Molecular scale description of interfacial mass transfer in phase separated aqueous secondary organic aerosol

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profiles using out of equilibrium simulations along distance-related reaction coordinates in biophysical contexts (Allen et al., 2014, e.g.).
This paper presents a molecular simulation study aimed at revealing the mechanism of water uptake in a vapor/hydroxy-cispinonic acid/water double interfacial system at two temperatures, characteristic of the planetary boundary layer and the upper troposphere. Free energy profiles of water uptake are generated using steered MD simulations, and are used to describe the 100 temperature dependence of the water uptake mechanism. Thermodynamic driving forces are identified by decomposing the free energy profiles into entropic and energetic contributions, and the causality between exact molecular scale representation of non-ideal mixing thermodynamics and observed increased CCN activities is inferred from the thermodynamic description.
Knowing the molecular-scale mechanism of water uptake, the usability of a single mass accommodation coefficient to describe gas to particle partitioning is assessed by modeling characteristic timescales and concentration distributions in the organic 105 shell. Finally, different scenarios through which LLPS affects cloud droplet activation and growth are identified and tested in the framework of the Köhler-theory.

Technical background
The molecular scale mechanism of water uptake is studied through the analysis of free energy profiles. This approach pro-110 vides a comprehensive overview of the gas-to-particle partitioning process. Molecular simulation methods to calculate free energy profiles, among them umbrella sampling, which is the traditional approach to obtain transfer coefficients (Sakaguchi and Morita, 2012) and steered molecular dynamics, which is used in this study, rely on forcing the system to follow a pathway along an aptly chosen set of reaction coordinates that provide a low-dimensional representation of the physical process. In umbrella sampling (Torrie and Valleau, 1977), the reaction coordinate space is mapped in a set of consecutive quasi-equilibrium 115 simulations, with the reaction coordinates restrained at a different value in each simulation. Quasi-equilibrium methods (Sakaguchi and Morita, 2012) provide a free energy estimate that artificially averages out effects of surface fluctuations (as a result of the method used to average the force as a function of the reaction coordinate) (Darvas et al., 2013;Braga et al., 2016;Klug et al., 2018) whose spatial and temporal scales are similar to those of a typical atmospheric water uptake event.
In steered MD (Park and Schulten, 2004), the system is pulled along the reaction coordinate space with the help of an external 120 harmonic bias at a constant finite velocity or with a constant finite force in several parallel realisations. Jarzynski's equality (Jarzynski, 1997) is used to estimate the free energy from the work profiles collected in each non-equilibrium simulation: where β = 1/k B T and k B is the Boltzmann constant and T is the temperature. A formal proof of Jarzinsky's equality for finite size systems, coupled to an external heat reservoir (a typical model of a canonical MD simulation) can be found elsewhere 125 (Cuendet, 2006;Schöll-Paschinger and Dellago, 2006). Besides free energy differences, steered MD can also be used to re-4 https://doi.org/10.5194/acp-2021-488 Preprint. Discussion started: 17 June 2021 c Author(s) 2021. CC BY 4.0 License. construct free energy profiles using different reweighting schemes (Gore et al., 2003). The reweighting is necessary as every "pulling simulation" relies on attaching a harmonic spring to the molecular system in the direction of the reaction coordinate (s(x, t))). This signifies adding an external time dependent bias (V [s(x, t)]) to the Hamiltonian (H 0 (x, t)) of the systems whose coordinates are denoted by x, yielding a perturbed Hamiltonian (H(x, t) = H 0 (x, t) + V [s(x, t)]), which does not correspond 130 to the unbiased statistical mechanical ensemble in question (Tuckerman, 2010). In this work we use the scheme introduced by Hummer and Szabo (Hummer and Szabo, 2001): where ... denote averaging over parallel realizations.
According to the second law of thermodynamics, it is only possible to provide an upper estimate of the equilibrium free 135 energy related to a process from the work performed, and the equality between work and free energy holds only in the idealised case of transitions that occur at vanishing velocity. Equations based on Jarzinksy's equality (Gore et al., 2003) can infer free energy profiles from work profiles accompanying the transition that occurs at finite speed. Jarzinsky's equality ensures that while the individual trajectories, from which the work along the time dependent reaction coordinate (s = s(t)) is estimated, drive the system out of equilibrium, the free energy difference is calculated from ensemble averages over the microstates 140 that describe a thermodynamic states along the path (Tuckerman, 2010). Thus instead of a single ideal thermodynamically reversible path, the free energy is estimated from a large number of irreversible pathways (that mimick the realistic uptake process) which are weighted according to their distance from the idealised path in the free energy representation. Jarzinsky's equality yields an estimate of the equilibrium free energy regardless of the velocity of the transition albeit based on a physically realistic set of sample processes.

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In practice, Jarzinsky's equality and steered molecular dynamics have been successful at examining finite speed transitions between two states of a molecular system, e.g.: protein or nucleic acid unfolding (Park and Schulten, 2004;Gore et al., 2003).
The timescale associated with a single water uptake event (impinging plus transport from the surface to the bulk) is ∼ 10 ns, surface residence times are ∼ 1 ns (Bzdek and Reid, 2017). These timescales are matched by the length of individual realizations in our steered MD simulations. Additionally, initializing each realization (out-of-equilibrium simulation) from different 150 starting configurations (Section 2.2) allows impact to happen at any point of the surface, thus incorporating thermodynamically suboptimal pathways -which have finite probability in experiments -are well represented in the sample. This approach confers an advantage for estimating the free energy profile compared to quasi-equilibrium approaches (i.e., umbrella sampling) in which the free energy represents the minimum energy pathway due to the time permitted for sampling the surface. In our systems, finite velocity pulling allows to sample transport through humps and wells of the corrugated intrinsic interface (Sec-155 tion 3.1.1). These corrugations represent thermodynamically different environments (Bartók-Pártay et al., 2008;Darvas et al., 2010a) for contact formation upon impact, and hence different transport pathways which can be relatively far away from the equilibrium one, but occur in real events with a finite probability. Note that exploring suboptimal pathways of interfacial mass transfer can be even more important in modeling transport through multicomponent surface films with heterogeneous lateral distributions. The steered MD method is illustrated in Figure 1. A sample steered MD trajectory is available as video supplement (https: . a) Example of the evolution of a steered MD simulation. b) Schematic summary of the free energy reconstruction protocol.

