- Email: [email protected]
UV–VIS absorption spectroscopy: Lambert-Beer reloaded
UV-VIS Absorption Spectroscopy: Lambert-Beer reloaded Werner M¨antele, Erhan Deniz PII: DOI: Reference:
S1386-1425(16)30555-8 doi:10.1016/j.saa.2016.09.037 SAA 14683
To appear in:
Please cite this article as: Werner M¨antele, Erhan Deniz, UV-VIS Absorption Spectroscopy: Lambert-Beer reloaded, (2016), doi:10.1016/j.saa.2016.09.037
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
UV-VIS Absorption Spectroscopy: Lambert-Beer reloaded Werner Mäntele*, Erhan Deniz
IP
Max-von Laue-Straße 1, D-60438 Frankfurt am Main, Germany
T
Institut für Biophysik, Johann Wolfgang Goethe-Universität Frankfurt am Main
SC R
Address correspondence to: [email protected]
Abstract:
UV-VIS absorption spectroscopy is used in almost every spectroscopy laboratory for routine analysis or research.
NU
All spectroscopists rely on the Lambert-Beer Law but many of them are less aware of its limitations. This tutorial discusses typical problems in routine spectroscopy that come along with technical limitations or careless selection
MA
of experimental parameters. Simple rules are provided to avoid these problems.
Glossary:
Decrease of light intensity of the measuring beam because molecules in the sample undergo a
D
Absorption:
TE
transition from the ground state to an excited state Entire loss of light energy upon passing through a sample
Transmission:
Ratio of light intensity before (I0) and after (I) the sample: (I/I0), often in percent 100x (I/I0)
CE P
Extinction:
A tutorial on UV-VIS spectroscopy? At first sight, this does not seem to be necessary. We all use in our labs UV-VIS
AC
spectrometers every day, either as routine instruments or for research, and thus should know the rules. Yet in more that 10% of the manuscripts in my inbox I see crude violations of Lambert-Beer’s law, either by wrong design of the experiment or because the prerequisites to apply the basic laws to measure transmission or absorption are not followed. Routine procedures bear the risk that potential pitfalls are not considered. Where are the problems? It starts with the fact that the terms “absorption” and “extinction” are very often used synonymously and used as labels at the ordinate of the spectrum plots. I wish we would be more precise here. “Absorption” is defined as the process whereby the light intensity from the measuring beam is diminished because molecules in the sample undergo a transition from the ground state (usually the singlet state S0 for molecules at room temperature) to an excited state S1, S2, or higher. “Extinction” refers to the entire loss of light energy upon passing through the sample. It includes absorption, but also light scattering and reflection, processes that have nothing to do with the absorption process. The extinction is thus equal to or higher than the absorption. The numerical value obtained in a UV-VIS spectroscopy experiment by application of Lambert-Beer’s law (historically more correct: the Bouguer-Lambert-Beer Law):
A log T log
I0 cd I
ACCEPTED MANUSCRIPT T: transmission; I0, I: intensity of the measuring beam before/after passing through the sample; : molar absorption coefficient; c: concentration; d: path length of the measuring beam in the sample.
is typically called “absorbance” , A, and plotted vs. the wavelength. Spectroscopy purists plot the molar absorption coefficient vs. the wavelength, and real hard core spectroscopists plot it vs. the wavenumber in cm .
T
-1
IP
Please note that both transmission and absorption are defined on the basis of the ratio of two intensities, before and after the sample. No matter what unit is used for I and I0, absorption and transmission are dimensionless. For
SC R
transmission, the value obtained is typically multiplied by 100 and denoted as %T. For absorption, it is rather a bad habit if spectroscopists use “absorbance units”, AU, or OD for “optical density units”. While these are merely semantic problems or badly defined physical magnitudes, the pitfalls on the technical side
NU
are more relevant. When we learnt about the use of the Lambert-Beer law in spectroscopy, we also learnt that it is only strictly valid if some fundamental conditions are fulfilled. The most relevant are: strictly monochromatic measuring light;
homogeneous distribution of the molecules in the sample;
passage of the complete measuring beam through the sample;
absence of light scattering and of photochemical reactions in the sample;
no reemission of the absorbed light by fluorescence,;
an ideal detection and processing of the intensity values I0 and I.
