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Modeling the Kinetics of Hydrogen Formation by Zerovalent Iron: Effects of Sulfidation on Micro- and Nano-Scale Particles Hejie Qin, Xiaohong Guan, Joel Z Bandstra, Richard L. Johnson, and Paul G. Tratnyek Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b04436 • Publication Date (Web): 01 Nov 2018 Downloaded from http://pubs.acs.org on November 4, 2018
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Environmental Science & Technology
Modeling the Kinetics of Hydrogen Formation by Zerovalent Iron: Effects of Sulfidation on Micro- and Nano-Scale Particles
1 2 3
Hejie Qin1, 2, Xiaohong Guan1, 2#, Joel Z. Bandstra3, Richard L. Johnson4, and Paul G. Tratnyek4*
4 5 6 1
7 8 9 10
2
State Key Laboratory of Pollution Control and Resources Reuse, College of Environmental Science and Engineering, Tongji University, Shanghai 200092, PR China
Shanghai Institute of Pollution Control and Ecological Security, Shanghai 200092, P.R. China
11 12 13 14 15 16 17
3
Department of Mathematics, Engineering, and Computer Science, Saint Francis University, P.O. Box 600, Loretto, PA 15940 4
OHSU-PSU School of Public Health, Oregon Health & Science University, 3181 SW Sam Jackson Park Road, Portland, OR 97239
18 19 20 21 22
*Corresponding author: Paul G. Tratnyek Email:
[email protected], Phone: 503-346-3431, Fax: 503-346-3427 # Co-corresponding author: Xiaohong Guan Email:
[email protected], Phone: +86-21-65980956
23 24 25
Keywords: Hydrogen Evolution Reaction, Corrosion, Passivation, Fe(0), Bimodal kinetics, Global Fitting, Sulfidation
26 27 28
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Abstract
31
The hydrogen evolution reaction (HER)
32
that generates H2 from the reduction of
nZVI
200
H2O by Fe0 is among the most fundamental H2 (µmol)
33
300
Global fitting with: A(1−e−k1t) + B(1−e−k2t) A(1−e−kt)
100
34
of the processes that control reactivity in
35
environmental systems containing
36
zerovalent iron (ZVI). To develop a
37
comprehensive kinetic model for this
38
process, a large and high-resolution data
39
set for HER was measured using five types of ZVI pretreated by acid-washing and/or sulfidation
40
(in pH 7 HEPES buffer). The data were fit to four alternative kinetic models using nonlinear
41
regression analysis applied to the whole data set simultaneously, which allowed some model
42
parameters to be treated globally across multiple experiments. The preferred model uses two
43
independent reactive phases to match the two-stage character of most HER data, with rate
44
constants (k’s) for each phase fitted globally by iron type and phase quantities (S’s) fitted as fully
45
local (independent) parameters. The first, faster stage was attributed to a reactive mineral
46
intermediate (RMI) phase like Fe(OH)2, which may form in all experiments during
47
preequilibration, but is rapidly consumed, leaving the second, slower stage of HER, which is due
48
to reaction of Fe0. In addition to providing a deterministic model to explain the kinetics of HER
49
by ZVI over a wide range of conditions, the results provide an improved quantitative basis for
50
comparing the effects of sulfidation on ZVI.
20
nZVI + S Alfa
10
Alfa + S
0 0
Time (h)
120
51 52
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Introduction
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The formation of H2 from decomposition of water is a process of great importance,1 which is
55
commonly known as the hydrogen evolution reaction (HER), especially when it occurs by
56
heterogeneous catalysis on noble metals like palladium2 or by reduction on readily-oxidized
57
metals like iron.3 In both of these systems, the mechanism of the hydrogen evolution reaction
58
(HER) involves formation of atomic H species at the metal surface (i.e., Hads), followed by
59
combination of the intermediate species and desorption of H2.4, 5 In the case of HER by Fe0, the
60
reduction of water is coupled to oxidation of Fe0, resulting in the overall redox reactions:
61
Fe# + 2H' O → Fe'* + 2OH+ + H'
(1)
62
Fe# + 2H * → Fe'* + H'
(2)
63
under circum-neutral/alkaline or acidic pH conditions, respectively.6, 7 As this reaction proceeds,
64
precipitation of Fe(OH)2 may become favorable, and then Fe(OH)2 may disproportionate to
65
magnetite and dihydrogen according to the Schikorr reaction:7, 8
66
3 Fe(OH)' → Fe1 O2 + H' + 2 H' O
67
if the conditions are suitable for this reaction to be significant.9-11 The sum of these reactions is: 3Fe# + 4H' O → Fe1 O2 + 4H'
68 69 70
(3)
(4)
so the overall stoichiometry of H2 from Fe0 could vary from 1:1 (eq 1 and 2) to 4:3 (eq 4). HER by the above reactions has been studied extensively, mainly due to its importance in
71
corrosion of ferrous metals,12, 13 but more recently because of its relevance to H2 fuel
72
production14, 15 and water-treatment processes that employ Fe0 for removal of contaminants. The
73
most common water-treatment application of Fe0 involves emplacement into the subsurface for
74
remediation of contaminated groundwater,16, 17 but these ZVI permeable reactive barriers (PRBs)
75
can be ineffective if HER results in enough accumulation of gaseous H2 in pore spaces to
76
obstruct groundwater flow.18 This mostly geotechnical concern has motivated several studies of
77
HER under water-treatment conditions,19, 20 but most studies have focused on HER for more
78
chemical-process related reasons. One such reason is that the formation of H2 provides a
79
relatively direct and efficient measure of the reactivity of Fe0—or, conversely, its passivation—
80
in environmental media. A second reason is that the reaction shown in eq 1 can be the 10/31/18
