Hope A Michelsen
email: hope.michelsen@colorado.edu

Meredith B Colket

Per-Erik Bengtsson

Andrea D ' Anna

Pascale Desgroux

Brian S Haynes

J Houston Miller

Graham J Nathan

Heinz Pitsch

Hai Wang

A Review of Terminology Used to Describe Soot Formation and Evolution Under Combustion and Pyrolytic Conditions

Keywords: soot, particles, particulates, inception, nucleation, incipient, nascent, agglomeration, aggregation, carbonization

This paper presents a glossary and review of terminology used to describe the chemical and physical processes involved in soot formation and evolution. This review is intended to aid in communication within the field and across disciplines. There are large gaps in our understanding of soot formation and evolution and inconsistencies in the language used to describe the associated mechanisms. These inconsistencies lead to confusion within the field and hinder progress in addressing the gaps in our understanding. This review provides a list of definitions of terms and presents a description of their historical usage. It also addresses the inconsistencies in the use of terminology in order to dispel confusion and facilitate the advancement of our understanding of soot chemistry and particle characteristics. The intended audience includes senior and junior members of the soot, black-carbon, brown-carbon, and carbon-black scientific communities, researchers new to the field, and scientists and engineers in associated fields with an interest in carbonaceous-material production via high-temperature hydrocarbon chemistry.

the terminology employed in the study of the production and evolution of soot. Although the focus of this review is on combustion-generated soot, much of the terminology also applies to carbonaceous-particle nucleation and growth under pyrolytic conditions. Knowledge of combustion-generated particles has grown and evolved over the decades with the continuous advancement of both experimental and numerical investigative tools. The ongoing discovery of new details has led to the progressive introduction of new terminology to describe them. This process has tended to be ad hoc, however, resulting in a number of inconsistencies and ambiguities, perhaps augmented by cross fertilization by researchers from disparate disciplines with different terminology to describe the same phenomenon. An additional important factor is that soot is not a uniquely defined material in size, morphology, or composition. The objective of the present review is therefore to address these inconsistencies and increase the precision of our terminology, with a view to advancing our understanding of soot chemistry and particle characteristics.

The need to clarify terminology related to soot formation and evolution was discussed during the 4 th International Sooting Flames Workshop, which took place in July 2018 in Dublin, Ireland. [START_REF]International Sooting Flame Workshop[END_REF] The present paper addresses this need by presenting a glossary of terminology that we believe is currently in use. Where appropriate, we have compiled brief histories and definitions of the terms frequently used to describe soot formation and evolution during combustion. Where there is ambiguity about the meaning of a word, we recommend guidelines for future usage. We prefer definitions that address the processes that physically control the particles and the physical characteristics of the particles themselves, as opposed to the sensitivity of various diagnostic approaches. Interpretations of data and implementation-based sensitivity of diagnostic techniques can change with time or between different researchers, but the physical characteristics of the particles, generated by a given process, do not. Defining terms relative to soot evolution facilitates developing a better understanding of the properties of the particles as they evolve and the processes that drive that evolution. We have, however, included a few operational terms that are particularly relevant to the field. We have avoided introducing new alternative expressions.

Overall, soot formation proceeds continuously from gas-phase hydrocarbon molecules to carbonized, aggregated particles. Because of the vast number of molecular changes in this process, it is customary to describe the overall process in terms of a series of simplified stages, as summarized in Fig. 1. The distinction between these stages is somewhat arbitrary, in that there is no sharp transition, except perhaps for the initial transition between gas-phase and condensedphase species. Furthermore, the relative importance of each stage depends on local combustion conditions (equivalence ratio, temperature, time, and pressure), together with the associated controlling chemistry. In this context, it is not surprising that some descriptive terms have become ambiguous and in need of clarification.

The first steps in the soot-formation process involve the production of gas-phase hydrocarbon soot-precursor species (Fig. 1a), followed by the transition of these species to condensed-phase particles (Fig. 1b). Experimental evidence suggests that these first particles are probably liquidlike [START_REF] Vander Wal | Soot Precursor Carbonization: Visualization Using LIF and LII and Comparison Using Bright and Dark Field TEM[END_REF][START_REF] Dobbins | Hydrocarbon Nanoparticles Formed in Flames and Diesel Engines[END_REF][START_REF] Zhao | A Comparative Study of Nanoparticles in Premixed Flames by Scanning Mobility Particle Sizer, Small Angle Neutron Scattering, and Transmission Electron Microscopy[END_REF][START_REF] Maricq | An Examination of Soot Composition in Premixed Hydrocarbon Flames Via Laser Ablation Particle Mass Spectrometry[END_REF][START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Kholghy | The Evolution of Soot Morphology in a Laminar Coflow Diffusion Flame of a Surrogate for Jet A-1[END_REF][START_REF] Russo | Dehydrogenation and Growth of Soot in Premixed Flames[END_REF] and have limited absorption in the visible spectrum. [START_REF] D'alessio | The Spectroscopic Characterisation of UV Absorbing Nanoparticles in Fuel Rich Soot Forming Flames[END_REF][START_REF] Basile | Coagulation and Carbonization Processes in Slightly Sooting Premixed Flames[END_REF][START_REF] Sgro | Detection of Combustion Formed Nanoparticles[END_REF][START_REF] D'anna | Nano-Organic Carbon and Soot Particle Measurements in a Laminar Ethylene Diffusion Flame[END_REF][START_REF] Sgro | Measurement of Nanoparticles of Organic Carbon in Non-Sooting Flame Conditions[END_REF] The process of this gas-tocondensed-phase transition is termed "particle inception" or "soot inception", but the first particles formed (Fig. 1b) cannot yet be classified as mature, solidified, and carbonized soot particles.

During soot inception, the incipient soot particles thus formed undergo rapid growth by both coagulation and gas-to-particle conversion. They also lose hydrogen through a high-temperature carbonization process, becoming partially graphitic (Fig. 1c). As they undergo this carbonization process, their optical properties evolve, such that they become able to absorb and emit light in the visible and near-infrared spectral regions; their density increases, and their surface reactivity may also change. As particles continue to evolve, they collide and form loosely bound agglomerates of quasi-spherical primary particles (Fig. 1d), which eventually become firmly bound, branchedchain aggregates of primary particles (Fig. 1e). [START_REF] Haynes | Soot Formation[END_REF][START_REF] Calcote | Mechanisms of Soot Nucleation in Flames: A Critical Review[END_REF][START_REF] Harris | Chemical Kinetics of Soot Particle Growth[END_REF][START_REF] Bockhorn | Soot Formation in Combustion: Mechanisms and Models[END_REF][START_REF] Richter | Formation of Polycyclic Aromatic Hydrocarbons and Their Growth to Soot: A Review of Chemical Reaction Pathways[END_REF][START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF] Figure 1. Schematic diagram of the major steps in soot formation and the representative species produced as the process proceeds. The relative scale of these images changes between the panels, with the structures ranging from < 1 nm (a) to ~100 nm (e).

A series of terms have been developed to describe the chemical and physical evolution associated with each of these stages. However, because the relative importance of each of these processes depends on the combustion environment, the prevailing terminology tends to differ somewhat between groups who target types of flames or combustion processes that produce soot with differing characteristics. In addition, many of these terms are ambiguous. For this reason, we have sought to identify the most prevalent terms and organize the associated discussion according to the most common usage. We have also aimed to ensure consistent terminology related to (1) combustion environments within a flame, (2) pyrolysis environments, including those tailored to generate specific products (e.g., carbon black), and (3) particulate pollutant emissions under conditions relevant to combustion exhaust streams, pool fire and wildfire plumes, and atmospheric evolution (i.e., black and brown carbon, elemental and organic carbon, smoke, and aerosol).

PAPER STRUCTURE

The terminology discussed in this paper is organized according to the stages of soot formation and evolution. Table 1 gives the section titles in which various terms are defined. The first section, entitled "All Stages", addresses vocabulary associated with soot in general and is not associated with the characteristics or relevant processes of particles in a single stage. The second section, "Gas-Phase Species", discusses terms related to the species involved in incipient soot formation and surface growth of particles. The third section, "Transition to First Particles", introduces terms related to the processes and physical phenomena potentially involved in the transition from gasphase precursors to condensed-phase particles. The fourth section, "First Particles", provides a glossary of terms used to describe the particles initially formed from gas-phase precursors. The fifth section, "Particle Growth", introduces terminology used to describe processes possibly responsible for the growth of particles during their evolution after inception. The sixth section, "Chemical Evolution", defines terms used to discuss physical properties of particles in different stages of evolution, general classifications of particles as they age, and the chemical processes responsible for changes in their properties. The seventh section, "Relevant Forms of Carbon", provides a glossary of the phases of carbon, some of which are not generally formed during combustion or only under special conditions but are listed for comparison. We placed this section after the sixth section because it is most closely related to the material properties of the particles as they evolve chemically. The eighth section, "Transition to Aggregates", introduces terms to describe morphological changes in particles as they evolve. The ninth section, "Oxidation and Breakup", describes terms used for discussing particle depletion by oxidation. The tenth and final section, "Associated Expressions", presents definitions for terms used for soot in atmospheric science and particle synthesis. It also defines terms used for assessing soot formation with respect to atmospheric emissions.

TERMINOLOGY All Stages

Particle and particulate: These terms are interchangeable. In the context of this discussion, a particle is defined as a small entity of solid or liquid matter distinguishable from the gas phase via such properties as density, specific heat, and the optical properties of scattering and absorption cross sections.

Soot: "Soot" refers to carbonaceous particles formed during the incomplete combustion or pyrolysis of hydrocarbons, including incipient soot particles, mature soot particles, and all of the intermediate particulate stages between inception, maturity, and complete oxidation to gas-phase species. This term also refers to species emitted from a flame and into the exhaust stream or outlet from a reactor.

Surface:

The particle surface is the first layer or first few layers of atoms or molecules physically or covalently bound to the particle at the interface between the particle and the gas phase.

Bulk:

The particle bulk is the rest of the particle that is not at the surface. [START_REF] Müller | Bulk and Surface Structural Investigations of Diesel Engine Soot and Carbon Black[END_REF][START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF] Mechanism: In combustion science, the word "mechanism" is frequently used to describe a set of elementary reactions involving multiple reactants and products, together with the corresponding rate coefficients compiled for inclusion in chemical kinetics models or reaction models. In chemistry, "mechanism" is used to describe a detailed chemical-reaction pathway or set of pathways leading from reactants to products. [START_REF] Johansson | Resonance-Stabilized Hydrocarbon Radical Chain Reactions May Explain Soot Inception and Growth[END_REF][START_REF] Berry | Physical Chemistry[END_REF][START_REF] Masterton | Chemical Principles[END_REF] "Mechanism" may also refer to a set of gassurface reactions at the particle interface or to detailed chemical pathways occurring at the particle surface (at any particle-maturity level), leading to soot mass growth or oxidation. See Chemisorption below.

