Beyond the numbers: the fundamental dilemma of size

This article is part of a series, where we explore the hidden complexities of PM_2.5—tiny airborne particles that impact air quality and health. We will uncover the ambiguities behind its measurement, the challenges in assessing health risks, and the surprising insights that emerge. Each article will tackle a different aspect of PM_2.5, shedding light on its hidden dilemmas and unanswered questions. Today’s article discusses the fundamental dilemma of particle size.

Introduction

I moved from Switzerland to England in the year 2021 to become an aerosol scientist. Since then, I have not only enjoyed a lot of fish and chips, but I also had the pleasure of visiting beautiful cities such as Bath, Canterbury, Ely, London, Norwich, Oxford, or Salisbury. These cities have something in common: they all have a cathedral. You may wonder: how does this relate to PM_2.5? Hang on!

Interestingly, depending on which city I have been to, I have heard conflicting claims about which cathedral is the largest in the UK. How can this be? Well, it mainly depends on what we mean by ‘large’. Do we mean height? If yes, what exactly is ‘height’? Is it the distance between the highest and the lowest points, or is it the distance between the highest point and ground level? What if the surrounding ground is uneven? Additionally, height alone might be unsuitable given that some cathedrals are less high but have a much bigger foundation. Maybe we should also consider the length and the width, but how do we combine these dimensions to get a meaningful and comparable metric? Let’s be honest: it is not possible to accurately describe the size of an irregularly shaped 3-dimensional object such as a cathedral using a 1-dimensional metric such as ‘meters’.

But wait, isn’t that exactly what the concept of PM_2.5 is doing? Yes! PM_2.5 corresponds to (more or less) irregularly shaped particles smaller than 2.5 micrometers. What do the 2.5 micrometers refer to? Height, width, or length of the particle? Or something else? The answer may surprise you, given that there is no clear answer.

Based on how the size of a particle is defined, we can end up with (drastically) different PM_2.5 concentration values. Regardless of what definition we use to describe particle size, we always have cases where the definition makes sense and cases where it doesn’t: it is a dilemma (more precisely a polylemma). Note that the volume, and therefore the mass and the mass concentration that the world focuses on when speaking about PM_2.5 “levels”, is a cubed function of the particle diameter. In other words, a small change in diameter leads to a massive change in mass. The mass of one large particle can be higher than the mass of thousands of smaller particles, making it critical to get the size cut-off right.

It is getting even wilder: did you know that PM_2.5, according to the WHO definition, also includes particles bigger than 2.5 microns? If this is new to you, then you will probably find today’s article and the following one informative. Let’s shed some light on the size-related limitations behind the concept of PM_2.5.

What do airborne particles look like?

I recommend looking at electron microcopy pictures to truly appreciate the diversity of different particle shapes as well as sizes. We have recently published a blog article that shows some pictures. It can be found here. Simple question: What is the size of the particles shown in those pictures, for example, in the case of soot (see below)? If you think about it, it becomes very complicated as it is conceptually impossible to accurately express the size of irregular particles using a 1-dimensional metric such as ‘micrometer’.

The emergence of PM₁₀ and PM_2.5 as a standard

To understand the current situation, we should first understand its history. Before 1984, the concept of ‘total suspended particles’ (TSP) was a standard for monitoring airborne particles. TSP does literally not differentiate between particle size and thus includes all particles regardless of size. This is great because particles are not assigned a particle size, so we do not need to think about the abovementioned problem. However, there are also issues with that. When playing the devil’s advocate, one could argue that this definition would also include a stone thrown into the air as it remains airborne until it hits the ground. How long does a particle need to be airborne to be called airborne? Moreover, TSP does not really reveal a lot about health risks, as only a fraction of TSP is small enough to be deposited in the lungs. Doesn’t this conflict with the purpose of air quality monitoring: to measure and mitigate the risk of air pollution to human health?

The limitations of TSP prompted the United States Environmental Protection Agency (EPA) in the 1980s to replace TSP with PM₁₀ as a national ambient air quality standard for particulate matter. The new PM₁₀ standard differentiated between particle size. The cut-off was set at 10 µm. Why? At that time, it was believed that this size was reasonable to differentiate between particles that can and cannot be deposited in human lungs. PM₁ and PM_2.5 were introduced to further account for different deposition rates in different lung regions based on particle size.