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stoichiometrically-dominant reaction during anaerobic corrosion, in which case it will largely
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control changes in solution and surface chemistry over time. A third reason is that HER
83
consumes ZVI that otherwise might contribute to reduction of contaminants, and this
84
competition is the main issue that limits the overall electron efficiency of (or selectivity for)
85
contaminant reduction during water treatment processes with ZVI.21, 22
86
Most of these chemical-process aspects of HER under conditions relevant to groundwater
87
remediation were first addressed in a series of studies by Reardon et al.11, 23-25 using various types
88
of granular iron, simulated groundwater conditions, and a unique method of measuring and
89
modeling changes in pressure to determine the rate of H2 formation. In these experiments, the
90
dose of Fe0 was high (1 kg L−1) and the length of the experiments was long (up to several
91
months), so dissolution of H2 into the Fe0 was significant. After correction for this effect, the rate
92
of HER showed a characteristic trend of increasing for about 50 h and then gradually declining
93
over about 1 month. The initial increase was attributed to breakdown of the aged, air-formed
94
oxide, passivation layer upon wetting of the materials, and the subsequent decrease was due to
95
accumulation of reaction products (iron oxides and other precipitates, OH−, and H2) that inhibit
96
corrosion of the Fe0 over longer time periods. Combining these processes into a model that fully
97
describes the asymmetric peak in the HER rate data was beyond the scope of Reardon’s studies,
98
but portions of the data were fit to give corrosion rate constants that were used to model the
99
potential accumulation of H2 gas under field-scale conditions.24
100
All of the above work was performed with micron- or larger-sized ZVI, which generally
101
does not become fully oxidized under conditions relevant to water treatment, so depletion of Fe0
102
does not contribute to plateauing in the HER data. In contrast, nano-scale ZVI (nZVI) can be
103
fully oxidized by H2O (eq 1) within days, which can contribute to plateauing in HER vs. time
104
data as the reaction approaches completion and allows calculation of the original Fe0 content of
105
nZVI from the final yield of H2. Both of these effects are of practical interest because they are
106
the converse of the factor that often limits field-scale application of nZVI: its limited capacity
107
and longevity as a reductant of contaminants.22 These issues, and the chemical-process aspects of
108
HER in water treatment applications of (n)ZVI noted above, have motivated a now significant
109
body of work done by measuring accumulation of H2 in the headspace of closed, well-mixed
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batch reactors containing (dilute) suspensions of nZVI.25-35 Despite the considerable range of
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conditions employed in these studies, they all report H2 concentration vs. time data that suggest 10/31/18
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gradually decreasing rates of HER, so the kinetics are likely to be controlled by one or more
113
processes that are common across the whole range of these systems. To diagnose the process(es) that control HER by suspensions of (n)ZVI, it would be
114 115
useful to have a kinetic model that can describe the whole range of H2 formation data. Most of
116
the kinetic data that have been reported to date either were not modeled (e.g. 29, 34) or were
117
divided into subsections and fitted as simple (pseudo) zero- or first-order processes.25, 27, 30, 31, 35,
118
36
119
described with simple models, as can be seen in the examples summarized in Figure S1 of the
120
Supporting Information. This tendency suggests additional processes must be considered to fully
121
describe the degree to which H2 production rates decrease with time. One study showed that this
122
could be done by modeling the HER reaction as reversible,30 which causes the apparent rate of
123
HER to decrease as H2 accumulates in the reactor headspace. However, the assumption of HER
124
reversibility is inconsistent with the high temperature and H2 partial pressure conditions that
125
usually are required to make the reverse of eqs 1, 2, or 3 significant.23, 37, 38
126
In most of these cases, there was significantly more curvature in the data than could be
Alternative processes that could account for the characteristic shape of the HER data
127
shown in Figure S1 include inhibition by other effects of corrosion on solution conditions (e.g.,
128
increased pH36) and alterations to the ZVl surface that result in lower reactivity (i.e., passivation
129
by a variety of mechanisms). The evaluation and selection among these possibilities was a major
130
objective of this study, with the overall goal of developing a kinetic model that is (i) flexible
131
enough to describe all of the major aspects of HER kinetics over the whole range of relevant
132
conditions, and yet (ii) deterministic enough to be useful in diagnosing the mechanisms that
133
control the kinetics of HER and related corrosion reactions, including the reduction of
134
contaminants. To ensure the generality of the resulting model, we calibrated it with a new and
135
extensive set of high-resolution kinetic data for HER kinetics by ZVI of five types (ranging from
136
freshly-prepared nZVI to highly-aged commercial micro-sized ZVI) with several types of
137
pretreatments (including acid-washing and sulfidation by three common sulfidation agents).
