Attenuated Total Reﬂection Fourier Transform Infrared...

Attenuated Total ReflectionFourier Transform InfraredSpectroscopy

Georg Ramer and Bernhard LendlVienna University of Technology, Vienna, Austria

1 Introduction 11.1 Introduction to Attenuated Total

Reflection Spectroscopy 11.2 History of ATR Spectroscopy 21.3 A Short Introduction to Mid-infrared

Fourier Transform Spectroscopy 32 Theoretical Aspects of Attenuated Total

Reflection Spectroscopy 52.1 Reflection, Total Reflection, and the

Attenuated Total Reflection Signal 52.2 Influence of the Measurement

Parameters on the Attenuated TotalReflection Signal 9

3 Practical Aspects of Attenuated TotalReflection Spectroscopy 133.1 Materials 133.2 Number of Reflections 133.3 Sample Preparation and Measurement

Protocols 143.4 Angle of Incidence 163.5 Surface Modification 17

4 Differences Between Attenuated TotalReflection Spectroscopy and TransmissionSpectroscopy 184.1 Comparison of Attenuated Total

Reflection Spectra and TransmissionSpectra 18

4.2 Sample Preparation 195 Applications 19

5.1 Biological and Medical Samples 195.2 Process Analytical Chemistry 205.3 Microscopy 205.4 Depth Profiling 21

6 Vendors 227 Further Reading 228 Future Trends 23

8.1 Hand-held Attenuated Total ReflectionInstruments 23

8.2 Waveguide Sensors 23

Acknowledgments 24Abbreviations and Acronyms 24Related Articles 24References 24

Attenuated total reflection Fourier transform infrared(ATR-FTIR) spectroscopy is now the most widespreadimplementation of mid-infrared (MIR) spectroscopy.While the FTIR technique allows the fast and stablecollection of MIR spectra, the ATR technique allowsmechanically stable, robust, and quick sampling. ATR-FTIR spectroscopy is routinely used in industrial andresearch laboratories. The ATR-FTIR technique findsapplication in, e.g. biology, medicine, forensics, processanalytical chemistry and organic chemistry. Even thoughATR spectroscopy is often treated as a routine technique,it has several intricacies that users should be aware of toavoid measurement errors and artifacts.

In this article, starting from the theoretical underpinningsof ATR spectroscopy, we aim to give novices in ATR-FTIR spectroscopy the knowledge to successfully use thistechnique and to avoid common errors. The theoreticaltreatment of ATR spectroscopy is complemented bypractical information about the routine and advanced usesof ATR spectroscopy. Furthermore, the reader will finddescriptions of future trends in ATR-FTIR and evanescentwave spectroscopy. Finally, a list of literature for furtherreading and a list of vendors of ATR accessories andtheir product lines are given to facilitate using the ATRtechnique.

1 INTRODUCTION

1.1 Introduction to Attenuated Total ReflectionSpectroscopy

The attenuated total reflection (ATR) technique is themost frequently used sampling technique for infrared (IR)spectroscopy.(1) IR light traveling in an optically densermedium is totally reflected at the interface to an opticallyrarer medium. Although the light rays as such do notpropagate into the optically rarer medium, an evanescentfield forms there. Through this evanescent field, the lightcan interact with samples placed at the interface, makingabsorption measurements possible.

The ATR technique usually needs hardly any samplepreparation. It allows quick and robust measurementsof solid as well as of liquid samples, including pastesand samples otherwise difficult to handle. Therefore,since its invention in the 1960s, the ATR technique has

Encyclopedia of Analytical Chemistry, Online © 2006–2013 John Wiley & Sons, Ltd.This article is © 2013 John Wiley & Sons, Ltd.This article was published in the Encyclopedia of Analytical Chemistry in 2013 by John Wiley & Sons, Ltd.DOI: 10.1002/9780470027318.a9287

2 INFRARED SPECTROSCOPY

gradually replaced other sampling methods for solid andliquid samples for many applications of IR spectroscopy.In principle, ATR spectroscopy can also be applied tothe measurement of gases; however, due to the shortinteraction length of the evanescent field with the sample,gas measurements are of low sensitivity.

This article aims at giving a practical and theoret-ical introduction to ATR spectroscopy. An overview ofcommon applications and designs of ATR accessoriesfor MIR spectroscopy is given. Practical aspects of ATRspectroscopy, including sample preparation, sampling,and common errors are explained. The current applica-tions of the ATR technique in a wide range of fields arereviewed. To make it easy for the reader to start using theATR technique, a list of vendors of ATR accessories andtheir respective products is given at the end of the article.As this article is introductory in nature, several sourcesrecommended for further reading are provided.

1.2 History of ATR Spectroscopy

Isaac Newton famously remarked: ‘If I have seen fartherit is by standing on the shoulders of giants’. It is thereforefitting that we start this short overview over the history ofthe ATR technique and its giants with his work entitledOpticks: Or, A Treatise of the Reflections, Refractions,Inflections and Colours of Light.(2) Starting with Optickshas another significance as well: N.J. Harrick, one of theinventors of the ATR technique, begins his fundamentalwork on ATR spectroscopy entitled Internal ReflectionSpectroscopy by quoting a passage from Opticks: Or, ATreatise of the Reflections, Refractions, Inflections andColours of Light (book III, part 1, query 29), whereNewton describes total reflection of light at the interfacebetween a glass prism and air:

The Rays of Light in going out of the Glass into a Vacuum,are bent towards the Glass; and if they fall too obliquelyon the Vacuum, they are bent backwards into the Glass,and totally reflected;[. . .]

and also notes, that light that should be totally reflectedwill pass into a second optically dense material when theinterfaces of both objects are placed close enough to eachother, even though they do not touch:

And this is still more evident by laying together two Prismsof Glass, or two Object-glasses of very long Telescopes,the one plane, the other a little convex, and so compressingthem that they do not fully touch, nor are too far asunder.For the Light which falls upon the farther Surface of thefirst Glass where the Interval between the Glasses is notabove the ten hundred thousandth Part of an Inch, willgo through that Surface, and through the Air or Vacuumbetween the Glasses, and enter into the second Glass,[. . .]

Several great minds have investigated total reflection overthe course of the following centuries. E. Hall notes, at thebeginning of The penetration of totally reflected light intothe rarer medium(3):

The problem [attenuated total reflection] was bothexperimentally and theoretically studied by Fresnel, andmore or less treated by Verdet, Young, Huygens, Biot,Babinet, Billet, Stokes, and other. The first reliablequantitative work was published by G. Quincke in 1886.

Total reflection was, however, first used in the twentiethcentury for absorption measurements.(4) In 1926, C.V.Raman,(5) who went on to discover the Raman effecta few years later, reexamined the principles of totalreflection. In the early 1930s, the principles of ATRabsorption measurements were worked out by Taylorand Glover,(6) Taylor and Durfee,(7) and Taylor andKing(8) and employed to determine the birefringenceof layers of organic acids. In their work, the principles ofATR spectroscopy are laid out correctly and employed tomeasure absorption spectra, to study surface layers, andto determine refractive indices.(4)

The next major steps in the development of theATR technique happened in quick succession in the late1950s and the early 1960s. At the Fourth InternationalConference on Molecular Spectroscopy (Bologna, 1959),Jacques Fahrenfort of the Royal Dutch Shell Laboratoriespresented a paper on the ATR technique.(4) In Decemberof the same year, at the Second International Conferenceon Semiconductor Surfaces (Maryland), Nicolas JamesHarrick of the Philips Laboratories suggested in acomment on a talk about ‘Infrared Methods Appliedto Surface Phenomena’ (R.P. Eischens) to use ATRmeasurements to study molecules adsorbed on thesurface.(4) Harrick had been studying internal reflectionand total internal reflection in semiconductors before.(9)

At this point, however, he presumably did know neitherof the works of Taylor et al. nor of Fahrenfort’stalk.(4)

In 1961, ‘Attenuated total reflection’(84) by Fahren-fort was published in Spectrochimica Acta. In thiswork, Fahrenfort introduced the theoretical underpin-nings of ATR spectroscopy. He showed two differentexperimental setups using either a hemicylindric KRS-5(Thallium Bromoiodide) or AgCl element to collect ATRspectra using a focused or a collimated beam. In thesame paper, Fahrenfort also showed the possibility forquantification in ATR spectra using Beer’s law and itslimitations. Finally, he suggested using this new techniqueto determine refractive index spectra of samples.

In 1967, Harrick published Internal Reflection Spectro-scopy,(10) which included a thorough treatment of thetheoretical foundations and practical considerations


ATTENUATED TOTAL REFLECTION FOURIER TRANSFORM INFRARED SPECTROSCOPY 3

0

100

200

300

400

1960 1980 2000

Year

Num

ber

of p

ublic

atio

ns

Figure 1 Plot of the number of publications on ATRspectroscopy over the past 50 years. Data were collectedfrom Scopus. Plotted are all publications listed in Scopus asdocument type ‘article’, ‘book’, ‘conference paper’, ‘review’, or‘article in press’ that contain ‘attenuated total reflection’ in title,abstract, or keywords.

regarding ATR spectroscopy. At that time, ATRspectroscopy had already taken off with over 600papers published.(11) Since then, the interest in ATRspectroscopy has steadily increased (Figure 1).

The ATR technique is sometimes also referred to asinternal reflection spectroscopy (IRS), especially in worksby Harrick, Milosevic, and Mirabella. It seems, however,that today the generally used term for the technique isATR. As reflection measurements at subcritical anglesof incidence will lead to spectra that are very differentto those measured at supercritical angles, it makes senseto make a distinction between general internal reflectionand ATR. Furthermore, the acronym IRS is also usedfor IR spectroscopy, which no doubt can be a source ofmix-ups. Finally, most citizens of the United States willhave mixed feelings about the IRS at best, as this acronymis also used for the Internal Revenue Service.

Other major steps in the general acceptance of theATR technique were the broader availability of fastIR instruments, made possible by the invention of theFTIR technique and the development of horizontallymounted ATR elements and cylindrical ATR elementsfor liquids.(4)

Today, the ATR technique is used in broad rangeof experimental settings, including routine measurementprotocols as well as advanced research applications.ATR-FTIR spectroscopy is a standard analytical toolfor identification of chemicals in many industries, e.g.the pharmaceutical and the petroleum industries. Fiberoptic or conduit-type ATR probes are used in processanalytical applications, for in-line measurements inlaboratory as well as in industrial-scale settings. TheATR-FTIR technique is used to investigate biologicalsystems, especially membranes. ATR-FTIR microscopycan be used to image human and animal tissues and hasalso found broad application in forensics and restorationscience. Angle-resolved ATR-FTIR spectroscopy is used

to determine depth profiles of thin layers and to determinethe orientation of molecules adsorbed on a surface.

