ATR-FTIR in catalysis
Study of homogeneous, heterogeneous and biocatalysts
ATR-FTIR in catalysis
Study of homogeneous, heterogeneous and biocatalysts
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op dinsdag 15 november 2011 om 10:00
door
Siegfried Alexander TROMP scheikundig ingenieur
Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. J. A. Moulijn
Prof. dr. ir. M. T. Kreutzer Prof. dr. G. Mul
Samenstelling promotiecommissie:
Rector Magnificus Voorzitter
Prof. dr. J. A. Moulijn Technische Universiteit Delft, promotor
Prof. dr. ir. M. T. Kreutzer Technische Universiteit Delft, promotor
Prof. dr. G. Mul Universiteit Twente, promotor
Prof. Dr. T. Bürgi Université de Genève
Prof. dr. I. W. C. E. Arends Technische Universiteit Delft
Dr. B. L. Mojet Universiteit Twente
Dr. E. L. Scott Universiteit Wageningen
Prof. dr. ir. H. van Bekkum Technische Universiteit Delft, reservelid
Het onderzoek beschreven in dit proefschrift is uitgevoerd bij Catalysis Engineering, ChemE, faculteit Technische Natuurwetenschappen, Technische Universiteit Delft (Julianalaan 136, 2628 BL Delft, Nederland), financieel ondersteund door de NRSCC.
ISBN 978-90-5335-489-6 © 2011 by S.A. Tromp
Chapter 1. Introduction
1
1.1. Background 1
1.2. Absorption spectroscopy 2
1.3. ATR spectroscopy 5
1.3.1. Measurement principle 5
1.3.2. Measurement of catalytic systems 7
1.3.3. Measurement equipment 12
1.4. Objective and outline of the thesis 14
1.5. References 15
Chapter 2. Optimization of signal-to-noise ratios for FTIR
analysis of aqueous catalytic systems using transmission
cells or ATR accessories
21
2.1. Introduction 23
2.2. General SNR equations 25
2.3. SNR equations for homogeneous systems 27
2.3.1. Optimum path length in ideal homogeneous systems 28
2.3.2. Optimum path length in transmission FTIR 33
2.3.3. Optimum path length in ATR 36
2.3.4. Comparison of SNR for transmission and ATR 43
2.4.2. Metal film catalyst 51
2.5. Detector saturation 57
2.6. Conclusions 63
2.7. Nomenclature 64
2.8. References 66
Chapter 3. Bottom-mounted ATR-probes: pitfalls that arise
from gravitational effects
69
3.1. Introduction 70
3.2. Experimental 72
3.2.1. Cold flow experiments 72
3.2.2. ATR-FTIR set-up 73
3.2.3. Naphthalene hydrogenation experiments 74
3.3. Results 75
3.3.1.Cold flow experiments 75
3.3.2. Naphthalene hydrogenation 77
3.4. Discussion 80
3.4.1. Cold flow experiments 80
3.4.2. Naphthalene hydrogenation 82
3.5. Conclusions 86
3.6. Nomenclature 87
Chapter 4. Mechanism of Laccase/TEMPO catalyzed
oxidation of benzyl alcohol
91
4.1. Introduction 92 4.2. Experimental 94 4.2.1. Materials 94 4.2.2. Reactions 95 4.2.3. Analysis methods 95 4.2.4. Simulations 974.3. Results and Discussion 98
4.3.1. TEMPO oxidation by laccase 100
4.3.2. Comproportionation reaction in the absence of laccase 102
4.3.3. Hydroxylamine oxidation in the presence of laccase 103
4.3.4. Reaction between benzyl alcohol and oxoammonium 105
4.3.5. The complete reaction 107
4.4. Conclusions 109
4.5. Nomenclature 110
4.6. References 111
Chapter 5. Membrane-Bound Hydrogenase from
P.
furiosus
; kinetics study of the oxidation of H
2and
evaluation of its potential for fuel cell applications
113
5.1. Introduction 115
5.2. Experimental 124
5.2.3. Reactions 125
5.3. Results & Discussion 126
5.3.1. MBH quantification 126
5.3.2. Kinetic analysis 127
5.4. Feasibility of MBH as a catalyst for fuel cell applications 131
5.5. Conclusions 143
5.6. Nomenclature 144
5.7. Literature 145
Chapter 6. Summary and evaluation
151
6.1 Evaluation of ATR-FTIR as an analysis method for catalysis 152
6.2 Study of specific catalytic systems 154
Samenvatting en evaluatie
157
6.1 Evaluatie van ATR-FTIR als analysemethode voor katalyse 158
6.2 Studie van specifieke katalytische systemen 160
Appendix A. Derivation of SNR equations for ATR-FTIR
spectroscopy
163
A.1. Effective path length 163
A.2. Path length of light through an ATR crystal 165
A.3. Matrix method 167
A.4. Derivation of SNR equations for metal films 168
A.5. Nomenclature 172
Acknowledgements 175
Publications and presentations
179
Introduction
1.1. Background
Most industrial reactions are catalyzed to enhance both reaction rates and selectivity towards desired products. Catalysis can be either homogeneous or heterogeneous. In homogeneous catalysis, the catalyst, reactants and products are present in the same fluid phase. In heterogeneous catalysis, the catalyst and reactants are not present in the same phase. Generally, the catalyst is a solid and the reactants and products are either present in a liquid or gaseous phase. This thesis focuses on liquid-phase reactions. Conventional analysis methods for performing kinetic and mechanistic studies of catalyzed liquid-phase reactions are off-line techniques. For heterogeneous catalysis, liquid-phase samples can be collected from the reaction mixture. This effectively quenches the reaction, assuming successful separation of the sample from the catalyst material. The concentrations of reactants and products can be subsequently analyzed using e.g. GC, GC-MS, HPLC, NMR or EPR. Although off-line analysis gives crucial information, valuable information of labile reaction intermediates and adsorbed compounds on the catalyst is lost. For homogeneous catalysis, reaction continues even after collection of a liquid sample and the reaction needs to be quenched by e.g. a liquid-liquid
using liquid nitrogen has been demonstrated to be possible within the
micro-second range, using dedicated equipment[1], allowing for off-line
analysis, even including reaction intermediates[2;3].
