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TitleUnder What Conditions Can Equilibrium Gas-Particle Partitioning Be Expected to Hold in the Atmosphere?

Permalinkhttps://escholarship.org/uc/item/1q16b592

JournalENVIRONMENTAL SCIENCE & TECHNOLOGY, 49(19)

ISSN0013-936X

AuthorsMai, HShiraiwa, MFlagan, RCet al.

Publication Date2015-10-06

DOI10.1021/acs.est.5b02587 Peer reviewed

eScholarship.org Powered by the California Digital LibraryUniversity of California

Under What Conditions Can Equilibrium Gas−Particle Partitioning BeExpected to Hold in the Atmosphere?Huajun Mai,† Manabu Shiraiwa,§ Richard C. Flagan,†,‡ and John H. Seinfeld*,†,‡

†Division of Engineering and Applied Science and ‡Division of Chemistry and Chemical Engineering, California Institute ofTechnology, Pasadena, California 91125, United States§Multiphase Chemistry Department, Max Planck Institute for Chemistry, 55128 Mainz, Germany

ABSTRACT: The prevailing treatment of secondary organic aerosol formation inatmospheric models is based on the assumption of instantaneous gas−particleequilibrium for the condensing species, yet compelling experimental evidenceindicates that organic aerosols can exhibit the properties of highly viscous,semisolid particles, for which gas−particle equilibrium may be achieved slowly.The approach to gas−particle equilibrium partitioning is controlled by gas-phasediffusion, interfacial transport, and particle-phase diffusion. Here we evaluate thecontrolling processes and the time scale to achieve gas−particle equilibrium as afunction of the volatility of the condensing species, its surface accommodationcoefficient, and its particle-phase diffusivity. For particles in the size range of typicalatmospheric organic aerosols (∼50−500 nm), the time scale to establish gas−particle equilibrium is generally governed either by interfacial accommodation orparticle-phase diffusion. The rate of approach to equilibrium varies, depending onwhether the bulk vapor concentration is constant, typical of an open system, or decreasing as a result of condensation into theparticles, typical of a closed system.

1. INTRODUCTION

Mounting evidence indicates that organic aerosols can exhibitthe properties of viscous, semisolid particles.1−12 In describingthe process of formation of secondary organic aerosol (SOA), ithas traditionally been assumed that condensing, low-volatilityoxidation products partition according to instantaneous gas−particle equilibrium.13 The assumption of instantaneous gas−particle equilibrium implies that the time scale to achieve thatequilibrium is short when compared to the time scales overwhich other processes, such as gas- and particle-phasedynamics, are occurring. Moreover, most current atmosphericchemical transport models incorporate the assumption ofinstantaneous gas−particle equilibrium in describing SOAformation. A consequence of a highly viscous aerosol phase isthat gas−particle equilibrium for condensing species may notbe established instantaneously, owing to the time associatedwith the transport processes in the gas phase, across the gas−particle interface, and within the particle itself. In this case, adynamic, rather than equilibrium, formulation of the SOAformation process is required. Because the computationalimplications of dynamic versus equilibrium model formulationsare significant, it is important to assess the conditions underwhich such a dynamic formulation is needed.Several recent studies have addressed the time scales

associated with the establishment of atmospheric gas−aerosolequilibrium. Shiraiwa and Seinfeld14 estimated the equilibrationtime scale of SOA gas−particle partitioning using a state-of-the-art numerical gas- and particle-phase transport model. Zaveri etal.15 developed a comparable framework for describing gas−

particle SOA partitioning that accounts for diffusion andreaction in the particle phase and includes the size distributiondynamics of the aerosol population. Liu et al.16 presented anexact analytical solution of the transient equations of gas-phasediffusion of a condensing vapor to and diffusion and first-orderreaction in a particle. These three studies provide thetheoretical and computational framework to estimate the timescale for establishment of gas−particle equilibrium. The presentwork assesses the regimes of parameter values associated withvarious limiting cases of gas−particle transport. On the basis ofthe analytical solution of Liu et al.,16 we derive expressions forthe time scales associated with the transport steps involved inSOA growth. We evaluate the overall time scale to achieve gas−particle equilibrium in both open and closed systems andcompare it to that obtained from the full numerical solution ofShiraiwa and Seinfeld.14