1.3 A Short Introduction to Mid-infrared FourierTransform Spectroscopy

1.3.1 The Mid-infrared Region of the ElectromagneticSpectrum

ATR spectroscopy is most often used in the MIR regionof the electromagnetic spectrum. The MIR region isusually defined as the wavenumber ν region from 4000 to400 cm−1 (from 2.5 to 25 μm). The predominant featuresin this spectral region are primarily due to molecularvibrations. These vibrations give information about thefunctional groups present in the molecule, as well as thestructure of the molecule.

While it is often a challenge to derive the structureof complex molecules solely from their IR spectra,these molecules can still be identified by their IRspectra, in a similar manner in which fingerprints areused for the identification of humans. This identifi-cation of molecules is either performed by compar-ison with reference spectra determined in the labor by using IR libraries. Such libraries are availablecommercially or for free. Examples for free librariesare the Spectral Database for Organic Compounds(http://riodb01.ibase.aist.go.jp/sdbs/cgi-bin/cre index.cgi?lang=en) or the National Institute of Standards and Tech-nology (NIST) Chemistry Webbook (http://webbook.nist.gov/chemistry/).

According to the harmonic oscillator model, theenergies of the vibrational states of the molecule are

Viν = hνi (υi + 12 ) (1)

υi is the vibrational quantum number and νi thefundamental frequency of the ith mode.(12) The selectionrules for IR spectroscopy only allow transitions of�υi = ±1, where the dipole moment μ changes duringthe vibration along the normal coordinate Qi :

∂μ

∂Qi

�= 0 (2)

1.3.2 Quantitative Mid-infrared Spectroscopy

IR spectroscopy does not only provide qualitativeinformation of a sample but can also be used forquantification. The latter is accomplished using the well-known Beer’s law. This law establishes a relation betweenthe path length l, the concentration c, the molar decadicabsorption coefficient ε, and the absorption A : A = lεc.The absorption is the negative decadic logarithm of thetransmittance (T ) of the sample: A = − log10(T ). T is the



ratio of light intensity measured before (I0) and afterthe sample (I ). Building a ratio of these so-called single-channel spectra I and I0ν permits the elimination ofintensity differences due to slight changes the emissionspectrum of the light source and due to fluctuations oflight absorption in the beam path. As it is usually notpractical to measure this intensity before the sample,I0ν is often determined in a measurement of a referencesample, e.g. pure solvent or a dry and clean ATR element,on which the sample is to be measured. This also servesto eliminate artifacts due to intensity losses that are notcaused by the sample, such as reflections at windows andreduced transmission on optical elements. The ratio ofthe single-channel measurements of the sample and thereference sample is then used to calculate the absorption.For polarized light, the absorption A of a band at a givenwavenumber also depends on the scalar product of thelight’s electric field vector and the change in the dipolemoment of the band(13):

A ∝∣∣∣∣ ∂μ

∂Qi

E

∣∣∣∣2

(3)

The largest A is measured, when the light is polarizedparallel to the dipole moment.

For general quantitation, neither l nor ε has tobe known. Instead, a calibration curve is recordedby measuring the absorption of samples with knownconcentrations of analyte at a specific wavenumber, e.g.in a flow cell with fixed l in the case of transmissionmeasurements. As the optical path length and theconcentration are independent of the wavenumber,Beer’s law also holds for integrated spectral features.Often, integrated bands are used instead of the absorptionat a single wavenumber to reduce the influence of noisein the spectra on the measurement results. Multivariatemethods can also be used, which combine informationfrom different parts of the spectrum to determine theconcentrations of the analytes. A good overview ofquantitation in MIR spectroscopy can be found in thebook titled Fourier Transform Infrared Spectrometry byP. R. Griffiths and J. De Haseth.(12)

1.3.3 Fourier Transform Infrared Spectroscopy

At of the time of writing this article, the predominanttechnique in MIR spectroscopy was Fourier transforminfrared spectroscopy. It has replaced dispersive tech-niques for IR spectroscopy in research, as well as inindustrial applications.

In dispersive spectrometers, a dispersive element suchas a grating or prism is used to split the light into its wave-lengths. Recording of I0 and I can be performed simul-taneously, measuring one wavelength after the other.

Fixed mirror

Source

Beam splitter

Sample

Moving mirror

l + Δl

l

Figure 2 Sketch of the beam paths in a Michelson interfer-ometer. Darker arrows denote higher light intensity.

E1

E2

E1 + E2

0

3λ4 4

λ

2λ

Δl = nλ+

Figure 3 Interference of two sine waves depending on thephase difference. Constructive interference happens when thepath difference �l in the two arms of the interferometer is awhole multiple of the wavelength.

In contrast, an FTIR instrument generates wavelengthinformation in an indirect way by first collecting an inter-ferogram I0(�l) followed by I (�l). These interferogramsare transformed mathematically into the desired singlebeam spectra I0 and I using the Fourier transform. Whilemany different types of interferometers exist, we will usethe Michelson interferometer (also used in the famousMichelson–Morley experiment(14)) to explain the generalprinciples. In this interferometer (Figure 2), light emittedby the source is split into two parts by a beam splitter.

One part is directed onto a fixed mirror, the otherone is directed onto a moving mirror. Both parts arethen reflected back onto the beam splitter. Again beingpartially reflected and transmitted at the beam splitter,the light is then recombined and can interfere with itself.The offset of the moving mirror �l leads to a phasedifference between the wave reflected off the fixed mirrorand that reflected off the moving mirror. Depending onthe wavelength of the light, this causes constructive ordestructive interference (Figure 3). The sample is then



probed by a beam that contains all wavelengths whoseintensities will, however, change during the displacementof the moving mirror.

Fourier transform instruments have two fundamentaladvantages when compared with similar dispersiveinstruments.(12) The first advantage concerns the signal-to-noise ratio (SNR). When spectra of M datapointsare measured with a Fourier transform and a dispersiveinstrument with equal throughput, resolution, andefficiency, the measurement time of the dispersiveinstrument must be M times that of the FT instrument toachieve the same SNR. For equal measurement times, theSNR of the dispersive instrument will be

√M times that

of the FT instrument (multiplex or Fellgett advantage).The second advantage of FTIR instruments is their

higher optical throughput in comparison with dispersiveinstruments (throughput advantage or Jacquinot advan-tage), as a circular beam shape is accepted by FTIRinstruments and such slits are no longer required.

Due to the short analysis times made possible by theFTIR technique and the possibility for molecular fingerprinting, FT MIR spectrometers are now found in almostall industries as tools for routine analysis to identifyincoming or outgoing chemicals and for quantification ofmain components of solids, as well as liquids and gases.

2 THEORETICAL ASPECTS OFATTENUATED TOTAL REFLECTIONSPECTROSCOPY

2.1 Reflection, Total Reflection, and the AttenuatedTotal Reflection Signal

Total reflection is a special case of reflection of anelectromagnetic wave at an interface between two media.The absorbance spectra measured in ATR spectroscopyare dependent on the intensity of the reflected lightrelative to that of the incident light. The relative intensityof the reflected light is given by the Fresnel equations.In the following section, these equations are derived.More in-depth explanations can be found in introductorytext books about electromagnetism, such as the one byPollack and Stump.(15) In this work, vectors such as theelectric field (E), the amplitude of the electric field ofan electromagnetic wave (E0), the wave vector (k), andthe position (x) are provided in bold font. Scalar values,e.g. time (t) and angular frequency (ω), are provided initalic font.

Generally, an electromagnetic plane wave can bedescribed by the following equation:

E(x,t) = E0ei(kx−ωt) (4)

The length of the wave vector of a plane wavepropagating in a medium is given by |k| = 2πn/λ0, whereλ0 is the vacuum wavenumber and n is the refractive index.Hence, for a wave propagating in a dielectric medium ofrefractive index n in the direction of the x-axis, Equation(4) can be transformed to

E(x,t) = E0ei(2πxn/λ0−ωt) (5)

The attenuation of the electric field in the mediumcan be described by using the complex refractiveindex n = n + ik instead of the real refractive index inEquation (5):

E(x,t) = E0ei(2πxn/λ0−ωt)e− 2πkλ0

x(6)

From (6) the physical quantity measured in IRspectroscopy, the light intensity I , can be calculated as

I (x) = cnε0

2

∣∣∣∣E0e− 2πkλ0

x

∣∣∣∣2

(7)

ε0 is the vacuum permittivity, c the speed of light, and n

the refractive index of the medium. Of practical interestfor most measurements is the determination of the ratioof the intensity of the light before and after traversingan absorbing medium of a given length. This ratio is alsofrequently expressed in percentage T (%) = I0 × 100%and called transmission. It only depends on the pathlength x through the medium and the absorbance index k

of the medium:I (d)

I (0)= e− 4πk

λ0d

(8)

By applying the decadic logarithm to both sides ofEquation (8), we get the familiar expression for theabsorption A:

A = − log10

(I (d)

I (0)

)= 4π log10(e)k

λ0d = αd (9)

α is called the linear decadic absorption coefficient. Inspectroscopy, especially when measuring analytes dilutedin a matrix, α is replaced by a product of the molardecadic absorption coefficient ε and the concentration toget Beer’s law:

A = εcd (10)

It allows the use of spectroscopic measurements forquantitative analysis of analytes in a given sample.

Our aim in explaining how ATR spectroscopy workson a theoretical level will now be to find a connectionbetween the absorption measured in transmission setups(see Equation 9) and the intensity ratio between the



x

z

y

n2

k2

k1 k3

n1

q2

q1 q3

x > 0x < 0

Figure 4 Reflection at an interface between two infraredtransparent, dielectric media (n1 > n2).

incident and the reflected light measured in ATRspectroscopy in a form similar to Beer’s law.

Consider two IR transmissive dielectric media withrefractive indices n1 and n2 with a common interface. Aplane wave traveling toward this interface at an angleof incidence θ1 will be partially reflected and partiallytransmitted (Figure 4). We expect an electric field of thefollowing form:

E(x,t) ={

E02ei(k2x−ω2t) x > 0E01ei(k1x−ω1t) + E03ei(k3x−ω3t) x ≤ 0

(11)

Maxwell’s equations tell us that the components of theelectric field (E) and the magnetic H-field tangential to theinterface are continuous across the boundary. The sameis true for the components of electric displacement field(D) and the magnetic B-field orthogonal to the interface:

E: E1,yz + E3,yz = E2,yz (12a)

H: H1,yz + H3,yz = H2,yz (12b)

D: ε1E1,x + ε3E3,x = ε2E2,x (12c)

B: μ1H1,x + μ3H3,x = μ2H2,x (12d)

If the electric fields are viewed on one point on theinterface, the continuity condition will be fulfilled for

C1e−iω1t + C3e−iω3t = C2e−iω2t (13)

and appropriate C1, C2, and C3. This condition can onlybe fulfilled when ω1,ω2, and ω3 are equal.

