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Infrared spectroscopy Molecular vibrations and sampling techniques Andras Larsson University of Linkping, Sweden

Introduction This chapter explains the fundamentals of molecular vibrations and discusses the nature of infrared (IR) light as well as the basics of IR spectroscopy. Common IR spectroscopical techniques and their areas of application are also described.

Background Infrared spectroscopy is also known as vibrational spectroscopy since the IR light excites vibrational motion of molecules. To understand the fundamentals of molecular vibrations, a brief description of the chemical bond in terms of classical mechanics is given. Covalent bonds in molecules are the result of interactions between the electron clouds of the participating atoms. The distance between the nuclei is dictated by the equilibrium between two opposing terms; a long range attraction (Coulomb force) and a short range repulsion of the positive charges of the nuclei. As a first approximation, a covalent bond can be thought of as a simple spring which obeys classical mechanics (Figure 1). The bond in a molecule consisting of two atoms can then be described by Hookes law

xkF = Eq. 1 where F is the force between the atoms, k is the force constant and x is the displacement from equilibrium. Since force is related to potential energy by F = -dU/dx, the force in Equation 1 corresponds to the potential energy U in Equation 2.

2)( xkU = Eq. 2 In this model, the potential energy plotted against internuclear separation has the shape of a parabola as seen in Figure 2. It should be noted that the parabola is a good approximation only for small deviations from the equilibrium distance between the nuclei. It cannot be correct for all extensions since it does not allow dissociation of a bond. At high vibrational excitations the motion of atoms allows the molecule to explore regions of the potential energy curve where the parabolic approximation is poor. Thus, that kind of vibrations is better described by anharmonic oscillations. The general shape of the true potential energy is also given Figure 2. Sometimes the Morse potential is used since it resembles the true potential more closely than the parabola, but for molecular vibrations induced by IR radiation the simple parabolic model is sufficient.

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Figure 1. Schematic illustration of two atoms with masses ma and mb at internuclear distance x. The bond between them can be described by a force constant k.

Figure 2. The molecular potential energy U plotted against the internuclear diatance x. For small deviations from the equilibrium distance xe the parabola (solid line) is a good approximation to the true potential curve (dashed line). Using Hookes law in Equation 1 as a starting point, an expression for the vibrational frequency can be found after a few mathematical operations.1 The resulting expression is given in Equation 3.

*21 mk

= where ba mmm

11*

1 += Eq. 3

This expression contains the reduced mass m* and the masses ma and mb of the participating atoms in Figure 1. Furthermore, at the atomic scale, quantum mechanical effects have to be considered. For the parabolic approximation with harmonic oscillations, the energy E associated with the vibration is quantised according to

)( += nhEn where n = 0, 1, 2 Eq. 4 h is Plancks constant and n signifies the vibrational quantum number and the corresponding energy level.2 Note that the energy levels are equidistant in the case of the parabolic model (Figure 3 A), while in the anharmonic case the energy gaps between levels decreases with increasing energy (Figure 3 B). Vibrational motion is a periodic, concerted displacement of the atoms in a molecule, which leaves the position of the centre of mass unchanged. Consider a linear molecule consisting of three atoms (e.g. CO2). When two neighbouring atoms in this molecule are displaced, the

U

xe x

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third one is naturally also affected. Figure 4 A illustrates two such vibrations, R and L. The linear combinations of R and L (1 = R+L, 2 = R-L) are shown in Figure 4 B and as can be seen these are independent vibrations since they can occur without affecting other atoms. These independent types of vibrations are called normal modes. From now on normal modes are the only modes considered and therefore the word normal is omitted. Apart from the vibrational modes seen in Figure 4 B, which are called stretches, vibrations like twist, wag, rock, torsion, scissor and bend also exists. The latter one is depicted in Figure 4 C. Generally, the most energetic of the vibrational modes is the stretching mode. Furthermore, asymmetric stretches normally correspond to higher energies than symmetric ones do.3

Figure 3. Distribution of energy levels n for the harmonic approximation (A) and for the true appearance of the potential curve (B).