TE
D
MA
Real life is not ideal, and so isn’t absorption spectroscopy. The first condition – strictly monochromatic light – is
CE P
already hard to guarantee. Our routine spectrometers typically use a tungsten-iodine light source for the near-UV to near IR spectral range (e.g. 380 – 1000 nm) and a deuterium discharge lamp for the UV from about 200 to 380 nm. A flip mirror is used to switch between the lamps. For a perfectly adjusted optics, the absorbance values of a sample before and after flipping this mirror should be identical, but most spectra (including the ones I see in
AC
incoming manuscripts) show an offset. In order to obtain “monochromatic light” (an euphemism, because strictly monochromatic would mean that the intensity is zero), most instruments use a grating monochromator that is moved by a stepper motor. The spectral bandwidth of the output of this monochromator is a compromise between intensity and spectral bandwidth set by the mechanical width of the monochromator output slit. Since 12 nm spectral bandwidth can be easily obtained with still sufficient light intensity, this is not really a problem. The pitfalls come from the fact that any grating monochromator uses the grating at a certain diffraction order: first, second, third and so on. The interference conditions of a grating state that at any output wavelength the grating is set, there is also intensity at higher orders, i.e. 2, 3 and so forth, albeit at much lower intensity. This means that if your monochromator is set at blue-violet light at 400 nm, the measuring beam also contains light at 800 nm. Just imagine that if your sample absorbs strongly at 400 nm but is transparent at 800 nm; the detector will not be able to correctly measure the residual intensity at 400 nm because of the fraction of light at 800 nm detected. Manufacturers of spectrometers cope with this physics of diffraction by placing so-called “order filters” in the beam after the monochromator that let the desired light pass and block or at least reduce the higher order light intensity. Nevertheless, there are traces of unwanted light in the measuring beam that limit the application of the Lambert-Beer law. This phenomenon is frequently called “spectral false light”, in contrast to “spatial false light” that we will deal with below.
ACCEPTED MANUSCRIPT Another source of spectral false light is stray light in the monochromator. This means that a small but noticeable fraction of the incoming white light will also appear at the output. For a well-designed monochromator, stray light -3
-5
is on the order of 10 to 10 of the incoming light intensity. Stray light is equally sensed by the photodetector and also limits the minimum measurable intensity – or the maximum of measurable absorbance.
T
A third source of spectral false light may occur if the sample is strongly fluorescent. Let us assume that the sample
IP
has a peak absorbance of 2 which means that only 1% of the measuring light is passing at this wavelength. If the fluorescence quantum efficiency of the sample is high, a high fraction of the absorbed photons (99% in our
SC R
example) is re-emitted as fluorescence. Again, the photodetector does not care whether it sees the residual intensity I (1% in our example) of the measuring light or the intensity caused by the re-emitted photons at a wavelength shifted to the red. If the detector is more sensitive for the fluorescence wavelength, the fluorescence intensity can appear even higher than the transmitted intensity. The precise estimation of this error source
NU
requires knowledge about the geometry of the sample, the optics and the detector. Molecules may diffuse and rotate while the molecule is in the excited state; fluorescence emission is thus not in the direction of the
MA
measuring beam, but rather isotropic.
There are means to get rid of the spectral false light caused by sample fluorescence. The best solution is a second monochromator between sample and detector, set at equal spectral resolution and moved synchronously with the
D
first monochromator. This guarantees that only the measuring light passes from the sample to the detector. This luxury solution solves the problem caused by fluorescent samples and the problem caused by stray light, but not
TE
the higher order problem, unless order filters are included, too. The cheaper solution is to increase the distance between the sample and the detector and to use a parallel beam of light for the absorption measurement. If so,
CE P
the transmitted measuring light I is recorded independent from distance r, while the intensity of the fluorescence 2
light will decrease approximately with 1/r because it is emitted almost isotropically. An even cheaper solution is dilution of the sample. As you dilute, the transmitted intensity I will increase while the emitted fluorescence
AC
intensity will decrease.
Spatial false light has many origins. There are trivial ones, such as incompletely filled cuvettes where the measuring beam partly passes above the sample, and this fraction reaches the detector unattenuated. There are badly adjusted cuvette holders that let part of the light pass sideways. You may think that I report problems that are typical for first-year students, but I have seen this for experienced senior scientists in research labs. The so-called microcuvettes that are popular because they require only small sample volumes are prone to this problem, since they have only a narrow slit for the sample with glass or plastic walls left and right. The slightest shift of these cuvettes causes the measuring beam to pass partly through the glass walls. The solution can be as trivial as the problem: tale a black felt pen and paint the glass walls left and right from the sample part until they are intransparent. There are also blackened cuvettes available; while they are more expensive, their use should be much preferred in particular for very small sample volumes. Light scattering in the sample is also a false light problems. The ideal sample in the sense of the Lambert-Beer law is a homogeneous solution without light scattering. Many chemical, biochemical or biological samples are suspensions or textured structures that exhibit light scattering. It is not always necessary to describe light scattering quantitatively, but spectroscopists at least should know about their impact on an absorption measurement.