When we set the plane of incidence to the xy-plane, thez components of the wave vector have to be zero. Theprojections of the wave vectors onto the y-vector are thenof the form |k1| sin(θ1). As we already know, that ω1,ω2,

and ω3 are all equal, the e−iωt term can be factored out ofEquation (12). From the resulting equation again usingthe continuity condition

C1ei|k1| sin(θ2)y + C3ei|k3| sin(θ3)y = C2ei|k2| sin(θ2)y (14)

it follows that the components of k1, k2, and k3 in theyz-plane have to be equal:

|k1| sin(θ1) = |k2| sin(θ2) = |k3| sin(θ3) (15)

As |kj | = 2πnj/λ0 (λ0 being the vacuum wavelength),the angle of incidence θ1 is equal to the angle of thereflected wave θ3. The angle of incidence and the angle ofthe transmitted wave are related by Snell’s law:

n1 sin(θ1) = n2 sin(θ2) (16)

The x component kx of the wave vector can becalculated once ky is known:

kx =√

|k|2 − k2y = |k| cos θ (17)

When the light passes from the optically denser intothe optically rarer medium (n1 > n2), there are angles ofincidence θ1 at which there are no real θ2 to fulfill Snell’slaw. The smallest angle for which this is true is the criticalangle θc:

θc = arc sin(

n2

n1

)(18)

For angles of incidence of θc or greater, no light willbe transmitted into the lower refractive index medium,instead all the incident light is reflected. This is calledtotal reflection.

The amplitudes of the electric field of the reflectedwave can be calculated using the continuity conditionsderived from Maxwell’s equations.(15) We have shownin the previous paragraphs that the ω are equal andthe y components of the wave vectors are equal, too.The continuity conditions can therefore be simplified toconditions for the amplitudes of the electric and magneticfields:

E: E0,1,yz + E0,3,yz = E0,2,yz (19a)

H: H0,1,yz + H0,3yz = H0,2,yz (19b)

D: ε1E0,1,x + ε3E0,3,x = ε2E0,2,x (19c)

B: μ1H0,1,x + μ3H0,3,x = μ2H0,2,x (19d)

First, we consider the case of parallel polarized light.This case is often indicated by the symbol ||, the index p, orthe acronym TM (transverse magnetic). In this case, the



magnetic field vector of the incident light is orthogonalto the plane of incidence, H0,j,y = 0 and H0,j,x = 0. Toapply the continuity conditions for the electrical field,the electrical field has to be split up into its componentparallel to the interface and its component perpendicularto the interface. When the electrical field is written as aproduct of a directional vector (E0,j ) and its length (E0j )

as E0,j = E0,j E0,j , geometrical considerations lead to

(E0,1 + E0,3)ε1 sin(θ1) = E0,2ε2 sin(θ2) (20a)

for the components perpendicular to the interface and

(E0,1 − E0,3) cos(θ1) = E0,2 cos(θ2) (20b)

for the components parallel to the interface. Next, wewant to calculate the amplitude reflection coefficientr|| = E0,3/E0,1 of parallel polarized light as the ratio ofthe electric field of the reflected and incident light. Thiscan be done by solving (20a) and (20b) which results in

r|| = ε2 sin(θ2) cos(θ1) − ε1 sin(θ1) cos(θ2)

ε2 sin(θ2) cos(θ1) + ε1 sin(θ1) cos(θ2)(21)

Using Snell’s law and εj = n2j for dielectric media, θ2

can be eliminated:

r|| =n2

2 cos(θ1) − n1

√n2

2 − n21 sin2(θ1)

n22 cos(θ1) + n1

√n2

2 − n21 sin2(θ1)

(22)

Light polarized perpendicular to the plane of incidenceis often indicated by the symbol ⊥, with the index s

(German: ‘senkrecht’, orthogonal) or the acronym TE(transverse electric). In this case, the continuity conditionsfor the electric field

E0,1 + E0,3 = E0,2 (23)

will not be enough to determine the reflection coefficient.Instead, we have to use the continuity condition for themagnetic field:

(H0,1 − H0,3) cos(θ1) = H0,2 cos(θ2) (24a)

(H0,1 + H0,3)μ1 sin(θ1) = H0,2μ2 sin(θ2) (24b)

Owing to the interdependence of the electric andthe magnetic fields in electromagnetic waves, H0,j =(2πnj/c0λ0μj )E0,j , the ratio of the magnetic fields ofthe incident and the reflected wave equals that of theirelectric fields:

r⊥ = μ2 cos(θ1) sin(θ2) − μ1 sin(θ1) cos(θ2)

μ2 cos(θ1) sin(θ2) + μ1 sin(θ1) cos(θ2)(25)

Employing Snell’s law and μj = 1 for dielectric media,θ2 can be eliminated:

r⊥ =n1 cos(θ1) −

√n2

2 − n21 sin2(θ1)

n1 cos(θ1) +√

n22 − n2

1 sin2(θ1)

(26)

Equations (21), (22), (25), and (26) are called theFresnel equations. From them, the ratio of the intensitiesof the incident and the reflected beam can be calculated asR⊥ = |r⊥|2 and R|| = |r|||2. Similarly to Equation (7), theintensity of the light is proportional to the square of theamplitude of the electric field. For nonabsorbing media,light will be totally reflected for angles of incidence abovethe critical angle R⊥ = R|| = 1 (Figure 5). To calculatethe reflection at an interface to an absorbing medium,the refractive index n2 in the Fresnel equations simplyhas to be replaced by its complex counterpart n2.(16)

The relations between the intensity of the incident andthe reflected light, expressed as reflection coefficient R,therefore are

R|| =

∣∣∣∣∣∣∣n2

2 cos(θ1) − n1

√n2

2 − n21 sin2(θ1)

n22 cos(θ1) + n1

√n2

2 − n21 sin2(θ1)

∣∣∣∣∣∣∣2

(27a)

0.000

0 15

0.25

0.50

0.75

1.00

R

45

qc/°60 75 9030

a = 0.0 cm–1

a = 102 cm–1

a = 103 cm–1

a = 104 cm–1

R⊥

R||

qc

Figure 5 Reflection of light at an interface between an opti-cally denser (n1 = 2.4) and optically rarer medium (n2 = 1.3).The line styles indicate different values for the linear decadicabsorption coefficient α of the optically rarer medium. Greylines denote orthogonal polarization and black lines denoteparallel polarization.



R⊥ =

∣∣∣∣∣∣∣n1 cos(θ1) −

√n2

2 − n21 sin2(θ1)

n1 cos(θ1) +√

n22 − n2

1 sin2(θ1)

∣∣∣∣∣∣∣2

(27b)

As can be seen in the example in Figure 5, withincreasing absorption coefficient of the sample, there is astrong change in the intensity of the reflected light. Theshape of the dependence of the reflection coefficient R onthe angle of incidence also changes in case of absorbingsamples. As Harrick(17) notes, ‘there is no longer a sharpcritical angle for the absorbing case as there was forthe nonabsorbing one and the reflectivity curves becomeless steep in this region’. As can be seen from Figure 5,the sensitivity for changes in the absorption coefficient islargest close to the critical angle.(17)

The reason for the absorption dependence of thereflection at the interface for angles above the criticalangle is the evanescent field, which stretches into therarer medium. If the angle of incidence is increased tovalues greater than θc, then k2,y will be an imaginarynumber. This means, for angles of incidence greater thanthe critical angle, the electric field (see Equation 11) inthe second medium takes the following form:

E(x, t) = E02ei

[y

2πn1λ0

sin(θ1)−ωt

]e−x

2πλ0

√n2

1 sin2(θ1)−n22 (28)

Hence, the electric field will follow an exponentialdecay in the second medium (see Figure 6).

A common measure for how far the field extends intothe optically rarer medium is the depth of penetration dp,defined as the depth at which the electrical field falls to1/e of the electrical field at the interface.

E(dp)

E(0)= 1

e(29)

dp = λ0

2π

√n2

1 sin2(θ1) − n22

(30)

0.0

0.0 0.5 1.0

0.5

1.0

yλ0

n1 n2

E (

y)E

(0)

Figure 6 Magnitude of the evanescent electric field in theoptically rarer medium for different angles of incidence. Theangle of incidence increases from 35° at the nock of the arrowto 85° at the arrowhead. n1 = 2.4 and n2 = 1.3.

This is, however, not the maximum sampling depth ofthe ATR measurement. Besides the depth of penetration,the effective thickness de is often used in ATRspectroscopy. Mirabella(18) defines this effective thicknessin the following way: ‘The thickness de is defined as thethickness of a film of the sample material that would givethe same absorbance for transmission at normal incidenceas that obtained in the IRS experiment.’ This definitionleads to the expression

A = − log10(R) = αde (31)

in analogy to transmission measurements to describethe intensity of the light before and after reflectionat the interface for ATR spectra. When measurementparameters, such as the real part of the refractive indexof the sample and the coverage of the ATR surface arekept constant between measurements, the ratio of thereflectance with and without the analyte can be used todetermine the analyte’s concentration:

Aanalyte = − log10

(I0 × Ranalyte

I0

)= εanalytecanalytede (32)

To be able to use Equations (31) and (32) practically,de has to be independent of α and canalyte, respec-tively, for all measured samples. For weakly absorbingsamples, an approximate de can be calculated from A =[− log10(e)4πk]/λ0de = log10(R) using first-order approx-imations in k(1,3):

de⊥ = λ0

n1

n21 cos(θ)

π(1 − n221)[sin2(θ) − n2

21]1/2(33a)

de|| = λ0

n1

× n21 cos(θ)[2 sin2(θ) − n221]

π(1 − n221)[(1 + n2

21) sin2(θ) − n221][sin2(θ) − n2

21]1/2

(33b)

where nij = ni/nj and n2 is real. The error betweenthe linear approximations using Equations (33a) and(33b) and the exact values calculated from the Fresnelequations is <10% for reflection losses smaller than 10%per reflection.(17) To measure highly absorbing samples,larger angles of incidence can be used. Similarly, toincrease the sensitivity without sacrificing the linearityof the measurement, multiple reflections can be used.(17)

In such multireflection ATR measurements, the lightis reflected several times off the interface betweenthe optical denser and the optically rarer medium.The absorption increases linearly with the number of



reflections N :

AN = −log10(RN) (34)

≈ εanalytecanalytedeN (35)

2.2 Influence of the Measurement Parameters on theAttenuated Total Reflection Signal

2.2.1 Wavelength

As can be seen from Equations (33a) and (33b), theeffective depth of penetration in an ATR setup dependslinearly on the wavelength of the incident radiation.Hence, assuming constant values for n1 and n2, bands withthe same absorption coefficient will appear higher at lowerwavenumbers than at higher wavenumbers (Figure 18).

