Reduction of 2,4,6-trinitrotoluene by iron metal: Kinetic controls on product distributions in batch experiments

Article abstract of DOI:10.1021/es049129p

The reaction kinetics and product distributions for the reduction of 2,4,6-trinitrotoluene (TNT) by granular iron metal (Fe⁰) were studied in batch experiments under a variety of initial concentrations of TNT and Fe⁰. Although the kinetics of TNT disappearance were found to behave in accord with the standard theory for surface-mediated reactions, a complex relationship was found between the initial concentrations of TNT and Fe ⁰ and the appearance of the expected nitro reduction product, 2,4,6-triaminotoluene (TAT). TNT was completely converted to TAT only when the initial concentration of TNT was low and/or the initial concentration of Fe ⁰ was high. Mathematical analysis of a range of generic reaction schemes that produce stable end products in addition to TAT showed that (i) surface complexation of TAT is insufficient to describe all of our data and (ii) polymerization reactions involving TAT and/or various reaction intermediates are the likely source of the incomplete conversion of TNT to TAT at high initial TNT concentration and low Fe⁰ concentration. The relationship between TAT production and reaction conditions is shown to imply that passivation due to reaction products is more likely when the ratio of initial TNT concentration to Fe⁰ concentration is high and, therefore, that passivation rates observed at the laboratory scale are likely to be faster than those which would be observed at the field scale.

Full text of DOI:10.1021/es049129p

Environ. Sci. Technol. 2005, 39, 230-238
0
C becomes largesare apparent only at high rpm, where mass
Reduction of 2,4,6-Trinitrotoluene by
Iron Metal: Kinetic Controls on
Product Distributions in Batch
Experiments
transport effects are small. Another interaction involving
mixing rate is with molecular structure, where it has been
shown that mass transport effects on contaminant disap-
pearance kineticsswhich generally become more significant
at low rpmsare apparent only with contaminants for which
reaction at the metal surface is comparatively fast (and
therefore not rate limiting). Such highly reactive contami-
nants include nitrobenzene (relative to the carbon tetra-
chloride) (3) and 1,1,1-trichloroethane (relative to 1,1,2-
trichloroethane) (4).
J O E L Z . B A N D S T R A , R O S E M A R I E M I E H R ,
R I C H A R D L . J O H N S O N , A N D
P A U L G . T R A T N Y E K *
In other cases, interactions arise from competition among
parallel reaction pathways or mechanisms. This is likely to
be the case for the chlorinated ethenes, which react with Fe0
by competing pathways (e.g., R- vs â-dechlorinations) and
mechanisms (e.g., electron transfer vs hydrogen atom
transfer). In fact, it has been argued that the relative rates of
reduction for trichloroethene (TCE) and perchloroethene
Department of Environmental and Biomolecular Systems,
Oregon Health & Science University, 20000 NW Walker Road,
Beaverton, Oregon 97006-8921
The reaction kinetics and product distributions for the
reduction of 2,4,6-trinitrotoluene (TNT) by granular iron metal
(
0
PCE) vary with pH and C in a manner that reflects the
0
combined influence of these factors on the kinetics of
hydrogen atom transfer (5). The nitro aromatics are a similar
case, where competing parallel reaction pathways (e.g., nitro
reduction vs coupling) and mechanisms (again, electron
transfer vs hydrogen atom transfer) are likely to produce
interactions among primary effects.
(
Fe ) were studied in batch experiments under a variety
0
of initial concentrations of TNT and Fe . Although the kinetics
of TNT disappearance were found to behave in accord
with the standard theory for surface-mediated reactions,
a complex relationship was found between the initial
0
concentrations of TNT and Fe and the appearance of the
Nitro aromatic compounds in general, and 2,4,6-trini-
trotoluene (TNT) in particular, have several properties that
make them well-suited for probing process-level questions
expected nitro reduction product, 2,4,6-triaminotoluene
(
TAT). TNT was completely converted to TAT only when
0
the initial concentration of TNT was low and/or the initial
regarding the reactivity of Fe . Among these properties is the
0
well-characterized array of parallel and sequential reaction
pathwayssresulting in mixtures of characteristic productss
that occur under reducing conditions. The framework of this
array involves the reduction of nitro groups, as shown in
Scheme 1 for TNT. In Scheme 1, each set of three arrows
represents the sequential reduction of a nitro group to an
amino group via the corresponding nitroso and hydroxy-
lamino intermediates (which are not shown). Some of these
intermediates have been detected during reduction of TNT
concentration of Fe was high. Mathematical analysis
of a range of generic reaction schemes that produce stable
end products in addition to TAT showed that (i) surface
complexation of TAT is insufficient to describe all of our data
and (ii) polymerization reactions involving TAT and/or
various reaction intermediates are the likely source of the
incomplete conversion of TNT to TAT at high initial TNT
0
concentration and low Fe concentration. The relationship
0
between TAT production and reaction conditions is
shown to imply that passivation due to reaction products
is more likely when the ratio of initial TNT concentration to
by Fe , but the yields have been small and transient (6, 7).
Various combinations of the nitroso, hydroxylamino, or
amino products can undergo coupling to form dimers or
bound residues (8-12), but these products are difficult to
extract or identify and have rarely been quantified. 2,4,6-
Triaminotoluene (TAT) is the most quantifiable product of
0
Fe concentration is high and, therefore, that passivation
rates observed at the laboratory scale are likely to be faster
than those which would be observed at the field scale.