Simulation details
Steered MD simulations were performed using the GROMACS 5.1.3 program package (Abraham et al., 2015). The PLUMED 2.5 plugin (Tribello et al., 2014); was used to implement and control the steered MD simulations. The system consisted of 165 a rectangular slab containing 5000 water molecules enclosed between two multilayers of hydroxy cis-pinonic acid (h-CPA), each of 125 molecules. The liquid slab was surrounded by a vapor phase from both sides ( Figure 1). The average widths of the layers along the Z axis of the simulation box being ∼ 6.5 nm, ∼ 2.5 nm and ∼ 6 nm for water, CPA and the vapor phase, respectively. The protocol to create and equilibrate such interfacial systems is described elsewhere Darvas et al., 2011b). A single water molecule is placed in the vapor phase of the preequilibrated interfacial system and pulled towards 170 the middle of the aqueous phase along the reaction coordinate (s(x, t)) -defined as the interface-normal (Z) component of the distance connecting its center of mass to that of the aqueous phase by harmonic bias having a force constant of k=1000 kJ mol −1 nm −1 . This condition satisfies the stiff spring approximation which enables the system to closely follow the path of the reaction coordinate by becoming the dominant force in the total dynamics Hummer and Szabo (2001).
100 parallel 6 ns-long realizations are performed at two temperatures, 200 and 300 K on the NVT (canonical) ensemble.

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The length of the simulation and the distance covered in the direction of the reaction coordinate results in an average pulling velocity of 1.2 nm ns −1 . The realizations differ in the initial position of the gas phase water molecule in the X,Y plane parallel to the surface of the liquid slab, and in the random seed which is used to set initial velocity distributions. The choice of pulling velocity is a crucial point in setting up the simulation. It should be low enough to ensure that final and initial states represent the equilibrium distribution (Tuckerman, 2010), and also to yield numerically treatable forces. On the other hand, it has to be large enough to be drive the dynamics of the system, and finally too low transition velocities will undersample higher work pathways.Temperature is kept constant by means of the V-rescale thermostat (Bussi et al., 2007). Water molecules are described by the TIP4P water model (Jorgensen et al., 1983) and h-CPA molecules by the OPLS potential (Jorgensen and Tirado-Rives, 1988). Alkyl groups are treated as united atoms, while other hydrogens are treated explicitly. Long range electrostatics are accounted for by the particle mesh Ewald method (Essmann et al., 1995) beyond a cutoff of 1 nm, while 185 Lennard-Jones interactions are smoothly truncated to zero beyond the same cutoff.

Results and discussion
Free energy profiles are interpreted in terms of the local characteristics of the simulated systems and a detailed mechanism of water uptake is proposed. The decomposition of the free energy profiles into enthalpic and entropic contributions allows us to identify the thermodynamic drivers of interfacial mass transfer of water. The effect of the complex water uptake mechanism on 190 particle growth and activation is then assessed by estimating interfacial transfer coefficients. Implications for droplet formation are then discussed in the light of partitioning timescale estimates, intraparticle distribution of water within the organic shell, and equilibrium saturation ratios.

Structural and thermodynamic characteristics
3.1.1 Intrinsic density profiles

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Local nanoscale fluctuations of fluid interfaces from capillary waves create surface corrugations (Rowlinson, 1982) whose amplitude varies between 0.3 and 1 nm depending on the chemical composition of the surface Darvas et al., 2011a). These corrugations do not average out during typical timescales of interfacial mass transfer of a water molecule and are enhanced when a molecule crosses the interface (Benjamin, 1993;Karnes and Benjamin, 2016;Benjamin, 2019). phase. Organic density profiles reveal that the thickness of the organic phase is ∼ 1.8 and ∼ 2.1 nm at 200 and 300 K, respec-tively, measured at 5% of the average height of the profile. It is sufficient to accommodate a disordered multilayer, but is too low to allow the formation of a bulk phase. The lack of a bulk phase is evidenced by the two neighboring peaks -characteristic of interfaces -in the density profile of the organic phase with no plateau at the bulk phase density (1.2 g cm −3 ) in between. A ∼ 85% local drop in the total density (sum of water an organic density) compared to that of bulk aqueous phase can be observed 215 at the Gibbs dividing surface of the two condensed phases at both temperatures. The affected region is wider at 300 K. The aqueous phase has two consecutive peaks characteristic of the first two molecular layers, followed by a bulk phase plateau.
The interface and subsurface structure are similar, but more pronounced at 200 K as result of reduced thermal motion which preserves layered structure at low temperatures. The interfacial region is characterized by an overlap between the organic and the water density profiles which is due to partial miscibility of the two phases. The width of this mixed region is 1.5 nm at 300 220 K and 1.2 nm at 200 K disregarding the small peak of organics in the bulk aqueous phase.

