Kinetic study of heterogeneous reaction of deliquesced NaCl particles with gaseous HNO3 using particle-on-substrate stagnation flow reactor approach

10026

J. Phys. Chem. A 2007, 111, 10026-10043

FEATURE ARTICLE

Kinetic Study of Heterogeneous Reaction of Deliquesced NaCl Particles with Gaseous HNO3

Using Particle-on-Substrate Stagnation Flow Reactor Approach

†

‡

,‡

,†

Y. Liu, J. P. Cain, H. Wang,* and A. Laskin*

William R. Wiley EnVironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory,

P. O. Box 999, MSIN K8-88, Richland, Washington 99352, and Department of Aerospace and Mechanical

Engineering, UniVersity of Southern California, Los Angeles, California 90089-1453

ReceiVed: March 12, 2007; In Final Form: June 12, 2007

Heterogeneous reaction kinetics of gaseous nitric acid with deliquesced sodium chloride particles NaCl(aq)

+

3 3

HNO (g) f NaNO (aq) + HCl(g) were investigated with a novel particle-on-substrate stagnation flow

reactor (PS-SFR) approach under conditions, including particle size, relative humidity, and reaction time,

directly relevant to the atmospheric chemistry of sea salt particles. Particles deposited onto an electron

microscopy grid substrate were exposed to the reacting gas at atmospheric pressure and room temperature by

impingement via a stagnation flow inside the reactor. The reactor design and choice of flow parameters were

guided by computational fluid dynamics to ensure uniformity of the diffusion flux to all particles undergoing

reaction. The reaction kinetics was followed by observing chloride depletion in the particles by computer-

controlled scanning electron microscopy with energy-dispersive X-ray analysis (CCSEM/EDX). The validity

of the current approach was examined first by conducting experiments with median dry particle diameter Dh

p

4

6

-2

)

0.82 µm, 80% relative humidity, particle loading densities 4 × 10 e N

s

e 7 × 10 cm and free stream

HNO

3

concentrations 2, 7, and 22 ppb. Upon deliquescence the droplet diameter Dh

d

approximately doubles.

The apparent, pseudo-first-order rate constant determined in these experiments varied with particle loading

and HNO concentration in a manner consistent with a diffusion-kinetic analysis reported earlier (Laskin, A.;

Wang, H.; Robertson, W. H.; Cowin, J. P.; Ezell, M. J.; Finlayson-Pitts, B. J. J. Phys. Chem. A 2006, 110,

3

-

15

3

-1 -1

1

0619). The intrinsic, second-order rate constant was obtained as kII ) 5.7 × 10 cm molecule

s

in the

limit of zero particle loading and by assuming that the substrate is inert to HNO

3

. Under this loading condition

the experimental, net reaction uptake coefficient was found to be γnet ) 0.11 with an uncertainty factor of 3.

Additional experiments examined the variations of HNO uptake on pure NaCl, a sea salt-like mixture of

NaCl and MgCl (Mg-to-Cl molar ratio of 0.114) and real sea salt particles as a function of relative humidity.

Results show behavior of the uptake coefficient to be similar for all three types of salt particles with Dh

uptake coefficient peaks around a relative

3

2

p

∼

0

.9 µm over the relative humidity range 20-80%. Gaseous HNO

3

humidity of 55%, with γnet well over 0.2 for sea salt. Below the efflorescence relative humidity the uptake

coefficient declines with decreasing RH for all three sea salt types, and it does so without exhibiting a sudden

3

shutoff of reactivity. The uptake of HNO on sea salt particles was more rapid than that on the mixture of

NaCl and MgCl

uptake of HNO

e Dh

2

, and uptake on both sea salt and sea salt-like mixture was faster than on pure NaCl. The

on deliquesced, pure NaCl particles was also examined over the particle size range of 0.57

3

p

e 1.7 µm (1.1 e Dh e 3.4 µm) under a constant relative humidity of 80%. The uptake coefficient

d

decreases monotonically with an increase in particle size. Application of a resistance model of reaction kinetics

and reactant diffusion over a single particle suggests that, over the range of particle size studied, the uptake

is largely controlled by gaseous reactant diffusion from the free stream to the particle surface. In addition, a

combined consideration of uptake coefficients obtained in the present study and those previously reported for

substantially smaller droplets (Dh

d

∼ 0.1 µm) (Saul, T. D.; Tolocka, M. P.; Johnston, M. V. J. Phys. Chem.

A 2006, 110, 7614) suggests that the peak reactivity occurs at a droplet diameter of ∼0.7 µm, which is

immediately below the size at which sea salt aerosols begin to notably contribute to light scattering.

Introduction

spheric heterogeneous reactions. Reactions involving aero-

sol are known to impact atmospheric composition and

Over the last few decades a great deal of attention has been

placed on the fundamental kinetics and mechanism of atmo-

1

-8

9-15

chemistry,

sky visibility

global radiative forcing and climate change,

1

6,17

18-22

and public health.

Sea salt aerosols,

*

Authors to whom correspondence should be addressed. H.W.: e-mail,

generated by wind-induced wave action and bubble bursting of

seawater, are the second largest component (by mass) of global

haiw@usc.edu; phone, (213) 740-0499; fax, (213) 740-8071. A.L.: e-mail,

Alexander.Laskin@pnl.gov; phone, (509) 376-8741; fax, (509) 376-6066.

2

3

†

‡

aerosol burden. These aerosols may undergo heterogeneous

reactions with trace species in the atmosphere, including OH,

Pacific Northwest National Laboratory.

University of Southern California.

1

Published on Web 09/13/2007

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10027

Yong Liu received his B.S. degree in Applied Chemistry, 1997, from

Fudan University in Shanghai, China. He did his graduate studies at

Fudan University (M.S., 2000) with Professor Xiaoyin Chen and then

at University of Michigan, Ann Arbor (Ph.D., 2005) under the direction

of Professor John R. Barker. Currently, he is a postdoctoral research

associate at the William R. Wiley Environmental Molecular Sciences

Laboratory at the Pacific Northwest National Laboratory with Dr.

Alexander Laskin. His research interests include heterogeneous atmo-

spheric chemistry, aerosol science and its applications to climate and

atmospheric chemistry, and environmental catalysis.

Hai Wang received his Ph.D. in Fuel Science in 1992 from Penn State. His

graduate research under the guidance of Professor Michael Frenklach

included development of a fundamental kinetic model of soot formation,

application of quantum chemistry and reaction rate theories in high-

temperature kinetics of aromatics, theories and applications of chemical

vapor deposition of diamond thin films, and chemistry in the interstellar

media. He was also involved in the development of the earlier versions

of the GRI Mech. He was a Professional Research Staff at Princeton

University from 1994 to 1996, working under the supervision of Profes-

sor Ed Law. During that period of time, his research included fundamen-

tal chemical kinetics of hydrocarbon combustion and laminar flames.

In 1997, he joined the faculty of Mechanical Engineering at the Univer-

sity of Delaware, and continued his studies of hydrocarbon reaction

kinetics at high temperatures. Currently he is a Professor of Aerospace

and Mechanical Engineering at the University of Southern California.

His recent research activities include the application of quantum chemis-

try and statistical mechanical theories in gas-phase and gas-surface chem-

ical kinetics, transport properties of reacting gases, and theory of molec-

ular and nanoparticle transport. His other research activities include

combustion generated particulates, atmospheric heterogeneous reaction

kinetics, catalysis, nanomaterial synthesis and characterization, and semi-

conductor metal oxides for chemical sensor and solar energy conversion

applications. He has published over 100 articles. He was the recipient

of the National Science Foundation Career Award in 1999 and the

Distinguished Paper Award from the Combustion Institute in 2006.

Jeremy Cain received a B.S. in Mechanical Engineering from the

University of Tulsa in 2003. He then began graduate studies in the

same discipline at the University of IllinoissUrbana, Champaign. His

research there was on the radiant ignition of solid rocket composite

propellant. Upon completion of his Master’s degree in 2005, he moved

to the University of Southern Californian to pursue a Ph.D study under

the direction of Professor Hai Wang. His research interests include gas-

phase and heterogeneous chemical kinetics, computational fluid dynam-

ics and reacting flow simulations, and quantum chemistry modeling of

reaction kinetics.

HNO3, O3, NO2, N2O5, and ClONO2. The net result is that inert

Alexander Laskin received his Ph.D. degree in 1998 from the Hebrew

University of Jerusalem, Israel. His graduate research under the guid-

ance of Professor Assa Lifshitz included studies of the kinetics and the

chemical reaction mechanisms of high temperature pyrolysis of aromatic

compounds. During a one-year postdoctoral appointment in 1999 at the

University of Delaware and Princeton University (joint position) with

Professors H. Wang and C. K. Law his research was focused on devel-

opment of comprehensive kinetic models for combustion of hydrocarbon

fuels. In 1999, Dr. Laskin joined the staff of the Pacific Northwest

National Laboratory (PNNL) as a post-doctoral researcher where he began

research focused on the chemistry of atmospheric aerosols. Currently he

is a Senior Research Scientist at the William R. Wiley Environmental

Molecular Sciences Laboratory of PNNL. His present and past research

interests include the following: environmental impact of aerosols; phys-

ical chemistry of gas-particle interactions; novel methods of aerosol collec-

tion and measurement; single-particle analysis of aerosols; source apportion-

ment of aerosols; combustion related aerosols; combustion chemistry

and chemical kinetics. He has authored and co-authored over 40 articles.

halides may be converted to a variety of photochemically

reactive halogen species,¹

-3,5,10,24-59

which lead to production

•

of reactive halogen species X and XO (X ) Cl and Br) upon

exposure to sunlight. There has been increasing evidence from

laboratory and field studies that these halogen atoms play pivotal

roles in the chemistry of the marine boundary layer.²

7,60-66

For

these reasons a quantitative understanding of the uptake and

kinetics of reactive gases on sea salt particles is critical toward

elucidating the overall halogen budget and tropospheric chem-

istry.

The reaction of NaCl with gaseous HNO3 has garnered great

recognition over the last two decades. Considerable

3,35,43-45,50,52,53,55,67-73

work

has been directed toward the uptake

mechanism and rate of HNO3 onto NaCl:

10028 J. Phys. Chem. A, Vol. 111, No. 40, 2007

Liu et al.

NaCl(s,aq) + HNO (g) f NaNO (aq) + HCl(g) (1)

3

The above acid replacement reaction releases HCl into the gas

phase and causes nitrate enrichment, leading to halide deficiency

in sea salt aerosols. In clean air where reactive species are

absent, HCl is quite stable because of its negligible cross section

7

4

for absorption of light with wavelength above 290 nm. Upon

entrainment into polluted air, however, HCl can undergo reaction

•

with OH to generate a highly reactive Cl atom and ultimately

form photochemically labile Cl2 and HOCl, as shown in Figure

1

. The generation of Cl‚ atoms in the lower atmosphere can

result in either ozone depletion or ozone formation, depending

on atmospheric conditions.⁷

4,75

Furthermore, reaction 1 is also

Figure 1. Heterogeneous reactions occurring in the marine boundary

one of the most prevalent pathways for sea salt aging in the

atmosphere.

3

layer: uptake of HNO onto NaCl and reaction of its product, HCl,

Sea salt aerosol can be entrained in atmospheric air and

transported over hundreds of miles. They are eventually removed

from the air by dry or wet deposition, but this process may

take anywhere from days to weeks to occur. The physicochem-

ical properties of sea salts can be altered considerably during

this transportation process. Reaction 1 leads to the formation

of nitrate salt particles that are more hygroscopic than NaCl

and do not readily crystallize. It also is known that the properties

of NaCl mixed with nitrate salt, including size, phase, water

content, and optical reflection and scattering, respond to

humidity much differently than those of pure NaCl. For example,

the presence of nitrate causes NaCl to attain a liquid phase near

or at its defects, steps and edges of the droplet surface, and the

reaction rate of NaCl in aqueous phase is known to be much

values substantially smaller, by more than an order of magnitude,

than that of an earlier study conducted for smaller droplets under

a relative humidity of 55%. Only one study has been reported

51

45

for droplet size larger than 1 µm.

