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.

Finding the links between reactive molecules involved in soot formation

tl:dr
We still don't know how soot forms and this is stopping us from eliminating it from internal combustion engines and furnaces. Recently, the molecules present, just before soot formation, were directly imaged. For the first time, many of the reactive edges could be seen. In this work, we computationally screened these reactive edges. We then considered all possible crosslinks between these edges. We discovered a new crosslink that allows the molecules to be stabilised by physically stacking on top of each other and then becoming bonded at their rim. This could help explain the rapid growth of soot particles in the flames and lead to new ways to clean up combusiton.

We have just published a new paper in the Journal of Physical Chemistry C. Here is the infographic/abstract figure.

Reactive molecules involved in soot formation

At the 37^th International Symposium on Combustion, an extraordinary paper was presented directly imaging the molecules present just prior to soot formation. In the case of most of these aromatic molecules it is the edge that is the most reactive and over the years many suggestions have been made but never directly observed. So here they are.

Here are some of the most exciting findings. 

Firstly, some were found to be crosslinked suggesting reactions between radicals and molecules during soot formation. This contradicted a commonly held view that only physical interactions and not chemical reactions were involved. 

Secondly, there were lots and lots of pentagonal rings. Out of the 49 molecules (above 4 rings) imaged 28 contained at least one pentagonal ring and 12 contained two pentagonal rings on their rim. Previously only six-membered rings were thought to be stable at flame temperature.

Thirdly, species very close to curvature integration were found. While curved 3D were unable to be imaged using this technique at present, the presence of the almost curved molecules was encouraging for our suggestion of curved aromatic molecules being important in soot formation as I have previously discussed in this blog. 

Finally, some of these pentagonal rings were found to have hydrogen added to them. This forms a completely new radical type (–CH=CH– + H → –C^•HCH₂–  which we found formed a localised π-radical).

Given the wide range of interesting new molecules that were found we considered how their reactivities compared.

We made use of computational chemistry to compute the energy needed to remove an electron from a particular spot on the "surface" of the molecular surface (average local ionisation energy). This told us how likely it was to form a bond with another molecule and therefore allowed us to compare their reactivities.

One significant surprise was the reactivity of pentagonal rings and a new localised π-radical on pentagonal rings B).

Many reactions are important in the flame

Now that the reactive sites were characterised we considered which crosslinks between them could be important in the flame. Below is a figure of the crosslink energies. The green indicates bonds that are strong enough to persist at the high temperatures within a flame.

Most crosslinks are well-known mechanisms, however, the reactions with the localised π-radicals B) were completely novel.

A new type of bonding is possible - rim-bonding

Most of the ideas for how the molecules in flames come together to form soot particles have been either stacked physically interacting interactions or chemical bonds in a long polymer that did not stack. However, the localised π-radicals B) allows for stacked and bonded structures that are strongly bound.

This could allow molecules to rapidly condense and then crosslink which could explain the rapid growth of soot. Below is a drawing of how such a cluster could form we are calling an aromatic rim-linked hydrocarbon.

We need to figure out the concentration of this reactive site in the flame. We also need to compare how all of the possible crosslinks contribute to soot formation. Once this is achieved we can consider how to stop particular reactive sites from being made and reduce soot emissions.

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.

Curving aromatic molecules

Credit: link

Aromatic molecules such as benzene and coronene (shown above) contain a hexagonal arrangement of carbon atoms. This gives a flat planar structure due to the geometry of hexagonal rings which are able to tessellate in two dimensions (see the tessellating tiles in the picture below). You can think of these hexagonal aromatics being like a flat saucers.

Credit: Paula Soler-Moya

A hexagonal arrangement of carbon atoms is the most stable (making grapite the most stable form of carbon, being made up of hexagonal sheets of carbon). The molecule shown below left (benzo(ghi)fluoranthene) would at lower temperatures and over longer times rearrange and form a completely hexagonal structure but in the formation of soot in a flame a faster reaction has been found with acetylene which forms the less stable corannulene molecule with a pentagon trapped within. Integration of this non-hexagonal rings into a hexagonal lattice does not leads to a net that can be nicely tessellated on a 2D surface but leads to a 3D warped structure - a bowl-like geometry. I have embeded an interactive 3D models of these two molecules so you can see this 3D curvature for yourself (click and drag to move the grey models around and zoom with your mouse wheel).

