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Journal of Environmental Science and Health, Part A
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http://www.informaworld.com/smpp/title~content=t713597268

Estimated congener specific gas-phase atmospheric behavior and fractionation
of perfluoroalkyl compounds: Rates of reaction with atmospheric oxidants, airwater partitioning, and wet/dry deposition lifetimes
Sierra Rayne a; Kaya Forest b; Ken J. Friesen a
a
Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba, Canada b Department of Chemistry,
Okanagan College, Penticton, British Columbia, Canada
Online Publication Date: 01 August 2009

To cite this Article Rayne, Sierra, Forest, Kaya and Friesen, Ken J.(2009)'Estimated congener specific gas-phase atmospheric

behavior and fractionation of perfluoroalkyl compounds: Rates of reaction with atmospheric oxidants, air-water partitioning, and
wet/dry deposition lifetimes',Journal of Environmental Science and Health, Part A,44:10,936 — 954
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Journal of Environmental Science and Health Part A (2009) 44, 936–954
C Taylor & Francis Group, LLC
Copyright
ISSN: 1093-4529 (Print); 1532-4117 (Online)
DOI: 10.1080/10934520902996815

Estimated congener specific gas-phase atmospheric behavior
and fractionation of perfluoroalkyl compounds: Rates of
reaction with atmospheric oxidants, air-water partitioning,
and wet/dry deposition lifetimes
SIERRA RAYNE1 , KAYA FOREST2 and KEN J. FRIESEN1
1

Downloaded By: [Canadian Research Knowledge Network] At: 16:09 10 July 2009

2

Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba, Canada
Department of Chemistry, Okanagan College, Penticton, British Columbia, Canada

A quantitative structure-activity model has been validated for estimating congener specific gas-phase hydroxyl radical reaction rates
for perfluoroalkyl sulfonic acids (PFSAs), carboxylic acids (PFCAs), aldehydes (PFAls) and dihydrates, fluorotelomer olefins (FTOls),
alcohols (FTOHs), aldehydes (FTAls), and acids (FTAcs), and sulfonamides (SAs), sulfonamidoethanols (SEs), and sulfonamido
carboxylic acids (SAAs), and their alkylated derivatives based on calculated semi-empirical PM6 method ionization potentials.
Corresponding gas-phase reaction rates with nitrate radicals and ozone have also been estimated using the computationally derived
ionization potentials. Henry’s law constants for these classes of perfluorinated compounds also appear to be reasonably approximated
by the SPARC software program, thereby allowing estimation of wet and dry atmospheric deposition rates. Both congener specific gasphase atmospheric and air-water interface fractionation of these compounds is expected, complicating current source apportionment
perspectives and necessitating integration of such differential partitioning influences into future multimedia models. The findings will
allow development and refinement of more accurate and detailed local through global scale atmospheric models for the atmospheric
fate of perfluoroalkyl compounds.
Keywords: Atmospheric oxidation, perfluorinated compounds, hydroxyl radical, nitrate radical, ozone, wet deposition, dry deposition,
congener profiles, air-water fractionation.

Introduction
The environmental occurrence and fate of perfluorinated
compounds (PFCs) has been attracting increasing research
attention over the past several decades. These compounds,
particularly the perfluoroalkyl derivatives with sulfonyl,
carboxyl, sulfonamide, and telomeric head groups, have
been widely used in a variety of industrial and consumer
products. The global manufacture, use, and disposal of
PFCs has resulted in their ubiquitous presence in all environmental matrices. As trace sampling and analysis methods for PFCs have improved, their presence in atmospheric
samples from around the globe has been reported, with
concentrations higher in urban than remote regions.[1−15]
The atmospheric presence of PFCs has raised three broad

Address correspondence to Sierra Rayne, Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba, Canada.
E-mail: rayne.sierra@gmail.com
Received March 1, 2009.

questions in the literature regarding whether atmospheric
exposure to PFCs is a health risk to humans and wildlife,
whether PFCs atmospherically degrade into new environmental contaminants or into products that increase existing contaminant burdens in aquatic and terrestrial systems,
and whether the troposphere is a vector for PFC transport,
and if so, how atmospheric processes alter PFC signatures
and their degradation product distributions.[16−18]
At present, the long-range transport of PFCs involves
several conceptual models that have been expounded in the
literature over the past decade. In general, these models
can be grouped into the following categories and combinations thereof, and are largely based on a suite of targeted
laboratory studies and the finding of perfluorinated acids
(PFAs; such as perfluorinated sulfonic acids (PFSAs) and
carboxylic acids (PFCAs)) in remote polar regions: (i) atmospheric transport and oxidation of more volatile precursors (e.g., fluorotelomers and perfluoroalkyl sulfonamides);
(ii) direct oceanic transport; and (iii) direct atmospheric
transport.[1,2,4,17,19−23] To test these different hypotheses, a
number of atmospheric PFC models with varying levels of

