Surface modulated dissociation of organic aerosol acids and bases in different atmospheric environments

Abstract The protonation state of organic acids and bases in aqueous aerosols has the potential to impact cloud activating properties by altering H+ concentrations, and consequently the aerosol chemistry and water activity, but is currently overlooked in most atmospheric aerosol models. We investigated the impact of organic aerosol acid–base dissociation on the cloud droplet number concentration and short-wave radiative effect from cloud formation in environments with varying aerosol concentrations, incorporating organic acid–base dissociation into the aerosol–chemistry–climate box model ECHAM6.3–HAM2.3. The degree of dissociation has previously been observed for several atmospheric organics with Brönsted acid or base character to be significantly modified in the aqueous surface, compared to the bulk solution. We introduced an empirical account of this mechanism for both acids and bases to explore the potential further impact on aerosol climate effects. Suwanee River Fulvic acid and decanoic acid were used as examples of acidic atmospheric organic aerosols and tributylamine and n-butylamine as examples of atmospheric organic bases. Our results show that accounting for the protonation equilibria of organic aerosol components, and their possible surface modulation, results in enhanced cloud droplet number concentration and a substantial short-wave radiative effect of clouds, in pristine, clean, as well as polluted environments. The dissociation of organic acids and bases leads to enhanced H+ concentrations in the aerosol, which further influences aqueous sulfur chemistry to drastically increase sulfate mass in the whole aerosol population. The increased sulfate mass contributes to a rise in the number of particles within larger size ranges, thereby increasing cloud droplet number concentrations. In addition, increased amounts of H+ ions and the resulting sulfate significantly increase the amount of available solute and water activity, leading to a higher number of cloud condensation nuclei, and consequently cloud droplets. The effect of acid–base dissociation on cloud properties is smaller for the investigated organic bases than for the organic acids in all environments. The surface modulation of the organic acid–base protonation equilibria has the largest effect on cloud properties in clean atmospheric environments. These results emphasize the potential importance of organic acid–base dissociation for aerosol-cloud-climate properties and their consideration in atmospheric models on both regional and global scales.


Introduction
Atmospheric aerosols affect the formation and properties of clouds, which can impact Earth's radiation budget and precipitation patterns (Stocker et al. 2013;Masson-Delmotte et al. 2021).Organic species represent a significant (20 À 90%) mass fraction of atmospheric aerosols (Kanakidou et al. 2005;Zhang et al. 2007).Specifically, organic compounds make up approximately 20 À 50% of the total aerosol mass at mid-latitude regions (Saxena and Hildemann 1996;Putaud et al. 2004), and approximately 90% in tropical forests (Andreae and Crutzen 1997;Roberts et al. 2001;Kanakidou et al. 2005).In the middle troposphere, approximately 70% of the total aerosol mass is reported to be organic (Huebert et al. 2004).The atmospheric organic aerosol (OA) fraction is chemically and physically complex, and their interactions with clouds are often identified as the largest source of uncertainty in climate projections (Seinfeld et al. 2016;Masson-Delmotte et al. 2021).
Organic aerosols may comprise significant fractions of species with either Br€ onsted acid or base character (Keene and Galloway 1984;Kawamura, Ng, and Kaplan 1985;Jacob 1986;Chebbi and Carlier 1996;De Angelis, Traversi, and Udisti 2012;Millet et al. 2015;Mochizuki et al. 2016;Wu et al. 2020;Chen et al. 2021).The concentrations of acidic or basic species affect the pH of aqueous aerosols by altering the H þ concentrations (Ault 2020;Pye et al. 2020), which in turn influence the protonation of individual acidic or basic aerosol components.The aerosol pH and aqueous protonation state of acidic and basic components can strongly affect aerosol chemistry (Hung, Hsu, and Hoffmann 2018;Wang et al. 2018) and phase state (Liu et al. 2019).For example, pH dependent sulfur oxidation (Liu, Clegg, and Abbatt 2020) and salt formation by organic acids or bases (Yli-Juuti et al. 2013) can each lead to formation of significant aerosol mass and alter the overall chemical composition.The chemical form (protonated or deprotonated) of the acidic or basic components of OA and contributions to the number of solute species in the aqueous aerosol phase can strongly affect water activity and condensation-evaporation equilibrium (Prisle 2006;Prisle et al. 2008;Frosch et al. 2011;Michailoudi et al. 2020).Size, chemical composition, and phase-state directly impact the cloud droplet formation potential of OA (McFiggans et al. 2006;Hallquist et al. 2009) and the radiative effect (RE) of clouds (Turnock et al. 2019).Therefore, the protonation state of the acidic or basic components of OA is expected to be an important factor influencing OA cloud formation.
Many atmospheric organic acids and bases, for example monocarboxylic acids and alkyl amines, also exhibit surface activity in aqueous solutions, such as aqueous aerosols and cloud droplets (Zhao, Subrahmanyan, and Eisenthal 1990;Yassaa et al. 2001;Mochida et al. 2003Mochida et al. , 2002;;Cheng et al. 2004;Prisle et al. 2010;Ottosson et al. 2011;€ Ohrwall et al. 2015;Prisle 2024).Surface active species (surfactants) have been reported in atmospheric OA from many different regions and environments (G� erard et al. 2016, 2019;Petters and Petters 2016;Nozi� ere et al. 2017;Krofli� c et al. 2018).Surfactants by definition adsorb to the aqueous solution surface, leading to enhanced surface concentrations compared to the interior (bulk).This results in a radial concentration gradient between the surface and bulk (Prisle et al. 2010;Malila and Prisle 2018;Bzdek et al. 2020;Lin et al. 2020, Lin, Malila, andPrisle 2018;Prisle 2021).For microscopic and submicron-sized droplets, both the surface and bulk are finite and the ratio of surface area to bulk volume can be orders of magnitude greater than for macroscopic solutions.In such small droplets, including atmospheric aqueous aerosols, the surface adsorption can result in bulk-surface partitioning, leading to significant redistribution of surface active OA mass from the bulk to the surface phase (Prisle et al. 2010;Lin, Malila, and Prisle 2018;Lin et al. 2020;Prisle 2021).The surface chemical and physical state may therefore significantly contribute to overall aerosol properties for such finite systems (Prisle et al. 2012;Prisle 2021).Werner et al. (2018) investigated the surface characteristics of simple mono-carboxylic acids and n-alkyl amines in dilute aqueous solutions corresponding to activating cloud droplets, using surface-sensitive X-ray Photoelectron Spectroscopy (XPS) in combination with high-brilliance synchrotron radiation.Across a wide range of solution pH, they observed a shift in the degree of protonation for both the Br€ onsted acids and bases toward the neutral species, compared to bulk solutions.The shifted acid-base equilibrium in the surface overall corresponded to an apparent shift in pK a of the order of 1 À 2 pH units for all organic acids and bases studied.Similar shifts in protonation degree were also previously observed using XPS for dilute solutions of decanoic (Prisle et al. 2012), propanoic, and octanoic acids ( € Ohrwall et al. 2015) near neutral pH, containing the ionic form in the bulk.Wellen, Lach, and Allen (2017) measured pH dependent surface tension for aqueous nonanoic and decanoic acid using surface tension titration combined with infrared reflection absorption spectroscopy and inferred that the so-called 'surface pK a ' was greater than the bulk pK a by 1 pH unit for nonanoic acid and 2 pH units for decanoic acid.
The acid-base dissociation of OA components in aqueous aerosols is currently not represented in most climate models, where all components in the OA fraction are considered undissociated in the aqueous phase.The H þ concentration in aqueous aerosols is therefore assumed to have no contribution from the organic fraction (Kanakidou et al. 2005;Hennigan et al. 2015).Recently, we introduced the dissociation of organic acids in an aerosol-chemistry-cloud box model (Sengupta, Zheng, and Prisle 2024) and also incorporated a simple representation of the effect of surface modulated suppressed acid dissociation due to surface activity of organic acids.We found that both bulk and surface modulated acid dissociation of OA can lead to significantly enhanced cloud droplet number concentrations (50 À 80%) and strong short-wave REs of clouds (−0:5 Wm −2 to −2 Wm −2 ), in clean environments.However, similar effects for atmospheric organic bases and their representation in cloud models are still unexplored.Here, we investigate the acid or base dissociation of atmospheric OA species and assess their effects in ambient environments with varying aerosol concentrations.We quantify the impact of both bulk and surface modulated acid-base dissociation on the cloud response for varying aerosol composition and in different environments and identify the atmospheric conditions where these effects may be the most significant.