Figure 4. Vibrational modes of the linear molecule CO2. A: Non-normal mode vibrations R and L. B: Linear combinations of R and L resulting in normal mode symmetric (1) and asymmetric (2) stretches. C: Normal bending modes (3). The modes in C are degenerate (perpendicular motions) and appear at the same frequency (energy). Note that the wavenumber positions are given and that higher wavenumber signifies higher energy. The simplest molecule contains only two atoms and it possesses one vibrational mode; a stretching mode. It is easy to see that as the number of atoms N in a molecule increases, the number of available modes increases. The exact number can be calculated and is equal to 3N-3-3 for non-linear molecules and 3N-3-2 for linear ones. 3N is the total degree of motional freedom, the second term corresponds to translational motion and the third term corresponds to rotational motion. Non-linear molecules have one less vibrational mode than linear molecules, due to their geometry. As an example, let us examine the H2O molecule. According to the formula just given, a H2O molecule should have 33-3-3=3 vibrational modes. Figure 5 shows the three modes of H2O, which are symmetric stretching, asymmetric stretching and symmetric bending. When comparing Figure 4 C and 5 it should be evident

xe x

U

n = 0

1

2 3

xe x

U

n = 0

1

2

3

A B

R

L

1 (1388 cm-1)

2 (2349 cm-1)

3 (667 cm-1)

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that the linear CO2 has two equal bending modes while for the bent H2O the combination of atomic displacements where the oxygen atom moves into the paper and the hydrogen atoms out of the paper (or vice versa), is in fact a rotation.

Figure 5. The three vibrational modes of a water molecule. The length of the arrows corresponds to the relative atom movements. Since the centre of mass remains stationary during vibration, the lighter hydrogen atoms move larger distances than the oxygen does. Now let us turn our attention to the source of energy; the IR radiation. Infrared light is electromagnetic waves in the m mm range and the corresponding energies coincide with the energy levels involved in molecular vibrations. The commonly used unit in this area of research is wavenumber ~ given in reciprocal centimetres (cm-1). The energy of the IR light ranges from 0.01 to 1.8 eV or 8 to 14500 cm-1. In order for a molecule to accept the energy in the IR light a certain criteria has to be fulfilled, i.e. there is a selection rule that states: a vibrational mode must change its dipole moment during the motion in order to be IR active. This can be expressed in the more compact form4-6

0=i

i rM Eq. 5

where Mi is the transition dipole moment for the mode i with the coordinate ri. This means that monoatomic (e.g. He) and homodiatomic symmetric substances (e.g. N2) are IR inactive, while asymmetric molecules containing polar groups (e.g. -CF, -COOH, -OH) are IR active. It should also be noted that the positions of the absorption peaks are influenced by the chemical environment, which induces chemical shifts. Apart from Mi, the absorption A depends on the magnitude of the electric field E of the IR radiation and on the angle between E and the principal axis of vibration Mi (Equation 6).4-7

A ii2222 cosEMEM = Eq. 6

This dependence on the angle between the two entities will have important implications on one of the applications discussed below; infrared reflection absorption spectroscopy (IRAS).

Infrared sampling techniques The IR spectroscopical techniques transmission, attenuated total reflection (ATR), IRAS and diffuse reflection (DR) are described in this section. Other modes of IR measurements include emission,8 transient,9 photoacoustic10 and beam deflection photothermal11

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spectroscopy, but none of these are discussed here. Since IR spectroscopy is based on molecular vibrations, it is a non-destructive technique, which is a great advantage in many cases. Infrared spectroscopists face the problem that air contains IR active species, namely carbon dioxide and water vapour. This obstacle is often overcome by using vacuum or purging the measurement chamber with IR inactive nitrogen gas or dry air. Furthermore, a reference spectrum is always needed to nullify the effects of the varying lamp intensity for different wavenumbers and absorption signatures of cuvettes, pellet materials, solvents, sample supports and measurement chambers including mirrors, depending on which method is used. As opposed to using a slit and diffraction grating and scan over the range of wavenumbers of interest, modern instruments normally measure on the whole range simultaneously. This convenience, which involves rapid collection of many samples, is facilitated by the use of a Michelson interferometer and Fourier Transformation of the signal.12 In many cases a deuterated triglycine sulfate (DTGS) detector is sufficient, but when the amount of sample is very small, as for example in IRAS, a more sensitive unit, like a liquid nitrogen cooled mercury cadmium telluride (MCT) detector, is needed. Sometimes IR data are presented in terms of transmittance T rather than A. The transmittance is related to A by the expression in Equation 7.

dcTI

IAref

=

=

= 1loglog 1010 Eq. 7

This equation also gives the relation between A and the intensity of the radiation that has passed through the sample I and the intensity of the reference radiation Iref, i.e. through a cuvette, reflection at a surface or similar depending on the mode of measurement. The absorbance can also be described by Lambert-Beers law in which c is the molar concentration (M), the molar extinction coefficient (L mol-1 cm-1) and d the path length (cm).