Gas-Phase Species

Soot precursors: Soot precursors are molecular gas-phase species that serve as the molecular building blocks of soot particles. They play a role in particle inception and mass/size growth. The specific species leading to soot inception have not been definitively identified. There could be many different soot precursors with roles that depend on local flame conditions. Early models assumed these species to be small hydrocarbons, such as acetylene and benzene. [START_REF] Lindstedt | Modeling of the Chemical Complexities of Flames[END_REF][START_REF] Leung | A Simplified Reaction Mechanism for Soot Formation in Nonpremixed Flames[END_REF][START_REF] Kennedy | Models of Soot Formation and Oxidation[END_REF] These and other models use surrogates for molecular species involved in the particle inception process, largely because of a lack of knowledge of the actual species, uncertainties in their kinetics, variations caused by investigation with different fuels or combustion conditions, and computational limitations. Potential candidates for precursors that drive inception include unsubstituted polycyclic aromatic hydrocarbons (PAHs), [START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Miller | Calculations of the Dimerization of Aromatic Hydrocarbons: Implications for Soot Formation[END_REF][START_REF] Totton | A Quantitative Study of the Clustering of Polycyclic Aromatic Hydrocarbons at High Temperatures[END_REF][START_REF] Elvati | Thermodynamics of Poly-Aromatic Hydrocarbon Clustering and the Effects of Substituted Aliphatic Chains[END_REF][START_REF] Mercier | Dimers of Polycyclic Aromatic Hydrocarbons: The Missing Pieces in the Soot Formation Process[END_REF] aliphatically bridged [START_REF] D'alessio | The Spectroscopic Characterisation of UV Absorbing Nanoparticles in Fuel Rich Soot Forming Flames[END_REF][START_REF] Chung | Peri-Condensed Aromatics with Aliphatic Chains as Key Intermediates for the Nucleation of Aromatic Hydrocarbons[END_REF][START_REF] Skeen | Near-Threshold Photoionization Mass Spectra of Combustion-Generated High-Molecular-Weight Soot Precursors[END_REF][START_REF] Cain | Molecular Characterization of Organic Content of Soot Along the Centerline of a Coflow Diffusion Flame[END_REF][START_REF] Minutolo | Spectroscopic Characterisation of Carbonaceous Nanoparticles in Premixed Flames[END_REF][START_REF] Sirignano | Detection of Aromatic Hydrocarbons and Incipient Particles in an Opposed-Flow Flame of Ethylene by Spectral and Time-Resolved Laser Induced Emission Spectroscopy[END_REF][START_REF] Adamson | Detection of Aliphatically Bridged Multi-Core Polycyclic Aromatic Hydrocarbons in Sooting Flames with Atmospheric-Sampling High-Resolution Tandem Mass Spectrometry[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Commodo | On the Early Stages of Soot Formation: Molecular Structure Elucidation by High-Resolution Atomic Force Microsceopy[END_REF] or substituted PAHs, [START_REF] Elvati | Thermodynamics of Poly-Aromatic Hydrocarbon Clustering and the Effects of Substituted Aliphatic Chains[END_REF][START_REF] Chung | Peri-Condensed Aromatics with Aliphatic Chains as Key Intermediates for the Nucleation of Aromatic Hydrocarbons[END_REF][START_REF] Cain | Molecular Characterization of Organic Content of Soot Along the Centerline of a Coflow Diffusion Flame[END_REF][START_REF] Adamson | Detection of Aliphatically Bridged Multi-Core Polycyclic Aromatic Hydrocarbons in Sooting Flames with Atmospheric-Sampling High-Resolution Tandem Mass Spectrometry[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Commodo | On the Early Stages of Soot Formation: Molecular Structure Elucidation by High-Resolution Atomic Force Microsceopy[END_REF] ions, [START_REF] Calcote | Mechanisms of Soot Nucleation in Flames: A Critical Review[END_REF][START_REF] Weilmünster | Large Molecules, Radicals, Ions, and Small Soot Particles in Fuel-Rich Hydrocarbon Flames Part I: Positive Ions of Polycyclic Aromatic Hydrocarbons (PAH) in Low-Pressure Premixed Flames of Acetylene and Oxygen[END_REF][START_REF] Martin | Flexoelectricity and the Formation of Carbon Nanoparticles in Flames[END_REF] radicals, [START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Johansson | Resonance-Stabilized Hydrocarbon Radical Chain Reactions May Explain Soot Inception and Growth[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Commodo | On the Early Stages of Soot Formation: Molecular Structure Elucidation by High-Resolution Atomic Force Microsceopy[END_REF][START_REF] Yuan | Study on Soot Nucleation and Growth from PAHs and Some Reactive Species at Flame Temperatures by ReaxFF Molecular Dynamics[END_REF][START_REF] Vitiello | Role of Radicals in Carbon Clustering and Soot Inception: A Combined EPR and Raman Spectroscopic Study[END_REF] and oxygenated hydrocarbons. [START_REF] D'alessio | The Spectroscopic Characterisation of UV Absorbing Nanoparticles in Fuel Rich Soot Forming Flames[END_REF][START_REF] Cain | Molecular Characterization of Organic Content of Soot Along the Centerline of a Coflow Diffusion Flame[END_REF][START_REF] Rusciano | Surface-Enhanced Raman Scattering Study of Nano-Sized Organic Carbon Particles Produced in Combustion Processes[END_REF][START_REF] D'anna | Combustion-Formed Nanoparticles[END_REF] The expression "soot precursor particles" is sometimes used to refer to incipient or young soot particles as a precursor to mature soot aggregates, [START_REF] Dobbins | Soot Precursors: Particles in Flames[END_REF][START_REF] D'anna | Spectroscopic and Chemical Characterization of Soot Inception Processes in Premixed Laminar Flames at Atmospheric Pressure[END_REF][START_REF] Vander Wal | Soot Precursor Material: Visualization Via Simultaneous LIF-LII and Characterization Via TEM[END_REF][START_REF] Reilly | Direct Observation of the Evolution of the Soot Carbonization Process in an Acetylene Diffusion Flame Via Real-Time Aerosol Mass Spectrometry[END_REF][START_REF] Dobbins | Soot Inception Temperature and the Carbonization Rate of Precursor Particles[END_REF][START_REF] Blevins | The Existence of Young Soot in the Exhaust of Inverse Diffusion Flames[END_REF][START_REF] Happold | Distinction of Gaseous Soot Precursor Molecules and Soot Precursor Particles through Photoionization Mass Spectrometry[END_REF][START_REF] Maricq | Physical and Chemical Comparison of Soot in Hydrocarbon and Biodiesel Fuel Diffusion Flames: A Study of Model and Commercial Fuels[END_REF] but we recommend restricting the use of "soot precursors" to refer to gas-phase species.

Surface-growth species: Surface-growth species are gas-phase molecular species that chemisorb, physisorb, condense, or deposit to or on the particle surface, thereby adding mass to the particle. Early experimental results suggested that acetylene was a likely candidate for driving mass growth of particles in flames at atmospheric and lower pressures. [START_REF] Harris | Surface Growth of Soot Particles in Premixed Ethylene/Air Flames[END_REF][START_REF] Haynes | The Surface Growth Phenomenon in Soot Formation[END_REF] Hydrogen atoms are also argued to play a role, via the Hydrogen Abstraction C2H2 Addition (HACA) mechanism, in maintaining the surface activity. [START_REF] Frenklach | On Surface Growth Mechanism of Soot Particles[END_REF] Hydrogen atoms or molecules may be released as part of the surface-growth process. Depending on the fuel and the flame environment, other species (e.g., acetylenic species, aromatics, PAHs, and radicals) may contribute, either by chemisorption, physisorption, condensation, or deposition. [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Johansson | Resonance-Stabilized Hydrocarbon Radical Chain Reactions May Explain Soot Inception and Growth[END_REF][START_REF] Frenklach | Detailed Modeling of Soot Particle Nucleation and Growth[END_REF][START_REF] Howard | Carbon Addition and Oxidation Reactions in Heterogeneous Combustion and Soot Formation[END_REF][START_REF] Benish | C2H2 and PAH as Soot Growth Reactants in Premixed C2H4-Air Flames[END_REF][START_REF] D'alessio | On the Relevance of Surface Growth in Soot Formation in Premixed Flames[END_REF] See Surface growth, Adsorption, Chemisorption, Physisorption, Condensation, and Deposition below.

Transition to First Particles

Condensed phase: Although "condensation" generally refers to the phase transition of gas-phase species to a liquid phase, [START_REF] Cernuschi | An Elementary Theory of Condensation[END_REF][START_REF] Mcdonald | Deposition": A Proposed Antonym for "Sublimation[END_REF][START_REF] Jacobson | Fundamentals of Atmospheric Modeling[END_REF][START_REF] Dymarska | Deposition Ice Nucleation on Soot at Temperatures Relevant for the Lower Troposphere[END_REF][START_REF] Veshkini | Application of PAH-Condensation Reversibility in Modeling Soot Growth in Laminar Premixed and Nonpremixed Flames[END_REF] both liquid and solid phases are referred to as "condensed phases".

The phase in which a material is thermodynamically stable depends on temperature and pressure.

For example, a substance that is in the condensed phase at room temperature may be in the gas phase at flame temperature. See Condensation and Deposition below.

Inception:

The word "inception" was introduced to the field of combustion science in the early 1980s to represent the transition from gas-phase-precursor species to condensed-phase (i.e., liquid or solid) particles. [START_REF] Haynes | Soot Formation[END_REF][START_REF] Harris | Chemical Kinetics of Soot Particle Growth[END_REF][START_REF] Richter | Formation of Polycyclic Aromatic Hydrocarbons and Their Growth to Soot: A Review of Chemical Reaction Pathways[END_REF][START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Johansson | Resonance-Stabilized Hydrocarbon Radical Chain Reactions May Explain Soot Inception and Growth[END_REF][START_REF] Kennedy | Models of Soot Formation and Oxidation[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Happold | Distinction of Gaseous Soot Precursor Molecules and Soot Precursor Particles through Photoionization Mass Spectrometry[END_REF][START_REF] Frenklach | Detailed Modeling of Soot Particle Nucleation and Growth[END_REF][START_REF] Benish | C2H2 and PAH as Soot Growth Reactants in Premixed C2H4-Air Flames[END_REF] The term was coined to describe gas-to-condensedphase transitions independently of specific mechanisms. Such a transition occurs when the properties (e.g., density, specific heat, and absorption and scattering cross sections) of the particle or cluster depart from those of the gas-phase species from which it is composed and begin to exhibit properties of a bulk material. [START_REF] Baron | Aerosol Fundamentals[END_REF] The details of this process are poorly understood. This term does not require knowledge of the mechanisms for initial-particle formation or the characteristics of the first particles formed. It has been used extensively in this context over the past four decades.

