Abstract. Refractory black carbon (rBC) in the atmosphere is known for its significant impacts on climate. The relationship between the microphysical and optical properties of rBC remains poorly understood and is influenced by its size and mixing state. Mixing state also influences its cloud scavenging potential and thus atmospheric lifetime. This study presents a coupling of a centrifugal particle mass analyser (CPMA) and a single-particle soot photometer (SP2) for the morphology-independent quantification of the mixing state of rBC-containing particles, used in the urban site of Beijing as part of the Air Pollution and Human Health–Beijing (APHH-Beijing) project during winter (10 November–10 December 2016) and summer (18 May–25 June 2017). This represents a highly dynamic polluted environment with a wide variety of conditions that could be considered representative of megacity area sources in Asia. An inversion method (used for the first time on atmospheric aerosols) is applied to the measurements to present two-variable distributions of both rBC mass and total mass of rBC-containing particles and calculate the mass-resolved mixing state of rBC-containing particles, using previously published metrics. The mass ratio between non-rBC material and rBC material (MR) is calculated to determine the thickness of a hypothetical coating if the rBC and other material followed a concentric sphere model (the equivalent coating thickness). The bulk MR (MRbulk) was found to vary between 2 and 12 in winter and between 2 and 3 in summer. This mass-resolved mixing state is used to derive the mass-weighted mixing state index for the rBC-containing particles (χrBC). χrBC quantifies how uniformly the non-rBC material is distributed across the rBC-containing-particle population, with 100 % representing uniform mixing. The χrBC in Beijing varied between 55 % and 70 % in winter depending on the dominant air masses, and χrBC was highly correlated with increased MRbulk and PM1 mass concentration in winter, whereas χrBC in summer varied significantly (ranging 60 %–75 %) within the narrowly distributed MRbulk and was found to be independent of air mass sources. In some model treatments, it is assumed that more atmospheric ageing causes the BC to tend towards a more homogeneous mixture, but this leads to the conclusion that the MRbulk may only act as a predictor of χrBC in winter. The particle morphology-independent and mass-based information on BC mixing used in this and future studies can be applied to mixing-state-aware models investigating atmospheric rBC ageing.

A novel inversion method is presented, which derives the two-variable number distribution for black carbon aerosol, using a coupled centrifugal particle mass analyzer (CPMA) and single particle soot photometer (SP2). The CPMA classifies all particles by their mass-to-charge ratio, and the SP2 detects the mass of refractive black carbon (rBC) in each individual particle. The results of the inversion are the simultaneous number distributions of both rBC mass and total particle mass. Using the distribution, the coating distribution on a population of rBC particles can be identified visually. Furthermore, the distribution can be integrated to find one-variable mass and number concentration distributions as a function of total or rBC particle mass. These capabilities were demonstrated via smog chamber experiments, where an organic (non-rBC) coating was grown onto uncoated rBC aerosol over several hours via photo-oxidation of p-xylene. The particle distributions were constructed using the inversion over a range of 1-60 fg of total particle mass. As the non-rBC coating thickness increased over time, a shift in the number distribution toward higher total mass was observed. At the end of the experiment, uncoated rBC was injected into the chamber, and the distribution was clearly resolved using the inversion. The CPMA-SP2 method offers several advantages over "SP-2 only" methods, namely, (i) coating mass information can be obtained over a wider range of total particle mass, (ii) total particle mass is measured directly, and (iii) it does not make core-shell morphology assumptions.

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<p><strong>Abstract.</strong> Refractory Black Carbon (rBC) in the atmosphere is known for its significant impact on the climate system in the atmosphere. The relationship between the microphysical and optical properties of rBC remain uncertain and are largely influenced by the size, coating thickness and mixing state of particles. This study presents a coupling of a centrifugal particle mass analyser (CPMA) and a single particle soot photometer (SP2) for the morphology-independent quantification of the mixing state of rBC-containing particles, used in the urban site of Beijing as part of the Air Pollution and Human Health-Beijing (APHH-Beijing) project during winter (10<sup>th</sup> Nov–10<sup>th</sup> Dec) and summer (18<sup>th</sup> May–25<sup>th</sup> June). An inversion method is applied to the measurements to present a two-variable distribution of both rBC core mass and total mass of rBC-containing particles and present the mass-resolved mixing state of rBC-containing particles. The mass ratio between non-rBC coating and rBC core (MR) is calculated to determine the coating thickness of the rBC-containing particles. The bulk MR was found to vary between 2–12 in winter and between 2–3 in summer. This mass-resolved mixing state is used to derive the mixing state index (χ) for the rBC-containing particles. χ quantifies whether the coating is evenly distributed across the rBC-containing particle population and is used to determine the degree of internal and external mixture of rBC-containing particles. The rBC-containing particles in Beijing were found to be 55%–70 % internally mixed in winter depending on the dominant air masses. χ of rBC-containing particles was highly positively associated with increased bulk MR, rBC mass loading or pollution level in winter, whereas χ of rBC-containing particles in summer varied significantly (ranging 60 %–75 %) within the narrowly-distributed bulk MR and was found to be independent of air mass sources. This concludes that the bulk MR may only act as a predictor of mixing state in winter, and χ is better to quantify the mixing state of rBC-containing particles. The same level of bulk MR corresponded with a higher χ in summer than in winter and this tended to suggest a limited formation of coatings on rBC largely depended on primary sources. However, with the higher Non-refractory PM<sub>1</sub> (NR-PM<sub>1</sub>) concentration in winter, the coagulation process may still lead relative thick coatings. In summer the higher secondary compounds made the rBC-containing particles more homogeneous. But due to the higher temperatures and limited pollution level, the coating thickness in summer is limited. The mixing state of rBC-containing particles should also depend on the coating formation mechanism, both primary source influence and secondary coating formation mechanism should be considered in interpreting the rBC-containing particles mixing state in the atmosphere. This particle morphology-independent and mass-based data format as introduced in this study could be conviently applied in particle-resolved or other process models to investigate atmospheric rBC aging and mixing state properties.</p>

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