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Behavior and fractionation of perfluoroalkyl compounds
scale and sophistication have also been developed.[4,24−27]
Recent work from Europe also indicates that PFC concentrations in remote areas fluctuate based on air mass
origin.[12] That the source of the air mass influences PFC
concentrations (and presumably isomer patterns) is an important finding, as it suggests atmospheric source apportionment studies are best served by application of back
trajectory models incorporating various degradation loss
processes (e.g., reactions with hydroxyl and nitrate radicals and ozone) and the relative magnitudes of wet and dry
deposition rates.
Given the large number of potential PFC congeners with
varying chain lengths, and our presently limited experimental database of physicochemical properties relevant for atmospheric modeling, there is a need to develop and validate
reliable congener specific methods for computationally estimating the atmospheric reactivity of these compounds. For
most organic compounds, reaction with the hydroxyl radical (hydrogen abstraction in saturated systems from both
C H and O H moieties [C H abstraction being generally
preferred due to the lower bond strength]; hydroxyl addition to the double or triple bonds and/or the aromatic ring
in unsaturated groups) is often the major loss process in
the troposphere, although reactions with nitrate radicals
at night can also be important. However, highly fluorinated alkanes such as the PFCs are not very reactive towards hydroxyl radicals – the reaction of perfluorinated carbons with hydroxyl radicals (e.g., CF4 +OH→CF3 +HOF)
is generally believed to be negligible.[28]
In addition, experimental work can be compromised by
impurities and other practical difficulties making accurate
determination of hydroxyl reaction rates challenging.[29]
The need for nitrate radical reaction estimates for PFCs
has also been previously identified.[18,26] For unsaturated
compounds, reaction with ozone can be a significant degradation pathway.[30,31] Given the difficulty in experimentally
determining these rate constants, a number of studies beginning in the late 1970s have developed structure-reactivity
models for estimating the gas phase reaction of organic
molecules with hydroxyl and nitrate radicals and ozone.[32]
Often these models use variables such as measured and
calculated ionization energies, bond dissociation energies,
torsional frequencies, absorption maxima, Taft and Hammett polarity parameters, NMR shifts, multivariate methods with a variety of molecular descriptors available from
modern computational tools, molecular orbital based approaches, and the functional group increments approach
pioneered by Atkinson.[26,34−48]
The current isomeric distribution of PFCs in environmental systems and their sources are not well known.[49]
As a result, multimedia models incorporating atmospheric
processes are often used to constrain PFC sources and explain distributions in terrestrial and aquatic compartments.
We have previously shown that thermodynamic computational methods cannot be reliably used to predict the possible isomers present and their relative source production

937
levels, probably because the electrochemical fluorination
methods used for some PFC production were likely under kinetic control for perfluoroalkyl chain rearrangements
during the energetic synthetic process.[50]
Consequently, without a means of predicting source PFC
congener profiles from first principles, it appears that further congener specific progress in the PFC field will need
to advance the analytical methods to help identify all potential congeners in both source mixtures and environmental samples (as with other multicongener contaminant classes such as the polyhalogenated biphenyls and
dibenzo[p]dioxins and furans, trace components could be
diagnostic for apportioning PFC sources), and to couple
this analytical progress with enhanced modeling tools for
evaluating the relevant environmental properties of individual isomers without authentic standards. To assist in
the development of more comprehensive congener specific
assessments regarding the environmental fate of PFCs, we
present here our findings on the validation of quantitative
structure-reactivity relationships for estimating the rates
of reaction of various PFC classes towards gas phase oxidants such as hydroxyl and nitrate radicals and ozone. In
addition, we also examine the validity and use of computationally estimated air-water partition coefficients for these
compounds to help contextualize the importance of the
major gas-phase atmospheric loss processes.

Materials and methods
Congener specific PFC identifications in the manuscript
refer to the general numbering approach published
elsewhere.[49] Gas-phase molecular structures were initially
optimized with the MM2 molecular mechanics energy minimization algorithm using a minimum RMS gradient of
0.100.[51] The gas phase structures were then further optimized using the PM6[52] method with MOPAC2009.[53]
Gas-phase geometry optimizations in MOPAC2009 were
conducted with the following keywords in the input
file header: PM6; BONDS; CHARGE = 0; SINGLET;
GNORM = 0.01.
Rate constants for the atmospheric reaction at 298 K
of saturated PFCs with hydroxyl radicals (kOH,298K ) were
estimated using the following equation from Gusten et al.
(95% confidence intervals about the regression are given in
parentheses; ionization potential (IP) has units of
eV) : − log kOH,298K (cm3 molec−1 s−1 ) = 0.79(±0.02) × IP
+ 3.06(±0.24).[54]
(1)
Rate constants for the atmospheric reaction at 298 K of
unsaturated PFCs with hydroxyl radicals were estimated
using the following equation from Gaffney and Levine:
log kOH,298K (cm3 molec−1 s−1 ) = −0.613(±0.039) × IP
− 4.68(±0.37).[55]
(2)

938

Rayne et al.

