Carbon Density Is an Indicator of Mass Accommodation Coefficient of

Article pubs.acs.org/JPCA

Carbon Density Is an Indicator of Mass Accommodation Coefficient of Water on Organic-Coated Water Surface Gözde Ergin and Satoshi Takahama* Atmospheric Particle and Research Laboratory, School of Architecture, Civil and Environmental Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland ABSTRACT: The condensational growth of a water droplet follows water vapor accommodation and is described by the mass accommodation coefficient, α. To determine α for droplets coated by straight chain and branched alcohols, we perform molecular dynamics simulations with umbrella sampling and direct impinging. The free energy profiles of water from gas phase to bulk water coated by organic are estimated by the former method. These free energy profiles exhibit a barrier to accommodation in the monolayers containing alcohols with zero and one-level of branching. However, the barrier is not observed for monolayers containing alcohols with two-levels of branching. These profiles and friction coefficients estimated from simulation are used to calculate α from the transition state and Grote−Hynes theory. Results are compared with sticking probabilities estimated from direct impinging simulations, and their differences are interpreted through processes included in each theory. At a low surface coverage of these surface active molecules, the underlying bulk solution is exposed and the resistance to vapor accommodation is reduced. We estimate the carbon density in water surfaces coated by straight-chain alcohols, branched alcohols, and straight-chain fatty acids used in study by Takahama and Russell,1 and show that this quantity is related monotonically to the mass accommodation coefficient.

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INTRODUCTION The mass accommodation coefficient (0 ≤ α ≤ 1) is defined as the probability of a vapor phase molecule entering into the bulk liquid phase after striking the surface.2,3 This parameter can regulate the dynamics of water uptake onto growing droplets and affect the final cloud droplet size distribution, and eventually impact radiative forcing. For instance, Chuang et al.4 found that the critical supersaturation required to grow an aerosol into a cloud droplet can be elevated when α is less than 0.1. Feingold and Chuang5 found that changes in α potentially induced by film-forming organic compounds can reduce the cloud droplet number distribution and its overall size distribution. Therefore, understanding the magnitude of α according to interfacial properties between gas and droplet is important for modeling the climate. Several studies have previously focused on estimating α of water and other molecules on aqueous inorganic atmospheric particles.6−11 Field studies show that organic surfactants on aerosol surfaces are prevalent,12−15 and chain length, density, solubility, reactivity, composition, and structure of organic films can influence the mass transfer between gas and liquid bulk.16−18 Studies have suggested that these films can be the primary driver in regulating the mass accommodation coefficient of water at cloud droplet interfaces.4,5,19,20 Growth processes of aerosols and droplets containing organic molecules still remain highly uncertain because of the numerous types of compounds that can be present in the atmosphere.21 Furthermore, mass transfer is more uncertain and poorly established than any other dynamic properties for organic aerosols.22 © XXXX American Chemical Society

Previous studies have shown that mass transfer of a molecule from the gas to condensed phase is reduced by (i) linear organic molecules with increasing hydrocarbon chain length and (ii) higher packing density of surfactants.1,16,17,23−26 Branched structures as those found in atmospheric organic aerosols lead to different packing arrangement on the surface than same number of straight organic molecules, and have led to reduced resistance to mass transfer of N2O5 even for a covered surface.16,27,28 In this work, we investigate how branching in alcohol monolayers on condensed-phase water affects its surface properties and the mass accommodation coefficients of water vapor molecules that may be relevant for growing cloud droplets. α is often estimated either by experimental studies or using the rules of classical statistical mechanics. Experimental methods obtain α indirectly. In the results the estimation of gas-phase diffusion rates is required to back-calculate α occurring at the interface.29 For instance the water α on condensed water surface is estimated in the range of 0.001 to 1 by experimental studies30,31 on the other hand molecular dynamics (MD) simulations consistency estimate this value as 1.1,8,29,32,33 Various MD simulations provide a qualitatively consistent molecular level picture by solving the Newton’s equation of motion and by recording the changing positions, velocities, and forces of the particles in the system. MD successfully estimates macroscopic thermodynamic and dyReceived: February 20, 2016 Revised: April 13, 2016