The purposes of the present study are to conduct a systematic

investigation of the kinetics of reaction 1 and to experimentally

determine the influences of particle size and humidity on the

uptake coefficient of HNO3(g) on NaCl. In addition, the uptake

on a sea salt-like mixture of NaCl and MgCl2 and sea salt

particles was examined in detail. The experiments were carried

out under conditions comparable to that of the ambient

atmosphere using a novel particle-on-substrate stagnation flow

reactor (PS-SFR) experimental approach. The PS-SFR approach

has emerged from a number of recent experimental develop-

44

faster than that in solid phase. Thus, the variations of these

properties may impact aerosol chemical reactivity and its effect

on climate, both directly (absorption and scattering of light) and

indirectly (cloud condensation nucleation activity).⁷

ments and studies of gas-to-particle heterogeneous chemistry

78-86

of aerosols.

In those studies, exposures of substrate-

deposited particles to hydroxyl (OH) radicals, ozone (O3), nitric

acid (HNO3), water vapor, and UV light were made and the

influence of particle composition, structure, and morphology

on the reaction mechanisms and relative rates in dry and moist

4,75

The kinetics of reaction 1 have been studied ex-

3

,35,43-45,50,52,53,55,67-73

tensively.

Despite being a rather simple

reaction, the reaction rate and its dependency on particle size

and relative humidity remain highly uncertain. For example,

the value reported for reactive fraction of collisions, i.e., the

uptake coefficient for reaction 1, spans several orders of

magnitude. References to a comprehensive account of those

86

air were elucidated. In our most recent study of the reaction

kinetics for gaseous hydroxyl radicals (OH) with deliquesced

sodium chloride particles, we demonstrated that fundamental

reaction kinetics data may be obtained from this type of

experiment after a quantitative analysis of the effects of gaseous

reactant transport from the bulk gas to the substrate surface.

Such effects arise from the close proximity of the reacting

particles mounted on the substrate. In that study the reaction

kinetics of substrate-deposited, micron-size NaCl particles was

examined using an automated X-ray microanalysis of the

chemical composition of individual particles following their

exposure to hydroxyl radicals. This manuscript presents a new

design of the experimental apparatus, in which the reactor

geometry and choice of flow parameters were guided by

computational fluid dynamics to ensure uniformity of the

diffusion flux to all particles undergoing reaction. The utility

of the experimental protocol and data interpretation is then

demonstrated using a case kinetic study of HNO3-to-NaCl

heterogeneous reaction.

3

,5,55,74

studies can be found in a number of recent publications.

The large discrepancy found in reactive uptake is generally

believed to stem from different amounts of water absorbed on

the salt surface.⁵²Water absorption usually occurs at or near

surface defects, steps and edges, and the extent of absorption

clearly depends on humidity.

Particles in the marine boundary layer are routinely exposed

76,77

to moist air with relative humidity (RH) > 75%.

Most

previous studies were conducted on NaCl crystals or powders

in vacuum or in dry air below the efflorescence relative humidity

(

ERH) of NaCl (∼45%). Earlier Knudsen cell and some flow

reactor experiments were very instrumental to elucidating the

fundamental mechanism of reaction 1, but they are of indirect

relevance to atmospheric chemistry because of the near vacuum

conditions employed in those studies. To date there are very

limited data available for HNO3(g) uptake onto deliquesced

NaCl or sea salt particles under conditions directly relevant to

atmospheric chemistry of sea salt aerosols. Table 1 summarizes

the reaction probabilities recently reported for HNO3(g) with

deliquesced NaCl and sea salt particles (droplets). Johnston and

Uptake of HNO3(g) on deliquesced NaCl particles was re-

cently carefully examined by Johnston and co-workers⁵using

a flow reactor coupled to a single particle mass spectrometer

(FR-SPMS). The particle diameter ranged from 0.1 to 0.23 µm

in their studies. In the present study we carried out a system-

atic investigation of the heterogeneous reaction kinetics for

deliquesced NaCl particles 1-3.4 µm in diameter using the

PS-SFR approach in combination with the CCSEM/EDX

particle analysis. We determined the reactive uptake of HNO3

as a function of relative humidity (20-80%) for NaCl, a

2,53

5

2,53

co-workers

observed the reaction kinetics and uptake in a

flow reactor for both NaCl and a mixture of NaCl and MgCl2

over a droplet diameter range 0.1-0.23 µm and relative

humidity range 10-85%. They reported uptake coefficient

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10029

3

TABLE 1: Reactive Uptake Coefficients Reported for HNO (g) onto Deliquesced NaCl and Sea Salt Particles at Room

Temperature

droplet diameter,

(µm)

[HNO

(ppb)

3

]

RH

(%)

exposure time, uptake coefficient,

t (s)

type of salt

experimental technique

D

d

γ

net

ref

a

NaCl

sea salt

NaCl

NaCl and NaCl/MgCl

NaCl, NaCl/MgCl

and sea SALT

FR-CIMS

2-4

∼370-740

2-575

60-380

60

75

55

80

10-85

20-80

6

>0.2

45

51

52

53

1

3

FR-N isotope tracer

∼0.07

0.2-2

31

<10

600-43200

0.5 ( 0.2

b

d

FR-SPMS

0.11-0.22

0.10-0.233

1.1-3.4

0.0049-0.012

d

2

FR-SPMS

PS-SFR CCSEM/EDX

0.023-0.126

c

0.026-0.2^d

2

,

∼2-20

this work

a

Flow reactor-chemical ionization mass spectrometer. ^bFlow reactor-single particle mass spectrometer. ^cParticles-on-substrate stagnation flow

d

reactor-computer-controlled scanning electron microscopy with energy-dispersed analysis of X-ray. Variation of the uptake coefficient is due to

RH, droplet size, and composition variation.

mixture of NaCl/MgCl2 characteristic of sea salt (XMg/Na )

0.114) and sea salt particles. Measurements yielded a net uptake

coefficient γnet ) 0.11 (× 2.9/÷2.8) under RH ) 80% for

deliquesced NaCl droplets roughly 1.6 µm in diameter. The

influences of particle size and relative humidity on the uptake

coefficient were also determined. Results from the present work

offer much needed kinetic data for atmospheric modeling and

insight into the humidity and particle size dependencies of

reactive uptake.

Experimental Section

Materials and Sample Preparation. Nearly monodisperse

NaCl particles were generated from an aqueous 0.5 M solution

of NaCl (Aldrich, Inc., 99.99% purity) using a home-built

nebulizer. The particles were dried in a diffusion drier (TSI,

Inc., model 3062) prior to sizing and substrate deposition with

a micro-orifice uniform deposit impactor (MOUDI) (MSP, Inc.,

model 110). Most experiments used stage 5 of the MOUDI to

collect dry particles approximately 0.8 µm in diameter, which

were deposited onto TEM grids (Formvar supported Carbon

film, 400 mesh nickel grids, Electron Microscopy Sciences, Inc.)

mounted on an appropriate impaction plate. The size uniformity

of deposited particles was confirmed by computer-controlled

scanning electron microscopy (CCSEM) analysis of over 3000

particles on several different grids. Figure 2 shows an SEM

image of a typical particle sample and its size distribution

measured from the equivalent circle diameter based on two-

dimensional projected area of the particles. In this particular

case the size distribution is log-normal with a median diameter

Dh p ) 0.80 µm and geometric standard deviation σ ) 1.2.

Particle Exposure Apparatus. A schematic of the experi-

mental reactor is shown in Figure 3. The reactor design was

based on a laminar jet of HNO3, highly diluted with moist

nitrogen, impinging onto a substrate-deposited sample. Principles

of fluid mechanics state that the axial convective velocity is

zero immediately above the surface; the transport of gaseous

reacting species to particle surfaces is purely accomplished by

molecular diffusion. The design was guided by computational

fluid dynamics (CFD) simulations to ensure reliability of the

kinetic measurements and to minimize systematic experimental

error. These simulations are discussed in detail later. In each

experiment one TEM grid loaded with NaCl particles of a known

number density Ns is placed atop a cylindrical Teflon sample

holder 1 in. in diameter. The sample and its holder were placed

inside a sealed borosilicate glass chamber constructed from

standard 75 mm joint with FETFE O-ring quick seal (Ace Glass,

Inc., part number 7646-18). The TEM grid was fixed in place

on the surface of the sample holder using a magnet embedded

inside the holder.

Figure 2. SEM image (top panel) and CCSEM measured particle size

distribution (symbols in the bottom panel) of a typical NaCl sample.

Size distribution may be fitted by a log-normal distribution (solid line).

Figure 3. Schematic of the experimental setup.

Nitrogen was used as a carrier gas and allowed to flow through

two bubblers containing concentrated HNO3 solution and

distilled water, respectively. Composition of the HNO3/H2O/

N2 mixture and its flow rate was controlled by three mass

The reactor and its gas delivery lines were built from glass

and Teflon parts; neither material reacts with the HNO3 vapor.

10030 J. Phys. Chem. A, Vol. 111, No. 40, 2007

Liu et al.

controllers installed upstream of the reactor, as shown in Figure

3. Readings of the rotameter installed downstream of the reactor

ensure no negative flow (into the apparatus) or leaks. A

chemiluminescence NOy analyzer (Thermo Electron, Inc., model

42C-Y) and an in-line relative humidity sensor (Honeywell, Inc.,

model HIH4000) were used to monitor HNO3 concentration and

RH, respectively. During each experiment, both measurements

were made continuously and fluctuations were smaller than 5%

and 1% in concentration and relative humidity, respectively.

The fact that HNO3 can absorb on the reactor wall required

some special considerations. At room temperature Teflon has

less than 5% HNO3 adsorption after minutes of HNO3 expo-

sure.⁸⁷Glass can be passivated to HNO3 adsorption after

exposure for several hours. To ensure no significant loss of

HNO3 on the walls of the apparatus and its gas lines, the reactor

was passivated before each experiment for at least 2 h with a

flow of the HNO3/H2O/N2 mixture. After a steady-state exposure

condition was established, the TEM sample grid was installed

by opening the reactor joint and then quickly sealing the joint

with screwlock pinch clamps. During sample installation the

desired HNO3 concentration and RH level were perturbed, but

they were recovered within 1 min. to the initially set values, as

confirmed by stable HNO3 concentration readouts during the

course of the experiments. The period of perturbation was

always substantially shorter than the total reaction time em-

ployed, which ranged from 8 to 300 min.

Figure 4. Top panels: SEM images of NaCl particles before (left)

and after (right) reaction with gaseous HNO of 6 ppb concentration,

3

8

0% RH and reaction time of 210 min. Bottom panel: typical EDX

The HNO3 passivation procedure was applied in all measure-

ments made at 80% RH. Under other RH values, particles were

first wetted by a moist airflow (RH ) 80%) generated by a

dew point generator (Li-Cor, Inc., model LI-610) for 2 min prior

to switching on a gas stream with a preset RH and HNO3

concentration.

spectra of individual NaCl particle before and after reaction.

equivalent intensities of corresponding peaks. Details of the

applied quantification method can be found elsewhere.⁸⁸

Experimental Protocol. Although the particle exposure

apparatus is quite different from that used in a previous study,⁸⁶

the experimental protocol is very similar. Briefly, a constant

flow of mixed HNO3/H2O/N2 gases impinges on NaCl deposited

onto the grid to provide a uniform HNO3 flux. The change in

In all studies the flow of gas with a controlled RH level and

HNO3 concentration is ejected at a rate of V ) 2 L/min (STP)

from a ¹/2′′ diameter (outer) borosilicate glass tube (inner

diameter d ) 0.8 cm). The flow impinges upon particles depos-

ited on a single TEM grid whose center is placed along the flow

tube centerline. The distance between the tube exit and the grid

EDX

Cl-to-Na molar ratio ([Cl/Na]_t) of reacted particles was

taken to quantify chloride loss from reaction 1, i.e.,

1

surface is L ) 0.2 cm (L/d ) /4). The experiments were

-

EDX

[

Cl ]

[Cl/Na]_t

d,t

conducted at ambient temperature and atmospheric pressure.