To make the relative band intensities more similar tothose in transmission spectra, the measured absorptionsin ATR spectra can be multiplied by the accordingwavenumber(1):

Acorr(ν) = AATR(ν)ν

νref(36)

In Equation (36), νref can be chosen at will, forexample, at a wavenumber where absorption in thetransmission spectrum and in the ATR spectrum aresimilar. This allows an approximation of spectra recordedin transmission setups from spectra collected using theATR technique. As this conversion does not consideranomalous dispersion, it is only an approximation. Itdoes, however, improve the results when ATR spectraare searched in libraries of transmission spectra.(19)

2.2.2 Angle of Incidence

A glance at the expressions for the effective thickness ofan ATR experiment (Equation 33) shows the importance

of the angle of incidence for ATR measurements. Whenthe angle of incidence is increased, the numeratorsin Equations (33a) and (33b) will increase and thedenominators will decrease. Accordingly a larger angle ofincidence will decrease the effective thickness of the ATRmeasurement. Hence, adjusting the angle of incidence ofan ATR measurement allows to tune the sensitivity of themeasurement.

Furthermore, it is important to ensure that the angleof incidence used is larger than the critical angle for thegiven ATR element and sample. As stated in Section 2,this condition is met, when n21 < sin(θ1). For dissolvedsamples, the refractive index of the solvent at thewavelength of the sodium D line (≈599 nm) can be usedto determine whether an angle of incidence is close tothe critical angle.(20) Tabulated values for the criticalangle calculated according to this method for the mostcommon solvents and ATR crystal material can be foundin Table 1.

2.2.3 Polarization of Incident Light

A comparison of the expression describing de⊥ and de||shows that in case of isotropic samples, the effectivethickness for parallel polarization will always be biggerthan that for perpendicular polarization.

When the analyte molecules or parts of theanalyte molecules have a fixed orientation rela-tive to the ATR element’s surface, the relationof the polarization-dependent signal intensities candeviate significantly from that predicted by the effec-tive thickness, because the angle between the elec-tric field vector of the incident light and ∂μ/∂Qi

also influences the strength of the absorption band(see Section 1.3.2). This effect can be employed to deter-mine the average orientation of, e.g. a functional groupin the sample.(1)

Table 1 Critical angles for common solvent (n2) –ATR material (n1) combinationsa

nα-Al2O3

1.74ZrO22.15

ZnSe2.20

KRS-52.37

ZnSe2.40

Cdiamond2.40

AMTIR2.50

CdTe2.65

Ge4.00

Methanol 1.33 50° 39° 38° 35° 34° 34° 33° 31° 20°

Water 1.33 50° 39° 38° 35° 34° 34° 33° 31° 20°

Ethanol 1.36 52° 40° 39° 35° 35° 35° 33° 31° 20°

EtOAc 1.37 52° 40° 39° 36° 35° 35° 34° 32° 21°

Hexane 1.37 53° 40° 39° 36° 35° 35° 34° 32° 21°

Cyclohexane 1.42 55° 42° 41° 37° 37° 37° 35° 33° 21°

DMF 1.43 56° 42° 41° 38° 37° 37° 35° 33° 21°

Glycol 1.43 56° 42° 41° 38° 37° 37° 35° 33° 21°

CCl4 1.46 57° 43° 42° 38° 38° 38° 36° 34° 22°

DMSO 1.48 59° 44° 43° 39° 38° 38° 37° 34° 22°

Toluene 1.49 60° 45° 43° 40° 39° 39° 37° 35° 22°

C6H5Cl 1.52 62° 46° 44° 40° 40° 40° 38° 36° 23°

a nD values for the solvents and refractive indices for the ATR materials were taken from Coates.(20)



K1

Ey qy

qx

y

x

m

Figure 7 Sketch of the orientation of the dipole moment of adiatomic molecule and the electric field of the incident wave for⊥ polarization. The sample–ATR element interface is parallelto the paper plane.

For ⊥ polarized light (Figure 7), the electric field onlyhas a component parallel to the interface; therefore, onlyvibrations where ∂μ/∂Qi is not orthogonal to the interfacewill interact with the incident radiation. If the absorptionof a sample with a marked direction (x ′) is placed on theATR and measured twice the orientation of ∂μ/∂Qi inthe xy-plane can be determined. The first measurementis done with x ′ parallel to the Ey field vector (Ax ′), thesecond one after rotating the sample by 90°(Ay ′). Theaverage orientation can then be calculated from(1)

Ax ′

Ay ′= 〈cos2 θx ′ 〉

〈cos2 θy ′ 〉 (37)

The angle brackets 〈·〉 denote the average.Light of parallel polarization has an electric field

parallel to the interface (Ex) as well as perpendicularto the interface (Ez) (Figure 8). Accordingly, spectracollected with this polarization can give information aboutthe orientation of dipole moment in the xz plane. Whenthe sample is rotated between measurements, informationin three dimensions is accessible. From A1 measured for

z

x

mqz

qx

Ez

Ex

k1

Figure 8 Sketch of the orientation of the dipole moment of adiatomic molecule and the electric field of the incident wave forpolarization.

x ′ parallel to Ex and A2 measured for y ′ parallel to Ex andusing 〈cos2(θ′

x)〉 + 〈cos2(θ′y)〉 + 〈cos2(θ′

z)〉 = 1, the anglesθi can be calculated from(1,21)

A1

A2=

〈cos2(θ′z)〉 + 〈cos2(θ′

x)〉|Ex |2|Ez|2

〈cos2(θ′z)〉 + 〈cos2(θ′

y)〉|Ex |2|Ez|2

(38)

The electrical fields at the interface are(1)

Ex =2n1 cos(θ)

√n2

1 sin2(θ) − n22√

n21 − n2

2

√(n1

1 + n22) sin2(θ) − n2

2

E0,|| (39a)

Ez = 2n21 cos(θ) sin(θ)√

n21 − n2

2

√(n1

1 + n22) sin2(θ) − n2

2

E0,|| (39b)

Mirabella(21) explains the experimental applicationof these theoretical considerations for solid samples.An in-depth introduction into the application of ATRspectroscopy to study the orientation of biologicalmembranes has been written by Goormaghtigh et al.(22)

2.2.4 Refractive Indices of Sample and Attenuated TotalReflection Element

The refractive indices of the sample and the ATR crystalalso influence the ATR spectrum. Usually, instead ofboth refractive indices only their ratio n21 = n2/n1 (indexmatching) is considered. Higher index matching will leadto a higher effective thickness.(17)

In general, the refractive index of the materials, sample,and ATR element alike is not constant, but insteadshows wavelength dependence. In wavenumber regionsfar from absorption bands, the refractive index changesvery slowly, with a positive slope ∂n/∂ ν > 0 (normaldispersion). However, close to absorption bands, that is,close to a peak in the imaginary part of the refractiveindex n, there will be a much more rapid change in thereal part of n. On the low wavenumber flank of theabsorption band, the real part of the refractive indexwill increase significantly above the values farther fromthe band, then drop to values below those farther fromthe absorption band at the high wavenumber flank andfinally increase again to values close to the starting value(Figure 9).

∂n/∂ ν < 0 is called anomalous dispersion. The inter-dependence of the real and the imaginary part of n

is described by the Kramers–Kronig relations.(23) WithP denoting the principal value of the integral and n∞denoting the refractive index at the upper integration



1.29

1.30

1.31

2000 1800 1600 1400 1200 10000.0

5.0

10

v /cm–1~

n (v

)/1

~

k (v

)/10

–3~

Figure 9 Anomalous dispersion in the vicinity of an absorp-tion band. n and k were calculated using the method of Huangand Urban.(24)

limit, these relations are

n(νa) = n∞ + 2π

P

∫ ∞

0

νk(ν)

ν2 − ν2a

dν (40a)

k(νa) = −2νa

πP

∫ ∞

0

n(ν) − n∞ν2 − ν2

adν (40b)

The change in the real part of the refractive indexacross an absorption band leads to an increase in theeffective thickness on the low wavenumber side of theband and a decrease in the effective thickness on the highwavenumber side of the band. When ATR spectra arecompared with spectra measured in transmission mode,this leads to a perceived increase in the absorption onthe low wavenumber side of a band and a perceiveddecrease in the absorption on the high wavenumberside of a band. The band maximum therefore appearsto be shifted toward lower wavenumbers. The severityof this effect also depends on the refractive index ofthe ATR crystal n1, because in the expressions for theeffective thicknesses in Equation (33), n2 only showsup in the ratio n2/n1. A higher n1 will lead to alower influence of anomalous dispersion. Furthermore,the effects are more pronounced for steeper than forflatter angles and for parallel than for perpendicularpolarization.(17)

The refractive index of materials used in IR optics,such as ATR elements, is also wavelength dependent.A plot of the dependence of the refractive indexon the wavelength of several materials commonlyused for IR optics can be found in Figure 10. Inaddition, the dispersion equations for these materialsare provided in Table 2. Optical constants for a muchwider range of optical materials have been compiled byWeber.(25)

KRS-5

ZnSeZnS

AgCl

Si

SiO2Al2O3

MgO

MgF2LiF

Ge

GaAs

CsI

Diamond

CaF2

BaF2

AMTIR-1

Wavenumber / 103 cm−1

n / 1

λ / μm

5 0.5

0 20 30101

1.5

2

2.5

3

3.5

4

4.51

Figure 10 Plots of the dispersion relation of commonmaterials for infrared optics and ATR elements (seeTable 2).

The dispersion equations in Table 2 are empiricalrelations based on the Sellmeier equation

n2(λ) = 1 + A1λ2

λ2 − λ21

+ A2λ2

λ2 − λ22

+ · · · (41)

or Sellmeier–Cauchy-like equations. In these empiricalrelations between the wavenumber and the refractiveindex, the coefficients Aj and λj are determined by fittingexperimental data.(45)

In short, factors that lead to an increased effectivethickness are

• better (closer to unity) index matching;• steeper angle of incidence;• parallel polarization of the incident light; and• lower wavenumber.

The effects of anomalous dispersion on the refractiveindex spectrum are bigger for

• better index matching;• a steeper angle of incidence; and• parallel polarization of the incident light.