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DOI: 10.1021/acs.jpca.6b01748 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 1. Chemical Structures and Formulas of the Simulated Organic Molecules

namic properties for different systems.34,35 Therefore, MD simulation has been commonly used as a tool in atmospheric research studies to estimate the α of water on bulk water,8,29,32 organic on bulk water,32,36−38 organic on bulk organic,22 and water on organic-coated bulk water.1,17,39,40 Several algorithms use MD to calculate α. One approach involves direct simulation of impinging events in which a large number of gas molecules striking a liquid surface are virtually explored, and the probability that these molecules will be absorbed into the bulk liquid is statistically estimated.1,11,29 While most straightforward, the precision of estimated α is limited by the number of simulations run. For instance, for 100 simulations, the estimate cannot be more precise than 0.01. In addition, the eventual classification of molecules which are not fully absorbed in solution and instead are adsorbed at the surface layer can be uncertain.1,11,22 Another approach relies on a numerical realization of statistical mechanics, in which the free energy profile of a molecule is estimated along its trajectory to accommodation.32,37,41 α is then approximated by relating macroscopic properties of free energy and friction coefficients within a chemical kinetic framework invoking theories such as transition state theory (TST), Grote−Hynes, Kramers, and others.32,39,42−46 Langevin dynamics is a hybrid approach which combines the dynamics of the impinging process in a reduced coordinate system, using similar macroscopic properties to approximate the effects of Brownian dynamics arising from microscopic interaction among atoms. Consequently, limiting the degrees of freedom allows a larger number of trajectories to be simulated but its interpretation can become complex when the dynamic properties of surface are changing drastically.39,47,48 In this manuscript, we use both free energy and impinging algorithm to estimate the α of water on condensed phase water coated by branched organics in order to understand the thermodynamic and kinetic limitations of mass transfer. These simulations provide a detailed information on both microscopic and macroscopic properties about the systems under controlled conditions. The remainder of this paper is organized as follows. In the Methods section the details of the MD simulations are given. The results of impinging and free energy profile

algorithms are compared in Results and Discussion. In this section we also discuss the effect of branching and carbon density on the α of water. Concluding remarks follow.

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METHODS A inclusive set of simulations concerning the α of water on condensed water coated with organic is studied. The simulated systems are (a) pure water surface and water surface covered by (b) 1-decanol (straight chain), (c) iso-undecanol (one-level of branching), (d) iso-decanol (one-level of branching), (e) 5,9dimethyl-1-decanol (two-levels of branching), (f) 3,7-dimethyl1-octanol (two-levels of branching). See Table 1 for chemical structures and formulas. These organics are used to examine the dependence of α on carbon density and branched structure. The surface density of simulated slabs are 24.8 Å2 per molecule. The x-, y-, and z-dimensions of the simulation cell are 24.9 Å × 24.9 Å × 124.3 Å. The z-axis is perpendicular to the interface and periodic boundary conditions are applied in all three directions. Initially the simulation cells consisted of equilibrated 512 water molecules in a cubic box of Lx = Ly = Lz = 24.9 Å. After, the z-dimension of box is extended to 124.3 Å in order to get sufficient vapor phase. Lastly, the water molecules are covered by 25 organic molecules on each surfaces of the slab for symmetry. The system spanning from the center of liquid bulk to gas phase represents the interface between the gas phase and a growing cloud droplet for which the Kelvin effect no longer plays a major role (larger than 50 nm).2 For example, in a 1 μm droplet, the simulated surface coverage of organics corresponds to a droplet surface less than 2%. The simulations are performed using Gromacs MD software.49 Rigid SPC/E50 water model is used to represent the water−water interaction. This potential is widely used due to the capability of reproducing the surface tension and density of water.32,36 Generalized AMBER Force Fields51 (GAFF) is applied to specify the all-atom intramolecular and intermolecular potentials between organic−water and organic−organic molecules. All bond lengths are constrained to their equilibrium values using LINCS52 linear constraint solver. Simulations are B