2. ANALYTICAL SOLUTION FOR TRANSIENTGAS−PARTICLE PARTITIONING

Transport of a vapor molecule to a particle involves three masstransfer processes that occur in series: (1) diffusion from thebulk of the gas phase to the particle surface, (2) transportacross the gas−particle interface, and (3) diffusion into theinterior of the particle. If reactions are occurring in the particle

Received: May 27, 2015Revised: August 25, 2015Accepted: September 4, 2015Published: September 4, 2015

Article

pubs.acs.org/est

© 2015 American Chemical Society 11485 DOI: 10.1021/acs.est.5b02587Environ. Sci. Technol. 2015, 49, 11485−11491

phase, these occur simultaneously with particle-phase diffusion.In the present work, we do not explicitly consider the effect ofchemical reactions. Any of these three processes can be rate-determining, depending on the particular set of conditions, andthe rate-determining step will govern the time scale forachieving gas−particle equilibrium. The mathematical state-ment of the transport problem joins gas-phase diffusion,accommodation at the particle surface, and diffusion into theparticle bulk. It is assumed that at t = 0 the particle is free of thecondensing species and that the bulk gas-phase concentrationof the condensing species is maintained as constant for t > 0.This latter condition restricts the analytical solution to a so-called open system, one in which the bulk vapor concentrationis maintained at a constant level. In the corresponding closedsystem, the total amount of vapor available is fixed so that ascondensation occurs the vapor concentration decreases. Theexact analytical solution of the coupled gas and particle phasetransport problem allows one to derive the expression for theoverall time scales to achieve equilibrium, from which one caninfer which transport step controls the overall approach toequilibrium. A general numerical simulation that treats bothopen and closed systems, such as that used by Shiraiwa andSeinfeld,14 can account for change of particle size withcondensation and generation or depletion of the vapor bychemical reaction.We consider the analytical formulation for transient gas−

particle partitioning of a species with a fixed concentration inthe bulk gas phase into a particle free of that species at t = 0.Letting G(r, t) and A(r, t) be the gas- and particle-phaseconcentrations of the transporting species, the transientboundary value problem describing the approach to equilibriumis16

∂∂

= ∂∂

+ ∂∂

⎡⎣⎢

⎤⎦⎥

A r tt

DA r t

r rA r t

r( , ) ( , ) 2 ( , )

b

2

2(1)

α∂∂

= −′

= ∂∂

=

=

⎜ ⎟

⎜ ⎟

⎛⎝

⎞⎠

⎡⎣⎢⎢

⎤⎦⎥⎥

⎛⎝

⎞⎠

DGr

v G R tA R t

H

DAr

14

( , )( , )

r R

r R

g pp

b

p

p (2)

= − −∞ ∞G r t GR

rG G R t( , ) [ ( , )]p

p (3)

=A r( , 0) 0 (4)

∂∂

==

⎛⎝⎜

⎞⎠⎟

A r tr

( , )0

r 0 (5)

where G∞ is the bulk gas-phase concentration of thecondensing species, Rp is the particle radius, α is theaccommodation coefficient of the condensing species on theparticle surface, v is the mean molecular speed of thecondensing species in the gas phase, Dg is the moleculardiffusion coefficient of the condensing species in the gas phase,Db is the molecular diffusivity of the condensing species in theparticle phase, and H′ is the dimensionless Henry’s lawconstant for the condensing species (H′ = HART). Equation 3expresses the steady-state diffusion profile in the gas phase.Under any circumstances, the time scale to establish a steady-state concentration profile in the gas phase is extremely short;

therefore, the steady-state gas-phase profile for the condensingspecies holds at all times.17

The use of a Henry’s law constant is customary whendescribing the equilibrium of a dissolved solute in a relativelydilute cloud droplet. Here, our primary interest concerns theequilibrium of a solute between the gas phase and asubmicrometer aerosol particle, for which a gas−particleequilibrium constant formulation is customary.1 The twoformulations for equilibrium can be related as follows.Assuming an ideal mixture, the equilibrium partial pressure ofcondensing species A is pA = xApA°, where pA° is the saturationvapor pressure of species A and xA is the mole fraction of A inthe particle phase. The mole fraction of the condensing speciesA is related to the mass fraction in the gas-phase, xA = (Ag/c*),where Ag is the the mass concentration of condensing species Ain the gas phase (g (m3 of air)−1) and c* is the saturation massconcentration of the condensing species. Assuming that themolecular weight of the condensing species A is identical tothat of the absorbing particle phase and that individualcondensing species A is one of many in the particle phase,the mole fraction of A can be written as

