Particle number size distributions (PNSD) measured from urban Beijing and Finnish boreal forest were used to provide constraints on typical conditions for atmospheric NPF. Measurements in Beijing were conducted at the BUCT site (39.94° N, 116.30° E), located on the west campus of Beijing University of Chemical Technology, representing polluted environments under the influences of strong anthropogenic emissions. Long-term measurements of atmospheric pollution with a focus on particulate matter pollution and new particle formation started in 2018. PNSD ranging from 1 nm to 10 µm was monitored using a home-built diethylene glycol scanning mobility particle spectrometer system (DEG-SMPS, 1–7.5 nm) and a particle size distribution system (3 nm–10 µm) (Liu et al., 2016; Cai et al., 2017a). Measurements at the Finnish boreal forest were conducted at the SMEAR (Station for Measuring Earth Surface–Atmosphere Relationships) II station (61.10° N, 24.17° E), located at Hyytiälä in southern Finland, representing relatively clean environments. Long-term measurements at SMEAR II started in 1995 (Nieminen et al., 2014). PNSD ranging from 3 nm–20 µm was measured using a differential mobility particle spectrometer (DMPS) (Aalto et al., 2001) and an aerodynamic aerosol spectrometer (APS, TSI 3321). Here we use the data measured until 2022 from Beijing and data in 2018–2019 from Hyytiälä. Detailed information on the measurement sites, instruments, and dataset have been reported elsewhere (Hari and Kulmala, 2005; Cai et al., 2021; Deng et al., 2022).

At both sites, standard data quality control procedures were applied, including removal of instrument artifacts and periods with abnormal meteorological conditions. NPF events were identified using established classification criteria based on the temporal evolution of PNSD (Dal Maso et al., 2005). New particle formation rate (J) was derived using a population balance equation with improved accuracy for the influence of coagulation (Cai and Jiang, 2017). GR was derived by tracking the trajectory of the growing new particle mode using the mode-fitting method (Stolzenburg et al., 2005). The value of CS_bg was taken as the average total CS during the nucleation period (determined using the measured J) of every NPF event, during which the contribution of freshly nucleated particles to the total CS was negligible for their small sizes. dp,end of the growing mode was determined at the end of observed NPF events, characterized by a dramatic change in the mode diameter of the growing new particles due to the change in meteorology.

We employ a zero-dimensional box model to simulate the competition of vapor uptake between new particles and background particles. The model tracks two particle populations: particles originating from NPF (the new particle mode) and background particles (the background mode), together with the concentration of a single representative condensing vapor. The initial diameter of new particles is set to 5 nm, bypassing the high sensitivity of particle survival probability to the CS and GR in the sub-5 nm particle size range (Kulmala et al., 2017, 2022; Cai et al., 2022). The initial number concentration of the new particle mode represents the total number of particles produced at 5 nm during an NPF event, which is obtained by integrating the 5 nm formation rate (J5) over the NPF period. Accordingly, the number concentration of the new particle mode can be expressed as: 1Nnpdp,np=Nnp0⋅P5nm→dp,np where dp,np is the count median diameter of the new particle mode, P is particle survival probability, and Nnp0 is the initial number concentration of the new particle mode. P is computed by calculating particle loss at every time step, accounting for both intramode coagulation (i.e., coagulation scavenging by background particles) and self-coagulation within the new particle mode.

The mass concentration of the new particle mode is 2Mnpdp,np=mnp⋅Nnpdp,np where mnp is the mean single particle mass of the new particle mode. Since particles within the same mode are not monodisperse, we assume that these particles follow a lognormal distribution and convert dp,np to the diameter of mean mass using the Hatch–Choate equation (Hatch and Choate, 1929). The geometric standard deviation of the new particle mode is set to 1.7, which is obtained from observed NPF events. This value overestimates the mass of new particles at small diameters (e.g., 10 nm), but does not affect the conclusions since new particle mass contribution at such sizes is negligible. Particle density is assumed to be 1400 kg m⁻³ (Stolzenburg et al., 2018).

