z

Inte

nsity

(cps

)

MassNaturalSelenium

77Se enrichedspike

74 0.89±0.04 0.063±0.009

76 9.37±0.29 1.03±0.07

77 7.63±0.16 91.1±0.7

78 23.77±0.28 3.9±0.3

80 49.61±0.41 3.4±0.2

82 8.73±0.22 0.54±0.04

77Se enriched spike

Sample

Mixture

Determination of selenium by IDA

Ion Ion sourcesource : : InductivelyInductivelyCoupledCoupled PlasmaPlasma

Concentration found c

MaterialReference

Value 80Se/ 77Se 78Se/ 77Se

Seronorm™Human Serum a 83 ± 3 83.6 ± 1.7 83.2 ± 2.0

SRM- 2670Freeze Dried Urine a 30 ± 8 31.1 ± 1.2 30.3 ± 0.5

IAEA H - 8Horse Kidney b 4.67 ± 0.30 5.3 ± 0.5 4.59 ± 0.07

NIST SRM 1577aBovine Liver b 0.71 ± 0.07 0.87 ± 0.05 0.70 ± 0.07

aconcentration in ng g-1 bconcentration in µg g-1 cAverage ± std. dev. (n=3)

Determination of selenium in certified referencematerials

Electron ionisation (electron impact)

A potential difference of 70 V is used to accelerate the electrons

to the anode

One of every 1000 molecules gets ionised

Positive ions are obtainedThe sample originates

usually in a Gas Chromatograph

Fragmentation in the electron ionisation source

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

280 285 290 295 3000

200000

400000

600000

800000

1000000

1200000

1400000

280 285 290 295 3000

500000

1000000

1500000

2000000

2500000

280 285 290 295 300

m/z m/z m/z

Natural Abundance TBT Mixture

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

280 285 290 295 3000

200000

400000

600000

800000

1000000

1200000

1400000

280 285 290 295 3000

500000

1000000

1500000

2000000

2500000

280 285 290 295 300

m/z m/z m/z

Natural Abundance TBT 119Sn-enriched TBT Mixture

Determination of tributyltin by IDA

Ion Ion sourcesource : : ElectronElectron IonisationIonisation

Fragment used: C 12H27Sn+

Minimal labelling in Organic Isotope Dilution Analysis

Comparison of single and multiple labellingComparison of single and multiple labelling

OH OHOH

Phenol 13C1-Phenol 13C6-Phenol

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

93 95 97 99 101 103 105 107

Abundance

Mass

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

93 95 97 99 101 103 105 107

Abundance

Mass

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

93 95 97 99 101 103 105 107

Abundance

Mass

Isotope Dilution Experiment for phenol

Ratio of molar fractions = Ratio of molar concentrations

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

X na

t/ X

lab

Molar ratio

Line of slope 1 and intercept 0

13C1

13C6

Heteroatom labelling in Organic Isotope Dilution Analysis

0

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

481.7 482.7 483.7 484.7 485.7 486.7 487.7 488.7 489.7 490.7

Rel

ativ

eab

unda

nces

ExperimentalTheoretical

O *Br

*Br

*Br

*Br

B

Exact mass

0

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

481.7 482.7 483.7 484.7 485.7 486.7 487.7 488.7 489.7 490.70

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

481.7 482.7 483.7 484.7 485.7 486.7 487.7 488.7 489.7 490.7

Rel

ativ

eab

unda

nces

ExperimentalTheoreticalExperimentalTheoretical

O *Br

*Br

*Br

*Br

O *Br

*Br

*Br

*Br

B

Exact mass

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

481.7 482.7 483.7 484.7 485.7 486.7 487.7 488.7 489.7 490.7

O Br

Br

Br

BrExperimentalTheoretical

Exact mass

Rel

ativ

eab

unda

nces

A

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

481.7 482.7 483.7 484.7 485.7 486.7 487.7 488.7 489.7 490.7

O Br

Br

Br

Br

O Br

Br

Br

BrExperimentalTheoreticalExperimentalTheoretical

Exact mass

Rel

ativ

eab

unda

nces

ANatural abundance

Isotopically labelledwith 81Br (99.53%)

Concentration of PBDE congeners 28, 47 and 99 determined in spiked water.

85 ± 198 ± 291 ± 1012 ± 1123 ± 381.7 ± 0.50.10 ± 0.08BDE-99

89 ± 2103 ± 291 ± 1212 ± 2128 ± 131.8 ± 0.20.3 ± 0.1BDE-47

87 ± 1100 ± 1102 ± 313.5 ± 0.5137 ± 291.8 ± 0.40.07 ± 0.04BDE-28

Recoveryb,c

(%)Concentrationb

(ng L-1)Recoveryb,c

(%)Concentrationb

(ng L-1)Recoveryb,c

(%)Concentrationb

(ng L-1)Concentrationb

(ng L-1)Congener

Level 3 aLevel 2 aLevel 1 aBlank

aSamples spiked at level 1, 2 and 3 wi th approximately 1, 10 and 100 ng L -1 of each congener respectively.

bThe uncertainties correspond to the standard deviation from 5 in jections of the same sample.

cThe recovery was calculated by s ubstracting the blank values and dividing by the theoretical concentration spiked.

