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Journal of Environmental Science and Health, Part A
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Linear free energy relationship based estimates for the congener specific
relative reductive defluorination rates of perfluorinated alkyl compounds
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 January 2009

To cite this Article Rayne, Sierra, Forest, Kaya and Friesen, Ken J.(2009)'Linear free energy relationship based estimates for the

congener specific relative reductive defluorination rates of perfluorinated alkyl compounds',Journal of Environmental Science and
Health, Part A,44:9,866 — 879
To link to this Article: DOI: 10.1080/10934520902958625
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Journal of Environmental Science and Health Part A (2009) 44, 866–879
C Taylor & Francis Group, LLC
Copyright
ISSN: 1093-4529 (Print); 1532-4117 (Online)
DOI: 10.1080/10934520902958625

Linear free energy relationship based estimates for the
congener specific relative reductive defluorination rates of
perfluorinated alkyl compounds
SIERRA RAYNE1 , KAYA FOREST2 and KEN J. FRIESEN1
1

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2

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

Linear free energy relationships (LFERs) were developed to estimate the congener specific relative rates of reductive defluorination
for a suite of perfluorinated compound (PFC) classes. The LFERs were based on the semiempirically calculated lowest unoccupied
molecular orbital energy (ELUMO ) using gas and aqueous phase computations with the PM6 and RM1 methods. PFC classes in the
modeling effort included the C1 through C8 perfluoroalkyl sulfonates (PFSAs), carboxylates (PFCAs), sulfonyl fluorides (PFSFs),
sulfonamides and their derivatives (SAs), and the perfluorotelomer alcohols (PFTAls), olefins (PFTOls), and acids (PFTAcs). Gas
and aqueous phase calculations using the PM6 method predict that branched PFSA, PFCA, and PFSF congeners will have more
rapid reductive defluorination kinetics than their linear counterparts. The RM1 method predicts that only PFSFs will display intrahomologue dependent branching effects. For the PFSAs and PFSFs, both the PM6 and RM1 methods predict no significant difference
in mean rates of reductive defluorination between the homologue groups. For the PFCAs, the PM6 method suggests no significant
difference in inter-homologue mean rates of reductive defluorination, whereas the RM1 method predicts a significant increase with a
lengthening perfluoroalkyl chain. All approaches used suggest that the intrahomologue variability in reduction rates increases with
increasing chain length for PFSAs, PFCAs, and PFSFs, implying that the larger homologue groups in these classes will see a more
rapid linearization of the congener profiles under reducing conditions than their lower homologue counterparts. Chain length has a
negligible effect on the estimated rates of SA reductive defluorination, but a significant role for the fluorotelomer derivatives. Ratios
of rates between the C8 :C1 straight chain telomeric congeners are expected to range up to 200-fold depending on the computational
combination. The kinetics for reductively defluorinating PFC starting materials will likely be 2 to 3 orders of magnitude more
rapid than for most of the partially defluorinated degradation products. Significant quantities of partially defluorinated PFCs are
thus expected to be observed under steady state conditions during reductive treatment processes, leading to a potentially significant
reservoir of these compounds residing in reducing environmental and biological systems.
Keywords: Reduction, perfluorinated compounds, defluorination, congener specific, perfluoroalkyl sulfonates, perfluoroalkyl carboxylates, perfluoroalkyl sulfonyl fluorides, perfluoroalkyl sulfonamides, perfluoroalkyl telomers.

Introduction
Perfluorinated compounds (PFCs) are used in a range of
products, most notably as surface active agents for a number of industrial and consumer applications. Because of
these historical and current anthropogenic use patterns and
subsequent release pathways, PFCs are widely reported as
global contaminants in various environmental compartments such as terrestrial and aquatic biota, waters and
wastewaters, soils and sediments, and the atmosphere.[1−3]

Address correspondence to Sierra Rayne, Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba, Canada.
E-mail: rayne.sierra@gmail.com
Received January 8, 2009.