ACCEPTED MANUSCRIPT For suspensions with particles at a size d much smaller than the wavelength (d<<), i.e. up to some tens of nm for the wavelengths used in UV-VIS spectroscopy, Rayleigh scattering is observed. Protein solutions are a typical 4
example. The scattered light is classical dipole radiation; the intensity varies with 1/ . Scattering for larger particles (d<), i.e. for cells and large nanoparticles sized up to some hundreds of nm, is described by the RayleighGans-Debye model. This implies an angular distribution of the scattering intensity different from Rayleigh
T
4
scattering, but also a 1/ dependence. Scattering from larger particles (d> or d>>) is described by the Mie
IP
scattering model or by Fraunhofer scattering, but these two are rare cases in bioanalytical spectroscopy.
SC R
We thus expect – on top of our absorption spectrum – a wavelength-dependent light scattering caused by Rayleigh or Rayleigh-Gans-Debye scattering, thus an “apparent absorption”, and we may call the sum of both terms “extinction” according to the discussion above. Since absorption and apparent absorption are essentially additive, they can be separated. Indeed they must be separated if quantitative absorption values are to be obtained from
NU
the absorption spectrum. For this procedure, I see frequently quite futile attempts. One possibility is to take values of the extinction outside the range of the absorption band(s) and use these to calculate, with a least-squares fit, a 4
MA
1/ function as a new “scattering baseline” for the entire extinction spectrum. If this is done carefully, a clean absorption spectrum can be obtained by subtraction of this baseline from the “extinction” spectrum. Instead of post-experiment procedures, a careful choice of the experimental setup can reduce light scattering.
D
Moving the detector closer to the sample is a simple option. Doing this, the detector area captures more of the
TE
scattered photons and the intensity loss by scattering is reduced. Some top spectrometers have a second separate sample compartment where the cuvettes are placed directly in front of the detector. This, however, bears the risk of also capturing more fluorescence photons as we discussed above. The sample-detector distance is thus a
and a hard place”.
CE P
compromise between reducing fluorescence and reducing light scattering; this may be the choice “between a rock
A radical procedure to reduce light scattering for biological samples is “refractive index matching”. It makes use of
AC
the fact that the scattering intensity of a suspension depends on the difference between the refractive index of the particle (the “scatterer”) and of that of the solvent around. Adding soluble macromolecules, e.g. long chain sugar molecules, to the solvent increases the refractive index of the solution. Once this refractive index exactly matches that of the particle, the suspension becomes clear- scattering is gone. Finally, we consider the insufficiency of the detection and signal processing unit for absorbance measurements. We expect from a photodetector high spectral sensitivity over the entire spectral range, low dark noise, high linearity for the conversion of light intensity to an electric signal, no drifts of the electric signal and no saturation for high intensity. This is daydreaming, but nevertheless engineers have done a good job. In order to measure an absorbance of 1, detection and signal conversion have to process two signals, I0 and I, that differ by a factor of 10 in amplitude. For absorbances 2, 3 or 4, this factor is 100, 1000 and 10000, resp.. These two signals must be amplified and digitized at a precision that allows the calculation of I0/I and log (I0/I) with sufficient precision. Digitization of an analog signal determines the resolution of the signal. If a signal of 1 Volt is digitized at 10
10 bit resolution, it is resolved in 2 = 1024 equal discrete steps, each approx. 1 mV. Needless to say that if I want to compare I0 and I that differ by a factor of 1.000 in amplitude, the resolution of an analog-to-digital-converter must be quite a bit higher.
ACCEPTED MANUSCRIPT Most signal processing units use analog-to-digital-converters that are at 16 bit resolution; they divide the analog 16
signal in 2 = 65.536 equal discrete steps. It is evident that even at that precision the digitization of the smaller of both signals will be precision-limited. Higher resolution analog-to-digital-converters are possible, but speed goes down and prize goes up.
T
I0/I ratio formation is the next step. We need not be mathematicians to see that the higher the absorbance and the
IP
smaller I is compared to I0, the more we move towards a division by zero. Small absolute differences in the measurement of I will cause large changes in the result. This is another reason to keep the absorbance low.