There are still large gaps in our understanding of the mechanisms controlling the transition from the gas-phase precursors to the condensed-phase particles and the characteristics of the "first particles" formed. "Inception" is thus still an appropriate term to represent this process. See also Nucleation below.

Nucleation: With respect to soot formation, "nucleation" also refers to the process of particle formation from gas-phase precursors. [START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Haynes | Soot Formation[END_REF][START_REF] Calcote | Mechanisms of Soot Nucleation in Flames: A Critical Review[END_REF][START_REF] Harris | Chemical Kinetics of Soot Particle Growth[END_REF][START_REF] Richter | Formation of Polycyclic Aromatic Hydrocarbons and Their Growth to Soot: A Review of Chemical Reaction Pathways[END_REF][START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Leung | A Simplified Reaction Mechanism for Soot Formation in Nonpremixed Flames[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Frenklach | Detailed Modeling of Soot Particle Nucleation and Growth[END_REF][START_REF] Benish | C2H2 and PAH as Soot Growth Reactants in Premixed C2H4-Air Flames[END_REF][START_REF] Prado | Soot Particle Nucleation and Agglomeration[END_REF][START_REF] Harris | Soot Particle Inception Kinetics in a Premixed Ethylene Flame[END_REF][START_REF] Glassman | Soot Formation in Combustion Processes[END_REF][START_REF] Mckinnon | The Roles of PAH and Acetylene in Soot Nucleation and Growth[END_REF][START_REF] Frenklach | Reaction Mechanism of Soot Formation in Flames[END_REF][START_REF] Zhao | Measurement and Numerical Simulation of Soot Particle Size Distribution Functions in a Laminar Premixed Ethylene-Oxygen-Argon Flame[END_REF][START_REF] Violi | Modeling of Soot Particle Inception in Aromatic and Aliphatic Premixed Flames[END_REF][START_REF] Singh | Numerical Simulation and Sensitivity Analysis of Detailed Soot Particle Size Distribution in Laminar Premixed Ethylene Flames[END_REF][START_REF] D'anna | A Model of Particle Nucleation in Premixed Ethylene Flames[END_REF][START_REF] Cain | Micro-FTIR Study of Soot Chemical Composition -Evidence of Aliphatic Hydrocarbons on Nascent Soot Surfaces[END_REF][START_REF] Teini | Observations of Nascent Soot: Molecular Deposition and Particle Morphology[END_REF][START_REF] Maricq | Soot Formation in Ethanol/Gasoline Fuel Blend Diffusion Flames[END_REF][START_REF] Desgroux | Study of the Formation of Soot and Its Precursors in Flames Using Optical Diagnostics[END_REF][START_REF] Veshkini | A Soot Particle Surface Reactivity Model Applied to a Wide Range of Laminar Ethylene/Air Flames[END_REF][START_REF] Commodo | Physicochemical Evolution of Nascent Soot Particles in a Laminar Premixed Flame: From Nucleation to Early Growth[END_REF][START_REF] Eberle | A Sectional PAH Model with Reversible PAH Chemistry for CFD Soot Simulations[END_REF][START_REF] Mao | Formation of Incipient Soot Particles from Polycyclic Aromatic Hydrocarbons: A ReaxFF Molecular Dynamics Study[END_REF][START_REF] Johansson | Radical-Radical Reactions, Pyrene Nucleation, and Incipient Soot Formation in Combustion[END_REF][START_REF] Kholghy | The Role of Reactive PAH Dimerization in Reducing Soot Nucleation Reversibility[END_REF][START_REF] Mao | Atomistic Insights into the Dynamics of Binary Collisions between Gaseous Molecules and Polycyclic Aromatic Hydrocarbon Dimers[END_REF][START_REF] Homann | Some New Aspects of the Mechanism of Carbon Formation in Premixed Flames[END_REF][START_REF] Wersborg | Physical Mechanisms in Carbon Formation in Flames[END_REF][START_REF] Siegmann | Clustering at High Temperatures: Carbon Formation in Combustion[END_REF][START_REF] Sabbah | Exploring the Role of PAHs in the Formation of Soot: Pyrene Dimerization[END_REF][START_REF] Camacho | Evolution of Size Distribution of Nascent Soot in n-and i-Butanol Flames[END_REF][START_REF] Eaves | The Importance of Reversibility in Modeling Soot Nucleation and Condensation Processes[END_REF][START_REF] Török | Investigation of the Absorption Ångström Exponent and Its Relation to Physicochemical Properties for Mini-Cast Soot[END_REF] Although "nucleation" has commonly been used interchangeably with "inception", it is more usefully distinguished from "inception" as a term that implies condensation or deposition, i.e., thermodynamically driven processes leading to particle formation by van der Waals or other interactions. In the context of classical nucleation theory, "nucleation" is exclusively used to describe the competition between the Gibbs free energy as a driving force for condensation and the surface tension that counteracts condensation. 100 "Inception", on the other hand, encompasses all mechanisms for particle formation, [START_REF] Haynes | Soot Formation[END_REF][START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Benish | C2H2 and PAH as Soot Growth Reactants in Premixed C2H4-Air Flames[END_REF][START_REF] Lahaye | Mechanisms of Carbon Black Formation: Correlation with the Morphology of Aggregates[END_REF][START_REF] Zhao | Measurement and Numerical Simulation of Soot Particle Size Distribution Functions in a Laminar Premixed Ethylene-Oxygen-Argon Flame[END_REF][START_REF] Cain | Micro-FTIR Study of Soot Chemical Composition -Evidence of Aliphatic Hydrocarbons on Nascent Soot Surfaces[END_REF][START_REF] Johansson | Radical-Radical Reactions, Pyrene Nucleation, and Incipient Soot Formation in Combustion[END_REF][START_REF] Siegmann | Clustering at High Temperatures: Carbon Formation in Combustion[END_REF] including thermodynamically driven phase transitions and kinetically driven chemical reactions. Hence, if the micro-processes of how particles are formed are not known or not well defined, we recommend the term "inception" as it is more general.

Chemical bonds:

A chemical bond is an attractive interaction between atoms that is strong enough to form a multi-atom complex with distinct chemical or physical character. 101 There are several types of bonds: electrostatic, covalent, and metallic. 101 The most important of these types for soot formation is the covalent bond. See Covalent bonds below.

Covalent bonds:

A covalent bond is a strong chemical bond formed by the sharing of an electron pair between neighboring atoms. 101,102 Van der Waals interactions and dispersion forces: Van der Waals interactions are relatively weak electrostatic forces between neutral molecules, 102-105 including radicals. [106][107][108][109] The attractive van der Waals forces include dipole attractions between polar molecules, induced-dipole attractions between polar molecules and non-polar molecules, and attractions between non-polar molecules, the latter of which are known as "dispersion forces" or "London dispersion forces". 102- 105 Dispersion forces are the most important of the van der Waals forces for interactions between PAHs. Furthermore, van der Waals forces can enhance collisional combination of primary particles by a factor of about two. 110 Repulsive van der Waals forces occur at short molecular separations and are due to electrostatic repulsions. A van der Waals complex is a multi-molecular structure trapped in a potential energy well, which is a minimum in potential energy with respect to inter-molecular distance and orientation; this potential-energy minimum results from the sum of the attractive and repulsive forces.

First Particles Formed

Incipient soot particles: "Incipient soot particles" are formed at inception. 14-16,18- 20,22,23,27,39,53,58,60,67,70,71,76-79,83,85,87-90,96 As with the term "inception", the expression "incipient soot particles" neither requires nor implies knowledge of the mechanisms by which they were formed (from the gas to the condensed phases) or of their initial characteristics. These terms have been used extensively in this context since their introduction in the early 1980s. [START_REF] Haynes | Soot Formation[END_REF] See also Nuclei, Nascent soot particles, and Nano-organic carbon particles below.

Nuclei:

The products of nucleation, or inception, are called "nuclei". [START_REF] Haynes | Soot Formation[END_REF][START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Leung | A Simplified Reaction Mechanism for Soot Formation in Nonpremixed Flames[END_REF][START_REF] Glassman | Soot Formation in Combustion Processes[END_REF][START_REF] Mckinnon | The Roles of PAH and Acetylene in Soot Nucleation and Growth[END_REF][START_REF] Frenklach | Reaction Mechanism of Soot Formation in Flames[END_REF][START_REF] D'anna | A Model of Particle Nucleation in Premixed Ethylene Flames[END_REF][START_REF] Maricq | Soot Formation in Ethanol/Gasoline Fuel Blend Diffusion Flames[END_REF][START_REF] Desgroux | Study of the Formation of Soot and Its Precursors in Flames Using Optical Diagnostics[END_REF][START_REF] Commodo | Physicochemical Evolution of Nascent Soot Particles in a Laminar Premixed Flame: From Nucleation to Early Growth[END_REF][START_REF] Homann | Some New Aspects of the Mechanism of Carbon Formation in Premixed Flames[END_REF][START_REF] Wersborg | Physical Mechanisms in Carbon Formation in Flames[END_REF][START_REF] Sabbah | Exploring the Role of PAHs in the Formation of Soot: Pyrene Dimerization[END_REF] The term "nuclei" is often used interchangeably with "incipient particles". In many other contexts, however, "nuclei" specifically refers to the product of homogeneous nucleation, or self-organizing, which triggers further growth by condensation or deposition. The expression "incipient particles"

does not imply a specific formation mechanism. However, those features of mature soot particles exhibiting disordered fine structure, around which more ordered structure is formed, are sometimes referred to as "nuclei" to represent the hypothesis that these particles may have been responsible

for initiating the growth of primary particles. [111][112][113] This definition is synonymous with "growth centers". See Growth centers below.