Rate constants for the atmospheric reaction at 298 K of
PFCs with nitrate radicals were estimated using the following equation from Sabljic and Gusten:
− log kNO3,298K (cm3 molec−1 s−1 ) = 2.16(±0.09) × IP
− 7.02(±0.87).[56]
(3)
Rate constants for the atmospheric reaction at 298 K of
unsaturated PFCs with ozone were estimated using the following equation from Grosjean and Williams:

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log kO3,298K (cm3 molec−1 s−1 ) = −1.357 (±0.196) × IP
(4)
− 3.92 (±1.78).[40]
The following experimental rate constants for the atmospheric reaction at 298 K of hydroxyl radicals (kOH,298K )
were used (all units are cm3 molec−1 s−1 ): 9.35 ± 2.05 ×
10−14 for C1 PFCA;[57] 1.69 ± 0.22 × 10−13 for C2 PFCA;[57]
1.69 ± 0.22 × 10−13 for C3 PFCA 1;[57] 1.69 ± 0.22 × 10−13
for C4 PFCA 4;[57] 1.54 ± 0.05 × 10−12 for C1 FTOl;[29] 1.3
± 0.2 × 10−12 for C4 FTOl 4 and 1.5 ± 0.3 × 10−12 for C6
FTOl;[58] 1.14 ± 0.23 × 10−12 for C4 FTOH 4;[20] 1.14 ±
0.23 × 10−12 for C6 FTOH 17;[20] 1.14 ± 0.23 × 10−12 for C8
FTOH 89;[20] 1.22 ± 0.26 × 10−13 for C1 FTAl hydrate;[59]
1.22 ± 0.26 × 10−13 for C3 FTAl hydrate 1;[59] 1.22 ± 0.26
× 10−13 for C4 FTAl hydrate 4;[59] 1.1 ± 0.7 × 10−12 for C1
PFAl (ref.[23] in[60] , but also quoted at 0.67 ± 0.40 × 10−12
as ref.[7] in[61] ); 0.68 × 10−12 for C1 PFAl (ref.[9] in[61] ); 0.65
± 0.05 × 10−12 and 0.54 ± 0.12 × 10−12 for C1 PFAl;[62]
0.60 ± 0.12 × 10−12 for C1 PFAl;[63] 0.48 ± 0.03 × 10−12
for C1 PFAl;[61] 0.53 ± 0.08 × 10−12 for C2 PFAl;[60] 0.58
± 0.06 × 10−12 for C3 PFAl 1;[64] 0.61 ± 0.05 × 10−12 for
C4 PFAl 4;[64] 3.74 ± 0.77 × 10−13 for C4 NEtSA 4;[65] and
5.80 ± 0.80 × 10−12 for C4 NMeSE 4.[66]
Values for Henry’s law constants, vapor pressures, water solubilities, and acidity constants were estimated using
SPARC version 4.2 (accessed February 2009)[67−70] with
default calculation parameters at 298 K using SMILES
notation[71,72] for the PFCs as input structures. The atmospheric residence time at 298 K (τa,298K ; base e) of PFCs was
calculated as τa,298K = 1/(kOH,298K + kNO3,298K + kO3,298K +
kWD,298K + kDD,298K ), where kWD,298K and kDD,298K are the
estimated rates of wet and dry deposition, respectively.[73]

Results and discussion
Prediction of reaction rate constants towards gas-phase
atmospheric oxidants
Rate constants were estimated for the atmospheric reaction at 298 K of hydroxyl radicals (kOH,298K ) and nitrate radicals (kNO3,298K ) with all C1 through C8 perfluorinated sulfonic acid (PFSA) and carboxylic acid (PFCA)
congeners, as well as the straight chain C2 through C15
perfluorinated n:2 telomer olefins (FTOls), terminal alcohols (FTOHs), aldehydes (FTAls), and acids (FTAcs), and
the straight chain C1 through C8 sulfonamides (SAs) and
their N-methyl (NMeSA), N-ethyl (NEtSA), N,N-dimethyl

Fig. 1. General structures of the PFC classes under consideration.

(NNdiMeSA), and N,N-diethyl (NNdiEtSA) derivatives,
sulfonamidoethanols (SEs) and their N-methyl (NMeSE)
and N-ethyl (NEtSE) derivatives, and sulfonamidoacetates
(SAAs) and their N-methyl (NMeSAA) and N-ethyl (NEtSAA) derivatives (Fig. 1) using established literature correlations with molecular ionization potentials. To the best
of our knowledge, this represents the first structure-activity
relationship that successfully predicts the kOH,298K values
of perfluorinated alkyl compounds. Rate constants for the
atmospheric reaction at 298 K of ozone (kO3,298K ) with
the FTOls were also estimated. The modeling approach
for kOH,298K was validated by comparison of predicted
rate constants for a group of 20 individual PFCA, FTOl,
FTOH, FTAl, PFAl, PFAl hydrate, N-EtSA, and N-MeSE
congeners (see Materials and Methods section for identities) with experimental values reported in the literature
(Fig. 2). No well-boundarized experimental kNO3,298K or
kO3,298K values are available for comparison with our estimated rate constants. Good agreement was observed between the predicted and estimated kOH,298K values for this
training set, with an average signed error of 0.17 log10 units
(49% error) and an average unsigned error of 0.20 log10
units (57% error), both less than the generally accepted
criterion of 0.3 log10 unit deviation (±100% error) from experimental values among various established atmospheric
oxidation prediction models.[30,74−76]
We note that atmospheric temperatures are generally
<298 K, but given the absence of a validated Arrhenius relationship for the broad range of perfluoroalkyl
compound classes under study, our estimates for 298 K
can be considered adequate for the screening level interpretations presented herein. For scaling the reaction rate
constants as inputs to more advanced atmospheric models, the relationships between Arrhenius parameters and