Transmission infrared spectroscopy In transmission mode, IR light is passed through the sample and the absorbance is recorded. Measurements are made in gas, liquid and solid phases and information about chemical composition, concentration, and film thickness can be obtained depending on which type of sample that is examined. When gas phase experiments are performed, a compartment sealed with IR transparent windows, is used. The typical path length in this case is 10 cm10 m. Liquid samples are sandwiched together with a well-defined spacer between two IR transparent windows. The thickness of the spacer is normally 5200 m. When a solvent is needed, it is important to ensure that it does not absorb in the regions of interest. Solid samples are grinded and incorporated into a pressed pellet or dissolved in an appropriate solvent and then cast onto a solid IR transparent window, commonly made from CaF2. Frequently used materials for producing pellets are the salts KBr, NaCl and CsI. The molecules in a pellet or in a solution are expected to be randomly orientated. A transmission spectrum provides information of all vibrational modes of a molecule. Due to intermolecular interactions, such as hydrogen bonding, the obtained spectra may vary with concentration. That is, at high concentration the molecules are close to each other and able to interact,

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while at low concentration they are separated and no interactions can take place. In Figure 6 two spectra of N-methylacetoamide are shown. In the high concentration case, the hydrogen bonds broaden the carbonyl band, whereas in the low concentration case, no hydrogen bonding takes place and the absorbance of the carbonyl gives rise to a sharp dip. The N-H group is affected in a similar fashion.

Figure 6. Infrared transmission spectra of N-methylacetoamide at high and low concentration. The arrows indicate the infrared signatures of hydrogen bonded and non-hydrogen bonded C=O and N-H groups, respectively.

Infrared attenuated total reflection (ATR) spectroscopy Infrared spectroscopy in ATR mode is a technique that provides information about chemical composition and coverage down to monolayer thickness. By varying the polarisation state of the incoming radiation, it is also possible to obtain information about molecular orientation.13,14 Yet another area of application is depth profiling.15 A crystal, that allows one or multiple reflections in the crystal-sample interface, is used. As the number of reflections increase, the sensitivity is enhanced. The general setup is shown in Figure 7 A. Either the sample is deposited onto the crystal itself or the sample is simply placed in close contact with the crystal (Figure 7 B). In the latter case a pressure is applied to ensure that no gaps are formed between the sample and crystal. This presents a problem when examining hard and/or rough samples. When the sample is deposited onto the crystal it is possible to make the measurement in liquid phase, which allows for adsorption studies of molecular and biomolecular species onto the surface over time (Figure 7 C).

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Sample

Crystal

IR radiation

Evanescent field

n1n0

1/e

A B C

Figure 7. Schematic illustrations of IR spectroscopy in ATR mode. A: general setup, B: measurement of a solid sample, e.g. thin polymeric film deposited onto a planar substrate (arrows indicate applied pressure), C: measurement of biomolecular interactions in liquid. Note that the extension of the evanescent field is not to scale in the different cases. Commonly used crystals are made from ZnSe or Ge, since they are IR transparent and have high refractive indices. Infrared radiation that hits the crystal-sample interface, at a fixed angle of incidence higher than the critical angle c is totally reflected and gives rise to an evanescenta wave. The evanescent wave propagates along the interface and interacts with the sample. The sample absorbs energy from the radiation and results in an absorption spectrum. The extension of the evanescent wave is described by the penetration depth dp, which is defined as the distance from the point of reflection to where the evanescent field has decayed to 1/e of that at the interface. Equation 815-18 can be used to determine dp and for IR radiation it is on the m scale.