Methods
We use ECHAM6.3-HAM2.3(here referred to as HAMBOX), which is a box model version of the aerosol-chemistry-climate model ECHAM-HAMMOZ (Tegen et al. 2019).HAMBOX includes the SALSA2.0sectional aerosol module (Kokkola et al. 2018), a sulfur chemistry module (Feichter et al. 1996), and a cloud activation scheme (Abdul-Razzak, Ghan, and Rivera-Carpio 1998;Abdul-Razzak and Ghan 2002).A simple representation of the HAMBOX structure is shown in Figure S1 of the Supplement.We implement the effect of organic acid-base dissociation in cloud activating properties by introducing it in the calculation of aqueous sulfur chemistry.We modify the H þ concentration in the aqueous aerosol to account for dissociation of organic acid or base, which further influences the aqueous sulfur chemistry and formation of secondary sulfate mass in the whole aerosol population.The sulfate mass in the aqueous aerosols in turn affects the number of cloud condensation nuclei.In addition, we introduce the impact of organic acid or base dissociation in the calculation of aerosol water activity.The water activity is increased from both enhanced sulfate aerosol mass and H þ ion concentrations from dissociation of the organic acids or bases, which leads to lower critical supersaturation required for cloud droplet formation.We calculate the cloud droplet number concentration (CDNC) for an air parcel, accounting for the dissociation of organic acids or bases at varying ambient aerosol concentrations, and compare to predictions for identical conditions without considering organic acid or base dissociation.The resulting CDNC is then used to estimate the shortwave RE from cloud formation for each aerosol load environment.

SALSA2.0 aerosol module in HAMBOX
The aerosol size distribution is calculated in SALSA2.0 using the sectional approach (Jacobson 2002(Jacobson , 2005) ) and represented by 10 size bins i.Here, we group the 10 size bins into four sub-ranges: Nucleation (nuc, i ¼ 1 and 2) with mean particle diameter d p ¼ 56 nm, Aitken (atk, i ¼ 3, 4, and 5) with d p ¼ 160 nm, Accumulation (acc, i ¼ 6, 7, and 8) with d p ¼ 485 nm, and Coarse (coa, i ¼ 9 and 10) with d p ¼ 1:85 lm: We consider three types of ambient environments in terms of aerosol concentration (load), described by three different initial aerosol number size distributions fN nuc , N atk , N acc , N coa g ¼ f50, 200, 100, 0g cm −3 (Low), f100, 400, 200, 0g cm −3 (Moderate), and f500, 2000, 1000, 0g cm −3 (High), as shown in Table 1.The Low and Moderate aerosol loads are representative of very clean and clean environments, respectively, such as European villages (Tunved et al. 2005(Tunved et al. , 2008)).The High aerosol load is representative of urban environments, such as European cities (von Bismarck-Osten et al. 2013).Detailed aerosol number size distributions in all 10 size bins are typically not available from ambient observations.Therefore, these initial distributions are used as input in HAMBOX, where the full distributions are then calculated using the method given by Jacobson (2005).
The aerosol chemical composition is represented in SALSA2.0 by model compound classes, specifically 'sulfate' (SU), 'organic aerosol' (OA), 'sea salt' (SS), 'black carbon' (BC), and 'mineral dust' (DU) (Kokkola et al. 2018).Of these, sulfate, organic aerosol, and sea salt constitute the soluble aerosol species and are considered as internally mixed in each size bin of the aerosol population.Black carbon and mineral dust represent insoluble species which are externally mixed with the soluble species in each size bin (Kokkola et al. 2018).We consider four different initial conditions with different organic mass fractions in the aerosol, denoted by v OA ¼ f0:2, 0:4, 0:6, 0:8g, to represent different environments where OA have been reported in varying concentrations.For example, in boreal forest environments, the OA mass fraction is reported around 0.6 ( € Aij€ al€ a et al. 2019).In marine environments, the OA mass fraction has been reported in a wide range, from 0.2 (O' Dowd et al. 2004) to 0.8 (Gantt et al. 2011) in smaller size (< 0:1 lm) aerosols like sea spray aerosol.The initial mass fractions considered for all model compound classes in these five conditions are shown in Table 2.
The properties (molecular weight, MW, and density, q) of the model compound classes are represented in HAMBOX by proxies.We use the default set-up for SU, SS, BC, and DU (Kokkola et al. 2018;Tegen et al. 2019).The properties of mineral dust are represented by a silicon dioxide tetramer (Lauer et al. 2005).BC is represented using the atomic weight and density of carbon.SU is represented by ammonium sulfate, and SS is represented by sodium chloride.These proxies remain consistent for all our simulations, and their properties are summarized in Table 3.
For each set of simulations, we assume that the entire OA mass is comprised of either an organic acid or base and represent the OA by one of the chosen proxies of atmospherically relevant surface-active organic acids or bases.We use Suwannee River Fulvic Acid (SRFA) and decanoic acid as proxies for atmospherically relevant organic acids.SRFA is a reference compound that is frequently invoked as a simple proxy for surface active humic-like atmospheric organics (Kiss, Tomb� acz, and Hansson 2005;Taraniuk et al. 2007;Salma et al. 2010;Prisle et al. 2012;Lin et al. 2020).Decanoic acid is an example of fatty acids reported in many environments (Khwaja 1995;Mochida et al. 2002) and has been used to represent surface active organic aerosol in previous studies (Prisle et al. 2010(Prisle et al. , 2012;;Michailoudi et al. 2020; Veps€ al€ ainen, Calder� on, and Prisle 2023).We use tributylamine and n-butylamine as proxies for atmospherically relevant organic bases, as they have been reported in the atmosphere (Hell� en, Kieloaho, and Hakola 2014) and are commonly used as references for atmospheric amines in modeling studies (Jen et al. 2016), as well as chamber experiments (Price et al. 2016).The molecular weights and densities of SRFA, decanoic acid, tributylamine, and n-butylamine are given in Table 3.