Alternatively, on-line analysis can be used, which means analysis while the reaction is taking place. Such on-line analysis allows for the detection of
reaction intermediates and compounds adsorbed on a catalytic surface[4-13].
Many analysis techniques can be applied on-line. This thesis focuses on (absorption) spectroscopic techniques in the IR to UV range, with a focus on ATR-FTIR (Attenuated Total Reflection – Fourier Transform InfraRed) spectroscopy, because of its wide applicability for studying catalysts and the nonintrusive detection of adsorbed compounds and reaction intermediates. Absorption spectroscopy in general is discussed in paragraph 1.2, ATR-FTIR for the study of catalysis is discussed in paragraph 1.3 and paragraph 1.4 states the objective and the outline of the thesis.
1.2. Absorption spectroscopy
Absorption spectroscopy is based on detection of the wavelength dependent absorption of light by a sample material. The absorbance is calculated from the difference in the intensity of light reaching a detector, for illumination with and without a given compound in the analyte, using Equation 1.1. 0 log I A I
1.1where I0 is the light intensity without the compound and I is the light
component cs, the extinction coefficient of the components εs and the path
length l as given by the Lambert Beer law, see Equation 1.2:
s s s
A 1.2 c l
The total absorbance is the sum of the absorbance of the individual components as determined by Equation 1.3.
s s
A
c l 1.3For a typical transmission set-up, see Figure 1.1a, the path length inside the sample is determined by the thickness of a solid material or by the distance between the transmission windows in a sample holder.
In this work, IR and UV-VIS spectroscopy are used, with a focus on mid-IR spectroscopy. Figure 1.1b shows the wavelength ranges of mid-IR to UV light and the ranges of the similarly named spectroscopic techniques, which differ slightly.
Modern IR spectroscopic techniques make use of an interferometer and corresponding conversion of measured interferograms into absorbance or transmission spectra using a Fourier transform. Spectrometers based on this concept are called Fourier transform infrared (FTIR) spectrometers. Set-ups used for transmission spectroscopy have a relatively simple design as shown in Figure 1.1. For cells with a longer path length, such as is common in UV-VIS spectroscopy of aqueous samples, cuvettes can be used instead of windows kept apart by a spacer.
detector light source spacer window window sample sample absorbance I0 I soou ht
UV VIS NIR MIR Far-IR
Far-IR MIR NIR UV-VIS 10-6 10-5 10-4 10-3 l.[m] light region spectroscopic technique wavenumber.[cm-1] 5.104 1.4.103 4000 400 10 a) b)
Figure 1.1. Transmission spectroscopy. a) a typical set-up for transmission
spectroscopy b) wavelength regions of light and the corresponding spectroscopic techniques. The techniques used for the work presented in this thesis are indicated in grey.
Transmission spectroscopy has several advantages but many important systems are not well-suited for study with transmission spectroscopy. Most homogeneous systems are well-suited for study with transmission spectroscopy. Exceptions are systems with viscous liquids, where window
deformation is difficult to prevent when thin cells are used[14]. Additional
experimental difficulties arise when components need to be added during measurement, because it is hard to mix rapidly inside transmission cells. Compared to homogeneous systems heterogeneous systems are much less suitable for transmission systems due to the diffraction of light at the phase
which is not subject to such diffraction effects.
1.3. ATR spectroscopy
1.3.1. Measurement principle
ATR spectroscopy is based on the principle that an evanescent standing wave forms above an optically dense surface if light reaches this surface at an angle of incidence larger than the critical angle. Figure 1.2 shows the behavior of light when it reaches the surface between an optically dense ATR crystal, such as silicon, zinc selenide or diamond, and an optically less dense sample at different angles. At angles of incidence smaller than the critical angle, part of the light reflects and part of the light is transmitted to the low optical density medium. At angles above the critical angle, all light is reflected and a standing evanescent wave is formed.
The critical angle αc, above which ATR spectroscopy is possible is given by
Equation 1.4[15]. 1 2 1 sin c n n
1.4where n2 is the refractive index of the sample and n1 is the refractive index
of the ATR crystal. With a common angle of incidence of 45°, the ratio of
n2 over n1 should be below 0.7, which is the reason that high refractive
ai at>ai n1 n2 ar ai at=90° n1 n2 ar
ai<critical angle ai=critical angle ai>critical angle ai n1 n2 ar evanescent wave p
Figure 1.2. Reflectance at the interface between the ATR crystal and a fluid at
incidence angles αi lower, equal to and higher than the critical angle. At critical
angles lower than the critical angle one fraction of the light is reflected and the other fraction transmitted. The right-hand situation describes ATR spectroscopy, where total reflection takes place. The insert schematically describes the evanescent wave protruding into the solution at such angles. The intensity of the wave decreases exponentially in a direction perpendicular to the surface.
The intensity of the evanescent wave decreases exponentially in intensity with distance from the surface. The distance at which the remaining intensity is e-1 is called the penetration depth[14;15], and is given by Equation 1.5.
2 02 2
1/ 2 1 2 2 sin p d n n 1.5where λ0 is the wavelength of the light in vacuum. The penetration depth of
the evanescent wave is typically in the order of the wavelength of the light. Based on the penetration depth, an effective path length can be
Lambert-ATR-FTIR can be compared to the performance of transmission FTIR systems as is shown in chapter 2 of this thesis.
1.3.2. Measurement of catalytic systems
This thesis focuses on the study of both homogeneously and heterogeneously (bio)catalyzed reactions with ATR spectroscopy. Figure 1.3 shows some the most common configurations for such studies and the comparison between the penetration depth and the thickness of the catalyst ‘layer’ for these configurations. Homogeneous (bio)catalysts can be studied with a configuration as shown in Figure 1.3a, while heterogeneous (bio)catalysts can be studied with configurations as shown in Figures 1.3b-1.3d.