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The Journal of Physical Chemistry A utilized with a cutoff distance of 12 Å. Verlet53 algorithm is used to solve the equations of motion with a time step of 2 fs. Simulation of Free Energy Profiles. Umbrella sampling and weighted histogram analysis (WHAM) methods are used to estimate changes in system free energy as the position of a water molecule is varied between the gas phase, organic, and bulk water solution.34,54,55 To use this method, a series of configurations is generated along a reaction coordinate, zdirection, between the gas phase water molecule and organiccoated bulk water. The gas water molecule is placed at the increasing center-of-mass (COM) distance from the organiccoated bulk with its position maintained by a biasing potential. Simulations are conducted by pulling the gas phase water molecule along the reaction coordinate through the bulk. Each simulation has a sufficient overlap region in the reaction coordinate to produce a smooth free energy profile. Equilibrated structures for umbrella sampling are created by a 100 ps energy minimization step under a canonical (NVT) ensemble. Temperature is maintained at 300 K using the Nosé−Hoover56 scheme. The gas phase water molecule is placed 5.5 nm away from the COM of the organic-coated bulk water. Then 200 independent simulations are generated by pulling the water molecule from the gas phase to bulk with 0.01 nm/ps and each performed for 10 ns. The weighted histogram analysis method (WHAM)57 is used to extract the potential of mean force (PMF) along this coordinate. α is calculated from free energies by applying the TST17,58 approach on barrier passage in the following form:

α TST

⎛ ΔG⧧ ⎞ ⎟ = exp⎜ − ⎝ RT ⎠

Grote−Hynes theory to correct and add the recrossing effect on the α values by estimating the transmission coefficient, κ, αGH = κα TST α GH2 = κα TST2

where α is the mass accommodation coefficient while considering the free energy barrier state and αGH2 is the mass accommodation coefficient while considering both the free energy barrier and surface-adsorbed states by using Grote− Hynes theory. The Grote−Hynes transmission coefficient, κ, is given by κ = [κ + ω⧧− 1

α = 1 − α TST2

(

exp −

(

exp

ΔG − RTsa

)

∞

dt exp( −κω⧧t )γ(z⧧ , t )]−1

(4) ⧧

where γ(z ,t) is the friction kernel at the barrier top z = z and ω⧧ is the free energy curvature. The friction kernel γ(z,t), is calculated from the force−force correlation function via ⎛ 1 ⎞ γ (z , t ) = ⎜ ⎟⟨R z(z , 0)R z(z , t )⟩z ⎝ MkBT ⎠

(5)

where Rz(z,t) is the random force on the z- direction and M is mass of the water molecule. Free energy curvature, ω⧧, can be estimated by fitting a harmonic equation to the free energy barrier32 ΔG[z] = ΔG B −

Mω⧧ 2 (z − z⧧)2 2

(6)

where ΔG[z] and ΔGB are the free energy values at position z and at the peak of the barrier, respectively. Simulation of Impinging Events. For this simulation, 100 impinging trajectories for each system are constructed for 100 ps to study the adsorption kinetics of water. The water molecule is initially placed in z coordinate at a distance larger than the cutoff distance for water−organic interactions and x, y coordinate-space is randomly selected from a uniform distribution. The initial velocity is determined randomly from the Maxwell−Boltzmann distribution at 300 K in the z direction. All simulations have been performed in microcanonical (NVE) ensemble to prevent velocity rescaling, but pressures and temperatures remain constant. The mass accommodation coefficient is statistically estimated from the observed events:1,2,8,11,59

(1)

ΔG⧧ + ΔGsa RT

∫0

⧧

The same approach is used on surface-adsorbed and barrier passages in the following form: TST2

(3)

GH

) (2)

⧧

where ΔG is the Gibbs free energy of barrier which is the difference between free energy values on the barrier and the gas phase, ΔGsa is the difference between free energy of the surfaceadsorbed state and the gas phase, R is the gas constant, and T is temperature. αTST and αTST2 correspond the mass accommodation coefficient when considering the free energy barrier and free energy barrier plus surface-adsorbed states, respectively. The PMFs estimated in our simulations technically correspond to the Helmholtz free energy under our NVT ensemble. However, as the organic-gas phase interface allows the volume of the bulk liquid to fluctuate, the free energies calculated from these simulations are equivalent to the Gibbs free energy difference under the NPT ensemble when pressure is 0.32 Equation 1 calculates the probability of finding the solute molecule at the free energy barrier relative to the gas phase state and eq 2 calculates the probability of finding the water molecule at the free energy barrier over the surface-adsorbed state relative to the gas phase. In theory, the TST approach provides the equilibrium property and obtains an upper bound to the α value because it is limited by its assumption of ignoring the recrossing event of solute molecule on the free energy barrier. However, it has been proposed that the solvent can recross the TST dividing surface.32 Here we have used the