The current weight of evidence indicates that PFCs are
bioaccumulative, persistent in environmental systems, have
the potential to be transported over long-range distances,
and may pose various toxicological effects at environmentally relevant concentrations.[4,5] The major classes of
PFCs include the perfluorinated sulfonates (PFSAs), carboxylates (PFCAs), telomeric alcohols (PFTAls), olefins
(PFTOls), and acids (PFTAcs), sulfonamides (SAs), and
their derivatives (Fig. 1).[1,6]
Field research efforts to date have typically focused
on characterizing levels and patterns of PFCs in the
environment and organisms, supplemented with the
development and application of multimedia models.[7−9]
A variety of techniques have been investigated for the
removal of PFCs from waste streams, including sorption and filtration,[10,11] biodegradation,[12−18] thermal

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Defluorination of perfluorinated alkyl compounds

867

Fig. 1. Structures of the PFC classes under consideration.

approaches,[19] sonochemical methods,[20,21] and direct and
catalyzed photodegradation.[22−26] In order to understand
how PFCs behave in natural systems and respond to treatment approaches, a knowledge base of physicochemical
properties[27−37] is also being generated by the scientific
community.
Despite the number of investigations regarding the partitioning behavior of PFCs and corresponding molecular
properties, the rates and products from atmospheric hydroxyl radical attack, and bioaccumulation, bioconcentration, and biotransformation studies, little is known regarding some potentially important routes of transformation.
Of note is the relative absence of information on reductive transformations of the highly oxidized perfluoroalkyl
chains. In both natural and anthropogenic reducing systems, reductive defluorination reactions of PFCs could play
an important role in their environmental and biological
fate. If PFCs are reductively transformed, such processes
could be exploited in the development of novel or modified
treatment methods, will need to be incorporated into environmental and pharmacological models when undertaking
source apportionment and loading studies, and the possible toxicological behavior of any partially defluorinated
products will need consideration. Until recently, it was generally assumed that the PFC perfluoroalkyl chains would
be relatively inert to reductive transformations. This belief
was driven primarily by information brought into the public domain through the release over the past two decades
of historical studies—usually narrowly applicable standard

methods—conducted by the major PFC manufacturers.
However, two studies have now provided proof-of-principle
that C2 to C8 PFSAs can be reductively defluorinated,[38,39]
opening up a promising new field of work for PFC researchers to determine if these findings can be extended
to other PFC classes such as the carboxylates and telomers, to new reducing systems, and across a wider range of
congeners within each PFC class.
The first of the pioneering reductive defluorination studies was by Hori et al.,[38] who reported on the degradation of the straight chain perfluorooctane sulfonate (C8
PFSA 89) and its corresponding C2 through C6 straight
chain analogs using zero valent iron, zinc, copper, and aluminum in subcritical water. Subsequently, Ochoa-Herrera
et al.[39] used vitamin B12 as the catalyst and Ti(III) citrate as the bulk reductant in anoxic aqueous solution to
achieve reductive defluorination of C8 PFSA 89 and some
of its monomethyl branched isomers (C8 PFSAs 83, 85, 86,
87, and 88). The rate constant for reduction of the branched
C8 PFSA isomers (kr = 0.0204 h−1 ) was reported to be several orders of magnitude slower than for chlorinated solvents such as carbon tetrachloride and tetrachloroethylene,
but more rapid than other halogenated organics such as
cis-dichloroethylene and some chlorinated benzenes. Perfluoroalkyl groups have also been recently hydrodefluorinated using silylium-carbonate catalysts,[40] but these catalysts require a C-H bond to be present on a vicinal carbon
to effect C-F bond cleavage. Thus, this approach has not
been proven applicable for perfluoroalkyl chains but may

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868
be useful on the partially defluorinated reduction products
of PFCs.
We have previously argued for the need to broaden current PFC investigations into the congener-specific domain,
particularly given the large number of possible congeners in
the higher homologue PFCs (e.g., there are 89 possible congeners on a perfluorinated C8 chain with a terminal head
group).[41] The previous and current research focus on the
straight chain members of each class and homologue group
is understandable, given how these isomers are typically the
major congeners in technical mixtures, and because authentic standards and well established analytical methods are
available for the straight chain compounds. However, the
lesson of history with other multi-congener contaminant
classes (most notably the halogenated dibenzo- p-dioxins
and furans and biphenyls) is that some congeners may dominate from a toxicological perspective even though their
contributions to the overall mass loading are minimal.
Furthermore, congener-specific partitioning and transformation pathways may exist that complicate simple massbalance type source apportionment efforts that do not
include higher levels of intra-homologue transformation
complexity. Consequently, the current study sought to develop a congener specific linear free energy based approach to estimate the relative rates of reductive defluorination for various PFC classes. In addition, we wanted
to examine whether any significant intra-class variations
exist in the rates of PFC reductive transformation that
may warrant future congener specific studies, and if so,
would help guide the research community in identifying
which PFC congeners would be of most value as authentic
standards upon which to test and calibrate the modeling
results.