Table 2 Dispersion equations of common infrared optical materialsa

Material Dispersion formula Range (μm) Source

Sapphire n2o = 1

1.4313496λ2

λ2 − (0.0726631)2+ 0.65054713λ2

λ2 − (0.1193242)2+ 5.3414021λ2

λ2 − (18.028251)20.22–5.0 26

n2e = 1 + 1.5039759λ2

λ2 − (0.0740288)2+ 0.55069141λ2

λ2 − (0.1216529)2+ 6.59273791λ2

λ2 − (20.072248)2

AMTIR-1 n2 = 1 + 5.298λ2

λ2 − (0.29007)2+ 0.6039λ2

λ2 − (32.022)21–14 27

BaF2 n2o = 1 + 0.643356λ2

λ2 − (0.057789)2+ 0.506762λ2

λ2 − (0.10968)2+ 3.8261λ2

λ2 − (14.3864)20.27–10.3 28

N-BK7 n2 = 1 + 1.03961212λ2

λ2 − 0.00600069867+ 0.231792344λ2

λ2 − 0.0200179144+ 1.01046945λ2

λ2 − 103.5606530.3–2.5 29

CaF2 n2 = 1 + 0.5675888λ2

λ2 − (0.050263605)2+ 0.4710914λ2

λ2 − (0.1003909)2+ 3.8484723λ2

λ2 − (34.649040)20.23–9.7 30

Diamond n2 = 1 + 4.3356λ2

λ2 − (0.1060)2+ 0.3306λ2

λ2 − (0.1750)20.225-∞ 31

CsI n2 = 1 + 0.34617251λ2

λ2 − (0.0229567)2+ 1.0080886λ2

λ2 − (0.1466)2+ 0.28551800λ2

λ2 − (0.1830)2+ 0.39743178λ2

λ2 − (0.2120)2+

3.3605359λ2

λ2 − (161.0)2

0.29–50 32

GaAs n2 = 3.5 + 7.4969λ2

λ2 − (0.4082)2+ 1.9347λ2

λ2 − (37.17)21.4–11 33

Ge n2 = 9.28156 + 6.72880λ2

λ2 − 0.44105+ 0.21307λ2

λ2 − 3870.12–12 34, 35

LiF n2 = 1 + 0.92549λ2

λ2 − (0.07376)2+ 6.96747λ2

λ2 − (32.79)20.1–10 30

MgF2 n2o = 1 + 0.48755108λ2

λ2 − (0.04338408)2+ 0.39875031λ2

λ2 − (0.09461442)2+ 2.3120353λ2

λ2 − (23.793604)2

n2e = 1 + 0.41344023λ2

λ2 − (0.03684262)2+ 0.50497499λ2

λ2 − (0.09076162)2+ 2.4904862λ2

λ2 − (23.793604)20.27–7 36

MgO n2 = 1 + 1.111033λ2

λ2(0.0712465)2+ 0.8460085λ2

λ2(0.1375204)2+ 7.808527λ2

λ2(26.89302)20.36–5.4 37

SiO2(α−quartz) n2o = 1 + 0.663044λ2

λ2 − (0.060)2+ 0.517852λ2

λ2 − (0.106)2+ 0.175912λ2

λ2 − (0.119)2+ 0.565380λ2

λ2 − (8.844)2+ 1.675299λ2

λ2 − (20.742)2

n2e = 1 + 0.665721λ2

λ2 − (0.060)2+ 0.503511λ2

λ2 − (0.106)2+ 0.214792λ2

λ2 − (0.119)2+ 0.539173λ2

λ2 − (8.792)2+ 1.807613λ2

λ2 − (197.709)20.18–0.71 38

Si n2 = 1 + 10.66842933λ2

λ2 − (0.3015116485)2+ 0.003043475λ2

λ2 − (1.13475115)2+ 1.54133408λ2

λ2 − (1104.0)21.36–11 39, 40

AgCl n2 = 1 + 2.062508λ2

λ2 − (0.1039054)2+ 0.9461465λ2

λ2 − (0.2438691)2+ 4.300785λ2

λ2 − (70.85723)20.54–21.0 41

T1[BrI] n2 = 1 + 1.8293958λ2

λ2 − (0.150)2+ 1.6675593λ2

λ2 − (0.250)2+ 1.1210424λ2

λ2 − (0.350)2+ 0.04513366λ2

λ2 − (0.450)2+ 12.380234λ2

λ2 − (164.59)20.58–39.4 42

β-ZnS n2 = 1 + 0.3390426λ2

λ2 − (0.31423026)2+ 3.7606868λ2

λ2 − (0.1759417)2+ 2.7312353λ2

λ2 − (33.886560)20.55–10.5 43

ZnSe n2 = 1 + 4.2980149λ2

λ2 − (1920630)2+ 0.62776557λ2

λ2 − (0.37878260)2+ 2.8955633λ2

λ2 − (46.994595)20.55–18 43

ZrO2:12%Y2O3 n2 = 1 + 1.347091λ2

λ2 − (0.062543)2+ 2.117788λ2

λ2 − (0.166739)2+ 9.452943λ2

λ2 − (24.320570)20.36–5.1 44

aExcerpt from Weber.(25)



3 PRACTICAL ASPECTS OF ATTENUATEDTOTAL REFLECTION SPECTROSCOPY

3.1 Materials

The material of an ATR element has a profound effect onthe experiment that can be performed with this element.Apart from a good transmission in the spectral rangeof interest as well as a higher refractive index thanthe sample, ATR elements also have to be chemicallyinert in the measurement environment and insoluble inthe intended sample. Usable wavelength regions andsolubilities of common materials for ATR elements canbe found in Table 3.

Mechanical properties of the ATR element alsoinfluence sampling. A hard ATR element allows to usemore force to press the sample against the surface of theelement to ensure a better contact. Softer materials willallow a better contact with brittle samples.

3.2 Number of Reflections

In the simplest ATR setup, light will be reflected offthe ATR element–sample interface once. This is, forexample, the case in a prism-shaped ATR element witha triangular cross-section. If an ATR element with atrapezoidal cross-section is used instead, the radiationwill bounce off the top and bottom surface multipletimes. In this case, the effective thickness of the setupincreases linearly by the number of reflections. In theory,the absorption measured in a setup using unpolarizedlight with N reflections is

A = − log10

(RN

⊥ + RN||

2

)(42)

The number of reflections, however, cannot beincreased without limit. The width of the IR beamincreases along its path through the ATR element. A high

beam width can lead to parts of the beam undergoingmore reflections at the interface than others,(10) whichin turn leads to nonlinearities in the measurement(Figure 11).

Owing to the high surface sensitivity of the ATRtechnique, the contact between the sample and the ATRelement is very important. For solid samples, this contactis often assured by pressing the sample onto the ATRelement mechanically. In a single bounce ATR, it iseasier to fully cover the smaller ‘hot’ zone of the ATRelement, where light can interact with the sample thanin a multibounce ATR, which has N such ‘hot’ zones.The Harrick SplitPea™ is one example of an ATR setupthat is specifically designed to have a small ‘hot’ spot andthereby increase the sensitivity for the measurement ofsolid samples.(16)

In multiple reflection ATR setups, either one or bothsides of the ATR element can be used for measurements.A common design of ATR setups uses a horizontallymounted ATR (HATR) element, where only the top ofthe element is covered with the sample. ATR accessorieswith this design are, for example, the Spectra-Tech ARK(Thermo Scientific), the Gateway (Specac), the OverheadATR (Bruker), and the HATR and ATRmax II™ (PikeTechnologies).

(a) (b)

(c)

Figure 11 Cross-section of single and multi reflection ATRelements. (a) Triangular, single reflection; (b) trapezoidal,multireflection; and (c) fiber waveguide.

Table 3 Optical and chemical properties of common materials for ATR elements

Material Trivial name Usable range(25,46) (cm−1) H2O solubility(46,47)(g L−1) Other solvents(47)

AgBr 20 000–300 8.4 × 10−5 NaClα-Alumina Sapphire 55 000–1800 ≈0 BasesGe33As12 Se55 AMTIR-1 11 000–750 ≈0BaF2 50 000–840 1.2CaF2 50 000–1140 ≈0Cdiamond Diamond 45 000–2500 and 1650 to < 200 ≈0Ge 5500–600 ≈0GaAs 11 000–580 ≈MgO Irtran-5® 62 500–1100 0.0062 Acids, NH4 saltsSiO2 Quartz 55 000–4000Si Silicon 8300–660 ≈0 HF + HNO3TlBr-TlI KRS-5® 20 000–250 0.05β-ZnS Cleartran 17 000–833 6.5 × 10−4 Acid



Sample in

Thermocouple

Sample out

Reflecting cone

Optical rays

ATR element

Figure 12 Cylindrical TNL-130H CIR element (Axiom Analytical Inc.) for use with FTIR spectrometers. (Reprinted withpermission of Axiom Analytical Inc.)

A special ATR element type designed for multire-flection measurements using a FTIR spectrometer iscylindrical in shape with conical ends. Focusing elements,such as parabolic mirrors, are used at the ends of the rodsto introduce light into the ATR element and reshape theexiting beam to conform to the expected beam path in aspectrometer. These cylindrical internal reflection (CIR)elements are usually used for the measurement of liquids.For that end, they have to be enveloped in a flow cell.It is possible to seal the flow cell toward the cylindricalelement using o-rings without reducing the light intensitysignificantly. Axiom Analytical offers a special type ofCIR element that is specifically designed for reproduciblemeasurements of liquids. This is achieved by restrictingthe angles of incidence to a small range (Figure 12).(48)

Thick fiber waveguides are similar to long cylindricalATR elements. Light travels along the waveguide and istotally reflected at the interface between the waveguideand air or sample as long as the angle of incidence islarger than the critical angle. They are based on IRtransparent fibers, such as chalcogenide glasses, fluorideglasses, silica-based glasses, thallium halides, and silverhalides.(49) Like in an ATR setup, the interaction betweenthe sample and the light happens via the evanescent field.Generally, fiber waveguides show a higher sensitivitythan ATR sensors as they have more reflections thanan ATR sensor. This sensitivity can be further increasedby changing the shape of the fiber: a tapered fiber willshow more reflections on the same length of the fiber,bending the fiber decreases the angle of incidence inthe fiber and thereby increases the effective thickness of

the measurement, and by forming the fiber into a loop,the number of reflections can further be increased.(49)

Selective layers can be used to enrich the analyte closeto the surface of the fiber and thereby increase thesensitivity.(50) Like ATR elements, fiber evanescent wavesensors (FEWSs) can be employed in flow cell setups, aswell as in remote setups, where additional fibers guidethe light from the light source to the FEWS and back tothe detector.(49)

3.3 Sample Preparation and Measurement Protocols

3.3.1 Liquid Samples

Liquid samples can be measured either in a flow cell orby using a trough. A flow cell makes the use of an ATRin an automated analytical system, such as a sequentialinjection analysis (SIA) or flow injection analysis (FIA)system possible. But even when the samples are injectedinto the flow cell manually, a flow cell offers the additionalbenefit of precluding sample evaporation. Flow cells arecleaned in between samples by flushing with solventinstead of wiping and applying solvent several times as intrough-type sampling equipment. Another reason to usea flow cell is when many similar samples are measuredand only the difference in the absorption between thepure solvent and sample dissolved in the solvent is ofinterest.

To assure a uniform attenuation of all of the incidentlight, it is important to that flow cells are keptcompletely free of air bubbles. If this is not achieved,nonlinearities in the recorded absorption spectra will



appear; furthermore, baseline shifts will complicate thequalitative interpretation of the recorded spectra. Toremove air bubbles from flow cells, it often helps to flushthe cell with a solvent with a lower surface tension thatis miscible with the solvent used in the measurement(such as ethanol when measuring with water as solvent).When the inside of the cell can not be visually inspected,air bubbles can be found by calculating an absorptionspectrum from a single beam measurement of a bubblefree cell filled with solvent (e.g. after flushing withethanol) and a recent single beam measurement. Whennew bubbles have formed In this absorption spectrum thebands of the solvent will show up as negative bands.

For viscous samples or when many different liquidsamples are to be measured, a trough can be better usedto hold the liquid on the ATR element. When using atrough, the ATR element has to be completely coveredwith the sample to avoid non-linearities in the measuredspectra.