α′ =

number of molecules entering the liquid phase number of molecular collisions with the surface

(7)

where α′ is sticking probability and considered as the mass accommodation coefficient. Confidence intervals for α′ are calculated by considering this coefficient as a binomial random variable1 by the method of Clopper and Pearson.60 Method Comparison. Impinging simulations are phenomenological in nature, and comparative analysis with transition state and Grote−Hynes theory are used to interpret the various processes that lead to reduction in mass accommodation (Figure 1 and Table 3). Trajectories in impinging simulations are classified into three types of events:

The notation is described in Table 2. The solute molecule encounters three situations on the surface during the C


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Figure 1. Schematic representation of the possible fates of an incoming molecule on the organic-coated water surface.

Table 2. Notation symbol

description

nabs n⧧ nscat n⧧scat n0scat

number of absorbed number of reaching the transition state total number of scattered number of scattered after reaching the transition state number of scattered before reaching the transition state

Figure 2. Free energy profiles of water insertion (left column) and density profiles (right column) for (a) pure water and water surface covered with (b) 1-decanol, (c) iso-undecanol, (d) iso-decanol, (e) 5,9-dimethyl-1-decanol, and (f) 3,7-dimethyl-1-octanol. z = 0 and ΔG[z] = 0 are set to the COM of bulk and the vapor-phase free energy, respectively. Black, red, and green lines on density profiles indicate the density of water, headgroup oxygen, and carbon, respectively.

Table 3. Comparison of Umbrella Sampling and Impinging Simulations Theory umbrella sampling

impinging simulation

interpretation

αTST, αTST2 κ αGH, αGH2

n⧧/n nabs/n⧧ α′ = nabs/n

probability, X(g) → X⧧ probability, X⧧ → Xabs probability, X(g) → Xabs

accommodation: absorption (1), scattering from surface (2), and scattering after reaching and/or passing the transition state (3) as shown in Figure 1. TST essentially captures the effect of the free energy barrier height for preventing an impinging molecule to reach the state X⧧, after which the molecule is assumed to proceed to its final (absorbed) state (case 2). Grote−Hynes theory additionally considers the reduction of molecules reaching the absorbed state due to barrier recrossing (case 3).

Figure 3. 3D structure of 1-decanol (left) and 3,7-dimethyl-1-octanol (right).

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the experimental free energy of water into bulk water61 −6.3 kcal mol−1 at 298 K. Densities of bulk water at 300 K for each system are estimated as 1000 kg m−3 which is also consistent with experimental values. The potentials used in these simulations correctly reproduce the energetic and dynamic properties of bulk water. The free energy profiles of water on organic-coated bulk water in Figure 2 show distinct trends. Free energy barriers of 3.5 kcal mol−1, 0.65 kcal mol−1, and 0.14 kcal mol−1 are observed for cases (b), (c), and (d), respectively. Barriers are not observed for cases (f) and (e). In addition, an energy well of approximately −0.6 kcal mol−1 has been observed at the interface between the organic layer and vapor phase, which is interpreted to be a surface-adsorbed state on the condensed surface.17,62 The different trends in free energy can be clarified by the number carbon density on the free energy barrier top. As seen in Figure 4 the height of the free energy barrier decreases as we increase the level of branching on the molecules. Long straight molecules can set up bigger temporary dipoles and lie closer together. However, the branched structure of the molecule prevents the surfactant from packing densely on the surface.16 Even though the organic molecules in cases (c) and (e) have a higher number of carbon atoms than in case (b), their number carbon density on the free energy barrier top is lower than that in case (b) due to the effect of the branched structure. Branched molecules are less efficient at packing than