Materials and methods
Computational approach
Congener specific PFC identifications in the manuscript
refer to the general numbering approach published
elsewhere.[41] Gas phase molecular structures were initially
optimized with the MM2 molecular mechanics energy
minimization algorithm using a minimum RMS gradient of 0.100. The gas phase structures were then further
optimized using the PM6[42] and RM1[43] methods with
MOPAC2009.[44] The PM6 method is an improvement on
the prior PM3[45] semiempirical computational method,
and the RM1 method is an improvement on the prior
AM1[46] semi-empirical method. Gas phase geometry optimizations in MOPAC2009 were conducted with the following keywords in the input file header: RM1 or PM6
(depending on desired method); BONDS; CHARGE = 0;
SINGLET; GNORM = 0.01. Aqueous phase geometry
optimizations in MOPAC2009 were conducted using the
COSMO method for investigating solvent phenomena[47]

Rayne et al.
with the following keywords in the input file header: RM1
or PM6 (depending on desired method); EPS = 78.4;
RSOLV = 1.0; BONDS; CHARGE = 0; SINGLET; LET;
DDMIN = 0.0; GNORM = 0.01.
LFER model development
The LFER model for estimating the relative rates of reductive defluorination (kred /kred,min )est within each PFC class
was developed via established relationships between the energy of the lowest unoccupied molecular orbital (ELUMO )
and surface area normalized reduction rate constants (kred )
using zero valent metal reductants (e.g., Fe, Mg) across a
range of halogenated aliphatic and aromatic contaminants.
In the absence of quantitative PFC kred benchmarks upon
which to anchor absolute kred estimates, values were normalized to the minimum estimated kred (kred,min ) within
each PFC class and modeling approach (i.e., the following
four gas and aqueous phase PM6 and RM1 combinations:
PM6(g) , PM6(aq) , RM1(g) , and RM1(aq) ).
Prior work has also shown that since calculated
ELUMO energies are generally reliable and consistent only
within a particular compound class, but often not between classes,[48] the kred /kred,min values were normalized
only within each PFC class. Based on this reasoning,
kred /kred,min values cannot be compared between PFC
classes, and can only be used to reliably identify relative
trends in reduction kinetics within individual PFC classes
and modeling combinations.
Scherer et al.[49] investigated the correlations between
ELUMO and the surface area normalized kred values for a
suite of chlorinated methanes, ethanes, and ethenes. Both
semiempirical gas phase and aqueous phase calculations
were performed with the AM1 and PM3 methods and the
COSMO technique, and ab initio gas phase calculations
were conducted at the 6-31G* level.
Solvation effects at the semiempirical level, or the use
of the higher level ab initio gas phase calculations, only
slightly improved the strong correlations (r2 > 0.76) between ELUMO and kred (log10 kred ∝ −1.5 × ELUMO ). Chen
et al.[50] also examined the rate constants for dechlorinating a range of chlorinated methanes, ethanes, and ethenes,
and found a strong correlation (r2 > 0.92) between ELUMO
and kred (log10 kred ∝ −1.5 × ELUMO ) using the AM1 and
MNDO semiempirical basis sets, with no significant difference in their model using gas or aqueous phase calculations. Similarly, Onanong et al.[51] focussed on a group
of chlorinated methanes, ethanes, and propanes and reported strong correlations (r2 > 0.86) between ELUMO and
kred (log10 kred ∝−1.65 to −1.95 × ELUMO ). With a group
of chlorinated benzenes and phenols, Liu et al.[52] found
a modest correlation (r2 = 0.40) between ELUMO and kred
(log10 kred ∝−1.2 × ELUMO ) using the PM3 method.
Other work by Patel and Suresh[53] on reduction by
a magnesium-silver system for chlorophenols reported a
strong correlation (r2 = 0.998) between ELUMO and kred

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Defluorination of perfluorinated alkyl compounds

869

Fig. 2. Potential reductive defluorination pathways for C8 PFSAs 10 and 89.