3.3.2 Solid Samples

For solid samples, a good contact of the sample and theATR element’s surface is not as easy to guarantee asfor liquids. The contact can be improved either by usinga mechanical clamp to press the sample onto the ATRelement, by melting the sample and letting it solidify asa film on top of the ATR element or by spin-coating theATR with the analyte. The contact between the ATRelement and the sample can also be improved by addinga soft, high index of refraction material (e.g. AgCl andAgBr) between the ATR element and the sample.(19) Themost common method to improve the contact is, however,using a mechanical clamp that presses the sample ontothe ATR element (Figure 13).

To check whether a good optical contact has been estab-lished, Mirabella(19) suggests to compare the absorptionsat || and ⊥ polarization for a 45° angle of incidence. Atthis angle of incidence, A‖ is twice as large as A⊥. Ekgasitand Padermshoke(51) propose to compare the normal-ized absorption spectra collected at || and ⊥ polarization.When there is no air gap, these spectra should be alike. Asecond method proposed by Ekgasit and Padermshoke(51)

is to compare a normalized ATR absorption spectrum ofthe sample recorded at any incidence with a transmis-sion spectrum of the sample. For two wavenumbers,the ratio of the absorption in the transmission spectraATrans(ν2)/ATrans(ν1) and the ratio of the absorption inthe ATR spectra AATR(ν2)/AATR(ν1) should be equal tothe ratio of the compared wavenumbers:

Figure 13 Thermo Fisher iD5 ATR accessory with a mechan-ical clamp to improve the contact between ATR element andsolid samples. (Reprinted with permission of Thermo FisherScientific.)

ATrans(ν2)/ATrans(ν1)

AATR(ν2)/AATR(ν1)= ν2

ν1

When a clamp is used to improve the contact betweenthe ATR element and the sample, background spectraare still collected from an empty ATR element that is nottouched by the clamp. Brittle samples should be groundbefore measurement. In any case, the ATR elementshould be fully covered with the sample to obtain bestresults.

Even if all the steps mentioned earlier are considered,the contact between the ATR element and the samplecan vary slightly from measurement to measurement. Thiswill impair the use of the ATR spectra for quantitativemeasurements. A common solution to this problem isto look for a band that should be constant acrossall samples of the measurement series (e.g. backbonebands in polymers and filler substances in pharmaceutics)and then use the ratio of this band and the band ofinterest for quantification.(19) Application of pressure toa solid sample, however, can cause additional difficulties.This can be the case when analyzing crystalline sampleswhich change their crystal structure upon application ofpressure. Therefore, in case of such polymorph samples,special attention has to be paid to assure proper spectrumacquisition.

3.3.3 Contaminants

The surface sensitivity of the ATR technique makesit especially sensitive to measurement errors due to



4000

Abs

orpt

ion/

a.u.

3500 3000 2500

Wavenumbers/cm–1

2000 1500 1000

Laboratory grease

Nitrile glove

Finger grease

PTFE

Ethanol

2-propanol

Water

Figure 14 Spectra of several contaminants in ATR measure-ments. The spectra were collected on a MIRacle singlereflection diamond ATR. (Reprinted with permission of PIKETechnologies.)

contamination of the surface of the ATR element. Thesecontaminations can be caused by insufficient cleaningprotocols or inadvertent touching of the ATR element.Griffiths and De Haseth(12) give as common contaminantsfinger grease, hand lotion, talc, plasticizers, and slipagents from laboratory gloves as well as silicon grease.Furthermore, all fluids that come into contact with theATR element have to be expected as contaminants. Also,a combination of otherwise unsuspicious things, such assolvents and cleaning procedures, can cause errors thatare hard to trace. Furthermore, when the sample does notfully cover the surface of the ATR element, bands causedby the material of the clamp will also show up in thespectrum. The spectra of several important contaminantsare shown in Figure 14.

Gases in the beam path will also interfere with themeasurement when their local concentration changesbetween measurements. Two gases whose bands oftenshow up in MIR spectra are water vapor and CO2(Figure 15).

3.3.4 Cleaning Attenuated Total Reflection Elements

Although most materials used to fabricate ATR elements,such as germanium, zinc selenide, or diamond, arerelatively robust, ATR elements are nonetheless sensitiveoptical instruments and should be treated as such.Generally, a combination of washing or flushing withfitting solvents and wiping with optical tissues is arecommended cleaning procedure. However, dependingon the fabrication of the ATR accessory, cleaning using anultrasound bath might also be possible. For dry powdersthat do not stick to the surface of the ATR element, a softbrush can be used as a cleaning implement.

4000

Abs

orpt

ion/

a.u.

3500 3000 2500

Wavenumbers/cm–1

2000 1500 1000

Carbon dioxide

Water vapour

Figure 15 MIR transmission spectra of CO2 and water vapor.(Created using data from Ref. 52.)

Depending on the design of the ATR setup, somefurther restrictions concerning possible cleaning toolsand protocols that go beyond those imposed by themechanical and chemical properties of the ATR mayapply. For ATR units where a glue used to hold the ATRelement in place is the fact that such a glue will mostlikely be more sensitive to organic solvents than the ATRelement itself has to be considered. If the materials usedfor the ATR accessory and their chemical and mechanicalresistance are not known, it is best to consult the vendorfor recommended cleaning procedures.

3.4 Angle of Incidence

The plane wave view of the ATR signal generation usedin Section 2 does not represent the complete picture. Ina normal ATR setup, there will be a range of anglesof incidence at once. However, as different angles ofincidence lead to different effective thicknesses, a widerrange of angles of incidence will decrease the range ofconcentrations at which the ATR signal is approximatelylinearly dependent on the concentration of the analyte.(48)

In ATR setups with a small ‘hot’ spot, as mentionedin Section 3.2, a wider range of angles of incidence isaccepted in trade for a higher sensitivity and a lowersample consumption. In these setups, the IR beam isfocused onto the interface between the sample and theATR element. For more sophisticated applications, suchas the determination of the complex refractive indexspectra of samples or for depth profiling, ATR setupswith a narrow range of angles of incidence are necessary.

Finally, many vendors offer variable angle ATR setupswhere the angle of incidence can be selected by the user(Figures 16 and 17).



Figure 16 Optical layout of the VeeMAX II variable angleaccessory with ATR. (Reprinted with permission of PIKETechnologies.)

Figure 17 Photograph of the VeeMAX II with ATR and oneof the exchangeable ATR elements. (Reprinted with permissionof PIKE Technologies.)

3.5 Surface Modification

The sensitivity and the selectivity of ATR measurementscan be enhanced by modifying the surface of the

ATR element. These modifications can increase thesensitivity by either increasing the electromagnetic fieldor selectively enriching the analyte in close vicinity of thesurface of the ATR element.

3.5.1 Attenuated Total Reflection–Surface-enhancedInfrared Spectroscopy

The intensity of the absorption bands in IR measurementscan be enhanced by introducing certain metal substratesinto the sample or depositing metal island films of afew nanometers on ATR elements before application ofthe sample.(53,54) This SEIRA effect is caused by twodifferent mechanisms, an electromagnetic and a chemicalmechanism. The electromagnetic mechanism of SEIRAworks through the increase in the electric field of theincident light close to the metal substrate. This increasein turn leads to an increase in the absorption.(54) ForATR geometries, only the electric field parallel to thesurface will be enhanced.(54) The chemical enhancementis in part due to orientational effects that align ∂μ/∂Qi

with the enhanced electric field vector. At the timeof writing, the sensitivity of measurements when usingSEIRA can be increased by one to two orders ofmagnitude. This is clearly smaller than the enhancementfactor found in surface-enhanced Raman spectroscopy(SERS). While SEIRA has shown itself to be a decisiveadvantage in advanced scientific experiments, so far ATR-FTIR/SEIRAS is not developed enough for routine use.

3.5.2 Selective Layers

Owing to the surface sensitivity of the ATR technique,the sensitivity of an ATR measurement for one analyteor a group of analytes in a sample can be increasedby selectively enriching them close to the surface ofthe ATR element. This can be achieved by placing afilm on top of the ATR element that shows a higheraffinity to the sample than to the matrix components.Several different types of such layers have been reportedin the literature. Polymer layers with a thickness ofa few micrometers have been shown to increase thesensitivity for the detection of organic analytes, suchas chlorinated hydrocarbons, in aqueous matrices(55,56)

by several orders of magnitude. Molecularly imprintedpolymers(57) (MIPs) are tailor-made to enrich one specificanalyte.(58) Dedicated sol-gels can also be used asenrichment layers in ATR spectroscopy.(59) Zeolites havebeen shown to allow the detection of gaseous analytesusing the ATR technique.(60,61)



4 DIFFERENCES BETWEEN ATTENUATEDTOTAL REFLECTION SPECTROSCOPYAND TRANSMISSION SPECTROSCOPY

4.1 Comparison of Attenuated Total ReflectionSpectra and Transmission Spectra

As stated in the previous section, Beer’s law is validfor ATR spectra, when certain constraints are met. Forspectroscopists, it is, however, not only the intensityof the absorption band that contains information butalso its shape, position, and relative sensitivity. Allthese properties can differ between transmission andATR spectra due to the different mechanisms withwhich the optical constants of the sample are convertedinto absorption spectra. And while the name ‘effectivethickness’ may evoke the image of a transmission cell ofa defined thickness, it has been shown in the earliersections to be only a theoretical construct that willchange across a spectrum depending on the wavenumberand the refractive index of the sample and the ATRelement. A visualization of the differences between theabsorptions measured in transmission (when reflectionsat the interfaces are neglected) and ATR spectra canbe found in Figure 18. With increasing wavenumber, theintensity of the bands decreases. As mentioned before,an increase in the refractive index of the ATR elementwill lead to a decrease in the magnitude of absorptionbands (Figure 19). In ATR spectra, due to anomalousdispersion, an increase in the absorption at one bandwill lead to a shift of the band maximum (Figure 20).This is another good reason to use integrals of spectralfeatures for quantitative ATR spectroscopy, in additionto the already mentioned improvement of the SNR. The

02500

50

100

150

2000 1500 1000

Abs

orpt

ion/

mA

U

v /cm–1~

Figure 18 Simulated spectra for a transmission setup(l = 2.5 μm) and for a n1 = 2.4 and θ = 45° ATR setup. Thespectrum for a transmission setup is plotted in black, the ATRspectrum for parallel polarization is denoted by a dark grey line,and that for perpendicular polarization is denoted by a lightergrey line. The intensities of the band in the ATR spectra visiblyincrease with decreasing wavenumber. The spectrum collectedwith parallel polarization shows more intense bands than thatcollected with perpendicular polarization.

Abs

orpt

ion/

mA

U

v /cm–1~

01600

100

200

300

1500 1400

Figure 19 Calculated ATR spectra for different refractiveindices of the ATR element n1. Along the arrow, n1 increasesfrom 2 to 4. The grey line marks the position of the bandmaximum in a transmission setup. When n1 increases, the heightof the band decreases. Owing to anomalous dispersion, themaximum of the band is shifted toward lower wavenumbers inthe ATR spectra.