138
The range of conditions we used in this study were selected to compliment other on-
139
going work on two related and priority aspects of ZVI reactivity: (i) the quantification of
140
selectivity among competing oxidation reactions22, 31, 35, 39 and (ii) the influence of sulfidation on
141
that selectivity.31, 35, 40-42 Most work on the selectivity of ZVI for reduction of water vs. reduction
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of contaminants has quantified electron efficiency from data obtained at a single time point, even
143
though it is expected that electron efficiency will evolve over time. To quantify electron
144
efficiency in a more general way, kinetic models are needed for each competing oxidation
145
reaction, such as the kinetic models for HER developed in this study. The other priority issue is
146
to better understand recent results showing that sulfidation of nZVI can inhibit HER without
147
significantly slowing contaminant reduction, thereby improving the electron efficiency—and
148
potentially the longevity—of nZVI during remediation applications.40, 41 The consequences of
149
this effect of sulfidation could be significant enough to alter the scope of application of other
150
types of ZVI in water treatment, but the kinetic data on HER has been insufficient to make
151
comparisons between different types of ZVI.
152
To determine the kinetic model that is most consistent with (i) the whole range of new
153
and old experimental data, (ii) a reasonable conceptual model for the controlling chemical
154
processes, and (iii) best statistical practices for fitting and selection among complex models, we
155
fit all of the data simultaneously to four alternative kinetic models using global, nonlinear
156
regression analysis. Advantages of global fitting were illustrated in a recent study where we
157
demonstrated that one kinetic model could fully describe a very complex system involving azo
158
dye reduction in aerobic suspensions of ZVI.43 In this study, we extend the use of global fitting
159
analysis even further, by using it to systematically compare alternative models of varying
160
complexity.
161
Experimental
162
Materials. Five types of ZVI were used, including three that are micro-sized (Alfa, Beijing, and
163
Hepure) and two that were nano-sized (Toda and CMC-nZVI). The first four were used as
164
received from the identified source and the fifth was prepared as we have done previously.44
165
Additional details on these materials and methods are given in the SI. Other reagents that were
166
used are reported in the SI. All solutions were prepared with deoxygenated deionized (DO/DI)
167
water in an anaerobic chamber, unless specified otherwise. DO/DI water was prepared by
168
sparging DI water with N2 for at least 0.5 h and left in the anaerobic chamber (100% N2, O2 < 0.8
169
ppm) overnight.
170
Methods. All experiments were performed in well-mixed, anaerobic, batch reactors. In some
171
cases, micro-sized ZVI (mZVI) was acid washed before use. The ZVI was treated with solutions 10/31/18
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containing several concentrations of sulfidation reagent (dithionite, sulfide or thiosulfate) for 12
173
h. In control experiments, 40-mL DO/DI water was used instead of sulfidation reagent. After
174
sulfidation/aging treatment, the ZVI samples were crimp sealed and mixed with 2 mM HEPES
175
buffer (pH 7.0) in 60-mL bottles on a rotator. At each sampling time, 2 mL of nitrogen was
176
injected into the vial, the vial was hand-mixed for 10 s, and then 2 mL of headspace was
177
withdrawn and injected directly into the gas chromatograph to determine H2 concentration in the
178
headspace. The measured H2 concentration was converted to quantity of H2 (as described in the
179
Supporting Information) and a correction was applied for the quantity of H2 lost due to serial
180
sampling. These calculations, and other experimental details, are elaborated in the Supporting
181
Information.
182
Results and Discussion
183
Kinetics and Stoichiometry of Hydrogen Evolution. Figure 1A shows a typical set of
184
concentration vs. time data for H2, dissolved Fe2+, and pH measured using a closed batch-reactor
185
containing one-type of ZVI, with and without pretreatment by acid-washing or sulfidation. For
186
all four treatment combinations, the HEPES buffer was sufficient to prevent any significant
187
changes in pH. However, both H2 and Fe2+ increased along similarly-shaped profiles suggesting
188
a gradual shift from faster to slower reactions controlled by a set of shared rate-controlling
189
process. The coupling between H2 and Fe2+ appearance is shown in Figure 1B and the slope of
190
the segments in these correlations represent the apparent, overall stoichiometry of HER in these
191
experiments. The data suggest two stages: a steeper segment during first 8 hr, followed by a
192
segment of shallower slope until the end of the experiments. Comparison between the four
193
treatment combinations (Figure 1B) reveals that the slope consistently decreased with acid
194
washing (circles vs. squares) and increased with sulfidation (red vs. blue).
195
The later segment in Figure 1B includes slopes 1.1±0.3 and 1.5±0.4, which are consistent
196
with the 1:1 stoichiometry predicted by eqs 1-2. The similarity among these values suggests that
197
HER—on the time scale of 10’s of hours and under the conditions of this study—is
198
predominantly due to conversion of Fe0 to dissolved Fe2+ (i.e. that there is little net precipitation
199
of new iron phases). While the data in Figure 1B are for micro-scale ZVI, which is not
200
significantly dissolved during these experiments, eqs 1-2 should also apply to experiments with
201
nZVI, which can be more completely dissolved. In our previous work with CMC-nZVI,31 the 10/31/18
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stoichiometry of eq 1 was assumed for calculations of Fe0 content from formation of H2 after
203
acidification, but this assumption was not tested or used on the data for CMC-nZVI in this study.