Free energy profiles
Helmholtz free energy profiles, which represent the thermodynamic state function on the canonical ensemble. While the Helmholtz free energy is formally different from the experimentally determined Gibbs free energy, in systems containing incompressible condensed phases the additional p∆V term is negligibly small; thus the two quantities can be assumed to be 225 the same within a small error. Free energy profiles with the reference state assigned to the bulk aqueous phase are shown as black solid lines in Figure 2 a) and b). Profiles are significantly different at the two temperatures which suggests that mechanism of gas-to-particle partitioning in LLPS particles is temperature dependent. Despite differences, simulations show two common characteristics: i) the negative free energy difference (∼ −14 kJ mol −1 at 300 K and ∼ −11 kJ mol −1 at 200 K) between the bulk aqueous and the vapor phase, which underlines that overall water uptake from the vapor phase is thermodynamically 230 favored, and, ii) the lack of a free energy barrier at the vapor/organic interface, which is the main difference between free energy profiles of transfer through hydrophobic media, for which large maxima have been observed leading to reduced surface accommodation coefficients (Sakaguchi and Morita, 2012;Ergin and Takahama, 2016).
The free energy profile at 300 K begins with a plateau characteristic of the vapor phase, followed by a steep decrease (∼ 5 kJ mol −1 ) at the vapor/organic interface. A monotonic decrease in the free energy profile characterizes the transfer of the 235 water molecule in the organic phase. The lack of a plateau is related to the fact that the organic layer is not thick enough to accommodate a bulk phase, which results in a position dependent anisotropy caused by the proximity of both interfaces in combination with the partial dissolution of the water in the organic phase, evidenced by non-zero water density up to s≈ 3.5 nm.
The presence of dissolved water molecules results in the increased slope of the profile near the water/organic interface. The free energy profile has a local minimum at the organic/water interface, and a global maximum (∼ 15 kJ mol −1 ) corresponding to the 240 first molecular layer of water, seen as a peak in the intrinsic density profile. A second peak and a smoothly decreasing region follow. The free energy profile at 200 K is considerably smoother; the magnitude of none of the features exceeds the energy of thermal motion (3/2k B T ) at the corresponding temperature, thus any small local minimum or maximum can be viewed as statistically insignificant. The minimum and the peak at the organic/water interface characteristic of the room temperature profile cannot be observed at low temperature. While vapor-to-organic transfer is a favorable and barrierless transition at both 245 temperatures, the transport between the organic shell and the core is hindered by the presence of the free energy barrier at 300 K, which diminishes at low temperature. Large temperature induced differences suggest that the thermodynamic driving forces are strongly temperature dependent. One possible explanation is that they are of entropic natrure, and their strength is explicitly scaled by the temperature through the −T ∆S term.

Internal energy and entropy profiles 250
To understand the thermodynamic drivers of water uptake, free energy profiles are decomposed into entropy and internal energy profiles shown in Figure 3. The sum of the interaction energies of the pulled water with the surrounding molecules is used as a surrogate for the internal energy, the calculation is described in details in Appendix B. The total entropy profile is obtained by subtracting the internal energy profile from the free energy profile, and some distinct contributions to the total entropy are calculated for a randomly selected realization (Appendix A). Internal energy profiles are smooth and show a similar overall behavior at the two temperatures. A small drop in the internal energy whose magnitude is ∼ 3 kJ mol −1 and ∼ 5 kJ mol −1 at the 200 and 300 K respectively indicates the formation of contact with the organic phase. It is however not sufficiently low compared to the internal energy observed in the subsequent bulk organic phase to energetically stabilise a surface adsorbed state. Both internal energy profiles have a plateau spanning the outer half of the organic phase, where water molecules from 265 the bulk aqueous phase do not penetrate. This is followed by a smoothly decreasing part which corresponds to the pulled molecule forming an increasing number of hydrogen bonds with both h-CPA and the water molecules dissolved in the organic phase. Near the organic-water interface and in the aqueous phase the internal energy profiles are close to identical at the two temperature, suggesting that specific features of the free energy profile are of entropic origin.
Total entropy profiles (Figure 3 b) bear all the features that appear in the free energy profiles and their shape is different at 270 the two temperatures. In the followings these profiles are further decomposed into specific terms: configurational, interfacial, conformational and orientational entropy. Configurational entropy profiles calculated using Schlitter's formula (Baron et al., 2006) as explained in Appendix B are close to constant throughout the condensed phase, −T ∆S config = 25 kJ mol −1 at 300 K and 14 kJ mol −1 at 200 K. They are thus not responsible for any of the features in the free energy profiles. Interfacial entropy (T ∆S IF ) at the vapor/organic interface is approximately 5 kJ mol −1 at 300 K and is negligibly small at 200 K (Appendix B).

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Despite of the positive value of interfacial entropy the overall entropy difference between the vapor and the organic phase is a small negative value, which -together with the moderate change in enthalpy at the interface -is responsible for the lack of surface adsorbed states. A possible explanation for the overall negative entropy is the ordering of the organic molecules at the surface which reduces orientational degrees of freedom in a similar manner as described later for the water/organic interface.
Conformational entropy profiles, calculated from the mole fraction profiles of the water and the organic molecules (Appendix 280 B), are shown in Figure 3 c). They exhibit a peak located at the organic/water interface at both temperatures and are close to zero elsewhere. These peaks represent the effect of non-ideal local mixing of two phases in this region. The conformational entropy peak is slightly higher at 300 K, mostly due to the higher temperature. This and the local ∼ 85% decrease in the total density in this region explain the presence of the free energy minimum at the organic/water interface. Lower density ensures the reduction of steric hindrance for any conformations without loosing hydrogen bonds. These explain the minimum 285 in the free energy profile observed at the water/organic interface at 300 K. High conformational degrees of freedom manifest in subsequent detaching/attaching of the pulled molecule between the organic and aqueous phase in varying orientations, which can be observed only in the 300 K simulations (video supplement available). The conformational entropy profile peak in the interfacial region is significantly (∼ 40%) smaller at 200 K. Additionally, the low density region is narrower due to the pronounced shoulder in the water density profile (Figure 2), thus steric effects are not as effectively reduced as at 300 290 K. The joint decrease of the magnitude of both contributions leads to the disappearance of the free energy minimum at the organic/water interface at 200 K.
Increased orientational order of molecules at interfaces of molecular liquids locally reduces orientational entropy, which is responsible for the free energy peak coinciding with the first two molecular layers of water in the 300 K simulations. Interfacial to an external axis. The peak shows that in the first layer water molecules tend to lie parallel to the surface, whereas the bulk phase distribution shows no significant preferences. Increased orientational order results in a decrease in orientational entropy, corresponding to the maximum of the free energy profile. The second layer of water has similar orientational preferences (Appendix B), which explains the subsequent smaller free energy peak. Similar results are found for 200 K (Appendix B), thus the observed temperature dependence results again from the explicit scaling of the importance of entropy with temperature.

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Orientational entropies are also estimated in 1 dimension (Appendix B), but due to symmetry reasons they do not give a quantitative description of the ensemble of ordering effects.

