ASTM E168-16(2023)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E168 − 16 (Reapproved 2023)
Standard Practices for
General Techniques of Infrared Quantitative Analysis
This standard is issued under the fixed designation E168; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope E932PracticeforDescribingandMeasuringPerformanceof
Dispersive Infrared Spectrometers
1.1 These practices cover the techniques most often used in
E1252Practice for General Techniques for Obtaining Infra-
infrared quantitative analysis. Practices associated with the
red Spectra for Qualitative Analysis
collection and analysis of data on a computer are included as
E1421Practice for Describing and Measuring Performance
well as practices that do not use a computer.
of Fourier Transform Mid-Infrared (FT-MIR) Spectrom-
1.2 This practice does not purport to address all of the
eters: Level Zero and Level One Tests
concerns associated with developing a new quantitative
E1655 Practices for Infrared Multivariate Quantitative
method. It is the responsibility of the developer to ensure that
Analysis
the results of the method fall in the desired range of precision
and bias.
3. Terminology
1.3 The values stated in SI units are to be regarded as
3.1 For definitions of terms and symbols, refer toTerminol-
standard. No other units of measurement are included in this
ogy E131.
standard.
4. Significance and Use
1.4 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the 4.1 These practices are intended for all infrared spectrosco-
responsibility of the user of this standard to establish appro- pists. For novices, these practices will serve as an overview of
priate safety, health, and environmental practices and deter- preparation, operation, and calculation techniques. For experi-
mine the applicability of regulatory limitations prior to use. enced persons, these practices will serve as a review when
Specific hazard statements appear in Section 6, Note A4.7, seldom-used techniques are needed.
Note A4.11, and Note A5.6.
5. Apparatus
1.5 This international standard was developed in accor-
dance with internationally recognized principles on standard-
5.1 The infrared techniques described here assume that the
ization established in the Decision on Principles for the
equipmentisofatleasttheusualcommercialqualityandmeets
Development of International Standards, Guides and Recom-
the standard specifications of the manufacturer. For dispersive
mendations issued by the World Trade Organization Technical
instruments,alsorefertoPracticeE932.ForFourierTransform
Barriers to Trade (TBT) Committee.
and dispersive instruments, also refer to Practices E1421 and
E932 respectively, and for microanalysis with these instru-
2. Referenced Documents
ments see Practice E334.
2.1 ASTM Standards:
5.2 In developing a spectroscopic method, it is the respon-
E131Terminology Relating to Molecular Spectroscopy
sibilityoftheoriginatortodescribetheinstrumentationandthe
E334Practice for General Techniques of Infrared Micro-
performance required to duplicate the precision and bias of a
analysis
method. It is necessary to specify this performance in terms
that can be used by others in applications of the method.
These practices are under the jurisdiction of ASTM Committee E13 on
6. Hazards
Molecular Spectroscopy and Separation Science and are the direct responsibility of
Subcommittee E13.03 on Infrared and Near Infrared Spectroscopy.
6.1 Users of these practices must be aware that there are
Current edition approved Jan. 1, 2023. Published January 2023. Originally
inherent dangers associated with the use of electrical
approved in 1964. Last previous edition approved in 2016 as E168–16. DOI:
10.1520/E0168-16R23.
instrumentation, infrared cells, solvents, and other chemicals,
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
and that these practices cannot and will not substitute for a
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
practical knowledge of the instrument, cells, and chemicals
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. used in a particular analysis.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E168 − 16 (2023)
7. Considerations for Quantitative Infrared accountfortheshiftoftheabsorbancemaximum.Thequestion
Measurements arises whether it is preferable to measure absorbances at fixed
wavenumber locations or at the observed maximum of the
7.1 Quantitative infrared analysis is commonly done with
analytical band. The best approach is empirical testing of both
grating, filter, prism, or interferometer instruments. The fol-
the fixed point and the tracking methods of evaluation.
lowing guidelines for setting up an analytical procedure are
7.1.6 Whenever possible, working directly in absorbance is
appropriate:
preferable. That is, either the instrument or associated data
7.1.1 Always operate the instrument in the most stable and
processor makes the necessary conversion from transmittance
reproducible conditions attainable. This includes instrument
to absorbance. If spectra cannot be obtained in absorbance,
warm-up time, sample temperature equilibration, and exact
thenEqA12.1andA12.2inAnnexA12canbeusedtoconvert
reproduction of instrument performance tests for both stan-
the data.
dardsandsamples.Aftercalibration,useequivalentsettingsfor
7.1.7 Use spectral regions offering the most information on
analyses. For all infrared instruments, refer to the manufactur-
the analyte. Select analytical wavenumbers where the compo-
er’s recommendations for the instrument settings. After
nent has a relatively large absorptivity. In addition, other
calibration, use these same settings for analysis.
analytes should have minimal effect on the measured absor-
7.1.2 The absorbance values at analytical wavenumbers
bance.