Energy: -2339647.6573446 Avogadro 28 32 0 0 0 0 0 0 0 0999 V2000 -1.4450 3.2780 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -2.6730 2.4230 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -2.5940 0.9420 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -1.2510 0.4030 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -0.0960 1.2390 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -0.0950 2.6780 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 1.2540 3.2770 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 2.4820 2.4210 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 2.4020 0.9400 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 1.0590 0.4020 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -0.8400 -1.0190 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 0.6470 -1.0200 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -1.9130 -1.9920 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -3.3090 -1.5120 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -3.6500 -0.0720 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 1.7190 -1.9930 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 3.1150 -1.5140 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 3.4580 -0.0750 -0.0200 C 0 0 0 0 0 0 0 0 0 0 0 0 -1.6990 -3.0520 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 -4.1120 -2.2390 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 -4.6900 0.2280 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 -3.6440 2.9030 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 -1.5540 4.3550 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 1.3640 4.3540 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 3.4530 2.9000 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 4.4980 0.2250 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 3.9180 -2.2420 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 1.5040 -3.0530 -0.0200 H 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 1 6 1 0 0 0 0 1 23 1 0 0 0 0 2 3 1 0 0 0 0 2 22 1 0 0 0 0 3 4 1 0 0 0 0 3 15 1 0 0 0 0 4 5 1 0 0 0 0 4 11 1 0 0 0 0 5 6 1 0 0 0 0 5 10 1 0 0 0 0 6 7 1 0 0 0 0 7 8 1 0 0 0 0 7 24 1 0 0 0 0 8 9 1 0 0 0 0 8 25 1 0 0 0 0 9 10 1 0 0 0 0 9 18 1 0 0 0 0 10 12 1 0 0 0 0 11 12 1 0 0 0 0 11 13 1 0 0 0 0 12 16 1 0 0 0 0 13 14 1 0 0 0 0 13 19 1 0 0 0 0 14 15 1 0 0 0 0 14 20 1 0 0 0 0 15 21 1 0 0 0 0 16 17 1 0 0 0 0 16 28 1 0 0 0 0 17 18 1 0 0 0 0 17 27 1 0 0 0 0 18 26 1 0 0 0 0 M END Energy: -2339647.6573446 Avogadro 30 35 0 0 0 0 0 0 0 0999 V2000 -1.4200 3.2390 0.0390 C 0 0 0 0 0 0 0 0 0 0 0 0 -2.6190 2.3660 0.0420 C 0 0 0 0 0 0 0 0 0 0 0 0 -2.5240 0.9410 -0.3280 C 0 0 0 0 0 0 0 0 0 0 0 0 -1.2840 0.5370 -1.0010 C 0 0 0 0 0 0 0 0 0 0 0 0 -0.0930 1.4030 -1.0030 C 0 0 0 0 0 0 0 0 0 0 0 0 -0.0940 2.7080 -0.3330 C 0 0 0 0 0 0 0 0 0 0 0 0 1.2310 3.2400 0.0400 C 0 0 0 0 0 0 0 0 0 0 0 0 2.4310 2.3690 0.0430 C 0 0 0 0 0 0 0 0 0 0 0 0 2.3370 0.9430 -0.3270 C 0 0 0 0 0 0 0 0 0 0 0 0 1.0980 0.5380 -1.0000 C 0 0 0 0 0 0 0 0 0 0 0 0 -0.8290 -0.8630 -0.9960 C 0 0 0 0 0 0 0 0 0 0 0 0 0.6440 -0.8630 -0.9960 C 0 0 0 0 0 0 0 0 0 0 0 0 -1.5940 -1.9150 -0.3190 C 0 0 0 0 0 0 0 0 0 0 0 0 -2.9780 -1.5650 0.0530 C 0 0 0 0 0 0 0 0 0 0 0 0 -3.4370 -0.1550 0.0490 C 0 0 0 0 0 0 0 0 0 0 0 0 1.4100 -1.9140 -0.3190 C 0 0 0 0 0 0 0 0 0 0 0 0 2.7930 -1.5620 0.0550 C 0 0 0 0 0 0 0 0 0 0 0 0 3.2510 -0.1520 0.0500 C 0 0 0 0 0 0 0 0 0 0 0 0 -0.8330 -3.1220 0.0590 C 0 0 0 0 0 0 0 0 0 0 0 0 -3.5830 -2.2990 0.5730 H 0 0 0 0 0 0 0 0 0 0 0 0 -4.3590 0.0860 0.5650 H 0 0 0 0 0 0 0 0 0 0 0 0 -3.5060 2.7160 0.5580 H 0 0 0 0 0 0 0 0 0 0 0 0 -1.4770 4.1910 0.5540 H 0 0 0 0 0 0 0 0 0 0 0 0 1.2870 4.1920 0.5550 H 0 0 0 0 0 0 0 0 0 0 0 0 3.3170 2.7190 0.5590 H 0 0 0 0 0 0 0 0 0 0 0 0 4.1730 0.0900 0.5670 H 0 0 0 0 0 0 0 0 0 0 0 0 3.3990 -2.2960 0.5740 H 0 0 0 0 0 0 0 0 0 0 0 0 0.6500 -3.1210 0.0590 C 0 0 0 0 0 0 0 0 0 0 0 0 -1.3450 -3.9230 0.5790 H 0 0 0 0 0 0 0 0 0 0 0 0 1.1630 -3.9220 0.5800 H 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 1 6 1 0 0 0 0 1 23 1 0 0 0 0 2 3 1 0 0 0 0 2 22 1 0 0 0 0 3 4 1 0 0 0 0 3 15 1 0 0 0 0 4 5 1 0 0 0 0 4 11 1 0 0 0 0 5 6 1 0 0 0 0 5 10 1 0 0 0 0 6 7 1 0 0 0 0 7 8 1 0 0 0 0 7 24 1 0 0 0 0 8 9 1 0 0 0 0 8 25 1 0 0 0 0 9 10 1 0 0 0 0 9 18 1 0 0 0 0 10 12 1 0 0 0 0 11 12 1 0 0 0 0 11 13 1 0 0 0 0 12 16 1 0 0 0 0 13 14 1 0 0 0 0 13 19 1 0 0 0 0 14 15 1 0 0 0 0 14 20 1 0 0 0 0 15 21 1 0 0 0 0 16 17 1 0 0 0 0 16 28 1 0 0 0 0 17 18 1 0 0 0 0 17 27 1 0 0 0 0 18 26 1 0 0 0 0 19 28 1 0 0 0 0 19 29 1 0 0 0 0 28 30 1 0 0 0 0 M END

Credit: Ikea

The curvature leads to many interesting physical properties of these molecules such as a permanent dipole moment and interesting electrical properties which might make these molecules useful for organic light emitting diodes or as electrical connections between molecular computers and metal contacts. More to come...

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.