0
TNT reduction by Fe , but the yield of this product varies
widely, and this variability has not been explained.
The kinetics of the steps shown in Scheme 1 have been
described for a variety of reducing systems, including some
that contain Fe (6-8, 13-15). For the disappearance of nitro
aromatic compounds, a number of standard primary effects
Introduction
A decade of intensive research into the kinetics and mech-
0
anisms of contaminant reduction by zero-valent iron metal
0
(
Fe ) has led to widespread consensus regarding the primary
have been noted, such as the linear dependence of kobs on
effects that influence this process. Many of these effects [e.g.,
contaminant disappearance rate constant (kobs) versus
concentration of Fe (F
0
contaminant (C )] can be described with simple quantitative
models. These models have been shown to apply over a wide
range of contaminants, zero-valent metals, and experimental
designs (1). However, as more high-quality data sets become
available, evidence is accumulating for more complex effects
that involve interactions among two or more primary effects.
One of the first interactions to be well-documented
0
is between the effects of C and mixing rate (e.g., rpm) for
batch experiments done with azo dyes (2). In this case, it was
shown that site saturation effectsswhich generally arise as
/2
F
m
and rpm1 (6, 8). The effect of rpm on the rate of
0
nitrobenzene reduction has been shown to reflect a mixture
of mass transport and surface reaction control (3), which
leads to the interaction between effects of rpm and molecular
structure that was noted above. Adsorption could also be
rate limiting, although it is difficult to distinguish this from
mass transport control with simple batch experiments (7).
Under experimental conditions that minimize the role of
mass transport, however, the kinetics of nitro reduction are
strongly affected by the presence of competing adsorbates
m
) or kobs vs initial concentration of
(
16).
In contrast to the abundance of detailed analysis on the
disappearance kinetics of nitro aromatic compounds under
reducing conditions, very little quantitative information is
available on the processes that determine the products of
*
Corresponding author telephone: (503)748-1023; fax: (503)748-
1
273; e-mail: tratnyek@ebs.ogi.edu.
2
30
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 1, 2005
10.1021/es049129p CCC: $30.25

2005 American Chemical Society
Published on Web 12/02/2004

SCHEME 1
this reaction. The data reported by Oh et al. (7, 17) are suitable
for quantitative kinetic analysis of products from nitro
reduction, and their modeling of these data has provided
was preconditioned in this environment for 2 d to stabilize
geochemical and Fe surface conditions (15, 19). Then, the
0
bottles were spiked with TNT stock solution to begin the
reaction. Initial TNT concentrations were varied between 4
and 352 µM. Measurements of pH in bottles containing the
0
evidence that the type of Fe affects the types of surface sites
that are involved in nitro reduction (18). However, such effects
may be coupled to other factors in a manner similar to the
examples given above of interactions that reflect parallel and
competing reaction pathways. In this study, we describe
0
same Fe concentrations used in the kinetic experiments
after 2 d pre-exposure gave a pH profile beginning at pH ≈
-
1
-1
9.4 at 17 g L and increasing to pH ≈ 9.9 at 100 g L (data
m 0
interactions between F and C on the distribution of reaction
not shown).
products, using TNT as a model for an environmentally
relevant nitro aromatic compound. The results show the rate
of TAT appearance and limiting amount of TAT that appears
Periodically, 400-µL samples were withdrawn from the
bottles, filtered through a 0.45-µm nylon filter, and analyzed
by HPLC using a platinum C-18 column (Alltech, Deerfield,
IL). The mobile phase used for analysis of TNT and
intermediates was 55:45 methanol/water at a flow rate of 0.9
m 0
in solution are dependent on F and C in a manner that
suggests a strong influence of polymerization reactions
between reduction intermediates and/or TAT; which, in turn,
are influenced by other variables such as pH of the solution
-
1
mL min , whereas TAT analysis was conducted with 5:95
methanol/ammonium acetate buffer (50 mM, pH 7) at a flow
0
-1
or composition of the oxide film on the Fe . Such complex
rate of 0.7 mL min . In all cases, TNT and products were
interactions have implications for interpretation of data from
controlled experiments in the laboratory and for the design
and performance evaluation of full-scale remediation opera-
tions in the field.
monitored at 254 nm.
Radiolabeled experiments were performed by replacing
the TNT stock solution with a solution of 14C-labeled TNT
(Perkin-Elmer Life Sciences, 1.48 GBq/mmol). Concentration
data for 14C-labeled batch experiments were collected in the
same manner as the unlabeled experiments. C activity was
determined by mixing 0.3 mL of sample with 5 mL of
ScintiVerse Scintillant (Fisher, Fairlawn, NJ) and measuring
total decays with a liquid scintillation counter. In some of
the cases where solution-phase radioactivity at the end of
the experiment was substantially lower than at the beginning,
the supernatant was adjusted to pH 5 by adding concentrated
hydrochloric acid, and concentrations and radioactivity were
re-analyzed as described above.