Generalization of the driving forces
The question whether the thermodynamic driving forces identified in the previous section are system specific or generalizable over a wider range of compositions that can yield LLPS particles is important for determining the level of confidence with 310 which implications to atmospheric aerosol can be stated based on these simulations. The most prominent characteristics of the free energy profiles are i) the lack of a minimum at the vapor/organic interface, ii) the minimum at the organic/water interface and iii) the maximum corresponding to the first layer of the aqueous phase.
Experimental and molecular simulation studies show that driving forces which lead to the appearance of these features are generally present in interfacial systems involving molecular liquids or solids. i) The value of the free energy at the vapor/organic 315 interface is moderated by the increased order of organic molecules which has been observed from experiments and simulations in pure water (Cipcigan et al., 2015), pure organics (Darvas et al., 2010a) as well as in concentrated (Darvas et al., 2010b) and dilute aqueous organic solutions (Takamuku et al., 1998;Pártay et al., 2008;Pojják et al., 2010;Ghatee et al., 2011;Makowski et al., 2016). ii) The density drop in the interfacial region and the enhanced local mixing which invoke the free energy minimum at the organic/water interface at 300 K are characteristic of any liquid/liquid interface Jorge et al., 2010;320 Darvas et al., 2011b320 Darvas et al., , 2013. The extent of local mixing is trivially determined by the hydrophilicity of the organic compound.
iii) Orientational preferences of water molecules near liquid/liquid or liquid/solid interfaces, which account for the maximum of the free energy profiles are also generally present in interfacial systems. They have been observed in molecular simulations several times at various liquid/liquid interfaces such as carbon tetrachloride/water Kertész et al., 2014) or dichloroethane/water  and proved to be enhanced next to a solid counter phase (Kertész et al., 2014).

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The strong temperature dependence follows directly from the entropic nature of these driving forces and the definition of the free energy, consequently besides the presence of the driving forces, their temperature dependence is also expected to be generally valid. LLPS is known to form if the O:C<0.8, the organic components in the examples listed above cover the complete O:C ratio range. Thus our findings are likely not system specific, and represent a typical behavior for sparingly soluble organic compounds present in the atmosphere, although exact values of the thermodynamic quantities can vary from system to system.
The following implications are thus quantitatively only valid for the water/h-CPA/vapor system, while qualitatively similar behavior can be expected for a wider variety of LLPS forming cases.
3.2 Implications for water uptake and particle growth kinetics

Interfacial transfer coefficients
Interfacial transfer coefficients are estimated from the activation free energies characteristic of the vapor-to-organic (k v/o ), 335 organic-to-water (k o/w ) and vapor-to-water (k v/w ) transfer using the transition state theory as: where i and j indicate the phases forming the interface in question. The corresponding activation free energies are illustrated using the 300 K free energy profile in Figure 4 a). While the transfer coefficient calculated here is conceptually different from the mass accommodation coefficient used in atmospheric applications, chemical kinetic frameworks are widely used to estimate 340 α from free energy profiles (Grote and Hynes, 1980;Taylor and Garrett, 1999;Truhlar and Garrett, 2000;Sakaguchi and Morita, 2012;Ergin and Takahama, 2016). We note that due to the lack of a well-defined bulk phase plateau in the organic phase we choose an average free energy characteristic of the middle of the organic phase as a reference value. This choice is arbitrary and a different definition may slightly modify obtained transfer coefficients, albeit without significantly altering values, trends and conclusions. Vapor-to-organic (surface) transfer coefficient (k v/o ) are near unity at both temperatures, whereas organic-345 to-water (core) transport is characterized by k o/w = 0.05 at 300 K, and k o/w = 1 at 200 K. To complete the analysis, we also estimate a hypothetical transfer coefficient of the uptake of water from the vapor phase by the aqueous core disregarding the organic phase, k v/w which is equal to 0.38 at 300 K and unity at 200 K.
The vapor-to-organic transfer coefficients resemble most closely the commonly used definition of the mass accommodation coefficient, which considers either adsorption at the surface or absorption in the first few molecular layers of the particle phase 350 as the final state of gas-to-particle partitioning. Due to the lack of maxima or minima at the vapor/oragnic interface, in our systems surface adsorbed states of the water are thermodynamically indistinguishable from those with the water absorbed by the subsurface region.
(a) The organic-to-water (k o/w ) and vapor-to-water transfer coefficients (k v/w ) are reduced compared to the mass accommodation coefficients (k v/o ) at room temperature owing to the free energy barrier corresponding to the first molecular layer of 355 water. As opposed to mass accommodation coefficients which show no temperature dependence, k o/w and k v/w follows a similar trend with temperature as that observed for water uptake on a hexadecanol monolayer (Davies et al., 2013), and on pure water (Davidovits et al., 2004). k o/w describes the lower bound of the probability of a gas phase water molecule being absorbed by the aqueous core of the phase separated particle. k v/w represents an upper bound of the same probability. The two values thus define the range of core uptake coefficients. The fact that core uptake coefficients differ significantly from mass 360 accommodation coefficients highlights the possibility that the traditional representation of water uptake by a single value of α or an effective uptake coefficient may have to be complemented by a temperature-dependent core uptake term to fully describe water uptake by phase-separated aerosol.
globally representative values proposed in modeling studies (Raatikainen et al., 2013), as well as with recent experiments which report large mass accommodation coefficients (Liu et al., 2019) and unhindered gas-to-particle partitioning of water and organics in phase separated particles (Gorkowski et al., 2017). While global datasets of CCN concentrations can usually be described by 0.1 < α < 1, implying uninhibited water uptake (Raatikainen et al., 2013), compressed hydrophobic organic films can result in mass accommodation coefficients as low as 0.001. In such systems, α is correlated with the integrated carbon In this framework, near-unity mass accommodation coefficients obtained from our simulations at both temperatures are not expected to alter droplet number concentrations, further supporting that kinetic delays do not explain the increased CCN activity of LLPS aerosol.