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Behavior and fractionation of perfluoroalkyl compounds

Fig. 2. Comparison of experimental (kOH,298K,exp ) and estimated
(kOH,298K,est ) logarithmic base 10 rate constants for the gas phase
reaction of hydroxyl radicals at 298 K with the calibration compound set. Error bars on x-axis are those quoted in the source
publication (see Materials and methods section for compound
identities, experimental kOH,298K values and associated errors,
and references). Error bars on y-axis are 95% confidence intervals
from the regression prediction equations. A 1:1 line (solid) and
upper and lower 2-fold deviations from the 1:1 line (dashed) are
shown for comparison.

kOH,298K values for other fluorocarbons[77] or general models with bond energies,[78] fragment methods,[76] and ionization potentials[79] could be used. Bond energies and
ionization potentials are not experimentally available for
the PFCs (nor are fragment constants for all potential
PFCs), and bond energy methods require knowledge of
the exact bond(s) undergoing cleavage (which is problematic for the complex array of products known to be obtained from reactions of some single PFC congeners with
hydroxyl radicals),[18,27,57−61,65,66] introducing further complexity and associated errors into the estimation approach.
However, it has previously been shown[65] that correcting
kOH,300K values for sulfonamides to estimated values at temperatures 40◦ C colder (260 K) than experimental using the
approach of Sulbaek-Andersen et al.[77] between activation
energies and kOH,298K values only increased the estimated
atmospheric lifetime by 1.6-fold, a ratio within the error of
the prediction method.
With similar reasoning, our estimated Henry’s law constants for all PFC classes will also vary with temperature,
but for consistency in comparison with the chemical degradation rate constants only values at 298 K are presented.
The freely available (i.e., SPARC and MOPAC) methods
used in this work will allow the interested reader to calculate the rate and partitioning constants at any temperature
desired for use in future modeling efforts. As well, we note
that gas-particle partitioning processes may be important
in assessing the atmospheric fate of PFCs, but the difficulty
in experimentally determining, modeling, and matching
observed gas-particle partitioning with theoretical expec-

939
tations has been noted by previous investigators.[6,65,80,81]
Once a more reliable understanding of the gas-particle partitioning for these compounds becomes available, the results can be incorporated into the general gas-phase framework presented here.
The kOH,298K values of all validation set compounds were
predicted within a factor of two from their experimental
values with the exception of the straight chain C4 NEtSA
(Fig. 2). The estimated kOH,298K value for this compound
was 2.3(0.8 to 6.5) × 10−12 cm3 molec−1 s−1 (range includes 95% confidence intervals on the estimate) as compared with the experimental value of 3.7(3.0 to 4.5) × 10−13
cm3 molec−1 s−1 reported by Martin et al.[65] The 6.2-fold
overestimation in gas phase hydroxyl radical reactivity for
this compound, in contrast with the good agreement between the predicted (6.6[2.4 to 18] × 10−12 cm3 molec−1
s−1 ) and experimental (5.8[5.0 to 6.6] × 10−12 cm3 molec−1
s−1 ) values for the straight chain C4 NMeSE[66] is difficult to
rationalize. For the C4 NMeSE, hydroxyl radical attack appears to involve both the alkyl chains (leading to products
such as the aldehyde via oxidation of the alcohol moiety)
as well as attack at the heteroatoms (resulting in PFSA and
PFCA products).[66]
In comparison, hydroxyl radical attack on the C4 NEtSA
yielded primarily the carbonyl α- and β-oxidation products
(i.e., ketone and aldehyde, respectively) on the ethyl chain,
although N H abstraction was noted as a possible contributing pathway.[65] Given that the only substantive difference between these two compounds is the replacement
of an amine N H group in the C4 NEtSA with a N CH3
group in the C4 NMeSE, the broad difference in both proposed mechanisms and rate constants warrants further experimental analysis. The current experimental data suggests
that this amine N H group deactivates the C4 NEtSA such
that it has a reported kOH,298K value 16-fold lower than
for the C4 NMeSE. In light of the mechanisms and products proposed for these two compounds, the reason for this
suggested deactivation is not clear.
Furthermore, Atkinson[30] has previously noted that the
reactions of hydroxyl radicals with aliphatic amines are
rapid (kOH,298K values on the order of 2 to 6 × 10−11 cm3
molec−1 s−1 ) and involve both C-H and N-H abstraction.
We note that our structure-activity model is also able to
accurately estimate the kOH,298K values of the four following model aliphatic amines (units are cm3 molec−1 s−1 ):
methylamine, PM6 = 3.2(1.2 to 8.5) ± 0.2 × 10−11 , lit. =
2.2 ± 0.2 × 10−11 ; ethylamine, PM6 = 4.0(1.5 to 11) ± 0.2
× 10−11 , lit. = 2.8 ± 0.3 × 10−11 ; dimethylamine, PM6 =
7.3(2.8 to 19) ± 0.2 × 10−11 , lit. = 6.5 ± 0.7 × 10−11 ; and
trimethylamine, PM6 = 13(4.9 to 33) ± 0.2 × 10−11 , lit. =
6.1 ± 0.6 × 10−11 in contrast to the result for NEtSA.
The kOH,298K values for SA reactivity are important in the
context of current conceptual and quantitative PFC atmospheric models. The available experimental kOH,298K values
for the C4 NEtSA and NMeSE have been generalized for all
SAs and SEs. As well, the results have been interpreted as
indicating that SEs do not likely contribute to the general

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940

Rayne et al.