)

(2)

[Cl^-]

[Cl/Na]_t₎₀

EDX

CCSEM/EDX Single-Particle Analysis. Computer-con-

trolled scanning electron microscopy (CCSEM) coupled with

energy-dispersed X-ray (EDX) spectrometry was used to

determine the elemental composition and loading density of

NaCl particles. The instrument used in this study is a FEI XL30

digital field emission gun environmental SEM. The microscope

is equipped with an EDAX spectrometer (EDAX, Inc., model

d,t)0

where the subscript d denotes the NaCl droplet and t the reaction

time. Figure 4 shows typical SEM images of NaCl particles

before and after exposure to gaseous nitric acid. Morphological

changes, indicative of reactive transformation, are clearly seen.

Evidence of reaction occurrence is also demonstrated in the EDX

spectra: comparison of the spectra before and after reaction,

as shown in Figure 4, reveal a depletion of chlorine.

2

PV7761/54 ME) that has an Si(Li) detector 30 mm in active

area and an ATW2 window, which allows X-ray detection from

elements higher than beryllium (Z > 4). The system is equipped

with Genesis hardware and software (EDAX, Inc.) for computer-

controlled SEM/EDX particle analysis. Particles were recognized

by an increase in the detector signal above a threshold value.

The program acquires an X-ray spectrum from each detected

particle. Particle imaging⁸⁵was made by acquiring the mixed

signal of backscattered (BSE) and transmitted (TE) electrons.

During the X-ray acquisition the electron beam scanned over

the particle projection area. The X-ray spectra were acquired

for 10 s at a beam current of ∼500 pA and an accelerating

voltage of 20 kV. These conditions are sufficient to collect

Three series of experiments were conducted. In series A the

apparent, pseudo-first-order rate constant was measured and the

uptake coefficient determined for HNO reaction with deli-

3

quesced NaCl particles of diameter Dh d ) 1.6 µm (median dry

diameter Dh p ) 0.8 µm) at 80% relative humidity. The measure-

ment was made over a range of free stream HNO3 concentrations

(2, 7, and 22 ppb) similar to the 10-20 ppb level reported in

8

9

polluted environments. For each HNO3 concentration a range

4

6

-2

of particle loadings (Ns ) 4 × 10 to 7 × 10 cm ) were used

and reaction times were varied accordingly. More than 150

samples were tested and analyzed. A vast majority of the

samples had less than 30% depletion of chloride. In series B

the influence of relative humidity on the reaction uptake was

quantified for NaCl, a mixture of NaCl + MgCl2 (XMg/Na )

0.114) and actual sea salt particles, all having Dh p ∼ 0.9 µm

∼

2000 photon counts per Na and Cl characteristic peaks. For

quantification of the EDX results, the Genesis software utilizes

a standardless microanalysis method that relates X-ray intensities

to elemental concentrations through theoretically calculated

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10031

Figure 5. False-color contours of HNO

ppm). Red corresponds to the highest value, and dark blue, to the lowest.

3

3 ∞

mass fraction computed with CFD modeling (L ) 0.4 cm, d ) 0.8 cm, V ) 2 L/min, and [HNO ] ) 1

(

dry size). Tests in series B were performed under extremely

diffusivity of HNO3 in N2 was calculated from the Lennard-

4

-2

92,93

small particle loading (Ns < 5 × 10 cm ) to ensure that the

measured uptake coefficient is that of the single-particle rate

constant. Series C experiments measured the uptake coefficient

as a function particle size (dry diameter, Dh p ) 0.54-1.7 µm;

wet diameter of deliquesced particles, Dh d ) 1.1-3.4 µm) under

RH ) 80%. For series A and C experiments the influence of

particle loading was eliminated by fitting the kinetic data as a

function of particle surface density Ns using a diffusion-kinetic

analysis, as will be discussed later.

Jones potential parameters

of collision diameter σHNO -N

3

2

1/2

) (σHNO + σN )/2 and well depth ꢀHNO -N ) (ꢀHNO ꢀN ) . For

3

2

3

2

3

2

9

4

N2, σ was taken to be 3.8 Å and ꢀ/kb ) 71.4 K, where kb is

the Boltzmann constant. For HNO3 the potential parameters were

9

5

estimated from the critical properties (critical volume Vc )

3

145.0 cm /mol and critical temperature Tc ) 520 K) using

9

6

empirical equations taken from Poling et al. ꢀ/kb ) Tc/1.2593

1

/3

and σ (Å) ) 0.809Vc , where Vc and Tc are in the units of

3

cm /mol and K, respectively. The diffusivity estimated in this

2

manner is DHNO -N ) 0.118 cm /s at 300 K, which is in

3

2

Computational Fluid Dynamics

reasonable agreement with the value of 0.135 cm /s estimated

4

5

by Abbatt and Waschewsky.

For particles larger than the mean free path of the gas, a key

process in the uptake of nitric acid is its diffusion from the gas

phase to the particle surface. Performing an accurate kinetic-

diffusive analysis for the interpretation of experimental data

requires that all particles experience the same or nearly the same

Results and Discussion

CFD Simulations and Reactor Design. Typical spatial

variations of HNO3 concentration are shown in Figure 5. Along

the centerline HNO3 maintains its free stream concentration until

a distance to the surface approximately 5% of the tube diameter,

at which the diffusion boundary layer starts. Because the surface

is assumed to be a complete sink for gaseous HNO3, its

concentration drops sharply toward the surface until it reaches

a value of zero there. Comparison of the results shown in Figure

5 to a similar display for the radial velocity component (not

shown) reveals very similar contours, indicating that flow

convection plays a large part in transport of HNO3 to the

diffusion boundary layer, as anticipated.

(

within a few percent) diffusive flux. The reactor implements a

two-dimensional, axisymmetric reacting gas jet impingement

onto NaCl particles deposited on a TEM substrate. The flow is

90

similar to the well-studied Heimenz flow but differs on two

important aspects: diffusion is present and the jet inside the

tube has a parabolic velocity profile arising from flowing

through an upstream pipe. An analytical solution for this type

of fluid motion, stagnation flow, exists only for a few special

9

0,91

cases,

with this case not being one of them. Thus, we

calculated the flow and HNO3 diffusive flux numerically with

FLUENT 6.2.⁹A computational domain of the reactor was

created in FLUENT’s pre-processor GAMBIT. Thin boundary

layer cells (40 µm thick) were defined above the grid holder

surface to capture the diffusion boundary layer. The model was

then imported into FLUENT to numerically solve the mass,

momentum, energy, and species conservation equations for

incompressible, laminar flow. Boundary conditions were chosen

such that the flow exiting the flow tube has a fully developed

parabolic velocity profile, and the HNO3 concentration im-

mediately above the sample holder surface is zero. These

conditions represent the “worst-case” scenario in terms of flow

nonuniformity, as the entire sample holder surface acts as a

complete sink to gaseous HNO3.

2

Under the condition that the heterogeneous reaction is

controlled by diffusion, the reaction rate is essentially determined

by the boundary layer thickness (l). It is seen that the variation

of this thickness is small near the tube centerline but increases

notably toward the edge of the tube. For the parameter

1

conditions chosen for the reactor (d ) 0.8 cm, L/d ) /4, and V

) 2 L/min), the boundary layer thickness is identical within a

radius of r ) 0.25 cm from the centerline and its thickness is

no larger than ∼0.05 cm, as seen in Figure 6. Even though this

value is obtained for [HNO3]∞ ) 40 ppm, similar results were

obtained for 2, 20, and 200 ppm in terms of the HNO3

concentration variation and the boundary layer thickness.

Computations for free stream HNO3 concentrations on the order

of those in the experiment (a few ppb) could not be accurately

resolved with FLUENT because of the large precision needed;

thus, parts-per-million levels were used in modeling. Particles

deposited on TEM grids placed within this radius of the

Parametric studies were performed by varying three key

reactor parameters shown in Figure 5: volumetric flow rate (V

)

0.25-4 L/min), inlet tube diameter (d ) 0.4 and 0.8 cm),

1

and tube offset distance (L, with L/d ) /4 and /2). The mass

10032 J. Phys. Chem. A, Vol. 111, No. 40, 2007

Liu et al.

These computational results led us to choose V ) 2 L/min,

1

d ) 0.8 cm and L ) 0.2 cm (L/d ) /4) for the experimental

reactor. Under these conditions the HNO3 flux within one TEM

grid radius (∼0.15 cm) is uniform to within 2%, even under

the worst case scenario of the entire sample holder surface acting

as an HNO3 sink. The computational results also suggest that,

under the current reactor design, multiple grids may be placed

near the centerline of the jet especially with a finite rate of

reaction.

An additional computational test was performed by assuming

that only the grid surface acts as a sink to gaseous HNO3, instead

of the entire grid holder surface. Figure 8 shows the high degree

of uniformity for [HNO3] above the grid surface. The changes

toward the edge of the disc are caused by discontinuity in the

surface boundary condition (i.e., going from the free stream

value outside the grid to zero at the grid surface). The distance

over which this occurs is negligible. As shown in Figure 9, the

profile of the HNO3 concentration is identical within a radius

of 0.13 cm. The concentration profile varies markedly only

within 0.1 mm from the grid perimeter, where the particle

samples are excluded from the experimental analysis. Note that

the nonzero value computed for r ) 0.15 cm arises from the

jump condition imposed in the CFD analysis to avoid discon-

tinuity. The point intended to be made is clearly shown: the

diffusive flux is constant over a majority of the grid sur-

face.

Figure 6. Axial variation of HNO

3

concentration normal to the

substrate surface for several radial distances, computed for d ) 0.8

1

cm, L/d ) /

4

3 ∞

, V ) 2 L/min, and [HNO ] ) 40 ppm in the free stream.

The surface of the TEM grid holder corresponds to z ) 0 cm, and the

exit of the flow tube is at z ) 0.32 cm.

Apparent Pseudo-First-Order and Intrinsic Second-Order

Rate Constants. As seen in eq 2, CCSEM/EDX analysis

-

measures the overall Cl loss from dry residues of the NaCl

particles, which can be expressed as follows:

d[Cl^-]

d

-

) k [Cl ]

(4)

I

d

dt

-

where [Cl ]d is the molar concentration of Cl in deliquesced

NaCl particles. If the apparent, pseudo-first-order rate constant

kI is a constant during reaction, its value may be estimated from

-

EDX

^[^C^l^/^N^a^]t

[Cl ]

1

t

d,t

1

) - ln

t

k_I) - ln

(5)

(

-

)

(

EDX

)

[

Cl ]

[Cl/Na]_t₎₀

d,t)0

Figure 7. HNO

immediately above the substrate surface, computed for L/d )

HNO ) 40 ppm, and (a) d ) 0.4 cm and (b) d ) 0.8 cm.

3

flux relative to that of the centerline (r ) 0)

1

EDX

d,t)0

4

/ ,

Table 2 lists the [Cl/Na] /[Cl/Na]

and kI values experi-

d,t

[

3 ∞

]

mentally determined for series A experiments with dry-particle

diameter Dh p ∼ 0.8 µm under the relative humidity of RH )

centerline (r ) 0.25 cm) are exposed to a nearly identical HNO3

flux. Outside of this radius the diffusion flux of HNO3 drops

because of radial diffusion and momentum entrainment, leading

to an increase in l.