204
Other work with the less-labile Toda nZVI27 assumed that the controlling reaction in closed
205
batch reactors over 100’s of days is eq 3 (i.e. formation of Fe3O4) and used the stoichiometry of
206
this reaction with measurements of H2 to characterize the decrease in Fe0 content of nZVI during
207
aging. The earlier, steeper segment in Figure 1B includes slopes 2.4±0.7 to 6.9±1.0, which are
208 209
considerably greater than can be explained by the stoichiometries of eqs 1-4. This result requires
210
that there be one or more additional mechanisms of producing Fe2+ that are not coupled to H2
211
formation, and the most likely explanation for this is desorption and/or (reductive) dissolution of
212
Fe2+ from preexisting iron oxides on the ZVI. This explanation is consistent with the higher Fe2+
213
concentration and Fe2+/H2 stoichiometry obtained with ZVI that was not pretreated by acid
214
washing (circles in Figure 1B), because acid-washing is well known to remove labile iron
215
oxides.45, 46 The effect of sulfidation on these data (blue markers in Figure 1B) is likely not due
216
to increased release of Fe2+, but rather decreased formation of H2, as expected from prior work31,
217
42
and discussed further below. w/ acid wash 40 7
25
6 H2 (+AW, −S) H2 (+AW, +S) Fe2+ (+AW, −S) Fe2+ (+AW, +S) pH (+AW, −S) pH (+AW, +S)
20 15
5 4
10
2 0
222 223
1.1±0.3
20 5.7±0.5 5.1± 0.3 −AW −S −AW +S +AW −S +AW +S
20
40
60
80
100
120
2.4±0.7 0 0
2
4
6
8
10
12
14
16
H2 (µmol)
Time (h)
218
221
6.9±1.0
10
0
220
1.5±0.4
3
5
219
B
30
Fe2+ (µmol)
30
pH
H2 or Fe2+ (µmol)
A
Figure 1. Representative time series data for Alfa ZVI with/without pretreatment by acid washing or sulfidation with sulfide. (A) Total H2 and Fe2+ (left axis) and pH (right axis) vs. time. (B) Stoichiometry of Fe2+ vs. H2. Reaction conditions: [ZVI] = 5.0 g/L, DIW with 2 mM HEPES with pHinit = 7.0, anoxic, room temperature. Solid lines in B are from regression of pooled data for the slow and fast portions of HER, and the slopes of these lines are annotated on the figure.
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The break in slope of Fe2+, H2, and Fe2+/H2 vs. time data shown in Figure 1A is too sharp
225
to be consistent with simple first-order appearance kinetics (Figure S3), but rather suggests a
226
transition from faster to slower HER due to a change in the rate controlling process(es). A
227
similar transition is evident in the data for all four treatment combinations shown in Figure 1,
228
most other treatment combinations shown in Figure S3-S6, and in much of the data on HER by
229
ZVI in batch systems that has been published previously (Figure S1). This transition could arise
230
from a variety of mechanisms, including the reversibility hypothesis that was discussed and
231
deemed unlikely in the introduction. Another possibility is that corrosion during the
232
preequilibration stage used in this study could result in accumulation of H2 within the ZVI,
233
which is released after replacement of the aqueous phase with fresh buffer. Desorption of H2
234
from ZVI has been observed in experiments done at higher pressures and over longer time
235
periods,47 but does not appear to have been significant under the conditions of this study.
236
Evidence for this conclusion includes the results shown in Figures S5 and S6, which do not
237
show the initial increase in H2 that would be expected if desorption of pre-formed H2 were
238
significant. A third possibility is that corrosion (by eqs 1-2) causes an increase in pH that
239
supressed the rate of further HER.27, 36 This effect is unlikely to be significant in well-buffered
240
systems—such as those used in this study (Figure 1A)—but it might contribute under other
241
conditions.
242
A fourth possible explanation for the characteristic shape observed in most HER data
243
involves replacement of more reactive surface phase by less reactive surface phase. A plausible
244
candidate for this transient reactive phase is amorphous ferrous oxyhydroxide that forms during
245
the preequilibration period, but then is consumed during the early fast stage of HER after the
246
aqueous phase was replaced by fresh buffer. In this study, no attempt was made to directly
247
characterize this transient phase—by electron microscopy or surface spectroscopy—but evidence
248
is available from other studies that Fe(OH)2 forms on ZVI under relevant conditions.7, 11, 48 That
249
Fe(OH)2 could contribute significantly to HER (by eq 3) was confirmed by control experiments
250
with freshly-synthesized Fe(OH)2, which are described in the SI (Figure S7). A transient,
251
reactive species like Fe(OH)2 is assumed in the modeling described below, but its exact
252
composition need not be specified for modeling the kinetics.
253
Modeling the Kinetics of Hydrogen Evolution. To accomplish the overall goal of obtaining an
254
optimal and general kinetic model for HER, we measured a large set of H2 vs time data using 5 10/31/18
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types of ZVI (at appropriate doses: 5 g/L for mZVI and 0.5 g/L nZVI), two primary treatment
256
variables (with and without acid washing or sulfidation), and two secondary treatment variables
257
(different types and doses of sulfidation agent), but otherwise consistent experimental variables
258
(buffer and pH, reactor configuration, mixing, etc.). All of these new time series data are shown
259
in Figures S8-S12, and a representative selection of the results is given in Figure 2. The range
260
of results seen in this new dataset covers the diversity of HER kinetics seen in previously
261
published data (Figures 1, S1, S3-S6), but the new data are more suitable for global fitting
262
because all of the experimental variables are systematically arranged and controlled. The
263
example results in Figure 2 show the global fit to our preferred kinetic model, which treats some
264
of the model parameters as optimized independently for all experiments (local variables), and
265
other parameters fitted to a single value for groups of experiments (global variables). The
266
agreement between the model and data in Figure 2 appears satisfactory, but other kinetic models
267
and combinations of local and global variables were considered, and four representative and
268
significant cases are discussed below. Alfa +0 µM Alfa +20 µM S Alfa +3000 µM S Model 4 Fits
14 12
120
A
100 80
H2 (µmol)
H2 (µmol)
10 8 6
0
0 0
269
272 273
60
20
2
271
B
40
4
270
Toda +0 µM Toda +3000 µM S Toda +9000 µM S Toda +18000 µM S Model 4 Fits
20
40
60 80 Time (h)
100
120
0
20
40
60 80 Time (h)
100
120
Figure 2. Representative time series data and fits to Model 4 (Global). (A) Alfa and (B) Toda, with sulfidation using sulfide at several doses. Markers show average and average deviation from duplicate experiments. Dashed curves are from global fitting.