≈+

≈xA

c AA

cA

p

OAp

p

OA

where Ap is the mass concentration of condensing species A inthe particle phase (g (m3 of air)−1) and cOA is the massconcentration of absorbing phase (g (m3 of air)−1). Thus, thedistribution factor fA, the ratio of particle-phase massconcentration to the gas-phase mass concentration, is

= =*

fAA

ccA

p

gOA

and fA = HARTwL = H′wL, where HA is Henry’s law constant (Matm−1) and wL is volume fraction of particle in the air ((m3 ofparticle) (m3 of air)−1). Thus, the partitioning equilibriumconstant is

= =*

KA c

A c/ 1

p

pOA

g

and the dimensionless Henry’s law constant H′ is formallyrelated to the gas−particle partitioning equilibrium constant by

ρ′ = =H Kcw

KpOA

Lp p

where ρp is the density of particle (g (m3 of particle)−1). Theequilibrium fraction of organic material in the particle phase is(1 + c*/cOA)

−1. Thus, for cOA = 1 μg m−3, a condensingsubstance with c* = 1 μg m−3 will reside 50% in the particlephase at equilibrium; a substance with c* = 0.01 μg m−3 willreside 99% in the particle phase.The solution for the normalized particle-phase concentration

of the condensing species defined by eqs 1−5 is15

∑ϕ η θη

β ηβ β

= −+ −

β θ

=

∞ −L

L L( , ) 1

2 e sin( )

[ ( 1)] sinn

n

n n12

n2

(6)

where ϕ = (A(r, t)/A∞), η = (r/Rp), θ = (Dbt)/Rp2, and A∞ =

H′G∞ and A∞ is the particle-phase concentration of thecondensing species at equilibrium with the gas-phaseconcentration G∞. βn is the nth positive root of

β β + − =Lcot 1 0 (7)

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where

=+

−

− −Lv

v vb

1

i1

g1

(8)

and the transport velocities for gas-phase diffusion, interfacialtransport, and particle-phase diffusion, respectively, are

α=′

= ′

=vD

R Hv

vH

vDR

,4

, andgg

pi b

b

p (9)

Physically, a limit of L≫ 1 implies that transport in the particlephase is much slower than that in the gas phase or across theinterface, and a limit of L≪ 1 corresponds to the case in whichparticle-phase diffusion is rapid relative to either gas-phasediffusion or interfacial accommodation.The time-dependent gas-phase concentration profile of the

condensing species is obtained from eq 6 on the basis of theequality of fluxes, eq 2

∑ ∑

η θ

η β α β

=

−+ −

−′

+ −

β θ β θ

∞

=

∞ −

=

∞ −⎡⎣⎢⎢

⎤⎦⎥⎥

GG

LL L

H Dv R

LL L

( , )

11

2e

( 1)8 e

( 1)n n n n12

b

p 1

2

2

n n2 2

(10)

The e-folding time scale to achieve overall gas−particleequilibrium partitioning is approximated by the exponent in thefirst term of the infinite series in eq 6.

τβ

=R

Deqp2

12

b (11)

This time scale represents that for the entire particle to achieveequilibrium with the bulk gas-phase concentration G∞. Threeimportant limits can be identified on the basis of eq 11.

If the transport resistance is dominated by gas-phasediffusion, i.e., vg ≪ vi and vg ≪ vb, then

≅′

≪LD

H D1

g

b (12)

and β1 ≅ (3L)1/2 ≪ 1. In this case, both interfacial equilibriumand a uniform particle-phase concentration are established(Figure 1a). Letting L → 0 in eq 6, ϕ η θ = − θ

→

−+

lim ( , ) 1 eL

L

0

3 ,

the time-dependent dimensionless concentration of thecondensing species in the particle phase is

ϕ η θ = − −′

⎛⎝⎜⎜

⎞⎠⎟⎟

D

H Rt( , ) 1 exp

3 g

p2

(13)

and the equilibrium partitioning time scale is governed bydiffusion in the particle phase,

τ = ′HR

D3eqp2

g (14)