Background particles are represented by a lognormal mode with an initial count median diameter of 100 nm and a geometric standard deviation of 1.7. Their initial number concentration was derived from the specified initial CS_bg. Self-coagulation within the background mode is included but contributes negligibly due to the low particle number concentration. An effective mass accommodation coefficient of background particles (αbg) is introduced to account for the observed phenomenon that background particles sometimes grow more slowly than new particles, reflecting a limited vapor uptake efficiency. We also examine the sensitivity of NPF mass contribution to αbg.

The budget of condensing vapors can be expressed as 3dNvdt=Qv-CSbg⋅fαbg+CSnp⋅Nv where Nv is gas-phase vapor concentration, Qv is the vapor source (i.e., production rate), f(αbg) is the Fuchs-Sutugin correction (Fuchs and Sutugin, 1971) for vapor uptake efficiency of the background mode, and CS_np is the condensation sink of the new particle mode. In this study, CS_bg is reported at αbg = 1.0, with the accommodation correction applied separately via f(αbg), such that CS_bg can be directly related to background particle concentration independently of uptake efficiency. A hypothetical vapor with a molar mass of 300 g mol⁻¹ and a density of 1400 kg m⁻³ is used to represent the ensemble of condensable vapors.

Under simplifying assumptions, expanding particle survival probability using the Kerminen–Kulmala equation (Kerminen and Kulmala, 2002) yields an analytical expression for the relative mass contribution of new particles: 4MnpMbg=dp,np0+GR⋅tdp,bg0+GR⋅fαbg⋅t3⋅Nnp0Nbg0⋅exp⁡γCSGR1dp,np0-1dp,np0+GR⋅t where Mbg is the background mode mass concentration, Nbg0 is the initial number concentration of the background mode, γ is a pre-factor the Kerminen-Kulmala equation, and CS is used herein to represent the total coagulation sink of new particles. Equation (4) shows that the factors governing the relative mass contribution of NPF can be reduced to four parameters: Nnp0, CS_bg0 (equivalent to Nbg0), Qv (determining GR), and αbg. However, because the response of NPF mass contribution to these parameters can be highly non-linear, we do not pursue a closed-form analytical solution and instead rely on numerical simulations.

The simulation results are derived based on a series of simplifications and assumptions. While these simplifications do not affect the proposed regime framework, they may lead to uncertainties in the predicted NPF mass contributions. Here we summarize the limitations of the model.

The zero-dimensional model assesses NPF processes within a hypothesized well-mixed air mass with uniform particle and vapor concentrations. It cannot resolve the influences of spatial heterogeneity and the diurnal evolution of the boundary layer on the NPF mass contributions. The vapor source Qv is assumed to be constant over the simulation period, whereas it is expected to vary diurnally and from day to day due to the variations in primary emissions, photochemical activity, and transport. Condensable vapors are represented by a single hypothetical species, which may not capture the synergistic effects of multicomponent condensation, volatility-dependent vapor uptake, and the possibility that different vapors dominate growth at different sizes or growth periods. The simulations use a fixed 48 h window, while the window for new particle growth during each episode varies with events. The observation results used to validate the input parameters for simulation are limited to two sites, which represent polluted and relatively clean environments but do not span the full range of atmospheric conditions and emission regimes. Extrapolating the results to other environments (e.g., marine, free-tropospheric, or polar atmospheres) should be made with caution. Overall, these uncertainties and limitations do not eliminate the main conclusion that NPF can contribute non-negligibly to aerosol surface area and mass under favorable conditions, but the reported mass contributions may need to be refined by more observational constraints and three-dimensional simulations.