should fall within the acceptably accurate range of the particu-
7.1.8 The performance of the spectrometer should be suffi-
larspectrometerused.Ingeneral,asingleabsorbancemeasure-
ciently good to give adequate linearity of response for the
ment will have the best signal-to-noise ratio when it is in the
3 desiredrangeofconcentrations.Thesignal-to-noiseratio,S/N,
range from 0.3 to 0.8 absorbance units (AU) (1). The
should be acceptable for the desired precision.
sensitivity of Fourier transform (FT-IR) spectrometers is such
7.1.9 Select analytical wavenumbers such that the linearity
that lower absorbance values can be used quite effectively,
of the absorbance-concentration relationship is least affected
provided that the baseline can be estimated accurately (see
by molecular interaction, dispersion in refractive index, and
Section 12). Absorbances greater than 0.8 AU should be
spectrometer nonlinearity.
avoided wherever possible because of the possibility of
instrumentally-causednon-linearity,bothfordispersive (2)and
8. Theory for a Single-Compound Analysis
FT-IR (3,4) spectrometers. Variation of the concentration and
samplepathlengthcanbeusedtoadjustabsorbancevaluesinto 8.1 Quantitative spectrometry is based on the Beer-
theoptimumrange.Whenmultiplecomponentsaredetermined
Bouguer-Lambert(henceforthreferredtoasBeer’s)law,which
inaparticularsample,itisacceptabletouseabsorbancevalues is expressed for the one component case as:
outside the optimum range, (5) however, absorbances greater
A 5 abc (1)
than1.5AUshouldbeavoided (2-4).Weakerabsorptionbands
where:
of high concentration components may be selected to provide
absorbance values within the optimal range. A = absorbance of the sample at a specified wavenumber,
7.1.3 The most accurate analytical methods are imple- a = absorptivity of the component at this wavenumber,
b = sample path length, and
mented with samples in solution. With liquid samples that are
c = concentration of the component.
notexceptionallyviscous,bestresultsareobtainedifthecellis
not moved after the first sample is introduced into the instru-
Since spectrometers measure transmittance, T, of the radia-
ment (the fixed-cell method). The reason is that sample cell
tion through a sample, it is necessary to convert T to A as
position is difficult to reproduce accurately by insertion into
follows:
typical cell holders. Suitable fittings and tubes can be attached
P
to the cell to allow sample changing in a flow-through manner.
A52logT52log (2)
P
When it is not practical to use a flow-through cell, the cell
shouldfittightlyintheholdersothatlateralandtiltingmotions where:
are restricted.
P = input radiant power at the sample, and
7.1.4 Unless there is reason to suspect deposition on or
P = radiant power transmitted through the sample.
contamination of the cell from the samples, it is generally
preferabletowashoutthecurrentsamplewiththenextsample,
9. Calibration for a Single-Component Determination
if sufficient sample is available.The volume of sample used to
9.1 Proper sample preparation is essential to quantitative
flushthecellshouldbeatleastfivetimes(andpreferablymore,
analysis. See Annex A4.
for example, 20 times) the volume between the sample inlet
9.1.1 Quantitative analysis has two distinct parts: calibra-
and cell exit points.
tion and analysis. For a simple one-component analysis, select
7.1.5 For some bands, the wavenumber of the maximum
an appropriate solvent that is essentially free from interfering
absorbance changes as a function of concentration. Similarly,
absorptions at the analytical wavenumber.
the position of the baseline points may change with concen-
9.1.2 For calibration, measure the absorbances, A,ofthe
tration. Selection of baseline points must be done carefully to
analyte solutions at several known concentrations, c.
Absorptivities, a, are then calculated, using Eq 1 with the
baseline corrections as described in Sections 12–14.
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
these practices. Alternatively,theabsorbances, A,ofasinglesolutioninseveral
E168 − 16 (2023)
cells of different, but accurately known, path lengths may be independent equations containing n absorbance measurements
measured;however,interactioneffectswillnotbeelucidatedin at nwavenumbersarenecessary.Thisisexpressedforconstant
this fashion. path length as follows:
9.1.3 Calculatetheaverageoftheseveral avaluesforfuture
A 5 a bc 1a bc 1····1a bc (4)
1 11 1 12 2 1n n
use, or draw an analytical working curve by graphing absor-
bance versus concentration for a constant path length as A 5 a bc 1a bc 1····1a bc
2 21 2 22 2 2n n
demonstrated in Fig. 1. Use the linear part of the curve to
·· ········ ······
calculate a.Thecalculationof awherecurvatureispresentwill
be discussed in 18.1 and 18.2.