If the transport resistance is dominated by interfacialaccommodation, i.e., vi ≪ vg and vi ≪ vb, then the parameterL can be approximated as

α≅

′≪L

v R

H D41p

b (15)

In this limiting case, the concentration profiles of thecondensing species in both the gas and particle phases areessentially uniform, owing to relatively rapid particle-phasediffusion (Figure 1b). The form of the dimensionlessconcentration of the condensing species in the particle phasein this limit is

Figure 1. Dimensionless concentration profiles in the particle and gas phase for three limiting cases: (a) gas-phase diffusion-limited partitioning, (b)interfacial-transport-limited partitioning, and (c) particle-phase diffusion-limited partitioning. The region η ≤ 1 corresponds to the particle phase.

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ϕ η θ α= − − ′→ +

⎛⎝⎜⎜

⎞⎠⎟⎟v

H Rtlim ( , ) 1 exp

34L 0 p (16)

and the equilibrium partitioning time scale in this case is

τα

= ′

HR

v

4

3eqp

(17)

If the overall transport resistance is dominated by particle-phase diffusion, i.e., vb ≪ vg and vb ≪ vi, then eq 7 reduces to

β π= −−

⎜ ⎟⎛⎝

⎞⎠n

L1

11n (18)

and

∑ϕ η θη π

πη= − − π θ

→ =

∞ −−

+ nnlim ( , ) 1

2 ( 1)e sin( )

L n

nn

01

12 2

(19)

The equilibrium partitioning time scale in this limit, depictedin Figure 1c, is simply that associated with diffusion in theparticle phase

τπ

=R

Deqp2

2b (20)

Table 1 presents parameter values that illustrate the threelimiting regimes of gas−particle equilibration. In each case, weconsider an organic species with saturation mass concentrationc* = 10 μg m−3, molecular weight M = 200 g mol−1, and a gas-phase molecular diffusivity Dg = 10−1 cm2 s−1. Gas-phase-diffusion-limited partitioning is likely to occur for large liquidparticles (i.e., droplets) with a vapor accommodation coefficientα close to 1.0. Interfacial-transport-limited partitioning will holdfor small, somewhat viscous particles with a relatively smallvapor accommodation coefficient. Finally, particle-phase-diffusion-limited partitioning is expected to occur for highlyviscous (e.g., semisolid) aerosols.

3. RESULTS AND DISCUSSION3.1. Analytical Time Scales. Figure 2 shows the

dependence of the analytical gas−particle partitioning timescale τeq on particle-phase diffusivity Db and accommodationcoefficient α for cloud droplets (Panel (a): Dp = 20 μm) andfine-mode aerosols (Figure 2b, Dp = 100 nm). The dashed linesin Figure 2 are intended to give a rough indication of the

Table 1. Examples of Three Limiting Casesa

gas-phase-diffusion-limited partitioning interfacial-transport-limited partitioning particle-phase-diffusion-limited partitioning

Rp (μm) 10 0.05 0.05Db (cm

2 s−1) 10−5 10−9 10−18

α 1 10−3 10−2

νg/νi = 2.25 × 10−2 νi/νg = 2.2 × 10−4 νb/νg = 10−6

νg/νb = 10−7 νi/νb = 2.2 × 10−7 νb/νi = 4.5 × 10−4

ac* = 10 μg m−3; M = 200 g mol−1; Dg = 0.1 cm2 s−1; and H′ = 1011. Because H′ and c* are related by H′ = ρp/c*, where ρp is the density of theparticle, c* = 10 μg m−3 corresponds to H′ = 1011, given ρp = 1 g cm−3.

Figure 2. Analytical equilibrium partitioning time scale as a function of particle-phase diffusivity Db and accommodation coefficient α for two particlediameters: (a) 20 μm and (b) 100 nm. Other physical parameters are identical for the two panels: M = 200 g mol−1, Dg = 10−1 cm2 s−1, H′ = 1011.