2

1

02

1

sin2

=

nn

n

d p Eq. 8

is the wavelength of the incoming light and n1 and n0 are the refractive indices of the crystal and the sample, respectively. In Figure 8, dp is plotted against and it is evident that the incident angle should be chosen somewhat higher than c to produce a robust setup, which does not vary drastically with small changes in the incident angle. Since dp is proportional to (and thus inversely proportional to ~ ), the sensitivity decreases towards shorter (higher ~ ), provided that the sample is thick enough for the longer . This means that the absorption intensities are expected to be lower at higher ~ . This is clearly seen when comparing an ATR spectrum with a transmission spectrum, such as in Figure 9. The data has been normalised with respect to the double peak below 1000 cm-1. When tracing the spectra towards higher ~ (i.e. shorter ) it is seen that the peak intensities in the ATR data becomes smaller compared to those in the transmission data.

a Evanescent comes from the Latin evanescere, which means vanishing

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Figure 8. The penetration depth dp of an evanescent wave into air from a ZnSe crystal as a function of the incident angle. The penetration depth is defined as the depth at which the evanescent wave has decayed to 1/e of that at the interface. For >c the E-field of the incident light gives rise to an evanescent wave, which propagates along the interface before the radiation is totally reflected. For c the evanescent wave is non-existent and instead the E-field is parted between the transmitted and reflected radiation. A refractive index for ZnSe of 2.42919 and a wavelength of 5000 nm (corresponding to 2000 cm-1) was used for the calculation of the curve.

Figure 9. Infrared spectra of a cyclo-olefin polymer (COP). The ATR instrument was equipped with a multiple reflection ZnSe crystal. Both experiments were carried out on a 75 m thick strip of sample. The data was normalised with respect to the intensity of the two small peaks at 939 and 920 cm-1.

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Infrared reflection absorption spectroscopy (IRAS) IRAS, IRRAS and RAIRS are all generally accepted acronyms of this technique, but here the term used is IRAS. This type of IR spectroscopy is extremely sensitive and allows detection of submonolayers on metals.20-22 Hence, it is very useful for studies of ultrathin layers such as self-assembled monolayers (SAMs) and Langmuir-Blodgett films. Information about the orientation of groups and molecules, chemical composition, coverage, molecular packing and thickness of monolayers can be extracted from the obtained reflection absorption (RA) spectra.23 To understand the principles of IRAS, we need to discuss the electrical components of the light in detail. The electric field of electromagnetic radiation incident at an angle with respect to the surface normal can be divided into two components, as seen in Figure 10. The incident s-polarisedb component Eis is perpendicular and the incident p-polarisedc component Eip is parallel to the plane of incidence, respectively. Upon reflection on a surface, the electric components go through phase shifts to an extent determined by and ~ , the state of polarisation and the properties of the substrate material. From now on, the discussion is limited to highly reflective metals. The phase shift of Eis is approximately 180, irrespective of the substrate material and the value of and ~ and (Figure 11).24,25 In other words, this component of the light cancels itself at the reflection and hence, the contribution from the s-component is very small. In practice, Eis is normally blocked by a polariser before the beam hits the sample. The phase of the p-component, on the other hand, is more sensitive to changes in and the substrate material. The wavenumber of the light also has an effect on the phase shift especially pronounced for angles of incidence in the range 80-90 which is evident in Figure 11. Here, an interesting property of metal substrates comes into play; metals allow very high angles of incidence without large phase shifts25 (for comparison, on glass the phase shift of the p-polarised component is 180 for angles of incidence greater than the Brewster angle,26,27 leading to cancellation of the p-component at the point of reflection). Therefore, a large can be used, leading to a beneficial geometry where the components Eip and Erp are nearly perpendicular to the surface and thus have large normal components. Since the reflection coefficient is close to unity for the commonly used metals, constructive interference between the two gives a resulting E-field perpendicular to the surface (ER) almost reaching double the magnitude of Eip or that of Eip and Erp together, under optimal conditions. However, when approaches 90, ER goes to zero since the phase shift approaches 180 and thus the p-components cancel each other. When approaches zero, ER again goes to zero since Eip and Erp becomes parallel to the surface and thus has small or no normal components. |ER| therefore passes through a broad maximum (Figure 12).22,28 The resulting A is dependent on |ER|2 (Equation 6) and the size of the area over which the field ER is exerted. The enlargement of the beam area on the substrate surface is described by 1/cos , which increases rapidly when goes to 90.22,28 The dashed curve in Figure 12 represents the driving force for vibrational excitation, which accounts for the phase shift dependence, the incidence dependence of the normal electric components, the surface enlargement factor and the square dependence of A on the E-field. The driving force

b s is an abbreviation for senkrecht, which is German for perpendicular c p is an abbreviation for parallel, which is the same in German and English

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approaches a maximum for around 88, depending on substrate material and ~ of the incident radiation, but for practical reasons the angle of incidence is typically chosen to be 85.22 As indicated before, ~ has a significant contribution to the phase shift in the optimal range of , which in turn affects the absorption asymmetrically. Therefore, the absorption peaks far from each other in a spectrum should not be compared.