Nascent soot particles:

In combustion science, this expression dates back to the 1970s and is most often used synonymously with "incipient soot particles". [START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Richter | Formation of Polycyclic Aromatic Hydrocarbons and Their Growth to Soot: A Review of Chemical Reaction Pathways[END_REF][START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Frenklach | Reaction Mechanism of Soot Formation in Flames[END_REF][START_REF] Totton | Modelling the Internal Structure of Nascent Soot Particles[END_REF][START_REF] Cain | Micro-FTIR Study of Soot Chemical Composition -Evidence of Aliphatic Hydrocarbons on Nascent Soot Surfaces[END_REF][START_REF] Teini | Observations of Nascent Soot: Molecular Deposition and Particle Morphology[END_REF][START_REF] Desgroux | Study of the Formation of Soot and Its Precursors in Flames Using Optical Diagnostics[END_REF][START_REF] Veshkini | A Soot Particle Surface Reactivity Model Applied to a Wide Range of Laminar Ethylene/Air Flames[END_REF][START_REF] Commodo | Physicochemical Evolution of Nascent Soot Particles in a Laminar Premixed Flame: From Nucleation to Early Growth[END_REF][START_REF] Eberle | A Sectional PAH Model with Reversible PAH Chemistry for CFD Soot Simulations[END_REF][START_REF] Camacho | Evolution of Size Distribution of Nascent Soot in n-and i-Butanol Flames[END_REF][START_REF] Eaves | The Importance of Reversibility in Modeling Soot Nucleation and Condensation Processes[END_REF][START_REF] Török | Investigation of the Absorption Ångström Exponent and Its Relation to Physicochemical Properties for Mini-Cast Soot[END_REF][114][115][116][117][118] In a limited number of studies, it has been used to indicate young soot, including incipient and partially aged particles. [START_REF] Benish | C2H2 and PAH as Soot Growth Reactants in Premixed C2H4-Air Flames[END_REF]119 "Nascent particles", "nascent smoke", and "nascent soot" are also used by atmospheric scientists [120][121][122][123][124][125][126] and medical biologists 127,128 to refer to the mature soot particles that exit from a combustor. To avoid confusion caused by the different meanings of this term in different fields, it is preferable to avoid this expression. We suggest instead the use of "incipient soot particles" to refer to the particles formed during inception and a different expression, such as "young soot", "partially aged soot", "partially carbonized soot", "partially graphitized soot", or "partially matured soot", to refer to particles that have evolved beyond the inception stage but have not yet become mature particles.

Nano-organic carbon (NOC) particles:

This expression is used to describe small particles with a relatively low molar carbon-to-hydrogen (C/H) ratio. Ex situ samples of soot collected from flames suggest that the C/H ratio for these particles is in the range of 1.4-2.5. [START_REF] Harris | Chemical Kinetics of Soot Particle Growth[END_REF][START_REF] Dobbins | Soot Precursors: Particles in Flames[END_REF][START_REF] Blevins | The Existence of Young Soot in the Exhaust of Inverse Diffusion Flames[END_REF][START_REF] Howard | Carbon Addition and Oxidation Reactions in Heterogeneous Combustion and Soot Formation[END_REF][START_REF] Homann | Some New Aspects of the Mechanism of Carbon Formation in Premixed Flames[END_REF]129 These particles are 1-6 nm in diameter, [START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Sgro | Detection of Combustion Formed Nanoparticles[END_REF][START_REF] D'anna | Nano-Organic Carbon and Soot Particle Measurements in a Laminar Ethylene Diffusion Flame[END_REF]130,131 spherical, [START_REF] Dobbins | Hydrocarbon Nanoparticles Formed in Flames and Diesel Engines[END_REF][START_REF] Maricq | An Examination of Soot Composition in Premixed Hydrocarbon Flames Via Laser Ablation Particle Mass Spectrometry[END_REF][START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Russo | Dehydrogenation and Growth of Soot in Premixed Flames[END_REF]132 liquid-like, [START_REF] Vander Wal | Soot Precursor Carbonization: Visualization Using LIF and LII and Comparison Using Bright and Dark Field TEM[END_REF][START_REF] Dobbins | Hydrocarbon Nanoparticles Formed in Flames and Diesel Engines[END_REF][START_REF] Zhao | A Comparative Study of Nanoparticles in Premixed Flames by Scanning Mobility Particle Sizer, Small Angle Neutron Scattering, and Transmission Electron Microscopy[END_REF][START_REF] Maricq | An Examination of Soot Composition in Premixed Hydrocarbon Flames Via Laser Ablation Particle Mass Spectrometry[END_REF][START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Kholghy | The Evolution of Soot Morphology in a Laminar Coflow Diffusion Flame of a Surrogate for Jet A-1[END_REF][START_REF] Russo | Dehydrogenation and Growth of Soot in Premixed Flames[END_REF] and nearly transparent in the visible and near-infrared spectral regions. [START_REF] D'alessio | The Spectroscopic Characterisation of UV Absorbing Nanoparticles in Fuel Rich Soot Forming Flames[END_REF][START_REF] Basile | Coagulation and Carbonization Processes in Slightly Sooting Premixed Flames[END_REF][START_REF] Sgro | Detection of Combustion Formed Nanoparticles[END_REF][START_REF] D'anna | Nano-Organic Carbon and Soot Particle Measurements in a Laminar Ethylene Diffusion Flame[END_REF][START_REF] Sgro | Measurement of Nanoparticles of Organic Carbon in Non-Sooting Flame Conditions[END_REF] They have been shown not to incandesce when irradiated with a laser, 131,[133][134][135][136][137] and thus they are not detected with the widely employed laser induced incandescence (LII) technique, but they do fluoresce upon UV excitation. 131,133,136 The collective evidence to date indicates that these particles are incipient particles, but they may represent a subset of the types of particles formed during inception under different conditions. See Incipient soot particles above.

Growth centers:

Growth centers are disordered or amorphous regions 1-4 nm in diameter located within the central portion of a primary particle. [START_REF] Müller | Bulk and Surface Structural Investigations of Diesel Engine Soot and Carbon Black[END_REF]113,[138][139][140][141][142][143][144][145] They are consistent with vestiges of incipient particles that may or may not have agglomerated before seeding further particle growth.

These features are sometimes referred to as "nuclei". [111][112][113] See also Nuclei above.

Clusters: A cluster is a group of similar objects, which are bound together, however loosely. It may also be a group of a few to thousands of atoms or molecules. 104 Large clusters of molecules may be held together in a nanometer-scale particle that possesses properties in between those of molecular species and bulk matter. 104 In soot science, "cluster" is used to describe a collection of molecular precursor species that form an incipient particle. [START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Johansson | Resonance-Stabilized Hydrocarbon Radical Chain Reactions May Explain Soot Inception and Growth[END_REF][START_REF] Schulz | Insights into Incipient Soot Formation by Atomic Force Microscopy[END_REF][START_REF] Frenklach | Detailed Modeling of Soot Particle Nucleation and Growth[END_REF][START_REF] Frenklach | Reaction Mechanism of Soot Formation in Flames[END_REF][START_REF] D'anna | A Model of Particle Nucleation in Premixed Ethylene Flames[END_REF][START_REF] Totton | Modelling the Internal Structure of Nascent Soot Particles[END_REF][START_REF] Teini | Observations of Nascent Soot: Molecular Deposition and Particle Morphology[END_REF][START_REF] Mao | Formation of Incipient Soot Particles from Polycyclic Aromatic Hydrocarbons: A ReaxFF Molecular Dynamics Study[END_REF][START_REF] Kholghy | The Role of Reactive PAH Dimerization in Reducing Soot Nucleation Reversibility[END_REF][START_REF] Sabbah | Exploring the Role of PAHs in the Formation of Soot: Pyrene Dimerization[END_REF][START_REF] Eaves | The Importance of Reversibility in Modeling Soot Nucleation and Condensation Processes[END_REF] Without defining the inception mechanism, such clusters could be held together by either van der Waals forces or covalent bonds. The term "cluster" is also used to describe aggregates or agglomerates of primary particles. It is usually clear in which way the word is being used from the context in which it is used. [START_REF] Maricq | Soot Formation in Ethanol/Gasoline Fuel Blend Diffusion Flames[END_REF][START_REF] Wersborg | Physical Mechanisms in Carbon Formation in Flames[END_REF][146][147][148] See Incipient soot particle above and Aggregates and Agglomerates below.

Liquid-like particles:

A liquid is a material that flows and is compliant and whose shape responds to forces such as that of gravity or surface tension. These characteristics allow a liquid to conform to the shape of its container. 104,149 Liquid-like particles would generally be nearly spherical as defined by surface tension. This term was coined to denote nano-sized particles that exhibit certain behaviors of a bulk liquid substance. Examples include the flattening of surfacecollected particles with surface morphology resembling that of wax splashing on a surface. [START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF] On average, liquids are amorphous and do not possess structural regularity or order. 104 Experimental investigations of incipient particles have suggested that these particles may be liquid-like at elevated temperatures. [START_REF] Vander Wal | Soot Precursor Carbonization: Visualization Using LIF and LII and Comparison Using Bright and Dark Field TEM[END_REF][START_REF] Dobbins | Hydrocarbon Nanoparticles Formed in Flames and Diesel Engines[END_REF][START_REF] Zhao | A Comparative Study of Nanoparticles in Premixed Flames by Scanning Mobility Particle Sizer, Small Angle Neutron Scattering, and Transmission Electron Microscopy[END_REF][START_REF] Maricq | An Examination of Soot Composition in Premixed Hydrocarbon Flames Via Laser Ablation Particle Mass Spectrometry[END_REF][START_REF] Abid | Size Distribution and Morphology of Nascent Soot in Premixed Ethylene Flames with and without Benzene[END_REF][START_REF] Kholghy | The Evolution of Soot Morphology in a Laminar Coflow Diffusion Flame of a Surrogate for Jet A-1[END_REF][START_REF] Russo | Dehydrogenation and Growth of Soot in Premixed Flames[END_REF] Particle Growth

Coagulation: Coagulation refers to the different processes that join particles together, including coalescence, aggregation, and agglomeration. [START_REF] Haynes | Soot Formation[END_REF][START_REF] Richter | Formation of Polycyclic Aromatic Hydrocarbons and Their Growth to Soot: A Review of Chemical Reaction Pathways[END_REF][START_REF] Wersborg | Physical Mechanisms in Carbon Formation in Flames[END_REF][START_REF] Siegmann | Clustering at High Temperatures: Carbon Formation in Combustion[END_REF]110,150 See Coalescence, Aggregation, and Agglomeration below.

Coalescence: Coalescence is the merging of two or more particles into one in a way that removes any boundary between them. This term generally refers to particles of miscible substances, such as water droplets or air bubbles. With respect to soot, however, it is used to describe the growth of liquid-like incipient particles through collisions that merge these particles. [START_REF] Haynes | Soot Formation[END_REF][START_REF] Harris | Chemical Kinetics of Soot Particle Growth[END_REF]113,[150][151][152][153][154] Coalescence is a possible outcome of coagulation. "Sintering" has also been used to describe the coalescence of liquid-like incipient particles. 155 Because of the inconsistent usage of "sintering" in the soot literature, we recommend avoiding its use in this context. In addition, using "coalescence", rather than "sintering", allows for greater consistency and connection with the large body of literature on this topic. See Sintering below.