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Hindered mass transfer of water between the organic shell and aqueous core together with uninhibited mass accommodation of water in LLPS aerosol results in different condensational growth rates of the core and shell, leading to a dynamic retention of water by the organic shell. We use the k v/o /k o/w ratio to estimate the extent of dynamic retention of water by the organic phase.
The value is approximately unity at 200 K, and about 20 at 300 K. The growth rate of the organic shell is thus substantially larger at 300 K than that of the core, which in agreement with results of multilayer kinetic model (KM-GAP) calculations 390 which also evidence faster condensational growth of the particle shell than of core (Shiraiwa et al., 2013). This suggests that the aqueous core contains less water and the organic shell is more dilute at any time during growth of the particle than predicted assuming that mass transfer kinetics can be described by a single α.
Retention of water in the organic shell due to reduced core uptake coefficient (organic-to-water or vapor-to-water transfer coefficient) may affect equilibrium properties (vapor pressure and surface tension) which determine cloud droplet growth and 395 activation. Increased water content of the organic shell can increase vapor pressure and surface tension, which both affect cloud droplet growth and activation. In the extreme case, inhibited transport between the shell and the core, indicated by reduced core uptake coefficients, may invoke swelling and -depending of the solubility of the organic compounds -dissolution of the shell. These hypotheses can be relevant if the vapor phase is in dynamic equilibrium with the organic shell containing an increased amount of water and this equilibrium is unaffected by the presence of the aqueous core, in other words water 400 uptake happens only by the shell. For this condition to hold gas-to-particle partitioning timescale of water (τ s ) should be significantly shorter than timescale of transfer from the shell to the core (τ c ). Timescales are estimated as the e-folding times of condensation-evaporation, assuming that both gas-to-particle and shell-to-core partitioning can be described as (Saleh et al., 2013):

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where F = (1+Kn)/(1+0.3773Kn+1.33Kn(1+Kn)/α) is the Fuchs-Sutugin correction factor, with Kn being the Knudsen number and α the transfer coefficient of the given process. For gas-to-particle partitioning Kn = 10 −2 , 10 −1 , 10 0 , α = 1, the gas phase diffusion coefficient of water is estimated at 0.26 cm 2 s −1 and 0.128 cm 2 s −1 at 300 and 200 K (Pruppacher and Klett, 2010), while d is the diameter of the particle (100 nm). For core-to-shell partitioning Kn is approximated as the ratio of the diameter of the h-CPA molecules and the width of the organic layer, α = k o/w in one set of calculations and α = k v/w 410 in another set, d is the core diameter, and the diffusion coefficient (D) is varied between 10 −3 and 10 −8 cm 2 s −1 . The ratio between the core and the full particle diameter is the same as the ratio of the width of the organic shell and the total system width.
Assuming the particle number concentration (N ) to be 1000 cm −3 , the equilibration timescale of gas-to-particle partitioning τ s is on the order of 1-2 minutes, similar to timescales reported for the equilibration of semivolatile molecules (Saleh et al., 2013). τ c /τ s > 10 3 in every case ( Figure 5); thus the hypothesis of equilibrium between the organic shell and the vapor phase 415 holds for our system at both temperatures and the water uptake by the particle core is somewhat hindered. The ratio of the timescales is at least three orders of magnitude even when the core and shell uptake coefficients are assumed to be both unity (200 K), owing to the difference between gas and particle phase diffusivity. Reduced core uptake coefficients further increase this difference by orders of magnitude depending on whether the upper (k v/w ) or the lower (k o/w ) estimate of the core uptake coefficient is used. In summary, as expected the equilibration timescale of gas-to-particle partitioning is sufficiently short to 420 assume equilibrium between the vapor phase and the organic shell, while core uptake may not reach equilibrium within a typical model of cloud updraft. Figure 5. The ratio of characteristic timescales of shell-to-core and gas-to-particle partitioning as function of bulk phase diffusivity of the water in the organic shell at varying gas phase Knudsen numbers and temperature. At 300 K model calculations are presented using both the lower and the upper of the core uptake coefficient.

The effect of bulk diffusion and non-uniform concentration distribution
The non-negligible free energy difference between the vapor/organic and the organic/water interface potentially alters the above described uniform increase of the water concentration in the shell and carries consequences for droplet growth and activation.