Abs

orpt

ion/

mA

U

v /cm–1~

01600 1500 1400

200

400

Figure 20 Calculated ATR spectra for different magnitudesof the absorption. Along the arrow, α increases from 0 to0.2 μm−1. The grey line marks the position of the band maximumin a transmission setup. While the height of the band in theATR spectra increases when α increases, the band maximumalso shifts due to an increase in the anomalous dispersion.Interactions between molecules have been neglected in thisexample.

shift of the maximum will have a lower impact on theintegral of the band than on the absorption measured atone wavenumber.

In transmission measurements, reflections at theinterfaces between different materials, e.g. betweenthe window and a sample solution, will give rise tointerference fringes that depend on the refractive indexof the materials and the length of the flow cell.(17) Whilethese fringes are often used to accurately determine theoptical path length of the flow cell, they also make thedetermination of absolute absorption spectra impossiblein transmission setups. Usually, liquids with known opticalconstants and low absorption are used as a reference whenabsolute values are required. These fringes cannot occurin ATR measurements, even when the sample is a thinlayer.



4.2 Sample Preparation

As of today the ATR technique has almost completelyreplaced sampling techniques which required cumber-some sample pre-treatment. This is why many youngscientists will learn of these legacy techniques in theoryonly or not at all.

For solid samples that are not thin or smooth enough tobe used directly in a transmission setup, there are severalways of sample preparation that can be used to bringthe samples in an appropriate form. The most commonones(62) are dissolution; grinding and mulling with a fluid;grinding and pressing into a disk together with KBr;remelting; pressing or casting into films; or pyrolysis.

When using the mulling method, samples are mixedwith a mulling fluid that has a refractive index similar tothe sample to reduce scattering and then spread betweentwo windows. The mulling fluid introduces additionalbands in the spectrum, therefore, when a complete MIRspectrum of the sample is needed, mulls in two differentfluids have to be prepared.

As in the preparation for mulls, the sample has to beground for the preparation of KBr disks. The groundsample is mixed with KBr. This mixture is then pressedto a small disk using an evacuated press. This disk isplaced in a holder to collect transmission spectra. TheKBr disk technique is quantitative. For hard, inorganicsamples, a few drops of ethanol can be added to makethe grinding easier. Transmission spectra collected withthe KBr disk technique will probably contain water bandsand some samples may undergo crystalline modificationdue to application of pressure. KBr disks can be kept in adesiccator for later examination.

If a sample has a low enough melting point, it can besmeared or pressed into a thin film on a warmed window.Soft samples can be pressed between two windows toreduce their thickness to an acceptable value. If thesample can be dissolved in a solvent that is easilyevaporated, it can be cast into a film on a window. Forvery small samples or samples that cannot be adequatelypressed to a film between two windows, a diamond anvilcell(63) can be used. In this type of cell, two diamonds areused to compress the sample. These diamonds are thenalso used as windows for the transmission measurement.

Finally, sample pyrolysis can be used as a pretreatmentstep. A part of the sample is placed in a glass tube andheated until it is decomposed. The residue, the pyrolyzate,is then scraped out of the tube and analyzed. As theresidue differs from the sample, special reference spectraof pyrolyzates have to be used for identification. Thegasses produced during pyrolyzation can also be collectedto measure their IR spectra.

In contrast, the sample preparation for ATR spec-troscopy is rather straightforward (see Section 3.3). For

soft solid samples, it is often enough to press the samplesagainst the ATR element using a mechanical clamp.

5 APPLICATIONS

5.1 Biological and Medical Samples

The MIR region of the spectrum gives a wide rangeof information about biological samples. This informa-tion includes the secondary structure, flexibility, andfunction of proteins,(64) the properties of lipids(65) andmembranes,(66) and conformational transitions and basepairing in nucleic acids.(67) The combination of strongabsorption of water, which is the predominant solventfor biological samples, and the presence of particles inbiological samples both are good reasons to prefer ATRmeasurements to transmission measurements for biolog-ical samples.

ATR techniques have been applied to blood andplasma samples to determine clinically important param-eters. In blood, the hematocrit could be determined; inplasma, cholesterol, glucose, total protein, triglycerides,urea, and uric acid could be quantified.(68) The concentra-tion of urea, creatinine, uric acid, sulfate, phosphate, andpH could be determined in urine samples with accuraciessufficient for clinical use.(68)

It was shown that cells can be classified into benign,hyperplasia, and malignant using ATR microscopy. Incontrast to transmission methods, ATR spectroscopyallows to measure tissue sections on IR intransparentglass slides.(68)

As the ATR element will be in contact with the sample,attention has to be paid to possible interactions betweenthe surface and sensitive biosamples. Nevertheless, ATRmicroscopy has been shown to be a viable tool toinvestigate colonies of microorganisms.(69)

ATR spectroscopy can also be employed to determinethe orientation of functional groups in membranes.(22)

The angle � of the dipole moment can be determinedfrom the ordering parameter,

S =⟨

cos2(�) + 12

⟩(43)

which is related to the dichroic ratio:

RATR = A||A⊥

= E2x

E2y

+ E2z

E2y

(1 + 3S

1 − S

)(44)

The coordinate system is oriented as in Figures 7 and 8.



5.2 Process Analytical Chemistry

Methods used in process analytical chemistry are differentto those of laboratory analysis in many ways. Processanalytical methods are optimized for speed, avoid manualsample handling and will often rely on sensor typemeasurements. Process analytical methods need to berobust enough to withstand industrial environments(vibrations, temperature changes, solvents, ...) and delivera predictable, constant performance over a long time.

Process analytical methods can be classified by theirintegration into the process into

• in-line: the sensor measures in the main processstream;

• on-line: the sensor measures in a side stream, samplepreparation steps can be included;

• at-line: the sensor is located close to the processstream, sampling and sample preparations is donemanually; and

• off-line: measurements are performed at a centrallaboratory.

ATR based methods can be used with all four of thesedegrees of integration. For off-line and at-line sampling,the common laboratory ATR accessories can be used.This approach is often used for rapid identification ofmaterials. For almost real-time monitoring of chemicalprocesses, on-line sampling ATR flow cells can beemployed. All parts of the flow cell – ATR elementitself, o-rings, glues, the holder of the ATR element –have to be chemically inert toward the chemicals theycome in contact with. Sensors placed on-line can usuallybe disconnected from the process for cleaning andmaintenance without shutting down the process.

Specially designed ATR probes can also be placedin-line for real-time process monitoring. There are twocommon designs for ATR in-line sampling, one uses acylindrical ATR element at the end of a cylindrical metalrod, the other places a flat ATR element at the endof this rod. Light guides in the metal rod guide the IRradiation to the ATR element. In the case of a CIRsensor, a reflector placed at the opposite end of the CIRelement reflects light back into a second light guide inthe metal rod. In the case of a flat element, the beampath in the ATR element leads from one guiding elementto the other with one or several reflections at the ATRelement–sample interface (Figure 21). As spectrometersare usually placed 2 m from the probe’s tip, the light hasto transverse a large distance.

To guide the light from the spectrometer to the ATRsensor and back, either optical fibers(71) or hollow opticalconduits(72) can be employed. Light is confined inside thefiber through total reflection. The attenuation in MIRwaveguides is in the range of 0.1–10 dB m−1 and strongly

Optical rays

Znse art couplingelement

Spring loaded seal

Diamond element

Air gap

DMD-270 diamond atr probe

Figure 21 DMD-270 diamond ATR probe (Axiom AnalyticalInc.) that can be used as an in-line sensor for processanalytical chemistry. (Reprinted with permission of AxiomAnalytical Inc.)

depends on the wavenumber of the light.(71) Silver halidefibers are fit for broadband MIR transmission.

Optical conduits are made out of pipes with a reflectivecoating on the inside to guide the light.(72) The lightpropagating in this pipe is approximately collimated, lightthat deviates too far from a beam path collinear withpipe is reflected back into the pipe by the reflectivecoating. Corner pieces with off-axis mirrors can be usedto change the direction of the light. Those arrangementsallow to bridge a distance of up to 2 m between thespectrometer and the ATR sensor element. Opticalconduits require a more elaborate alignment each timethey are put in place as compared to fiber optic probes.Furthermore, optical conduits also require a dry air purgefor optimal performance, the higher effort in alignmentand maintenance is, however, offset by a broader spectralcoverage.

5.3 Microscopy

The Rayleigh criterion describes the resolution (i.e.the minimum distance between two points to resolvethem as two distinct points) in microscopes: d =1.220λ/n1 sin(θ). n1 is the refractive index of the mediumthe sample is immersed in, θ is the angle of the mostextreme ray. Therefore, placing a high refractive index



ATR element on the sample can significantly improve thespatial resolution of the measurement.

For IR microscopy using the ATR technique, an ATRelement is placed on the sample in the beam path ofan IR microscope. In first experiments by Nakano andKawata,(73) a germanium hemisphere was placed onto thesample. An off-axis mirror was used to direct light comingfrom the interferometer toward the interface between thesample and the ATR element. Cassegrain optics wereemployed to collect the reflected light and focus it ontothe detector. A piezo stage was used to move the sampleacross a range of about 100 μm to collect scans of thesample. As Nakano and Kawata noted, only scanning thesample without adjusting the optics meant that larger scanranges would lead to optical aberrations.

A different approach for IR microscopy is nowtaken by several vendors of commercially availableATR objectives for modern IR microscopes (Figure 22).These can be used to view the sample through theoptical beam path as well as taking ATR measurements.For viewing the sample between measurements, theATR element can be retracted into the objective. Formeasurements, it is extended and then pressed ontothe sample with a predefined force. To measure severalpositions, the sample is first shifted vertically away fromthe ATR element, then translated sideways so thatthe next measurement spot comes to rest below theATR objective, finally it is moved upward again forthe measurement. In these objectives, the position of theATR element relative to the optics is the same for allmeasurement positions, the scan range is not limited bythe optics. Movements of the sample are controlled by acomputer controlled stage.

The ATR element will leave visible deformations in softsamples. Therefore, to guarantee an even contact between

Figure 22 Bruker 20× ATR objective.

the sample and the ATR element, measurement positionson soft materials should be placed far enough apart, sothat the indentations formed by the ATR elements donot overlap. In ATR microscopic measurements of wet orsticky samples (e.g. tissue sections), the cleanliness of theATR element should be checked after each measurement,as traces of the sample can be stuck to the surfaceand lead to contamination and errors in the followingmeasurements.