Cloud microphysics in HAMBOX
From the total aerosol mass and composition, the resulting cloud droplet number concentrations and consequent short-wave RE are calculated with the HAMBOX cloud microphysics module given by Abdul-Razzak and Ghan (Abdul-Razzak, Ghan, and Rivera-Carpio 1998;Abdul-Razzak and Ghan 2002).The cloud microphysics used in this work includes the calculation of critical supersaturation (S i ) and activated fraction (n i ) for each aerosol size bin i. Detailed descriptions of the parameterizations and equations used to calculate these cloud activation factors are available from Abdul-Razzak and Ghan (2002) and Abdul-Razzak, Ghan, and Rivera-Carpio (1998) and briefly summarized here.
First, the maximum critical supersaturation for the air parcel is calculated as where g is the surface tension correction factor and f is the correction factor for Kelvin term in the K€ ohler curve (for details, see equations 5 and 6 in Abdul-Razzak and Ghan 2002).S e is the effective critical supersaturation for the air parcel, given by Here, I ¼ 10 is the total number of aerosol size bins i, N i is the number of particles in each bin i, and S i is  Riddick, Bunger, and Weissberger (1970).
the critical supersaturation for each bin, given by where D wet is the droplet diameter and d p is the dry particle diameter.The effect of an insoluble core within the aerosol particle consisting of BC and DU is considered in the calculation of d p according to equations 17.38 and 17.39 in Seinfeld and Pandis (2006).
The terms A and B in Equation (3) are calculated as where M w ¼ 0.018 kg mol −1 is the molecular weight of water, r w ¼ 0:073 N m −1 is the surface tension of pure water, q w ¼ 1000 kg m −3 is the density of water, R ¼ 8.314 J K −1 mol −1 is the ideal gas constant, T ¼ 293 K is the temperature, and n s is the number of moles of solute obtained from the mass fractions of soluble species v OA , v SU , and v SS (Table 2).
With the maximum supersaturation of the air parcel, the activation of each bin is determined by comparing S max with S il and S iu (the lower and upper critical supersaturation bounds of the bin).The number of activated particles (n i ) in each size bin (i) is given by and S il and S iu are obtained using Equation (3) for the diameters of the smallest particle (d il ) and largest particle (d iu ) in each size bin.The average activated fraction (n) for all size bins is then calculated by The total number of activating particles is given by the CDNC, which is calculated using the number of activating particles within each size bin, as The CDNC calculated using Equation ( 9) accounting for organic acid or base dissociation is denoted by CDNC HA and the change in CDNC with respect to no organic dissociation (CDNC 0 ) is The change in cloud-top albedo (Da) at constant cloud liquid water content, LWC ¼ 0.03 g m −3 (Jim� enez-Rodr� ıguez et al. 2021), is calculated from DCDNC following the method outlined by Bzdek et al. (2020) as The short-wave RE is then calculated as where F 0 ¼ 340 W m −2 is the incoming solar flux at the top of the atmosphere, E LWC ¼ 0:3 is the fractional coverage of different types of clouds, and T LWC ¼ 0:76 is the transmittance of the atmosphere at visible wavelengths, assumed constant for all simulations.For all HAMBOX cloud microphysics calculations, we assume a constant cloud temperature of 271 K, cloud pressure of 101 kPa, cloud fraction of 0.3, saturation ratio of gas phase water of 0.3, and updraft velocity of 0.3 m s −1 , consistent with Tegen et al. (2019).The simulation time was 1 h in all cases, with 1 s time steps.

Protonation state of OA in HAMBOX
We consider organic acid or base dissociation in both aerosol chemistry (Sections 2.3.1 and 2.3.2) and water activity (Section 2.3.3)calculations in HAMBOX.

OA acid or base dissociation in aerosol chemistry
When no organic aerosol acid-base dissociation (no diss) is considered, the default H þ concentration in HAMBOX is denoted by ½H þ � 0 and obtained from the water and aqueous phase sulfate concentrations as where LWC ½g m −3 � is the cloud liquid water content, MW SO 2− 4 is the molar weight of the sulfate anion, and the soluble sulfate concentration SU ½ � is obtained from the summation of soluble sulfate (obtained from v SU , Table 2) in all bins.H þ ½ � initial ¼ 2:5 � 10 −6 mol L −1 is the hydrogen ion concentration obtained from cloud pH ¼ 5, which is assumed to be uniform for all size bins and consistent with the pH of warm, low lying tropospheric clouds (Pye et al. 2020).
We introduce organic acid or base dissociation to the sulfur chemistry module by modifying Equation ( 13) to obtain the total hydrogen ion concentration in the aerosol population as where ½H þ � HA is the concentration of the hydrogen ions dissociated by the OA acid or base.
For organic acid dissociation, we consider HA to be an organic acid with only one ionizable hydrogen, such that the acid dissociation degree a is given by where ½HA� tot is the total concentration of the organic acid derived from organic mass fraction v OA : For a highly diluted solution (e.g., ½HA� tot < 0:001 mol L −1 ), we assume the mole fraction based mean activity coefficient, c 2 6 ¼ 1, and under these conditions the relationship between a and the acid dissociation constant K a is ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Based on the well-known bulk pK a and defined input organic mass fractions, we then derive the hydrogen ion concentration from organic acid dissociation, ½H þ � HA , using Equation ( 15) and the total hydrogen ion concentration in the aerosol population, ½H þ � tot , using Equation ( 14).This pK a represents acid dissociation of the OA in the aqueous bulk and is denoted by pK bulk a : For dissociation of organic bases, we consider the conjugate protonated form as an extremely weak acid, which dissociates to produce the neutral base and one hydrogen ion.The acid dissociation constant is then given by where pK b is bulk base ionization constant obtained from literature.pK bulk a for dissociation of the bases in the aqueous bulk is obtained from Equation ( 17) using the commonly known pK b from literature.Similarly to organic acid dissociation, we then use Equations ( 15) and ( 14) to obtain ½H þ � HA from organic base dissociation, and the consequent ½H þ � tot , respectively.The pK bulk a values for all organic acids and bases used here are given in Table 3.

