Published: 2024-04-08 | Categories: [»] Engineeringand[»] Optics.

Now that we have a [»] working spectrometer in the visible range, it’s time to do something with it!

A long time ago, I have shown how light can be absorbed by molecules in solution to make a [»] flow sensor out of it. It is time to revisit the concept of light absorption, but in a much more detailed way this time. Have you ever wondered why some liquids were transparent and others had a color, or why some liquids had denser colors than others at the same concentration? Let’s dig into these concepts here.

To assist us in our experimental work, I made the setup shown in Figure 1. As always, you can download all the files required for reproduction [∞] here under a CERN OHL-W-V2 open-hardware license.

Figure 1 – Experimental setup

The liquid to be analyzed is placed in a standard square spectroscopy cuvette (a purchase reference given in the BOM file). For most work, you can use disposable polystyrene plastic cuvettes provided they match the dimension of the one given in the BOM. Note that polystyrene cuvettes are not compatible with some solvents like acetone.

A close-up of the cuvette holder is given in Figure 2. It can be printed out of PLA without any issue. At the moment, you can ignore the screws as they are necessary only for quantitative analysis. If you wish to already include the screws, you will need to use threaded inserts as well. Avoid excessive pressure with the screws, they just need to contact the cuvette to enforce repeatable positioning.

Figure 2 – Cuvette holder

The idea is to shine broadband white light through the cuvette and collect the transmitted light to forward it to our [»] 350-700 nm spectrometer. This means we also need a source of white light. Here, I’m using the Quartz-Tungsten-Halogen (QTH) lamp system shown in Figure 3. It’s just a relay system that picks up the light from the QTH bulb to re-image it on a SMA fiber connector. Image quality is not mandatory here as we’re merely looking for light collection to make the system more efficient than just putting the fiber in front of the light bulb itself. All the necessary information is included in the file package here-above and are under the same open-hardware license.

Figure 3 – Quartz-Tungsten-Halogen light source system

A few remarks can be made about the light source that you can use for absorbance spectroscopy:

- White LEDs are generally not suitable for spectroscopy because their spectrum is not too narrow. They usually have a sharp peak in the blue region followed by a blob in the green/red region. They typically don’t cover the near-UV (<400 nm) and near-infrared (>700 nm) regions at all. On the other hand, colored LED can still be used very efficiently if you target a specific narrow band like we did in our [»] flow-sensor.

- Quartz-Tungsten-Halogen lamps are a much better choice over white LEDs because they can cover a range as large as 360-3800 nm. However, not all lamps are made equal and if you want a real broadband lamp that is stable over time you will need to pay the price for them. For instance, Thorlabs proposes the SLS201L that covers the 360-2600 nm region but with a price tag of 1,100 EUR. Far more accessible are the small QTH10 lamps that I’m using in this post and which cost less than 200 EUR. The downside is that the range is then limited to 400-2200 nm and the lifetime of the lamp is shorter as well. If you can afford a SLS201L, you can replace the complete system of Figure 3 and inspect the 375-400 nm region which is out of reach of the cheaper QTH10 lamp.

- Deuterium and Xenon lamps have more intensity in the UV region but are almost a tenfold-time more expensive than QTH lamps. One promising idea to explore would be to check if Xenon lamps for cars emit enough light in the 375-400 nm such as to provide a low-cost alternative to the more expensive QTH and Xenon/Deuterium lamps. I did not push this idea further so tell me if you have some experimental results to back up this idea.

A typical emission spectrum of a QTH10 lamp measured by our 350-700 nm spectrometer is shown in Figure 4 along with a white LED spectrum from a desk lamp. The QTH lamp offers slightly more energy in the 400-450 nm region and reveals itself especially useful in the NIR range above 650 nm. Since none of the sources I have can cover the 375-400 nm range, all the spectra reported in this post starts at 400 nm.

Figure 4 – Typical emission spectrum of a QTH10 lamp vs white LED

The experimental system of Figure 1 relies on fibers and you will need to collimate their light using either a camera at infinity or an autocollimator. At the emission side, I recommend using a 400 µm solarization resistant fiber for UV-enriched light and a 50 µm fiber at the collection side. This will lower the resolution but, at contrario to emission spectroscopy, we usually don’t need much resolution for the analysis of absorbance of liquids as the peaks tend to be very broad. You will need to adjust the XY position of the collection fiber to maximize the light intensity received by the spectrometer. In my experience, light throughput in absorbance spectroscopy is rarely an issue so you should get plenty of signal without too much issue.