The electrospray as ion source

Ideal for the determination of peptides and proteins.

No fragmentation (protonated molecular ion).

Ionisation suppression by the matrix.

Triple quadrupole in combination with SRM (Selected Reaction Monitoring).

The electrospray as ion source

The electrospray as ion source

0.00

0.05

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0.20

0.25

0.30

0.35

0.40

0.45

0.50

1589.8 1590.8 1591.8 1592.8 1593.8 1594.8 1595.8 1596.8 1597.8

Exact mass

Rel

ativ

e ab

unda

nce

The calculated mass isotopomer distribution and their uncertaintiesfor the dimethylated peptide DAEPDILELATGYR (NIST 8327) bothusing natural abundance (grey bars) or 99% enriched 13C (white bars) formaldehyde as reagent.

Solution containing the enrichedtracers and internal standards

SamplesStandards

BlanksICP-MS

C CR R

R R

R R

R Rs stst n

m n

sp m

sp st

= ∗−−

∗−

−1

1

On-line Isotope Dilution Analysis

Isotope tracer for drinking water analysis

Analytical CharacteristicsElement L.D.

method(Ăg L-1)

L.D. required(Ăg L-1)

Precision(%)

Accuracy(%)

Applicationrange

B 0.24 100 3.9 4.3 L.D.-100

Al 1.1 20 2.0 1.0 L.D.-1000

Cr 0.02 5 2.2 0.8 L.D.-250

Mn 0.02 5 1.7 1.1 L.D.-1000

Fe 0.75 20 0.3 -2.4 L.D.-1250

Ni 0.04 2 2.2 1.4 L.D.-1500

Cu 0.18 200 1.5 3.2 L.D.-200

As 0.01 1 3.6 1.6 L.D.-1000

Se 0.29 1 2.4 3.2 L.D.-300

Cd 0.01 0.5 1.6 -4.5 L.D.-200

Sb 0.01 0.5 2.1 -5.6 L.D.-100

Hg 0.08 0.1 3.3 2.9 L.D.-200

Pb 0.29 2.5 1.4 -3.2 L.D-200

Reference materials: NIST-1643e and SLRS-4

NIST-1643e (Ăg L-1) SLRS-4 (Ăg L-1)

Element Determined Certified Determined Certified

B 147.72 ± 18.14 157.9 ± 3.9 n.d n.c.

Al 135.5 ± 1.0 141.8 ± 8.6 52.12 ±0.33 54 ± 4

Cr 20.44 ± 0.17 20.40 ± 0.24 0.36 ± 0.02 0.33 ± 0.02

Mn 38.68 ± 0.23 38.97 ± 0.45 3.24 ± 0.05 3.37 ± 0.18

Fe 96.27 ± 1.48 98 .1 ± 1.4 98 ± 2 103 ± 5

Ni 61.67 ± 0.94 62.41 ± 0.69 0.64 ± 0.06 0.67 ± 0.08

Cu 21.95 ± 0.62 22.76 ± 0.31 1.9 ± 0.1 1.81 ± 0.08

As 58.9 ± 2.3 60.45 ± 0.72 0.68 ± 0.04 0.68 ± 0.06

Se 12.22 ± 0.99 11.97 ± 0.14 n.d n.c

Cd 6.42 ± 0.09 6.568 ± 0.073 0.010 ± 0.002 0.012 ± 0.002

Sb 59 .06 ± 0.53 58.30 ± 0.61 0.25 ± 0.01 0.23 ± 0.04

Hg 1.0 Ăg L-1 R = 97% 1.0 Ăg L-1 R= 96%

Pb 19.74 ± 0.23 19.63 ± 0.21 < L.D 0.086 ± 0.007

SPIKEFLOW

FROM ANALYTICAL COLUMN

VENT

TO MS

FURNACE

FROM ANALYTICAL COLUMN

TO MS

FURNACEVENT SPIKE

FLOW

GAS CYLINDER FILLED WITH 13CO2DOPED HELIUMMASS FLOW

CONTROLLER

COMBUSTION FURNACE

GC COLUMN

INJECTION PORT

6-WAY VALVEMASS

SPECTROMETER

T

Pr = pristanePh = phytane (isoprenoids)

Direct analysis of diesel fuels

Conclusions

We can take advantage of the isot opic nature of the elements forthe development of alternative measurement techniques in chemical metrology .

Isotope Dilution Analysis is traceable directly to the international System of Units and can be considered a primary measurement technique .

Different ion sources can be used for the measurement of isotopeabundances by Mass Spectrometry with applications in elemental, organic and biochemical analysis .

On-line isotope dilution analysis can be considered an alternative for the development of routine procedures for trace elements and organic compounds .