Aqueous sulfur chemistry in HAMBOX
We use the aqueous sulfur chemistry module of HAMBOX (Feichter et al. 1996), with modifications described in Sengupta, Zheng, and Prisle (2024), to calculate the aqueous phase secondary sulfate concentration ½SO 2− 4 � 00 in the aerosol population formed from the oxidation of SO 2 by H 2 O 2 and O 3 in aqueous droplets.The sulfur chemistry module is coupled to the aerosol microphysical module in SALSA2.0,such that, at any time t, the total mass of sulfate in the aerosol is given by where mðSUÞ 0 is the initial mass of SU obtained from v SU in Table 2, and mðSO 2− 4 Þ 00 t is the secondary sulfate mass calculated in the sulfur chemistry module at time t.For each time step, mðSUÞ t is calculated in SALSA2.0 using the mðSO 2− 4 Þ 00 t obtained from the aqueous sulfur chemistry module.Then mðSUÞ t is used in the calculation of the aerosol microphysical processes in SALSA2.0,which includes nucleation, condensation, coagulation and hydration processes, in each time step.During these aerosol microphysical processes, the particles that grow or shrink out of the boundaries of their size bins are redistributed to the corresponding new size bins (Jacobson 2005).Thus, a new size distribution is calculated from enhanced sulfate mass in the aerosol population, at each time step.
For all simulations in the sulfur chemistry module, we assume initial ½SO 2 �, ½H 2 O 2 �, and ½O 3 � in cloud are fixed at 5, 1, and 50 ppb, respectively (Tilgner et al. 2021).SO 2 in an aqueous environment exists in the bisulfite form (HSO The bisulfite anion reacts with H 2 O 2 through the mechanism: The reaction rate for this H 2 O 2 oxidation pathway can be written as where ½H þ � tot is calculated using Equation ( 14), and the rate constant k 4 is calculated by where T ¼ 271 K is the cloud temperature.Equation ( 21) is pH insensitive (Liu, Clegg, and Abbatt 2020) and used in this work to determine the aqueous secondary sulfate concentration from the H 2 O 2 oxidation for simulations where organic acid or base dissociation is not considered.
For the simulation scenarios considering organic acid-base dissociation, we calculate ½SO 2− 4 � 00 from the H 2 O 2 oxidation by following the procedure given by Liu, Clegg, and Abbatt (2020), which is valid for pH > 2: Here, we use the general acid catalysis reaction mechanism, replacing Equations ( 20b) and (20c) with The rate expression for ½SO 2− 4 � 00 formation from this mechanism is where K a1 is the first acid dissociation constant of H 2 SO 3 and k is a constant derived from the reaction rate coefficient and the thermodynamic equilibrium constants.k HA is the overall rate constant for the general acid catalysis mechanism approximated by log k HA ¼ −0:57ðpK a Þ þ 6:83 (Drexler et al. 1991;Liu, Clegg, and Abbatt 2020).This approximation for k HA in relation to the pK a of an organic acid was derived for an ionic strength of I ¼ 0.5 mol kg −1 (Liu, Clegg, and Abbatt 2020).Therefore, we assume this same ionic strength for aqueous droplets in all our calculations.O 3 reacts with HSO − 3 in the aqueous phase according to The secondary sulfate concentration from the O 3 oxidation is then given by where rate constants k 51 and k 52 are calculated from and Secondary sulfate concentrations calculated in the aqueous phase sulfur chemistry module gives the mðSO 2− 4 Þ 00 t and the mðSUÞ t from Equation (18).The new size distribution calculated from the modified total sulfate mass in the aerosol population in SALSA2.0 changes the droplet sizes D wet : Therefore, the critical supersaturation S i in each bin is affected according to Equation (3) from enhanced sulfate mass in the aerosol when considering the organic acid or base dissociation.The modified sulfate mass from acid or base dissociation of OA leads to changes in the cloud activating properties by modifying the size of the aqueous aerosols, which is a significant contributor to the cloud droplet nucleating ability of aqueous aerosols (Dusek et al. 2006).

Organic dissociation in water activity
Water activity in aqueous aerosols is a measure of the availability of water in the system relative to pure water.It is defined as the ratio of the vapor pressure of water in the solution to the vapor pressure of pure bulk water under the same conditions.The water activity of aqueous aerosols is influenced by the modification of the amount of solute in the aerosol.
In HAMBOX, the default number of moles of solute, without considering organic acid or base dissociation, is given by where the n SU , n OA , and n SS are the initial number of moles of sulfate, organic aerosol and sea salt, respectively, obtained from the initial mass fractions v SU , v OA , and v SS , given in Table 2. i SU ¼ 3, i OA ¼ 1, and i SS ¼ 2 are the corresponding van't Hoff factors, such that sulfate and sea salt are considered to be fully dissociated, while OA is considered as undissociated (no diss).We consider the effects of organic acid-base dissociation in the calculation of n s by modification of two parameters.Firstly, the number of moles of soluble sulfate at time t, n SU, t , is calculated using mðSUÞ t obtained from Equation (18).Secondly, the van't Hoff factor for organic acid dissociation, i OA , is modified to reflect acid or base dissociation of the OA.We calculate i OA from the dissociation degree, a (Equation ( 16)), using where n ions is the number of ions formed from one molecule of the organic acid or base.The total available number of moles of solute at time t, n s, t , is then calculated for simulations considering OA acid or base dissociation using n s is modified at each time step by introducing OA acid or base dissociation according to i OA from Equation ( 30) and modified sulfate mass from Equation ( 18).These changes in n s are reflected in the Raoult term B (Equation ( 4)) which affects the critical supersaturation S i for each aerosol size bin, at each time step.

Surface modulated organic acid or base dissociation
In addition to the representation of bulk organic acid-base dissociation (as described in Sections 2.3.1, 2.3.2, and 2.3.3),we here introduce an empirical representation of the surface specific shift in acid-base protonation equilibrium as observed in XPS experiments (Prisle et al. 2012;€ Ohrwall et al. 2015;Werner et al. 2018).
The effect of surface modulated organic dissociation is introduced by shifting the bulk pK a of each acid or base according to the shifts of surface titration curves for atmospheric organic acids and bases observed in surface sensitive XPS experiments (Prisle et al. 2012;€ Ohrwall et al. 2015;Werner et al. 2018).The shifted pK a values are then used to determine the corresponding surface modulated dissociation degrees (a) and van't Hoff factors of the organic acids and bases, calculated using Equations ( 16) and (30), respectively.We here refer to these shifted pK a values as the surface modulated apparent pK a , however, we strongly emphasize that the pK a , which is an intrinsic property of each organic compound in bulk aqueous solution, is not itself changed.Only the dissociation responses of the organic acids and bases to a given pH of the solution are changed in the surface (Prisle et al. 2012;€ Ohrwall et al. 2015;Werner et al. 2018).For the organic acids, the modified dissociation response in the surface results in higher apparent pK a compared to the aqueous bulk solution.We consider pK bulk a þ 1 and pK bulk a þ 2 as representative values, corresponding to less strong and stronger surface effects on the entire droplet, consistent with the observed surface shift in pK a of 1-2 pH units.From Equation ( 16), a is smaller with increasing pK a , and therefore the shifted pK a results in suppressed dissociation of the acids.For the organic bases, the modified dissociation response in the surface results in lower apparent pK a compared to the bulk.We use pK bulk a − 1 and pK bulk a − 2 to represent weaker and stronger influence of surface properties.Since a increases with decreasing pK a , the shifted pK a results in enhanced dissociation of the bases.The values of surface modulated pK bulk a þ 1 and pK bulk a þ 2, for decanoic acid and SRFA, and pK bulk a − 1 and pK bulk a − 2, for tributylamine and n-butyl amine, are given in Table 3.