(log10 kred ∝−2.6 × ELUMO using the data in Figure 8 from
ref.[53] ; note: the authors regressed kred versus ELUMO in this
figure, although the raw data was provided in ref.[53] for our
current re-analysis) using the AM1 method.
Other groups have found improved LFER correlations
with kred using a multiple regression approach,[50,52,54−56]
primarily based upon coupling carbon-halogen bond dissociation energies (D(R−X) ) with other descriptors such as
the overall standard free energy of reaction ( G◦rxn ) for a
particular reduction pathway. However, these more complex LFERs have been restricted to simple haloalkanes
with one or two carbon chain lengths, where either the major primary reductive dehalogenation product is known,
or the molecular simplicity allows ready calculation of a
limited number of products. Multiple dependent variable
approaches such as these, having a path dependence built
into the LFER modeling approach, cannot be practically
applied to complex and larger molecule multi-congener
contaminant classes such as the environmentally relevant
PFCs.
The number of potential congeners in each homologue
group increases exponentially with chain length for PFCs
having >4 carbons in the perfluoroalkyl chain,[41] and each
congener has a number of distinct C-F bonds, leading to an
intractably large number of possible mechanisms and products arising from reductive defluorination. An example of
the potential number of reductive defluorination pathways
with differing energy profiles to illustrate this issue is given
in Figure 2 for the highly branched C8 PFSA 10 and the
linear C8 PFSA 89.
For these reasons, LFERs and their quantitative
structure-activity and structure-property counterparts
(QSARs and QSPRs, respectively) for PFCs are likely best
approached initially by way of univariate models such as

presented here, following which more complex multivariate
models can be developed to test detailed hypotheses on a
select group of congeners. Based on our review of the most
relevant available published regression constants between
ELUMO and kred , we chose to apply a conservative model
for kred values, log10 kred ∝−1.5 × ELUMO , as developed by
Scherer et al.[49] This regression constant of −1.5 between
ELUMO (in units of eV) and log10 kred (in arbitrary units for
our purposes) results in a 31.6-fold increase in kred for each
one eV decrease in ELUMO .
By comparison, the use of the less conservative regression constant of −2.6 from Patel and Suresh[53] would result
in a 398-fold increase in kred for each one eV decrease in
ELUMO . Assuming that the congener specific reduction patterns of PFCs follows that of other halogenated aliphatic
compounds, our approach may be underestimating actual
and relative kred values by an order of magnitude or higher.
At the present time, the lack of authentic standards for
various linear and branched PFC standards prevents calibration of our model, but we hope that such calibration
will be feasible in the near future as synthetic and purification methods for congener specific PFC standards improve.
Thus, the congener specific differences in relative rates of
reductive defluorination we report below for a number of
PFC classes should likely be considered conservative estimates that may be underestimating actual differences by
several fold or higher.
We stress that for strictly abiotic reduction reactions, it is
likely reasonable to assume that a LFER between the rate of
reduction and molecular properties such as ELUMO can apply across a range of compounds. However, for biotic processes, if enzymatic binding/associations are required,[57]
then various structural features and atom specific properties may be as important as bulk molecular descriptors,

870
thereby complicating the extension of LFERs to these types
of processes.
Data analysis

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Differences in the mean (kred /kred,min )est values between
homologue groups within each computational combination were evaluated using the parametric Tukey-Kramer
test with pairwise comparisons for one-way layout design
in the KyPlot v. 2.0 b. 15 statistical package (Dr. Koichi
Yoshioka, Department of Biochemistry and Biophysics,
Graduate School of Allied Health Sciences, Tokyo Medical and Dental University, Tokyo, Japan). Non-parametric
Kendall rank correlation analysis[58] was performed using
Wessa.net (v. 1.1.23-r3).[59]

Results and discussion
Perfluoroalkyl sulfonates, carboxylates, and sulfonyl
fluorides
Gas and aqueous phase PM6 calculations predict that
branched PFSA congeners in each of the C2 through
C8 homologue groups will be reductively defluorinated
more rapidly than the straight chain members (Fig. 3).
In comparison, the RM1 method suggests no difference
in (kred /kred,min )est values between branched and linear