Fig. 3. Estimated logarithmic base 10 rate constants at 298 K (log10 kx,298K ) for the gas phase reaction of hydroxyl radicals (closed
circles; log10 kOH,298K ) and nitrate radicals (open squares; log10 kNO3,298K ) with the C1 through C8 (a) PFSA and (b) PFCA congeners.
Error bars are 95% confidence intervals from the regression prediction equations.

global PFC atmospheric burden and are thus not likely
transported to remote locations prior to their degradation
into other products (which include SAs). By comparison,
SAs are thought to degrade much less readily, and likely
exhibit direct global transport mechanisms and are likely
to be transported to remote locations (in addition to their
production from precursors such as SEs).[14] Our findings
suggest that SAs are much more labile towards hydroxyl
radical attack than previously thought, which may reduce
their capacity to contribute to the observed SA loading –
and that of their degradation products, the PFCAs and PFSAs – in remote regions below what is currently believed.
Until the discrepancy between the single experimental data
point and the estimation results can be resolved, caution
should be exercised with regard to use of any kOH,298K values for SAs in atmospheric modeling efforts.
Modeling suggests that chain length has little effect on
the kOH,298K and kNO3,298K values for the straight chain C1
through C8 PFSAs and PFCAs (Fig. 3). Similar to our findings, Hurley et al.[57] reported that chain length has little effect on the kOH,298K values for the straight chain C1 through
C4 PFCAs (their relatively large error for trifluoroacetic
acid [C1 PFCA; ±22%] suggests that this compound may
not have a significantly lower kOH,298K value than the corresponding C2 through C4 isomers).[57] However, our findings
suggest that branching of the perfluoroalkyl chain greatly
decreases a congener’s reactivity towards hydroxyl or nitrate radical attack relative to more linear analogs, with estimated PFSA and PFCA intra-homologue rate constant
differences of up to 0.6 log10 units (4-fold) for kOH,298K values and up to 1.6 log10 units (40-fold) for kNO3,298K values
between the most branched and linear end members. Thus,
provided PFSAs and PFCAs remain in the gas phase during

atmospheric transport for a sufficient length of time to react
with hydroxyl or nitrate radicals, significant isomeric fractionation of their congener signatures could occur. The potential importance of this possible isomeric discrimination
towards gas phase oxidation relative to other atmospheric
removal processes, such as wet and dry deposition, as well
as air-water interfacial fractionation, is discussed in more
detail later. As well, it is generally believed that PFSAs and
PFCAs may exist primarily in the particle phase during atmospheric transport, which may prevent their reaction with
gas phase oxidants such as hydroxyl and nitrate radicals.
Additional environmental monitoring data and calibrated
models are required to better understand the gas-particle
partitioning of these compounds.
Consistent with current literature expectations based on
the limited experimental datasets,[20,29,58−66,82−86] the modeling approach does not predict any chain length effect on
kOH,298K and kNO3,298K values for the straight chain fluorotelomers or sulfonamides and their respective derivatives
(Table 1). As discussed by Vesine et al.,[58] the primary
step in the reaction of FTOls with hydroxy radicals is an
electrophilic addition of OH to the double bond. The dominant regiochemistry is thought to be OH addition to the
terminal carbon of the alkene moiety. Although terminal
OH addition to the FTOl alkene is expected to dominate,
resulting in the major products of this oxidative mechanism being the terminal alcohol FTOHs, hydroxyl radical
attack could lead to production of PFAls as an intermediate between the starting materials and any PFCA oxidation
products.[18,27,82] The PFAls also can exist as hydrates in the
atmosphere, and Sulbaek Andersen et al. have reported that
these compounds have several fold lower reactivity than the
corresponding non-hydrated aldehydes.[59]

Behavior and fractionation of perfluoroalkyl compounds
Table 1. Estimated logarithmic base 10 rate constants at 298
K for the reaction of hydroxyl radicals (log10 kOH,298 ), nitrate
radicals (log10 kNO3,298K ), and ozone (log10 kO3,298K ) with the
C1 through C8 straight chain members of various PFC classes.
Error bars are 95% confidence limits obtained from the predictive
regression equations.