Long-term observations show that NPF events routinely produce a growing particle mode, reaching sizes (e.g., ∼ 100 nm) that significantly contribute to aerosol mass after growth for 1–2 d. At the end of analyzed NPF events in urban Beijing (see Sect. 4.1), the growing mode reached a count median diameter (dp,end) of 50–220 nm with an average value of 103.5 nm, and the number concentration was on average 6.8 × 10³ cm⁻³ with values occasionally exceeding 10⁴ cm⁻³. The corresponding mass concentration was on average 39.7 µg m⁻³, with values approaching ∼ 100 µg m⁻³ in a severe haze episode (Fig. S1 in the Supplement). At the Finnish boreal forest site (Hyytiälä site), the average number and mass concentration of the growing mode at the end of NPF event were 1.3 × 10³ cm⁻³ and 5.4 µg m⁻³, respectively (Fig. S2), consistent with the cleaner environment compared to urban Beijing (Kulmala et al., 2025). While particles in the observed growing mode also originate from primary particle emissions and transport, i.e., the number and mass contributions reported above should not be taken as from NPF alone, these observations confirm that NPF events, under favorable conditions, can produce particles with sizes that are relevant to aerosol surface area and mass. This motivates a process-level analysis in which new particles and background particles are treated explicitly as two modes (see Sect. 3.2).

The key mechanistic question is whether NPF-derived particles can acquire significant mass from condensable vapors in competition with pre-existing background aerosols, which is fundamentally a question of the relative CS of these two competing aerosol populations. Figure 1 shows the simulated evolution of particles with a constant vapor source (Qv) that limits the total availability of vapors. The new particle mode grows from an initial diameter of 5 to ∼ 150 nm with an average GR of ∼ 3 nm h⁻¹, consistent with observation results in the planetary boundary layer (Nieminen et al., 2018; Kerminen et al., 2018; Stolzenburg et al., 2023). Despite the CS of new particle mode (CS_np) being initially negligible, it increases rapidly as particles grow, surpassing the CS of background mode (CS_bg) within 6 h and becoming the dominant vapor sink in the later stage of the event. Compared to another scenario without NPF, the total CS with NPF increases markedly.

With a higher CS than the background mode, the new particle mode accumulates mass exceeding the background mode after a time lag (Fig. 1c). Similar evolution of particle size distributions, i.e., significant growth in mass-size distribution following the growth in number-size distribution, has been observed during atmospheric NPF events (Fig. S3). We note that although the constant vapor source used in Fig. 1 limited the total aerosol mass, this hypothesis holds only in the absence of heterogeneous chemistry and is not supported by atmospheric measurements. In the real world, heterogeneous chemistry can contribute additional mass preferentially on the high-CS new particle mode (Wang et al., 2010), amplifying the NPF mass contribution beyond the simulation results. Figure S4 shows that there is no strong correlation between new particle growth rate and the background CS, indicating that the competition of vapor between the two modes is not the governing factor for the rate of gas-to-particle conversion. Following this measurement fact, we also perform a simulation with constant vapor concentration (corresponding to a near constant growth rate), which shows a significant NPF mass contribution (Fig. S5). Nevertheless, we adopt the constant vapor source hypothesis in the following model simulations, which provide a conservative lower bound on NPF mass contributions, and focus on the relative contribution.

To map the conditions under which NPF mass contribution is significant or negligible, we first show the response and sensitivity of NPF mass contribution after 48 h of simulation to atmospheric conditions characterized by key influencing parameters (Fig. 2). Under the various simulated conditions, CS_np increases rapidly as new particles grow within ∼ 12 h of simulation and drives a sustained accumulation of the mass of new particles, indicating that prolonged continuous growth is not a prerequisite for large NPF contribution to CS. Figure S6 shows that increasing the initial number concentration of new particles produced (Nnp0) leads to a significant elevation in CS_np and only a moderate reduction in CS_bg. Interestingly, the mass of the new particle mode is insensitive to Nnp0 above ∼ 10⁴ cm⁻³ (Fig. 2b), showing that NPF mass contribution is mainly determined by the occurrence of NPF event or not but not its intensity. This is mainly because the available mass is limited by vapor production under a fixed vapor source, and also mass gains in the new particle mode are partially offset by increased scavenging of new particles by background particles, which transfers mass to the background mode.