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A more detailed understanding of these effects can be obtained by converting the free energy profile using the expression ∆G(s) = −k B T ln c rel (s) into a probabilistic density profile c rel (s), which corresponds to an equilibrium concentration profile of the condensing water in the organic phase at arbitrary values of the vapor pressure. This equilibrium concentration profile is calculated under the assumption of instantaneous diffusion and bears no information about the surrounding relative humidity (RH), and is valid for a mostly-organic shell (as the free energy profiles were derived for pulling simulations of single water 430 molecules). The effect of non-instantaneous bulk phase diffusion of water and RH are accounted for by a correction factor, f : C v and D p are the vapor phase concentration of water and the bulk phase diffusion coefficient of water in the organic phase, respectively, ω is the mean thermal velocity of water in the vapor phase, α is the mass accommodation coefficient, and ρ p is the density of the organic phase (1.2 g cm −3 in our calculation). The correction factor was adapted from Shiraiwa and 435 Pöschl (2020), who derived an expression to account for the effect of diffusivity on gas-to-particle partitioning by introducing a penetration-depth-dependent definition of the mass accommodation coefficients of organic molecules absorbed by aerosol particles used in particle growth kinetic models (Shiraiwa et al., 2012).  Figure 6 shows the equilibrium diffusion-corrected concentration profiles at RH=95% at 300 K (a) and at 200 K (b). Condensing water molecules show a strong preference to be accommodated near the organic/water interface, while the vicinity of 445 the vapor/organic interface is depleted in water at 300 K ( Figure 6) a)) for bulk phase diffusion coefficient values characteristic of the liquid phase (10 −3 < D p < 10 −9 cm 2 s −1 ). A much less pronounced concentration gradient, about an order of magnitude smaller than that found at room temperature, can be observed at 200 K if liquid phase diffusivities are assumed. The effect of diffusion is negligible in the 10 −3 < D p < 10 −6 cm 2 s −1 diffusivity range. The steepness of the concentration gradient is reduced by 40 and 85% for D p = 10 −7 and D p = 10 −8 cm 2 s −1 at 300 K, and by 30 and 82% for D p = 10 −8 and D p = 10 −9 450 cm 2 s −1 at 200 K. Slow diffusion in highly viscous liquid and semisolid states (D p < 10 −10 cm 2 s −1 ) cancels the effect of thermodynamic preferences, and result in uniform concentration profiles at both temperatures. Concentration profiles are not sensitive to varying RH, thus only one characteristic example is shown in Figure 6. Water's diffusion coefficient in h-CPA is estimated from separate unpublished MD simulations to be 10 −5 − 10 −6 cm 2 s −1 at 300 K depending on concentration, and 2015). This means that room temperature concentration profiles are virtually unaffected by bulk phase diffusion, as liquid-like diffusivities apply. Diffusion control is only probable for diffusion coefficients characteristic in semisolid particles. At 200 K, the originally small concentration gradient is further reduced by slow diffusion. Bulk phase diffusion becomes the governing process for water uptake at low temperatures, regardless of the assumed value of the diffusion coefficient.
The quantitative description is only valid for the system studied and magnitudes may vary as a function of the composition of 460 the organic shell. However, like main driving forces of the water uptake process, the formation of the concentration gradient can be expected in generic LLPS particles regardless of their actual chemical composition. The shape of the concentration profiles may change for a thicker organic layer having a bulk phase corresponding to a constant plateau in the free energy profile, which converts into a constant concentration region in the middle of the organic phase. Nevertheless, the maximum of the concentration profile coincides with the minimum of the free energy profile at the organic/water interface, which is determined 465 predominantly by local entropy increase due to the lower density and increased conformational degrees of freedom, which is universal at boundaries between condensed phases. Similar considerations are valid for the minimum of the concentration profile, which is observed at the vapor/organic interface, whose value mainly depends on an interplay between intermolecular interactions, orientational order of the vapor/organic interface and interfacial entropy, which are largely insensitive to the thickness of the organic phase. The significant enrichment of the water/organic interfacial region in water may lead to a local 470 dissolution of the organic phase. However, even when dissolution of the organic phase occurs, the strong preference of water molecules to be accommodated in the inner part of the organic shell results in depleted water concentrations at the surface, which ensures the presence of an organic rich film at the surface, and hence maintains low surface tensions despite of the elevated water concentration in the organic shell even when relative humidity approaches 100%. This is consistent with recent experiments and model calculations which conclude that LLPS persists up to very high relative humidities (Liu et al., 2018).

Equilibrium saturation ratios
The dynamics of water uptake affects the composition profile within the particle, hence the equilibrium vapor pressure of water over its evolution. For instance, kinetic hindrance of water molecules moving between organic shell and aqueous core will lead to higher water content in the outer shell than one in which such hindrances do not exist. Concentration profiles of water within the shell affect the water mole fraction and also droplet surface tension. Based on the findings from previous sections, three 480 distinct scenarios through which LLPS may affect equilibrium saturation ratios of water are considered (Table 1). Given a fixed mass of dry substance, we use Köhler theory to calculate differences in equilibrium saturation ratios based on these assumptions how the driving force for water vapor condensation may be affected by chemical distribution and transport dynamics within an individual particle. Scenario (i) is valid at 300 K until the overall water concentration in the shell becomes too large for the  (Hyvärinen et al., 2006) * * γ = 60 mN m −1 (Hyvärinen et al., 2006) † γ = 72 mN m −1 (Vargaftik et al., 1983) gradient to prevent the formation of a well mixed aqueous layer at the surface. Scenario (ii) is a model of the 200 K behavior as 485 well as that of 300 K from the point where the concentration gradient cannot prevent the presence of a non-negligible amount of water in the surface layer. Scenario (iii) is a hypothetical case that provides a lower bound on the water content in the shell. Scenario (iv) provides a base case where the distribution of species are considered to be homogeneous throughout the particle. Köhler curves for 50 nm dry diameter particle containing 90% organic with 10% salt ((NH4)2SO4). The inset shows Köhler curves for a dry particle which contains organics only. Black curve: well mixed case; blue curve: scenario 1 (hindered core uptake with concentration gradient); red curve: scenario 2 (hindered core uptake without concentration gradient); yellow curve: scenario 3 (unhindered core uptake without concentration gradient) Köhler curves are calculated for particles having a 50 nm dry diameter consisting of 90% organic compounds and 10% ((NH 4 ) 2 SO 4 ) and 100% organic with no salt (Figure 7). LLPS always tends to lower the critical supersaturation (S c ) and 490 increase the critical diameter (d c ) compared to what is found for the well mixed case (iv). The lowering of the S c ∼ 0.05 % is the least pronounced if LLPS is preserved but only shell growth occurs, which is the scenario (iii) which describes the effect of hindered core uptake without concentration gradient. A moderate lowering of S c ∼ 0.25% is found for the scenario in which LLPS maintains moderate surface tension (the surface is a saturated mixture of h-CPA and water) with uniform core and shell growth, that non-hindered core uptake (ii). Finally, S c is the lowest if the concentration gradient is taken into account 495 (by assuming a pure organic surface) (i), in this case the critical supersaturation is reduced by ∼ 0.35%. Trends are largely similar but more pronounced if the aqueous phase is assumed to contain only organics. In summary, LLPS -as a result of lower surface tensions characteristic of a saturated mixture -reduces critical supersaturations, while kinetic hindrance of the core uptake acts in the opposite direction since it increases the mole fraction of water in the organic shell. However, the concentration gradient and the resulting low surface tension characteristic of a pure or nearly pure organic surface imparts a 500 strong effect, and invoke the strongest reduction in S c compared to the well mixed case among all the investigated scenarios.