Surface growth: Surface growth describes the process by which gas-phase species are added to the surface to increase the mass of a soot particle. Surface growth can occur at any stage of maturity by processes including condensation, deposition, physisorption, and chemisorption, any of which can generally be referred to as "adsorption". See Adsorption, Chemisorption, Physisorption, Condensation, and Deposition below.

Condensation: Condensation is the thermodynamic phase transition of a gas to a liquid and is the reverse of vaporization. [START_REF] Cernuschi | An Elementary Theory of Condensation[END_REF][START_REF] Mcdonald | Deposition": A Proposed Antonym for "Sublimation[END_REF][START_REF] Jacobson | Fundamentals of Atmospheric Modeling[END_REF][START_REF] Dymarska | Deposition Ice Nucleation on Soot at Temperatures Relevant for the Lower Troposphere[END_REF][START_REF] Veshkini | Application of PAH-Condensation Reversibility in Modeling Soot Growth in Laminar Premixed and Nonpremixed Flames[END_REF] In soot science, "condensation" has been used in the past to represent a heterogeneous gas-to-particle conversion without regard to the state of the condensed phase. [START_REF] Haynes | Soot Formation[END_REF][START_REF] Frenklach | Detailed Modeling of Soot Particle Nucleation and Growth[END_REF][START_REF] Eaves | The Importance of Reversibility in Modeling Soot Nucleation and Condensation Processes[END_REF]148,[156][157][158] However, using "condensation" to describe any gas-to-particle conversion is inconsistent with the common usage in other fields, including physics, chemistry, and atmospheric and aerosol science, and it is recommended that this terminology no longer be used in describing soot processes other than when discussing the thermodynamic phase transition to produce a liquid phase by physical condensation of gaseous components. We recommend using "deposition" to represent a gas-to-solid phase transition and "adsorption" to describe interfacial uptake of material that is not the result of a thermodynamic phase transition. If the binding mechanism is known, "chemisorption" or "physisorption" may be used. See Deposition, Adsorption, Chemisorption, Physisorption and Vaporization, evaporation, and boiling below.

Vaporization, evaporation, and boiling: Vaporization is the thermodynamic phase transition of a liquid to a gas and is the reverse of condensation. [START_REF] Cernuschi | An Elementary Theory of Condensation[END_REF][START_REF] Mcdonald | Deposition": A Proposed Antonym for "Sublimation[END_REF][START_REF] Jacobson | Fundamentals of Atmospheric Modeling[END_REF][START_REF] Dymarska | Deposition Ice Nucleation on Soot at Temperatures Relevant for the Lower Troposphere[END_REF][START_REF] Veshkini | Application of PAH-Condensation Reversibility in Modeling Soot Growth in Laminar Premixed and Nonpremixed Flames[END_REF] Evaporation is the vaporization process that occurs when the vapor pressure of the substance is lower than its saturation pressure at that temperature. 159 Evaporation takes place at the gas-liquid interface. 159 Boiling is the vaporization process that occurs at temperatures at or above the boiling point at a particular pressure. 159 See Condensation above.

Deposition: Deposition is the thermodynamic phase transition of a gas directly into a solid and is the reverse of sublimation. [START_REF] Mcdonald | Deposition": A Proposed Antonym for "Sublimation[END_REF][START_REF] Jacobson | Fundamentals of Atmospheric Modeling[END_REF][START_REF] Dymarska | Deposition Ice Nucleation on Soot at Temperatures Relevant for the Lower Troposphere[END_REF][START_REF] Veshkini | Application of PAH-Condensation Reversibility in Modeling Soot Growth in Laminar Premixed and Nonpremixed Flames[END_REF]160 Deposition can proceed by formation of electrostatic, covalent, or metallic bonds, depending on the material. When the uptake of material onto a solid surface is not the result of a thermodynamic phase transition, "adsorption" should be used to describe the process. If the adsorption binding mechanism is known, "chemisorption" or "physisorption" may be used. See Sublimation, Adsorption, Chemisorption, and Physisorption below.

Sublimation: Sublimation is the thermodynamic phase transition of a solid directly into a gas and is the reverse of deposition. [START_REF] Mcdonald | Deposition": A Proposed Antonym for "Sublimation[END_REF][START_REF] Jacobson | Fundamentals of Atmospheric Modeling[END_REF][START_REF] Dymarska | Deposition Ice Nucleation on Soot at Temperatures Relevant for the Lower Troposphere[END_REF][START_REF] Veshkini | Application of PAH-Condensation Reversibility in Modeling Soot Growth in Laminar Premixed and Nonpremixed Flames[END_REF]160 See Deposition above.

Physisorption: Physisorption or physical adsorption is the binding of atoms or molecules directly to a surface via dispersion or van der Waals forces. 102,161 This term describes the physical binding mechanism and is generally used for monolayer or sub-monolayer interactions; these characteristics make it distinguishable from the thermodynamic phase transitions of condensation and deposition. Binding energies (energies of adsorption) are usually small, i.e., in the range of 0.1-80 kJ/mol. 102,162,163 For a PAH physisorbed to graphite, graphene, carbon nanotubes, or soot, binding energies are on the order of 2.5-6 kJ/mol per carbon atom. [164][165][166][167] Such bound states are generally only stable at low temperatures 162 and are transient or short-lived at elevated temperatures, 168 where desorption becomes significant. The enthalpy of physisorption is of the same order of magnitude as the enthalpy of condensation. 102

Chemisorption: Chemisorption or chemical adsorption is the binding of atoms or molecules directly to a surface through surface chemical bonds, i.e., via covalent bonds. 102,161,169 This term describes the molecule-surface binding mechanism and is generally used for monolayer or submonolayer interactions; chemisorption is thus distinguishable from the thermodynamic phasetransition processes of condensation and deposition. Chemisorption can occur at gas-liquid, 170,171 gas-solid, 169,[172][173][174] or liquid-solid interfaces. [174][175][176] As with other chemical reactions, reaching a state in which the molecules or atoms are chemisorbed to a surface may involve overcoming a reaction barrier to adsorption. 161,173,177 Sequential chemisorption can lead to multilayer growth of new material at a surface. 175 Chemisorption binding energies (energies of adsorption) are on the order of 100-400 kJ/mol, 102,163,178,179 i.e., orders of magnitude larger than physisorption binding energies. Chemisorbed species may be relatively stable at moderate flame temperatures. The rate of desorption of chemisorbed molecules may become significant at higher temperatures, depending on the binding energy and possible reaction barrier to desorption.

Adsorption and desorption: "Adsorption" refers to the binding of atomic or molecular species to a solid or liquid surface by any mechanism and can lead to sub-monolayer, monolayer, or multilayer coatings. 172,180 The reverse of adsorption is desorption. 102

Chemical Evolution

Graphitization: Graphitization is a process by which the graphitic crystallite fine structure of a carbonaceous material increases in long-range order within, and perpendicular to, the aromatic layers. [START_REF] Haynes | Soot Formation[END_REF][181][182][183][184] The ratio of carbon sp 2 -to-sp 3 bond hybridization increases with the size of the crystallite-layer planes, while the interlayer spacing decreases to approach that of graphite. 113,141,[183][184][185][186][187] Graphitization involves the scavenging of interstitial carbon atoms from between layer planes, lateral crystallite growth, and bond rearrangement. 183,188 Some carbonaceous materials, including some forms of turbostratic graphite, are non-graphitizing, i.e. they cannot undergo full graphitization to the most ordered form of graphite. [181][182][183][184]186,187,189,190 Carbonization: Carbonization is the pyrolytic conversion of hydrocarbon species and substituted hydrocarbons towards elemental carbon (i.e., pure carbon). It is marked by an increase in the carbon-to-hydrogen (C/H) ratio. Carbonization occurs by dehydrogenation, functionalgroup elimination, and molecular rearrangement. [START_REF] Vander Wal | Soot Precursor Carbonization: Visualization Using LIF and LII and Comparison Using Bright and Dark Field TEM[END_REF][START_REF] Richter | Formation of Polycyclic Aromatic Hydrocarbons and Their Growth to Soot: A Review of Chemical Reaction Pathways[END_REF]191 Carbonization is generally accompanied by graphitization. [START_REF] Russo | Dehydrogenation and Growth of Soot in Premixed Flames[END_REF]112,186,187,192 Some carbonaceous materials, known as non-graphitizing materials, cannot fully graphitize. [181][182][183][184]186,187,189,190 See Graphitization above.

Annealing: Annealing is usually a thermally induced reactive process. During thermal annealing, a material is heated to a high temperature, held at that temperature for some time, and slowly cooled so that it reaches an equilibrium phase, or a low-energy structure, at the temperature to which it is cooled. 193,194 For metals, thermal annealing generally entails diffusion of atoms displaced from the lattice and defect annihilation through recombination at vacancy sites. 195,196 Annealing in carbon materials is proposed to occur via two mechanisms: (1) migration of displaced carbon atoms caught between graphitic layer planes and Frenkel defect annihilation at vacancy sites, [197][198][199] or (2) higher-barrier carbon-network rearrangements and growth, vacancy migration and clustering within layer planes or fullerene structures, and Schottky defect annihilation at crystalline edge sites. 188,197 Soot aging: Soot aging during combustion is the process of particle evolution from incipient soot particles toward mature soot particles. [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Kennedy | Models of Soot Formation and Oxidation[END_REF]113 Historically, this term was initially used to describe decreased reactivity of the surface as the particle evolves at high temperature. [START_REF] Frenklach | Detailed Modeling of Soot Particle Nucleation and Growth[END_REF] In general, aging involves carbonization, graphitization, and, in most cases, particle coagulation and growth.