RESULTS AND DISCUSSION Free Energy and Density Profiles. Density and free energy profiles for the insertion of a water molecule into bulk water and organic-coated bulk water calculated by umbrella sampling are shown in Figure 2 cases (a)−(f). Figure 3 shows three-dimensional (3D) structures of 1-decanol and 3,7dimethyl-1-octanol molecules. We can explain the effect of branching on bulk water and organic molecule structures with the help of Figure 3 and density profiles in Figure 2. Branching hinders the ordering of organic molecules; thus the distribution of the headgroup oxygen (Figure 2) spreads in the organic layer as the level of branching increases. Additionally, this disorder effects the position of bulk water molecules. Their penetration depth in the organic layer, also identified and termed “water fingers” by Sakaguchi and Morita,17 also increases with the level of branching. This effect is especially true for molecules that have the same number of carbon atoms (Figure 2) for cases (b), (d), and (f). Quantitatively, the maximum penetration depth of the water molecule from the center of the box for cases (b), (d), and (f) are 1.65 nm, 1.74 nm, and 2.00 nm, respectively. The solvation free-energies of water into bulk SPC/E water at 300 K are estimated to be (a) −7 kcal mol−1, (b) −6.9 kcal mol−1, (c) −7.1 kcal mol−1, (d) −7.2 kcal mol−1, (e) −7.2 kcal mol−1, and (f) −7.4 kcal mol−1. These values are comparable to D


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Figure 4. ΔG‡ values of the free energy barrier in cases (a)−(f) as a function of the number carbon density at the top of the free energy barrier.

Figure 5. Friction kernel for water at the free energy barrier in case (a) 1-decanol-coated water. The inner plot shows the long-time tail of the water friction kernel in which the axes and units are same as in the main figure.

the straight chain layer. Thus, in contrast to straight chain monolayers, branched monolayers show no significant effect on free energy profiles. Mass Accommodation. α from TST. The αTST values in Figure 6 are calculated by using eq 1 and shown in Table 4 for cases (b)−(f). A free energy barrier is not observed for pure water (a) and two-levels of branching organic molecules (e) and (f). When the local free energy minima is considered as a surface-adsorbed state and eq 2 is used, αTST2 are smaller than αTST for cases (c), (d), (e), and (f) due to the increased free energy barrier height. Case (a) remained the same because there is no minimum. Additionally in case (b) the free energy barrier is high enough that αTST2 remained the same as αTST. Diminishing magnitude of ΔG⧧ increases the uncertainty in calculated α values. However, the magnitude of the free energy barrier in all cases are significantly higher than the average total kinetic energy of the water molecule per degree of freedom (kBT/3 = 0.2 kcal/mol) when we assume the existence of a surface-adsorbed state. α from Grote−Hynes Theory. We have used Grote−Hynes theory in cases (b) to (f) to reduce the error in TST from the water molecule recrossing in the transition-state dividing surface. The free energy of pure water, case (a), does not show any barrier, thus the Grote−Hynes theory is not applied. Equations 3 and 4 are used to correct the α values. Force−force correlation is calculated at the top of the free energy barrier in eq 5. The COM of the gas phase water molecule is held constant relative to the COM of the organiccoated bulk water. The force exerted on the gas phase water molecule in the z- direction is collected for 60 ps. Figure 5 displays the friction kernel for a gas phase water molecule at the

free energy barrier for the 1-decanol-coated water system in case (b). The form of the friction kernel is similar to that found in related systems:17,32,63 the typical initial fast relaxation in ∼0.1 ps simulation time, followed by a much slower relaxation as shown in the inset plot in Figure 5. The calculated values of ω⧧ and κ in cases (b) to (f) are summarized in Table 4. Curvature, ω⧧, of free energy barrier decreases as the level of branching increases and this can also be physically seen by checking the curvature of the free energy barriers in Figure 2. The change in mass accommodation coefficients when applying the Grote−Hynes theory has been shown in Figure 6. The role of nonequilibrium effects (recrossing events) become increasingly important with the influence of branching and reduction in free energy barrier height. α′ from Impinging Simulations. α′ values with their 95% binomial confidence intervals for cases (a)−(f) can be seen in Table 4. In contrast to past studies,1,8,11,22 we do not find any molecules that remained in the interface region at the end of our simulations, thus permitting classification of each impinging event into one of the categories shown in eq 8. The unit α′ for water on the pure water is in agreement with previous MD simulations studies.1,29,64,65 All α′ values for organic-coated surfaces are within statistical uncertainty, and far below unity. Even with a comparable surface coverage of organic molecules to straight chain fatty acids studied by Takahama and Russell,1 we find that the branched structure in the hydrocarbon backbone does not necessarily lead to reduced hindrance to mass accommodation. However, the dominant mechanism to accommodation is scattering (rather than adsorption followed by desorption from the interface), as for the fatty acid systems. A surface-adsorbed state at the interface