Rayne et al.
congeners within a homologue group. No significant differences were observed in the mean (kred /kred,min )est values between homologue groups within each computational
combination due to the increasing intra-homologue variability with increasing homologue number: PM6(g) (C1 =
1.21, C2 = 1.02, C3 = 1.18 ± 0.23 [± std. dev.], C4 = 1.74
± 0.73, C5 = 1.86 ± 0.74, C6 = 2.18 ± 0.98, C7 = 2.57 ±
1.32, and C8 = 3.00 ± 1.75; p-values ranging from 0.28 [C5
vs. C8 ] to ∼1); RM1(g) (C1 = 2.18, C2 = 1.92, C3 = 1.65 ±
0.36, C4 = 2.39 ± 1.66, C5 = 2.29 ± 1.19, C6 = 2.43 ± 0.94,
C7 = 2.53 ± 0.94, and C8 = 2.79 ± 1.05; p-values ranging
from 0.57 [C3 vs. C8 ] to ∼1); PM6(aq) (C1 = 1.00, C2 = 1.28,
C3 = 1.48 ± 0.12, C4 = 2.02 ± 0.72, C5 = 2.12 ± 0.73, C6 =
2.44 ± 1.11, C7 = 2.79 ± 1.45, and C8 = 3.04 ± 1.55; pvalues ranging from 0.46 [C5 vs. C8 ] to ∼1); and RM1(aq)
(C2 = 1.51, C3 = 1.48 ± 0.35, C4 = 1.37 ± 0.25, C5 = 1.42
± 0.17, C6 = 1.47 ± 0.17, C7 = 1.60 ± 0.32, and C8 = 1.68
± 0.35; p-values ranging from 0.12 [C6 vs. C8 ] to ∼1).
For all estimates in the current work, relative values
should be taken to apply at 25◦ C. In general, activation energies for the abiotic transformation of halogenated
aliphatic compounds in aqueous solution are about 100 ±
10 kJ/mol.[56,60,61] These small differences in reported activation energies suggests that the relative orders and rates of
reductive defluorination for the PFSA, PFCA, and PFSF
congeners in this manuscript may apply to non-standard
state temperatures more representative of ambient environmental and biological systems. However, the determination

Fig. 3. Estimated relative rate constants for the abiotic reductive defluorination of the C1 through C8 PFSA congeners using the
PM6 ((a) gas phase and (c) aqueous phase) and RM1 ((b) gas phase and (d) aqueous phase) methods. Vertical dashed lines represent
divisions between adjacent homologue groups.

Defluorination of perfluorinated alkyl compounds
Table 1. τ coefficients and p-values of the Kendall rank correlations for the gas and aqueous phase PM6 and RM1 method
based estimated relative rate constants for the abiotic reductive
defluorination of PFSAs, PFCAs, and PFSFs.
PFSAs
Pair

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τPM6(g),RM1(g)
τPM6(g),PM6(aq)
τPM6(g),RM1(aq)
τRM1(g),PM6(aq)
τRM1(g),RM1(aq)
τPM6(aq),RM1(aq)

τ

p-value

0.156 0.005
0.826
∼0
0.225 5 × 10−5
0.094
0.09
0.343 5 × 10−10
0.240 1 × 10−5

PFCAs
τ

p-value

PFSFs
τ

p-value

0.169 0.002
0.034
0.53
0.707
∼0
0.867
∼0
0.109
0.04
0.353 6 × 10−11
0.241 7 × 10−6 −0.037
0.49
0.815
0
0.355 5 × 10−11
0.198 0.0002 0.317 4 × 10−9