As a result, the carbon-to-hydrogen (C/H) ratio increases; [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Harris | Surface Growth of Soot Particles in Premixed Ethylene/Air Flames[END_REF]113,148,200,201 the long-range carbonlattice fine structure increases; [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF]201 the density increases, [202][203][204] the solubility in organic solvents decreases, 205,206 and both the absorption cross section and emissivity increase dramatically at longer wavelengths. [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF]200,201,207,208 In addition, property changes of the primary particles influence whether particles coalesce or agglomerate during coagulation. Liquid-like incipient particles may coalesce. [START_REF] Haynes | Soot Formation[END_REF][START_REF] Harris | Chemical Kinetics of Soot Particle Growth[END_REF]113,[150][151][152][153][154] As these particles age, coalescence becomes impossible, and particles agglomerate instead of coalescing. Further aging is associated with graphitic surface growth that leads to the transition of agglomerates into aggregates. 138,209 Some soot models include terms that allow for a reduction in surface reactivity (controlling surface growth) as a result of surface aging at high temperatures where HACA is the predominant surface-growth mechanism. [START_REF] Frenklach | Detailed Modeling of Soot Particle Nucleation and Growth[END_REF][START_REF] Veshkini | A Soot Particle Surface Reactivity Model Applied to a Wide Range of Laminar Ethylene/Air Flames[END_REF][210][211][212][213][214][215] It is unknown whether surface aging proceeds by the same process as that leading to aging of the bulk particle. Experimental and modeling results have suggested that, for at least some conditions (e.g., at lower temperature), the bulk particle may mature more rapidly than the surface because of addition of new material to the surface, which prevents the surface from maturing. [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF]214 In atmospheric science, particle aging involves surface reactions, coagulation with other particles, and adsorption of coatings. All of these processes can influence chemical, optical, and physical (e.g., size and morphology) properties. 216,217 Some studies refer to aspects of the aging process as "sintering" of the carbonaceous material within primary particles, 218,219 but the chemical mechanisms that lead to soot aging are very different from the processes that cause sintering of other materials. 220,221 We thus recommend avoiding the use of "sintering" in this context. See

Coalescence above and Agglomeration, Aggregation, and Sintering below.

Maturity and maturity level:

The definition of the term "maturity" is the "quality or state of being mature or fully developed". 222 Hence the maturity level of a soot particle describes how much it has evolved from inception towards a fully mature graphite-like particle. [START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Desgroux | Study of the Formation of Soot and Its Precursors in Flames Using Optical Diagnostics[END_REF]204,[223][224][225][226][227][228][229][230][231][232] The surface of the particle can have a different maturity level from that of the bulk. [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF]225,226 Young soot particles: Young soot particles are those in an early stage of development between inception and full maturity. [START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF][START_REF] Skeen | Near-Threshold Photoionization Mass Spectra of Combustion-Generated High-Molecular-Weight Soot Precursors[END_REF][START_REF] Blevins | The Existence of Young Soot in the Exhaust of Inverse Diffusion Flames[END_REF][START_REF] Harris | Surface Growth of Soot Particles in Premixed Ethylene/Air Flames[END_REF]113,148,186,187,200,201,207,208,227 Partially matured soot particles and partially graphitized soot particles: Partially matured or partially graphitized soot particles have undergone some high-temperature aging but have not reached full maturity. These partially graphitized particles are in an intermediate stage between inception and maturity. 191,228 This expression may refer to (1) incompletely carbonized particles undergoing finite-rate carbonization 20 or (2) inhomogeneous particles containing completely carbonized and non-carbonized material. [233][234][235][236] An example of the second type of particle is one whose bulk has been carbonized but whose surface is undergoing rapid growth by hydrocarbon adsorption or deposition. [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF] This type of particle may be more prevalent in turbulent environments, where intermixing of mature soot particles and precursors occurs, and in wildfire and exhaust plumes in which particles are cooled in the presence of semi-volatile gas-phase byproducts. 233,237 Mature soot particles: Mature soot particles are particles that have fully evolved at high temperature. Such particles are refractory and can be heated to the sublimation point of graphite (~4000 K), 226,228,238 are insoluble in polar and non-polar solvents, 226,238 have a molar carbon-tohydrogen (C/H) ratio ranging from ~8 to ~20, [START_REF] Kholghy | The Role of Reactive PAH Dimerization in Reducing Soot Nucleation Reversibility[END_REF]223,224,227,230 and absorb strongly over a broad wavelength range from ultraviolet (UV) to infrared (IR). 226 These characteristics are predominantly defined by the particle's fine structure, which is described as being polycrystalline turbostratic graphite with coherent domains (crystallite regions without major defects or dislocations) slightly larger than 1 nm in diameter and 4-5 layers in thickness with an interlayer spacing of 0.34-0.35 nm. [START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Desgroux | Study of the Formation of Soot and Its Precursors in Flames Using Optical Diagnostics[END_REF]113,138,141,186,226,229,231,232,[239][240][241] Mature soot particles also tend to be strongly bound into ramiform aggregates of monodisperse primary particles. 132,[242][243][244][245] For combustion conditions near the sooting threshold, however, primary-particle monomers with diameters as small as 2-3 nm and optical properties consistent with mature soot have been observed. [246][247][248][249][250] Similar observations have been made of primary-particle monomers with very ordered crystalline fine structure and diameters of ~5 nm in a co-flow diffusion flame. 251 There has been one suggestion to refer to mature soot particles as "nano-sphere soot". 252 However, this term could be confused with synthesized "carbon nanoparticles (CNPs)" or "nano-organic carbon (NOC) particles". See Nano-organic carbon particles above and Carbon nanoparticles below.

Fine structure: In the context of the material characteristics of soot, "fine structure" is used to refer to the internal structure or crystalline organization of the particle. 242,253 It is sometimes also referred to as "nanostructure". [START_REF] Müller | Bulk and Surface Structural Investigations of Diesel Engine Soot and Carbon Black[END_REF]112,139,145,[254][255][256] Basic structural unit (BSU): The basic structural unit of a crystalline material is the unit cell, the smallest repeated sub-structure in the periodic atomic arrangement. Mature soot particles consist of material often described as polycrystalline turbostratic graphite, which is not a singlecrystal material with a well-defined unit cell. The BSU for mature or partially mature soot is generally considered to be defined by the coherent domains or crystallites. In mature soot the BSU is usually 4-5 layers of graphene that are slightly larger than 1 nm in diameter with an interlayer spacing of 0.34-0.35 nm. 113,138,141,183,186,201,239,241,257 Dispersion exponent: The dispersion exponent is a variable that accounts for the wavelength dependence of the absorption cross section and emissivity of soot particles in the visible and near-IR spectral regions (See Black-body radiation below). The dispersion exponent is a continuously variable function that is anti-correlated with the soot maturity level. Mature soot has a dispersion exponent of ~1, whereas the value for young soot in flames has been measured to be as high as ~5. [START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF][START_REF] Török | Investigation of the Absorption Ångström Exponent and Its Relation to Physicochemical Properties for Mini-Cast Soot[END_REF]225,[258][259][260][261][262][263][264][265][266][267] Atmospheric scientists usually refer to the dispersion exponent as the "Ångström exponent" or "Ångström coefficient". See Ångström exponent below.

Black-body radiation:

An object that absorbs all photons that strike it, independently of wavelength, is known as a "black body". 102 The radiation emitted from such an object follows the temperature-dependent Planck function with an emissivity of one. The absorption cross section and emissivity are related by the principle of detailed balance, as given by Kirchhoff's law. 268 A gray body is an object that has an absorption cross section that is independent of wavelength, but, unlike a black body, a gray body does not absorb all photons that impinge on it. Gray-body radiation follows a Planck function with a constant emissivity that is less than one. 269 Very few objects are true black or gray bodies, including soot, even when mature. In the visible and near-IR spectral regions, the emissivity of soot is approximately inversely proportional to the wavelength raised to the dispersion (or Ångström) exponent. [270][271][272] Incipient particles tend to absorb in the UV region of the spectrum but are nearly transparent in the visible and near-IR and are far from black or gray bodies. [START_REF] D'alessio | The Spectroscopic Characterisation of UV Absorbing Nanoparticles in Fuel Rich Soot Forming Flames[END_REF][START_REF] Basile | Coagulation and Carbonization Processes in Slightly Sooting Premixed Flames[END_REF][START_REF] Sgro | Detection of Combustion Formed Nanoparticles[END_REF][START_REF] D'anna | Nano-Organic Carbon and Soot Particle Measurements in a Laminar Ethylene Diffusion Flame[END_REF][START_REF] Sgro | Measurement of Nanoparticles of Organic Carbon in Non-Sooting Flame Conditions[END_REF] As the particles mature, carbonize, and graphitize, their absorption cross sections and emissivity increase and broaden substantially. Mature soot particles absorb and emit at wavelengths in the UV, visible, and IR spectral regions, and their radiative emission is sometimes referred to as "quasi-black-body radiation" or "pseudo-black-body radiation". 20,226,273- 278 Relevant Forms of Carbon Amorphous carbon: Amorphous carbon (a-C) and hydrogenated amorphous carbon (a-C:H) are materials characterized by some short-range order but no long-range order (i.e., the π electrons are largely localized) and a mixture of sp 2 and sp 3 hybridization. [279][280][281] Both a-C and a-C:H are semiconductors. 279,280 Whereas a-C is composed of predominantly sp 2 -hybridized carbon, a-C:H is largely sp 3 hybridized. 279 High-resolution transmission electron microscopy, X-ray diffraction, and Raman spectroscopy measurements suggest that the structure of incipient or young soot particles can be described as amorphous or hydrogenated amorphous carbon. [START_REF] Vander Wal | Soot Precursor Material: Visualization Via Simultaneous LIF-LII and Characterization Via TEM[END_REF]113,186,187,192 This description is consistent with particles composed of aromatic species or a mixture of aromatic and aliphatic content.

Graphene: Graphene is a single layer of carbon atoms arranged in a hexagonal lattice, i.e., a honeycomb structure of six-membered rings. 282 Each carbon atom is covalently bound to three other carbon atoms, and all bonds are sp 2 hybridized.

