A Middle Way: A Review of Physical + Chemical Pathways to Soot Inception

tl;dr Our new preprint "Carbonaceous nanoparticle formation in flames" is out.

The paper is now published in Progress in Energy and Combustion Science

 

A middle way can refer to many things. In common usage it refers to a comprise between two positions. In philosophy or religion, it can refer to a rejection of extremes as exemplified by Aristotle’s golden mean that “every virue is a mean between two extremes, each of which is a vice”. In logic it can refer to a fallacy - halfway between a lie and a truth is still a lie and therefore some care is required in proposing such compromising positions. In science it has been used for a variety of justifiable and unjustifiable positions. One famous example being the middle way between physical scales and another being a position we recently put forward for the formation of the pollutant soot.

In the influential paper “The middle way” published in the Proceedings of the National Academy of Sciences of the USA in 2000, Laughlin et al. discussed the challenge in probing the scale between the atomic and macroscopic dimensions. In this mesoscopic region significant gaps exists in our understanding of how atoms and molecules interact, organise and form complex structures. This intermediate scale is too large to be measured by analytical chemical approaches and too small to be approached from the macroscale. Examples include protein folding, high temperature superconductors and disordered or topologically frustrated materials.

Our recent study on the formation of the pollutant soot illustrates the challenges probing the mesoscopic scale nicely. Figure 1 below shows a schematic of the transformation of fuel molecules into the pollutant soot. Only in the last 5 years have experimental techniques allowed for the aromatic soot precursor molecules as well as the earliest nanoparticles to both be directly imaged. Mass spectrometry has also allowed for the mass of the clustering molecules to be measured during soot formation. However, the mechanism by which these molecules cluster continues to baffle combustion scientists. The prize sought is the ability to understanding and potentially halt the emission of these toxic pollutants from internal combustion engines that damage almost every organ in our bodies as well as contribute to climate change. 

Figure 1 – Schematic for the transformation of fuel into soot inside a flame with insets showing the experimental results from which the schematic is derived. High resolution atomic force microscopy (HRAFM)from Commodo et al. 2019, Helium ion microscopy (HIM) from Schnek et al. 2013, high resolution transmission electron microscopy (HRTEM) from Martin et al. 2018 and scanning electron microscopy (SEM) from Orion carbons. 

Our modelling efforts also struggle to traverse the molecule to nanoparticle transition in soot formation. There are two main classes of models that have been proposed for soot formation. The first is physical nucleation where aromatic molecules grow until the intermolecular interactions between the molecules allows them to stick together and condense. The second is chemical inception where bonds form between the molecular systems. Only recently have accurate computational approaches been developed to explore these suggestions.

Concerning physical nucleation, Prof. Kraft’s group worked with the physical chemist Prof. Alston Misquitta (Queen Mary University) in the 2010s to accurately compute the intermolecular interactions between aromatic species (using a symmetry adapted perturbation with a hybrid density functional approach). From these results it was clear that the clustering species seen in the flame are far too small to possess the significant intermolecular energies required for physical nucleation mechanism. For my PhD, I explored electrical enhancements to physical nucleation that arise from curved aromatic species that possess a strong electric polarisation. While this electrical effect may help explain the electrical control of soot formation it alone cannot justify a nucleation mechanism either.

Concerning chemical inception, we recently undertook a systematic study of the bonds that could form between reactive aromatic soot precursors with Prof. Xiaoqing You’s group at Tsinghua University (made possible by the CARES programme). This was only possible due to the direct imaging of the reactive aromatics in 2019 (see Figure 1) and the recent advances in density functional computational techniques optimised for radicals (the meta hybrid GGA density functional method M06-2X). Figure 2 shows the systematic comparison that was possible with such an approach for small aromatic molecules. The green coloured grid squares correspond with thermally stable species. Mr Angiras Menon was recently able to compute the rate at which each of these crosslinks forms and compared them with the speed of soot formation. We found that for these small species none of the crosslinks formed sufficiently fast enough to explain the rapid clustering of molecules into soot nanoparticles.

Figure 2 – Bond energy between various reactive aromatic soot precursors. Green indicates bonds that have enough thermal stability to be considered as important in flames.