·· ········ ······ ······
NOTE1—Inpractice,thecalibrationcurvemaynothavea yinterceptof
·· ········ ······ ······
zero.Thiscouldbeduetoavarietyoffactorsincluding,butnotlimitedto,
incompletely resolved analyte bands, reflection losses, and solvent inter-
ferences. It is important that the method used to calculate the calibration A 5 a bc 1a bc 1····1a bc
i i1 1 i2 2 in n
curve not force the y intercept to be zero.
where:
9.1.4 For analysis, dissolve the unknown in the solvent,
A = total absorbance at wavenumber i,
i
measuretheabsorbance, A,anddeterminetheconcentration, c,
a = absorptivity at the wavenumber i of component n,
in
of the analyte graphically or by calculation. Convert this
b = path length of the cell in which the mixture is sampled,
concentration in solution to the concentration in the unknown
and
sample.
c = concentration of component n in the mixture.
n
9.1.5 Both analysis time and chance of error are less if the
10.2 During calibration, concentrations c are known, and
n
concentrations of the unknowns and the cell path length are
baseline corrected absorbances A are measured. The experi-
kept the same over a series of analyses, and the concentrations
mental absorptivity-path length products a b are then calcu-
in
of the calibration solutions have bracketed the expected high
lated(seeNote2).Duringanalysis,theabsorptivity-pathlength
and low values of the unknown solutions (6, 7).
products a b are known, and the absorbances A are measured.
in
10. Theory for Multicomponent Analysis The unknown concentrations are then calculated (see Section
17). Therefore, accurate calibration generally requires that
10.1 Beer’s law is expressed for a mixture of n indepen-
experimental absorptivity values be obtained from at least n
dentlyabsorbingcomponentsatasinglepathlengthandsingle
standards. The following requirements must be met:
wavenumber as:
10.2.1 The number of standards must be equal to or greater
A 5 a bc 1a bc 1······1a bc (3)
1 1 2 2 n n
than the number of analytes, n, and
10.2.2 The number of analytical wavenumbers, i, must be
Eq3definesanabsorbanceatawavenumberasbeingdueto
equal to or greater than the number of independent
the sum of the independent contributions of each component.
components, n.
In order to solve for the n component concentrations, n
NOTE 2—All absorbance conversions use transmittance (that is, the
decimal value), not percent transmittance. Regardless of form (that is,
decimal or percent), the term transmittance refers to the term P/P of Eq
2, and should not be called transmission. (See Terminology E131).
10.3 The first requirement allows the analyst to use more
thantheminimumnumberofstandards.Over-determinationof
standards permits error estimation in the analytical result. The
second requirement allows the use of more than the minimum
number of peaks for specifying a chemical system, where at
least one distinctive band is selected for each component
(7-10).
10.4 The procedures used in multicomponent analysis will
be discussed further in the following section which is also an
introduction to general solution phase analyses.
11. Multicomponent Solution Analysis
11.1 For the quantitative analysis of mixtures, Eq 4 is
applicable. The absorptivities a of the n components of the
in
mixture at the ith analytical wavenumber are determined from
absorbance measurements made on each component taken
individually. These absorbances must be measured under
conditions (sample path length, temperature, pressure, and
solvent) identical to those used for the unknowns, and they
FIG. 1 An Analytical Working Curve should be corrected for baselines as discussed in Sections 12 –
E168 − 16 (2023)
14.Absorbancemeasurementsaremadewithconcentrationsof
the analyte bracketing the amounts expected in the unknown
samples.
11.2 Where possible, prepare samples as dilute solutions
and place in cells of appropriate path lengths (typically 0.2 to
1.0 mm). Use lower concentrations in longer path length cells
rather than higher concentrations in shorter path length cells to
obtain absorbance values in the 0.3 to 0.8 range. Lower
concentrations will minimize nonlinear effects due to disper-
sion (that is, change of refractive index with wavenumber).
Where freedom from intermolecular effects is uncertain or
where intermolecular effects are known to be present, calibra-
tion must be based on measurements taken from synthetic
mixtures of all components as described in 15.1.2.
11.3 Dissolve a known weight of a pure component in a
suitable infrared solvent. Measure the absorbance at all ana-
lytical wavenumbers and correct for baselines as discussed in
Sections 12 – 14. Repeat this procedure for several concentra-
tions covering the range of concentrations expected in the
samples to be analyzed, remembering that concentrations of
components must be linearly independent. Plot absorbance
versus concentration. Similarly, construct analytical curves for
FIG. 2 A Zero-Absorbance Baseline
this component at each of the other analytical wavenumbers.
Repeat this procedure for each of the n components. Thus,
there are i plots for each component, or a total of i×n
14. Baseline Method (7)
analytical curves, each yielding one of the values of a b.
in
14.1 The cell-in-cell-out technique was the method of
11.4 The number of standard mixtures required is at least
choice for early single-beam infrared instruments. After the
equal to n, the number of components. For each analytical
advent of double-beam dispersive spectrometers, the baseline
wavenumber, there will be a set of at least n equations in n
method has been the method of choice. Portions of the data
unknowns. The n sets of equations can be solved directly for
around the base of the bands are picked as baseline references.
the values of a b. If more than n synthetic mixtures are used
There are two common variations.
in
asstandards,aleast-squaresprocedurecanbeusedtocalculate
14.2 When one baseline point is chosen, the value of an
the values of a b. To repeat, in order to obtain information
in
absorbance minimum, A , is subtracted from the absorbance
about errors, at least one more mixture than the number of
maximum, A , as demonstrated in Fig. 3. The point of
analytes is needed.
minimumabsorbanceisadjacenttooratleastinthevicinityof
the band under evaluation.