SC R
How do we notice any of these limitations in an absorbance measurement? How do we detect violations of the Lambert-Beer law ? Very typically, the band profiles change. They are typically Voigt profiles – Gaussian distributions of Lorentz profiles – but become flat at the top and finally saturate in absorbance, no matter how concentrated the absorber is. Tops of the bands exhibit either strong noise (no wonder if we force division by
NU
zero), or are completely flat when the spectrometer software determines that “infinity” really must be some arbitrary maximum value of, say, five units. The linear relation between concentration and absorbance gets lost.
MA
Instead of determining quantitatively a concentration from a sepctrum, you might as well throw dice. Figure 1 illustrates this problem. Spectra of human serum albumin at increasing concentrations were taken on one of our routine spectrometers, neither badly adjusted on purpose, nor tuned to optimum. The series of spectra
D
shows band profile deformations starting at extinction values above approx. 1.5. The inset shows the
TE
concentration as determined from the absorbance of the aromatic amino acid side chains at 279 nm vs. the real
AC
CE P
concentration.
ACCEPTED MANUSCRIPT What should the minimum precautions be? In view of all these more or less hidden pitfalls that can mess up an absorption measurement, a careful procedure should start with instrument checks. 1.
Take the time to have a look at the measuring beam of your spectrometer and how it is placed with
T
respect to the cuvette. Simply set the monochromator to 500 nm, a wavelength where eye sensitivity is
IP
highest, and check whether the beam is well centered in the cuvette and whether there might be spatial false light. Check whether the sample filling volume is sufficient. If necessary, readjust the sample
2.
SC R
position.
Run the spectrometer across the desired wavelength range without any sample or reference cuvette, just air against air. Is the absorbance baseline thus obtained flat or does it show offsets whenever a lamp or order filter switch occurs? Adjustment of the optics may be necessary.
Magnify this baseline to see the noise. What is the root mean square level of this noise in terms of
NU
3.
absorbance? For samples at low extinction, this noise-equivalent absorbance will be your detection limit. Block the light path and measure a dark spectrum. The absorbance should max out everywhere; this will
MA
4.
give you an idea what your system does when insufficient light gets through the sample. 5.
Repeat the procedure in 1 with a pair of matched cuvettes both filled with the same buffer/solvent. I
D
know that this procedure is rather old style, but having a pair of matched cuvettes, i.e. cuvettes made from the same glass or quartz material and with pathlengths as similar as possible, warrants a precise
TE
subtraction of buffer absorbance. Refrain from using plastic cuvettes for quantitative measurements if possible; their optical quality is not very high. Again magnify the baseline thus obtained to see the noise.
6.
CE P
This will tell you the usable spectral range. Use the pair of matched cuvettes for the sample and the reference buffer/solvent to run a spectrum. If you don’t have such a pair, at least use the same cuvette for the measurement of the background and the sample spectrum. If absorbance exceeds a value of 1-2, then dilute and repeat. Aiming at a maximum
AC
absorbance below 1 will prevent the fluorescence problem discussed above and guarantee a linear relationship between absorbance and concentration. Lambert & Beer will bless you for that. 7.
If you are concerned that the lower concentration obtained by dilution might have an impact on your sample, for example disaggregation of a protein, then use matched cuvettes with a shorter path length instead of dilution. There are standard cuvettes from quartz or glass at 1 cm, 5mm, 2mm, 1mm and lower pathlengths, some even from plastic materials.
8.
If a scattering background is observed, try to reduce scattering by changing the geometry, i.e. move the sample and reference cuvettes closer to the detector if possible.
9.
4
Once the scattering is minimized on the experimental side, fit a 1/ function to the spectrum obtained, but exclude data points at and immediately around the absorption band(s). 4
10. Subtraction of this 1/ function will typically result in a rather clean absorption spectrum that can be used for quantitative evaluation. All the pitfalls discussed here apply to standard absorption spectroscopy in vitro. They may have a different impact depending on the instrument used. Once spectroscopic experiments are performed outside a well designed
ACCEPTED MANUSCRIPT instrument, for example by using fiber optics in situ or in biomedical spectroscopy in vivo, problems can become significantly worse. In summary, it is easy to obtain clean, linear and quantitative absorption spectra if these rules are followed. . I would not rely on post-experimental processing of miserable data. Unfortunately, the instrument manufacturers
T
try to convince you that “their” instrument can cope with these problems, but that’s mostly a marketing claim. I’d
IP
rather wish they would build into their software a few program lines that warn the user. At absorbance values up to about 1.5, the display should show a green light indicating that everything is OK. Above an absorbance of 1.5 to
SC R
2, an orange warning should flash up saying “you are about to leave the validity of Lambert-Beers Law”, and above an absorbance of 2, a warning light should appear in red and say “you just violated Lambert-Beers Law”.