Figure 1.3. ATR spectroscopy for the study of different catalytic systems. a)
homogeneous catalyst b) suspended slurry catalyst c) immobilized catalyst on porous support material d) immobilized (nonporous) metal film
Several methods exist to study heterogeneous catalysts with ATR-FTIR. As shown in Figure 1.3b, slurry catalysts can be studied with ATR spectroscopy,
for immobilized catalysts. Nevertheless, the slurry catalyst concentration was found to be sufficient to detect surface species on the catalyst as shown
by Hamminga et al.[7;16], allowing for the elucidation of reaction mechanisms.
Catalysts can also be immobilized on top of an ATR crystal, see Figure 1.3c, which optimizes the detectability of surface species on the catalyst. The most common immobilization procedure is the drying of a catalyst suspension on the crystal. Despite the general mechanical instability of such
films, the catalysts are often stable under flow-through conditions[17]. Both
supported catalysts, such as on alumina[18-21] or titania[22;23], as well as metal
and metal oxide catalysts, such as platinum[24], tantalum oxide[25;26] and
titania[27;28] have been immobilized.
A key parameter for such coatings is the thickness of the catalyst layer. In order to maximize the signal of the absorbed species and minimize the absorption from the bulk liquid, the catalyst layer should exceed the penetration depth. The concentration measured by ATR-FTIR spectroscopy is the volumetric molar average. Therefore, if the space taken up by the catalyst increases, the concentration of the bulk species measured
by ATR-FTIR decreases. Ortiz-Hernandez and Williams[20] have shown that
for Pd/Al2O3 catalysts, contributions to the signal from bulk liquid are minimized if the deposited catalyst layer is, on average, at least a factor 10 thicker than the penetration depth.
If the catalyst layer is too thick, concentration gradients will occur along the catalyst layer, see Figure 1.4. Therefore, the upper limit to the catalyst layer thickness depends on the reaction and mass transfer rates.
c)
a) b)
Figure 1.4. reactant concentration CA for different reaction rates and catalyst layer
thickness. Here, CA is the bulk concentration, uncorrected for porosity a) thin
catalyst layer b) thick catalyst layer with relatively slow kinetics c) thick catalyst layer with relatively quick kinetics
Calculations of the reactant concentration as a function of the catalyst layer thickness are important to prevent misinterpretation of spectral data, as discussed in chapter 3 of this thesis. If the reaction and mass transfer rates are known in detail, dedicated experiments can be carried out in which the layer thickness is varied in order to study the catalyst at different reactant and product concentrations[29;30].
Model catalysts, such as metal films, can also be studied with ATR spectroscopy. For such purposes, the catalyst is prepared directly on the
ATR crystal[31]. Germanium and silicon are the most suitable crystal
materials for the study of metal films due to their high stability and
refractive index[17]. The high refractive index results in a low penetration
depth and therefore a high ratio between absorption by adsorbed and bulk species. The study of metal catalyst films poses a number of difficulties. Firstly, metals are strong infrared absorbers, resulting in anomalous band
shapes of adsorbed molecules[32]. Secondly, nanometer-scale thin films are
required to retain sufficient light for measurements. In the process of
nanometers and the exact effects are often unclear, making data interpretation difficult. However, the light absorption by adsorbed
molecules can be enhanced about three orders of magnitude[34;35], allowing
for very sensitive detection of adsorbed molecules. Spectroscopy based on this principle, called surface enhanced infrared absorption spectroscopy (SEIRA), is increasingly applied[36-40].
Enzymes
For enzymatic systems, the same considerations apply as for other homogeneous and heterogeneous catalysts. However, some additional factors need to be taken into account:
1) The concentration of active sites is low, due to the high molar mass of enzymes;
2) Enzymes are often available only in small quantities;
3) The reaction environment is usually aqueous. Water is a strong infrared absorber and its spectrum is influenced by the presence of solutes, making subtraction of the water bands difficult.
Because of the above reasons, a large part of enzymatic research is focused on study the protein backbone, which makes up the largest fraction of the enzyme. Infrared spectroscopy can be used to elucidate the (secondary)
protein structure of the enzyme[41-45], also allowing for the study of protein
folding, unfolding and misfolding[46-49].
Enzymes can be studied in solution, with a typical concentration range of
0.1-1 mmol/L[50], or as a protein film on an ATR crystal. Such protein films
are often prepared by drying a protein solution on an ATR crystal [51-54]. In
stationary protein ‘layer’.
An experimental procedure is currently being developed in our lab to immobilize integral membrane-bound enzymes on an ATR crystal. The aim is to obtain a high enzyme concentration close to the ATR crystal while retaining the enzyme’s natural environment. In this procedure, washed
membranes and a silicon ATR crystal are biotinilated[58;59], meaning that
biotin is chemically attached. Streptavidin, a protein that strongly binds biotin on four of its active sites[60-62], can be used to anchor the biotinilated membranes layer by layer to the biotinilated ATR crystal. The procedure is shown in Figure 1.5. Si O NH 2 O O Si O NH2 O O Si O NH2 O Silanes Si O NH O O Si O NH O O Si O NH O biotin biotin biotin Si O NH O O Si O NH O O Si O NH O biotin biotin integral protein membrane streptavidin streptavidin
IR light in IR light out
biotin biotin
SiO2/SiOH
cytoplasmic protein
Figure 1.5. Membrane immobilization procedure for the study of integral proteins.
Membranes are first washed to remove non-integral proteins and are subsequently biotinilated. The silicon ATR crystal is first activated with plasma, silanised with APTES and biotinilated. Streptavidin and biotinilated membranes can be added layer by layer.
ATR-FTIR. However, the detection limit for ATR-FTIR spectroscopy is
generally too low to study such protein monolayers[63]. SEIRA spectroscopy
was recently found to be suitable for the study of hydrogenase
monolayers[63-65], due to an absorbance enhancement of two orders of
magnitude[50].
1.3.3. Measurement equipment
Several types of measurement equipment exist for the study of catalytic systems with liquid phase reactants. Important is that the equipment is stable under the operating conditions of the reaction, that reactants and catalyst can both be easily supplied and removed and that experiments are reproducible.