of both the rates of reduction and their associated Arrhenius parameters for various representative linear and
branched congeners from different homologue groups in
each of these 3 contaminant classes will be required to better constrain the real world applicability of our results.
Similarly, while absolute reduction rates may vary with
different reductants,[62] the relative rates of reduction for
a given reductant should correlate with the relative standard reduction potentials of the target compounds (with
the assumption of a constant mechanism).[56] With this assumption and our use of ELUMO values as a proxy for the
standard reduction potentials[62] of PFCs, the calculated
(kred /kred,min )est values should apply across a wide range of
potential PFC reductants.
With the exception of the PM6 gas and aqueous phase
calculations (Kendall rank correlation coefficient, τ , of
0.83; Table 1), only modest correlations were noted among
the other computational combinations (τPM6(g)−RM1(g) =
0.16; τRM1(g)−RM1(aq) = 0.34; τPM6(g)−RM1(aq) = 0.23;
τRM1(g)−PM6(aq) = 0.09; τPM6(aq)−RM1(aq) = 0.24), showing a
relative high degree of variability both within and between
the methods. Only one combination had a non-significant
(p > 0.05) Kendall rank correlation (p = 0.09 for RM1(g) PM6(aq) ; p-values ranged from ∼0 to 0.005 for all other
combinations). For homologue groups with multiple congeners (i.e., C3 through C8 ), all approaches indicated that
the range of estimated kred /kred,min within each homologue
group (the kred,max /kred,min ratio) increases with increasing chain length (kred,max /kred,min : PM6(g) , C3 = 1.32, C4 =
2.46, C5 = 3.10, C6 = 4.19, C7 = 7.16, C8 = 8.93; RM1(g) ,
C3 = 1.36, C4 = 4.70, C5 = 4.70, C6 = 4.15, C7 = 5.55,
C3 = 5.41; PM6(aq) , C3 = 1.12, C4 = 2.34, C5 = 2.78, C6 =
4.08, C7 = 6.46, C8 = 5.94; RM1(aq) , C3 = 1.40, C4 = 1.44,
C5 = 1.49, C6 = 1.64, C7 = 2.45, C8 = 2.94).
As discussed in the Introduction, only two previous studies have investigated methods for reductively defluorinating
PFCs.[38,39] No detailed kinetic analysis was provided by
Hori et al.[38] on the rates of reductive defluorination for
the straight chain C2 to C8 PFSAs by zero valent metals,
preventing the benchmarking of our results against this

871
dataset. However, Hori et al.[38] did report approximately
equal amounts of PFSA starting material remaining after
replicate trials for each of these straight chain congeners under replicate treatment conditions (C2 = 4.2%, C3 = 3.6%,
C4 = 3.7%, C6 = 4.7%, and C8 = 0.5 to 2.2%), suggesting
little difference in their relative rates of reductive defluorination. These findings are consistent with our LFER
based estimates that also predict only modest differences
in the rates of reductive defluorination for these straight
chain PFSAs. Similarly, Ochoa-Herrera et al.[39] reported
reductive defluorination rates using vitamin B12 /Ti(III) citrate for the C8 monomethyl branched PFSAs 83 through
88 that appear to differ from each other only by a factor
of 2 or less, consistent with the predictions of our LFER
model. Their reported rate constant of 0.0204 h−1 for PFSAs 83 through 88 can be tentatively used to benchmark our
LFER model based kred /kred,min values shown in Figure 3
for this catalyst/reductant system. Although this rate constant appears to refer to the composite degradation of all
monomethyl branched C8 PFSA congeners, its application
to our LFER model data yields a range of kr values from
0.02 to 0.2 h−1 for all C1 through C8 PFSA congeners. The
highest/lowest estimated rate constants for reduction using vitamin B12 /Ti(III) citrate in each modeling combination are as follows: PM6(g) , 0.020 (straight chain C7 PFSA
39) to 0.21 h−1 (1,1 ,2,2 -tetramethylbutyl substituted C8
PFSA 23); RM1(g) , 0.020 (1-methylpropyl substituted C4
PFSA 2 and 1,1 -dimethylpropyl substituted C5 PFSA 2)
to 0.14 h−1 (2,2 ,3,3 -tetramethylbutyl substituted C8 PFSA
28); PM6(aq) , 0.020 (the C1 PFSA trifluoromethyl sulfonic
acid) to 0.17 h−1 (1,1 ,2,2 -tetramethylpropyl substituted C7

PFSA 5); and RM1(aq) , 0.020 (1,1 -dimethylpentyl substituted C7 PFSA 25) to 0.071 h−1 (1,2,2 ,3-tetramethylbutyl
substituted C8 PFSA 26).
However, we note that Ochoa-Herrera et al.[39] suggested
the straight chain C8 PFSA 89 was completely recalcitrant
to their reduction methodology. Our model does predict
that the rates of reductive defluorination for C8 PFSAs 83
through 88 will indeed be greater than that for C8 PFSA 89,
consistent with the results of Ochoa-Herrera et al.,[39] but
that the rate difference between these branched congeners
and C8 PFSA 89 will likely be small (less than a factor of
1.5). Additional investigations are needed to explain the
apparently unique recalcitrance of C8 PFSA 89 towards reductive defluorination using vitamin B12 /Ti(III) citrate (in
contrast to the high reactivity of some branched congeners
with the same reducing system) reported by Ochoa-Herrera
et al.,[39] while Hori et al.[38] reported relatively rapid and
near complete reductive defluorination by zero valent iron
for this straight chain homologue (and its shorter straight
chain analogs) in a manner consistent with our LFER
model.
As with the PFSA calculations, the gas and aqueous phase PM6 results suggest that within each homologue group, more branched PFCA congeners will be

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Rayne et al.