These detailed studies left us with the uncomfortable conclusion that the two main routes proposed for soot formation were unable to describe it. However, something did catch our attention crosslinks that allowed the molecules to both bond and stack, see Figure 2 B), C) and D) sites. This opened up another possibility that both physical and chemical mechanisms could cooperatively contribute to soot formation. Upon exploring these possibilities, we found that π-radicals on five membered rings, site B), formed highly localised states that did not become deactivated as the molecule grew in size, unlike their hexagonal ring equivalent, thereby remaining highly reactive. This allowed for an additive contribution between the physical interactions and the chemical bond only in these so-called aromatic rim-linked hydrocarbons (ARLH). Figure 3 shows the various mechanisms placed on a C/H versus molecular weight schematic to show the middle way suggested.

Figure 3 – A middle way is schematically shown between physical and chemical mechanisms for soot formation. 

As mentioned at the beginning of this article claims to middle ways are poor arguments unless they can be justified. Currently, we have shown that the addition of physical interactions and chemical bonding considerably increases the thermodynamic stability of aromatic rim-linked hydrocarbons. However, we have yet to show that such species can explain the rapid formation of soot in the flame. This requires the collision efficiency between these species and the concentration of the localised π-radicals on five-membered rings to be determined. Experiments are underway in the community to probe such species and close this missing gap between the micro and mesoscale of soot formation.

Are any reactions fast enough for soot formation?

tl;dr In order to stop soot pollution, we need to know what reactions cause soot to form. We used the computer to work out how fast a variety of different reactions between soot molecules to see what reactions could be forming soot. Most of the reactions are too slow and suggest larger molecules are required. 

Soot continues to be a problem for our climate by warming the atmosphere and melting ice. It also damages our bodies and causes significant health impacts. Some recent studies are coming out showing a strong relationship between polluted areas and places where the COVID-19 virus has taken many lives. For example in 66 administrative regions in Italy, Spain, France and Germany, 78% of COVID-19 deaths occurred in the five most polluted regions. (Ogen 2020). With a recent study based in the USA finding that for every 1 microgram per cubic metre of PM2.5 soot pollution is associated with an 11% increase in COVID-19 death rate? (Wu et al. Sci. Adv. 2020). Frustratingly we are still unable to describe how soot forms at the molecular scale and this is inhibiting our ability to reduce the emission of these toxic pollutants.

In this paper, my coworkers and I were able to run a series of calculations on the computer to systematically compare the speed of many reactions thought to happen in the flame. We refined a table of bond energies that we proposed in a previous paper (see this blog post) and by reordering the grid we found that we could categorise reactions into four main classes depending on the type of reactive site involved. 

Next we computed the reaction rate between each of these bonds using transition state theory. This involved computationally stretching the bonds until they were about to break and then determining the likelihood of a collision between these molecules leading to that transition state and ultimately the product with the bond formed. This allowed for a map of reaction rates versus temperature to be plotted and for the various reactions to be compared. 

Surprisingly we found that for all of the reactions between these small aromatics the reaction rates are too low to explain soot formation. This includes all of the mechanisms proposed to date involving small aromatic molecules found in flames. 

So we looked for various effects that could stabilise and enhance the reactions as the molecules enlarge. We found that for the localised pi-radicals the dispersion forces could enhance the equilibrium constant for dimerisation. It is unknown how this effect will impact the forward and backward rate constants but it is suggestive of an enhancement to the forward rate. 

There is more work to be done to work out whether this stabilisation of the larger localised pi-radical dimers will speed up the reactions to explain soot formation and whether they are in high enough concentration. However, we think the main contribution of this paper is being able to rule out a large number of possible reactions that have previously been proposed for soot formation. This is discussed in more detail in the review article that is currently online as a preprint. 

Combustion webinar - Carbonaceous nanoparticle formation in flames

At the end of last month Prof. Kraft, my PhD supervisor, presented the recent work on soot formation from the Computational Modelling group. I helped plan out the talk with colleagues and it is a very nice overview of the research we have been doing recently on the formation of soot. It is definitely for a more technical audience so be warned. For a less technical description, I recommend the webinar I recently gave at Churchill College. 

Are new reactive molecules present in flames?

tl;dr

Which reactive molecules lead to the formation of soot? Recently we showed that adding hydrogen to the edges of soot molecules makes the edges reactive. In this paper, we showed that these sites are very common in flames, making them likely to be important for soot formation.