The most common equipment types for the study of heterogeneous catalytic systems are depicted in Figure 1.6. Homogeneous catalytic systems can be studied with most types of measurement equipment. For the study of heterogeneous catalytic systems, the particle distribution is important. A reproducible particle density within the range of detection of ATR can be obtained either by vigorous mixing of the suspension, see Figure 1.6a and 5b, or by applying a stable coating on top of the ATR crystal, see Figure 1.6c.
a) c) ATR crystal liquid / gas stirrer catalyst particle evanescent wave ATR crystal ATR probe light entering to detector stirrer catalyst particle evanescent wave ATR crystal ATR probe to detector catalyst particle evanescent wave ATR crystal flow-through cell b) reactants products
Figure 1.6. ATR spectroscopy measurement equipment a) ATR probe b) autoclave
with mounted ATR probe c) flow-through cell
Figure 1.6a shows a very versatile system with a movable ATR probe. The light is transferred to and from the ATR probe with either a guided mirror system or through hollow fibers. Such a probe is often used in open glassware. In order to study reactions at elevated pressure, a probe can be mounted to an ATR autoclave as shown in Figure 1.6b. Such a set-up was also used in the study described in chapter 3 of this thesis.
stable immobilized catalyst layer on top of the ATR crystal. Reactants can flow along the catalyst layer and changes in the reactant composition can be introduced to study the reaction mechanism and kinetics. In chapter 4, such a set-up was used for sample analysis.
1.4. Objective and outline of the thesis
The objective of this thesis is to evaluate the advantages and disadvantages of ATR-FTIR spectroscopy as a versatile analysis method for studying (bio)catalytic reactions and to create guidelines for optimal performance of ATR-FTIR set-ups.
In order to obtain this objective, equations are derived in chapter 2 to calculate the signal-to-noise ration (SNR) for ATR-FTIR set-ups. The SNR determines both the detection limit and the error in quantitative analysis. The number of internal reflections and the crystal material that optimize the SNR can be found with these equations, thus presenting a guideline for choosing the optimum configuration for ATR-FTIR spectroscopy. Equations are derived for homogeneous as well as heterogeneous (bio)catalytic systems and therefore provide a broad basis for catalysis research with ATR-FTIR spectroscopy.
The SNR for ATR-FTIR and transmission spectroscopy are compared for the study of homogeneous catalysis. Since both are suitable for studying such catalysis, comparison of the SNR can provide a guideline for choosing between these alternatives.
In chapter 3, the performance of the most versatile equipment type for ATR-FTIR spectroscopy in terms of pressure and temperature, the ATR
involved in particle suspension are studied. Since ATR-FTIR spectroscopy is a local analysis technique, concentration gradients could influence the observed concentrations leading to systematic errors in observed reaction rates. Guidelines are given to optimize the performance of ATR autoclave set-ups.
Chapters 4 and 5 of the thesis are aimed at the application of ATR-FTIR and other spectroscopic techniques to study the kinetics of specific (bio)catalyzed reactions. The guidelines developed in chapters 2 and 3 are used to optimize the performance.
The oxidation of benzyl alcohol by air, catalyzed by the organocatalyst TEMPO and the enzyme laccase, is investigated in chapter 4. The time-course of the organocatalyst is followed with a combination of several techniques, including ATR-FTIR spectroscopy. An attempt is made to elucidate the reaction mechanism and construct a kinetic model.
In chapter 5, hydrogen oxidation kinetics of membrane-bound hydrogenase (MBH) from the thermostable archaeon Pyrococcus furiosus are studied. In particular, the dependence on redox mediator concentration and temperature on the kinetics is studied. Additionally, the potential of using MBH for hydrogen oxidation in a fuel cell at elevated temperatures is evaluated.
Chapter 6 contains a summary and evaluation of the work presented in this thesis.
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Optimization of signal-to-noise ratios for
FTIR analysis of aqueous catalytic
systems using transmission cells or ATR
accessories
A study was carried out to optimize the signal-to-noise ratio (SNR) for FTIR analysis of homogeneous as well as heterogeneous catalytic systems in an aqueous environment. Both a transmission configuration and an ATR configuration were considered. Equations to calculate the SNR for an ATR configuration were developed in analogy to existing equations for a transmission configuration. Based on the developed equations, the optimum number of internal reflections and path length can be calculated. For homogeneous systems, the SNR for both a transmission and an ATR configuration were calculated and compared. As a test case, the SNR of myoglobin-bound carbon monoxide in an aqueous environment was calculated for several different configurations. A transmission configuration with calcium fluoride windows and a 60 μm path length was found to be optimal. For heterogeneous systems, SNR equations were derived for both powder catalysts and metal film model catalysts, deposited on an ATR crystal. For metal film catalysts, the high absorption coefficient was found
to lead to a low number of internal reflections for optimum SNR. The situation where the optimum configuration results in a light intensity that is too high for the detector was addressed. Three solutions are presented, viz., using an interference filter, decreasing the aperture and increasing the path length. An equation was derived to maximize the SNR within the detector limits for the latter two options. It was found that increasing the path length was more favorable and therefore the optimum path length is higher than the optimum path length would be if no detector saturation occurs.
2.1. Introduction
The signal-to-noise ratio (SNR) is a widely used parameter to assess sensitivity, where the signal is the parameter of interest and the noise is a random error. In FTIR spectroscopy the relevant signal is the absorbance,
which is linearly related to the concentration by the Lambert-Beer law[1]. A
higher SNR increases the chance of detection of compounds and decreases the error in quantification of detected compounds. It is especially important to maximize the SNR for systems that contain very low concentrations of the analyte, as is usually the case for (bio)catalytic systems, and for systems where short time-scale detection is required, such as is often the case for most operando experiments. Averaging spectra increases the SNR through the square-root law but comes at the loss of valuable time-dependent information.
Another way to enhance the SNR is to use a more suitable detector. The error in measured intensity in FTIR is generally dominated by the detector
noise[2]. The SNR can vary more than an order of magnitude[3], depending
on the type of detector used. Advances in detector sensitivities and in electronic noise reduction are therefore important for future research using FTIR spectroscopy.