Results
We present results of activated fraction (n) of the aerosol population, for the organic aerosol fraction represented by the acid and base proxy species in question, in environments with varying aerosol concentrations, and considering organic dissociation according to bulk (pK bulk a ) and surface modulated (pK bulk a þ 1, pK bulk a þ 2 for organic acids, and pK bulk a − 1, pK bulk a − 2 for organic bases) properties.Results are compared to predictions without accounting for organic acid or base dissociation (no diss).We then show the effect on cloud activating properties, in terms of changes in cloud droplet number concentration (CDNC) and the corresponding short-wave radiative effect (RE) from cloud formation.

Organic acids
Figure 1 shows the activated fraction n (Equation ( 8)) of the aerosol population, for the OA acids with initial organic mass fractions v OA ¼ f0:2, 0:4, 0:6, 0:8g: n is shown for droplet sizes D wet ranging from 0.317 to 40 mm, averaged across all aerosol size bins after 1 h of simulation time, for varying pK a representing bulk (pK bulk a , shown in blue) and surface (pK bulk a þ 1 in orange, and pK bulk a þ 2 in green) OA acid dissociation.The results are shown using SRFA (panels a, b, c) and decanoic acid (panels d, e, f) as OA proxies, for varying environments represented by Low (panels a and d), Moderate (panels b and e), and High (panels c and f) aerosol concentrations (as given in Table 1).The activated fraction obtained considering no organic dissociation, 'no diss' (black dashed line), is shown in each panel for reference.
For SRFA, the activated fraction with pK bulk a ranges from 0:00075 À 0:00074 for Low, 0:085 À 0:080 for Moderate and 0:034 À 0:033 for High aerosol concentrations, with increasing v OA ¼ 0:2 − 0:8: When considering the surface modulated suppressed organic acid dissociation with pK bulk a þ 1, n ranges from 0:00053 À 0:00055 for Low aerosol load.The total aerosol number concentration is here of the order N � 10 8 m −3 and therefore even the small activated fraction results in significant number of activated particles.For Moderate and High aerosol concentrations, n ranges from 0:022 − 0:029 and 0:0157 − 0:0151, respectively, as v OA changes from 0.2 to 0.8.Under the stronger suppression of dissociation with pK bulk a þ 2, the activated fraction ranges from 0:00051 − 0:00053 for Low, 0:016 − 0:022 for Moderate and 0:0155 − 0:0150 for High aerosol concentrations, with increasing v OA between 0.2 and 0.8.For comparison, the 'no diss' activated fraction for the whole same range of v OA is 0:00047 for the Low aerosol concentration, which is � 58% smaller than that for pK bulk a , � 13% smaller than for pK bulk a þ 1, and � 9% smaller than for pK bulk a þ 2: For Moderate aerosol concentration the 'no diss' activated fraction ranges from 0:0084 À 0:0073, which is significantly smaller (� 900%) than that obtained for pK bulk a and surface modulated acid dissociation (162% for pK bulk a þ 1 and 91% for pK bulk a þ 2).For High aerosol concentration, 'no diss' activated fraction ranges from 0:0153 À 0:0138, which is � 120% smaller than that obtained for pK bulk a under the same conditions, and 6 − 8% smaller than that obtained for the surface modulated organic acid dissociation.
For decanoic acid, n for pK bulk a ranges from 0:00049 − 0:00050 for Low, 0:011 − 0:015 for Moderate and 0:015 − 0:014 for High aerosol concentrations, on increasing v OA from 0.2 to 0.8.For pK bulk a þ 1, n ranges from 0:00048 − 0:00049 for Low, 0:0098 − 0:0116 for Moderate, and 0:015 − 0:013 for High aerosol concentrations, when increasing v OA from 0.2 to 0.8.Under the stronger suppression of organic acid dissociation with pK bulk a þ 2, n ranges from 0:00047 − 0:00048 for Low, 0:0089 − 0:0094 for Moderate and 0:0153 − 0:0132 for High aerosol concentrations, with increasing v OA : For comparison, the 'no diss' activated fraction for the same range of v OA (0.2 to 0.8) is constant at 0:00047 for Low (2, 4, and 7% smaller than that obtained for pK bulk a þ 2, pK bulk a þ 1, and pK bulk a , respectively), from 0:0084 − 0:0071 for Moderate (25, 38, and 55% smaller than that obtained for pK bulk a þ 2, pK bulk a þ 1, and pK bulk a , respectively) and from 0:015 − 0:013 for High aerosol concentrations (4, 7, and 15% smaller than that obtained for pK bulk a þ 2, pK bulk a þ 1, and pK bulk a , respectively).The activated fraction changes when OA acid dissociation is considered compared to 'no diss', for both acidic OA proxies, SRFA, and decanoic acid.The activated fraction is higher for SRFA OA than for decanoic acid, for all aerosol concentrations, and the difference is greatest for Moderate aerosol concentration.This is because SRFA is a stronger acid with lower (bulk) pK a and therefore ½H þ � tot from SRFA dissociation under the same conditions is expected to be higher than that from decanoic acid dissociation.The surface specific effects are more visible in Low aerosol concentration for both acids, as the activated fraction with surface modulated organic dissociation is higher than 'no diss' and comparable to bulk organic dissociation under the same conditions.For the High aerosol concentration, the activated fraction for both acids with surface modulated organic dissociation is very close to the value for 'no diss' and therefore the surface specific effects are not noticeable in this aerosol environment.This can be explained by the smaller amount of available water for activation as the liquid water content is assumed to be constant and, with increasing aerosol concentration, the amount of available water for activation is smaller.
As discussed in the Section 2.3, acid dissociation of the OA impacts n by modifying the S i in each size bin by changing D wet and n s in Equation ( 4), by increasing ½H þ � tot (Equation ( 14)) and consequently mðSO 2− 4 Þ 00 t (Equation ( 18)) in the aerosol population.Since ½H þ � tot is expectedly lower when dissociation is suppressed, bulk organic acid dissociation shows a higher activated fraction than the surface modulated organic acid dissociation for SRFA and decanoic acid in all aerosol concentrations considered.However, for both organic acids, ½H þ � tot is sufficient to decrease the S i and translate into an increased activated fraction compared to no organic dissociation for both bulk and surface modulated suppressed organic acid dissociation.

Organic bases
Figure 2 shows the activated fraction n (Equation ( 8)) of the aerosol population, for the OA bases with initial organic mass fractions v OA ¼ f0:2, 0:4, 0:6, 0:8g: n is shown for droplet sizes D wet ranging from 0.317 to 40 mm, averaged across all aerosol size bins after 1 h of simulation time, for varying pK a representing bulk (pK bulk a , shown in pink) and surface (pK bulk a − 1 in blue, and pK bulk a − 2 in yellow) OA base dissociation.The results are shown using tributylamine (panels a, b, c) and n-butylamine (panels d, e, f) as OA proxies, for varying environments represented by Low (panels a and d), Moderate (panels b and e), and High (panels c and f) aerosol concentrations (as given in Table 1).The activated fraction obtained considering no organic dissociation, 'no diss', is shown in each panel (black dashed line) for reference.
Including base dissociation of the OA, the activated fraction decreases only slightly compared to not considering organic base dissociation.The base dissociation effect is only somewhat significant for higher v OA in Moderate and High aerosol concentrations, suggesting that the effects of OA base dissociation on the activated fraction is less than that from OA acid dissociation.