The uniformity of the boundary layer in the radial direction

with respect to reactor parameters may be further examined by

8

0%. In this series of experiments the HNO3 concentration in

the free stream was varied from 2 to 22 ppb. The data given in

the table allow us to determine the second-order rate constant,

kII, which is related to kI by

k ) k [HNO ]

3 s

(6)

I

II

plotting the diffusion flux jHNO ,s,

3

d[HNO₃]

Because of diffusive competition for HNO3 among adjacent

droplets, the HNO3 concentration immediately above the droplet

surface [HNO3]s is expected to be smaller than the free stream

value. Thus, kI depends on both kII and the gas-phase diffusion

rate to the substrate surface, which is dependent on the particle

surface density Ns. It should be noted that the second-order rate

constant does not always measure the chemical reaction rate,

because the reaction rate of a single particle may still be

diffusion-controlled.

j

) -D

(3)

HNO₃,s

HNO -N

|

3

2

dz

surface

Figure 7 shows the variation of jHNO ,s normalized by its

3

maximum value as a function of r and V. Comparing results

obtained with the two different flow tube diameters, the radial

variation of the diffusion flux is smaller for the larger tube (d

)

0.8 cm) than that for the smaller tube (d ) 0.4 cm). Also,

the diffusion flux is less sensitive to flow rate variations for

the larger tube. A similar effect is observed by decreasing the

tube offset distance (L/d).

A previous diffusion-kinetic analysis⁸⁶used a one-dimensional

model of coupled gas-surface reaction and gas diffusion through

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10033

Figure 8. Mass fraction contours of [HNO

3

3 ∞

] directly above the grid (diameter ) 0.3 cm). Boundary conditions are [HNO ] ) 20 ppm and

3

[HNO ] ) 0 on the grid surface. The computation used L ) 0.2 cm, d ) 0.8 cm, and V ) 2 L/min.

The solid line of Figure 10 represents the fit to data using eq

. The fitting includes only data of Table 2 (solid symbols), all

7

4

-2

of which were observed for Ns > 4 × 10 cm . The data clearly

cluster around the fitted line with a degree of scatter consistent

with the uncertainties of the data points. We also included in

the figure an auxiliary set of data obtained for Dh p ) 0.77 µm

under the relative humidity of RH ) 80% but with quite small

Ns values (Table 3). Again, these data values are consistent with

14

-3

the fit. The intercept is found to be 1.8 × 10 cm s. Assuming

δks , 1 for the experiment yielded kII ) 5.7 × 10 cm

molecule

-

15

3

-

1 -1

s

with an uncertainty of a factor of ∼3, as shown

by the dashed lines of Figure 10.

The surface reaction rate constant ks is the product of the

sticking probability and the wall collision rate constant. Though

some loss of HNO3 to the substrate might occur, it cannot be

very large, as a dependence of chloride loss on Ns would not

have been observed. The sticking probability of HNO3 on carbon

substrate has not been determined. For the assumption δks , 1

-

4

to be valid, this probability must be smaller than 10 , which

is quite reasonable considering that the HNO3 vapor concentra-

tion employed in the current experiment is substantially below

Figure 9. Axial variation of [HNO

computational case described in Figure 8. The profiles at locations

within r ) 0 to 0.13 cm are exactly the same.

3

] at several different radii for the

-

5

its saturation pressure at 300 K (Psat ) 6 × 10 atm).

a stagnant gas film above the substrate surface, and showed

that kI may be related to Ns by

Equations 4-7 assume formal stoichiometry of reaction 1:

the uptake of 1 molecule of HNO3 (or the formation of nitrate

in particle) corresponds to the loss of 1 chloride ion. This

assumption was verified from changes observed for both N-to-

[

HNO₃]_∞

(1 + δk_s)

-

-k_It

)

+ V [Cl ] δe ^‚^Ns

(7)

d

d,0

[

]

^kI

k_I_I

Na and O-to-Na atomic ratios of reacted particles. The pseudo-

EDX

In the above equation ks is the rate constant of HNO3 reaction

with the substrate surface, δ is a parameter and equal to

first-order rate constants, determined from [N/Na]

and[O/

t

EDX

Na]_t, are compared to those determined from [Cl/Na]_t, as

shown in Figure S2 of the Supporting Information. The close

match of the three data sets indicates that indeed the reaction

stoichiometry is conserved over the experimental conditions of

this study. In principle, any of the three data sets could be used

for kI determination, but the quantitative detection of low-Z

elements, such as N and O, is typically less accurate than Cl

because of a number of inherent constrains of the CCEM/EDX

l/DHNO -N and Vd is the droplet volume. Equation 7 shows that

3

2

[HNO3]∞/kI varies linearly with Ns: the intercept is related to

the second-order rate constant in the limit of low surface density

-

-k t

I

Ns f 0 and the slope is Vd[Cl ]d,0δe

. Figure 10 shows the

[HNO3]∞/kI data of Table 2 plotted as a function of particle

-

k t

I

loading. Despite the fact that b depends on e

, δ and Vd, all

-

k t

I

of which vary with time, the variation of the product Vdδe

has been shown to be insignificant.⁸⁶

85

particle analysis.

As expected from eq 7 and confirmed from the data shown

in Figure 10, the pseudo first-order rate constant depends on

the particle loading Ns, but whether the observed rate constant

is time invariant remains a question. We analyzed the [HNO3]∞/

kI values taken at several particle loadings but over a range of

reaction times (8 < t < 300 min). The analysis shows no

discernible, systematic variation of [HNO3]∞/kI as a function

of time, as shown in Figure S1 of the Supporting Information.

In addition, the fact that the [HNO3]∞/kI values shown in Figure

Experimental Net Uptake Coefficient. The experimental net

uptake coefficient γnet is customarily calculated by

/

-

4k [Cl ]

V_d2k [Cl ] Dh

I

d,0

II

d,0

d

^γnet

)

(8)

cj_H_N_O₃[HNO ] S

3 cj_H_N_O₃

is the apparent, pseudo-first-order rate constant in the

I

3 ∞

d

where k^/

10 overlap reasonably well among the three experimental series

limit of Ns f 0, Vd/Sd is the droplet volume-to-surface area

4

confirms the pseudo-first-order reaction conditions of our

experiments and that the first-order rate constant is indeed time

invariant over the range of reaction time studied.

ratio, cj HNO ) 3.18 × 10 cm/s is the mean molecular speed of

3

HNO3, and Dh d is the deliquesced droplet diameter. Equation 8

would be exact if the heterogeneous reaction occurs around the

10034 J. Phys. Chem. A, Vol. 111, No. 40, 2007

Liu et al.

TABLE 2: Summary of Experimental Conditions (Series a) and Pseudo-First-Order Rate Constants^a

0^-

4

N

)

time

(min)

10 k

6

10^-⁴

(cm

N

)

time

(min)

10 k

6

1

(

s

I

s

I

-

2

EDX

-1

-2

EDX

-1

cm

[Cl/Na]_t

[Cl/Na]_t₎₀

(s

)

[Cl/Na]_t

[Cl/Na]_t₎₀

(s

)

A1: [HNO

3

]

∞

) 2.0 ( 0.0 ppb, Dh

p

) 0.76 ( 0.04 µm

4

5

6

8

( 0

( 2

( 3

35

30

25

0.73 ( 0.17 1.11 ( 0.05 197 (× 1.7/÷2.1)

0.52 ( 0.16 1.11 ( 0.05 361 (× 1.5/÷1.6)

0.75 ( 0.18 1.11 ( 0.05 215 (× 1.7/÷2.3)

74 ( 13

81 ( 12

85 ( 27

150

180

120

300

720

0.71 ( 0.12 1.11 ( 0.05

0.73 ( 0.11 1.11 ( 0.05

0.73 ( 0.19 1.12 ( 0.05

0.67 ( 0.12 1.12 ( 0.05

0.93 ( 0.07 1.11 ( 0.05

0.95 ( 0.10 1.12 ( 0.05

0.97 ( 0.08 1.11 ( 0.05

0.96 ( 0.07 1.11 ( 0.05

0.99 ( 0.09 1.11 ( 0.05

50 (× 1.4/÷1.6)

46 (× 1.4/÷1.5)

39 (× 1.7/÷2.3)

48 (× 1.4/÷1.5)

24 (× 1.5/÷1.9)

9 (× 1.8/÷3.1)

7 (× 1.7/÷2.9)

3 (× 1.6/÷2.3)

3 (× 1.9/÷6.0)

0.82 ( 0.15 1.11 ( 0.05 166 (× 1.7/÷2.4) 105 ( 23

0.75 ( 0.20 1.11 ( 0.05 218 (× 1.8/÷2.6) 121 ( 24

0.85 ( 0.11 1.11 ( 0.05 148 (× 1.6/÷1.9) 219 ( 52

0.87 ( 0.16 1.11 ( 0.05 135 (× 1.9/÷3.5) 253 ( 48

0.92 ( 0.15 1.11 ( 0.05 102 (× 2.0/÷6.9) 658 ( 150

0.93 ( 0.14 1.11 ( 0.05 115 (× 2.0/÷6.4) 765 ( 170

0.95 ( 0.13 1.11 ( 0.05 102 (× 2.0/÷7.9)

1

2

3

2 ( 3

3 ( 2

6 ( 8

1 ( 8

A2: [HNO

3

]

∞

) 6.8 ( 0.7 ppb, Dh

p

) 0.81 ( 0.08 µm

9

( 3

10

20

0.96 ( 0.12 1.12 ( 0.05 250 (× 2.0/÷6.4)

0.99 ( 0.10 1.12 ( 0.05 206 (× 2.0/÷7.5)

0.95 ( 0.12 1.12 ( 0.05 266 (× 1.9/÷4.9)

0.83 ( 0.18 1.10 ( 0.05 225 (× 1.6/÷2.1)

78 ( 7

86 ( 8

89 ( 7

98 ( 18

60

45

60

200

0.91 ( 0.07 1.10 ( 0.05

0.98 ( 0.07 1.11 ( 0.06

0.95 ( 0.11 1.11 ( 0.06

0.97 ( 0.06 1.10 ( 0.05

0.90 ( 0.12 1.11 ( 0.06

0.94 ( 0.07 1.10 ( 0.05

0.97 ( 0.10 1.11 ( 0.06

0.97 ( 0.05 1.10 ( 0.06

0.98 ( 0.05 1.10 ( 0.05

52 (× 1.5/÷1.8)

45 (× 1.8/÷3.4)

57 (× 1.9/÷4.9)

34 (× 1.6/÷2.5)

57 (× 1.8/÷2.9)

43 (× 1.6/÷2.2)

37 (× 1.9/÷6.4)

10 (× 1.6/÷2.5)

9 (× 1.6/÷2.4)

1

2

3

5

1 ( 3

2 ( 3

8 ( 9

2 ( 10

4 ( 9

6 ( 7

9 ( 15

3 ( 13

4 ( 11

0.86 ( 0.15 1.10 ( 0.05 206 (× 1.8/÷3.1) 105 ( 22

0.84 ( 0.12 1.10 ( 0.05 223 (× 1.6/÷2.1) 107 ( 13

0.89 ( 0.12 1.10 ( 0.05 174 (× 1.7/÷2.7) 116 ( 35

0.87 ( 0.17 1.10 ( 0.05 191 (× 2.0/÷4.7) 319 ( 28

0.99 ( 0.07 1.11 ( 0.05

93 (× 1.8/÷3.7) 348 ( 39

0.97 ( 0.08 1.11 ( 0.05 111 (× 1.8/÷3.2)

A3: [HNO ) 22 ( 2 ppb, Dh ) 0.85 ( 0.09 µm

3

]