The main types of detectors used for FTIR are pyroelectric detectors such as deuterated triglycerine sulphate (DTGS) detectors and photoconductive detectors such as mercury cadmium telluride (MCT) detectors. Pyroelectric detectors are based on a temporary voltage produced upon heating or cooling of the detector material, e.g. due to the absorbance of a photon. This voltage is a result of a slight shift of atom positions within the detector material’s crystal structure. Photoconductive detectors are based on semiconductor materials. Photons striking the detector material cause a shift
of electrons across the band gap, which results in a measurable decrease in electrical resistance.
Photoconductive detectors have a higher light sensitivity and a shorter response time than pyroelectric detectors, allowing for higher signal-to-noise ratios. A disadvantage of photoconductive detectors is the requirement of cooling, often using liquid nitrogen, due to their sensitivity to thermal noise. Another disadvantage is the nonlinearity at high photon fluxes, leading to negative deviations from Beer’s law [5]. In this chapter, the nonlinearity at higher photon fluxes is not taken into account directly. However, it is assumed that above a certain photon flux, nonlinearities are too high to effectively compensate, giving effectively a ceiling to the detector functionality. Not disregarding the importance of the detector choice, an effort is made in this chapter to find the optimum SNR conditions with a given detector and light source.
Detection becomes increasingly difficult if another infrared absorbing compound is present in much larger concentrations as is the case for aqueous environments. Increasing the path length of the light increases the signal but also strongly decreases the light reaching the detector and therefore results in a significant rise of the noise level of the experiment. Thus, an optimum path length exists where the SNR reaches a maximum. For transmission FTIR, a rule of thumb is that the measured absorption
should ideally be 1/ln(10)[4] or 0.48[6]. Many users are not aware that an
optimum path length exists and relations to find an optimum path length are much desired[6]. Jensen and Bak[8] recently set up relations to calculate the SNR and optimum path length for solutes in an aqueous environment for transmission (near-)infrared spectroscopy. In this chapter of the thesis,
using an analogy to the work of Jensen and Bak[8], these relations are
compare transmission and ATR spectroscopy, also including the choice of the crystal or window material and the angle of incidence of the light for ATR. For ATR, besides a homogeneous system, an immobilized powder catalyst and a metal film on top of the ATR crystal, functioning as a model catalyst, is considered.
The calculated optimum configuration might result in an unfeasible system if high light intensities are predicted to be preferred, leading to undesired detector saturation. Several methods are available to prevent detector saturation. The most common method is nonselective blocking of a fraction of the light by means of an aperture or a filter is compared with the alternative of using a longer path length. Due to the strong light absorption by water, elongating the path length leads to a decrease in light intensity. Alternate options to selectively use part of the light in order to obtain spatial resolution are discussed.
The aim of this chapter is to design the configuration of FTIR set-ups that optimizes the signal-to-noise ratio (SNR) for detecting low-concentration analytes in an aqueous solvent. The optimum configuration is chosen based on the type of accessory used (transmission cell or ATR-accessory), the material type and the path length of the light in the aqueous environment. Firstly, SNR relations for FTIR spectroscopy will be described in general. Secondly, an optimum SNR configuration is determined for transmission infrared spectroscopy. As a test case, the detectability of CO adsorbed to iron of the active site of myoglobin in an aqueous environment is
considered, which has a band position of 1944 cm-1. The detectibility of
iron-bound CO is of importance for many systems such as for hydrogenase, which contains a CO-ligand bound to its iron-containing active site. To put the work in a broader perspective, CO is also often applied as a probe for in-situ FTIR spectroscopy on catalytic sites in general[9,10].
Thirdly, SNR relations for ATR spectroscopy will be described, while using an analyte adsorbed on a metal film deposited on an ATR crystal as example, as well as the effects to be expected if a powdered catalyst is deposited on the surface of the ATR crystal.
Finally, options to prevent detector saturation are given and compared.
2.2. General SNR equations
The relevant signal in quantitative analysis is the absorbance of the solute. This absorbance is calculated from the intensities of a sample and a reference spectrum, as measured by the spectrometer, using Equation 2.1.
0 log I A I
2.1where I is the measured intensity of the sample and I0 is the reference
spectrum. In this chapter of the thesis, we assume that the solvent, in this case water, is taken as a reference spectrum. The absorbance measured can be used to calculate the concentration of the solute, using the Lambert Beer law[1], Equation 2.2:
s s
A c l 2.2
where A is the absorbance of the solute, εs is the extinction coefficient of
the solute and l is the spectral path length.
Because the absorbance of the solute is the relevant signal, the relevant noise is the (random) error in the calculated absorbance. The error in
absorbance can be calculated from the errors in measured intensities by error propagation[8].
The error in measured intensity σI in FTIR is generally dominated by the
detector noise [2], which is often considered to be constant and independent
on the measured intensities[8]. We assume that the error in intensity
measured is equal to the detector noise and independent on wavelength and light intensity.
As we assume that the solvent is the dominant absorber in the system, and
the solute is present in small concentrations, the intensities I and I0 are
nearly equal. Under the given assumptions, Equation 2.3 can be used to calculate the error in absorbance, or noise, for a spectrum.
2 ln 10 I A I 2.3where σA is the error in the calculated absorbance of the solute and σI is the
error in the measured intensity of the sample spectrum. With σI being a
constant, the error in the calculated absorbance is inversely linear to the intensity.
The total error in the absorbance σA,N can be decreased by averaging
multiple spectra to obtain a final spectrum. The noise σA,N can be calculated
from the noise of a single spectrum σA using the square-root law in
Equation 2.4, , A A N N 2.4
where N is the number of spectra used for averaging. The noise decreases by the square-root of the number of spectra.
The signal-to-noise ratio (SNR) of a spectrum can be calculated by dividing the absorption (signal), by the error in absorption (noise) as given by Equation 2.5. s A A SNR 2.5
Combining Equation 2.5 with Equations 2.2 and 2.3 gives Equation 2.6, the general equation for the SNR of absorbance spectra in FTIR systems, which is valid for both transmission and ATR configurations.
ln 10 2 I s s I SNR c l 2.6In order to use Equation 2.6 to find the path length that maximizes the signal-to-noise ratio, an equation for the intensity is required. This equation is different for homogeneous and heterogeneous systems as will be shown in the following paragraphs.