Organic acids
Figure 3 shows the change in cloud droplet number concentration, DCDNC (Equation ( 10)), with respect to 'no diss', as a function of initial organic mass fraction v OA for the OA acid proxies, SRFA (panels a, b, c), and decanoic acid (panels d, e, f).DCDNC is shown for varying pK a corresponding to bulk (pK bulk a , in blue), and surface modulated (pK bulk a þ 1, in orange, and pK bulk a þ 2, in green) organic acid dissociation, in varying environments represented by Low (panels a and d), Moderate (panels b and e), and High (panels c and f) aerosol concentrations (as given in Table 1).
For SRFA, DCDNC for pK bulk a ranges from À 0:23% to À 0:03% for Low, from 47 − 58% for Moderate and from 120 − 135% for High aerosol concentrations, with increasing v OA : On considering surface modulated suppressed acid dissociation with pK bulk a þ 1, DCDNC ranges from À 0:13% to 0:02% for Low, from 35 − 42% for Moderate and from 4 − 25% for High aerosol concentrations, with increasing v OA : Under the stronger suppression of acid dissociation with pK bulk a þ 2, the DCDNC ranges from À 0:3% to 0:07% for Low, from 27 − 42% for Moderate and from 2 − 23% for High aerosol concentrations, corresponding to increasing v OA from 0.2 to 0.8.Surface specific effects of organic acid dissociation are more visible in the Moderate aerosol concentration for SRFA.As surface modulated OA acid dissociation did not significantly impact the activated fraction for High concentration, the DCDNC resulting from pK bulk a þ 1 and pK bulk a þ 2 are very small compared to 'no diss'.The OA bulk acid dissociation with pK bulk a , however, shows DCDNC > 100%: This is due to the change in size distribution for SRFA acid dissociation in the High aerosol concentration environment, shown in Figure S2 in the Supplement.After one hour of simulation time, the SRFA size distribution shows an increased number concentration of larger sizes for the OA bulk acid dissocition, pK bulk a : The mean size of aerosols in the population has increased due to coagulation growth, and this shift in size results in the production of more cloud condensation nuclei (CCN) (Jacobson 2002(Jacobson , 2005)).As a result, the DCDNC compared to 'no diss' is higher than expected from the activated fraction for pK bulk a : DCDNC for SRFA at Low aerosol concentration is < 0:1% for all pK a and v OA considered.This is unexpected, as the activated fraction obtained under these conditions is still larger than from 'no diss'.The size distributions in Figure S2, and the change in total number of particles (DN) compared to 'no diss' in the Accumulation and Coarse size ranges shown in Figure S6 of the Supplement, show that for pK bulk a the number of particles in the Accumulation size range (N acc ) decreases by approximately two orders of magnitude compared to 'no diss' after one hour of simulation time.This leads to a decrease in the numbers of CCN.Although the activated fraction increases due to high sulfate mass in the aerosol population, the total numbers of CCN in this case is too small compared to 'no diss' to result in significant DCDNC: For decanoic acid, DCDNC ranges from 5 − 15% for Low, from 16 − 40% for Moderate and from 26 − 50% for High aerosol concentrations, with increasing v OA at pK bulk a .On considering surface modulated suppressed dissociation with pK bulk a þ 1, DCDNC ranges from 4:5 − 14% for Low, from 9 − 26% for Moderate and from 24 − 48% for High aerosol concentrations, with increasing v OA : Under the stronger suppression of acid dissociation with pK bulk a þ 2, DCDNC ranges from 4 − 13% for Low, from 4 − 11% for Moderate and from 22 − 41% for High aerosol concentrations, with increasing v OA : Therefore, for decanoic acid, OA acid dissociation with both bulk and surface properties results in considerable change in CDNC from 'no diss', at all aerosol concentrations.The size distribution and chemical composition of the soluble bins after one hour of simulation time is shown in Figure S3 and Table S1, respectively, of the Supplement for all aerosol concentrations for bulk ðpK bulk a Þ and surface modulated ðpK bulk a þ 1 and pK bulk a þ 2Þ organic acid dissociation.For High aerosol concentration, DCDNC for decanoic acid ranges between 24 − 48% with increasing v OA from 0.2 to 0.8.This DCDNC seems large considering that the activated fractions n obtained for 'no diss' and all representations of organic acid dissociation are similar, as shown in Figure 1.This may be explained by a change in the total number of particles in the Accumulation (DN acc ) and Coarse (DN coa ) size ranges, compared to 'no diss', as shown in Figure S7 in the Supplement.Although the size distribution after one hour of simulation time does not change as much for decanoic acid as for SRFA, the number of particles in both Accumulation and Coarse mode size ranges increases significantly.Particles in these size ranges are the major sources of CDNC (Anttila et al. 2012;Hegg et al. 2012;Wang et al. 2020) and therefore the increase in the number of Accumulation and Coarse mode particles results in an increase in DCDNC by 24 − 48% for bulk ðpK bulk a Þ and surface modulated ðpK bulk a þ 1 and pK bulk a þ 2Þ organic acid dissociation, even though the activated fractions were quite similar to that for 'no diss'.

Organic bases
Figure 4 shows the change in cloud droplet number concentration DCDNC (Equation ( 10)) with respect to 'no diss', as a function of initial organic mass fraction v OA for the OA base proxies.DCDNC is shown for varying pK a corresponding to bulk (pK bulk a , in pink), and surface modulated (pK bulk a − 1, in blue, and pK bulk a − 2, in yellow) organic base dissociation, using tributylamine (panels a, b, c), and n-butylamine (panels d, e, f) as OA proxies.DCDNC is shown for varying environments represented by Low (panels a and d), Moderate (panels b and e), and High (panels c and f) aerosol concentrations (as given in Table 1).
For tributylamine, DCDNC ranges from À 0:06% to À 0:27% for Low, from À 0:04% to À 1:1% for Moderate and from 0:07 − 0:01% for High aerosol concentrations, with increasing v OA for pK bulk a : On considering surface modulated suppressed base dissociation with pK bulk a − 1, DCDNC ranges from À 0:05% to À 0:1% for Low, from À 0:046% to À 0:08% for Moderate and between 0:035 − 0:02% for High aerosol concentrations, as v OA increases from 0.2 to 0.8.Under the stronger suppression of base dissociation with pK bulk a − 2, DCDNC ranges from À 0:02% to À 0:03% for Low, from À 0:015% to 1:1% for Moderate and between 0:05 − 0:01% for High aerosol concentrations, with increasing v OA : For nbutylamine, DCDNC ranges from À 0:06% to À 0:145% for Low, from À 0:04% to À 0:9% for Moderate and between 0:08 − 0:02% for High aerosol concentrations, with increasing v OA for pK bulk a : On considering surface modulated suppressed base dissociation with pK bulk a − 1, DCDNC ranges from À 0:03% to À 0:02% for Low, from À 0:045% to À 0:065% for Moderate and between 0:045 − 0:03% for High aerosol concentrations, as v OA increases from 0.2 to 0.8.Under the stronger suppression of base dissociation with pK bulk a − 2, the DCDNC ranges from 0:005% to À 0:04% for Low, from À 0:02% to 1% for Moderate, and from 0:062% to À 0:015% for High aerosol concentrations, with increasing v OA : For both bases, DCDNC is <0.1% at Low and High aerosol concentrations, and <1% in the Moderate aerosol concentration.This suggests that the dissociation of organic bases (treated as extremely weak acids) does not significantly affect the CDNC production under the simulation conditions.This is also observed from the mass fractions v OA , v SU , and v SS (Table S1 in the Supplement) which show no significant change at time t ¼ 1 h compared to the corresponding initial mass fractions at t ¼ 0. Figures S4 and S5 in the Supplement show the size distribution of aerosols for tributylamine and n-butylamine OA proxies, respectively, after one hour of simulation time for representations of bulk and surface modulated organic base dissociation, compared to 'no diss'.No significant change in the size distributions is observed for the organic bases under the simulation conditions.Though tributylamine is a much larger molecule with a much higher molecular weight than n-butylamine, the base strength given by the pK b is similar for both bases.Therefore, for the current representation of the base dissociation in cloud microphysics, these bases behave similarly under the simulation conditions.