Once you have connected the source of Figure 3 and the spectrometer to the absorbance setup of Figure 1 and aligned everything, you can start measuring. As always, taking a dark measurement (with the lamp switched off) in the same experimental conditions (ambient light, exposure and gain) is always a good thing. Here, we will also take a bright reference measurement. The bright reference is the opposite of the dark one: you switch the light on and measure a cuvette filled with pure water in the same experimental conditions as your other measurements (exposure, gain etc.). We will use the bright reference measurement to compensate for the spectral inhomogeneity of the lamp and the relative efficiency of the spectrometer (as shown in Figure 4). The equation that we will be using to report our data is

where T is called the transmittance, exp is the experimental measurement, dark is the dark reference measurement and bright is the bright reference measurement.

For liquids that have very strong absorbances, we can also introduce the absorbance, A,

e.g. a transmittance of T=10% equals to an absorbance of A=1.

Since the transmittance, T, is always lower than 100%, the absorbance, A, is always a positive number.

Now that we have a working setup, we can start measuring liquids with it. Since our spectrometer covers the visible range, we can pick any liquid that has a color we can see. Preferably, the liquid shouldn’t be turbid (i.e. it should be transparent). Here, I’m using Cu2+ copper chloride solutions but you can use anything you’d like. I’ve shown a typical transmission spectrum along with a picture of the liquid in the cuvette itself in Figure 5.

Figure 5 – Spectrum of a copper chloride in isopropanol solution

In Figure 5, we see that the copper chloride solution transmits light in the green region but that the blue and red regions has lower or almost no transmission. When we shine white light through this solution, the red and blue wavelengths are absorbed and the green/yellow part of the spectrum passes through. This explains the green/yellow tint of the liquid.

What happens is that the solvated copper ions are able to promote their electrons to a higher energy state when they receive photons of the right energy. This is usually represented as

where M is the initial state, a quantum of energy brought by a photon and M* the excited, higher-energy, state.

Most molecules exhibit this behavior in the UV region because it usually requires tremendous amounts of energy to promote an electron to an excited state, but some molecules or atoms have electrons that require lower transition energies which will then occur in the visible. Examples are transition metals (copper, iron, manganese…) salts and highly saturated organic molecules like carotene. Absorbance spectroscopy is therefore more useful in the UV, as you have access to much more molecules, but it’s also more difficult to set in place than visible spectroscopy specifically because a lot of things absorb in the UV (most glasses and even air below 200 nm!). For practical reasons, I choose to stick to the visible region first and study transitions metals which are an ideal target in that wavelength range.

An interesting experiment is to dissolve the same copper chloride salt in different solvents: isopropanol (i-PrOH), water (H2O) and ammonia (NH4OH) and observe the color change. The results are shown in Figure 6.

Figure 6 – Copper chloride in various solvents

In Figure 6, we see that isopropanol, ammonia and water give different colors but also that ammonia, at the same concentration of Cu2+ ions, has a much deeper absorbance. The complete combination of a molecule or ion with its surroundings must therefore be considered to fully explain the absorbance in liquids and not just the molecule or ion that you wish to study. If the colors were due to the copper chloride alone, we wouldn’t have observed any change in Figure 6.

Absorbance spectroscopy is therefore extremely helpful in understanding properties of molecules and their interaction with solvents, even in today’s modern chemistry. We’re going out of my comfort zone here, but I would like to explain what I understood after (weeks of) research on the topics. I’m also using a fairly simplified description to give you a general feeling of what is going on, which implies some shortcuts. Take my words with caution.

We’ll delve first into a quick review of atoms and molecules before moving on to the interaction of light with matter, the process studied by the various types of spectroscopy techniques.

Quantum physics predicts that electrons do not move freely around atoms but are restricted to specific regions in space around the nucleus. Different electrons of different energies will occupy different regions known as atomic orbitals which you may have heard at either University or advanced chemistry classes in high school. [∞] Wikipedia has a very detailed article about atomic orbitals that I can recommend for extended readings. Figure 7 shows some of these common atomic orbitals. The different orbitals are given with their name and the σxy reference plane to orient them in space. Black/White is a convention to indicate the sign of the wave function of the orbital but plays no role in the probability distribution of the electron.