2.3. SNR equations for homogeneous systems
The equations to calculate the optimum path length for an ideal homogeneous system are deducted in paragraph 2.3.1. In paragraphs 2.3.2 and 2.3.3, losses due to reflection and absorption by used optical materials are included in the equations, for respectively transmission cells and ATR accessories. In paragraph 2.3.4, the SNR of transmission cells are compared
with ATR accessories for a system of CO detection at 1944 cm-1 in an aqueous environment.
2.3.1. Optimum path length in ideal homogeneous systems
Assuming negligible reflection and absorption by auxiliary optical materials, the intensity of the light that is not absorbed when illuminating an aqueous sample with a solute Iid can be calculated with Equation 2.7.
10 wacwal id src
I I
2.7 where Isrc is the source intensity of the light after subtraction of e.g. stray
light, εwa and cwa are the extinction coefficient and concentration of water
and l is the path length. Equations 2.6 and 2.7 can be combined to write the SNR as a function of the path length:
ln 10 10 2 wacwal src id s s I I SNR c l 2.8where SNRid is the SNR for an ideal homogeneous system. By setting the
derivative with respect to the path length to zero, the path length that minimizes the SNR can be found, see Equation 2.9.
1 ln 10 opt wa wa l c 2.9Here lopt is the optimum path length for SNR minimization. Substituting the
using a water spectrum taken with a known path length to calculate the optimum path length.
ln 10 opt wa l l A 2.10The absorption at the optimum path length can be obtained from Equation 2.10, yielding Equation 2.11.
, 1 ln 10 wa opt A 2.11Equation 2.11 gives a very convenient parameter to evaluate the deviation
of a given set-up from the optimum path length[4]. If the absorption
coefficient within the area of importance is close to 1/ln(10), the path length was chosen correctly. A deviation means that the path length is not optimal. Using a water spectrum, Equation 2.10 can be used to find the optimum path length at every wavenumber, as shown in Figure 2.1.
1.E-06 1.E-05 1.E-04 1.E-03 400 800 1200 1600 2000 2400 2800 3200 3600 4000 Wavenumber [cm-1] lopt [m ]
Figure 2.1. Optimum path length calculated with Equation 2.10 using an
absorption spectrum of water in a transmission cell with a path length of 25 μm using a single CaF2 window spectrum as a background. The dashed line shows the
optimum path length at 1944 cm-1, which is found to be 60 μm. Absorption
resulting in a path length lower than ~10 μm was not accurate due to the very low resulting signal.
For the test-case of Fe-CO detection in myoglobin, an optimum path length of 60 μm was found.
A second conclusion to be drawn from Figure 2.1 is that, depending on the wavenumber at which detection is required, the optimum path length can vary more than two orders of magnitude. Due to the very strong absorption
between 3600 and 3100 cm-1 the remaining light intensity is low and
background drift due to interference fringes and reflection by the window materials influence the spectrum significantly. In this area, the water spectrum is not accurate and as a result, the calculated path length is
inaccurate. An optimum path length lower than 1.10-5 m is estimated in this
area.
The highest value for the SNR for an ideal homogeneous system, SNRopt,id
can be found at the optimum path length and can be calculated with Equation 2.12, a combination of Equations 2.8 and 2.9.
, 2 src s s opt id wa wa I I c SNR c e 2.12
The equation for the SNR as a function of the path length, Equation 2.8, can be made dimensionless by dividing the SNR and the path length by the optimum SNR (Equation 2.12) and the optimum path length (Equation 2.9)
respectively. This strongly simplifies the equation, as found by Jensen and Bak[8]. 1 x rel SNR e x 2.13
where SNRrel is defined as the SNRid divided by SNRopt,id and x is the
dimensionless length expressed as a multiple of the optimum path length. With this powerful equation, the effect of deviation from the optimum path length on the relative SNR can be easily predicted as shown in Figure 2.2a. The loss in SNR can be compensated for by averaging spectra, as calculated by Equation 2.4. The number of averaged spectra required to obtain a spectrum of the same quality as a single spectrum taken at the optimum path length is shown in Figure 2.2b.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 x [-] SNR re l [-] 1 10 100 0 1 2 3 4 5 x [-] N [-]
Figure 2.2. Effect of the path length on the SNR. Here x is the dimensionless path
length defined as l/lopt. a) Relative SNR as a function of the relative path length. b)
Number of averaged spectra required to obtain a spectrum of equal quality to a spectrum taken at the optimum path length
As can be seen from Figure 2.2, the SNR rapidly decreases above and below the optimum path length. As a result, the number of averaged spectra required to maintain the spectral quality increases rapidly. At a path length of only five times the optimum path length, which is low compared to the more than two orders of magnitude in deviation of the optimum path length for water (see Figure 2.1), 100 spectra are required to maintain the
spectral quality. Given the fact that all spectra take equally long to measure, the required number of spectra gives an indication of the time resolution possible at a given path length.
One of the objectives in this chapter is to compare different configurations. In order to enable such a comparison, the SNR can be written in a more convenient form by expressing the SNR in a term independent on the configuration, SNRid, and a term dependent of the configuration.
2.3.2. Optimum path length in transmission FTIR
Figure 2.3 shows a typical transmission configuration for FTIR spectroscopy, where light is transmitted through two windows and an aqueous sample contained between these windows.
detection infrared light spacer twi l twi window window sample Isrc I
Figure 2.3. Transmission FTIR configuration. The transmission windows have a
thickness twi and the sample is contained between these windows. The thickness of
the spacer defines the path length l.