The four kinetic models for HER were selected based on prior work, most of which is
274
summarized in the introduction, and derivations from physico-chemical considerations, which
275
are presented in Supporting Information. In this study, all the model derivations are based on the
276
hypothesis that the decrease in rate of HER is caused by a first-order decrease in quantity of Fe0
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available for reaction with H2O (S, eq 5) and the overall rate law for HER is assumed to be
278
pseudo-first order in S (eq 6). 45
279
46
= −𝑘 • 𝑆
4[>? ]
280
46
(5)
= 𝑘>? • 𝑆
(6)
281
where kH2 is the hydrogen evolution rate constant, k is the decay of reactive phase, and S0 is the
282
initial surface of S. The subscripts (1 or 2) indicate the parameters corresponding to Phase 1 or 2,
283
respectively. In Model 1, it was assumed that one reactive phase is responsible for HER, whereas the
284 285
other three models reflect the hypothesis that HER arises from reaction of two phases on the
286
ZVI. In Model 2, it was assumed that the more reactive phase produces the initial fast stage of
287
HER, a less reactive phase gives the slower stage of HER, and Phase 1 is replaced by Phase 2
288
according to a first-order rate law. Model 3 is similar to Model 2, but includes decay of Phase 2
289
to products that do not contribute to HER. Model 4 assumes the two phases act independently
290
(e.g., as Fe0 and FeII sites on ZVI with pits in an oxide coating49), the quantities of which decay
291
by independent first order processes (using the same formulation as eq 5). Therefore, for Phase 1
292
and 2,
293
𝑆B = 𝑆B,# e+DE6
(7)
294
𝑆' = 𝑆',# e+D?6
(8)
295
The rate law for HER was assumed to be pseudo-first order in S1 and S2 (eq 9). The composition
296
of the phases was assumed to be constant for each ZVI type across all of the conditions tested,
297
with the differences in observed HER kinetics being due to changes in the quantities of the two
298
reactive phases (S1, and S2). Therefore, 4[>? ]
299
46
= 𝑘>?,B • 𝑆B + 𝑘>?,' • 𝑆'
(9)
300
Combining and solving these terms gives equations for Model 4. The six physical parameters (k1,
301
k2, S1, S2, kH2,1, kH2,2) were arranged into four fitting parameters (k1, A, k2, B), so the model could
302
be fit using eq 10, with A and B defined by eqs 11-12. [H' ] = 𝐴 • (1 − e+DE6 ) + 𝐵 • (1 − e+D?6 )
303
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𝐴=
305
𝐵=
DL? ,E •5E,M DE
DL? ,? •5?,M D?
(11)
(12)
Major characteristics of the models above are summarized in Table 1, and further
306 307
qualitative discussion of their relevance is given below. For Models 2 and 3, fitting all the
308
parameters independently resulted in large uncertainties despite the constraint provided by
309
globally fitting the whole dataset. This was due to covariance among some combinations of
310
parameters, which results in χ2 minima that follow contours between the parameter combinations
311
rather than defining unique optimal values of the individual parameters. Much like we did in a
312
previous study,50 this challenge was overcome by fitting combinations of related parameters. The
313
combinations that gave the best results are shown in Table 1 and Figures S13-S18.
314
Table 1. Summary of kinetic models for HER.
315
1
316
2
317 318 319
Model
Format1
Parameters2
Statistics3
1. Uniform passivation
Single first-order exponential appearance term (eq S7)
k, A
45 (243)
Misses curvature due to stage transition. (Figure S8)
2. Replacement of one reactive phase with another
Sum of a zero-order linear appearance term and a first-order exponential appearance term (eq S14)
k S1,0•kH2,2 kH2,1/kH2,2
7.2 (238)
Fits transition between stages, but misses the curvature in Stage 2. No failures. (Figure S9)
3. Advanced phase replacement model
Sum of three first-order exponential appearance terms which share some parameters (eq S18)
k1, k2 S1,0•kH2,2 kH2,1/kH2,2
5.3 (233)
Fits transition and curvatures in both stages. No failures. (Figure S10)
4. Independent changes in two reactive phases
Sum of two independent first-order exponential appearance terms (eq 7 or S24)
k1, A, k2, B
L: 1.6 (207) G: 3.8 (211)
Fits transition and curvatures in both stages. No failures. (Figure S11-S12)
Results
Equation numbers refer to the model descriptions in Supporting Information. For the minimally-global fits, parameters in bold were grouped by iron type. 3 Reduced chi-square = total chi-square/(degrees of freedom). Degrees of freedom (number of points – number of fitted parameters) given in parenthesis. For model 4, the minimally-global fit is L, the more fully global fit is G.