12. Baselines in General
14.3 Two points may be needed if the band of interest is
12.1 Any quantitative method depends on the choice of a
superimposed on a sloping background. Manually a line is
reproducible baseline. The correction of raw data for baseline
drawn from one side to the other as in Fig. 4. The absorbance
absorbance is important in some methods. The guiding factor
of the band is calculated as the value at the peak maximum A
in baseline selection is the reproducibility of the results.
minusthebaselineabsorbanceminimum A .Aninappropriate
Methods used for drawing baselines with computerized instru-
choiceofbaselineinthissituationmayhavedeleteriouseffects
ments are similar in most ways to those for data recorded on
on the accuracy of the final calculation.
chart paper. Where differences exist, they will be explained in
NOTE3—Theabovebaselinecorrectionprocedureshouldbeperformed
Annex A1.
only if the spectrum is plotted in absorbance units. When the spectrum is
plotted in transmittance, the two baseline transmittances and the transmit-
13. Single Wavenumber Measurement
tance at the analytical wavenumber should be converted to absorbance.
The corrected baseline absorbance can be calculated by Eq A12.1 in
13.1 Atechnique known as the “cell-in-cell-out” method is
AnnexA12.Conversiontoabsorbanceisrequiredbecauseaslopinglinear
often used in single-beam infrared work. In this method, a baseline in transmittance becomes curved in absorbance.
blank (that is, solvent in cell, potassium bromide (KBr) pellet,
15. Nonsolution Analyses
orothersubstrate)ismeasuredatafixedwavenumberandthen
the analyte readings are recorded (7). In the simplest cell-in- 15.1 Liquids:
cell-out method, a zero absorbance baseline is used (see Fig. 15.1.1 Analyzing a liquid mixture without the use of a
2). If the spectrum cannot be obtained in absorbance, the diluting solvent is sometimes complicated by intermolecular
absorbance is calculated as in EqA12.1 where T = 1.0 and T forces. An absorption band may undergo intensity changes or
2 1
= transmittance at the analyte wavenumber (1, 6) (see Note 2). frequency shifts, or both, relative to the same absorption band
E168 − 16 (2023)
chosen for the analysis and substitute them (along with the
known concentrations) in Eq 4. Solve for the absorptivity-path
length products, a b directly from the set of n simultaneous
in
equations, or use a multivariant method (see Annex A8)if
sufficient data are available.
15.1.3 If the concentrations in the unknowns vary widely,
calculation of a second set of the a b products is recom-
in
mended.Asecond set may be necessary due to the presence of
intermolecular influences, and the differences in the values of
the absorptivities thus determined will indicate the extent of
these influences.
15.1.4 A single set of absorptivities may not suffice to
analyze mixtures throughout all possible concentration ranges
of the components, in which case, narrowing the range of
concentrations is recommended.
15.1.5 Since the a b products are calculated directly in this
in
procedure, it is not necessary to plot analytical curves.
15.2 Solids:
15.2.1 For cast films, pressed films, or pellets, follow the
same general procedure as for liquids (see 15.1). Measure the
thickness of each film and apply a proportional correction for
deviations from standard thickness.
FIG. 3 A One-Point Baseline
NOTE 4—The spectra of films and pellets can be complicated by the
presence of a fringe pattern. For pellets and films, follow the suggestions
in A4.5.1.2 and Note A5.1, respectively. A fringe pattern is undesirable
because analyte absorbance values can be altered by its presence.
15.2.2 In cases where all components of a mixture are
determined to a total of 100%, it is usually sufficient to
determineonlytheratiosofabsorbances.Insuchcases,itisnot
necessary to know the thickness of the sample layer; it is only
necessary to know the ratio of the components. However, a
knowledgeofthethicknessisneededtodeterminethepresence
of impurities because the total then will be less than 100%.
15.2.3 The above procedure for films is also used with
powders prepared as mulls. Measurement of thickness can be
accomplishedbyaninternalstandardtechniqueasdescribedin
A4.4.2. This involves the addition to the sample of a known
weight ratio of a compound having an absorption band of
known absorptivity that does not overlap the bands of the
sample.
15.2.4 When powders are measured as pressed plates or
pellets, analytical curves are prepared in the same manner as
solutions, see Sections 9 and 11.
15.3 Gases:
15.3.1 All calibration measurements for a given analysis
must be made at a fixed total pressure. This pressure must be
equal to the total pressure employed in the analysis. An
FIG. 4 A Two-Point Baseline
analysis may be set up in either of two ways:
15.3.1.1 Method 1—A fixed sample pressure is established
that is a fraction of the total pressure obtained by addition of a
ofthecomponentinsolution.Theabsorbancecontributionofa
nonabsorbing diluent gas.
component in a mixture can seldom be calculated from its
absorbance measured in the pure state. It is desirable to 15.3.1.2 Method 2—A fixed sample pressure is used as the
determine the absorptivities from known mixtures having total pressure.Analytical curves are prepared by introducing a
proportions near those of the samples. pure component at various measured pressures which bracket
15.1.2 Preparemixtureshavingknownconcentrationsofthe the expected component pressures in the sample.Adiluent gas
various components covering the expected ranges. Measure is then added to bring the total pressure up to the established
baseline corrected absorbances at each of the wavelengths value.