Table 4. Results for Cases (a)−(f) in Present MD Simulationsa umbrella sampling case (a) (b) (c) (d) (e) (f) a

α

TST

1 2 × 10−3 0.36 0.9 1 1

α

TST2

− 2 × 10−3 0.26 0.47 0.54 0.64

‡

ω [ps]

κ

− 3.80 1.92 2.00 1.68 1.81

− 0.40 0.08 0.09 0.03 0.08

impinging simulation α

GH

− 8 × 10−4 0.02 0.08 − −

α

GH2

− 8 × 10−4 0.02 0.04 0.01 0.05

‡

n /n

nabs/n‡

α′

1[0.96−1] 0[0−0.04] 0.02[0.002−0.07] 0.38[0.28−0.48] 0.1[0.05−0.17] 0.34[0.24−0.44]

1[0.96−1] 0[0−0.04] 0[0−0.04] 0.18[0.11−0.27] 0.11[0.05−0.19] 0.12[0.06−0.2]

1[0.96−1] 0[0−0.04] 0[0−0.04] 0.07[0.03−0.14] 0.01[0−0.01] 0.04[0.01−0.1]

Dashes mean there is no free energy barrier for these systems; thus, Grote−Hynes theory is not applied. E


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Figure 6. Mass accommodation coefficient for cases (b) to (f) from TST, Grote−Hynes theory, and impinging simulations. Values are shown in logarithmic scale in order to emphasize the effect of κ on α. Gray lines in impinging plot indicate the inaccessible region with 100 simulated trajectories.

Therefore, we introduce the integrated carbon density as a metric that better captures the effect of local molecular structure on the overall reduction on α. This metric characterizes the combined effect of molecule packing density, molecule ordering, and distribution of carbon and oxygen in the organic monolayer. To explore a wider range of surface coverage by organic molecules on mass accommodation coefficients, we have performed another set of simulation for a water slab covered with 1-decanol at a surface density of 64 Å2 per molecule. 25 organic and 1024 water molecules are placed in a 40 Å × 40 Å × 124.3) Å simulation cell. At this low surface coverage, 1decanol molecules gather to one side of the surface and the covered and uncovered surface areas are nearly equal (Figure 7). Such clustering of organic molecules have been reported in

between the gas phase and organic monolayer that might result from the local energy minima66 observed in umbrella sampling is not observed in these impinging simulations. The local minima in umbrella sampling may result from the unconstrained degrees of freedom in x- and y-dimensions that the molecule fixed at z may be allowed to explore, while such states are not sampled in these impinging simulations. Comparison. In comparing results from the umbrella sampling and impinging simulations (Table 4 and Figure 6), we find that n⧧/n values are significantly smaller than the mass accommodation coefficients estimated by the transition state theory. Since the system is allowed to relax for each position of the molecule along the z-coordinate, TST underestimates the scattering on account of underestimating the dynamic resistance (which is macroscopically interpreted as friction) to an incoming molecule. These results are consistent with those of Sakaguchi and Morita,17 who found a similar overestimation in αTST with respect to n⧧/n estimated by Langevin dynamics, since TST does not consider the friction resistance of the molecule in reaching the top of the free energy barrier. The transmission coefficients from impinging (nabs/n⧧) and Grote−Hynes theory (κ) agree in the order of magnitude, even tough the barrier regions of cases (e) and (f) are broad, flat, and poorly described by the Grote−Hynes. While the mass accommodation coefficients from TST and n⧧/n are not entirely consistent with each other, the overall mass accommodation coefficient by the Grote−Hynes theory, αGH and α GH 2 , agree within uncertainty of the impinging simulations, α′. In cases (e) and (f), the Grote−Hynes theory could not be applied without considering the surface-adsorbed state because these systems do not have free energy barrier. The comparison of the αGH, αGH2, and α′ indicates that the thermodynamics of the system is not enough to explain the reduction in mass accommodation. In impinging simulations most of the solute molecule scattered after reaching the free energy barrier. That means for the systems we simulated, the mass accommodation process is more kinetic limited than the thermodynamic one. The nonequilibrium correction with Grote−Hynes on the mass accommodation coefficients estimated by TST allowed us to estimate the similar results with impinging simulations. Effect of Carbon Density. Carbon density at the apex of the free energy barrier (Figure 4) is closely related to the magnitude of the barrier. However, this barrier height and reduction in α estimated by TST underestimates the large number of scattering events due to barrier recrossing.