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Class
FTOl
FTOH
FTAl
FTAc
SA
NMeSA
NEtSA
NNdiMeSA
NNdiEtSA
SE
NMeSE
NEtSE
SAA
NMeSAA
NEtSAA

log10 kOH,298K
(cm3
molec−1 s−1 )

log10 kNO3,298K
(cm3
molec−1 s−1 )

log10 kO3,298K
(cm3
molec−1 s−1 )

−11.8 ± 0.8
−11.8 ± 0.5
−11.7 ± 0.5
−12.5 ± 0.5
−12.2 ± 0.5
−11.6 ± 0.5
−11.6 ± 0.5
−11.2 ± 0.4
−11.2 ± 0.4
−11.4 ± 0.5
−11.2 ± 0.4
−11.3 ± 0.4
−11.9 ± 0.5
−11.4 ± 0.5
−11.4 ± 0.5

−18.1 ± 1.9
−16.8 ± 1.9
−16.5 ± 1.8
−18.7 ± 1.9
−18.0 ± 1.9
−16.2 ± 1.8
−16.4 ± 1.8
−15.2 ± 1.8
−15.1 ± 1.8
−15.9 ± 1.8
−15.2 ± 1.8
−15.4 ± 1.8
−17.1 ± 1.9
−15.8 ± 1.8
−15.9 ± 1.8

−19.7 ± 4.1
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a

Of note is that PFCA formation from the aldehyde precursors is apparently limited to the hydrated mechanistic pathway,[59] although the presence and absence of NOx
complicates interpretations regarding PFCA yields from
FTOHs.[82] FTOHs with terminal alcohol substitution undergo near quantitative hydrogen abstraction from the terminal carbon to give FTAls.[18,20,82] These FTAls can then
also undergo further terminal carbon oxidation by hydroxyl
radicals to yield FTAcs, as well as undergo other oxidation
mechanisms to yield PFCAs.[18,82] Our modeling results incorporate all these classes, and the findings provide equivalent absolute and relative hydroxyl radical rate constant
magnitudes to the corresponding previous experimental reports. Ellis et al.[20] noted in their work that the application
of Kwok and Atkinson’s[44] widely used structure-activity
relationship for kOH,298K estimation resulted in overprediction of the kOH,298K values for the C4 , C6 , and C8 FTOHs
by about a factor of 4.
Our modeling approach only slightly overestimates the
kOH,298K values of these compounds by factors of 1.5. Thus,
our model appears to be the best approach to date for
estimating the gas-phase hydroxyl radical rate constants for
perfluoroalkyl compounds, particularly given the known
difficulty in modeling these types of compounds with other
well known structure-activity methods.[44,87]
The SAs and their derivatives are a difficult group of
contaminants for which to address environmental fate issues, particularly those related to source apportionment.
Like the PFSAs and PFCAs, the sulfonamides have been
produced historically using methods that yielded both lin-

941
ear and branched congeners, and more recently by methods
giving only (or at least, dominantly) linear congeners.[2,17]
The sulfonamides may also, similar to the telomers, degrade
into PFCAs via atmospheric oxidation pathways.[65,66]
Thus, the ability to discriminate between these two possible
sources of PFCAs has been linked to the source profiles,
whereby the sulfonamides would be expected to have both
branched and linear congeners present (at least for historical sources of sulfonamides), while the telomers are strictly
linear isomers.[17]
In this context, though, the high levels of potential mixing among both current and historical direct PFSA and
PFCA inputs to environmental systems, as well as that
from precursors and their partitioning, suggests that much
additional work will be required before we obtain reliable
source apportionment methods for the perfluoroalkyl acids.
Unlike the PFSAs and PFCAs, the sulfonamides comprise
a large number of individual classes (e.g., SAs, NMeSAs,
NEtSAs, SEs and their derivatives, SAAs and their derivatives) that result in an intractably large number of individual isomers (i.e., there are 1771 congeners in the eleven C1
through C8 sulfonamide classes, of which we have only considered the 88 straight chain members here). As a result,
a better understanding of any perfluoroalkyl branching effects on the reactivity of these classes is best approached
by way of examining a reduced representative suite of linear and branched congeners. The lowest kOH,298K values
for the C8 PFSAs and PFCAs relative to the corresponding linear isomer were for branched compound 1 (1-ethyl1 ,2,2 -trimethylpropyl); and thus, we tested the presence
of a branching effect on the SAs using this perfluoroalkyl
chain isomer.
We found the following substantial differences between
predicted kOH,298K values (in cm3 molec−1 s−1 ) for the C8
1-ethyl-1 ,2,2 -trimethylpropyl (1) and n-octyl (89) isomers
for each of the following classes: SA, 1 (2.6 × 10−13 ), 89
(6.3 × 10−13 ); NMeSA, 1 (1.3 × 10−12 ), 89 (2.9 × 10−12 );
NEtSA, 1 (1.2 × 10−12 ), 89 (2.3 × 10−12 ); NNdiMeSA, 1
(2.7 × 10−12 ), 89 (6.7 × 10−12 ); NNdiEtSA, 1 (3.3 × 10−12 ),
89 (7.1 × 10−12 ); SE, 1 (2.2 × 10−12 ), 89 (3.7 × 10−12 );
NMeSE, 1 (3.3 × 10−12 ), 89 (7.0 × 10−12 ); NEtSE, 1 (3.4
× 10−12 ), 89 (5.6 × 10−12 ); SAA, 1 (6.9 × 10−13 ), 89 (1.3
× 10−12 ); NMeSAA, 1 (1.7 × 10−12 ), 89 (3.9 × 10−12 ); and
NEtSAA, 1 (2.1 × 10−12 ), 89 (3.7 × 10−12 ). Thus, it appears
the kOH,298K and kNO3,298K values for sulfonamides and
their derivatives will also display branching effects (about
a 2-to 3-fold lower reactivity for the branched congener 1
relative to corresponding linear congener 89) in a similar
manner to the PFSAs and PFCAs, resulting in potential gas
phase fractionation of multicongener sulfonamide profiles
towards a more linear isomeric signature.
Estimation of Henry’s law constants
To contextualize the calculated kOH,298K and kNO3,298K (and
kO3,298K for the FTOls) values, the wet (kWD,298K ) and dry