E168 − 16 (2023)
15.3.2 In Method 2, the analytical curve preparation does
not allow for the possibility of band broadening for different
components.Thisfactorismoreproperlyaddressedbyfollow-
ing Method 1 where the same diluent gas is employed for
sample preparation and calibration. Low molecular weight
gases frequently produce very strong, sharp absorption fea-
tures. Addition of a diluent gas and use of pressure less than
atmospheric may be necessary. Absorbances are measured for
eachstandardatthewavenumbersselectedforanalysis.Where
possible, integrated absorbances (see AnnexA3) are preferred
to offset the effect of small pressure variations. The absor-
bances are plotted against the partial pressures (or mole
fractions) to produce analytical curves.
16. Difference Method
16.1 Spectral subtraction using a computer is a common
practice in qualitative infrared analysis. This technique is also
used to perform quantitative infrared analyses. The advantage
of spectral subtraction (the difference method) is that small
concentration differences can be measured with greater accu-
racy than is possible on superimposed bands.
16.2 A generalized procedure follows and is illustrated in
Fig. 5. All spectra are obtained using samples of well charac-
terized path length and concentration. Fig. 5(c) shows the
spectrum of Z, an unknown mixture containing components X
and Y. Using a subtraction routine, the spectrum of X is
removed using the isolated, in this case higher, wave-number
bands of X as a guide (11). The concentration of Y is
ascertained from Fig. 5(d) by reference to an analytical curve
or by calculation as described in 9.1.3.
16.3 The same result is achieved with a noncomputerized
double-beam spectrometer by placing sample X in the refer-
ence beam, and the unknown mixture in the sample beam. If
the sample and reference are in solution, a variable path length
cell can be used in the reference beam to remove spectral
contributions due to X (7, 12).
17. Calculation Methods
17.1 Matrix Inversion:
17.1.1 After the values of the a b products have been
in
FIG. 5 An Example of Difference Spectroscopy
determined for a given set of n components, according to 10.2,
substitutethenumericalvaluesintoEq4.Solvethe nequations
for concentrations, c , in terms of the baseline corrected
n 17.2 Matrix inversion is a convenient method to calculate
absorbances, A , by matrix inversion (6). The inverted equa-
n
concentrations from the simultaneous equations presented in
tions will have the following form:
Eq4.Programsforsolvingsimultaneouslinearequationsusing
matrix-inversion techniques are available on many program-
C 5 A F 1A F 1····1 A F (5)
1 1 11 2 12 n 1n
mable calculators and computers and are contained in most
C 5 A F 1A F 1····1A F
2 1 21 2 22 n 2n
commercial quantitative analysis programs. Classical least
squares regression (CLS) is simply a sophisticated method of
·· ····· ····· ···· ·····
matrix inversion (see Annex A8).
·· ····· ····· ···· ·····
18. Correction for Curvature in Beer’s Law Plots
·· ····· ····· ···· ·····
18.1 In some cases, the analytical curve of one or more
analytes of a mixture will exhibit curvature to such an extent
C 5 A F 1A F 1····1A F
n 1 n1 2 n2 n nn
thatthevalueoftheslopemaydiffersignificantlybetweenlow
where F aretheinvertedcoefficients.Thereaftercalculation and high concentrations. Two methods are acceptable: a
in
of individual sample concentration is simply done by substi- non-linear regression using a computer or graphical method as
tuting the measured absorbance values, A , in the equations. immediately explained. If the graphical method (see 9.1.3)is
n
E168 − 16 (2023)
used,andiftheconcentrationsofanalytesfallinthelinearand tions from Beer’s law. Quantitative bias depends upon mini-
low range, then the values of the slope for the linear range can mizing determinate error.
be used. However, if the concentration is in the higher range, a
19.3 Indeterminate, or random, error arises from uncontrol-
correction is necessary. The following method is recom-
lable variables, and limits the precision with which measure-
mended:
ment can be made. Often the major indeterminate errors are
18.1.1 The concentration of the component under consider-
introduced by variation in sample positioning and errors in
ation ranges in the sample between c and c in Fig. 1. Draw a
1 2
determining the baseline. However, if these are held constant,
straight line between A and A . The slope of this line is the
1 2
the major contributing indeterminant error frequently is detec-
valueof a bthatisusedinEq4.Theinterceptofthislinewith
in
tor noise, which is usually independent of signal. Therefore,
the absorbance axis yield the value of a correction term, A ,
thenoiseintransmittanceunitsisindependentoftheamountof
whichmustbesubtractedfromthemeasuredabsorbanceofthe
lightreachingthedetector.Forareviewofthesourcesofnoise
sample at the analytical wavenumber of the analyte. This
in Fourier transform instruments, see Ref (11) and Practice
subtracted result is substituted for A in Eq 4 at this analytical
E1421.
wavenumber. If the concentration of the component under
19.4 For quantitative infrared spectrometry, the operative
scrutiny should happen to fall outside the range c to c , it will
1 2
equation for determining concentration from transmittance
be necessary to repeat the above procedure to determine the
measurements is Beer’s law as follows:
slope and intercept for the new concentration range.