Figure 7 – Schematic representation of common atomic orbitals

In molecules, these atomic orbitals can sum up to form [∞] molecular orbitals. A molecular orbital can have a “better” electron distribution than the separated atomic orbitals, leading to a lower overall energy in which case it will be favored as the system tends to lower its energy to a minimum. We say that it’s a bonding molecular orbital. At contrario, the electron distribution in the molecular orbital might be worse, energetically speaking, than the separated atomic orbitals in which case we say it’s an anti-bonding molecular orbital. Finally, when no energy change is observed between the molecular orbital and the separated atomic orbitals, we say it’s a non-bonding molecular orbital.

Combining atomic orbitals is merely a matter of decomposing the initial atomic orbitals into a new basis made by the molecular orbitals. This is the topic covered by the Linear Combination of Atomic Orbitals (LCAO) theory. One of the consequences of this decomposition method is that, if you end up with a bonding molecular orbital you also end up with its opposite anti-bonding molecular orbital.

The interesting property of molecular orbitals is their associated energies. I said that one molecular orbital had lower energy than the separated atomic orbitals due to a better electron distribution over the molecule and vice-versa for the second molecular orbital. When atoms bring in their electrons, they are distributed among these molecular orbitals, with at most two electrons per orbitals. If we have a little number of electrons, we can fill them up into the low energy molecular orbitals first resulting in an overall lower energy of the molecule compared to atoms taken separately. This is the reason atoms tend to stick up together to form molecules. It’s also the reason we call these lower energy orbitals “bonding”. The anti-bonding orbitals have the exact opposite effect: they destabilize the molecule and make the atoms want to split up. When your molecule is completely saturated in number of electrons, all the bonding and anti-bonding orbitals are filled, resulting in no overall energy gain and no reason for the atom to stick together to form a molecule. That’s the reason hydrogen forms H2 molecules while helium doesn’t. Both have a 1s-1s bonding molecular orbital and 1s-1s anti-bonding molecular orbital, but while H2 has two electrons that can be fed into the bonding orbital only, He2 would have four electrons to be distributed which would occupy both the bonding and anti-bonding orbitals – yielding no overall energy benefits to produce He2 over two separate He atoms.

Figure 8 shows a molecule of ethylene with its “π” bonding orbital and it’s “π*” anti-bonding orbital. The naming of these orbitals (π, π*) is specific to molecules that have a plane of symmetry. You will also encounter σ, σ* and n molecular orbitals in these molecules. Note that not all molecules have a plane of symmetry but many organic molecules who are accessible in UV-VIS spectroscopy do and the π, π* and n molecular orbitals are frequently involved in this range of spectroscopy technique. The naming convention is not relevant for a general understanding of the spectroscopy process but I’m putting it here because you will often see these names pop up in spectroscopy and chemistry textbooks. If you wish to know more about this, you can consult the Wikipedia page on [∞] molecular symmetry, a branch of group theory which is very useful in chemistry and spectroscopy. Figure 8 also orders the molecular orbitals according to their relative energy levels with the bonding orbital being more stable than the anti-bonding one. In ethylene, electrons reside in the π bonding orbital and the π* orbital is initially empty.

Figure 8 – π and π* molecular orbitals in ethylene

As we have already mentioned, an electronic transition is a process that occurs when an electron is promoted from a low-energy molecular orbital to a higher-energy molecular orbital. In absorbance spectroscopy we’re inducing electronic transition by providing the required energy gap using photons which are captured (absorbed) by the molecule to produce the electronic transition. The electron then decays to its default (more stable) energy state through various processes involving returning the energy to the surrounding medium (e.g. heat or emission of a photon).

Different electronic transitions require different energies and therefore occur at different wavelength ranges (the lower the wavelength, the more energy photons have). In the molecules with a plane of symmetry, the σ→σ* requires the most energy and usually end up in the far UV (<150 nm) which is very difficult to access experimentally. n→σ* requires a bit less energy but are still in a difficult range to access experimentally (usually between 150-250 nm). π→π*, or even better, n→π*, are the transitions that are the most studied as they occur in the near UV to visible range (200-700 nm). Although they are still typically found in the UV region, classical examples of n→π* transitions are those of the carbonyl group (C=O) which can be found near 270 nm. A classical example of π→π* transition are unsaturated carbons bonds (C=C) such as in ethylene but which occur at a higher energy level of 175 nm. Conjugated polyenes (alternating C=C by C-C bonds) have the same π→π* transitions except the energy gap decreases as the number of conjugations increases. Carotene, with its 11 conjugated C=C bonds has π→π* transitions in the visible range near 450 nm, explaining its characteristic orange color.