NU
Further reading:
AC
CE P
TE
D
MA
Werner Schmidt: Optical Spectroscopy in Chemistry and Life Sciences. Wiley VCH, 2005
S1386-1425(16)30555-8 doi:10.1016/j.saa.2016.09.037 SAA 14683
To appear in:
Please cite this article as: Werner M¨antele, Erhan Deniz, UV-VIS Absorption Spectroscopy: Lambert-Beer reloaded, (2016), doi:10.1016/j.saa.2016.09.037
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
UV-VIS Absorption Spectroscopy: Lambert-Beer reloaded Werner Mäntele*, Erhan Deniz
IP
Max-von Laue-Straße 1, D-60438 Frankfurt am Main, Germany
T
Institut für Biophysik, Johann Wolfgang Goethe-Universität Frankfurt am Main
SC R
Address correspondence to: [email protected]
Abstract:
UV-VIS absorption spectroscopy is used in almost every spectroscopy laboratory for routine analysis or research.
NU
All spectroscopists rely on the Lambert-Beer Law but many of them are less aware of its limitations. This tutorial discusses typical problems in routine spectroscopy that come along with technical limitations or careless selection
MA
of experimental parameters. Simple rules are provided to avoid these problems.
Glossary:
Decrease of light intensity of the measuring beam because molecules in the sample undergo a
D
Absorption:
TE
transition from the ground state to an excited state Entire loss of light energy upon passing through a sample
Transmission:
Ratio of light intensity before (I0) and after (I) the sample: (I/I0), often in percent 100x (I/I0)
CE P
Extinction:
A tutorial on UV-VIS spectroscopy? At first sight, this does not seem to be necessary. We all use in our labs UV-VIS
AC
spectrometers every day, either as routine instruments or for research, and thus should know the rules. Yet in more that 10% of the manuscripts in my inbox I see crude violations of Lambert-Beer’s law, either by wrong design of the experiment or because the prerequisites to apply the basic laws to measure transmission or absorption are not followed. Routine procedures bear the risk that potential pitfalls are not considered. Where are the problems? It starts with the fact that the terms “absorption” and “extinction” are very often used synonymously and used as labels at the ordinate of the spectrum plots. I wish we would be more precise here. “Absorption” is defined as the process whereby the light intensity from the measuring beam is diminished because molecules in the sample undergo a transition from the ground state (usually the singlet state S0 for molecules at room temperature) to an excited state S1, S2, or higher. “Extinction” refers to the entire loss of light energy upon passing through the sample. It includes absorption, but also light scattering and reflection, processes that have nothing to do with the absorption process. The extinction is thus equal to or higher than the absorption. The numerical value obtained in a UV-VIS spectroscopy experiment by application of Lambert-Beer’s law (historically more correct: the Bouguer-Lambert-Beer Law):
A log T log
I0 cd I
ACCEPTED MANUSCRIPT T: transmission; I0, I: intensity of the measuring beam before/after passing through the sample; : molar absorption coefficient; c: concentration; d: path length of the measuring beam in the sample.
is typically called “absorbance” , A, and plotted vs. the wavelength. Spectroscopy purists plot the molar absorption coefficient vs. the wavelength, and real hard core spectroscopists plot it vs. the wavenumber in cm .
T
-1
IP
Please note that both transmission and absorption are defined on the basis of the ratio of two intensities, before and after the sample. No matter what unit is used for I and I0, absorption and transmission are dimensionless. For
SC R
transmission, the value obtained is typically multiplied by 100 and denoted as %T. For absorption, it is rather a bad habit if spectroscopists use “absorbance units”, AU, or OD for “optical density units”. While these are merely semantic problems or badly defined physical magnitudes, the pitfalls on the technical side
NU
are more relevant. When we learnt about the use of the Lambert-Beer law in spectroscopy, we also learnt that it is only strictly valid if some fundamental conditions are fulfilled. The most relevant are: strictly monochromatic measuring light;
homogeneous distribution of the molecules in the sample;
passage of the complete measuring beam through the sample;
absence of light scattering and of photochemical reactions in the sample;
no reemission of the absorbed light by fluorescence,;
an ideal detection and processing of the intensity values I0 and I.