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location of the transition regions between those representingdifferent controlling mechanisms. Although our principalinterest in this work is the equilibration behavior of organicatmospheric aerosols, it is also informative to examine theimplications of the theory for typical cloud droplets. Theequilibration time scale for a solute dissolving in a cloud dropletwith typical aqueous-phase diffusivities is gas-phase diffusioncontrolled for values of α = 0.01. Because of the relatively largesize of cloud droplets, theoretical gas−droplet equilibrationtime scales are much longer than the typical lifetime of a clouddroplet. Most relevant for the present work is Figure 2b. Forparticles in the size range of typical atmospheric organicaerosols (∼50−500 nm), the gas−particle equilibration timescale is governed by either interfacial accommodation orparticle-phase diffusion. For α ≳ 0.01 and Db ≲ 10−13 cm2 s−1,gas−particle equilibration is controlled by particle-phasediffusion. When α ≲ 0.01, interfacial accommodation iscontrolling, and τeq is asymptotically proportional to α. For α≳ 0.1, the time scale for a fine mode aerosol particle to achievegas−particle equilibrium is on the order of minutes for all butthe smallest particle-phase diffusion coefficients. For submi-crometer atmospheric aerosols, gas-phase diffusion of thecondensing species is not a limiting process to achieve gas−particle equilibrium. The transitional boundaries betweenlimiting regimes can be defined approximately by theintersection of the corresponding asymptotic solutions. Forexample, a rough indication of the particle size range where thetransition between gas-phase-diffusion-limited and interfacial-transport-limited regimes occurs can be obtained by combiningeqs 14 and 17.

α=

R

D

v

4p

g

(21)

Figure 3 shows τeq as a function of particle diameter Dp andHenry’s law constant H′ and c* with α = 1.0. Figure 3a is for Db= 10−8 cm2 s−1, and Figure 3b is for Db = 10−13 cm2 s−1. ForSOA, the gas−particle equilibrium state is commonlycharacterized by the gas-phase saturation mass concentrationc* and the gas−particle partitioning equilibrium constant Kp,which as we have shown can be related to H′. τeq increases withparticle diameter because the smaller surface area per unitvolume for larger particles is less efficient for vapor uptake.Gas−particle partitioning between a highly volatile organiccompound (c* ≳ 106 μg m−3) and a liquid particle (Figure 3a)is rapid. If the condensing species is less volatile, then morematerial ultimately condenses into the particle at equilibrium.The larger amount of condensing material must be transportedinto the particle through the gas phase and the interface, whichleads to a longer equilibration time. Because particle-phasediffusion alone does not depend on the volatility of thecondensing species, the limiting step changes from particle-phase diffusion toward interfacial transport or gas-phasediffusion for low volatility species. Figure 3b presents thecomparable calculation for a highly viscous particle. Owing tohindered diffusion in the particle phase, equilibration times arelonger than in the liquid particle for the same particle size andspecies volatility.

3.2. Numerical Simulation in Open and ClosedSystems. An alternative to the analytical evaluation ofequilibration time scales is detailed numerical simulation ofthe process of vapor molecule diffusion to and uptake in aparticle or a population of particles. The kinetic multilayermodel (KM-GAP)18,19 for gas−particle interactions in aerosolsand clouds allows evaluation of τeq by numerically simulatingthe evolution of the condensing species concentrations in gasand particle phases.14 The model is general in terms of whether

Figure 3. Analytical equilibrium partitioning time scale as a function of particle diameter Dp and Henry’s law constant H′ (or equivalent saturationmass concentration c*). (a) Liquid particles; Db = 10−8 cm2 s−1. (b) Highly viscous particles; Db = 10−13 cm2 s−1. Other physical parameters areidentical for the two panels: M = 200 g mol−1, Dg = 10−1 cm2 s−1, ρp = 1 g cm−3, α = 1.

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the overall system is open (vapor concentration maintained asconstant) or closed (finite amount of vapor). The analyticalsolution above assumes an open system, i.e., the bulk gas-phaseconcentration of the condensing species is constant. In a closedsystem, the bulk gas-phase concentration decreases ascondensation into the aerosol phase proceeds.It is instructive to compare the analytical approximation for

τeq on the basis of eq 11 with that derived from numericalsimulation using KM-GAP. We consider numerical simulationof a population of particles growing in open and closed systems.For simplicity, gas- and particle-phase chemical reactions arenot considered in this comparison. Figure 4a shows theequilibrium partitioning time scale as a function of saturationmass concentration c* at different particle number concen-trations caer in a closed system. The analytical approximationand the numerical simulation are essentially identical forrelatively volatile species, c* ≳ 103 μg m−3. The analyticalprediction based on the assumption of a fixed bulk gas-phaseconcentration of the condensing species and the numericalsimulation based on a closed system in which the bulkconcentration declines with time begin to diverge for c* ≲ 103