In my previous blog post, I talked about our systematic comparison of possible crosslinks between reactive aromatic molecules that had recently been detected using atomic force microscopy. This gave the bond energies and allowed us to work out which bonds could be stable at flame temperature. It showed that adding hydrogen to a pentagonal ring gives a reactive localised π-radical that allows crosslinking and stacking.  

In our recent paper that just got accepted in the Proceedings of the Combustion Institute, "Reactive localised π-radicals on rim-based pentagonal rings: properties and concentration in flames" (see preprint here), we showed that these reactive sites are present in the flame in significant concentrations. 

To show what we mean by localisation the electron's spin density is shown below. The spin density shows where the reactive electron is likely to be able to form a bond with higher values indicating higher reactivity. We find two classes of π-radicals, those that 1) delocalise in 6-membered ring aromatic molecules and 2) reactive localised π-radical for pentagonal rings or methylene (–CH2) that does not delocalise across the molecule. 

While these reactive sites have been seen in molecules sampled from the flame it was not clear whether they also exist in the flame. For example, sampling these molecules from the flame could lead to hydrogen being added while the molecules in the flame could actually be lacking this hydrogen i.e. it could be an artifact of sampling. 

In order to determine if these species are present in the flame, we calculated all of the reactions that could allow hydrogen to be added or removed (thanks to Angiras and Dingyu for this). We could then consider, given the concentrations of hydrogen species in the flame, what sort of concentration we would expect. The reactions are shown below (those barrierless reactions do not make computing the rates very easy but it can be done with sufficient approximations).

We found that between 1-10% of the molecules contained a localised π-radical on their rim-based pentagon (for between 1400-1500K which are temperatures within a flame where soot begins to form). Comparing these results with the HR-AFM structures recently imaged we found a consistent frequency of rim-based pentagonal sites with a ratio of 27:12:4 for the unsaturated, saturated and partially saturated rim-based pentagonal rings, showing that these species are present in the flame in significant concentrations.

We explored another exciting possibility - that multiple localised π-radicals are present on a single molecule. These species are also likely to be present in reasonable fractions (thanks to Gustavo and Angiras for developing the KMC simulations). Of the molecules that were recently imaged using HR-AFM, over half contained one rim-based pentagon and roughly a quarter had two rim-based pentagons suggesting that the formation of multiradicals in flames is likely.

These results suggest a new mechanism for soot formation where molecules with two or more localised π-radicals can polymerise (a rapid chain reaction) - what we called the aromatic rim-linked hydrocarbon mechanism (ARLH).

There is a nice historical connection with New Zealander Prof. John Abrahamson, Canterbury University. During a sabbatical in the '70s at the Chemical Engineering department at the University of Cambridge (where I did my PhD) he wrote a paper proposing that the partial saturation of aromatic platelets forms soot (see structure below). I spoke with him recently during the lockdown in New Zealand about the HR-AFM results that show partial saturation of aromatic platelets and our results showing the localised π-radicals and he was happy to hear about the recent insights and how close he got in 1977.

Abrahamson, John. "Saturated platelets are new intermediates in hydrocarbon pyrolysis and carbon formation." Nature 266.24 (1977): 323-327.

The Chemical History of a Candle and Structure of an Ember - Webinar

A webinar presented on the 6th of May 2020 for the Churchill College MCR, University of Cambridge, by Jacob W. Martin.

Abstract: Grab a hot chocolate and get cosy for a fireside chat about a candle's flame and the embers left behind. Following the lead of Michael Faraday in his 1848 Royal Institution Christmas lectures, I will provide an updated chemical history of a candle - including some experiments for you to try at home. The fun doesn't end there - after a flame is extinguished, there's a wealth of discoveries to be made in the embers. Understanding the structure of these carbon materials begins with Rosalind Franklin, best-known for her work on DNA, and continues with simulations on a supercomputer. While there are still many unanswered questions around flames and carbon materials, these recent insights are enlightening and important for cleaning up our planet.

Combustion science for Climate Solutions - Pint of Science

I recently gave a presentation at a Pint of Science event in Singapore entitled "Combustion Science for Climate Solutions". Here are the slides with my transcript added into the slides.