∞

p

3

4

5

7

8

3 ( 7

10

40

10

15

25

0.85 ( 0.20 1.10 ( 0.05 431 (× 2.0/÷5.7) 105 ( 21

0.81 ( 0.13 1.10 ( 0.05 498 (× 1.6/÷2.1) 165 ( 30

0.91 ( 0.12 1.10 ( 0.05 315 (× 1.8/÷3.3) 180 ( 39

0.90 ( 0.17 1.10 ( 0.05 329 (× 2.1/÷9.6) 199 ( 38

0.75 ( 0.12 1.10 ( 0.05 632 (× 1.5/÷1.7) 204 ( 25

0.17 ( 0.07 1.09 ( 0.06 772 (× 1.3/÷1.2) 243 ( 68

0.85 ( 0.18 1.10 ( 0.06 418 (× 2.0/÷4.6) 254 ( 39

0.70 ( 0.18 1.13 ( 0.05 801 (× 1.6/÷1.9) 285 ( 24

0.70 ( 0.15 1.10 ( 0.05 503 (× 1.6/÷1.8) 286 ( 33

0.59 ( 0.14 1.13 ( 0.05 429 (× 1.4/÷1.5) 326 ( 59

12

20

25

20

25

20

0.90 ( 0.08 1.11 ( 0.05 287 (× 1.5/÷1.8)

0.84 ( 0.09 1.14 ( 0.05 252 (× 1.4/÷1.6)

0.82 ( 0.12 1.13 ( 0.05 211 (× 1.5/÷1.8)

0.73 ( 0.31 1.13 ( 0.05 302 (× 2.3/÷5.2)

0.86 ( 0.11 1.13 ( 0.05 180 (× 1.5/÷1.9)

0.85 ( 0.09 1.10 ( 0.05 213 (× 1.5/÷1.8)

0.93 ( 0.15 1.12 ( 0.06 153 (× 2.0/÷7.0)

0.87 ( 0.14 1.13 ( 0.05 171 (× 1.7/÷2.5)

0.84 ( 0.08 1.14 ( 0.05 253 (× 1.4/÷1.5)

0.94 ( 0.08 1.11 ( 0.05 136 (× 1.6/÷2.2)

6 ( 23

1 ( 29

4 ( 8

5 ( 10

3 ( 23

5 ( 18

1 ( 31

1 ( 28

1

04 ( 23

a

I

All of the experiments were conducted at RH ) 80%. Uncertainty values represent one-standard deviation. k is the apparent, pseudo-first-order

rate constant of chloride loss, determined from eq 5, and the uncertainty factors in parentheses correspond to ( one standard deviation in

EDX

[

Cl/Na]_t

and [Cl/Na]_t₎₀.

rather than the entire sphere. Thus, a simple correction has to

be made to account for this effect, which effectively increase

the uptake coefficient by a factor of 2, i.e.,

-

4

k [Cl ] Dh

II

d,0

d

γ_n_e_t

)

(9)

3

cj_H_N_O₃

The above equation was used in all subsequent analysis to obtain

the uptake coefficient.

The droplet diameter Dh d may be calculated from the known

dry particle diameter and thermodynamic properties and hy-

9

7

groscopic growth data of NaCl particles. Under 80% RH,

-

[

Cl ]d,0 ) 5 M and the ratio of droplet to dry particle diameters

Dh d/ Dh p ) 2, i.e., 0.8 µm dry NaCl particles become 1.6 µm

droplets when deliquesced. Using this Dh d value and the kII value

discussed earlier, we obtain γnet g 0.11 (×2.9/÷2.8) for RH )

8

0%. In spite of the size effect on reactive uptake (to be

Figure 10. Experimental values of [HNO

µm NaCl particles and RH ) 80%, as a function of particle number

density N on the substrate surface. Key: symbols, experimental data;

line, fit to data. The error bar on each data point represents one standard

deviation for [Cl]d,t/[Cl]d,t)0. Dashed lines represent the uncertainties

of the fit.

3

]

∞

/k

I

, measured for ∼0.8

discussed later), this value is about a factor of 2 larger than

initial net uptake coefficient reported by Saul et al. (γnet,0 )

0

53

s

.05) for much smaller droplets ( Dh d ) 0.1 µm) under the same

humidity. In addition, the current γnet value is a factor of 2

4

5

smaller than that Abbatt and Waschewsky obtained for 3 µm

deliquesced NaCl droplets under 75% relative humidity. The

current uptake coefficient is similar to those reported for HNO3

uptake onto water droplets (γnet ranging from 0.03 to 0.11) from

droplet train and single droplet studies.

tions were reported for heterogeneous N2O5 uptake onto sea

entire sphere of the droplet. As will be shown later, the reactive

uptake observed in the present study is largely controlled by

diffusion of gaseous HNO3 onto individual droplets even in the

limit of Ns f 0. The substrate-based experiment inherently limits

the diffusion flux of the gaseous reactant over a hemisphere

9

8-101

Similar observa-

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10035

TABLE 3: Summary of Experimental Conditions (Series B) and Pseudo-First-Order Rate Constants^a

10^-

4

N

)

time

10 k

5

[

HNO

3

]

∞

s

I

-

2

EDX

-1

(ppb)

(cm

(min)

[Cl/Na]_t

Series B1: NaCl

RH ) 80%; Dh ) 0.77 ( 0.05 µm

[Cl/Na]_t₎₀

(s )

p

4

3

1

2

.0

.5

.0

.8

.0

6.3 ( 1.6

4.1 ( 1.0

4.6 ( 1.2

3.6 ( 0.9

3.0 ( 0.7

30

20

0.47 ( 0.09

0.60 ( 0.22

0.64 ( 0.25

0.82 ( 0.22

0.70 ( 0.22

1.08 ( 0.05

1.07 ( 0.07

1.06 ( 0.05

1.07 ( 0.05

4.6 (×1.3/÷1.3)

4.8 (×1.8/÷2.3)

4.2 (×2.0/÷3.0)

2.2 (×2.2/b)

3.5 (×1.9/÷2.9)

RH ) 70%; Dh

) 0.80 ( 0.05 µm

0.77 ( 0.29

0.81 ( 0.17

0.76 ( 0.19

0.80 ( 0.17

0.86 ( 0.18

2.0

2.5

2.4

2.2

3.1 ( 0.8

7.9 ( 2.0

4.5 ( 1.1

2.4 ( 0.6

4.5 ( 1.1

25

15

1.07 ( 0.05

1.06 ( 0.05

2.2 (×2.5/÷b)

1.8 (×1.9/÷3.4)

3.8 (×1.8/÷2.9)

3.3 (×1.8/÷3.1)

2.3 (×2.2/÷b)

RH ) 60%; Dh

) 0.84 ( 0.05 µm

0.65 ( 0.18

0.71 ( 0.14

0.75 ( 0.16

0.84 ( 0.13

0.89 ( 0.12

3

2

.5

.0

.8

.6

2.1 ( 0.5

4.6 ( 1.2

2.3 ( 0.6

4.5 ( 1.1

3.0 ( 0.7

15

10

1.02 ( 0.07

1.03 ( 0.07

1.02 ( 0.07

1.03 ( 0.06

4.9 (×1.8/÷2.3)

4.1 (×1.6/÷2.1)

3.4 (×1.8/÷2.9)

3.4 (×1.9/÷4.2)

2.4 (×2.1/÷b)

RH ) 50%; Dh

) 0.82 ( 0.05 µm

0.95](0.18

0.86 ( 0.17

0.88 ( 0.20

0.75 ( 0.18

0.70 ( 0.20

2.0

2.8

3.5

2.1 ( 0.5

3.6 ( 0.9

3.2 ( 0.8

2.7 ( 0.7

1.7 ( 0.4

8

10

1.04 ( 0.07

1.04 ( 0.05

1.8 (×3.6/÷b)

3.1 (×2.3/÷b)

2.8 (×2.6/÷b)

5.4 (×1.9/÷3.1)

6.6 (×1.9/÷2.9)

RH ) 40%; Dh

) 0.76 ( 0.03 µm

0.84 ( 0.12

0.83 ( 0.14

0.93 ( 0.11

0.88 ( 0.16

0.86 ( 0.14

3

.6

.7

.5

.6

.5

2.1 ( 0.5

4.9 ( 1.2

3.7 ( 0.9

4.2 ( 1.1

2.9 ( 0.7

20

25

1.04 ( 0.07

1.7 (×1.8/÷3.5)

1.8 (×1.9/÷4.1)

0.9 (×2.4/÷b)

1.3 (×2.3/÷b)

1.2 (×2.1/÷8.2)

RH ) 30%; Dh

) 0.78 ( 0.03 µm

0.93 ( 0.06

0.88 ( 0.08

0.87 ( 0.15

0.94 ( 0.07

0.92 ( 0.07

4

3

.1

.9

2.7 ( 0.7

3.2 ( 0.8

3.1 ( 0.8

3.2 ( 0.8

4.1 ( 1.0

30

36

30

1.04 ( 0.07

0.6 (×1.9/÷5.4)

0.9 (×1.7/÷2.8)

0.8 (×2.2/÷b)

0.5 (×2.1/÷b)

0.7 (×1.9/÷6.0)

RH ) 20%; Dh

) 0.75 ( 0.04 µm

0.92 ( 0.18

0.84 ( 0.21

0.85 ( 0.26

0.95 ( 0.08

0.95 ( 0.09

4

.5

.4

3.6 ( 0.9

3.8 ( 1.0

3.0 ( 0.7

4.7 ( 1.2

2.0 ( 0.5

60

1.04 ( 0.07

0.3 (×3.1/÷b)

0.6 (×2.4/÷b)

0.6 (×2.9/÷b)

0.2 (×2.4/÷b)

Series B2: NaCl/MgCl (XMg/Na ) 0.114)

2

RH ) 80%; Dh

10

p

) 0.87 ( 0.02 µm

0.95 ( 0.14

2

.2

.0

2.4 ( 0.6

5.0 ( 1.3

4.6 ( 1.2

3.2 ( 0.8

1.10 ( 0.07

1.10 ( 0.09

2.4 (×2.2/÷b)

2.0 (×2.8/÷b)

1.1 (×3.4/÷b)

1.8 (×2.4/÷b)

0.97 ( 0.17

1.02 ( 0.12

0.98 ( 0.12

RH ) 70%; Dh

) 0.94 ( 0.03 µm

0.97 ( 0.29

1

2

.9

.8

.0

6.0 ( 1.5

3.9 ( 1.0

3.5 ( 0.9

5.7 ( 1.4

10

1.10 ( 0.08

2.1 (×4.0/÷b)

1.8 (×2.2/÷b)

1.5 (×2.4/÷b)

2.3 (×2.2/÷b)

0.98 ( 0.10

1.00 ( 0.09

0.95 ( 0.13

RH ) 60%; Dh

) 0.89 ( 0.03 µm

0.78 ( 0.19

2

.4

.5

.2

.3

3.2 ( 0.8

5.2 ( 1.3

11.0 ( 2.8

10.7 ( 2.7

15

10

1.10 ( 0.07

3.8 (×1.9/÷2.9)

3.6 (×2.2/÷6.5)

2.5 (×2.7/÷b)

2.0 (×2.5/÷b)

0.79 ( 0.24

0.95 ( 0.20

0.97 ( 0.15

RH ) 50%; Dh

p

) 0.89 ( 0.02 µm

1.00 ( 0.08

1.01 ( 0.10

2

.2

.1

5.7 ( 1.4

9.8 ( 2.4

6.3 ( 1.6

8

5

1.10 ( 0.07

1.9 (×2.2/÷b)

2.7 (×2.6/÷b)

2.8 (×2.5/÷b)

RH ) 40%; Dh

15

) 0.87 ( 0.04 µm

0.92 ( 0.09

5

4

.6

.2

.1

.8

3.3 ( 0.8

2.3 ( 0.6

5.7 ( 1.4

7.6 ( 1.9

1.10 ( 0.07

1.9 (×1.7/÷2.8)

2.2 (×1.7/÷2.9)

3.1 (×1.9/÷4.1)

2.5 (×1.8/÷3.1)

10

0.96 ( 0.06

0.91 ( 0.12

0.94 ( 0.08

1

0036 J. Phys. Chem. A, Vol. 111, No. 40, 2007

TABLE 3 (Continued)

HNO

Liu et al.