A52logT 5 abc (6)
18.2 In some binary mixtures, pure bands representing the
individual components are not present. However, single bands c 5 A/ab (7)
or groups of bands, as intensities or area, can be ratioed and
Todeterminetheeffectofrandomerror(inthemeasurement
plotted to the known concentrations (13). These calibration
of transmittance) (1, 12, 15) on the concentration, it is
curvesarealmostalwayscurved,butasexplainedinRef. (13),
necessary to calculate the partial derivative as follows:
curved absorbance/concentration plots are not a problem since
δc 2loge 20.434
numerous computer programs are available for non-linear
5 5 (8)
δT abT abT
regression analysis.
The standard deviation of the concentration s can be given
c
19. General Considerations for Statistical Evaluation
by:
19.1 The statistical evaluation of experimental data and the
0.434
parameters necessary for reporting statistical confidence are
s 5 s (9)
S D
c T
abT
describedinthissectionandinAnnexA6.Thereliabilityofan
experimentally measured quantity is an important factor which
where s is the standard deviation of the transmittance
T
must be considered in evaluating any experimental technique.
measurement. The relative standard deviation of the concen-
This reliability can be described by two terms: precision and
tration is:
bias. The precision of a technique refers to the reproducibility
s 0.434 s
c T
of replicate measurements; the bias represents the degree to 5 (10)
S DS D
c logT T
which the measured quantity approaches the true value. The
and the standard deviation of the transmittance is calculated
sources of experimental error limiting bias or precision, or
both, are broadly classified as determinate or indeterminate from Eq A6.6 for a series of n measurements of T. s can be
T
determined from the noise in the 100% line since generally s
error (1, 14, 15).
T
will be independent of T.
19.2 Determinate error is systematic error which can be
attributed to definite causes. In quantitative infrared analyses,
20. Keywords
determinate error may arise from problems such as optical
misalignment, photometric inaccuracy, stray radiant power, 20.1 infrared spectroscopy; molecular spectroscopy; quan-
poor spectral resolution, improper sample handling, or devia- titative analysis
E168 − 16 (2023)
ANNEXES
(Mandatory Information)
A1. BASELINE PROCEDURES FOR COMPUTERIZED INSTRUMENTS
A1.1 Obtaining a Good Spectrum for Baseline Procedures the sample spectrum. This paragraph describes in general how
subtraction works with both FT-IR and dispersive spectra.
A1.1.1 There are two ways to get good (FT-IR) spectra. For
A1.1.3 For dispersive, optical-null instruments, the selec-
the first method, three steps are necessary. 1) Obtain both
tion of instrumental settings or mode (for example, resolution,
single-beam background and single-beam sample spectra. 2)
scanning region, etc.) are based on sample characteristics and
Ratio the single-beam sample to the single-beam background
the absorbance of the functional group being measured.
spectrum. This provides a spectrum in transmittance and
A1.1.4 Ingeneral,forbothspectrometertypes,spectraldata
requires conversion to absorbance. 3) Convert to absorbance
are collected by the cell-in-cell-out method of 14.1.Abaseline
by computing the negative logarithm of the transmittance
method is then used to obtain the actual quantitative data.
spectrum.The background can be that of the open beam, or an
These methods are demonstrated in Figs. 2-4.
aperturing device, or an accessory, such as anATR or gas cell
or a liquid cell containing solvent used to dissolve the analyte.
A1.2 Calculation Procedure
NOTE A1.1—Dispersive duel-beam instruments perform the above by
A1.2.1 The calculation of data with one baseline point is
using the reference beam to obtain a background simultaneously. Hence,
discussed in 14.2.
the reference beam should contain similar beam limiting accessories as
A1.2.2 Automatic computation of peak absorbance with a
used in the sample beam. In some cases, for example with a gas cell, the
two-pointbaselineismoresubjecttoerror.Thecalculationsare
above approach is impractical. The alternative is to run spectra of the
sample and the empty accessory separately, then using the computer
based on the point-slope method, where the hypotenuse of a
software to subtract the empty accessory from the sample. Keep in mind
righttriangleisthedesiredslopingbaselineasshowninFig.4.
that these spectra must be in absorbance.
The slope of the baseline may be either positive or negative.
The peak absorbance is the result of the following:
A1.1.2 The second method similar to A1.1 is frequently
used when the spectrum of the sample material contains
A 2 A w 2 w
~ !~ !
3 2 1 2
A 5 A 2 A 2 (A1.1)
~ !
extraneous absorption features (for example, solvents or impu- 1 2
w 2 w
~ !