Organic acids
Figure 5 shows the short-wave RE (Equation ( 12)) with respect to 'no diss', as a function of initial organic mass fraction v OA for the acid OA proxies.RE is shown for varying pK a corresponding to bulk (pK bulk a , in blue), and surface modulated (pK bulk a þ 1, in orange, and pK bulk a þ 2, in green) organic acid dissociation, using SRFA (panels a, b, c), and decanoic acid (panels d, e, f) as OA proxies.RE is shown for varying environments represented by Low (panels a and d), Moderate (panels b and e), and High (panels c and f) aerosol concentrations (as given in Table 1).
The short-wave RE behaves as expected from the predicted DCDNC in Figure 3.A considerable cooling effect compared to 'no diss' is seen for Moderate aerosol concentration, with the strongest effect for the bulk acid dissociation condition.However, RE is also significant for surface modulated suppressed acid dissociation at Moderate aerosol concentration.The same is not seen for High aerosol concentration, as expected from the DCDNC predicted for these conditions.Here, the surface modulated suppression of acid dissociation shows a small cooling effect at the higher v OA , but the bulk acid dissociation shows a strong cooling effect for all v OA considered.From Figures 1 and S2 in the Supplement, RE for High aerosol concentration can be explained by two factors, limited availability of water and high coagulation aerosol growth.The liquid water content in HAMBOX is considered to be constant and therefore, for High aerosol concentration, the amount of water available is not sufficient to activate all particles.This effect is seen for the surface modulated suppressed acid dissociation condition.However, for bulk acid dissociation, the aerosol size distribution shows that coagulation growth leads to larger particle sizes compared to 'no diss' and more potential CCN.For Low aerosol concentration, the trend in RE is explained by the concentration of sulfate (from Table S1 in the Supplement) and the aerosol size distributions.The pK bulk a ¼ 2:18 (Table 3) for SRFA is sufficiently low that the amount of H þ dissociated from SRFA OA produces high amounts of secondary sulfate, such that v SU � v OA and v SS , as seen in Table S1 of the Supplement.However, in Low aerosol concentration environment, the aerosol number is sufficiently low that the probability of coagulation growth is very small.For Moderate aerosol concentration, the high sulfate mass leads to coagulation growth, while the number of particles in Accumulation and Coarse size ranges are also high enough to generate sufficient CCN, such that the RE from all OA dissociation representations show a significant cooling effect compared to no dissociation.
For decanoic acid, RE ranges from À 0:18 Wm −2 to À 0:62 Wm −2 for Low, from À 0:6 Wm −2 to À 1:5 Wm −2 for Moderate, and from À 1 Wm −2 to À 1:5 Wm −2 for High aerosol concentrations, for increasing v OA with pK bulk a : On considering surface modulated suppressed acid dissociation with pK bulk a þ 1, RE ranges from À 0:2 Wm −2 to À 0:6 Wm −2 for Low, from À 0:4 Wm −2 to À 1 Wm −2 for Moderate and from À 0:8 Wm −2 to À 1:3 Wm −2 for High aerosol concentrations, with increasing v OA : Under the stronger suppression of acid dissociation with pK bulk a þ 2, RE ranges from À 0:18 Wm −2 to À 0:57 Wm −2 for Low, from À 0:2 Wm −2 to À 0:5 Wm −2 for Moderate, and from À 0:7 Wm −2 to À 1:2 Wm −2 for High aerosol concentrations, with increasing v OA : For decanoic acid, the relatively higher pK bulk a compared to SRFA leads to lower concentration of dissociated hydrogen ions under similar conditions.The only exception is the High aerosol concentration, where the lower than expected DCDNC and RE can be explained by the limited water available for CCN activation due to the constant liquid water content in the box model.

Organic bases
Figure 6 shows the short-wave RE (Equation ( 12)), with respect to 'no diss', as a function of initial organic mass fraction v OA for the OA base proxies.RE is shown for varying pK a corresponding to bulk (pK bulk a , in pink), and surface modulated (pK bulk a − 1, in blue, and pK bulk a − 2, in yellow) organic base dissociation, using tributylamine (panels a, b, c) and n-butylamine (panels d, e, f) as OA proxies.RE is shown for varying environments represented by Low (panels a and d), Moderate (panels b and e), and High (panels c and f) aerosol concentrations (as given in Table 1).
For both organic bases considered, the predicted RE is slightly positive for pK bulk a and pK bulk a − 1, and slightly negative for pK bulk a − 2: For all representations of pK a , RE < 60:5 Wm −2 from both bases in all environments.Therefore, no significant effect of the dissociation of bases (when considered as extremely weak acids) is observed in the RE of clouds under the simulation conditions.This is expected from the DCDNC shown in Figure 4. Similarly to the organic acids (Figure 5), the strongest effect of OA acid-base dissociation is seen for the Moderate aerosol concentration.

Discussion
Overall, the effects of OA acid or base dissociation on cloud activation and radiative properties are greatest when considering the conditions of bulk dissociation, but still significant even when potential surface-modulated acid-base dissociation is also included.For the dissociation of organic acids, cloud properties depend on the balance between coagulation growth resulting from additional mass of secondary sulfate produced by increased H þ concentration and the number of aerosols in larger size ranges (N acc and N coa ), in each aerosol concentration environment.For low aerosol concentrations, although the secondary sulfate mass from acid dissociation is quite high, the aerosol number in Accumulation and Coarse mode size ranges is sufficiently low that the probability of coagulation growth is very small.In high aerosol concentrations, the secondary sulfate mass from acid dissociation, as well as N acc and N coa are quite high.However, due to the condition of the box model where liquid water content is considered constant, the amount of available water is not sufficient for activation of all aerosols.In moderate aerosol concentrations, both secondary sulfate mass, mðSO 2− 4 Þ 00 , and N acc and N coa simultaneously increase the numbers of CCN.Therefore, the effects of organic acid dissociation and its surface modulation on the cloud properties is most significant in Moderate aerosol concentration environments.
The dissociation of basic OA affects the cloud activating properties of aqueous aerosols to a much smaller extent than OA acid dissociation.The effect of base dissociation is only somewhat significant for higher initial OA mass fractions in moderate and high aerosol concentrations.In the current representation of base dissociation in cloud properties, both the organic bases considered exhibit similar behavior under the simulation conditions.While tributylamine is a much larger molecule with a significantly higher molecular weight than n-butylamine, their similar base strengths, as indicated by the pK b (Table 3), show that, in this context, base strength is more influential than molecular weight in affecting the cloud activation properties.
Our empirical model for surface modulation of pK a is based on XPS experiments which represent the current state-of-the-art in the field of molecular surface science for liquid mixtures (Prisle 2024).As in the XPS experiments, we have used simple mixtures containing one organic acid or base.Despite acknowledging that surface modulation may differ in complex mixtures compared to simpler ones studied here, this work lays the foundation for understanding the atmospheric impact of these mechanisms.The empirical model presented here enables extending the observations from the nanoscale to the macroscale, encompassing a wide size range and varying concentrations representative of real atmospheric aerosols.