Conclusions
Steered MD simulations of water uptake by a model LLPS aerosol particle consisting of a hydroxy-cis-pinonic acid surface layer and a pure aqueous core at two temperatures corresponding to the boundary layer (300 K) and to the top of the troposphere (200 K) were performed to investigate the mechanism of water uptake by LLPS aerosol via detailed analysis of the free energy profiles of the corresponding transfer process. In particular, the following questions were addressed: i) How does the uptake mechanism depend on temperature? ii) To what extent and under what conditions can water uptake by particles containing internal interfaces be described with a single uptake coefficient? iii) What role does the internal interface play in the water uptake mechanism? iv) How can the relationship between non-ideal mixing in LLPS particles and their increased CCN activity be explained on a molecular level? 510 These questions are answered using a novel combination of free energy profiles of interfacial transfer estimated from steered MD simulations and intrinsic surface analysis, which removes artificial smoothing and systematic errors caused by thermal fluctuations of liquid surfaces from estimates in interfacial properties and density profiles. Free energy profiles together with their entropic and energetic contributions were used to determine the water uptake mechanism, map the effect of the presence of an internal surface on the shape of the free energy, energy and entropy profiles and identify main thermodynamic driving 515 forces behind the observed mechanism. Using steered MD in this context presents an advancement over previous approaches.
The choice of the method can be rationalised by considering that each finite velocity pulling simulation used for estimating the free energy based on Jarzinsky's equality closely mimicks one realistic interfacial mass transfer event. The ensemble averaging ensures that a variety of potential pathways is included in the free energy estimate. Implications for realistic atmospheric processes were presented in the form of model calculations that link the molecular scale mechanism to the increased CCN 520 activity of LLPS aerosol quantitatively for our model system and qualitatively for generic LLPS particles.
Our findings can be summarized as follows: i) The mechanism of water uptake (the shape of the free energy profile) is strongly temperature dependent. All minima and maxima can be attributed to entropic contributions, the minimum at the organic/water interface is due to a local maximum of the conformational entropy, while the subsequent maximum is a consequence of increased ordering of the water molecules in the first molecular layer of the aqueous phase. Due to the explicit 525 temperature dependence of the weight of the entropy term in the free energy profile, features disappear at low temperature, however structural properties shaping entropy profiles are generally present in liquid/liquid and liquid/solid interfacial systems arbitrary composition. ii) Mass accommodation (vapor-to-organic transfer) coefficients were found to be near unity at both temperatures, which is in accordance with globally representative values. The core uptake (organic-to-water transfer) coefficient is reduced at room temperature (k o/w =0.05), while at low temperature k o/w =1. This suggests that a single uptake coefficient 530 is sufficient to describe the water uptake mechanism at 200 K, while core uptake might have to be taken into account for the higher temperature. iii) Model estimates of shell and core uptake timescales revealed that depending on the particle phase diffusion coefficient shell uptake is at least four orders of magnitude faster that of core transfer. The slow diffusion of water in the organic shell can cause water to accumulate in the shell. This difference is further increased by 1-2 orders of magnitude if core uptake coefficient as a result of interfacial ordering of water molecules, leading to even more retention of water in the 535 organic shell. iv) Converting free energy profiles into diffusion corrected concentration profiles allowed us to determine how molecular scale non-idealities in the solution structure can lead to enhanced surface activity. The molecular-scale explanation of the effect of non-ideal mixing on CCN activity lies in a non-uniform distribution of water molecules within the organic shell observed for liquid particles at 300 K. The concentration distribution has a maximum near the organic/water interface, indicating that the condensing water molecules tend to accumulate near the aqueous phase and leaves the surface depleted in water. In other words, the observed concentration gradient maintains low surface tensions (nearly pure organic surface) and the LLPS state even when RH approaches 100%. Köhler calculations reveal consequent reduced surface tensions are able to compensate the unfavorable effect on hindered core uptake on critical supersaturations.
In summary, our results point out that a single uptake coefficient is sufficient to describe water uptake in LLPS aerosol at low temperature, while at room temperature the models based on the complete uptake mechanism might be preferred. The 545 effect of non-ideal mixing -usually accounted for in the form of Flory-Huggins parameter in continuum model calculations -are attributed to non-uniform distributions of the condensing water which maintain surface tension at low values even at high RH. The generalizability of thermodynamic driving forces suggests that the development of detailed models of aerosol growth kinetics incorporating these findings is possible, when combined with more rigorous and quantitative studies.
The strong temperature dependence of the water uptake mechanism, core uptake coefficient, as well as the presence non-550 uniform distribution of water within the organic shell at room temperature suggest that a detailed description of water uptake including these effects in a temperature dependent manner is necessary to improve aerosol growth kinetic models. The driving forces responsible for the typical features of the free energy profiles are generally valid for a wide range of liquid/vapor,liquid/liquid and liquid/solid surfaces. They presumably depend only weakly on the chemical nature of the organic compounds, which suggest that developing such a parametrization is feasible.

A1 Intrinsic surface analysis and intrinsic density profiles
We label molecules of the organic/water interface in a time resolved manner using the ITIM method (Sega et al., 2018). ITIM selects interfacial molecules by solely geometric criteria, thus it is considerably faster than alternative methods with essentially no loss in accuracy (Jorge et al., 2010). The ITIM method uses a probe sphere with a radius determined from the position of the first peak of the corresponding radial distribution functions, in our case a value of r = 0.2 nm is used. The probe sphere 565 is moved along a grid of testlines (a 200 × 200 grid is used in our analysis) perpendicular to the macroscopic plane of the interface. Once the probe sphere touches a an atom, the molecule to which it belongs to is labeled as interfacial. Contact is determined based a Pythagorean criterion. The list of surface molecules allows for selective estimation of various properties of the surface and the bulk and provides a means to reconstruct the intrinsic density profiles:

570
where A is the macroscopic surface area of the interface, x i ,y i and z i are the Cartesian coordinates of the atoms constituting the system and z is the position with respect to the local interface. ξ(x i , y i ) ∼ kT /q 2 is the capillary wave mode spectrum, with q being the wave vector. In simple terms intrinsic density profiles are anchored to the first molecular layer of one of the condensed phase (the aqueous phase in our case), instead of being calculated along an external grid, thus they are able to resolve the near-surface fine structure of the density profiles which are otherwise washed away by capillary wave fluctuations.