14
Methods
2,4,6-Trinitrotoluene (TNT) was purchased from ChemSer-
vice (West Chester, PA); 2-amino-4,6-dinitrotoluene (2-
ADNT) and 4-amino-2,6-dinitrotoluene (4-ADNT) were
purchased from Sigma/Supelco (Bellefonte, PA); 2-hydroxy-
lamino-4,6-dinitrotoluene (2-HADNT), 4-hydroxylamino-2,6-
dinitrotoluene (4-HADNT), 2,4-diamino-6-nitrotoluene (2,4-
DANT), 2,6-diamino-4-nitrotoluene (2,6-DANT), and 2,4,6-
triaminotoluene (TAT) were purchased from AccuStandard
Sequential extractions were performed with 14C-labeled
TNT under anoxic conditions in 53-mL centrifuge vials. A
centrifuge vial containing 5 g of Peerless Fe was filled with
deionized water and 0.2 mL of [ C]TNT stock solution
resulting in an initial concentration of 264 µM. After being
mixed for 24 h, the supernatant was removed and the Fe0
was washed once with methanol. 5 mL of the respective
solvent was then added to the Fe , mixed for 24 h, and
separated by centrifugation. The extraction solvents, in order
of application, were acetonitrile, NaOH (pH 11), EDTA (pH
(
New Haven, CT). All chemical standards were >99% purity
and used as received.
0
0
Granular Fe was obtained from Peerless Powders and
1
4
Abrasives (Detroit, MI, “PMP Traditional” Size 8/50, >90%).
To remove fines, this material was sieved to the 18-35 mesh
0
size fraction. When not in use, the Fe was stored in a vacuum
0
desiccator. Only one batch of Fe was prepared, and all
0
analyses were performed with subsamples from this prepa-
2
ration. The specific surface area, determined by BET N gas
2
-1
adsorption, was 1.54 m g
.
1
1), HCl (pH 4), and EDTA (pH 3).
Batch experiments were conducted under anoxic condi-
tions in 60-mL serum bottles containing 1, 2, 3, and 6 g of
0
-1
Results
Fe , which correspond to 17, 33, 50, and 100 g L , respectively.
The bottles were filled with N -sparged deionized water (no
2
Kinetic Experiments and Data Fitting. Concentration time
series collected from batch experiments (e.g., Figure 1)
showed that TNT is reduced to TAT with some of the known
buffer, no headspace), sealed, and mixed by rotation at 20
rpm with the plane oriented 85° from horizontal. The Fe0
VOL. 39, NO. 1, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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231

where kTAT is a first-order rate constant, TAT
∞
is the
concentration of TAT at t f ∞, and TAT exp(-kTATt)
∞
represents the disappearance of a parent compound from
which TAT is produced. The TAT appearance data show only
a small amount of the positive concavity that is expected
during the early stages of a reaction that proceeds through
intermediate compounds. This suggests that the rate-limiting
process for TAT appearance is the disappearance of TNT.
We fit analytical solutions for the rate laws, obtained by
direct integration of eqs 1 and 2, to the TNT and TAT data
using Levenberg-Marquardt square error minimization (20).
In all cases, the total concentration (TNT
constant (kTNT or kTAT) where treated as fitting parameters.
Since TAT did not always complete the mass balance, we
fit the TNT disappearance and TAT appearance kinetics as
independent processes so that TAT need not equal TNT
0 ∞
or TAT ) and rate
∞
∞
0
and kTAT need not equal kTNT. The results are tabulated as
Supporting Information (Table S1), and some of the fitted
time courses are shown in Figures 2 and 3.
Effect of Initial Conditions. By performing batch experi-
FIGURE 1. TNT disappearance, transient 2-HADNT, 2-ADNT, 2,4-
DANT, and 2,6-DANT, and TAT appearance in batch reactors with
0
ments with different Fe concentrations (F
m
) and initial TNT
concentrations (TNT ), we explored the effects of reaction
0
-
1
TNT
0
) 176 µM and G
m
) 50 g L . Data for radioactivity in solution
from C-labeled TNT are plotted on the right axis (scaled so that
the calculated initial radioactivity corresponds to TNT ).
conditions on the kinetics of TNT reduction and on the
appearance of reduction products. Given the likely presence
14
0
0
of reduction products bound to the Fe surface (7, 16, 21)
and the implications of this bound residue for long-term
reactivity of the Fe , we designed our experiments to highlight
mass balance (i.e., TAT appearance).
intermediates in this reaction sequence appearing briefly at
low concentrations. These results are consistent with previous
studies that have examined the reaction mechanism of nitro-
aromatic reduction (8) and the relative abundance of the
intermediate species (7). Points that fell below the detection
limit have been omitted from Figures 1-3 and from the fitting
described below.
Analyses performed after 24 h of reaction indicate that
TNT and all reactive intermediates were entirely consumed
and that TAT was a stable end-product. In a number of cases
0
Figure 2 shows the results of batch experiments at TNT
0
-
1
)
176 µM with F
the surface mediated nature of the reaction, the rate of TNT
disappearance increases with F . TAT appearance, however,
responds to F in an unexpected fashion. TAT is close to
zero for F
e 33 g L- (Figure 2A) but increases to give nearly
complete mass balance at F
m
) 17, 33, 50, and 100 g L . Consistent with
m
m
∞
1
m
-
1
m
) 100 g L (Figure 2D). This
effect is inconsistent with simple partitioning of TAT onto
(Figures 2 and 3), the final TAT concentration was significantly
0
the Fe surface because a larger surface area would sequester
less than the initial TNT concentration. Experiments with
radiolabeled TNT showed that the mass imbalance was not
more TAT, not less.