Graphite:

Graphite is a crystalline form of carbon in which layers of graphene are stacked. The graphene layers are aligned relative to one another in an alternating pattern, such that half of the carbon atoms in one layer align with carbon atoms in the adjacent layers and the other half of the carbon atoms in that layer align with the centers of the hexagonal rings of the adjacent layers. 280,283 Turbostratic graphite: Turbostratic graphite is graphite in which the stacking of the graphene layers is uncorrelated or random. 184,280,283 It is sometimes referred to as "non-graphitic carbon". 189,190 Some forms of turbostratic graphite can be graphitized at high temperature (>~2000 K), and some cannot. 190 The interlayer spacing for turbostratic graphite is 0.3440 nm whereas that of graphite is 0.33539 nm. 280

Polycrystalline graphite: Polycrystalline graphite describes a material composed of multiple crystallites of graphite, which may or may not be aligned relative to one another. 183,283 Glassy carbon: Glassy carbon is a chemically inert non-graphitic and non-graphitizable form of disordered, sp 2 -hybridized carbon with low porosity, high thermal stability, and low density. [284][285][286][287] Diamond: Diamond is a crystalline form of carbon arranged in a lattice in which each carbon atom is covalently bound to four other carbon atoms in a tetrahedral structure. All bonds are sp 3 hybridized. Diamond is not naturally formed at atmospheric pressure, but it can be formed at very high pressures and is observed to form during the detonation of carbon-rich explosives. [288][289][290][291] Fullerenes: Fullerenes are composed of curved sheets of predominantly five-membered and sixmembered rings of carbon that form enclosed structures. 280 The most well-known and stable of these structures is buckminsterfullerene, which is a sphere of 60 carbon atoms in the design of a soccer ball or European football. 292 Fullerenes are formed during combustion under rare conditions, 293,294 particularly at high temperatures, 293,295 low pressures, 293 and long residence times. 296

Carbon onions: Carbon onions are nested fullerenes that can be formed during the annealing of soot particles at high temperatures, 297-300 by electron bombardment of soot at moderate temperatures, 198,301 or during the detonation of carbon-rich explosives. 289 The center can be as small as buckminsterfullerene (0.71 nm in diameter) with an interlayer spacing of 0.33-0.34 nm, such that a carbon onion with four shells can be as small as 2.72-2.88 nm. 301,302 Such a particle, composed of nested icosahedral fullerenes, i.e., C60@C240@C540@C960, 302 would have 1800 carbon atoms.

Carbon nanotubes: Carbon nanotubes are elongated fullerenes. 280 They can be single-walled, i.e., an elongated version of C60, or multi-walled, i.e., an elongated version of carbon onions.

Transition to Aggregates

Primary particles: In combustion science, primary particles are the sub-units, i.e., the elementary building blocks, of soot aggregates. [START_REF] Haynes | Soot Formation[END_REF][START_REF] Wang | Formation of Nascent Soot and Other Condensed-Phase Materials in Flames[END_REF]303 Primary particles are sometimes referred to as "monomers". 304 This expression is used differently in atmospheric science, where "primary particles" refers to solid or liquid particles emitted directly into the atmosphere. [START_REF] Baron | Aerosol Fundamentals[END_REF]305,306 In atmospheric science, primary particles are distinguished from secondary particles, which are produced in the atmosphere from gas-phase emissions. [START_REF] Baron | Aerosol Fundamentals[END_REF]305 In combustion science, an aggregate or agglomerate may be considered to be a secondary particle, but "secondary particle" is not generally used to refer to an aggregate or agglomerate.

Agglomeration and agglomerates: Agglomerates are groups of particles loosely held together, and agglomeration is the process that forms them. [START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Baron | Aerosol Fundamentals[END_REF]197,307,308 Such particles are also known as flocculates. [START_REF] Baron | Aerosol Fundamentals[END_REF] With respect to soot, "agglomerates" refers to multiple primary particles loosely attached to one another. It may also be used to refer to loosely held collections of multiple aggregates. The forces that hold agglomerates together depend on the types of particles and associated agglomeration processes. For soot, agglomeration mechanisms are unknown, but the forces are likely electrostatic forces, such as van der Waals forces. Agglomeration of primary particles occurs prior to aggregation. See Van der Waals interactions above.

Aggregation and aggregates: Aggregates are particles composed of two or more smaller particles firmly bound together. [START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Baron | Aerosol Fundamentals[END_REF]197,307,308 Aggregates cannot easily be broken apart, in contrast to agglomerates, which are only loosely held together. Mature soot particles are formed as aggregates of primary particles by the growth of layers of graphene on the surface of agglomerates of primary particles. 138,209 Super-aggregates: The term "super-aggregates" has been used to describe very large aggregates whose diameters are on the order of 2-100 m. [309][310][311][312][313][314][315][316] These particles have been observed in flames for conditions under which the soot concentration is very large [309][310][311][312] or the residence times are much longer than typically encountered in the laboratory or in technical combustors, such as those in inverted flames, 315,316 wildfires, 314 and large pool fires of several meters in diameter and length. 309,313 The mechanisms controlling their formation are less well investigated than for smaller soot aggregates, but they are hypothesized to be formed by diffusion-controlled agglomeration of aggregates. [309][310][311][312]315,316 Dendritic: "Dendritic" means branched and is used to describe the branched-chain fractal-like morphology of mature soot particles. [START_REF] Michelsen | Probing Soot Formation, Chemical and Physical Evolution, and Oxidation: A Review of In Situ Diagnostic Techniques and Needs[END_REF][START_REF] Johansson | Evolution of Maturity Levels of Particle Surface and Bulk During Soot Growth and Oxidation in a Flame[END_REF]225,238,[317][318][319][320] Ramiform and ramified: "Ramiform" and "ramified" are synonymous with "dendritic" and are used to describe the branched-chain fractal-like morphology of mature soot particles. [START_REF] Lahaye | Mechanisms of Carbon Black Formation: Correlation with the Morphology of Aggregates[END_REF][321][322][323][324][325][326][327] Morphology: With respect to soot, "morphology" usually refers to the size and shape of the aggregate. 242 This term may also refer to the size and spherical or non-spherical shape of the primary particles. "Structural morphology" is sometimes used to represent the fine structure of the particle, 328 but we suggest using "fine structure", "internal structure", "crystalline structure", or "nanostructure" for such phenomena to avoid confusion.

Fractal dimension:

The fractal dimension (or Hausdorff dimension 147,329,330 ) of a soot particle is a parameter used to characterize the morphology of the dendritic agglomerate/aggregate. Based on the mathematical description of fractal structures, the morphology of a fractal aggregate is scale invariant, i.e., aggregates appear to have the same structure over multiple size scales. 147,331 Typical values for uncoated mature-soot particles freshly emitted from the combustor are in the range of 1.7-1.9. 147,243,[329][330][331][332][333][334][335][336] For perspective, a straight line has a fractal dimension of 1, and a sphere has a fractal dimension of 3. Determining the fractal dimension of a soot particle is often complicated and is usually accomplished by inspecting transmission electron microscopy (TEM) images of particles collected on a two-dimensional substrate 147,329,330,[335][336][337][338][339] or analyzing light-scattering measurements. 331,335 It has also been shown that, with appropriate corrections for the flow conditions in the electrostatic classifier, 304 the fractal dimension can be derived by combining particle-mass and electric-mobility measurements; 336 normally such measurements are used to derive a related parameter known as the "mass-mobility exponent" 219,304,[340][341][342][343][344][345] or "mass-fractal dimension". [346][347][348][349] Restructuring: Restructuring refers to a change of the morphology of a particle. With respect to soot, this term usually applies to the collapse of an aggregate from a dendritic structure with a fractal dimension of ~1.8 to a compact structure with a fractal dimension >2. 180,317,336,341,346,[349][350][351][352][353][354][355][356][357] Restructuring usually occurs when the particles are coated with adsorbates prone to hydrogen bonding, which typically happens as the aggregates age in the atmosphere or cool in a tailpipe or exhaust plume.

Sintering: In materials science, sintering refers to the bonding and coalescence of particles into a larger cohesive structure at high temperature by mass-transport mechanisms including flow of material following melting, surface diffusion, and grain-boundary diffusion. Such processes are not likely to occur with mature, carbonized, and aggregated particles because these particles are composed of covalently bound graphite crystallites that do not melt or readily migrate. 358 Some studies have described the evolution of the soot fine structure during soot aging as "sintering" of the primary particles, 218,219 but we recommend referring to these processes as "soot aging". One study presented experimental evidence for a reduction in surface area of soot aggregates during pyrolysis, which the authors referred to as "sintering", 359 but the evidence presented in this paper is consistent with aggregate restructuring and is unlikely to be attributable to a sintering process.

"Sintering" has also been used to describe the coalescence of liquid-like incipient particles. 155 Because of the inconsistent usage and resulting confusion associated with "sintering", we recommend the use of "coalescence" to describe this process, which is consistent with the vast body of literature on this topic. See Soot aging, Restructuring, and Coalescence above.

Oxidation and Breakup

Oxidation: With respect to soot, "oxidation" usually refers to the reaction of O2, O, or OH with the particle to form CO, CO2, and H2O. [360][361][362][363] Oxidation reduces soot mass by converting the solidphase particle to gas-phase products. At elevated temperatures, soot can also be oxidized by other oxygen-containing species, such as CO2 to form 2CO or H2O to form CO and H2. 364 Fragmentation: With respect to oxidation of soot particles, "fragmentation" refers to the process of the breaking-up of the particles into smaller particles. 361,[365][366][367] As over-layers of graphene are oxidized, connections between primary particles are weakened, which can cause aggregates to break apart at the interface between primary particles. In addition, primary particles may also break apart. 365,367 Fragmentation of primary particles is hypothesized to occur via oxygen diffusion into the bulk of the primary particles. 361,365

Associated Expressions

Black carbon (BC): Mature soot particles that are emitted into the atmosphere fall into a category of strongly absorbing atmospheric particles called "black carbon (BC)" or "black-carbon particles". 238,[368][369][370][371][372] Mature soot particles represent the vast majority of atmospheric black carbon.

Previous reviews of atmospheric particles have suggested that "black carbon" be used to refer strictly to mature soot particles. 369 The proposed definition specifically recommends that BC particles are formed during combustion or pyrolysis and have the following characteristics: strong absorption in the visible spectral region, sublimation temperature of ~4000 K, graphitic fine structure, morphology of aggregated spheres, and lack of solubility in polar and non-polar solvents. 369,372 Such particles are often measured using LII and are referred to as "refractory black carbon (rBC)". 369,370 See Mature soot particles above.

Brown carbon (BrC): Brown carbon is a broad category of atmospheric particles that includes young soot particles emitted into the atmosphere. These particles absorb less strongly and broadly than black carbon, 369 ,373 and they are usually soluble in some organic solvents. 369 ,373,374 Compared to black carbon, their absorption spectrum is enhanced at short visible wavelengths relative to longer wavelengths, making them appear brown rather than black. 238,373 Brown-carbon particles are consistently observed in association with biomass or biofuel burning and may be emitted directly into the atmosphere from such sources. 236 They can be produced as secondary organic aerosols by condensation of semi-volatile or non-volatile hydrocarbons often emitted into the atmosphere during incomplete combustion or pyrolysis, such as from smoldering fires, or from biogenic sources. 233,236,375 They may also be composed of humic-like substances from soil. 233,236 Elemental carbon: "Elemental carbon (EC)" is an expression used by the atmospheric-science community to describe particles that are emitted by combustion sources 376 and that are extremely high in carbon relative to other elements, 372 are refractory and can be heated to the sublimation point of graphite (~4000 K), and are resistant to oxidation at temperatures below 340 °C. 370,377 In combustion science, such particles are referred to as "mature soot particles". See Mature soot particles above.