3 2
rities). In this approach, the single-beam spectrum of the
where:
sample and the single-beam spectrum of the solvent or impu-
A = corrected absorbance of the peak at w ,
rity are each ratioed against the single-beam background
A = uncorrected absorbance at w ,
1 1
spectrum. Both transmittance spectra are converted to absor-
A = baselineabsorbancepointatthelowerwavenumber w ,
2 2
bance. The absorbance spectrum of the solvent or suspected
and
impurity is then scaled by multiplying it by a factor chosen to
A = baseline absorbance point at the higher wavenumber
minimize all spectral features caused by the solvent or impu-
w .
rity. The impurity or solvent spectrum is then subtracted from
A2. GENERAL CONSIDERATIONS FOR BAND AREA
A2.1 All data should be expressed in absorbance as a band area is found to be more accurate than peak-height
function of wavenumber.
measurements because one is, in effect, averaging multipoint
data.
A2.2 Band shape changes can cause peak-height data to be
nonlinear. Band area, however, may remain essentially unaf-
A2.4 Whenintegratedareaisusedforquantitativeanalyses,
fected by the changes in shape of the band because band area
the reliability of the results frequently depend on the baseline
is a function of the total number of absorbing centers in the
treatment selected. The accuracy by band area is often im-
sample. If the shape change is caused by changes in intermo-
proved by limiting the range of absorbances. The wings
lecular forces, even band area may not be linear.
contribute very little signal while contributing substantial
uncertainties to the total area.Auseful guideline is to limit the
A2.3 Band area is calculated by integrating across band-
integration limits to absorbance values which are no smaller
width. Band area is advantageous when band shape undergoes
than 20% to 30% of the peak absorbance.
change as a function of increasing concentration. Frequently,
E168 − 16 (2023)
A3. CALCULATION OF BAND AREA
A3.1 In reference to Fig.A3.1, when no baseline points are where I is given by Eq A3.1.
used for an area calculation, the area between lower and upper
A3.3 If a two-point baseline treatment is used with absor-
wave-number limits is the following:
bances A 2 at wavenumber w and A 3 at wavenumber w,as
W 2 w 3
I 5 A ∆1A ∆1···1A ∆ (A3.1)
w4 w411 w521
shown in Fig. A3.3, the formulation is as follows:
where:
I 5 I 2 I (A3.3)
2 0 2b
I = integrated absorbance (area),
np
A 2 A w 2 w 1j∆
~ ! ~ !
w3 w2 4 2
∆ = sampling interval in wavenumbers,
I 5 A 1 ∆(A3.4)
F S DG
2b ( w2
~w 2 w !
j51
A = absorbance measured at the designated interval, 3 2
w = lower wavenumber limit, and
w = upper wavenumber limit.
and I is given by Eq A3.1.
The number of points in the sum is np=(w4− w5)/∆.
NOTEA3.1—The algorithms above are not the most accurate, but as ∆
A3.2 In reference to Fig. A3.2, for a one-point baseline
becomes smaller, all methods (that is, trapezoidal and Simpson’s rule)
treatment w with a corresponding absorbance A , the area I
approximate the same value.
2 w2 1
is as follows:
I 5 I 2 I (A3.2)
1 0 1b
I 5 I 2 ~A !~w 2 w !
1 0 w2 5 4
I 5 I 2 @~∆ ~np 21!!#
1 0 w2
FIG. A3.1 Band Area With Zero-Absorbance Baseline
E168 − 16 (2023)
FIG. A3.2 Band Area With a One-Point Baseline
FIG. A3.3 Band Area With a Two-Point Baseline
E168 − 16 (2023)
A4. SAMPLE PREPARATION
A4.1 Where possible, solution techniques are recom- A4.4.3 Break up the mixture and distribute it over the
mended. However, other methods are discussed. mortar surface by gentle grinding with the pestle. Rub to an
extremely fine powder by vigorous back and forth grinding
A4.2 Liquids—Liquids may be measured either neat or
untilthemixturebecomescakedandtakesonasmooth,glossy,
preferably, as solutions in a sealed cell of suitable path length
light-reflecting surface.
(15).
A4.4.4 Add one drop of mulling agent (see Note A4.5),
grind with a rotary motion, using a smooth, hard mortar and
A4.3 Solution Techniques:
pestle, until all of the mixture is picked up and suspended.The
A4.3.1 For liquids and solids, the following procedures are
suspension should be viscous, not fluid.
recommended but may not be all encompassing:
NOTE A4.5—Mineral oil, fluorinated hydrocarbon, or appropriate sub-
A4.3.2 Choose a solvent that has minimal absorbance at the
stances can be used as the mulling agent. Matching the refractive indices
analytical wavenumbers and that will completely dissolve the
as closely as possible gives best results.
sample.
A4.4.5 Transfer the sample to a clean, flat salt plate with a
A4.3.3 Measure a specified amount of sample into a volu-
clean, rubber policeman or clean, plastic spatula.
metric flask or other suitable container, and add some of the
NOTE A4.6—A discussion of salt plates and cell-window materials is
solvent to be used. The analyte must be completely dissolved.
covered in Practice E1252.
A4.3.4 Allow for temperature equilibration to the same
A4.4.6 Cover with a second clean, flat plate; squeeze and
temperature as that used for the standards.
rotatetoobtainthedesiredthicknessandtoremovealltrapped
A4.3.5 Make up to volume or weight with solvent and mix
air.
thoroughly.