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942
(kDD,298K ) deposition rates of these compounds were calculated at 298 K and compared to estimated average atmospheric lifetimes towards each oxidant assuming global
average concentrations of hydroxyl (5 × 105 radicals cm−3 )
and polluted atmosphere concentrations of nitrate (2.4 ×
108 radicals cm−3 ) and ozone (7 × 1011 radicals cm−3 ).[30,88]
While concentrations of hydroxyl and nitrate radicals and
ozone can vary widely from region to region, these values
are adequate for an assessment of long-range atmospheric
transport potential and in determining the potential importance of congener specific atmospheric fractionation
towards interpreting PFC profiles reported from both populated and remote regions.
For local and regional scale atmospheric modeling, we
note that our rate constants will be of use with these more
case study type investigations. To estimate kWD,298K and
kDD,298K values, we followed the method of Brimblecombe
and Dawson[89] and Shepson[90] for kWD,298K and that
of Pul et al. for kDD,298K [73] as applied by Ellis et al.[20]
and Martin et al.[65] Under this approach, kWD,298K =
(Rr Ee(−z/Zx) )/(Zx (Heff + ϕ)) and kDD,298K = vDD /Zx =
1/[(ra +rb +rs )× Zx ], where Rr is the annual rainfall rate
(3.2 × 10−8 m s−1 ), E is the enhancement factor due to
evaporation of falling rain droplets (1.33), z is the characteristic height of stratus clouds (3500 m), Zx is the scale
height (2300 m), Heff is the dimensionless gas-aqueous effective Henry’s law constant at a relevant pH value, ϕ is
the fraction of air volume occupied by liquid water (1 ×
10−6 ), ra (192 s m−1 ) and rb (67 s m−1 ) are aerodynamic
and transport resistance terms, respectively, and rs is the
water surface resistance term (rs = Heff × rw , where rw is
assumed to be 105 for most organic compounds).
To calculate congener specific kWD,298K and kDD,298K values, Heff values are the primary variable. Little experimental
data is available regarding air-water partitioning of PFCs,
necessitating the interim application of estimated values.
It is important to note that for acidic PFCs (e.g., PFSAs,
PFCAs, FTAcs, SAs, NMeSAs, NEtSAs, SEs, and SAAs)
with pKa values near the acidities of natural waters (i.e.,
where total PFC concentrations at a given pH value may
contain significant contributions from non-volatile ionized
species), the Heff value will be pH dependent according
to the following formula, Heff = H◦ /(1+10pH−pKa ), where
H◦ is the pure component (non-ionized molecular form)
Henry’s law constant.[8] For non-acidic PFCs at environmentally relevant aqueous pH values (e.g., FTOls, FTOHs,
FTAls, and tertiary amidic SA and SE derivatives), H◦ is
equal to Heff , and the Heff value determined or estimated
at a particular pH value will apply across all pH values
relevant for natural aquatic systems.
While we would expect the FTAcs and SAAs to have
carboxylate pKa values between about 3 and 4 (SPARC estimates a pKa of between 2.8 and 3.1 for the FTAcs and a
value between 3.9 and 4.0 for all SAAs, decreasing slightly
with increasing chain length for both classes), consistent
with other members from the general class of aliphatic car-

Rayne et al.
boxylic acids,[91] and which can likely be reliably estimated
by computational methods such as SPARC, little reliable
information is available regarding the pKa values of the
PFSAs.[92] Thus, methods that demonstrably estimate an
Heff value for FTOls, FTOHs, FTAls, and FTAcs that is
validated by comparison to available experimental values
will likely also provide a sufficiently accurate corresponding pKa value (where appropriate) to allow calculation of
a reliable Heff value at any relevant environmental pH.
However, as we discuss in more detail next, the pKa values for the PFSAs and PFCAs are currently not well constrained, and caution must be exercised in extrapolating
any Heff values that agree with experimental values for a
particular pH value to other pH values for which experimental Heff measurements are not available. The amidic
nitrogen-hydrogen bond in primary and secondary substituted perfluoroalkyl sulfonamides (e.g., SAs, NMeSAs,
NEtSAs, SEs, and SAAs) is also acidic at environmentally
relevant pH values, with linear congeners displaying pKa
values up to several units lower than the most branched
isomers.[93] It appears that SPARC may be able to reliably estimate the pKa values of the primary and secondary
amides for these PFC classes,[93] and thus, the corresponding current modeling efforts incorporate the estimated pH
dependence of Heff values.
The only Heff related experimental data available for the
PFSAs are a water solubility range of 520 to 570 mg/L
and a vapor pressure of 3.3 × 10−4 Pa for the C8 PFSA
89 (i.e., linear PFOS), giving a calculated Heff of 3.1 ×
10−6 atm L mol−1 for pure water at an unspecified pH.[94]
This compares reasonably with a SPARC estimated value
of 1.5 × 10−7 atm L mol−1 at pH 7, particularly given the
uncertainties in the experimental values for vapor pressure
and solubility, as well as the known issues in estimating
Henry’s law constants from these physicochemical properties compared to direct measurements. For the PFCAs,
experimental Heff data are only available for C1 PFCA (i.e.,
trifluoroacetic acid) and C7 PFCA 39 (i.e., PFOA). SPARC
estimates the Heff value for these two compounds at pH 7
as 9.6 × 10−8 and 7.3 × 10−8 atm L mol−1 , respectively. Li
et al. provide the only experimental Heff value for C7 PFCA
39 of 2.5 × 10−2 atm L mol−1 at pH 0.6.[95] The corresponding SPARC Heff value at pH 0.6 is in good agreement at
3.92 × 10−3 atm L mol−1 .
Based on a number of assumptions, Armitage et al.[25]
calculated a dimensionless Heff for C7 PFCA 39 of 1.7 ×
10−8 , which agrees reasonably well with the SPARC value of
3 × 10−9 . In addition, while the water solubility of C7 PFCA
39 as estimated by SPARC (320 mg/L assuming a melting
point of 52◦ C[8] ) is significantly lower than the reported
values of 3500 mg/L,[96] 4100 mg/L,[97] and 9500 mg/L,[98]
the SPARC estimated vapor pressures for the linear C7 ,
C8 , C9 , C10 , and C11 PFCAs (with literature values[99] in
parentheses) are 1160 Pa at 59.3◦ C (128 Pa), 4910 Pa at
99.6◦ C (1120 Pa), 10500 Pa at 130◦ C (3129 Pa), 4140 Pa at
112◦ C (616 Pa), and 5500 Pa at 128◦ C (856 Pa), respectively,