Fig. 4. Estimated relative rate constants for the abiotic reductive defluorination of the C1 through C8 PFCA congeners using the
PM6 ((a) gas phase and (c) aqueous phase) and RM1 ((b) gas phase and (d) aqueous phase) methods. Vertical dashed lines represent
divisions between adjacent homologue groups. Note that the (n+1) rule, whereby “n” is the length of the perfluoroalkyl chain (and
does not include the carboxylate carbon in the PFCA head group) as described in ref.[41] , applies to the numbering system used for
PFCA congeners and homologues (e.g., n-PFOA is C7 PFCA 39, n-PFNA is C8 PFCA 89, etc.).

reductively defluorinated more rapidly than their straight
chain counterparts (Figs. 4a and c). In contrast, the RM1
method predicts that there will be no significant trends in
(kred /kred,min )est values as a function of perfluoroalkyl chain
branching (Figs. 4 b and d). No significant differences were
observed in the mean (kred /kred,min )est values between homologue groups within the gas phase PM6 calculations:
C1 = 1.00, C2 = 1.21, C3 = 1.63 ± 0.32, C4 = 2.03 ± 0.82,
C5 = 2.27 ± 0.78, C6 = 2.69 ± 1.09, C7 = 3.15 ± 1.29, and
C8 = 3.54 ± 1.44; p-values ranging from 0.09 [C5 vs. C8 ]
to ∼1. Qualitatively similar findings were obtained from
the aqueous phase PM6 calculations, although one homologue group combination (C5 vs. C8 ; p = 0.018) had a significantly different mean (kred /kred,min )est value: C1 = 1.00,
C2 = 1.07, C3 = 1.35 ± 0.44, C4 = 1.74 ± 0.58, C5 = 1.86
± 0.48, C6 = 2.27 ± 0.69, C7 = 2.59 ± 0.80, and C8 = 2.91
± 1.00; p-values ranging from 0.018 [C5 vs. C8 ] to ∼1.
However, the RM1 gas and aqueous phase data displayed
significantly higher mean (kred /kred,min )est values for the C7
and C8 PFCA homologues relative to all lower homologue
groups (p-values ranging from <2 × 10−6 to 0.04 for the
gas and aqueous phase data; including a higher mean C8
value versus the C7 group, p < 2 × 10−6 for both gas
and aqueous phases), but no significant differences between

any combinations among the C1 through C6 homologues
(p-values ranging from 0.08 to ∼1). An increasing trend
of mean (kred /kred,min )est values is clearly evident with increasing chain length for both the gas and aqueous phase
datasets: RM1(g) , C1 = 1.00, C2 = 4.21, C3 = 8.56 ± 0.69,
C4 = 14.3 ± 4.5, C5 = 18.9 ± 7.5, C6 = 27.8 ± 7.9, C7 =
38.8 ± 9.9, and C8 = 51.4 ± 11.8; RM1(aq) , C1 = 1.00,
C2 = 5.49, C3 = 11.8 ± 4.6, C4 = 20.0 ± 8.9, C5 = 27.5 ±
11.6, C6 = 45.0 ± 12.6, C7 = 61.6 ± 16.8, and C8 = 84.4 ±
20.9. A similar pattern to the PFSAs in the Kendall rank
correlation results for the PFCAs was observed.
All computational combinations had significant rank
correlations (p-values ranging from ∼0 to 0.04), but only
modest τ -values ranging from 0.11 to 0.82. Of note is the
much improved correlation coefficient between the RM1
gas and aqueous phase results for the PFCAs (τ = 0.82)
compared to the correlation between these two methods for
the PFSAs (τ = 0.34). For the C3 through C8 PFCA homologue groups, all approaches indicated that the range
of estimated kred /kred,min within each homologue group
increases with increasing chain length (kred,max /kred,min :
PM6(g) , C3 = 1.32, C4 = 2.37, C5 = 2.84, C6 = 3.99, C7 =
4.02, C8 = 4.86; RM1(g) , C3 = 1.12, C4 = 2.27, C5 = 5.47,
C6 = 2.63, C7 = 3.01, C8 = 2.93; PM6(aq) , C3 = 1.43, C4 =

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Defluorination of perfluorinated alkyl compounds

873

Fig. 5. Estimated relative rate constants for the abiotic reductive defluorination of the C1 through C8 PFSF congeners using the
PM6 ((a) gas phase and (c) aqueous phase) and RM1 ((b) gas phase and (d) aqueous phase) methods. Vertical dashed lines represent
divisions between adjacent homologue groups.