10^-

4

N

time

10 k

5

[

3

]

∞

s

I

-

2

EDX

-1

(ppb)

(cm

)

(min)

[Cl/Na]_t

[Cl/Na]_t₎₀

(s )

RH ) 30%; Dh

p

) 0.83 ( 0.02 µm

0.83 ( 0.29

6

.0

.5

.0

4.2 ( 1.0

2.3 ( 0.6

3.3 ( 0.8

3.7 ( 0.9

30

1.10 ( 0.07

1.6 (×2.6/÷b)

1.1 (×1.8/÷2.9)

1.7 (×2.0/÷3.8)

1.5 (×2.1/÷6.0)

0.90 ( 0.11

0.80 ( 0.20

0.83 ( 0.21

RH ) 20%; Dh

p

) 0.92 ( 0.05 µm

0.92 ( 0.08

4

5

4

.8

.0

.6

.4

7.4 ( 1.8

3.3 ( 0.8

3.5 ( 0.9

8.3 ( 2.1

60

1.10 ( 0.07

0.5 (×1.6/÷2.4)

1.2 (×1.9/÷2.9)

0.5 (×1.9/÷4.4)

0.3 (×2.5/÷b)

0.73 ( 0.22

0.91 ( 0.13

1.00 ( 0.12

Series B3: Sea Salt

RH ) 80%; Dh

p

) 0.83 ( 0.02 µm

3

2

.0

.4

.1

3.0 ( 0.7

2.0 ( 0.5

2.3 ( 0.6

2.8 ( 0.7

15

10

0.79 ( 0.16

0.81 ( 0.26

0.90 ( 0.16

0.91 ( 0.26

0.99 ( 0.11

1.01 ( 0.13

1.01 ( 0.15

1.02 ( 0.13

2.3 (×2.3/÷b)

3.4 (×3.2/÷b)

1.5 (×4.0/÷b)

1.5 (×5.3/÷b)

RH ) 70%; Dh

p

) 0.90 ( 0.05 µm

0.76 ( 0.23

0.76 ( 0.25

0.74 ( 0.25

3.0

3.1

2.8

6.0 ( 1.5

3.6 ( 0.9

3.2 ( 0.8

15

1.02 ( 0.18

1.01 ( 0.15

2.9 (×2.8/÷b)

3.2 (×2.6/÷b)

RH ) 60%; Dh

) 0.89 ( 0.05 µm

0.83 ( 0.23

2.0

1.9

2.0

3.2 ( 0.8

4.6 ( 1.2

1.1 ( 0.3

3.9 ( 1.0

10

1.01 ( 0.15

2.9 (×3.3/÷b)

1.7 (×3.9/÷b)

2.4 (×3.7/÷b)

2.3 (×2.6/÷b)

0.89 ( 0.18

0.85 ( 0.24

0.86 ( 0.10

RH ) 50%; Dh

p

) 0.88 ( 0.04 µm

0.78 ( 0.17

0.70 ( 0.16

0.87 ( 0.26

2.3

2.4

2.3

7.7 ( 1.9

5.7 ( 1.4

3.9 ( 1.0

15

10

1.01 ( 0.15

2.6 (×2.3/÷b)

3.8 (×2.0/÷3.5)

2.1 (×4.4/÷b)

RH ) 40%; Dh

) 0.92 ( 0.04 µm

0.89 ( 0.38

3.5

4.5

3.5

3.0

3.3 ( 0.8

4.0 ( 1.0

5.7 ( 1.4

6.9 ( 1.7

15

1.01 ( 0.15

1.3 (×6.6/÷b)

3.2 (×3.4/÷b)

1.6 (×4.9/÷b)

0.9 (×5.6/÷b)

0.75 ( 0.33

0.85 ( 0.33

0.91 ( 0.23

RH ) 30%; Dh

p

) 1.01 ( 0.09 µm

0.85 ( 0.25

6.5

5.5

5.0

4.8 ( 1.2

6.4 ( 1.6

5.4 ( 1.4

6.1 ( 1.5

30

25

1.20 ( 0.09

1.19 ( 0.08

1.13 ( 0.15

1.19 ( 0.15

1.9 (×2.1/÷4.9)

1.1 (×2.0/÷6.5)

0.6 (×3.1/÷b)

0.9 (×2.5/÷b)

1.01 ( 0.13

1.01 ( 0.11

1.02 ( 0.12

RH ) 20%; Dh

) 0.95 ( 0.10 µm

1.04 ( 0.08

1.00 ( 0.14

1.02 ( 0.15

4.0

2.5 ( 0.6

4.5 ( 1.1

2.7 ( 0.7

60

1.16 ( 0.15

1.14 ( 0.12

1.19 ( 0.15

0.3 (×2.8/÷b)

0.3 (×2.6/÷b)

0.4 (×2.6/÷b)

a

Uncertainty values represent one-standard deviation; k

I

is the apparent, pseudo-first-order rate constant of chloride loss, determined from eq 5,

EDX

b

and the uncertainty factors in parentheses correspond to ( one standard deviation in [Cl/Na]

determined because of the small extent of reaction; i.e., the lower uncertainty limit is given by zero extent of reaction.

and [Cl/Na]_t₎₀

. The lower limit cannot be

t

salt and water droplets,⁵⁴^,¹⁰²^,¹⁰³all of which are likely to stem

from gas-phase diffusion being a rate-limiting step, as will be

elaborated further in the size dependence section of this

manuscript.

According to eq 9 the size of deliquesced or effloresced

particles is required for uptake coefficient calculation. Dry

particle size Dh p can be obtained from CCSEM data. Because

the growth factor of NaCl and sea salt particles relative to their

dry forms can be calculated on the basis of Tang’s results,⁹⁷

we were also able to determine droplet diameter Dh d of

deliquesced particles at a given RH. Also, RH-dependent

chloride concentration in NaCl and mixture of NaCl/MgCl2 has

RH Dependence. Relative humidity varies widely in the

atmosphere, ranging from a highly moist environment (RH >

8

0%) in the marine boundary layer to very arid condition in

the upper troposphere. Thus, it is of particular interest to quantify

the effects of relative humidity on the reactive uptake. In series

B experiments the uptake coefficient was determined over the

RH range of 20-80%. The conditions employed and kinetic

data obtained for this series of experiments are listed in Table

53

been reported recently. The growth factor of NaCl/MgCl2 and

-

[Cl ] in the sea salt are not yet available and had to be estimated

-

from the growth factor of the sea salt and the [Cl ] in the

mixture of NaCl/MgCl2, respectively. We do not expect that

the results would be considerably affected by these assumptions.

Figure 11 shows uptake coefficients measured over a broad

range of RH for NaCl particles with Dh p ∼ 0.9 µm. The overall

trend and values of HNO3 uptake are in good agreement with

data published previously, although the agreement may be

3, which includes data for pure NaCl, the NaCl/MgCl2 mixture,

and real sea salt. The particle loadings were consistently small

5

-2

(

Ns < 10 cm ) in comparison to series A experiments, thus

ensuring all measurements to be in the limit of small particle

loading, as demonstrated in Figure 10.

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10037

mixture and sea salt promote reactive uptake. Particles are in

liquid form for RH > ERH. Reducing RH below ERH causes

particles to crystallize. Albeit a nominally “solid” state, the small

amount of highly hygroscopic magnesium salts remain liquid

on the particle surface, which facilitates reactive gas uptake in

5

0,55

the NaCl/MgCl2 mixture and sea salt.

Similarly, it was

recently reported that reactive uptake of N2O5 is enhanced on

5

4,103

sea salt particles, as compared to NaCl particles.

There are some qualitative discrepancies between the present

5

3

work and that of Saul et al. for NaCl/MgCl2 particles at low

humidity, as seen in Figure 11. The disagreements could arise

from several differences between the two studies. The sea salt

surface was reported to behave as a “saturated solution” with

1

06-108

respect to the uptake and reaction of HNO3.

At the onset

of exposure to HNO3 the uptake coefficient decreases invariably

with the passage of time due to HNO3 solubility and reaction

with more hygroscopic component of sea salts, such as MgCl2

in “saturated solution”. The uptake coefficient levels off at a

lower value after longer exposure. The time dependence is

qualitatively consistent with SO2 uptake onto sea salt particles.¹

In the work of Saul et al. the maximum exposure time was 10

s. For such a short period of reaction time HNO3 reacts with

the more soluble MgCl2 in “saturated solution.” The resulting

uptake coefficient essentially measures the overall HNO3 uptake

onto the MgCl2 solution. In contrast, exposure times greater than

8 min were applied in our study. Thus, over a large portion of the

09

Figure 11. Values of initial uptake coefficient γnet as a function of

relative humidity for NaCl, mixture of NaCl/MgCl (XMg/Na ) 0.114)

2

and sea salt particles. Solid symbols are experimental data of this work

with Dh

p

∼ 0.9 µm. The open symbols represent data taken from Saul

5

3

et al. for deliquesced particles with Dh

d

∼ 0.1 µm. Lines are drawn to

help show trends.

fortuitous because γnet is particle-size dependent. For compari-

son, data from Saul et al.⁵³( Dh d ∼ 0.1 µm) are also included in

the figure. The uptake coefficient initially increases with a

decrease in RH, reaches its maximum at RH ≈ 55%, and then

decreases as RH is further lowered. This behavior may be

explained by considering the variation of chloride concentration.

Over the RH range 55-80% a decrease in RH is accompanied

reaction period the surface MgCl species were probably absent

2

due to their consumption earlier in the reaction, leading to an

overall reactive uptake onto sea salt particles. Therefore, the

discrepancies could be caused by different time scales employed

in the two studies. Also, the droplet size employed in the two

studies differs by an order of magnitude. Thus, the different

uptake behavior could be the result of different surface composi-

tion and morphology. Because neither information is available

from the earlier study, the discussion above remains speculative

and additional studies are required to resolve the discrepancy.

-

by an increase in [Cl ] in the droplets, leading to a larger

reactive uptake, as predicted by eq 8. Below the efflorescence

relative humidity (ERH ≈ 45%), the reactive uptake drops

rapidly, but a sudden “shutoff” in reactivity was not observed.

Rather, fairly considerable HNO3 uptake onto NaCl particles

was measured (γnet ) 0.04-0.10) under quite dry conditions

52

Particle Size Effect. Johnston and co-workers reported that

the HNO reactive uptake on NaCl droplets increases linearly

3

(

RH ∼ 30%). It is reasonable to expect that under this humidity

with the droplet diameter. Within the range of droplet diameters

there could still be trace amounts of surface absorbed water,

which results in enhanced ionic mobility on the surface and

subsequent replenishment of fresh NaCl onto the surface for

studied (0.1-0.23 µm), diffusion to/from the interface or

reaction at the interface, mass accommodation at the gas-

particle interface and HNO solubility were concluded not to

3

5

further exposure.

be the limiting factors for HNO uptake. Rather, the uptake

3

Comparison of NaCl to Sea Salt. Sea salt is a multicom-

ponent inorganic salt. Besides the most abundant component,

NaCl, it also contains magnesium salt constituents (e.g., MgCl2‚

coefficient was limited by reaction rates within particles and,

thus, closely follows the Dh_ddependency seen in eq 8sa

conclusion that is quite reasonable for the droplet sizes studied.

What was troubling is that when the data of Tolocka et al.⁵²is

extrapolated to 3 µm droplet, at which the uptake coefficient

6H2O, MgSO4‚H2O, KMgCl3‚6H2O). These minor constituents

104

are more hygroscopic than NaCl. Thermodynamic predic-

1

05

45

tions of the mineral sequences expected for evaporation of

seawater indicate that magnesium salts are always crystallized

last in the sequence as a result of their higher solubility.