Conclusions
We investigated the aerosol-cloud-climate effects in a box model by evaluating key parameters, including cloud droplet number concentration and aerosol short-wave radiative effect, for OA comprising organic acids and bases in different aerosol concentrations and with different assumptions of acid-base dissociation: (1) following well-known bulk solution dissociation properties, (2) accounting for surfacemodulation of dissociation as observed in recent laboratory experiments, and (3) the current standard of no considerations of dissociation.
Our results show that dissociation of organic acids leads to enhanced CDNC and a strong short-wave RE of clouds.Therefore, the acid dissociation effects of OA are important to consider in climate models, especially in environments where organic acids are found in high aerosol fractions, such as industrial areas (Di Filippo et al. 2010;Zhao et al. 2014) or forest regions (Kavouras, Mihalopoulos, and Stephanou 1998;Villanueva-Fierro, Popp, and Martin 2004).Conversely, we found that the dissociation of organic bases has a comparatively smaller impact on CDNC and the short-wave RE of clouds.While the influence of organic bases may be less pronounced, it remains a valuable aspect to consider, particularly in specific environmental conditions or regions where organic bases play a more significant role, such as agricultural areas or coastal regions (Kuhn et al. 2011;Shen et al. 2023).
We found that for both organic acids and bases, the effect of OA acid-base dissociation and its surface modulation on the cloud properties is most prominent in moderately clean environments, representative of for example European villages.The effect is strongly significant for the dissociation of organic acids, and therefore important to consider in regional climate models for such environments.In more pristine environments with low aerosol concentrations, the effect of organic acid dissociation on aerosol-cloud properties is smaller, but still important for accurate predictions.In more polluted environments where aerosol concentrations are very high, effects of organic aerosol acid dissociation on cloud properties is less prominent, but still significant.
As many atmospheric organic aerosol components have acid-base characteristics (Pye et al. 2020), their dissociation can have significant impacts on cloud properties.This work highlights the importance of including effects of organic acid or base dissociation in atmospheric models of both regional and global scales.Furthermore, considering the abundance of surfactant species in atmospheric OA, and high surface to bulk volume ratio and significant bulk-surface partitioning of surfactant species in small droplets, we propose that the effects of organic acid-base dissociation and its potential size-dependent surface modulation, offer valuable insights to resolving knowledge gaps concerning atmospheric organic aerosols.

Figure 1 .
Figure 1.The average activated fraction, n, of the aerosol population with droplet sizes D wet ¼ 0:317 − 40 lm considering Low (a, d), Moderate (b, e), and High (c, f) aerosol loads, after 1 h of simulation time, for varying initial organic mass fractions (v OA ), calculated using Equation (8), corresponding to representations of bulk (pK bulk a , blue) and surface modulated (pK bulk a þ 1, orange, and pK bulk a þ 2, green) organic dissociation, considering (a,b,c) SRFA, and (d,e,f) decanoic acid as the proxy for the organic fraction.The 'no diss' average activated fraction is shown as a black dashed line.

Figure 2 .
Figure 2. The average activated fraction, n, of the aerosol population with droplet sizes D wet ¼ 0:317 − 40 lm considering (i) Low, (ii) Moderate, and (iii) High aerosol concentrations, after 1 h of simulation time, for varying initial organic mass fractions, v OA , calculated using Equation (8), corresponding to representations of bulk (pK bulk a , pink) and surface modulated (pK bulk a − 1, blue, and pK bulk a − 2, yellow) organic dissociation considering (a,b,c) tributylamine, and (d,e,f) n-butylamine as the proxy for the organic fraction.The 'no diss' average activated fraction is shown as black dashed lines.

Figure 3 .
Figure 3.The change in cloud droplet number concentration, DCDNC, calculated using Equation (10) with respect to 'no diss' considering (a,b,c) SRFA, and (d,e,f) decanoic acid as the proxy for the organic fraction, shown as a function of initial organic mass fraction v OA , assuming organic acid dissociation according to bulk (pK bulk a , blue) and surface modulated properties (pK bulk a þ 1, orange, and pK bulk a þ 2, green), after 1 h of simulation time, under conditions of Low (a, d), Moderate (b, e), and High (c, f) aerosol concentrations.

Figure 4 .
Figure 4.The change in cloud droplet number concentration, DCDNC, calculated with respect to 'no diss' using Equation (10), considering (a,b,c) tributylamine and (d,e,f) n-butylamine as proxy for the organic fraction, shown as a function of initial organic mass fraction v OA , assuming organic acid dissociation according to bulk (pK bulk a , pink) and surface modulated properties (pK bulk a − 1, blue, and pK bulk a − 2, yellow), after 1 h of simulation time, under conditions of Low (a, d), Moderate (b, e) and High (c, f) aerosol concentrations.

Figure 5 .
Figure 5.The short-wave RE, calculated using Equation (12), with respect to 'no diss' considering (a,b,c) SRFA, and (d,e,f) decanoic acid as the proxy for the organic fraction, shown as a function of initial organic mass fraction v OA , assuming organic acid dissociation according to bulk (pK bulk a , blue) and surface modulated properties (pK bulk a þ 1, orange, and pK bulk a þ 2, green), after 1 h of simulation time, under conditions of Low (a, d), Moderate (b, e), and High (c, f) aerosol concentrations.

Figure 6 .
Figure 6.The short-wave radiative effect (RE), calculated with respect to 'no diss' using Equation (12), considering (a,b,c) tributylamine, and (d,e,f) n-butylamine as proxy for the organic fraction, shown as a function of initial organic mass fraction v OA , assuming organic base dissociation according to bulk (pK bulk a , pink) and surface modulated properties (pK bulk a − 1, blue, and pK bulk a þ 2, yellow), after 1 h of simulation time, under conditions of Low (a, d), Moderate (b, e), and High (c, f) aerosol concentrations.

Table 1 .
Initial aerosol number concentration in each size sub-range used in HAMBOX-SALSA2.0, for each of the aerosol load environments considered.

Table 2 .
Initial aerosol mass fractions of all model compound classes in the four different environmental scenarios considered.

Table 3 .
Proxies for the aerosol model compound classes and their physical properties used in the model simulations. c