) 50 g L-
1
1
4
Figure 3 shows experiments performed at F
with TNT
m
due to products in the solution phase (cf., C-labeled data
0
) 3.5, 35, 176, and 352 µM. The data in Figure 3
in Figure 1). This is consistent with the finding that reduction
products of nitro-aromatic compounds adsorb to the Fe0
indicate that, in contrast to our previous findings (6), TNT
disappearance rates decreased only slightly with increasing
TNT . The difference between this result and our previous
0
surface (16). However, decreasing the pH to 5 by addition of
HCl at the end of an experiment did not release a significant
additional quantity of TAT, and serial extraction experiments
yielded only a few percent of the missing radio-activity (data
not shown). These results indicate that some of the reaction
result is probably due to differences in the kinetic regime
under which the experiments were performed. The current
work was performed under mass transport or sorption limited
conditions, so we do not expect to see the influence of
accumulation of adsorbed products that we reported previ-
ously (6).
0
products were irreversibly bound to the Fe surface.
We found the kinetics of TNT disappearance to be
accurately described with a first-order rate law:
The data in Figure 3 indicate a nonlinear relationship
between TAT appearance and TNT
to solution-phase TAT when TNT
but a significant portion of the TNT is unaccounted for when
0
. TNT is mostly converted
d[TNT]
)
-kTNT[TNT]
(1)
0
e 35 µM (Figure 4A,B),
dt
TNT
0
g 176 µM (Figure 4C,D). The same trend was observed
where kTNT is the observed first-order rate constant. Pre-
-1
in batch data with F
only at TNT
which gave TAT
time courses for these experiments not shown).
The trend of decreasing mass balance with increasing
m
) 17 g L , which gave TAT
∞
≈ TNT
0
-1
0
-1
liminary experiments with low F
m
(13 g of Fe L , data not
0
) 3.5 µM and in batch data with F
≈ TNT
m
) 100 g L ,
shown) exhibited a steep initial drop followed by slower first-
order disappearance of TNT. This bimodal behavior is
consistent with mixed control of the kinetics by reversible
formation of a reactive surface complex (i.e., by mass
transport and/or adsorption) and irreversible surface trans-
formations (7). To minimize complications due to this
bimodal behavior and to achieve appreciable yields of TAT,
∞
0 0
for all cases except TNT ) 352 µM
(
0
TNT
0
suggests that the capacity of Fe to produce TAT can
. One explanation for
be overwhelmed by increasing TNT
0
0
this could be passivation of the Fe surface by TNT reduction
products, thereby preventing further reaction and causing
the accumulation of undetected intermediate species. Re-
spike experiments, however, indicated that, while some
m
we chose to focus on relatively high F , which produced
mass transport and/or sorption limited behavior.
The observed kinetics of TAT appearance could also be
described with a first-order rate law:
0
passivation occurred, the Fe was still reactive toward TNT,
both in the sense of TNT disappearance and in the sense of
TAT appearance (data not shown). The processes that yield
incomplete mass balance must, therefore, produce stable
d[TAT]
dt
)
kTATTAT exp(-kTATt)
(2)
∞
0
end-products and leave the Fe at least partially reactive.
2
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 1, 2005

FIGURE 2. TNT disappearance (closed circles) and TAT appearance (open circles) in batch reactors with TNT
0
m
) 176 µM and G ) (A)
-
1
1
7, (B) 33, (C) 50, and (D) 100 g L .
) 50 g L- and TNT
1
) (A)
FIGURE 3. TNT disappearance (closed circles) and TAT appearance (open circles) in batch reactors with G
.5, (B) 35, (C) 176, and (D) 352 µM.
m
0
3
Identification of processes that meet these criteria is the
principal subject of the remainder of this work.
the average value of the last few TAT points in the relevant
time series. Therefore, we chose to analyze the variables
controlling TAT appearance (and the behavior of kTAT noted
Quantitative Analysis. Figures 4 and 5 depict, in graphical
form, the fitting results described above and tabulated in the
above) using TAT
∞
as the dependent variable rather than
k .
TAT
Supporting Information. The plot of kTNT against F
A) shows a linear relationship, as has been reported
previously for TNT (6) and many other contaminants (22,
3). The slope of this line gives the surface area normalized
m
(Figure
4
Figure 5 shows TAT plotted against F and TNT . TAT
∞
m
0
∞
increases with respect to each of these variables, but in most
cases, TAT∞ appears to approach a horizontal asymptote
(which, if the slope is everywhere positive, is expected since
TAT e TNT ). In the case of F (Figure 5A), the value of the
2
-
3
-1
-2
rate constant, kSA ) 2.03 ( 0.10 × 10 min
value reflects the range of TNT that were included in the
calculation, even thoughsas noted aboveshigh TNT ex-
periments produce slightly lower rate constants than low
TNT experiments (probably due to the increased influence
of surface reaction kinetics for the high TNT experiments).
m
L. This
0
∞
0
m
0
0 0
asymptote is TNT , while for TNT (Figure 5B) the asymptotic
value appears to be a function of F . In general, to approach
m
0
a horizontal asymptote with positive slope, a function must
have negative concavity (i.e., curved downward). This feature
is apparent in the plot of TAT versus TNT (Figure 5B) but
0
The value of kSA reported here is about twice the value that
∞
0
0
we have reported previously for Peerless Fe (6, 15) but is
is less apparent in the plot of TAT∞ versus Fm (Figure 5A)
well within the range of kSA values that we reported previously
where the 176 and 352 µM data display mostly positive
0
-1
for similar types of Fe and the range of kSA values for TNT
concavity (i.e., curved upward), especially for Fm < 50 g L .