Figure 2b (and Fig. S7) shows a strong and non-linear dependence of NPF mass contribution on CS_bg0, which results from the non-linear response of particle survival probability to CS (Kulmala et al., 2017; Cai et al., 2022). Consistently, in terms of particle number that determines the occurrence of NPF events, CS has been identified as a governing factor in polluted environments such as urban Beijing (Cai et al., 2017b; Deng et al., 2021), whereas in cleaner environments such as Hyytiälä, CS has only a weak negative association with NPF occurrence (Dada et al., 2017). We could hence conclude that the critical CS threshold for significant NPF mass contribution is ∼ 0.01 s⁻¹ under the simulation conditions in Fig. 2b.

Sufficient vapor is a prerequisite for significant new-particle mass (Figs. 2c and S8), yet it does not have a strong influence on the relative mass contributions of the new particle mode and the background mode for Qv above a certain threshold (∼ 10⁴ cm⁻³ s⁻¹). At the highest vapor source examined (Qv = 10⁶ cm⁻³ s⁻¹), the background mode grows rapidly and enhances the scavenging of new particles, partially offsetting the benefit of higher GR for new particle survival (Fig. S9).

Measurements show that the GR in the sub-25 nm size range tends to increase with particle size, partly attributable to the diminishing Kelvin effect (Yli-Juuti et al., 2011; Tröstl et al., 2016; Deng et al., 2020). This finding also extends to sizes over 100 nm if only monotonic growth periods are accounted for; however, the average increase in the size of background particles over the whole growth event is sometimes slower than smaller new particles (Paasonen et al., 2018; Dai et al., 2023). This may reflect an ineffective vapor uptake of large background particles characterized by αbg below unity, i.e., vapor molecules colliding with the particle surface are not effectively incorporated into the bulk. For instance, the importance of particle-phase diffusion increases with particle size and may retard vapor uptake of large particles (Zaveri et al., 2014). Laboratory measurements have reported αbg on the order of 0.01–1.0 (Davidovits et al., 2006; Liu et al., 2019). For organic-coated or highly viscous particles, the αbg can be substantially lower than 1.0 (Zaveri et al., 2022). Considering that our atmospheric measurement results show that background particles grow slower than new particles, we take αbg = 0.1 as a representative default input for simulation and explore its influences on the mass contribution. Figure 2d shows that the mass contribution of the new particle mode increases as αbg decreases from 1.0 to 0.1. This dependence diminishes as αbg decreases further to 0.01, in which range vapor uptake is dominated by the new particle mode under the simulated condition (Fig. S10).

The findings above are summarized in Fig. 3. The results reveal a three-regime structure governed primarily by the initial CS_bg (CS_bg0). One regime is characterized by significant NPF contributions. Under low background aerosol concentrations (CS_bg0 < 0.001 s⁻¹, regime I), such as on clean days in boreal forest and in remote marine boundary layers (Zheng et al., 2021), new particles develop a mass comparable to or exceeding that of background particles. When CS_bg0 falls below 0.0001 s⁻¹, the total aerosol mass becomes NPF-dominated with only a minor contribution from background particles. Another regime is a background-dominated regime, characterized by high background aerosol concentrations (CS_bg0 > 0.01 s⁻¹, regime III), corresponding to polluted days in environments influenced by strong human activities. Under such conditions, new particles are rapidly removed by coagulation scavenging before they can grow to sizes with significant mass contributions. Even with the most favorable αbg (0.01) representing strongly retarded vapor uptake by background particles, the contribution from the new particle mode is less than 10 % (Fig. S11). In the intermediate range between these two regimes is a transitional regime (CS_bg0 = 0.001–0.01 s⁻¹, regime II). Whether the new particle mode in this transitional regime makes a significant mass contribution is also influenced by other parameters, with αbg being a key influencing factor. Note that although CS_bg0 governs the threshold separating these three regimes in the simulation results, Fig. S11 shows that the threshold values are also affected by Qv and αbg. While Fig. S12 validates this three-regime structure for conditions with a constant vapor concentration (rather than a constant Qv), the threshold values may need re-evaluation when applied to other conditions and environments.