Fingerprinting soot: finding curved aromatics in soot

Fingerprints of molecules in soot particles imaged in an electron microscope showing curved species in the early flame. 

Fingerprinting is a unique way of identifying people by reading off the ridges found on a person's fingers. In a new paper, I and some colleagues used an electron microscope to image the fingerprint of aromatic molecules in early soot particles, finding evidence for a large number of curved molecules, which could be important for reducing soot pollution. Here is a link to the paper or to the open access preprint, "Flexoelectricity and the Formation of Carbon Nanoparticles in Flames". Here is a short video explaining the findings.

Soot emissions cause many deaths around the world while also contributing to global warming, but scientists are still at a loss to explain how soot is formed. We have previously suggested a new mechanism where aromatic molecules curve via pentagon integration and become electrically polarised, interacting strongly with charged species produced in the flame. However, as of yet, no one had measured just how curved (and therefore polar) the molecules are in the early soot particles.

To answer this question we imaged the molecules in soot on the nanoscale. To collect some soot we injected a small copper grid covered in amorphous carbon into a flame very similar to a candle. Soot stuck to the amorphous carbon and using an electron microscope we were able to image the molecules in the soot particles sticking to the grid. As you can see in the first image of this post we could convert the dark regions of the image, corresponding to aromatic molecules on their side, into lines. We could determine how many molecules that we imaged indicate pentagonal ring integration and we found this value to be greater than 62.5% of the fringes. This high amount suggests that they are important for soot formation.

We found even in the earliest soot particles sampled at the lowest height, which give us the most insight into soot formation, long fringes 0.9-1.0 nm in length are present (around 15 aromatic rings). We then simulated three curved aromatic molecules of the same length with one, two and three pentagonal rings, providing different amounts of curvature, and computed the tortuosity/curvature. From this analysis, we could conclude that early soot particles (at 10 mm above the flame) have a tortuosity/curvature indicating that two pentagons rings are integrated. Below is a figure of the molecule which corresponds to the average species around 1 nm in width with two pentagonal carbon rings. 

 

Computing the electric polarisation due to the curved structure, we found a large value of 5.32 debye - around three times that of water, which is substantial. Below is a plot of the electric potential around the molecules introduced earlier.

We found this molecule bound very strongly to charged chemi-ions which are produced in abundance in the flame, using computer simulations. 

The strong interactions of these polar aromatic with chemi-ions need to be explored in more detail as it might help explain many of the electrical effects that have been seen, such as the ability of an electric field to stop soot formation in certain circumstances.

Polar aromatic molecules

We have recently published a paper on an interesting class of curved aromatic molecules. Here is an interactive 3D model of one of the molecules we studied. Click and drag to rotate the model in 3D, zoom in and out with the mousewheel.

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In short

• We found that this curving of the molecules shifted the electrons from the concave to the convex side of the molecule which makes quite a large electric field. 
• This is quite a strange finding mainly because most aromatic molecules are usually considered electrically non-polar.
• These curved molecules have been spotted (using electron microscopes) in soot particles, carbon battery electrodes and carbon water filters. 
• The electric field around these molecules will have a huge impact on how they interact with polar molecules such as water and many pollutants the electric field will also provide significant interactions with ions such as lithium used in batteries. 

You can read the full preprint of the paper for free on our website

Want to know more about polar molecules, why these aromatic molecules are polar and more about what this could mean for carbon research please read on.

What are polar molecules?

You may have heard that water is polar and other substances are non-polar like oil. Polar refers to the electric field around the molecule which has two poles a negative and a positive pole/end. For two opposite charges the potential is plotted below where red denotes a negative potential and blue a positive potential. The lines are lines of constant potential and are like contour lines on a map of a volcano denoting regions with the same value/height.

Credit: link

The dipole moment is defined as the distance the charges are separated multiplied by the difference between the two charges. Two opposite elementary charges (charge of an electron) separated by 0.1 nm gives a dipole moment of 4.8 D (debyes).