0
and Fe that have been reported by others (6, 15).
Since we expect the TAT versus F curve to approach TNT0
∞
m
A plot of kTAT versus F
m
(Figure 4B) shows features that
cannot be explained on the basis of the standard theory for
as F f ∞, the curve must have an inflection point (i.e., a Fcrit
m
below which little TAT is produced and above which nearly
all TNT is converted to TAT).
surface mediated chemical kinetics. For each value of TNT
TAT ≈ 0 at low F but increases linearly at high F
of the increase appears to decrease with increasing TNT
and the F
be larger for higher values of TNT
between kTAT and F could arise if the rate of TAT appearance
is controlled by TNT disappearance. If this were the case,
0
,
k
m
m
. The slope
Both the positive slope of TAT
negative concavity with respect to TNT
∞
with respect to F
m
and the
are inconsistent with
0
0
m
beyond which kTAT increases linearly appears to
. A linear relationship
significant adsorption of nitro reduction products, in contrast
to previous suggestions (16). As noted above, adsorption
0
m
would be expected to produce ∂TAT
increasing the adsorbent concentration (i.e., F
increase the amount of TAT that is adsorbed. At constant F
adsorption would be expected to produce ∂TAT /∂TNT
0 (as is observed) because increasing TNT would increase
the adsorbed concentration. Adsorption would, however,
produce TAT versus TNT profiles with zero concavity at
both low TNT
and high TNT
/∂F
< 0, because
∞
m
m
) would
however, the linear relationship would hold even at low F
m
m
,
and the slope would be independent of TNT
0
.
∞
0
>
Comparing kTAT to our fitted values of TAT
∞
(Figure 4C)
0
reveals a relationship between these parameters. This could
either indicate that the processes causing TAT to be less
than TNT are occurring throughout the course of the
reaction, or simply, that the fitting parameters kTAT and TAT
are covariant. Of the two parameters, TAT is more robust
because it is largely independent of modeling details (e.g.,
order of reaction); in fact, nearly identical TAT values to
those found by first-order fitting could be obtained by taking
∞
∞
0
0
0
where a linear isotherm would be expected
0
where saturation of adsorption sites would
∞
∞
occur. Since, under an adsorption mechanism, the slope of
the low TNT portion of the curve would be <1 while the
slope of the high TNT region would be equal to 1, the
transition from linear adsorption to site saturation behavior
0
∞
0
VOL. 39, NO. 1, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
233

∞
m 0
FIGURE 5. Fitted TAT plotted against (A) G and (B) TNT . The
coarse dashed line in panel B represents complete conversion of
TNT to TAT. Curves shown are the result of multi-variate fitting of
m
eq 13 with K(G ) given by eq 21.
SCHEME 2
FIGURE 4. Rate constants obtained from fitting (A) TNT disap-
pearance curves, (B) TAT disappearance curves plotted against G
and (C) fitted TAT values plotted against kTAT. A table of the fitting
results is included in the Supporting Information.
m
,
∞
would display positive concavity. This is in contrast to the
data in Figure 5B, which appear to possess a slope equal to
1
at low TNT
0
and a concave down transition to slope ≈ 0
“
Branch”, “Couple”, and “Partition” to denote the source of
at high TNT .
0
a specific UNK species. No subscript is used when a statement
applies to all three processes.
Modeling
The branching scenario involves the formation of a
product (or products) from the milieu of intermediates that
Scenarios Leading to Incomplete Mass Balance. To produce
the partial mass balances that we observed, there must be
reaction pathways that do not lead to TAT or reactions that
involve the transformation of TAT to undetected products.
These processes can be arranged into three scenarios:
branching, partitioning, and coupling (Scheme 2). INT
denotes a generic and/or lumped intermediate (which could
include the various intermediates shown in Scheme 1 as well
as TNT), and UNK represents undetected (unknown)
(
during the time course of our experiments) does not react
further to form TAT. To produce incomplete mass balance,
the branching reaction must be irreversible on the time scale
of our experiments. Physically, a branching reaction might
arise in this system due to coupling of nitroso intermediates
with hydroxylamino intermediates, forming a polymeric
0
substance that is likely to be sequestered on the Fe surface
(24).
0
productssmost likely residing on the Fe surfacesthat are
responsible for the incomplete mass balance that we often
observed. In the following analysis we employ the subscripts
In the coupling scenario, TAT reacts with INT and, once
all the INT is gone, the reaction stops, leaving the remaining
2
34
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 1, 2005

TAT unreacted. This scenario could arise in a polymerization
reaction similar to that leading to a branching scenario but
with TAT as one of the reactants (8). The branching scenario
is formally a subset of the coupling scenario. However, since
the coupling scenario involves the added complexities
associated with a feedback loop, we chose to analyze the two
as separate cases.
This notation is employed throughout the rest of the paper.
