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.