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Behavior and fractionation of perfluoroalkyl compounds

943

Fig. 4. Comparison between SPARC calculated and semiempirical PM6 method estimated (from ref.[92] for PFSAs and ref.[102] for
PFCAs) pKa values for the (a) PFSAs and (b) PFCAs. A 1:1 line (dashed) is shown for comparison.

indicating modest agreement with experimental data with
SPARC overestimating the vapor pressures by 4- to 10- fold.
The Henry’s law constant of C1 PFCA has been determined at between 1 × 10−4 and 2 × 10−4 atm L mol−1 at
assumed pKa values between 0.2 and 0.5.[100,101] By comparison, SPARC estimates a Heff value of 6 × 10−2 at pH
values in this acidity range. However, the current version
(v. 4.2) of SPARC estimates an anomalously high pKa of
1.14 for trifluoroacetic acid, slightly improved relative to
previous reports of 1.4 from prior SPARC versions, but
still substantially higher than the experimental values between 0.3 and 0.6.[102,103] By comparison, v.4.2 of SPARC
gives a pKa of −0.16 for C7 PFCA 39, equal to historical
calculations with prior versions of this software.[102,103] As
we[102,103] and others[23,104−108] have argued, the pKa values of the PFCAs are the subject of dispute (with proposed
acidity constant values for C7 PFCA 39 ranging over several
orders of magnitude), resulting in potential questions about
prior determinations of PFCA physico-chemical properties
at pH values greater than about −2 to −3 (where all parties
agree ionization would be near completely suppressed).
The SPARC-calculated pKa values for the C1 through
C8 congeners also do not agree well with values obtained
by the semiempirical PM6 method pKa prediction algorithm (Fig. 4; PM6 estimates of pKa for PFSAs and PFCAs
taken from ref.[92] and[102,103] , respectively). Although we
cannot resolve the differences in experimental and SPARCestimated Heff values for trifluoroacetic acid at low pH values, we note that Ellis et al.[13] used an Heff value of 1 ×
10−4 atm L mol−1 when modeling the atmospheric concentrations of this compound in rainwater near Toronto,
Ontario, Canada. Given a pH range of 4.0 to 4.5 for rainwater in Southern Ontario (National Atmospheric Deposition Program/National Trends Network data for 2007;
http://nadp.sws.uiuc.edu/), SPARC predicts Heff values
ranging from 4 × 10−5 (pH 4.4) to 1 × 10−4 (pH 4.0) atm
L mol−1 , equal to the Heff values currently being used in

atmospheric models for this compound. In sum, the experimental data to date for PFSAs and PFCAs suggests
SPARC may provide an adequate screening assessment of
the congener specific Henry’s law constants for these two
PFC classes, and we have used the SPARC derived Heff
values without correction.
As noted above, the pH being considered for the atmospheric fate of PFSAs and PFCAs will play a major role
in the relative importance of various processes. This fact is
illustrated in Figure 5 showing SPARC estimated Heff values for C8 PFSA 89, C1 PFCA, and C8 PFCA 39 that vary
over six orders of magnitude between the environmentally
relevant pH values of 3 and 9. Similarly, with pKa values
of some congeners between 6 and 7,[93] acidic sulfonamide
groups will also play an important role in various partitioning processes. Consequently, studies into the atmospheric

Fig. 5. pH dependence of SPARC estimated Heff values for C8
PFSA 89 (linear PFOS; solid line), C7 PFCA 39 (linear PFOA;
dashed line), and C1 PFCA (trifluoroacetic acid; dashed-dot-dot
line).


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