Apart from the example of carotene, we have seen that most transitions of organic molecules with a plane of symmetry happen in the UV range which is out of reach of our 350-700 nm spectrometer. But it is possible to have other types of transitions than the one involving σ, π and n orbitals. Among the most accessible transitions are those involving d atomic orbitals which are commonly found in transition metals such as copper, as illustrated experimentally in Figure 6. The very small differences of energies between the d orbitals explain that these transitions occur in the visible this time. Note that we are still talking about molecular orbitals which, this time, result from the interaction of the overlap between the d atomic orbitals of the copper ion and the s or p orbitals of the solvent.

With this brief introduction, we understand where the color of copper chloride solutions come from (electronic transitions) and we can even explain, at least qualitatively, why the wavelength changes as we change the solvent (because the transition energy change induced by the solvent orbitals with the copper orbitals). What we still don’t explain is why some solvents produce extremely strong absorbance compared to others as found experimentally in Figure 6. A similar observation would also be met in UV spectroscopy with some transitions being favored over others, resulting in stronger absorbance peaks at specific wavelengths and not others.

To answer this question, we need to come back to the physics of the absorption process itself. As we said, molecules consist of atoms with electrons distributed among multiple molecular orbitals, some occupied and some not. Atoms are positively charged while electrons are negatively charged creating, at any moment in time, a dipole moment. The electrical field of the light wave interacts with this dipole moment in an oscillatory pattern. The likelihood of having an electron promoted from one occupied molecular orbital to a second, unoccupied, molecular orbital is proportional to the overlap between the two molecular orbitals and the dipole moment through the square of an operator called the transition dipole moment (more information on [∞] Wikipedia):

with ψ the initial wave function, ψ* the excited wave function and μ the dipole moment.

The transition probability can be anything from highly probable to highly improbable, leading to some absorption peaks stronger than others. Fortunately, we don’t have to solve the here-above integral and the study of the symmetry properties of the molecule can already help us identify which transitions are authorized by symmetry and which are not. Experimentally, it is observed that transitions authorized by symmetry have very high absorbance peaks while those who aren’t have much lower ones, but do not necessarily mark a complete absence of absorbance. While these rules go a touch beyond the scope of this post, you can already remember than a transition is authorized by symmetry if the symmetry properties of the overlap between the initial and excited molecular orbitals are the same as the symmetry properties of any of the XYZ axis over the complete symmetry operations that leaves the molecule geometry unchanged. I will go further into this topic in a future post when I have time.

As an illustration, the n→π* transition of the carbonyl group (C=O) in formaldehyde is not authorized by symmetry and yields a weak absorbance peak while the π→π* transition of the same carbonyl group is now authorized by symmetry, yielding a much stronger absorbance peak even if the required energy for the π→π* transition is higher than for the n→π* transition. In ethylene (Figure 8) and, more generally speaking in conjugated polyenes such as carotene, the π→π* is authorized by symmetry as well. A diagram of the different molecular orbitals and associated energy levels of the carbonyl group is given in Figure 9. The same phenomenon occurs with our copper chloride solutions. With water and isopropanol, the copper ions form an octahedral complex and the d orbitals of the solvated ion do not have a compatible overlap symmetry with any of the XYZ axis, leading to a weak absorbance. On the other hand, with ammonia, the copper ions form a tetrahedral complex whose d orbitals now have a compatible overlap symmetry with one the XYZ axis, leading to a very strong absorbance. The mathematical analysis of the symmetry properties of the solvated copper ion is a bit more complicated to perform but the underlying theory is the same. We’ll stick to this introductory conclusion here.

Figure 9 – The carbonyl molecular orbitals and associated energy levels

You probably better understand why UV and visible spectroscopy keep playing an important role even in today’s modern chemistry. And we only scratched the surface here! In a future post, I will dig as well into a quantitative analysis of absorbance spectroscopy which is one of the oldest “modern” analysis techniques of chemistry.

I hope this post has been useful for you :) don’t hesitate to share your comments on the [∞] community board to let me know!

I would also like to give a big thanks to Young, Naif, Sebastian, James, Lilith, Alex, Stephen, Jesse, Jon, Cory, Sivaraman, Karel, Themulticaster, Tayyab, Samy, David, Kirk, Michael, Shaun, Dennis and M who have supported this post through [∞] Patreon. I also take the occasion to invite you to donate through Patreon, even as little as $1. I also wanted to address a special extra thanks to all of the people who sent me very kind messages in the difficult moments I’ve recently be going through!

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