Note that the old TSP and new PM₁₀ standards account for particle mass regardless of the chemical composition as well as toxicity. In other words, a particle of sea salt is treated as risky as an asbestos particle if both particles have the same size and mass. Why did the EPA in 1984 not account for the toxicity of individual particles? Simple answer: the chemical composition and hence toxicity of ambient PM is unknown until someone analyses it. Chemical characterisation is difficult, and even if we succeed, we often do not really know what to do with that data: the toxicity of different types of PM is poorly understood. Even if someone accurately determines the composition and toxicity of today’s PM, it may change tomorrow if the wind direction changes.

I hope it became clear that one cannot easily attribute a 1-dimensional particle size to airborne particles, unless we talk about very regular particle shapes like spheres or cubes. However, the reality when monitoring ambient air quality is different: we have no clue what particle shapes we are dealing with, as this depends on the emission sources. We likely have a mix of different and changing shapes. This is a challenge, and yet, it is extremely important to differentiate between different particle sizes, especially with respect to human health. So how did the United States Environmental Protection Agency solve that problem when it introduced the new PM₁₀ standard?

Aerodynamic diameter

The US Environmental Protection Agency in the 1980s was well aware of the challenge of particle shape and size, given that this issue has likely been known for as long as aerosol science as a discipline exists. The solution to the problem was simple: they coupled the new PM₁₀ standard to the aerodynamic diameter. What does that mean?

Let’s think of a known particle with spherical shape, density 1 g/mL, and diameter 1 µm and let’s compare that with a particle of unknown shape, density, and size. Now, let’s make an experiment where we put both particles 1 meter above ground in still air (see illustration below).

In this scenario, the particles are only exposed to gravity and aerodynamic drag as they fall towards the ground. Both particles are quite small, so it takes them a while to settle. Let’s say they reach the ground at the same time, after 60 minutes. Does this observation tell us anything about our unknown particle? Yes! Now we know that our unknown particle has the same settling velocity as a spherical particle with a density of 1 g/mL and a diameter of 1 µm. We still do not know the shape, size, or density, but we know that the total of all properties combined resulted in a similar aerodynamic behavior as the known particle with a diameter of 1 µm.

The above-mentioned thought experiment is exactly what aerosol scientists came up with to express the size of particles based on their aerodynamic behavior. It is important to understand that this solution is not absolute, instead, it is relative to an imaginary particle with a spherical shape and an arbitrary density of 1 g/mL. The ‘true’ particle size, shape, and density remain unknown. We can conclude that the new PM₁₀ standard from 1984 only includes airborne particles that settle slower as spherical particles with a density of 1 g/mL and a diameter of 10 µm.

Why was the PM₁₀ standard defined like that? Well, whether a particle can reach the human lungs depends mainly on the aerodynamic properties, so to me, it makes a lot of sense why PM₁₀ was defined like that. Note how this consideration changes when we want to investigate the implications of PM on climate, for example. In that case, we may want to use optical properties to express particle size, given that the impact of PM on climate is (at least partly) determined by interactions between the particles and light.

When referring to PM_2.5 or PM₁₀, most scientists and policymakers (including the WHO guidelines) refer to aerodynamic diameter. However, if no definitions are given, it is unclear whether a PM_2.5 or PM₁₀ value refers to aerodynamic diameter or something else.

Conclusion

Even though we may not want to hear it, it’s simply impossible to accurately describe the size of a 3-dimensional, irregularly shaped object (such as PM_2.5) using a 1-dimensional metric (such as a micrometer). It is important to understand that this limitation has nothing to do with measurement inaccuracy: even if we have an ideal instrument (which doesn’t exist in reality), we will never be able to fully describe the size of PM with just ‘micrometer’ as a metric. In other words, there is no such thing as a true size for these particles, and therefore, it cannot be measured, regardless of how accurate an instrument is. Think of a world map: regardless of how the Earth’s surface is portrayed on a map, it will always be distorted. Why? Because one cannot display something 3-dimensional on a 2-dimensional plane.

Fortunately, aerosol scientists came up with the concept of ‘aerodynamic diameter’, where the size of an airborne particle is expressed based on its aerodynamic properties in comparison to an imaginary reference particle. Aerodynamic diameter gives us a solution to the fundamental dilemma. Every particle has a true aerodynamic diameter, and monitor manufacturers can try to measure it as accurately as possible. But how well does it translate into the real world? That’s the topic of the next article.