Figure 10. The electric vectors of the incident light upon reflection at a metal substrate. The incident angle is and at optimal conditions Eip and Erp interfere constructively and results in ER, while Eip and Ers cancels each other at the point of reflection.

Figure 11. When reflected on a gold substrate, s-polarised light is not affected significantly by and has nearly a constant phase shift of about 180. In contrast, p-polarised light has a very small phase shift for low values of and a dramatic increase towards 180 at high incident angles. There is a small dependence of the wavenumber, as seen when comparing the two wavenumbers 2823 cm-1 (solid line) and 1008 cm-1 (dashed line). Refractive indices for gold of 2.141+21.9i and 12.24+54.7i,29 respectively, were used. The phase shifts were calculated by combining the Fresnel equations and Snells law.26

ERErp

Eip

Eis

Eip

Eis

Ers

Erp

Ers

- 11 -

Figure 12. The solid line shows the behaviour of |ER| normalised with the angle independent |Eip|. For angles of approaching zero, ER goes to zero since the normal components of Erp and Eip goes to zero. When approaches 90, ER goes to zero since the phase shift of Eip goes to 180 and therefore interacts destructively with Erp. The dashed line corresponds to the driving force for the vibrational excitation, which combines the effects accounted for in the solid line with the square dependence of A on |ER| and the surface enlargement of the beam area on the substrate. The maximum value is reached at around 88. A refractive index for gold of 4.007+31.7i29 (which corresponds to 1936 cm-1) was used for the calculation of the curves. The fact that the resulting E-field is perpendicular to the substrate at the reflection is very useful since it renders possibility to determine the orientation of molecules on the surface. This is one of the great advantages with IRAS. Looking back at Equation 6 we can now formulate a surface dipole selection rule stating: only the vibration modes in adsorbed molecules that have a transition dipole moment with a component perpendicular to the surface can be seen in IRAS. The surface selection rule can be written as

A ii2222 cos MnMn = Eq. 9

where n is the substrate normal. Figure 13 illustrates the surface selection rule in theory and compares different tilt angles of the molecules in a SAM. An example, where the surface selection rule was used to determine the orientation of the molecules in such a monolayer, is seen in Figure 14. A comparison between the amide I and II bands in transmission mode and RA mode is shown in Figure 14 A. The transmission spectra display absorption at both amide I and II, which is expected since the molecules EG4 and EG6 contains amide bonds and are randomly distributed. EG4 and EG6 are thiols with four and six terminal ethylene glycol units, respectively. In the RA spectra, the amide I absorption is absent, while that of amide II is still present. This phenomenon is explained by the uniform orientation of the thiols (Figure 14 B), which are all aligned at a specific angle due to the close packing which occurs in quality SAMs. The tilt angle depends on the substrate used, which is commonly gold. More specifically, in this case the C-N-H bend and the C-N stretch of amide II display a transition dipole moment with a component parallel to the surface normal n , while that of the C=O stretch of amide I is aligned perpendicular to n .30,31

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Due to the high sensitivity of IRAS, and the small amount of sample (monolayer thickness) that is normally examined, the problem with IR active contents in air is more pronounced. The vacuum solution to remove the IR active components in the measurement chamber is, however, unsuitable due to the risk of backflow of oil-containing air from the pump. Although slightly time-consuming, purging the instrument with nitrogen gas is the favoured method in this case.

Figure 13. Illustration of the surface dipole selection rule. A: The transition dipole moment can be divided into two components, one which is perpendicular and one which is parallel to the plane of incidence. Only the latter one (Mi cos ) is parallel to the surface normal and the electric field ER and hence IR active. B: Comparison between different in IRAS demonstrating the possibility to extract information about the molecular orientation in a SAM. In transmission mode, e.g. in a KBr pellet, the molecules are expected to be randomly distributed and thus all are present.