575
Intrinsic number density profile are used to compare free energy profiles with in a qualitative manner. The ITIM algorithm in particular allows for the separation of the surface molecules from those belonging to the bulk, and thus repeating the algorithm on the remaining bulk phase molecules can yield consecutive subsurface layers.

Appendix B: Thermodynamic Analysis
The free energy profiles were decomposed into energetic and various entropic contributions in order to understand the effects 580 responsible for the features observed in the in the free energy profiles

B1 Internal energy and hydrogen bonding
The internal energy profile of the transfer process is estimated as the sum of the interaction energy between the pulled water molecule and the organic and water molecules weighted by the local mole fraction of the above two.
585 with E i (p, s) and E i (p, w) being the interaction energy between the pulled molecule and the solutes/water, calculated as the sum of short-term Coulombic and Lennard-Jones interactions (example values are listed in Table B1). x l s (s) and x l w (s) are local mole fraction profiles of the water and the organics. Local mole fraction profiles are calculated from the number of water and organic molecules found within 1 nm of the pulled molecule. The cutoff distance of 1 nm corresponds to the cutoff used in the simulations for short range interactions. This calculation is only plausible because solute/water interactions in the OPLS    The formation of hydrogen bonds is a major energetic driving force of the water uptake process. Figure B2 shows the number of total hydrogen bonds along the direction of the reaction coordinate.

B2.1 Interfacial entropy
Interfacial entropy accompanying any molecular transfer across phase boundaries can be calculated using the following formula from statistical thermodynamics (Ward, 2002): where T V and T L are the temperatures of the vapor and the liquid phase, P sat and P V are the saturated and the actual vapor pressure, v L is the specific volume of the liquid phase ω i are the vibrational frequencies and q vib is the vibrational partition function. Figure B3 shows the modeled T ∆S IF profiles at the two simulated temperatures, the values corresponding to the 605 vapor pressures in the simulation box are highlighted with asterisks. The vapor pressure in the simulation box is estimated assuming the presence of the pulled molecule only in the vapor phase, using the universal gas law.

B2.2 Conformational entropy
The conformational entropy profile is estimated as: 610 where x i (s) denotes mole fraction profiles of the components of the systems, with s being the reaction coordinate used in the steered MD simulations.

B2.3 Configurational entropy
We calculate configurational entropy according to Schlitter's formula (Baron et al., 2006), thus based on the covariance matrix ((D)) of the atomic coordinates between two distinct groups of atoms, one being the pulled molecule and the other is either the 615 ensemble of the solutes or waters constituting the bulk phase.
where h is the Planck's constant divided by 2π Two different contributions of the configurational entropy are considered i) between the pulled molecule and the solutes and between the pulled molecule and the solvents. In similar manner as for the internal energy, the weighted sum of these two yields the configurational entropy profile along the reaction coordinate (s), with 620 the weights being the local mole fractions of the water and the solute, whose calculation is described in the previous section.

B2.4 Orientational entropy
We propose an equation which can serve as a qualitative descriptor of the entropy related to the orientation of the molecules based on equations for translational (Bhandary et al., 2016) and translational-orientation entropy terms. (Piaggi and Parrinello,27 https://doi.org/10.5194/acp-2021-488 Preprint. Discussion started: 17 June 2021 c Author(s) 2021. CC BY 4.0 License. function (g(θ)) of the angle (θ) between the dipole vector of the water molecules and the surface normal axis, we obtain an expression for orientational entropy: S or = −2πk B g(θ)lng(θ) − g(θ) + 1 sinθdθ This expression is evaluated for angular distribution functions calculated in the first two molecular layers and the bulk of the aqueous phase, to highlight the effect of increased molecular order on the free energy profiles. The separation of interfacial 630 water molecules and those constituting the second layer is performed by two consecutive repetitions of the ITIM algorithm, using the output bulk phase of the first one as input for the second one. At both temperatures the bulk phase orientational entropy is higher (−T ∆S is lower) than in the first two layers due to stronger ordering in the first two interfacial layers ( Figure B4). We note that equation B5 cannot completely describe the entropy loss due to preferential ordering of the water molecules at the interface since due to its point group symmetry (C 2v ), 635 the orientation of water molecules with respect to an external vector or plane cannot be described with a single angle, instead the joint distribution of two angles is necessary. The development of an adapted expression of the orientational entropy of such cases is however out of the scope of this study. The one dimensional representation is incomplete and thus gives only a qualitative insight but the temperature dependence of T ∆S or within the layers is clear, the extension of the orientational entropy formula to multiple dimensions is part of ongoing work. To complete the description of orientational differences 640 between the surface and the bulk of the aqueous phase, we calculate joint distributions of angles cosθ' and φ, which are chosen to fully describe the orientation of water molecules with respect to the normal vector of the macroscopic surface (Bartók-Pártay et al., 2008), in the first two molecular layers and the bulk. θ' and φ are defined in a Cartesian frame centered on the water molecules, the z axis points from the water oxygen towards the midpoint of the segment connecting the hydrogen atoms, the y axis is parallel to that segment, and the x axis is perpendicular to both z and y. θ' is the angle between the macroscopic surface 645 normal vector (Z) and the molecule centered z axis, and φ is the angle between the x axis and the projection of the surface normal vector to the x,y plane.  Figure B5 shows orientational maps in the first two molecular layers and the bulk of the aqueous phase. In the first layer water molecules show a very strong preference to be aligned with dipole vectors parallel to the surface or slightly tilted towards the bulk aqueous phase, orientation I. in Figure B5 a) and c). In another distinguished orientation, which appears a remarkable difference between our system and aqueous interfaces of hydrophobic organic compounds (dichloromethane and dichloroethane) studied previously , where preferred orientations were only found in the first molecular 655 layer of water in direct contact with the organic phase, that the second layer is more ordered than the bulk phase, it is due to the fact that h-CPA mixes more readily with water then hydrophobic organics, thus h-CPA molecules can penetrate into the second and third molecular layer as well into the bulk phase, and contact with the dissolved organic molecules promotes orientations that are similar to those found at the interface. We also note that the preferred orientations found of interfacial waters are universal across a large spectra of organic/water interfaces.