320
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Once the kinetic models were selected, they were fitted to the whole HER dataset,
322
initially with all model parameters fully local (i.e., independently optimized to the results of each
323
experimental time course), and then using those results for initial guesses while fitting with
324
various combinations of variables treated as global (i.e., optimized to a common value across
325
multiple experiments). The fitting results were evaluated based on (i) visual comparison of the
326
data and fits (e.g., Figures S8-S12), (ii) inspection of the uncertainties in each fitting parameter
327
(e.g., S13-S18), and (iii) the overall reduced chi-square (Tables S1). For all four models, a
328
baseline best fit was chosen that is “minimally global” in that parameters were grouped only
329
where this resulted in a large decrease in degrees of freedom and is strongly supported by
330
physico-chemical considerations. In most cases, this compromise resulted in globally fitting
331
some of the model parameters by iron type and fitting the other parameter(s) as local. The exact
332
assigment of global vs. local variables in all of the reported fits can be determined from Figures
333
S13-S18 and Tables S2-S6. Model 1 does not appear to have been used previously, but a first order dependence on S
334 335
is embedded in the model for HER kinetics described by Liu and Lowry.27 In this study, fitting
336
Model 1 to our whole dataset—using the minimally-global constraint that k should be constant
337
for each type of Fe0—also did not fully capture the shape (bimodal character) or degree of
338
curvature in our HER data (Figure S8). The inability of Model 1 to describe the bimodal
339
curvature of the data for nZVI, especially CMC-nZVI, is clearly evident in the H2 vs time plots
340
(Figure S8) and consistent with the relatively large reduced chi-square value (Table 1).
341
However, the systematic lack of fit to Model 1 is not reflected in the fitting coefficient
342
uncertainties, which appear to be uniformly acceptable across the whole data set (Figures 3 and
343
S13).
344
For Model 2, these constraints were implemented by fitting k and kH2,1/kH2,2 as global
345
within each iron type and S1,0•kH2,2 as local to each experimental condition, based on
346
considerations described in the Supporting Information. In general, Model 2 describes the data
347
well, including the overall degree of curvature and the position and sharpness of the break in
348
slope that divides the first and second stages (Figure S9), with acceptable uncertainties in all the
349
fitting parameters (Figure S14). Despite having more parameters than Model 1, Model 2 had
350
fewer degrees of freedom due to fitting the parameters in three groups with one local and two
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global by iron type, which resulted in a greatly improved reduced chi-square (Table 1).
352
However, most of the fits slightly underrepresent the degree of curvature in stage 2 (esp. for
353
nZVI) and the model is too constrained to represent the intersecting time-courses for the few
354
treatment combinations that exhibit this complication (e.g., Beijing ZVI + sulfide, Beijing +
355
dithionite, and Toda + sulfide). Most of these differences between the model fits and the data can
356
be explained by the lack of a mechanism to decrease the rate of HER during stage 2, which is
357
included in Model 3.
358
For model 3, as with Model 2, the composition of the two phases was assumed to be
359
constant for each ZVI type across all of the conditions tested, with the differences in observed
360
HER kinetics being due to changes in the quantities of the two reactive phases (S1, and S2).
361
Therefore, k1, k2, and kH2,1/kH2,2 were fit as global within each iron type and only S1,0•kH2,2 was
362
fit as local to each experimental condition. As expected, Model 3 fits the curvature in stage 2
363
better than Model 2, but it does not reproduce the crossing of time-courses in the three treatment
364
combinations noted above (Figure S10). The uncertainties in the fitting parameters for Model 3
365
are similar to those of Model 2, except for Beijing and Hepure ZVI where k2 is poorly defined
366
because there was not enough curvature during stage 2 of HER (Figure S15). Compared with
367
Model 2, Model 3 has one more (global) fitting parameter, slightly fewer degrees of freedom,
368
and a slightly smaller reduced chi-square (Table 1). Since the overall advantages of Model 3 are
369
modest, it was concluded that they do not justify its greater mathematical complexity and
370
potential for overparameterization (especially with smaller data sets).
371
For Model 4, the intial fitting was performed with the same arrangement of global and
372
local parameters as the previous models (global k’s and local S’s, designated 4L), and the results
373
are shown in Figures S11 and S16. All features in the dataset are fully described when the data
374
were fit this way—including the crossing of time-courses in the three treatment combinations
375
that were outliers above—and the reduced chi-square is the smallest of all the models tested in
376
this study. However, the fitting parameters for Beijing ZVI are poorly defined (best seen in the
377
large RSDs in Figure S16), again because there was not enough curvature in the data during
378
stage 2 (as noted for Model 3). Furthermore, the nearly perfect fit to the outlier time-courses that
379
challenged the previous models may reflect unwarranted statistical flexibility in Model 4L,
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because the model does not contain any new physical process(es) that would explain these
381
results.
382
Considering the overall success and specific limitations of Model 4L, we tried further
383
constraining the fitting such that k1 was global across the whole data set (designated Model 4G).