The light intensity of the light reaching the detector is lower than for the ideal case (Equation 2.7), due to reflection and absorption by the transmission windows. This can be corrected for by multiplying the ideal intensity with a factor representing the fraction of the light that is not
The SNR is linearly dependent on the intensity, see Equation 2.6, and is given in Equation 2.15. tr id I f I 2.14 tr tr id SNR f SNR 2.15
The factor ftr is independent on the path length and can be calculated with
Equation 2.16. 2 10 wicwi twi tr t f f 2.16
where ft accounts for reflection losses and the term in the exponent
accounts for absorbance losses by the windows. εwi.cwi represents the
wavenumber-dependent absorption coefficient of the window, twi is the
thickness of a single window and ft is the fraction of the light that is not
reflected at the four interfaces of the windows with the gas and liquid phases. The fraction of light that is not reflected can be calculated with Equation 2.17.
1
1
1
1
t air water water air
f R R R R 2.17
where Rair and Rwater are the fraction of the light reflected at the interface of
the window with air and water respectively. Assuming an angle of incidence
of 90o, a simplified form of the fresnel equations, Equation 2.18, can be
2 1 2 1 2 n n R n n
2.18where n1 and n2 are the refractive indices of the materials on both sides of
the surface. It should be noted that windows with a large refractive index will result in a larger reflection. This is one of the reasons why windows of a relatively low refractive index material (n=1.4) such as CaF2 are often used in transmission cells. Due to the mirroring between the windows, light can interact with the sample multiple times, resulting in interference fringes. This is especially the case for empty cells due to the low refractive index of air (n=1). For an aqueous system (n=1.4), internal mirroring is often minimal and the extra absorbance is neglected. Finally, some windows are coated with a layer with a refractive index between that of air and the window material in order to diminish the reflection. The windows are not assumed to have such a layer in this study.
The SNR can be calculated from the optimum SNR of an ideal system (Equation 2.12) by including the factor representing the losses due to the transmission set-up (Equation 2.16) and due to deviation from the optimum path length: , , 1 , tr tot tr id opt x tot tr tr SNR f SNR where f f e x 2.19
The factor ftot,tr can conveniently be used to compare different
configurations. A higher ftot,tr corresponds to a higher SNR, where ftot,tr=1 is
As an example, the effect of using common 50 μm spacers (x=0.83) instead of spacers of the optimum path length of 60 μm (x=1), see Figure 2.1, has been evaluated. Spacers of 60 μm are generally not available, thus, spacers
of 50μm would be a good choice. Because ftr is similar for both situations,
ftot,tr is only dependent on x. The deviation from the optimum path length
results in a ratio of ftot,tr of 0.982, corresponding to a loss in SNR of 1.8%.
2.3.3. Optimum path length in ATR
The SNR for an ATR accessory can be calculated following a procedure analogous to the procedure followed for transmission FTIR. Such analogy is allowed for because the evanescent wave protruding from the ATR surface can be converted to an equivalent path length for a transmission
configuration, as is shown in appendix A.1[11]. Figure 2.4 shows an ATR
crystal with multiple internal reflections and is used to visualize the meanings of some of the symbols in this paragraph.
l=nr
.d
e
a
de de de de
Infrared light detector
ATR crystal
Figure 2.4. Multiple internal reflection element
For strongly absorbing compounds a correction for the effective path
length, such as provided by the Kramers-Kronig relations[12], is required for
detailed comparison with the transmission path length. Such corrections can be important for quantitative determination of concentrations, but the
errors are generally below 10%[11], which is not expected to strongly effect
Many ATR set-ups are equipped with a multiple internal reflection element as shown in Figure 2.4. The total path length depends on the number of internal reflections and the effective path length as given in Equation 2.20.
r e
ln d 2.20
where nr is the number of internal reflections and de is the effective path
length for a single reflection. Using Equation 2.20 for the path length, ATR spectroscopy can be compared with the ideal system of a similar path length. In analogy to Equations 2.14 and 2.15, the remaining light intensity and SNR after losses due to reflection and absorption by the ATR crystal are given by Equations 2.21 and 2.22.
ATR id
I f I 2.21
ATR ATR id
SNR f SNR 2.22
Both reflection and absorbance losses by the crystal contribute to the factor
fATR as shown in Equation 2.23.
10 cc lc c ATR t
f f 2.23
where ft accounts for reflection losses and the term in the exponent
accounts for absorbance losses by the windows. εc.cc represents the
through the crystal. In contrast to ftr for transmission configurations, fATR is
dependent on the path length, due to the dependence of lc on the number of
internal reflections and therefore the path length. In this chapter of the thesis, a commonly used trapezoid-shaped ATR crystal with detection on
one side of the crystal is assumed. The dependence between lc and l is
derived in appendix A.2 for such crystals and is given by Equation 2.24. 2 cos cos c c c e t t l l d 2.24
where α is the angle of incidence and tc is the crystal thickness. The first
term in the relation is linearly dependent on the path length, the second term is independent on the path length. This term compensates for the shorter path length the light needs to travel through the crystal for the first internal reflection.
The fraction of light that is not reflected can be calculated with Equation 2.25. This fraction is equal or higher than for a transmission set-up (see Equation 2.17), because no reflection losses at the interface between the crystal and the aqueous sample need to be taken into account.
1
1
t air air
f R
R 2.25Due to the dependence of fATR on the path length, the optimum path length
is vice versa dependent on fATR. In order to include this dependence to find
the optimum path length, the SNR, see Equation 2.22, is written as a function of the path length by combining Equations 2.8, 2.23 and 2.24:
cos 2cos ln 10 10 10 2 c c c c wa wa c c e t c t c c l d t src ATR s s I f I SNR c l 2.26By setting the derivative to the path length of the right-hand side of Equation 2.26 to zero, the path length that maximizes the SNR can be found, see Equation 2.27.
, 1 2 ln 10 cos opt ATR c wa wa c c e l t c c d
2.27The optimum path length for ATR is shorter than for transmission spectroscopy (see Equation 2.9) due to the extra term in the denominator describing the path length dependent losses due to absorption by the ATR crystal.
It could be convenient to express the optimum path length as a function of the absorbance of water and the crystal in order to relate an existing spectrum to the optimum path length as was done in Figure 2.1 for transmission spectroscopy. Equation 2.28 gives the absorbance by water
and the crystal, where lc is substituted with Equation 2.24 to express the
absorbance as a function of the path length. 2 cos cos c c wa wa c c c c e t t A c c l c d
2.28Substituting Equation 2.28 into Equation 2.27 gives lopt,ATR as a function of
the absorbance, Equation 2.29, and the absorbance at this optimum path length, Equation 2.30.