Figure 7. x and y projection of 1-decanol and water molecules positioned on a surface at a spacing of 64 Å2 per molecule. Green, red, and gray colors indicate carbon, oxygen, and hydrogen atoms, respectively.

previous experimental and modeling studies,15,40,67 suggesting its relevance for atmospheric droplets. Approximating α′ = 0 and α′ = 1 for a covered and uncovered surface, respectively, we estimate the overall as α′ for this system based on the proportion of coverage: α′ = (fraction of uncovered surface × 1) + (fraction of covered surface × 0)

(9)

α value is calculated as 0.5 with using eq 9. We present this result together with α′ values from Table 4 and Takahama and Russell1 for straight-chain fatty acid with C14 at a molecular coverage of 29 Å2 per molecule and with C8 at two molecular F


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mechanism for increase in α in accordance with the proportion of exposed surface. As in a previous study,1 scattering rather than adsorption and desorption is found to be the dominant mechanism for reducing the mass accommodation coefficient for surfaces coated with an organic monolayer. Upon the observation of the role in the hydrocarbon backbone in the scattering process and reducing α′, we estimate the integrated carbon density in the monolayer for each system. A monotonic decrease in α′ with respect to this density is found for straight-chain alcohols, branched alcohols, and straight-chain fatty acids from this and previous work.1 The integrated carbon density includes information about the surface coverage of molecules and their arrangement, each of which does not exhibit strong correlation with α′.

coverages, 18 and 29 Å2 per molecule, in contrast to the 24.8 Å2 per molecule for the branched alcohols used this study (Figure 8). The x-axis shows the integrated carbon density calculated by

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AUTHOR INFORMATION

Corresponding Author

Figure 8. Relationship between α′ and integrated carbon density: Red, case (a); black, case (b); yellow, case (c); purple, case (d); turquoise, case (e); and green, case (f). Orange square is for the 1-decanol system at lower surface density. α′ for pink, blue, and brown crossed data are for octanoic, compressed octanoic, and myristic acid systems, respectively, and taken from Takahama and Russell.1

*E-mail: satoshi.takahama@epfl.ch. Phone: +41 21 6935777. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge EPFL for discretionary funding, and Professor Akihiro Morita for his advice on Grote−Hynes theory and helpful discussion.

taking the integral of carbon density along upper half of the organic layer in z-coordinate (Δz) and dividing it by Δz. The projected surface coverage used to describe the arrangement of hydrocarbon backbone on the surface by Takahama and Russell1 can be conceptualized as a manifestation of this integrated carbon density.

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REFERENCES

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CONCLUSIONS In this work, we present the mass accommodation dynamics of water condensation on bulk water coated by branched organic molecules using MD simulation with umbrella sampling and impinging simulations. α is calculated from free energy (and friction) estimates and sticking probabilities of water vapor on (a) pure water surface and water surface covered by (b) 1decanol (straight chain), (c) iso-undecanol (one-level of branching), (d) iso-decanol (one-level of branching), (e) 5,9dimethyl-1-decanol (two-levels of branching), (f) 3,7-dimethyl1-octanol (two-levels of branching). The free energy profiles exhibit a barrier from 0.14 to 3.5 kcal mol−1 to the passage for straight chain and molecules with onelevel of branching, while no barrier is observed for pure water and two-levels of branching molecules. However, all cases except pure water show a minima (approximately −0.6 kcal mol−1) at the interface of the gas and organic monolayer, suggesting the possibility for the water vapor molecule to find itself in a surface-adsorbed state. When the free energy barrier is high enough, the surface minima does not affect the value of α; however, it becomes important when there is no or low free energy barrier. TST underestimates the number of molecules scattered before reaching the free energy barrier compared to the impinging simulations, as it does not consider the dynamic resistance to this point. However, additional reductions in α due to friction considered between the energy barrier maximum and the absorbed brings Grote−Hynes estimates to within uncertainty of impinging simulations (α < 0.07). At reduced surface coverage, organic molecules cluster together and leave patches of the underlying water exposed, suggesting a G


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