If we assume that mTAT ) mUNK, we can derive a formula for
∞
TAT by integrating the ratio of the rate of TAT production
to the rate of UNKBranch production from t ) 0 to t ) ∞ (details
given in the Supporting Information):
κ(F )
m
TAT ) TNT
0
(10)
In the partitioning scenario, TAT undergoes further
reaction to form undetected species. The reaction, in this
scenario, must be reversible, otherwise TAT would disappear
entirely. Such a scenario could arise from the reversible
∞
1
+ κ(Fm)
where κ ) kTAT/kUNK. Equation 10 satisfies eq 3 if and only
if ∂κ/∂F > 0 (proof given in Supporting Information),
implying that the rates of processes leading to TAT must
increase with F faster than the rates of processes leading to
UNKBranch. Equation 10 satisfies eq 4 if and only if ∂ κ/∂F
0 for 0 < F e Fcrit, where Fcrit is the inflection point in TAT
versus F (Figure 5A). This implies that the concavity of kTAT
with respect to F must be large as compared to the concavity
of kUNK (proof given in Supporting Information).
Equation 10 is linear with respect to TNT and, therefore,
0
m
sorption of TAT to the Fe surface. Since we have already
noted that adsorption cannot explain all aspects of our data,
we have included the partitioning scenario mainly for
completeness. However, we note that other reversible
reactions involving TAT could exist, the character of which
we address later.
To define models for TAT appearance based on the three
scenarios represented in Scheme 2, we require that the
models conform to the following criteria, which derive from
our discussion of the trends represented in Figure 5:
m
2
2
m
>
m
∞
m
m
0
does not satisfy eq 6. This is a result of the assumption, used
in deriving eq 10, that mTAT ) mINT. To see this, we assume
that fTNTfINT(t) in eq 7 is a Dirac-δ style pulse (modulated
∂
TAT∞
g 0
(3)
(4)
0
by TNT ) at t ) 0 such that eq 7 becomes
∂Fm
d[INT]
dt
mTAT
mUNK
2
g0 Fm < Fcrit
) -kTAT(F )[INT]
- kUNK(F )[INT]
(11)
∂
TAT∞
m
m
)
0 Fm ) Fcrit
e0 Fm > Fcrit
2
{
∂
Fm
with the initial condition
∂
∂
TAT
∞
[
INT]t)0 ) TNT0
(12)
g 0
e 0
(5)
(6)
TNT0
which is equivalent to assuming that the branching occurs
at TNT rather than at INT. Integrating eq 6 from t ) 0 to t
) ∞ and substituting eq 11 on the right-hand side yields a
2
∂
TAT∞
2
∂TNT0
relationship for TAT
Information):
∞
(details given in the Supporting
Rate equations can be developed for each of the regimes
shown in Scheme 2 by assuming reaction rates that are
proportional to the concentrations of the reacting species
TNT0
κ(Fm)
TAT )
dw
∆m
(13)
∞
∫
0
(
including, where appropriate, the reactive surface area).
κ(F ) + w
m
Owing to their linearity, the rate equations produced by this
procedure do not meet the criteria of eqs 3-6. The goal of
the modeling analysis that follows is to determine what
modifications must be made to the standard rate equations
in order to satisfy the above criteria and, in particular, to
determine whether recourse must be made to factors that
are not explicitly depicted in Scheme 2 (e.g., effects of pH or
where κ ) kTAT/kUNK, ∆m ) mUNK - mTAT, and the dummy
variable (w) has been substituted for [INT]. Equation 13
reduces to eq 10 when mUNK ) mTAT and satisfies eq 5 for all
κ, mUNK, and mTAT. Equation 6 is satisfied if and only if mUNK
>
mTAT (proof given in Supporting Information); therefore,
the rates of processes leading to UNKBranch must increase
with INT concentration faster than the rates of processes
leading to TAT.
2+
[
Fe ] in solution).
Branching. A model for the branching scenario can be
written by assuming that the rates of TAT and UNKBranch
formation obey a power law in INT concentration with rate
Coupling. A model can be written for the coupling
scenario in a fashion similar to the branching scenario with
the addition of a TAT concentration dependence to the rate
of UNKCouple formation:
constants that depend on F (25-29):
m
d[INT]
dt
mTAT
)
fTNTfINT(t) - kTAT(F )[INT]
-
m
d[INT]
dt
mTAT
mUNK
)
)
fTNTfINT(t) - kTAT(F )[INT]
-
kUNK(F )[INT]
(7)
(8)
m
m
nTAT
mUNK
νINTkUNK(F )[TAT] [INT]
(14)
m
d[TAT]
dt
mTAT
)
kTAT(F )[INT]
m
d[TAT]
dt
mTAT
kTAT(F )[INT]
-
m
d[UNKBranch
]
mUNK
nTAT
mUNK
)
kUNK(F )[INT]
(9)
m
νTATkUNK(F )[TAT] [INT]
(15)
(16)
m
dt
where
fTNTfINT(t) is a generic function representing the
d[UNKCouple]
nTAT
mUNK
)
νUNKkUNK(F )[TAT] [INT]
m
production of INT, k’s are rate constants, m’s are the orders
of reaction with respect to INT, and all concentrations are
initially zero. The parameter subscripts in eqs 7-9 correspond
to the product of the relevant reaction so that, for instance,
dt
where νTAT, νINT, and νUNK are stoichiometric factors such
mTAT is the INT reaction order for the INT f TAT reaction.