The atomic nuclei are small and positively charged and can be considered as point charges however the electrons are not well defined but spread out over space due to quantum mechanics. In this case we can define the molecular dipole as a sum of the dipole moment from the nuclei, as point charges, and the dipole from the electron density which can be unevenly shared between the atoms. The picture below on the left shows the electron density in gray at a certain value (kind of like a 3D contour) as a surface for hydrochloric acid. You can see more electron density on the chlorine atom, this is mainly because the chlorine nucleus has a charge of +17 compared with the hydroge nuclei which only has a charge +1, but there is also even more electron density on the chlorine nuclei than enough to cancel the positive nuclei making the potential on this surface more negtaive on the chlorine side than the hdyrogen side (seen in the figure below right). Giving HCl a dipole moment of 1.08 D. 

The cloud of electrons becomes very repulsive when molecules approach each other past the surface we have drawn. So you can think of this surface as the place where the molecules will touch each other (this surface is near the electron density value of 0.001 eÅ$^{-3}$). You might know that opposite charges attract so if you line up two molecules of HCl with the negative chlorine of one pointing towards the positive hydrogen of the other they will be attract each other. Below is a picture showing the attractive and repulsive ways of orienting two polar molecules. The Greek delta character δ is used to denote partially charged regions as the ends of the molecule do not have point charge of +1 but are only partially charged.

Credit: link and recoloured

Water is the most commonly known polar molecule. Below I am plotting the electric field around a water molecule along with the potential at the interaction surface. 

As these is a assymmetry to the electric potential (i.e. one side is positive and the other negative) water has a dipole moment of 1.85 D in the gas phase. This allows water to strongly interact with other water molecules and is what holds water together as a liquid at room temperature when similar sized molecules such as methane are no where near being liquid. Methane is a gas at room temperature and needs to be cooled to -161.5 °C before it becomes a liquid. Below is an animation of water molecules attracting each other (often called a hydrogen bond). Apart from the amazing fact of being a liquid at room temperature water forms a strange cage structure when it freezes which takes up more room than the liquid meaning it is less dense and allows solid water to uniquely float on the liquid.

Credit: CSIC

Credit: Qwerter

If you have a balloon handy you can do a simple experiment to convince yourself that water is polar. Rubbing a balloon with a cloth or on your head removes positive charge and leaves the balloon with a negative charge. Holding the balloon near a stream of water the positive side of the water molecule will be attracted to the negative charge on the balloon and it will bend the water toward itself.

Credit: Link

To put a scale in your mind as to the common range of dipole moments I have added the table below.

Table of the dipole moment in Debye units (1 D = 3.336×10^-30 C m) taken from Israelachvili 1992
Molecule	Formula	Dipole moment
Ethane	$\text{C}_2\text{H}_6$	0
Benzene	$\text{C}_6\text{H}_6$	0
Carbon tetrachloride	$\text{CCl}_4$	0
Carbon dioxide	$\text{CO}_2$	0
Chloroform	$\text{CCl}_3$	1.06
Hydrochloric acid	$\text{HCl}$	1.08
Ammonia	$\text{NH}_3$	1.47
Phenol	$\text{C}_6\text{H}_5\text{OH}$	1.5
Ethanol	$\text{C}_2\text{H}_5\text{OH}$	1.7
Water	$\text{H}_2\text{O}$	1.85
Cesium Chloride	$\text{CsCl}$	10.4

You will notice the aromatic molecule benzene does not have a dipole moment in the next section we will explore why this is the case.

Are planar aromatic molecules polar?

Benzene is the simplest aromatic molecule. It is made of six carbon atoms arranged into a hexagonal ring (below left). Adding six more hexagonal rings of carbon you can produce coronene a large polycyclic aromatic hydrocarbon with seven hexagonal rings of carbon (below right).

Plotting below the electrostatic potential of these two molecules looking side on (perpendicular to the aromatic plane) the electric field around planar aromatic molecules can be viewed. Around the hydrogen atoms, often called the rim of the PAH, the potential is positive. The top and bottom near the carbon atoms is negative. This can be explained by the bonding but we will leave this for another post.

As you can see there is no one side that is negative and another that is positive (no assymmetry). The potentials are mirror images. There is no net dipole moment for planar aromatic molecules i.e. they are non-polar. This means they will only have weak interactions with polar molecules such as water making aromatics insoluble in water.

This arrangement of charged regions is called a quadrupole and is one moment higher than the dipole. Below are some point charge representations of a quadrupole and a contour plot of a quadrupole.