A4.4.7 Visually observe the scattering of light passing
A4.3.6 Aqueoussolutionscanbeanalyzedusingflatsurface through the sample. As a guideline, the sample may appear
or circular ATR techniques.
slightly hazy, but objects on the far side should be distinguish-
able.
NOTEA4.1—Forotherdifficultsolutes,suchaselastomersandtars,itis
frequently more convenient to roughly weigh the solute in a suitable
A4.5 Solids By Pressed-Pellet Technique (8, 12):
container, add solvent from a graduated cylinder, dissolve, and run the
analysis. The concentration is then obtained by doing a percent solids
A4.5.1 Particle size of the sample should be reduced to less
content on an aliquot from the remaining solution.
thantheanalyticalwavelength.Thisisrelativelyeasyformany
NOTEA4.2—Solventinfluenceoroverlapontheabsorptionbandstobe
sampleswithoutincurringanychangeinthesample.However,
measured must be recognized and taken into account in the calculation.
polymorphic changes, degradation, and other changes may
NOTE A4.3—For best results, measure unknown sample solutions at
occur during grinding. If such changes do happen and are not
concentrationsthatwillplacetheanalyteabsorbancesintherangeofthose
used for calibration.
controlled, the method will not be valid.
A4.5.1.1 Grinding conditions must be established for the
A4.4 Solids by Mull Techniques (8, 12):
particular sample type since grinding severity can affect
A4.4.1 The following is the recommended procedure for
absorption-band intensity.
preparing solids by mull techniques; however, other methods
A4.5.1.2 Weigh the preground sample and powdered potas-
also may be appropriate. Average particle size of the sample
siumbromide(KBr)orotheralkalihalideinspecifiedamounts
should be reduced to less than the analytical wavelength. The
(sample weight should be about 1% of the KBr weight; about
particle size reduction is relatively easy for many samples
350 mg KBr is appropriate for a 13mm disk to avoid
without incurring any change in the sample. However, poly-
interference fringes), and mix by hand in a mortar.This should
morphic changes, degradation, and other changes may occur
be a mixing step rather than a grinding step.
during grinding. If such changes do occur and are not
A4.5.1.3 Place the mixture in an appropriate evacuable die,
controlled, the method will not be valid. If changes are
evacuate to at least 15 mm Hg and press at sufficient pressure
suspected, other techniques such as attenuated total reflectance
to produce a transparent disk. Follow the manufacturer’s
(12) or diffuse reflectance (11) should be investigated.
recommendation as to pressure for a particular die. Other
methods, such as minipress cells are also used, but these
A4.4.2 Weigh slightly more than the minimum amount of
methods may not be as satisfactory due to crazing caused by
sample required, and then weigh the desired amount of an
trapped air and water vapor.
appropriate internal standard. Mix thoroughly.
NOTE A4.7—Precaution: During pressing operations, place the die
NOTEA4.4—An appropriate internal standard (7, 11, 12) is a substance
symmetrically in the press. Otherwise, the die may forcefully slip out of
that (a) exhibits a band in a suitable region of the spectrum, and as close
the press, causing personnel injury or damage to surrounding equipment.
to the analyte’s wavenumber as possible, (b) is not present in the sample,
Some laboratories require safety shields in front of presses.
and(c)doesnotreactchemicallywithordissolveinthesampleormulling
agent.An alternative to a separate internal standard is to use a band in the NOTE A4.8—Since the purity of alkali halide powders are not all the
sample that does not change as the moiety of interest is varied. This same, the same alkali halide powder should be used for the sample and
approach is very useful in polymer analyses. blank.
E168 − 16 (2023)
NOTE A4.9—If a steel-ball mill is used, clean, dry, rust-free stainless
closed-loop pumping system of known volume. A known (or
steel vials and balls are recommended. A blank pellet (7) is made in the
unknown) sample can be injected from a gas syringe into the
same manner as for the sample using the same ball-mill equipment, and
closed loop containing a diluent gas. The closed loop greatly
procedures.
reduces the time for mixing and helps to provide a homoge-
NOTEA4.10—Samples may undergo polymorphic changes or reactions
such as oxidation, ion exchange, or salt formation with the alkali halide
neous sample for analysis.
material. These events may also invalidate a method.
NOTE A4.11—Precaution: Safety considerations require the use of
A4.6 Gaseous Samples (12, 15, 16, 17):
proper pressure reduction valves for metering gases into a sample bomb.
Take precaution when mixing potentially hazardous or reactive gases.
A4.6.1 Take care that samples do not affect cell windows,
NOTE A4.12—All measurements for calibration and analysis under a
mirror, or interiors.
given analytical system should be at a single, reproducible total pressure,
A4.6.1.1 Either fixed or variable path length cells can be
since the band intensity is a function of the partial pressure of the analyte,
used for gas analyses. Cells with path lengths from 1 cm to 20
the total pressure of the sample, and the total pressure within the cell and
m are readily available and other lengths can also be obtained.
the temperature.
A4.6.1.2 Cells can be filled through the use of a vacuum
NOTEA4.13—Mixingdoesnothappenautomatically.Attentionmustbe
system coupled to a pressure
...