μg m−3. This divergence is the result of two effects that are notexplicitly treated in the analytical solution: (1) particle sizechange (The KM-GAP model tracks the change of particle sizedue to condensation of vapor.) and (2) vapor depletion (In aclosed system, as vapor condenses on the particle, the bulk gas-phase concentration decreases.) Each of these two effectsbecomes negligible for a sufficiently volatile condensing species(c* ≳ 103 μg m−3) because an overall smaller amount of vaporspecies condenses into the particles. Consequently, the gas−particle equilibrium time scale computed from KM-GAP showsno dependence on the aerosol number concentration caer in this

region. For condensing species with a saturation massconcentration in the range 2 × 102 μg m−3 ≲ c* ≲ 103 μgm−3, the discrepancy between the open and closed systemarises from the effect of particle growth. The equilibriumparticle size increases dramatically in this region, as shown inFigure 4b, so the actual time for the system to achieve gas−particle equilibrium can be considerably longer than thatestimated on the basis of the initial particle size. For decreasingparticle concentration caer, the equilibrium particle sizeincreases, because a greater amount of vapor condenses intoeach particle. For number concentrations characteristic of urbanconditions (caer = 105 cm−3), the condensing vapor isdistributed over a relatively large number of particles, and theeffect of particle size change on the equilibration time scale isnegligible, as shown in Figure 4b. However, in the closedsystem, the effect of gas-phase depletion begins to dominate theequilibrium time scale: As the vapor becomes depleted, aprogressively smaller amount of vapor transfers into the particlephase, and the equilibrium time scale decreases.For less volatile vapor, c* ≲ 2 × 102 μg m−3, in the closed

system, gas−particle partitioning is dominated by gas-phasedepletion of the condensing species. Less volatile condensingspecies transfer predominantly into the particle phase, and asvolatility decreases, τeq and the equilibrium particle sizeeventually become independent of the volatility of thecondensing species because virtually all of it effectivelycondenses.

3.3. Implications for Atmospheric Models. Atmosphericmodels simulate the formation and growth of organic aerosols.At present, these processes are assumed in most models to bethe result of instantaneous gas−particle equilibrium. Inaddition, most atmospheric models do not resolve the ambient

Figure 4. Effect of an open vs closed system. The analytical equilibration time scale for the open system is given by eq 11. The equilibration timescale for the closed system is computed by the KM-GAP numerical model. (a) Equilibrium partitioning time scale as a function of saturation massconcentration c* at different particle number concentrations caer for both open and closed systems. (b) Equilibrium particle growth factor in theclosed system as a function of particle number concentration from KM-GAP. Physical parameters used in the KM-GAP model simulations are α =1.0, τd = 10−9 s, ρp = 1 g cm−3, Db = 10−8 cm2 s−1, Dg = 10−1 cm2 s−1, M = 200 g mol−1, and Dp,0 = 200 nm.

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aerosol size distribution. Under a number of ambient situations,the rate at which that equilibrium is achieved can be slowerthan the rates at which other atmospheric processes arechanging. The numerical machinery needed to resolve thesemicroscopic gas−particle interactions would add substantiallyto an already heavy computational load. Using a combination ofanalytical transport theory and numerical modeling, the presentwork delineates the broad conditions governing the time scalesfor establishing gas−particle equilibrium. These conditionsdepend on the surface accommodation coefficient and volatilityof the species in question, the diffusivity of the condensingorganic species in the particle phase, and the particle size. Inmost ambient modeling circumstances, surface accommodationcoefficients for condensing species and viscosities of particles(from which diffusion coefficients have to be inferred) are notknown with precision. Thus, a high degree of uncertainty willattend any computation based on microscopic particledynamics; nonetheless, the results of the present work providea framework for estimation of the possible effect of non-equilibrium growth in atmospheric models of organic aerosols.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: seinfeld@caltech.edu. Phone: (626) 395-4635.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work was supported by National Science Foundation grantAGS-1523500.

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Environmental Science & Technology Article

DOI: 10.1021/acs.est.5b02587Environ. Sci. Technol. 2015, 49, 11485−11491

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