384
The main reason for this choice was to test the hypothesis that the reactive phase during stage 1
385
might have the same rate constant for HER because it was the same material, formed in situ
386
under conditions common to all the experiments in this dataset. The resulting fits (Figures S12
387
and S17) describe the full range of results nearly as well as Model 4L, but slightly less well for
388
the more extreme outlier cases (esp. Toda with 0-3000 uM sulfide) and with a reduced chi-square
389
between that of Models 3 and 4L (Table 1). The most significant aspect of this result is
390
verification that the rate of HER during stage 1 can be described with a single rate constant,
391
which is consistent with this phase being controlled by a common species like Fe(OH)2. In
392
addition, the surprisingly small uncertainty in the global value of k1 seems to have constrained
393
the fitting in a way that produces a more balanced distribution of relative standard deviations for
394
the other fitting parameters (cf. Figures S16 and S17). Considering the diversity of materials
395
and conditions included in the dataset for this study, the results obtained with Model 4G should
396
be robust, however less controlled conditions could result in more diverse results during stage 1.
397
Interpretation of the Modeling Results. To further evaluate the alternative models included in
398
this study, and to advance the interpretation of the modeling results with respect to the physico-
399
chemical processes controlling HER, we performed correlation analysis on the fitting parameters
400
between models or within each model (Figure S18). Many of the fitting parameters involving
401
quantities of reactive phases (S0, S1,0, or S2,0) show strong correlations between the models (red
402
markers in Figure S18), so we rearranged the results for models 2 and 3 into the form kH2•S0/k
403
for correlation analysis versus the similarly-defined parameters A and B in Models 1 and 4
404
(Figure S19).
405
There are strong correlations between kH2•S0/k for different models but equivalent stages
406
(i.e., stage 1 vs 1 and 2 vs 2), all of which are shown with color backgrounds in Figure S19, and
407
two representative examples are shown in Figure 3. For the correlations between Models 1, 2,
408
and 3 (yellow background, Figure 3A), the data for each iron type fall almost exactly on the 1:1
409
contours because the parameterization of these models is very similar. The correlations involving
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Model 4L or 4G (pink background, Figure 3B) exhibit moderately strong but variable degrees of
411
clustering along the 1:1 contours because the independence of the two stages in Model 4 allows
412
variance in the data to partition freely between the stage parameters. In addition to differences in
413
the strength of these correlations, these data form diagonal clusters that distribute along different
414
1:1 contours for the different ZVIs. Beijing and Hepure deviate from 1x only because—as noted
415
above—the lack of curvature in Stage 2 for these two ZVIs results in non-unique minima for the
416
Phase 2 fitting parameters. Despite the seperation of some data along different 1:1 contours, the
417
overall trend across all the kH2•S0/k correlations (Figure 3 and S19) suggests clusters by iron
418
type that distribute from lower-left to upper-right in the order Alfa < Beijing < Hepure < Toda ~
419
CMC-nZVI, which corresponds to increasing overall rate of HER. 10
A
10
5
4
B
10 x
Model 3 (kH2,2•S1,0/k2)
Model 2 (kH2,2•S1,0/k)
6 4 2
1x
1 6 4 2
10
4
100x 10 10 10
3
2
1x
1
0.1 6
10 6
422 423 424 425
426
2
4 6
1
2
4 6
10
2
2
Model 3 (kH2,2•S1,0/k1)
420 421
0.1
0 4
6 8
10
2
4
6 8
100
2
4
Model 4L (kH2,2•S2,0/k2 (B))
Figure 3. Representative correlations between kH2•S0/k (μmol) for combinations of stage and model. (A) Model 2 vs. Model 3; and (B) Model 3 vs. Model 4L for stage 2. Parts A and B correspond to Figure S19.08 and S19.20, respectively. Marker color represents iron type, as defined in Figure S19. Dose of the sulfidation agent is represented by markers: triangles = none, squares = low, diamonds = medium, circles = high. Sulfidation agent type is not shown.
Using the preferred model (Model 4), the results obtained for A and B (kH2•S0/k for stage
427
and phase 1 and 2, respectively) can be used to compare the influence of treatments on HER
428
kinetics. In Figures S16-S17, sulfidated materials usually gave lower A and B values, consistent
429
with slower overall HER due to this treatment. The fitted values of A and B also related to the
430
limiting value of H2 generation for each stage (e.g., as t → ∞, eq 10 becomes [H2] = A + B), so,
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sulfidation evidently decreased the capacity for H2 production. These trends are consistent with,
432
but not as easily identified in, the original time series data such as in Figure 2. Other treatment
433
factors (sulfidation agent, concentration, and/or acid washing) do not show strong effects on the
434
time series data (Figures S11-S12) or the fitting coefficient values (Figures S16-S17). These
435
results are consistent with previous work showing that different sulfidation agents have similar
436
effects,42 but suggest that sulfidation might be effective at doses lower than has been used in
437
most previous work. In addition, sulfide at high concentration (3 mM) gave less inhibition of
438
HER unless is was previously acid washed, suggesting that the benefit of sulfidation by sulfide
439
might be limited by its alkalinity, which might be an advantage of using dithionite and
440
thiosulfate to passivate ZVI with respect to HER.
441
Since A and B include information about both the quantity and rate of reaction of the two
442
phases, it may be possible to simulate the whole range of observed HER time-series shapes using
443
only these two parameters. Figure 4 shows simulations using Model 4 and representative values
444
of the model parameters starting from the fitted values in Table S5. The shapes of the time-series
445
simulations in Figure 4 covers the whole range of results seen in this study and in prior work
446
(Figures S1). In Figure 4, the shapes have been subjectively classified into sharp, medium, and
447
smooth, based on the acuteness of the transition between stages 1 and 2 of the reaction.