TE
D
MA
Real life is not ideal, and so isn’t absorption spectroscopy. The first condition – strictly monochromatic light – is
CE P
already hard to guarantee. Our routine spectrometers typically use a tungsten-iodine light source for the near-UV to near IR spectral range (e.g. 380 – 1000 nm) and a deuterium discharge lamp for the UV from about 200 to 380 nm. A flip mirror is used to switch between the lamps. For a perfectly adjusted optics, the absorbance values of a sample before and after flipping this mirror should be identical, but most spectra (including the ones I see in
AC
incoming manuscripts) show an offset. In order to obtain “monochromatic light” (an euphemism, because strictly monochromatic would mean that the intensity is zero), most instruments use a grating monochromator that is moved by a stepper motor. The spectral bandwidth of the output of this monochromator is a compromise between intensity and spectral bandwidth set by the mechanical width of the monochromator output slit. Since 12 nm spectral bandwidth can be easily obtained with still sufficient light intensity, this is not really a problem. The pitfalls come from the fact that any grating monochromator uses the grating at a certain diffraction order: first, second, third and so on. The interference conditions of a grating state that at any output wavelength the grating is set, there is also intensity at higher orders, i.e. 2, 3 and so forth, albeit at much lower intensity. This means that if your monochromator is set at blue-violet light at 400 nm, the measuring beam also contains light at 800 nm. Just imagine that if your sample absorbs strongly at 400 nm but is transparent at 800 nm; the detector will not be able to correctly measure the residual intensity at 400 nm because of the fraction of light at 800 nm detected. Manufacturers of spectrometers cope with this physics of diffraction by placing so-called “order filters” in the beam after the monochromator that let the desired light pass and block or at least reduce the higher order light intensity. Nevertheless, there are traces of unwanted light in the measuring beam that limit the application of the Lambert-Beer law. This phenomenon is frequently called “spectral false light”, in contrast to “spatial false light” that we will deal with below.
ACCEPTED MANUSCRIPT Another source of spectral false light is stray light in the monochromator. This means that a small but noticeable fraction of the incoming white light will also appear at the output. For a well-designed monochromator, stray light -3
-5
is on the order of 10 to 10 of the incoming light intensity. Stray light is equally sensed by the photodetector and also limits the minimum measurable intensity – or the maximum of measurable absorbance.
T
A third source of spectral false light may occur if the sample is strongly fluorescent. Let us assume that the sample
IP
has a peak absorbance of 2 which means that only 1% of the measuring light is passing at this wavelength. If the fluorescence quantum efficiency of the sample is high, a high fraction of the absorbed photons (99% in our
SC R
example) is re-emitted as fluorescence. Again, the photodetector does not care whether it sees the residual intensity I (1% in our example) of the measuring light or the intensity caused by the re-emitted photons at a wavelength shifted to the red. If the detector is more sensitive for the fluorescence wavelength, the fluorescence intensity can appear even higher than the transmitted intensity. The precise estimation of this error source
NU
requires knowledge about the geometry of the sample, the optics and the detector. Molecules may diffuse and rotate while the molecule is in the excited state; fluorescence emission is thus not in the direction of the
MA
measuring beam, but rather isotropic.
There are means to get rid of the spectral false light caused by sample fluorescence. The best solution is a second monochromator between sample and detector, set at equal spectral resolution and moved synchronously with the
D
first monochromator. This guarantees that only the measuring light passes from the sample to the detector. This luxury solution solves the problem caused by fluorescent samples and the problem caused by stray light, but not
TE
the higher order problem, unless order filters are included, too. The cheaper solution is to increase the distance between the sample and the detector and to use a parallel beam of light for the absorption measurement. If so,
CE P
the transmitted measuring light I is recorded independent from distance r, while the intensity of the fluorescence 2
light will decrease approximately with 1/r because it is emitted almost isotropically. An even cheaper solution is dilution of the sample. As you dilute, the transmitted intensity I will increase while the emitted fluorescence
AC
intensity will decrease.
Spatial false light has many origins. There are trivial ones, such as incompletely filled cuvettes where the measuring beam partly passes above the sample, and this fraction reaches the detector unattenuated. There are badly adjusted cuvette holders that let part of the light pass sideways. You may think that I report problems that are typical for first-year students, but I have seen this for experienced senior scientists in research labs. The so-called microcuvettes that are popular because they require only small sample volumes are prone to this problem, since they have only a narrow slit for the sample with glass or plastic walls left and right. The slightest shift of these cuvettes causes the measuring beam to pass partly through the glass walls. The solution can be as trivial as the problem: tale a black felt pen and paint the glass walls left and right from the sample part until they are intransparent. There are also blackened cuvettes available; while they are more expensive, their use should be much preferred in particular for very small sample volumes. Light scattering in the sample is also a false light problems. The ideal sample in the sense of the Lambert-Beer law is a homogeneous solution without light scattering. Many chemical, biochemical or biological samples are suspensions or textured structures that exhibit light scattering. It is not always necessary to describe light scattering quantitatively, but spectroscopists at least should know about their impact on an absorption measurement.