, ln 10 cos opt ATR c c c l l t A c
2.29
, 1 ln 10 cos c opt ATR c c t A c 2.30Interestingly, the absorbance at the optimum path length does not equal 1/ln(10), the well-known rule of thumb also given by Equation 2.11. For a trapezoid-shaped ATR crystal with absorbance on only one side of the crystal, as considered in this chapter of the thesis, the optimum absorbance is actually lower than 1/ln(10). This is due to the nonlinearity of the ratio of lc over l, as detailed in appendix A.2. The maximum deviation in the optimum absorbance, and therefore the optimum path length, is 50%. The deviation decreases at decreasing crystal absorption coefficient and crystal thickness.
In analogy to Equation 2.19 for transmission set-ups, the SNR for ATR accessories is given by Equation 2.31 as a function of the optimum SNR for an ideal system.
, , cos 1 , 10 2 cos c c c ATR tot ATR opt id
c t x t wa wa tot ATR c wa wa c c e SNR f SNR where f c f e x t c c d
2.31Using Equation 2.31, ftot,ATR can be used to compare different configurations.
Figure 2.5 shows the effect of the refractive index and the absorption coefficient εc.cc on ftot,ATR.
As can be seen from Figure 2.5a, ftot,ATR is at its maximum around the critical
angle, which is the angle above which attenuated total reflection takes place.
At angles just above the critical angle, the ratio between l and lc is at its
maximum, and therefore the absorbance by the crystal is at its minimum for a given path length. Care has to be taken not to operate too closely to the critical angle in order to avoid artifacts in the data[12]. Furthermore, a large penetration depth is often undesirable for heterogeneous systems because bulk species absorption is increased. This makes detection of the smaller
adsorbed species bands more difficult[13]. The critical angle of ZnSe
interfacing an aqueous environment is 33°, which is close to the standard 45° incidence angle of the light and is therefore close to optimal for operation.
0.0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 Angle of incidence [°] ftot, ATR [m ] ZnSe
critical angle ZnSe Germanium critical angle Ge 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.002 0.004 0.006 0.008 0.010 Crystal thickness [m] ftot, A T R [m] ZnSe (0.8 m-1) 8 m-1 0.08 m-1
Figure 2.5. Sensitivity of ftot,ATR towards several parameters at optimum path
length. a) effect of angle α for ZnSe (n=2.43) and Ge (n=4.02) for a crystal thickness of 2.10-3 m. b) effect of crystal thickness t
c for ZnSe (absorption
coefficient εc.cc=0.8m-1) and for different absorption coefficients, at an angle of 45°.
Figure 2.5b shows the effect of crystal thickness on ftot,ATR. For ZnSe,
absorbance losses are only 3% for a standard thickness of 2.10-3 m and 13%
for a high thickness of 1.10-2 m, assuming an absorption coefficient εc.cc of
0.8 m-1. The absorption coefficient is dependent on the crystal material, the
wavelength and even the presence of impurities in the crystal[14]. Assuming
the same refractive index as ZnSe (n=2.43), but an absorption coefficient of
ZnSe (0.8 m-1)
8 m-1
8 m-1, the effect of crystal thickness on ftot,ATR is much stronger, as can be expected. For a crystal thickness of 2.10-3 m, ftot,ATR decreases by 23%.
2.3.4. Comparison of SNR for transmission and ATR
In contrast with transmission FTIR, the absorption by the crystal in ATR-FTIR is dependent on the path length. The SNR ratio for the two configurations is therefore also dependent on the path length as shown in Equation 2.32. 2 cos 2 cos , , , , 10 10 c c c wi wi wi tc c cc l de t c c t tot tr t tr trans
ATR tot ATR t ATR
f f SNR SNR f f 2.32
where the first and second terms on the right-hand side of the Equation are respectively independent and dependent on the path length. The SNR of transmission becomes relatively better at larger path lengths due to the increased absorbance by the crystal in the ATR set up.
The fraction of the light not reflected at the windows and crystal, ft is
dependent on the refractive index of the optical material. Refractive indices are slightly dependent on the wavelength of the light. A comparison was
made for a wavenumber of 1944 cm-1, the location of Fe-CO bands in
myoglobin. Table 2.1 gives an overview of the transmitted fractions for both a transmission and an ATR configuration. The transmission cell is assumed to be filled with water.
n Rair Rwater ft,tr ft,ATR CaF2 1.40[15] 0.03 0.00 0.94 0.95 ZnSe 2.43[16] 0.17 0.08 0.57 0.68 Silicon 3.43[17] 0.30 0.19 0.32 0.49 Germanium 4.02[18] 0.36 0.25 0.23 0.41 diamond 2.40[19] 0.17 0.08 0.58 0.69
Table 2.1. Reflection for optical materials with different refractive indices for both
FTIR and ATR configurations. Rair and Rwater are the fractions of light reflected at
respectively an air-crystal and water-crystal interface as calculated with Equation 2.18. Numbers in gray represent configurations that are uncommon; Silicon and Germanium have a high refractive index, making them less suitable as a window material; diamond windows cannot be created at sufficient size; CaF2 is not suitable
for ATR due to its high critical angle.
As can be seen in Table 2.1, reflection can contribute significantly to intensity losses and therefore SNR. The material choice strongly influences the remaining intensity, especially for a transmission configuration. The
value of Rair can be lowered by applying a coating, but applying a coating on
the detection side to decrease Rwater requires careful consideration.
Due to path length dependent absorption losses of the ATR crystal, the optimum path length is shorter than for transmission FTIR as shown by division of Equations 2.9 and 2.27 in Equation 2.33.
, , 1 2 cos opt tr c c c opt ATR e wa wa l t c l d c 2.33
If absorbance by the crystal material is negligible (εc.cc<<εwa.cwa), the optimum path length is the same for both configurations.