1.95, C5 = 2.07, C6 = 2.77, C7 = 3.68, C8 = 4.27; RM1(aq) ,
C3 = 1.76, C4 = 2.70, C5 = 5.55, C6 = 2.58, C7 = 3.29,
C8 = 3.29).
Both gas and aqueous phase PM6 and RM1 calculations
predict that branched PFSF congeners in each of the C2
through C8 homologue groups will be reductively defluorinated more rapidly than the straight chain members (Fig.
5). No significant differences were observed in the mean
(kred /kred,min )est values between homologue groups within
each computational combination: PM6(g) (C1 = 1.10, C2 =
1.05, C3 = 1.24 ± 0.13, C4 = 1.61 ± 0.72, C5 = 1.75 ± 0.64,
C6 = 2.05 ± 0.92, C7 = 2.43 ± 1.21, and C8 = 2.76 ± 1.61;
p-values ranging from 0.33 [C5 vs. C8 ] to ∼1); RM1(g) (C1 =
4.37, C2 = 3.03, C3 = 2.42 ± 1.11, C4 = 2.63 ± 1.32, C5 =
3.08 ± 1.36, C6 = 3.32 ± 1.25, C7 = 3.44 ± 1.38, and C8 =
3.78 ± 1.47; p-values ranging from 0.54 [C4 vs. C8 ] to ∼1);
PM6(aq) (C1 = 1.00, C2 = 1.02, C3 = 1.30 ± 0.07, C4 = 1.90
± 0.95, C5 = 1.98 ± 0.70, C6 = 2.36 ± 1.23, C7 = 2.90 ±
1.66, and C8 = 3.30 ± 2.28; p-values ranging from 0.41 [C5
vs. C8 ] to ∼1); and RM1(aq) (C1 = 1.35, C2 = 1.55, C3 =
1.29 ± 0.40, C4 = 1.33 ± 0.14, C5 = 1.49 ± 0.26, C6 = 1.61
± 0.24, C7 = 1.64 ± 0.35, and C8 = 1.79 ± 0.47; p-values
ranging from 0.21 [C4 vs. C8 ] to ∼1).
The Kendall rank correlation analysis for the PFSFs was
qualitatively similar to that obtained for both the PFSAs

and PFCAs, with modest τ -values ranging from −0.037
to 0.867 and p-values ranging from ∼0 to 0.53. No significant correlations (p > 0.05) were observed between
the PM6(g) –RM1(g) (p = 0.53) and RM1(g) -PM6(aq) (p =
0.49) combinations, suggesting a wide difference in the
computational results for these two semi-empirical methods on the sulfonyl fluoride class. For the C3 through
C8 PFSF homologue groups, all approaches indicated
that the range of estimated kred /kred,min within each homologue group increases with increasing chain length
(kred,max /kred,min : PM6(g) , C3 = 1.16, C4 = 2.55, C5 = 2.80,
C6 = 3.99, C7 = 5.53, C8 = 8.57; RM1(g) , C3 = 1.96, C4 =
4.04, C5 = 4.93, C6 = 5.00, C7 = 6.05, C8 = 6.39; PM6(aq) ,
C3 = 1.08, C4 = 2.94, C5 = 2.80, C6 = 4.31, C7 = 7.24,
C8 = 11.82; RM1(aq) , C3 = 1.57, C4 = 1.27, C5 = 1.66,
C6 = 1.72, C7 = 2.52, C8 = 3.08).
In summary, gas and aqueous phase calculations using the semiempirical PM6 method predict that branched
PFSA, PFCA, and PFSF congeners will have more rapid
reductive defluorination kinetics than their linear counterparts in each of the C3 through C8 homologues. In contrast, the RM1 semiempirical method predicts that only
PFSFs will display intra-homologue dependent branching
effects on the estimated rates of reductive defluorination,
with no corresponding branching effect for the PFSAs and


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