ACCEPTED MANUSCRIPT For suspensions with particles at a size d much smaller than the wavelength (d<<), i.e. up to some tens of nm for the wavelengths used in UV-VIS spectroscopy, Rayleigh scattering is observed. Protein solutions are a typical 4
example. The scattered light is classical dipole radiation; the intensity varies with 1/ . Scattering for larger particles (d<), i.e. for cells and large nanoparticles sized up to some hundreds of nm, is described by the RayleighGans-Debye model. This implies an angular distribution of the scattering intensity different from Rayleigh
T
4
scattering, but also a 1/ dependence. Scattering from larger particles (d> or d>>) is described by the Mie
IP
scattering model or by Fraunhofer scattering, but these two are rare cases in bioanalytical spectroscopy.
SC R
We thus expect – on top of our absorption spectrum – a wavelength-dependent light scattering caused by Rayleigh or Rayleigh-Gans-Debye scattering, thus an “apparent absorption”, and we may call the sum of both terms “extinction” according to the discussion above. Since absorption and apparent absorption are essentially additive, they can be separated. Indeed they must be separated if quantitative absorption values are to be obtained from
NU
the absorption spectrum. For this procedure, I see frequently quite futile attempts. One possibility is to take values of the extinction outside the range of the absorption band(s) and use these to calculate, with a least-squares fit, a 4
MA
1/ function as a new “scattering baseline” for the entire extinction spectrum. If this is done carefully, a clean absorption spectrum can be obtained by subtraction of this baseline from the “extinction” spectrum. Instead of post-experiment procedures, a careful choice of the experimental setup can reduce light scattering.
D
Moving the detector closer to the sample is a simple option. Doing this, the detector area captures more of the
TE
scattered photons and the intensity loss by scattering is reduced. Some top spectrometers have a second separate sample compartment where the cuvettes are placed directly in front of the detector. This, however, bears the risk of also capturing more fluorescence photons as we discussed above. The sample-detector distance is thus a
and a hard place”.
CE P
compromise between reducing fluorescence and reducing light scattering; this may be the choice “between a rock
A radical procedure to reduce light scattering for biological samples is “refractive index matching”. It makes use of
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the fact that the scattering intensity of a suspension depends on the difference between the refractive index of the particle (the “scatterer”) and of that of the solvent around. Adding soluble macromolecules, e.g. long chain sugar molecules, to the solvent increases the refractive index of the solution. Once this refractive index exactly matches that of the particle, the suspension becomes clear- scattering is gone. Finally, we consider the insufficiency of the detection and signal processing unit for absorbance measurements. We expect from a photodetector high spectral sensitivity over the entire spectral range, low dark noise, high linearity for the conversion of light intensity to an electric signal, no drifts of the electric signal and no saturation for high intensity. This is daydreaming, but nevertheless engineers have done a good job. In order to measure an absorbance of 1, detection and signal conversion have to process two signals, I0 and I, that differ by a factor of 10 in amplitude. For absorbances 2, 3 or 4, this factor is 100, 1000 and 10000, resp.. These two signals must be amplified and digitized at a precision that allows the calculation of I0/I and log (I0/I) with sufficient precision. Digitization of an analog signal determines the resolution of the signal. If a signal of 1 Volt is digitized at 10
10 bit resolution, it is resolved in 2 = 1024 equal discrete steps, each approx. 1 mV. Needless to say that if I want to compare I0 and I that differ by a factor of 1.000 in amplitude, the resolution of an analog-to-digital-converter must be quite a bit higher.
ACCEPTED MANUSCRIPT Most signal processing units use analog-to-digital-converters that are at 16 bit resolution; they divide the analog 16
signal in 2 = 65.536 equal discrete steps. It is evident that even at that precision the digitization of the smaller of both signals will be precision-limited. Higher resolution analog-to-digital-converters are possible, but speed goes down and prize goes up.
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I0/I ratio formation is the next step. We need not be mathematicians to see that the higher the absorbance and the
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smaller I is compared to I0, the more we move towards a division by zero. Small absolute differences in the measurement of I will cause large changes in the result. This is another reason to keep the absorbance low.