that
VOL. 39, NO. 1, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
235

0
νINT + νTAT
and partition coefficient on F
reactants and, therefore, to assume that reaction rates obey
a power law with respect F (28, 29):
m
is to treat Fe surface sites as
TNT ) [TNT] + [TAT] + [INT] +
[UNKCouple
]
0
νUNK
m
(
17)
∆
λ
and nTAT is the order of the coupling reaction with respect
to TAT. Setting nTAT ) 0 and νTAT ) 0 gives the branching
model described above. In the case where mUNK ) mTAT, an
κ(Fm) ) κ Fm
(21)
where κ ) kTAT/kUNK (as in eq 10 but with the Fm dependence
factored out), ∆λ ) λTAT - λUNK, and λ is the order of each
reaction with respect to reactive surface area. The conditions
given above imply that, for each of the three models, ∆λ >
∞
equation for TAT can be found by dividing eq 15 by eq 16
and integrating the result (details given in Supporting
Information):
1
.
nTAT
TNT - TAT
νINT - νTAT
TAT∞
0
∞
w
Under the power law assumption, a fitting equation can
)
dw (18)
∫
0
nTAT
be derived for TAT
branching:
∞
versus F
m
(Figure 5A) from eq 10 for
κ(F ) - νTATw
m
where κ ) kTAT/kUNK and w has been substituted for [TAT].
Equation 18 satisfies eqs 3 and 4 if and only if ∂κ/∂F > 0 and
> 0 (proof given in Supporting Information).
κFm∆
λ
m
TAT ) TNT
0
(22)
2
2
∞
∂
κ/∂F
m
∆λ
1
+ κFm
Equation 18 satisfies eqs 5 and 6 for any nTAT >0. The coupling
model, therefore, has the same essential features with respect
To achieve the sharp increase in TAT
∞
that we observed in
to F
m
as the branching model but produces the observed
without need for nonlinearity
the data, it was necessary to set ∆λ to fairly large values (6.7
for 176 µM, 3.6 for 352 µM). Since λUNK g0, this result indicates
that λTAT must be significantly greater than 1. It is reasonable
to expect the INT f TAT reaction to depend on F
of λTAT . 1 are physically unrealistic. If we set λTAT ) 1 and
TAT ) 0, the model does not reproduce the positive concavity
and inflection point that are shown in Figure 5A. Adding
nonlinearity to the concentration dependence of the reaction
rates (i.e., by employing eq 13 or eq 18) does not significantly
decrease the value of ∆λ needed to replicate the TAT
data. This is not surprising because the conditions that
) do not depend on the values of the
behavior with respect to TNT
0
in the INT reaction orders. The required nonlinearity is
supplied by the TAT term in the UNKCouple formation rate,
indicating that both nonlinearity in the reaction order of
individual species and nonlinearity in the overall order of
reaction can give the behavior that we observed in Figure 5B.
Partitioning. We can derive a model for the partitioning
scenario by assuming equilibrium conditions between TAT
m
, but values
λ
-
1
and UNKPartition with a partitioning coefficient (κ ) that
∞
versus
m
depends on F :
F
m
mTAT
were derived for κ(F
m
mTAT
mTAT
(
TNT - TAT )
INT or TAT reaction orders.
(m
)
0
∞
1
UNK
Although the application of a power law expression
)
(19)
mUNK
κ(F )
accurately reproduces the behavior of TAT
values of the fitted parameters indicate that additional
chemical factorssfactors indirectly influenced by F smust
∞
versus F
m
, the
m
TAT∞
m
mTAT and mUNK are stoichiometric factors, and a mass balance
be involved in determining the distribution of material
between TAT and UNKBranch (or UNKCouple). Since λTAT ) 1 is
consistent with our analysis, we hypothesize that, while the
rate of the INT f TAT reaction is adequately modeled with
a power law expression, the rate of the INT f UNKBranch (or
UNKCouple) reaction depends on solution chemistry. Given
the acid/base-catalyzed nature of many polymerization
reactions (24, 30), it seems likely that pH may be influencing
TAT appearance, though we cannot rule out other factors
such as [Fe2 ].
condition has been applied to obtain the right-hand side of
eq 19. In the absence of nonlinearity (i.e., mTAT ) mUNK), eq
19 reduces to the same form as eq 10:
1
/m
κ(F )
m
TAT ) TNT
(20)
∞
0
1
1/m
+ κ(Fm)
where m ) mTAT ) mUNK. As with the branching and coupling
scenarios, κ can be interpreted as a ratio of rate constants,
κ ) kUNKfTAT/kTATfUNK. Equation 19 satisfies eqs 3 and 4 if
+
The character of the partitioning scenario can be inves-
tigated by deriving a fitting equation from eq 19 under a
2
2
and only if ∂κ/∂F
Supporting Information), indicating that the partitioning
reaction must be shifted toward TAT with increasing F and
that the shift must be stronger (i.e., higher order) than linear.
Differentiation of eq 19 with respect to TNT shows that the
partitioning model will satisfy eq 5 for any values of mTAT and
UNK, but eq 6 will be satisfied if and only if mUNK > mTAT
proof given in Supporting Information), indicating that
m
> 0 and ∂ κ/∂F
m
> 0 (proof given in the
-
1
power law assumption for the partition coefficient κ . In
the case of mUNK ) mTAT ) 1, the fitting equation is identical
to eq 22; therefore, the fitting results for the branching
scenario also apply to the partitioning scenario. In this case,
the large values obtained for ∆λ imply that the reaction order
m
0
m
(
with respect to F
m
for the UNKPartition f TAT reaction is
significantly greater than that for the TAT f UNKPartition
nonlinearity plays the same role for the partitioning scenario
as it does for the branching and coupling scenarios.