Therefore, dried sea salt particles have multilayered structure

with the highest soluble and most abundant MgCl2 salt at the

top surface layer. In laboratory studies of heterogeneous aerosol

reactions, NaCl is often used as a proxy for sea salt particles.

To examine whether this is a good model for reactive uptake

of real sea salt, we investigated HNO3 uptake on a mixture of

NaCl/MgCl2 and sea salt particles with dry diameter of Dh p )

was reported by Abbatt and Waschewsky to be >0.2, initial

uptake continues to follow an apparent, linear dependency,

increasing monotonically with an increase in the droplet

diameter. For such a large uptake coefficient and considering

that the droplet diameter is substantially larger than the mean

free path of the gas, gaseous reactant diffusion to the droplet

surface should play an important role. For example, taking the

reactive uptake to be diffusion controlled with

8D

HNO -N

3

2

∼

0.9 µm. The results are shown in Figure 11. The dependency

Γ_g)

(10)

^D^d^c^j HNO3

of γnet on the relative humidity is similar for all three salts tested.

Quantitatively, NaCl/MgCl2 and sea salt take up HNO3 more

rapidly than NaCl does, though the differences among these

samples are within margins of uncertainty. The apparent higher

reactive uptake of HNO3 is probably attributable to the following

we found that the uptake coefficient should eventually decease

with an increase in droplet diameter. Thus, although a monotonic

increase in the uptake coefficient with an increase in droplet

size is expected for small particles, this trend cannot be

-

+

two factors. Higher [Cl ]/[Na ] ratios in both NaCl/MgCl2

10038 J. Phys. Chem. A, Vol. 111, No. 40, 2007

Liu et al.

TABLE 4: Summary of Experimental Conditions (Series C) and Pseudo-First-Order Rate Constants^a

10^-Ns

4

time

(min)

10 kI

5

[

HNO3]∞

-

2

EDX

-1

(

ppb)

(cm

)

[Cl/Na]_t

[Cl/Na]_t₎₀

(s )

Series C1: Dh p ) 0.57 ( 0.05 µm

3

2

.6

.2

.0

1.9 ( 0.5

6

0.59 ( 0.20

0.68 ( 0.27

0.75 ( 0.16

0.77 ( 0.13

0.82 ( 0.16

0.79 ( 0.13

0.84 ( 0.12

0.85 ( 0.17

0.94 ( 0.14

0.87 ( 0.14

0.89 ( 0.12

0.93 ( 0.12

0.95 ( 0.11

0.96 ( 0.09

0.99 ( 0.10

1.00 ( 0.10

0.99 ( 0.10

0.99 ( 0.08

0.99 ( 0.07

1.00 ( 0.09

1.01 ( 0.07

0.97 ( 0.10

1.07 ( 0.07

1.04 ( 0.07

1.04 ( 0.09

131 (×.9/÷2.7)

102 (×2.5/÷20.4)

93 (×2.0/÷4.2)

80 (×1.9/÷4.1)

60 (×2.4/÷b)

72 (×1.9/÷4.6)

53 (×2.1/÷b)

8.7 (×2.6/÷b)

3.6 (×3.8/÷b)

5.3 (×3.3/÷b)

9.9 (×1.9/÷4.6)

6.1 (×2.4/÷b)

4.7 (×2.8/÷b)

6

5

2.2 ( 0.5

3.6 ( 1.3

5

5.0 ( 1.3

5

6.8 ( 1.7

5

9.6 ( 2.4

5

32.5 ( 10.0

33.8 ( 8.2

35.6 ( 11.0

39.4 ( 1.1

42.5 ( 9.8

49.4 ( 18.0

30

Series C2: Dh p ) 1.21 ( 0.14 µm

3.2

2.0

2.5

2.3 ( 0.6

3.8 ( 0.9

2.3 ( 0.6

4.8 ( 1.2

4.9 ( 1.2

24.4 ( 5.2

26.9 ( 4.9

24.4 ( 5.7

21.9 ( 4.9

23.8 ( 6.1

15

0.98 ( 0.14

0.99 ( 0.10

1.03 ( 0.10

0.65 ( 0.20

0.77 ( 0.20

0.97 ( 0.21

1.03 ( 0.10

0.98 ( 0.12

0.94 ( 0.17

0.97 ( 0.16

1.16 ( 0.06

1.17 ( 0.06

1.16 ( 0.06

1.15 ( 0.06

1.14 ( 0.06

19 (×2.0/÷6.8)

9.8 (×1.7/÷2.8)

7.0 (×1.9/÷5.7)

24 (×1.6/÷1.9)

19 (×1.8/÷2.4)

3.0 (×2.5/÷b)

1.9 (×2.2/÷b)

2.8 (×1.9/÷5.5)

3.4 (×2.1/÷b)

3.0 (×2.2/÷b)

28

30

40

35

90

Series C3: Dh p ) 1.70 ( 0.04 µm

2.7

3.0

2.7

3.2

2.7

3.0

2.7

1.0 ( 0.7

1.1 ( 1.0

1.5 ( 1.0

1.9 ( 0.9

2.7 ( 1.1

3.8 ( 0.7

4.3 ( 1.1

4.4 ( 0.9

5.0 ( 1.0

5.0 ( 1.1

240

0.79 ( 0.24

0.88 ( 0.23

0.98 ( 0.30

0.88 ( 0.20

0.87 ( 0.17

0.79 ( 0.24

0.78 ( 0.29

0.88 ( 0.20

0.98 ( 0.30

0.88 ( 0.23

0.87 ( 0.17

1.19 ( 0.10

1.17 ( 0.05

1.19 ( 0.10

1.17 ( 0.05

1.19 ( 0.10

2.8 (×2.0/÷3.3)

2.6 (×2.1/÷6.0)

1.5 (×3.1/÷b)

180

210

240

210

180

240

2.0 (×2.0/÷4.1)

2.2 (×1.8/÷2.6)

2.8 (×1.9/÷3.2)

2.9 (×2.2/÷4.6)

2.1 (×1.9/÷3.7)

1.4 (×3.1/÷b)

2.6 (×2.1/÷5.6)

2.1 (×1.8/÷2.7)

a

All of the experiments were conducted at RH ) 80%. Uncertainty values represent one standard deviation. k

I

is the apparent pseudo-first-order

rate constant of chloride loss, determined from eq 5, and the uncertainty factors in parentheses correspond to ( one standard deviation in

Cl/Na]_tand [Cl/Na]_t₎₀

EDX

b

[

. The lower limit cannot be determined because of the small extent of reaction; i.e., the lower uncertainty limit is given

by zero extent of reaction.

satisfactorily explained over a wide range of particle sizes within

the realm of a resistance model of sequential gaseous reactant

diffusion, mass accommodation, dissolution and reaction. This

is particularly true for particles with diameter substantially larger

than the mean free path of the gas.

In the above expression 1/Γg, 1/R, 1/Γsol, 1/Γrxn, and 1/Γd

represent the resistances to reaction due to gaseous reactant

diffusion, mass accommodation, HNO₃dissolution in the

droplet, chemical reaction in the condensed-phase and aqueous-

phase diffusion, respectively. Under the condition of the current

study where the exposure time is relatively long, eq 11 is only

approximate because of changes expected in chemical composi-

tion of the droplet as the reaction proceeds. Nonetheless, the

equation is useful for understanding the rate-limiting processes

during HNO3 uptake.

74

To provide better insight into the variation of reactive uptake

as a function of droplet size and expand the available dataset,

we determined the uptake coefficient as a function of droplet

diameter from 1 to 3.6 µm under RH ) 80%. Table 4 lists of

the kinetic data measured for this series of experiments. Figure

1

2 presents the values of the uptake coefficient as a function of

It is known that R does not substantially contribute to overall

5

2,53

45,52,53

uptake.

^I^tⁱ^s^a^l^s^o^r^e^p^o^r^t^e^d^t^h^a^t¹^/^Γsol is insignificant relative

droplet diameter. Literature data

are also included for

to 1/γnet in the flow reactor study with maximum exposure time

of 10 s. It has been previously shown that Γsol can be expressed

as

comparison. The variation of the uptake coefficient from the

present work differs qualitatively from those of Johnston and

co-workers.⁵²In the range of droplet size studied, γnet decreases

monotonically with an increase in droplet size. Taking these

data together reveals a characteristic rise-then-fall behavior,

which is in fact expected by considering the various kinetic and

diffusion effects. Specifically, we make use of the resistance

model,⁷in which the overall net uptake coefficient is expressed

in terms of the sum of resistances corresponding to a number

of sequential and parallel processes,

74

D_l

4

HRT

^Γsol

)

(12)

cj_H_N_O₃πt

x

4

where H is Henry’s law constant, Dl is the aqueous-phase

diffusion coefficient, and t is the contact time between HNO3

and the droplet. All our experiments have exposure times longer

than 5 min. For t ) 10 min, Γsol is approximately 0.05, which

indicates HNO3 dissolution to be unimportant, as will be

discussed below.

1

)

+

(11)

^γnet

^Γg

R

⁽^Γ^s^o^l⁺^Γrxn⁾

^Γd

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10039

Excluding the contribution of aqueous-phase diffusion for the

time being, eq 11 can be reduced to

1

)

+

(13)

γ_n_e_tΓ_r_x_n+ Γ_s_o_lΓ_g

where

/

-

4

k [Cl ] D

II d d

Γ_r_x_n

)

(14)

3

cj_H_N_O₃

and the expressions for Γsol and Γg have already been given. In

/

II

eq 14, k is an intrinsic, second-order rate constant of the gas-

surface reaction without being influenced by gaseous diffusion.

/

By using k as a single adjustable variable and fitting the γnet

II

53

value of Saul et al., we obtain a prediction by the simplified

model (11), shown as the dark solid line in Figure 12. Also, k

/

II

-

13

3

-1 -1

was found to be 1 × 10

cm molecule s , which is

Figure 12. Experimental values of γnet under RH ) 80% as a function

of droplet diameter. Key: symbols, experimental data; dark solid line,

considerably smaller than the collision limit. Because the

/

-13

3

-1 -1

dissolution of HNO3 on deliquesced particle is expected to be

eq 13 without considering Γsol (k ) 10

cm molecules

s ,

II

/

2

52

D

^H^N^O^-^N2 ) 0.118 cm /s). The original data of Tolocka et al. are in

error due to a systematic measurement problem for the gas-phase

HNO . These data are multiplied by a factor of 10 to match the more

3

recent datum of Saul et al. The data point reported by Abbatt and

rapid, this k value would indicate that for the smaller droplets

3

II

52,53

studied previously

the reactive HNO3 uptake might be

53

limited by HCl formation in the droplet, a finding consistent

5

2

/

45

with the conclusion reached previously. Using k ) 1 ×

Waschewsky is the lower-limit under 75% RH over a droplet diameter

II

-

13

3

-1 -1

of 2-4 µm.

1

0

cm molecule s , we find Γrxn to be unity for a 2 µm

droplet, which is substantially larger than the Γsol value estimated

earlier. For this reason Γsol was excluded from the analysis.

The simple model (13) captures, for the most part, the

characteristic dependence of γnet on the droplet diameter. For

larger particles the slightly larger deviation may be caused by

aqueous-phase diffusion of the chloride ion, which is not

considered in eq 13. It has been shown in the study of reactive

uptake of ozone by oleic acid aerosols¹that aqueous-phase

oleic acid diffusion plays an important role in the decrease of

some of the nitric acid is consumed by secondary reactions in

the flow reactor, leading to an artificially large uptake coef-

ficient.