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How do we notice any of these limitations in an absorbance measurement? How do we detect violations of the Lambert-Beer law ? Very typically, the band profiles change. They are typically Voigt profiles – Gaussian distributions of Lorentz profiles – but become flat at the top and finally saturate in absorbance, no matter how concentrated the absorber is. Tops of the bands exhibit either strong noise (no wonder if we force division by
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zero), or are completely flat when the spectrometer software determines that “infinity” really must be some arbitrary maximum value of, say, five units. The linear relation between concentration and absorbance gets lost.
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Instead of determining quantitatively a concentration from a sepctrum, you might as well throw dice. Figure 1 illustrates this problem. Spectra of human serum albumin at increasing concentrations were taken on one of our routine spectrometers, neither badly adjusted on purpose, nor tuned to optimum. The series of spectra
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shows band profile deformations starting at extinction values above approx. 1.5. The inset shows the
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concentration as determined from the absorbance of the aromatic amino acid side chains at 279 nm vs. the real
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concentration.
ACCEPTED MANUSCRIPT What should the minimum precautions be? In view of all these more or less hidden pitfalls that can mess up an absorption measurement, a careful procedure should start with instrument checks. 1.
Take the time to have a look at the measuring beam of your spectrometer and how it is placed with
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respect to the cuvette. Simply set the monochromator to 500 nm, a wavelength where eye sensitivity is
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highest, and check whether the beam is well centered in the cuvette and whether there might be spatial false light. Check whether the sample filling volume is sufficient. If necessary, readjust the sample
2.
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position.
Run the spectrometer across the desired wavelength range without any sample or reference cuvette, just air against air. Is the absorbance baseline thus obtained flat or does it show offsets whenever a lamp or order filter switch occurs? Adjustment of the optics may be necessary.
Magnify this baseline to see the noise. What is the root mean square level of this noise in terms of
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absorbance? For samples at low extinction, this noise-equivalent absorbance will be your detection limit. Block the light path and measure a dark spectrum. The absorbance should max out everywhere; this will
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give you an idea what your system does when insufficient light gets through the sample. 5.
Repeat the procedure in 1 with a pair of matched cuvettes both filled with the same buffer/solvent. I
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know that this procedure is rather old style, but having a pair of matched cuvettes, i.e. cuvettes made from the same glass or quartz material and with pathlengths as similar as possible, warrants a precise
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subtraction of buffer absorbance. Refrain from using plastic cuvettes for quantitative measurements if possible; their optical quality is not very high. Again magnify the baseline thus obtained to see the noise.
6.
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This will tell you the usable spectral range. Use the pair of matched cuvettes for the sample and the reference buffer/solvent to run a spectrum. If you don’t have such a pair, at least use the same cuvette for the measurement of the background and the sample spectrum. If absorbance exceeds a value of 1-2, then dilute and repeat. Aiming at a maximum
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absorbance below 1 will prevent the fluorescence problem discussed above and guarantee a linear relationship between absorbance and concentration. Lambert & Beer will bless you for that. 7.
If you are concerned that the lower concentration obtained by dilution might have an impact on your sample, for example disaggregation of a protein, then use matched cuvettes with a shorter path length instead of dilution. There are standard cuvettes from quartz or glass at 1 cm, 5mm, 2mm, 1mm and lower pathlengths, some even from plastic materials.
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If a scattering background is observed, try to reduce scattering by changing the geometry, i.e. move the sample and reference cuvettes closer to the detector if possible.
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Once the scattering is minimized on the experimental side, fit a 1/ function to the spectrum obtained, but exclude data points at and immediately around the absorption band(s). 4
10. Subtraction of this 1/ function will typically result in a rather clean absorption spectrum that can be used for quantitative evaluation. All the pitfalls discussed here apply to standard absorption spectroscopy in vitro. They may have a different impact depending on the instrument used. Once spectroscopic experiments are performed outside a well designed
ACCEPTED MANUSCRIPT instrument, for example by using fiber optics in situ or in biomedical spectroscopy in vivo, problems can become significantly worse. In summary, it is easy to obtain clean, linear and quantitative absorption spectra if these rules are followed. . I would not rely on post-experimental processing of miserable data. Unfortunately, the instrument manufacturers
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try to convince you that “their” instrument can cope with these problems, but that’s mostly a marketing claim. I’d
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rather wish they would build into their software a few program lines that warn the user. At absorbance values up to about 1.5, the display should show a green light indicating that everything is OK. Above an absorbance of 1.5 to
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2, an orange warning should flash up saying “you are about to leave the validity of Lambert-Beers Law”, and above an absorbance of 2, a warning light should appear in red and say “you just violated Lambert-Beers Law”.
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Further reading:
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Werner Schmidt: Optical Spectroscopy in Chemistry and Life Sciences. Wiley VCH, 2005