Fitting. We parametrized the models presented above by
nonlinear square error minimization using both a single
variable approach and a multivariate approach. In the single
reaction, which is the opposite of what would be expected
0
if adsorption of TAT to the Fe surface was controlling TAT
∞
.
m
Modifying the F dependence to involve additional chemical
factors (as we suggested for the branching scenario) could
also be done for the adsorption model. Such a modification,
however, would have to be strong enough to overcome the
tendency for more material to adsorb to more adsorbent,
making the success of such a modification unlikely.
Equation 13 for branching, eq 18 for coupling, and eq 19
variable approach, the TAT
TNT were fitted together, and in a separate exercise, the
TAT vs TNT data with the same F were fit together. In the
multivariate approach, TAT is treated as a function of both
and TNT , and all TAT data were treated together.
The TAT versus TNT data (Figure 5B) were fit by treating
) as an adjustable parameter. To fit the TAT versus F
data, however, the functional form of κ(F ) must be assumed.
One way to interpret the dependence of the rate constants
∞
versus F
m
data with the same
0
∞
0
m
∞
F
m
0
∞
∞ 0
for partitioning can each be fit to the TAT versus TNT data
by treating κ as an adjustable parameter. All three scenarios
were capable of fitting the data equally well. In each case,
∞
0
κ(F
m
∞
m
m
the sharpness of the transition from TAT
horizontal asymptote increased with the degree of nonlin-
∞
) TNT
0
to a
2
36
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 1, 2005

earity (i.e., ∆m ) mUNK - mTAT in eqs 7-20 and/or nTAT in
eq 18). The fitting results indicate a sharp transition (e.g.,
∆
m as large as 4.6 for eq 13), but the data are too sparse to
produce definitive information about the nature of this
transition. The existence of such a transition is, however,
clearly indicated by these data, and nonlinearity in the TAT
disappearance mechanism is sufficient for its description.
Since we expect that, for the branching and coupling
models, mTAT ) 1, the nonlinearity in INT reaction orders
indicates that the INT f UNK reactions are multi-molecular.
This is consistent with the interpretation of these reactions
as polymerization of the intermediates and/or TAT. At high
0
TNT , the concentrations of the intermediates become large
and the rate of polymerization increases relative to the rate
of TAT production, leading to an overloading of the capacity
0
of the Fe to produce TAT without completely passivating
the surface. In the context of the partitioning scenario, the
interpretation of Figure 5B and the required nonlinearity is
less clear. As noted above, the observed behavior is not
0
consistent with simple adsorption of TAT to the Fe surface.
The nonlinearity could be rationalized by assuming that the
forward reaction (TAT f UNK) is multi-molecular, which
could arise if TAT undergoes a reversible coupling reaction
with itself.
In total, these results indicate that the processes control-
ling TAT appearance are a combination of coupling and
branching reactions with reaction rates that are sensitive to
solution conditions. Lumping these processes into a single
model would lead to eqs 14-17 for coupling, of which, eqs
FIGURE 6. Fraction of passivated surface based on Scheme 3 plotted
as a function of G for each of the values of TNT used in this study.
m
0
results indicate that significant passivation is likely when
TNT /F is large (i.e., the flat portion of the curves on the left
side of Figure 6) as is the case in most laboratory investigations
of passivation, while systems with small TNT /F would
passivate more slowly. The transition (with respect to both
and TNT ) between the two regimes is sharp, implying
0
m
7
-9 for branching are a special case. Fitting eq 13 for
0
m
branching (with eq 21 substituted for κ) to our TAT data
∞
with the multivariate approach shows that the branching
scenario is sufficient to describe all of our data. The
multivariate fitting results are shown in Figure 5. The fitted
parameters from the multivariate approach are consistent
with the results above that indicate significant nonlinearities
in both ∆λ and ∆m, which may be due to polymerization
reactions involving TAT and/or various reaction intermedi-
ates.
F
m
0
that the rates of surface passivation found for respike batch
experiments (16) and laboratory column experiments (19,
33-35) will tend to overestimate the passivation rates that
apply to most field conditions.
Acknowledgments
This work was supported, in part, by the Strategic Environ-
mental Research and Development Program (SERDP, Projects
CU-1176 and CU-1232). This report has not been subject to
review by SERDP and therefore does not necessarily reflect
their views, and no official endorsement should be inferred.
Implications for Scaling Passivation Kinetics. Aromatic
amines inhibit corrosion reactions both by competition for
active sites (31) and by polymer film formation (32) and,
therefore, the fate of TAT can be expected to effect the
0
longevity of Fe -based remediation technologies. To inves-
tigate the implications of our results for surface passivation,
we can use our modeling results to show how the coverage
Supporting Information Available
Fitting results, derivations, and proofs. This material is
available free of charge via the Internet at http://pubs.acs.org.
of surface sites will vary with both TNT
0
m
and F . To do this,
we assume that UNK precipitates onto active sites to form
passive sites and that UNK precipitates onto passive sites
with no effect on the reactivity of the site.
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