Last, it is important to note that the characteristic rise-then-

fall behavior of γnet exhibited in Figure 12 is expected for a

large number of heterogeneous aerosol reactions. Sensitivities

to kinetic rate and diffusivity variations are presented in the

figure. The position of the peak is clearly dependent on the

details of the reaction kinetics and diffusivity. We previously

used a similar technique and determined the uptake coefficient

10

-

uptake coefficient with increasing size. Because NO3 is

-

physically larger than Cl and it also has a larger polarizability

-

than Cl , it probably has a higher propensity to stay at the

•

of OH to be >0.1 on deliquesced NaCl droplets 1.8 µm in

interface. This speculation is consistent with recent findings that

86

diameter under RH ) 80%. This uptake coefficient was not

-

111,112

the Br ion tends to migrate to the surface in seawater.

corrected for half-sphere diffusion; thus, it is likely to be a factor

-

The tendency of NO3 to stay at the interface would inhibit

Cl diffusion to replenish its concentration at the interfacial layer

of ∼2 lower than it should be. Because the intrinsic reaction of

-

•

OH with NaCl is known to be fast and molecular dynamics

to some extent. The effect should be more appreciable for larger

droplets.

simulations show that the uptake coefficient can be as large as

1

13,114

0.83,

the uptake at that droplet size must also be diffusion

Regardless, the combined experimental and modeling results

shown in Figure 12 clearly demonstrate that finite rate reaction

kinetics is the major contributor to reactive uptake for droplet

diameter below 0.7 µm and gaseous diffusion becomes a limiting

factor of HNO3 uptake in addition to aqueous diffusion for larger

droplets. Thus, the current analysis is consistent with the

•

2

controlled. Using an OH diffusivity of 0.33 cm /s and eq 13,

we obtained a γnet value of ∼0.2, which is in close agreement

with the substrate-based experiment upon a factor of 2 correc-

tion, as discussed above.

Significance and Limitations of the Method. A majority

of methodologies and techniques used to study heterogeneous

reaction kinetics of atmospheric relevance monitor changes in

the gas-phase concentrations, whereas measurements of the solid

phase are typically used to provide fundamental, albeit rather

qualitative, information about reaction mechanisms. Several

52,53

conclusion of Johnston and co-workers,

that their data fall

in the kinetic-controlled region. Another interesting conclusion

from the current study is that the peak uptake coefficient occurs

immediately below the size at which sea salt aerosols begin to

contribute notably to light scattering and backscattering.

Our conclusion that the uptake is diffusion controlled for

3

,6,115

recent review articles

about aerosol heterogeneous chem-

istry have markedly specified the need for development of

experimental methodologies to measure uptake on isolated

particles and not bulk powders or solids to remove uncertainties

droplets larger than 0.7 µm is consistent with the findings of

_A_b_b_a_t_t_a_n_d_W_a_s_c_h_e_w_s_k_y_,₄5 even though their reported uptake

coefficient is considerably larger than the value reported here

for a comparable droplet size. In that study the uptake coefficient

was measured somewhat indirectly by following the disappear-

ance of vapor-phase HNO3 by chemical ionization mass

spectrometry. The HNO3 concentration employed was substan-

tially higher than those of the current study. It is possible that

6

inherent to bulk sample measurements. With an increased

recognition of the need to understand and quantify changes in

individual particles due to their atmospheric reactions, more

attention is being given now to the application of single particle

analysis techniques to study kinetics of gas-to-particle reac-

1

0040 J. Phys. Chem. A, Vol. 111, No. 40, 2007

Liu et al.

tions.⁵²^,⁵³^,⁸⁶^,¹¹⁶^,¹¹⁷One specific recommendation from these

reviews is that laboratory studies should also capture realistic

atmospheric conditions of relative humidity, temperature, pres-

sure, reaction time, and trace reactive gas concentrations relevant

to the atmosphere. For example, this and many other studies

have demonstrated that water plays an important role that can

fundamentally affect the kinetics and mechanisms of atmo-

spheric gas-to-particle reactions. There are many more gas-phase

components that might be similarly influential in heterogeneous

aerosol chemistry. For instance, recently Shaka et al. dem-

onstrated that the reaction of gaseous OH with chloride ions

can modulate sea salt alkalinity and enhance the uptake and

oxidation of SO2 by sea salt aerosol.

Application of the presented PS-SFR experimental approach

for laboratory studies of atmospheric gas-to-particle chemistry

is fairly straightforward because it can provide many of the

realistic atmospheric conditions previously mentioned. In ad-

dition, the approach can be used for studies of heterogeneous

atmospheric chemistry of field collected particles, and particles

after sequential exposures to different reactive gases and their

mixtures. This novel approach is well suited for applications in

surface science and chemical catalysis studies. The key require-

ments are that the substrate reactivity is small compared to that

of the deposited particles and that chemical changes in the

particles can be followed quantitatively in response to the

reaction.

knowledge of the particle morphology. Supported by a number

of microscopic studies indicating that a freshly deliquesced NaCl

and sea salt particles are well-approximated by a sphere tangent

85,119,120

to the substrate,

we used the perfect sphere approxima-

tion throughout this work. In our previous study of heteroge-

8

6

neous reaction of NaCl with OH radicals, however, we found

that SEM images taken after the reaction showed a halo of

residue around each vacuum-dried particle, indicating that during

the reaction NaCl droplets wetted the substrate and spread to

approximately twice its spherical wet diameter. We assessed

the magnitude of this effect on the surface area available for

the reaction by considering the reacted particle as a spherical

cap with volume equal to that of a sphere. We estimated that

the surface area of a spherical cap was only a factor of 1.3 larger

1

18

8

6

than that of a perfect sphere. Wetting the substrate and

spreading of the particle contour in that study was likely due to

the formation of a highly hygroscopic mixture of NaOH and

79

NaOCl as the reaction products. In contrast, thorough inspec-

tion of the SEM images of this study indicated no evidence of

such an effect. This might be just a coincidence because dry

density and hygroscopic growth factors of NaCl and NaNO3

97,121,122

particles are almost identical at 80% RH.

Therefore, sizes

of particles studied in this work are generally not expected to

be altered considerably during the reaction. Regardless, uncer-

tainty introduced by particle morphology is less significant

compared to the overall uncertainty of composition measure-

ments.

Several details of the experiment and data analysis are worthy

of further discussion: (a) the effect of substrate reactivity, (b)

the limited range of the reaction extent that can be detected

and used for kinetic analysis and (c) estimation of particle size

and morphology. As to the first issue, the underlying assumption

of the experiment is that the substrate is uncreative, i.e., HNO3

consumption by the substrate does not affect kinetics of the

HNO3-to-NaCl reaction (δks , 1 in eq 7). If some of the reactive

gas molecules are removed by the substrate, values of kI and

γnet would be underestimated. Hence, as discussed in this

Conclusions

Heterogeneous reaction kinetics of gaseous nitric acid with

deliquesced sodium chloride, NaCl/MgCl2 mixture (representa-

tive of sea salt) and sea salt particles were investigated with a

novel particle-on-substrate stagnation flow reactor (PS-SFR)

experimental approach. Particles deposited on a TEM grid are

exposed to gaseous HNO3 by impingement of an axisymmetric

gas jet under conditions, including particle size, relative

humidity, and reaction time, relevant to the atmospheric

chemistry of sea salt particles. Chemical composition of particles

is measured with the CCSEM/EDX technique. Computational

fluid dynamics simulations were carried out to ensure optimal

operation of the particle exposure experiments and assess the

influence of several key reactor parameters on the uniformity

of reaction across the particles deposited surface. The optimal

reactor parameters were implemented in the reactor design and

operation.

_m_a_n_u_s_c_r_i_p_t_a_n_d_i_n_o_u_r_e_a_r_l_i_e_r_p_u_b_l_i_c_a_t_i_o_n_,86 a rigorous view of

the uptake coefficients reported here is that they represent only

the lower limits. Thus, our approach will be the most useful

for cases where the particles are highly reactive. It is also

important to note that although the exact reactivity of the

substrate is not known, its relative inertness with respect to the

HNO3-to-NaCl reaction is clearly inferred from the rise of the

[HNO3]/kI values at high particle density Ns, as seen in Figure

1

0. This dependence of kI on Ns would not have been observed

if the reaction kinetics was limited by the substrate reactivity.

The reaction extent that can be measured and then used for

kinetic analysis is limited to a fairly narrow range. First, the

CCSEM/EDX method of analysis is not sensitive enough to

detect less than ∼10% of the reaction extent. On the other hand,

an inherent assumption adopted for the data analysis of this study

is that we use the initial chlorine concentration for calculations

Three series of experiments were conducted in which the

particle loading, free stream HNO3 concentration, reaction time,

particle size, and relative humidity were varied for one or more

types of salt particles. The first series of experiments was

conducted for Dh p ) 0.8 µm particles under 80% relative

humidity with the objective to assess the role of diffusion-kinetic

coupling arising from competition for gaseous HNO3 among

adjacent droplets on the TEM grid surface. Results show that

the variation of the apparent, pseudo-first-order rate constant

with particle loading and HNO3 concentration in the free stream

is entirely consistent with a diffusion-kinetic analysis previously

-

of the uptake coefficient ([Cl ]d,0 ) 5 M, eq 9), while the

chlorine concentration is constantly decreasing as the reaction

proceeds. To keep our experimental data as close to this

assumption as possible, we conducted almost all of the experi-

ments under conditions with the reaction extent being limited

to <30%. Again, given that the chloride concentration in eq 9

is overestimated, the value derived for γnet represents a lower

limit for the reaction probability.

8

6

reported. Extrapolation of the data to the low particle density

limit yielded an intrinsic, second-order rate constant k ) 5.7

II

-

15

3

-1 -1

× 10

cm molecule

s . Under the same condition the

In the case of substrate-deposited particles, calculation of their

surface areas (Sd in eq 8) available for reaction requires

initial, net reaction uptake coefficient was found to be γnet )

0.11 with an uncertainty factor of 3.

Feature Article

J. Phys. Chem. A, Vol. 111, No. 40, 2007 10041

An additional series of experiments examined the variations

of HNO3 uptake on pure NaCl, a sea salt-like mixture of NaCl

and MgCl2 (Mg-to-Cl molar ration of 0.114) and real sea salt

particles as a function of relative humidity. For three types of

salt particles, all with Dh p ∼ 0.9 µm, behavior of the uptake

coefficient is similar over the relative humidity range 20-80%.

The uptake was found to peak around a relative humidity of

National Laboratory (PNNL). PNNL is operated by the U.S.

Department of Energy by Battelle Memorial Institute under

contract No. DE-AC06-76RL0 1830.

Supporting Information Available: Seven plots indicating

variations of [HNO3]/kI as a function of reaction time for seven

fixed values of particle number on the substrate (Ns) (Figure

S1). Values of 1/kI as a function of particle number density on

the substrate surface (Ns), determined experimentally from Cl

depletion, N and O enhancements for the three series of

experiments (Figure S2). This material is available free of charge

via the Internet at http://pubs.acs.org.

55% with γnet well over 0.2 for sea salt. Below the efflorescence

relative humidity the uptake coefficient decreases rapidly

without a sudden extinction in reactivity. Due to the higher

hygroscopicity of magnesium salt, the uptake of HNO3 on sea

salt particles was more rapid than that on the mixture of NaCl

and MgCl2, and uptake on both sea salt and sea salt-like mixture

was faster than on pure NaCl.

References and Notes

(

1) Ravishankara, A. R. Science 1997, 276, 1058.

The uptake of HNO3 on pure NaCl particles was also

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(

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8

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(

1

(

5

2,53

smaller droplets ( Dh d ∼ 0.1-0.23 µm)

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(

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(

Last, we note that sea salt particles of micron size are

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Kinetic study of heterogeneous reaction of deliquesced NaCl particles with gaseous HNO3 using particle-on-substrate stagnation flow reactor approach

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