To acquire two-dimensional (2-D) maps withoutmoving the ATR across the sample, a focal planearray (FPA) detector can be used. FPAs are a typeof detector consisting of several single detecting elementsthat are arrayed in a grid and read out separately(12)

much like the charge coupled device (CCD) in a digitalcamera. An image of the sample in contact with theATR element is formed on the FPA and a spectrumis collected for each individual pixel of the FPA.These spectra then correspond to different sections ofthe sample. When using a germanium ATR element,a wavelength-dependent spatial resolution of 2–4 μmcan be achieved. Alternatively, a single reflection ATRelement in combination with a FPA detector can alsobe used for imaging of samples. Using this macroimaging approach, a spatial resolution of about 18 μmhas been demonstrated.(74) Samples imaged with thismacro imaging approach are polymers, biological andpharmaceutical materials, as well as microfluidic systemsplaced on top of the ATR element.

5.4 Depth Profiling

The strong dependence of the evanescent field on thedistance from the interface between sample and ATRelement already suggests that this technique can beused for depth profiling. By decreasing the angle ofincidence, the evanescent field can be extended furtherinto the sample. There are several ways to calculate depthprofiles – profiles of either spectra or concentrations withrespect to the distance from the ATR element–sampleinterface. Ekgasit and Ishida(75) explain the use of theinverse Laplace transform and iterative methods usingeither a multifrequency approach or a multiangle ofincidence approach.

For the inverse Laplace transform, several ATR spectraat different known angles of incident with either ⊥ or ||polarization have to be collected. These spectra can beconverted to depth profiles using the inverse Laplacetransform.

For both iterative methods, the samples are consideredto consist of several isotropic horizontal layers. Eachof these layers has an unknown spectrum of complexrefractive indices n(ν). These are to be determined.



For the iterative method using a multifrequencyapproach, an ATR spectrum collected at a known angleof incidence as well as the optical constant spectra of theanalytes in the sample are needed. Several wavelengthsare selected by the user. From these wavelengths and theexpressions for the evanescent field, a matrix equationconnecting the molar fractions of the constituents in eachof the layers of the sample and the measured absorptionsis built. As the mean squared electrical field (MSEF)needed for this equation depends on the optical constantsof the layers, this equation has to be solved iteratively.

The drawback of this method is that n(ν) has to beknown for all constituents of the samples. This canbe challenging as these optical constants can often notbe found in the literature. Furthermore, in mixtures,the interactions between the constituents can cause theoptical constants of the mixture to deviate from the sumof the optical constants of the constituents. This effectcan be ameliorated by excluding bands of the analytes,which are known to shift or broaden in mixtures from thecalculations.

For the iterative method using a multiple angleapproach, several ATR spectra collected at differentknown angles of incidence are needed. For each ofthe measured wavenumbers, a system of equationsconnecting the absorption with the optical constantscan be built. Starting from an estimate for the MSEF,the refractive indices are calculated. Then – iteratively –the values for the refractive indices and the MSEF areimproved. As this method does not need reference valuesfor n(ν) of the components, interactions between theconstituents will not cause problems.

Kazarian et al.(76 – 78) showed a combination of ATR-FTIR depth profiling and imaging to get the three-dimensional chemical information of their sample. Theyemployed an FPA detector and an ATR of a triangularcross-section. A slit was placed in the beam path betweenthe lens focusing light onto the ATR element–sampleinterface. By moving this slit, the angle of incidence of the

light onto the interface could be set. Films of thicknessesbetween 240 and 400 nm could be resolved.

6 VENDORS

In this section, an overview over vendors of ATRaccessories is given. The information was either suppliedby the vendors themselves or taken from their respectiveWeb pages. Web addresses and general information aboutthe vendors can be found in Table 4. An overview aboutthe types of ATR equipment available is given in Table 5.

7 FURTHER READING

The other articles on IR spectroscopy in the Encyclopediaof Analytical Chemistry offer the reader an overviewof other aspects, theoretical as well as practical, of IRspectroscopy.

Concise information about ATR-FTIR spectroscopycan be found in the chapters ‘Principles, Theory andPractice of Internal Reflection Spectroscopy’,(79) ‘DepthProfiling by ATR’,(75) and ‘Macro and Micro InternalReflection Accessories’(11) of the Handbook of Vibra-tional Spectroscopy.(80) More extensive information aboutthe theory and application of ATR spectroscopy can befound in Mirabella’s Internal Reflection Spectroscopy(81)

and Harrick’s Internal Reflection Spectroscopy.(17) A veryrecent monograph about the theoretical underpinningsof ATR spectroscopy is Internal Reflection and ATRSpectroscopy.(1)

The FTIR technique gets an exhaustive treatment inFourier Transform Infrared Spectrometry(12) by Griffithsand De Haseth.

A good resource for tables of physical properties ofoptical materials is the Handbook of Optical Materials.(25)

Table 4 Overview of vendors of ATR equipmenta

Web site Spectrometer Compatible

Agilent Technologies www.home.agilent.com YesAxiom Analytical www.goaxiom.com No a.m.m.Bruker Optics www.brukeroptics.com YesHarrick Scientific www.harricksci.com No a.m.m.Mettler-Toledo www.mt.com YesPerkin-Elmer www.perkinelmer.com YesPIKE Technologies www.piketech.com No a.m.m.Smiths Detections www.smithsdetection.comSpecac www.specac.com No a.m.m.Thermo Fisher Scientific www.thermofisher.com Yes

aa.m.m., all major manufacturers.



Table 5 Types of ATR accessories available from vendors at the time of writinga

HATR(single)

HATR(multi) CIR

Variableangle

CIR Probe Microscope Portable

Agilent • • •Axiom • •Bruker • • • • • •Harrick • • • •Mettler-Toledo •Perkin-Elmer • • •Pike • • • •Smiths Detections •SpecAc • • •Thermo Fisher • • • • • •aInformation is either from personal communication or from the vendor’s Web pages.

8 FUTURE TRENDS

8.1 Hand-held Attenuated Total ReflectionInstruments

The ATR technique can be used to measure almost anysample that can be brought in contact with the ATRelement. As the ATR element is usually connectedto a rather bulky spectrometer, it is necessary tobring the sample to the ATR element. Movable ATRprobes, such as the Axiom Dipper allow a little moreflexibility. Recently, portable ATR instruments havebecome available. The Thermo Scientific TruDefenderFT (Figure 23) is a hand-held (1.3 kg, battery powered)FTIR spectrometer with a diamond ATR element forsampling. The instrument is optimized for portableuse. Diamond ATR spectra are collected with acarbon film heated to 750°C as a light source andan uncooled DLaTGS detector. The spectral range ofthe instrument is 4000–650 cm−1 with a resolution of4 cm−1. The TruDefender is used by firemen, militarypersonnel, and law enforcement to identify unknownsubstances. The users themselves are not expected toknow about spectroscopy; instead, the instrument usesspectral databases and algorithms for identification. Theinstrument is also employed as a tool for quality controlin industrial applications.

Similar portable ATR-FTIR spectrometers are avail-able from Smiths Detection and Bruker Optics. In thefuture, we expect a further miniaturization of ATRspectrometers, made possible by micro-opto-electro-mechanical systems (MOEMS), new tunable laser lightsource and new, smaller detectors.

8.2 Waveguide Sensors

An evanescent field-based sensor type that has recentlybeen investigated by several groups for the use in MIRsensors are waveguide sensors. These sensors can eitherbe built by modifying fiber waveguides (Section 3.2) or

Figure 23 Photograph of the TruDefender hand-heldATR-FTIR spectrometer. (Reprinted with permission ofAnalyticon Instruments.)

constructed in a dedicated fashion using microfabricationtechniques.

Waveguides fabricated using microfabrication tech-niques are usually planar. This makes it easier to growthem on flat substrates, such as wavers, and allows touse established techniques used in the fabrication of inte-grated devices, such as quantum cascade lasers (QCLs).In the simplest case, these waveguides consist of threelayers: a substrate layer, a guiding layer, and a coverlayer. In waveguide sensors, the cover layer is usually the



sample. Like in ATR and fiber waveguide sensors, theguiding layer has to have a refractive index higher thanthe other layers to be able to guide the light.

The substrate lends mechanical stability to the guidinglayer, which therefore can be fabricated to be very thin.When the thickness of the guiding layer is decreaseddown to the order of magnitude of the wavelength ofthe light, models using several discrete total reflectionsas in an ATR are no longer true. Instead, light travels inthese waveguides in the form of one or several orthogonalmodes.(82) These modes have electric and magnetic fieldamplitudes that only depend on the position in the cross-section of the waveguide. The electric and the magneticfields will also stretch into the layers outside the guidinglayer in the form of an evanescent field. As in anATR, this evanescent field interacts with the sample.The attenuation of the light in the waveguide depends onthe imaginary part of the refractive index of the sample.This allows absorptions measurements. Like in an ATRsetup the attenuation of the light in the waveguide is alsoinfluenced by the real parts of the refractive indices ofthe sample and the waveguide. The waveguide for UV,VIS, and NIR wavelengths has been studied in the fieldof photonics. The knowledge gained in these fields cannow be applied to build integrated MIR sensors that alsocontain a (laser) light source and a detector on a singlechip.(83)

ACKNOWLEDGMENTS

The authors would like to thank Anette Fey of AnalyticonInstruments, David Pfeiffer of Thermo Fisher Scientific,Jenni Briggs of Pike Technologies, Steven W. Sharpeof the Pacific Northwest National Laboratories andMike Doyle of Axiom Analytical for their time andassistance. Engelene Chrysostome, Karin Wieland, andAndrea Ramer served as proof readers and test audience.Financial support was provided by the Austrian researchfunding association (FFG) under the scope of theCOMET program within the research network ‘‘ProcessAnalytical Chemistry (PAC)’’.

ABBREVIATIONS AND ACRONYMS

ATR-FTIR Attenuated Total Reflection FourierTransform Infrared

ATR Attenuated Total ReflectionCCD Charge Coupled DeviceCIR Cylindrical Internal ReflectionFEWSs Fiber Evanescent Wave SensorsFIA Flow Injection Analysis

FPA Focal Plane ArrayHATR Horizontally Mounted AtrIRS Internal Reflection SpectroscopyIR InfraredMIPs Molecularly Imprinted PolymersMIR Mid-InfraredMOEMS Micro-Opto-Electro-Mechanical

SystemsMSEF Mean Squared Electrical FieldNIST National Institute of Standards and

TechnologyQCLs Quantum Cascade LasersSERS Surface-Enhanced Raman SpectroscopySIA Sequential Injection AnalysisSNR Signal-to-Noise Ratio2-D Two-Dimensional

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2. I. Newton, Opticks: or, A Treatise of the Reflections,Refractions, Inflections and Colours of Light, 4th edition,W. and J. Innys, London, 1730.

3. E.E. Hall, ‘The Penetration of Totally Reflected Light intothe Rarer Medium’, Phys. Rev., 15, 73–106 (1902).

4. F.M. Mirabella, ‘History of Internal ReflectionSpectroscopy’, in Internal Reflection Spectroscopy, ed.F.M. Mirabella, Marcel Dekker, Inc., New York, 1–16,Chapter 1, 1993.



5. C.V. Raman, ‘Huygens’ Principle and the Phenomena ofTotal Reflexion’, Trans. Opt. Soc., 28, 149 (1926).

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