ER ER

Mi sin (inactive)

Mi cos (active)

AbsAbs Abs Abs

IRAS = 0

IRAS = 45

IRAS = 90

Transmission All

Mi

n n

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Figure 14. A: Infrared RA spectra of the thiols EG4 and EG6. Comparsion of amide I (EG4: 1633 cm-1) and amide II (EG4: 1560 cm-1) bands in KBr transmission spectra (dashed lines) and RA spectra (solid lines) of SAMs. Reprinted with permission from Dr. Ramas Valiokas.30 B: Self-assembled monolayer of EG4 thiols on a gold surface. The amide bonds are encircled by the ellipse. C: Transition dipole moments of the C=O (amide I) and C-N (amide II) modes. Besides monolayers, this technique is also used for measurements of thicker films, such as hydrogels. Figure 15 gives a brief description of the method of producing a poly EG (PEG)-containing hydrogel. The grafting process is photoinduced and is based on free radical polymerisation of methacrylate monomers and occurs during UV exposure. In Figure 16 a series of different mixing ratios between the two different monomers used, is given.32 These hydrogels are about ten times as thick as the previously discussed SAMs.

Low pressureair RF plasma O

OH

O O OOH

OOH

O O O O OUV lightCOP substrateCOP substrateCOP substrate

OH

O

O

10

OH

O

O

OH

O

O

10

254 nm

PEG10MAHEMA

OH O

O

Figure 15. The process of producing a PEG-containing hydrogel. Peroxides and other reactive species are induced on the COP surface upon air plasma treatment. UV irradiation generates surface radicals, which interact with monomers (PEG10MA and HEMA) in the solution. A grafting chain reaction is thereby initiated and a matrix is formed.32

S

NH

O

O

O

OH

O

S

NH

O

O

O

OH

O

S

NH

O

O

O

OH

O

S

NH

O

O

O

OH

O

S

NH

O

O

O

OH

O NHO

MC=O

MC-N

A B C

n

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Figure 16. Infrared RA spectra of matrices prepared by UV grafting of the two methacrylate monomers PEG10MA and HEMA. These films are about ten times as thick as the SAMs in Figure 14.32

Diffuse reflection (DR) infrared spectroscopy In DR IR spectroscopy, spectra of powders and rough surfaces can be recorded (Figure 17). The obtained information includes chemical composition and concentration. However, interpretation of DR IR data can be troublesome due to the existence of two different types of reflectance, namely specular (i.e. regular) reflectance and diffuse (i.e. scattered) reflectance.16,33,34 The specular reflectance is unwanted in diffuse reflectance experiments, but occurs to a varying extent depending on the setup. A large portion of the incident IR radiation is lost since it is diffusely scattered over the entire hemisphere over the sample. To minimise the losses, some sophisticated system of mirrors and optics is needed to collect and refocus the light. Compared to transmission IR, DR offers the possibility to measure on samples of higher concentrations, which sometimes is advantageous. In addition, some samples simply scatter too much of the incoming radiation for transmission spectroscopy, in which case DR is an interesting alternative.

IR radiation

Figure 17. Schematic illustration of the principle of DR spectroscopy. The reflected light is collected and refocused before it hits the detector. In contrast to most other spectroscopical techniques, no exact relationship between the recorded data and the refractive index of the sample exists in DR spectroscopy.35 A number of theories has been proposed to describe the complex situation and one the most popular ones is Kubelka-Munk (K-M) theory.36 One result of this theory is the K-M function F which is given by

SK

RRF ==

2)1( 2 Eq. 10

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where R is the reflectance, K is the absorbance and S is the scattering. Instead of the normally used absorbance, DR spectra are normally presented as plots of F against ~ . An example of this is shown in Figure 17, where the desorption of methanol from -alumina was studied.

Figure 17. The diffuse reflectance infrared spectrum for a saturated overlayer of methanol on -alumina as a function of temperature. (a) Saturation spectrum at 293 K. The sample was progressively warmed in a helium flow to (b) 373, (c) 473, (d) 573, (e) 673, (f) 773, and (g) 873 K. The sample was held at the desorption temperature for 15 min, and then allowed to cool to room temperature, where the spectrum was acquired. All spectra are background subtracted, where the spectrum of the clean, activated catalyst has been subtracted from the dosed/heated spectrum.37

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