So how can we make an aromatic molecule polar. The next section will show that curvature integration is the key.

Curved aromatics are polar

Curvature is integrated into aromatic molecules when a non-hexagonal ring of carbon atoms is integrated into the normally closed 

Corannulene is experimentally known to contain a dipole moment of 2.07 D. This is quite a large dipole moment close to that of water. Below I have plotted the electric field around water, corannulene and coronene far away from the molecules (around 4 nm).

Comparing corannulene to water a similar potential is seen at the far field, however, close to the molecule there is a negative potential near the concave side of the bowl. Comparing corannulene to coronene the positive region around the hydrogen atoms is similar in both molecules, however, there is a shift of the negative potential to the convex surface of the curved corannulene. This turns out to be due to an effect called flexoelectricity. By flexing the molecule you shift electrons from the concave to the convex surface leading to the dipole you see.

We used a supercomputer to calculate the electron density around some very large curved aromatic molecules. From this we could determine the dipole moment with very good accuracy (less than 2% error for corannulene compared with experiment). The figure below shows the strong scaling of the dipole moment with the size of the molecules. The size range found in soot and other carbon materials is around 10-20 aromatic rings shown as the shaded grey area. This indicates that curved fragments in carbon materials can have a significant dipole moment of 2-6 D.

Why is this result so exciting?

There are many carbon materials that contain these curved aromatic molecules such as soot (pollutant from engines that contributes to global warming), carbon blacks (used in inks and tires), activated carbon (used in water filters, they are also used as an antidote to poisons as they are very good at sucking up organic molecules and metals) and battery carbon electrodes. To date very few people have considered these molecules to contain a dipole moment and what impact that has on their performance.

The considerable dipole moment we predict will have a huge impact on how the carbon materials interact with other molecules here are a few potential important interactions.

• In batteries positively charged lithium ions will interact strongly with the dipole moment on the curved molecules.
• In soot formation charged chemi-ions will interact strongly with curved aromatic molecules in the flame.
• In activated carbon a strong interaction is expected between the dipole moment and adsorbents that are charged or polar.  

If you are interested in how you can include these effects into computer simulations of carbon systems read on.

Simulating carbon materials with curvature in the computer

Many important properties of carbon materials could be potentially optimised if we can tune the curvature in carbon materials. A simple mathematical representation in the computer is needed to model these properties. A common representation of the electric field in computer simulations around the molecule is to use point charges at each atom (usually much less than an atomic charge) and then fit the electrostatic potential around the molecule by adjusting these charges to match the electric field far away from the molecule. We usually also add a repulsive mathematical function so that the molecule cannot get too close to another. This means the potential is only important outside this region which can be thought of as an interaction surface. This means we need to correctly describe the electrostatic at and outside the interaction surface. A previous PhD student Tim Totton along with Dr. Alston Misquitta developed a forcefield for planar PAH molecules and found that atomic centred point charges do a good job of describing the electric field around these molecules. Below is a picture of the electric potential around coronene calculated from a full quantum mechanical simulation (DFT) and using point charges centred at each atom. The far right shows an overlay of the two showing remarkable agreement.

When we tried the same fitting of the electrostatic potential for corannulene using atom centred point charges we found a very bad fit. The first problem was the magnitude of the dipole moment was reduced to 1.73 D. The reason the fit was so poor is due to the flexoelectric effect which occurs perpendicular to the rings. This means dipoles must be included on the pentagonal carbon atoms to correctly describe these. We made use of atom-centred multipoles (monopole+dipole+quadrupole) to correctly describe the polarisation and the quadrupoles provide better description of the potential around the hydrogen atoms. Below is a figure of the potential around corannulene for point charges and for multipoles.

These atom centred multipoles descriptions of molecular electrostatics have recently been integrated into different molecular dynamics packages such as Tinker, OpenMM and DL_POLY. Get in contact if you are interested in simulating a certain carbon system and I would be happy to work with you on it.

Molecular tennis: Can nascent soot burn from the inside?

After arriving at the lab in Februrary I started working with Peter Grančič on collision studies of gas molecules with clusters of flat carbon molecules which resemble the very early soot particles (nascent soot) found in flames. So here is the paper.

I prepared some slides to explain the research.

If you don't have access to the journal you can read the preprint on our groups website.