Organic carbon: "Organic carbon (OC)" describes atmospheric particles composed of carbon combined with hydrogen, oxygen, nitrogen, sulfur, and/or other elements. 372 Most of these particles absorb strongly in the IR and UV but are nearly transparent in the visible and near-IR spectral regions. 236 Some of them, however, absorb in the visible and UV regions and are referred to as "brown-carbon particles". Incipient soot particles and young soot particles are included in this category of atmospheric particles. See Brown carbon above.

Ångström exponent:

The Ångström exponent or coefficient is a variable used to express the wavelength dependence of the absorption cross section and emissivity of black and brown carbon in the visible and near-IR regions of the spectrum. 373,[378][379][380] It is sometimes referred to as the "absorption Ångström exponent (AAE)" or "absorption Ångström coefficient (AAC)". An

Ångström exponent close to one is associated with black carbon, whereas brown carbon has an Ångström exponent that can be considerably larger than one. 373,[378][379][380][381][382][383][384] In combustion science, the Ångström exponent is generally referred to as the "dispersion exponent"; it is continuously variable and anti-correlated with soot maturity level. Although the Ångström exponent is continuously variable between values associated with black and brown carbon, the value at which black carbon is distinguished from brown carbon is not precisely defined. 373,380 In addition, the adsorption or attachment of non-absorbing material to black carbon particles (i.e., via internal mixing) can increase the Ångström exponent, [378][379][380][383][384][385] and mixtures of course and fine particles may further influence its value. 383,386 See Blackbody radiation and Dispersion exponent above.

Carbon black: Carbon black represents a wide variety of engineered forms of mature soot. [START_REF] Lahaye | Mechanisms of Carbon Black Formation: Correlation with the Morphology of Aggregates[END_REF]242,387 Carbon nanoparticles (CNPs): The expression "carbon nanoparticles (CNPs)" is usually used to represent deliberately synthesized nanometer-scaled carbonaceous particles, including fullerenes, single-and multi-walled carbon nanotubes, and quantum dots. [START_REF] Teini | Observations of Nascent Soot: Molecular Deposition and Particle Morphology[END_REF][388][389][390][391][392] Aerosol: An aerosol is an ensemble of liquid and/or solid particles suspended in a gaseous medium, [START_REF] Baron | Aerosol Fundamentals[END_REF]305 whereas an aerosol particle is a single particle in an ensemble of suspended particles. 305

Smoke: Smoke is a suspension of combustion-generated particles that is concentrated enough to be visible to the naked eye. 393 These particles are usually mature or nearly mature soot particles, but may include less mature soot particles that have coagulated or are coated with semi-volatile combustion by-products. Smoke can also include emissions of condensed unburned fuel, partially oxidized fuel species, charred fuel fragments, water droplets, and other co-emitted by-products of combustion. 394,395 Smoke number: The smoke number is a metric developed to assess qualitatively the production of soot emissions from jet engines and other combustors. 396 The original purpose of the smoke number was to minimize visibility of the smoke plume from aircraft engines. Smoke number represents the fractional reduction in reflectance by a smoke filter due to the blackening of its surface by soot contained in exhaust gases. This standard is being replaced by new criteria on sootmass and particle-number emissions. 396

Smoke point (SP): Measurement of the smoke point is a standardized test method to estimate the propensity of kerosene or an aviation jet fuel to produce soot emissions in a combustor (ASTM D1322). 397 A wick flame is created using the test fuel, and the smoke point is the height above the wick at which visible soot is first observed by eye. Hence, fuels with higher smoke points have a lower propensity to produce soot. "Smoke point" can also refer to the burning point, that is, the temperature at which a heated oil or fat begins to continuously produce a visible bluish 'smoke' plume. See Threshold sooting index and Yield sooting index below.

Sooting threshold:

The sooting threshold is generally identified for burner-stabilized premixed flames as the smallest equivalence ratio, or carbon-to-oxygen (C/O) ratio, at which soot luminescence is observable. [START_REF] Desgroux | Study of the Formation of Soot and Its Precursors in Flames Using Optical Diagnostics[END_REF][398][399][400] The sooting threshold has typically been determined by observations of the onset of visible soot luminosity [400][401][402][403][404] or visible light absorption [START_REF] Sgro | Measurement of Nanoparticles of Organic Carbon in Non-Sooting Flame Conditions[END_REF] as the fuel, fuel-to-oxidizer ratio, or some other parameter is varied. As noted previously, [START_REF] Desgroux | Study of the Formation of Soot and Its Precursors in Flames Using Optical Diagnostics[END_REF]405 this expression is an example of an imprecise operational term that depends on how the soot onset is observed and interpreted.

Threshold sooting index (TSI):

The threshold sooting index is a standard of measurement developed in the 1980s 406 to rank the propensity of various hydrocarbon fuels to produce soot. The method uses the smoke-point (SP) configuration but reduces the subjectivity of assessments by eye in the SP tests. The technique was subsequently extended to complex surrogates and heavily sooting fuels. 397,407 The TSI can be related to the SP via the molecular weight (MW) of the fuel: TSI = a (MW/SP) + b, where a and b are apparatus-specific empirical parameters. 408,409 See also

Smoke point above and Yield sooting index below.

Yield sooting index (YSI): Yield sooting index was introduced in 2007 as an improvement over TSI using a much more accurate technique than the SP (i.e., laser-induced incandescence, LII) to measure soot volume fraction. 410 Although LII is frequently used to measure volume fraction for YSI, [409][410][411][412][413] laser extinction 414,415 and color-ratio pyrometry 416,417 are also used with the assumption of the optical properties of mature soot particles. YSI is measured on an experimental configuration different from that for the SP and TSI for determination of the propensity of a given fuel to produce soot. The measurement of YSI uses a well-established co-flow non-premixed methane flame with a defined thermal profile to which small amounts of a selected fuel are added. The soot volume fraction (fv) is measured on the flame axis by LII, along the line-of-sight if extinction is used, or radially integrated if spatially resolved color-ratio pyrometry is used. [409][410][411][412][413]416,417 YSI is calculated according to YSI = Afv,max + B, where fv,max is the maximum in fv with respect to height in the flame, which is usually along the flame axis for the low-sooting methane flames typically used. The empirical apparatus-specific constants, A and B, are chosen to give a value for YSI of 0 for nhexane and 100 for benzene. [409][410][411][412][413]416,417 YSI has been found to be more accurate than the SP and TSI for aircraft fuels and has been applied to diesel fuels as well. See also Smoke point and Threshold sooting index above.

Non-volatile particulate matter (nvPM) and volatile particulate matter (vPM): Non-volatile particulate matter is a term used by the aircraft industry and others to represent the component of particles that are not volatile below 350 °C. 418,419 Volatile components, i.e., volatile particulate matter, include H2SO4, water, unburned fuel, and polycyclic aromatic hydrocarbons. 419 The nvPM contributions to particulate matter are solid and consist primarily of mature soot particles. 306,419

CONCLUSIONS

In this review of the terminology employed in the study of soot chemistry, properties, and modeling, we have sought to synthesize a consistent framework to describe these highly complex processes and to highlight a few terms that we suggest avoiding in order to minimize confusion.

Nevertheless, the processes and transitions between one state and another are not yet well-defined and likely depend on conditions. Hence, this review may need to be expanded in the future, as the community's understanding of soot evolves. For example, we may need to revise our description of the soot inception processes and introduce more specificity to the terminology as the understanding of the details grows beyond its presently limited status. We can also anticipate that new terms will need to be developed to describe the levels of maturity of the particles as they evolve from incipient soot particles to mature soot particles.

In addition to facilitating communication within the field of soot science, this review is meant to enable better communication between scientific communities. The last section, in particular, is a potential springboard for enhancing the understanding of the underlying physical and chemical characteristics of combustion-generated black-and brown-carbon particles in the atmosphere.

Because there is a very poor understanding in the atmospheric community of how these particles are produced, their descriptions tend to be phenomenological rather than physically based.

Enabling better communication between these communities is likely to increase the understanding of soot emissions in both communities.

Better communication between the soot-science and materials-synthesis communities is also potentially useful for advancing targeted carbonaceous-materials production and product innovation. There are exciting developments in the production of exotic materials, such as nanodiamonds and carbon nanocones, nanodisks, nanotubes, and other nanostructures. [420][421][422][423][424][425][426][427][428][429][430] Understanding the conditions under which such materials are produced is likely to lead to a better understanding of soot chemistry. We thus hope that the present review will serve to bring more consistency to the field of soot science, to facilitate collaborations and bridging between fields associated with the growth of carbonaceous materials at high temperature, and to aid the advancement of combustion science by highlighting gaps in our understanding of soot formation.

Table 1 .

 1 Terms defined in the paper

	All Stages	Gas-Phase	Transition to	First	Particle
	Particle	Species Soot precursors	First Particles Inception	Particles Incipient soot particles Coagulation Growth _ _ _

ACKNOWLEDGMENTS

We have all benefitted from the enormous contributions from Prof. Heinz Gg. Wagner (1928Wagner ( -2020) ) who was one of the early pioneers of the field of soot-formation chemistry. This paper was submitted on the 100 th birthday of Dr. Rosalind Franklin; we are honored to acknowledge her with tremendous gratitude for her early contributions to this field. We are grateful to Lukas Berger, Antonio Attili, Joel Corbin, and Alex Laskin for reading the manuscript and providing thoughtful input. HAM was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences as part of the Gas-Phase Chemical Physics Program under a sub-contract from Sandia National Laboratories and the College of Engineering and Applied Sciences at the University of Colorado Boulder. MC is indebted to both the Air Force Office of Scientific Research (AFOSR), through Dr. Julian Tishkoff, and the Strategic Environmental Research and Development Program with team leadership by Mel Roquemore for sustained multiyear funding. JHM was supported by the U. S. National Science Foundation under Grant Number CBET-1706757 with Drs. Song-Charng Kon and Harsha Chelliah serving as technical monitors. GJN acknowledges support from the Australian Research Council through grant DP19010112. HP acknowledges support from Deutsche Forschungsgemeinschaft (DFG) and the Research Association for Combustion Engines (FVV) under grant numbers PI 368/25-1 (DFG) and 6013970 (FVV). HW acknowledges support from AFOSR under Grant FA9550-19-1-0261.

AUTHOR INFORMATION

Corresponding Author

*Hope A. Michelsen, Rady Department of Mechanical Engineering, University of Colorado Boulder, 1111 Engineering Drive, UCB 427, Boulder, CO 80309, orcid.org/0000-0001-5802-6615, Email: Hope.Michelsen@colorado.edu.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interests.

For Table of Contents Only