448
Comparison of the simulation results included in Figure 4 also reveals an interesting
449
characteristic of this model: the overall shape of the HER curves is not controlled just by A and
450
B, but it also depends on A/B. Relating this characteristic of the model to mechanistic aspects of
451
HER during corrosion of ZVI is one example of how this model might be useful in future work.
452
Model 4 and the simulations in Figure 4 may also be applicable to other cases where appearance
453
kinetics is controlled by two phases with limited capacity (e.g., desorption in multiphase systems
454
subject to aging or fouling, or biotransformation in mixed cultures of competing degraders).
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25
Sharp
(A, B, A/B) 15, 15, 1.0 1.6, 2.8, 0.57 9, 20, 0.45
Medium 1, 2, 0.5 1.8, 7, 0.26 4, 23, 0.17
H2 (arbitrary scale)
Smooth 0.5, 1.8, 0.28 2, 13, 0.15 2.2, 20, 0.11
20
15
10
5
0 0
20
40
456 457 458
60
80
100
120
Time (h)
455
Figure 4. Simulations using Model 4, values of A and B in the legend, and representative values of k from this study.
While Model 4 accurately describes HER by ZVI over a considerable range of
459
conditions, and is suitable for a variety of diagnostic and predictive applications, there are
460
several possible limitations to the model that cannot be fully addressed due to limitations in the
461
scope of this study. First, the time scale for the collected data was limited to several days, so
462
prediction of HER kinetics, or capacity over longer time periods, or to complete consumption of
463
Fe0, would involve extrapolation beyond the conditions for which the model has been validated.
464
Second, all of the fitted data were obtained using buffered media where pH changes were
465
negligible. Clearly, corrosion of Fe0 in less-well buffered systems favors increased pH, which
466
should inhibit the primary HER reactions (eqs 1-2), and this possible feedback was not
467
incorporated in the models used in this study. Third, this study—like most prior studies of HER
468
kinetics by ZVI for environmental applications—was done using well-mixed batch reactors, and
469
a variety of other processes (spatial gradients, gas bubble formation, etc.) might become
470
important under column or field conditions.
471
Implications for Water Treatment. The evolution of H2 from reduction of H2O is a prominent
472
aspect of the corrosion of Fe0, whereas abiotic “geochemical” routes of H2 formation are less
473
favorable or well characterized.51 This study shows that the overall kinetics of HER in batch
474
reactors containing ZVI exhibit an early stage of fast H2 accumulation, which probably is the
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result of an authigenic, secondary, and high-reactive phase that is derived from Fe0. This phase is
476
likely to consist of Fe(OH)2 or related Fe(II) oxyhydroxides, which are weaker reductants than
477
Fe0 thermodynamically, but can be more effective kinetically due to their high and labile reactive
478
surface area. Such iron-based “reactive mineral intermediate” phases (RMIs) play a prominent
479
role in determining the structure and reactivity of oxide passive films during corrosion52-54 and a
480
wide range of biogeochemical processes (e.g.,55-59). The possibility that RMIs contribute to in
481
situ contaminant reduction has been investigated using green rust,60 FeS,61 Fe3O4,62 and most
482
recently Fe(OH)2.62 The latter is particularly relevant to this study because it provides speciation
483
modeling and spectroscopic evidence that active formation of Fe(OH)2 is required for TCE
484
reduction by magnetite.62
485
This study was able to resolve and model the contribution of RMIs to HER because the
486
experimental conditions (preequilibrated closed batch reactors, etc.) allowed decay of the RMI
487
phase responsible for the initial rapid stage of HER, leaving the slower but more sustained HER
488
by Fe0. It is likely that this transition from initial-phase (RMI) to second-phase (Fe0) controlled
489
kinetics also applies to other reactions, and this undoubtedly is one reason for the deviations
490
from first-order disappearance of contaminants seen in many studies of contaminant reduction by
491
Fe0 in batch reactors.63 Under column or field conditions, the processes that form and consume
492
RMIs may become balanced, resulting in steady-state conditions where measured reaction rates
493
(HER, contaminant reduction, iron dissolution, etc.) are the sum of the contributions by all
494
reactive phases. However, columns and field sites might still exhibit zones of different reactivity
495
when the reactive phases are non-uniformly distributed along the flow path.
496
Finally, while this study demonstrates that measurements of H2 formation can be an
497
efficient and powerful approach to characterizing the reactivity of ZVI, we did not investigate
498
whether rates of contaminant reduction follow the same trends. So, for example, while this work
499
confirms that HER is increased by acid-washing and decreased by sulfidation, it does not address
500
whether these treatments have more or less effect on the selectivity of ZVI for HER vs.
501
contaminant reduction.
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Acknowledgements
503
This material is based on work supported by the Strategic Environmental Research and
504
Development Program of the U.S. Department of Defense, Award Numbers ER-2308, ER-2620,
505
and ER-2621. The author Hejie Qin thanks the support from the program of China Scholarships
506
Council, and National Natural Science Foundation of China (Grants 21777117, 21522704, and
507
51478329). This report has not been subject to review by any sponsor and therefore does not
508
necessarily reflect agency views and no official endorsements should be inferred. Miranda J.
509
Bradley contributed the surface area measurements.
510
Supporting Information Available:
511
Supporting Information is available free of charge at the ACS Publications website (DOI:
512
10.1021/acs.est.xxxxxxx), including: method details, model derivations, primary data and fitting
513
results, and fitting coefficient values.
514
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