Independent Quantification of Electron and Ion Diffusion in Metallocene-Doped Metal-Organic Frameworks Thin Films

Article abstract of DOI:10.1021/jacs.9b03609

The chronoamperometric response (I vs t) of three metallocene-doped metal-organic frameworks (MOFs) thin films (M-NU-1000, M = Fe, Ru, Os) in two different electrolytes (tetrabutylammonium hexafluorophosphate [TBAPF₆] and tetrabutylammonium tetrakis(pentafluorophenyl)borate [TBATFAB]) was utilized to elucidate the diffusion coefficients of electrons and ions (D_e and D_i, respectively) through the structure in response to an oxidizing applied bias. The application of a theoretical model for solid state voltammetry to the experimental data revealed that the diffusion of ions is the rate-determining step at the three different time stages of the electrochemical transformation: an initial stage characterized by rapid electron diffusion along the crystal-solution boundary (stage A), a second stage that represents the diffusion of electrons and ions into the bulk of the MOF crystallite (stage B), and a final period of the conversion dominated only by the diffusion of ions (stage C). Remarkably, electron diffusion (D_e) increased in the order of Fe < Ru < Os using PF₆ ^1- as the counteranion in all the stages of the voltammogram, demonstrating the strategy to modulate the rate of electron transport through the incorporation of rapidly self-exchanging molecular moieties into the MOF structure. The D_e values obtained with larger TFAB^1- counteranion were generally in agreement with the previous trend but were on average lower than those obtained with PF₆ ^1-. Similarly, the ion diffusion coefficient (D_i) was generally higher for TFAB^1- than for PF₆ ^1- as the ions diffuse into the crystal bulk, due to the high degree of ion-pair association between PF₆ ^1- and the metallocenium ion, resulting in a faster penetration of the weakly associated TFAB^1- anion through the MOF pores. These structure-function relationships provide a foundation for the future design, control, and optimization of electron and ion transport properties in MOF thin films.

Full text of DOI:10.1021/jacs.9b03609

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Article
Independent Quantification of Electron and Ion
Diffusion in Metal-Organic Frameworks Thin Films
Paula J Celis-Salazar, Meng Cai, Clark Cucinell, Spencer R
Ahrenholtz, Charity C Epley, Pavel M. Usov, and Amanda J Morris
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.9b03609 • Publication Date (Web): 04 Jul 2019
Downloaded from http://pubs.acs.org on July 4, 2019
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Independent Quantification of Electron and Ion Diffusion in
Metallocene-doped Metal-Organic Frameworks Thin Films
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Paula J. Celis-Salazar, Meng Cai, Clark A. Cucinell, Spencer R. Ahrenholtz, Charity C. Epley, Pavel M.
Usov, Amanda J. Morris*
Department of Chemistry, Virginia Tech, Blacksburg, Virginia, 24061, United States
ABSTRACT: The chronoamperometric response (I vs. t) of three metallocene-doped metal-organic frameworks (MOFs) thin films
(M-NU-1000, M = Fe, Ru, Os) in two different electrolytes (tetrabutylammonium hexafluorophosphate [TBAPF
tetrabutylammonium tetrakis(pentafluorophenyl)borate [TBATFAB]) was utilized to elucidate the diffusion coefficients of electrons
and ions (D and D , respectively) through the structure in response to an oxidizing applied bias. The application of a theoretical model
6
] and
e
i
for solid state-voltammetry to the experimental data revealed that the diffusion of ions is the rate-determining step at the three different
time stages of the electrochemical transformation: an initial stage characterized by rapid electron diffusion along the crystal-solution
boundary (Stage A), a second stage that represents the diffusion of electrons and ions into the bulk of the MOF crystallite (Stage B),
and a final period of the conversion dominated only by the diffusion of ions (Stage C). Remarkably, electron diffusion (D
e
) increased
as the counter anion in all the stages of the voltammogram, demonstrating the strategy to
modulate the rate of electron transport through the incorporation of rapidly self-exchanging molecular moieties into the MOF
1
-
in the order of Fe < Ru < Os using PF
6
1-
structure. The D
e
values obtained with larger TFAB counter anion were generally in agreement with the previous trend, but were on
1-
1-
average lower than those obtained with PF
6
. Similarly, the ion diffusion coefficient (D
as the ions diffuse into the crystal bulk, due to the high degree of ion-pair association between PF and the metallocenium ion,
resulting in a faster penetration of the weakly associated TFAB anion through the MOF pores. These structure-function relationships
provide a foundation for the future design, control, and optimization of electron and ion transport properties in MOF thin films.
i
) was generally higher for TFAB than for
1-
1-
PF
6
6
1
-
1
. INTRODUCTION
materials are still lacking. In principle, the charge propagation
in frameworks can be facilitated by three different mechanisms:
11
Metal-organic frameworks (MOFs) are prominent materials
1) ligand-node orbital energy overlap,
2) π-stacking
12
with considerable promise in many fields such as
electrocatalysis, electronics and batteries. These hybrid multi-
interactions between planar linkers, and 3) redox hopping
between the neighboring centers. Indeed, the latter mechanism
1, 2
13
dimensional arrays of inorganic nodes connected by organic
ligands have arisen as potential candidates to satisfy the current
demands for cleaner energy and its environmentally sustainable
was demonstrated experimentally by quantifying the apparent
diffusion coefficient (Dapp) in Co-based MOF thin films,
suggesting that charge conduction occurs through discrete
3
,
4
13
storage.
Recently, the fabrication of MOF thin films on
ambipolar redox-hopping steps.
conductive substrates, have facilitated their electrochemical
characterization, and improved the utility of these systems in a
wider variety of applications.3
If
electrochemical charge transport should depend on the rate of
electron diffusion (D ) from one redox center to another along
the framework backbone, and the rate of ion diffusion (D
a
redox hopping mechanism is operative, the
e
Although originally most MOFs were considered electrical
insulators, several examples of MOFs capable of efficient
i
)
1
3
through the MOF pores to maintain the electroneutrality. The
is related to the homogeneous self-exchange rate of the redox
centers, whereas D is primarily dependent on the ion size, MOF
5
-7
charge transport have been reported. Careful selection of
ligands and nodes with appropriate electronic properties in the
MOF synthesis, could lead to the extended structures containing
D
e
i
pore size, and the ion pairing ability. Although Dapp has been
calculated by electrochemical and/or spectroscopic
measurements, it lacks information regarding the contributions
from electron diffusion and ion diffusion. Despite the
importance of these diffusion terms for understanding the
overall charge transport properties in MOFs, there are no
detailed reports examining their relative contributions towards
this process. This information is vital for establishing structure-
function relationships for the design of conductive frameworks.
6,
7
charge transport pathways.
Similarly, post-synthetic
modifications (PSM) of existing MOFs have shown to be an
8, 9
effective strategy for incorporation of electroactive moieties.
In particular, the use of coordinatively unsaturated metal
clusters has been extensively employed to append the redox-
8
, 10
active species inside the frameworks.
While these synthetic approaches have contributed to the
development of an extensive variety of conductive MOFs,
detailed studies on the mechanism of electron transport in these
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Previously, a theoretical model capable of individually
quantifying and was developed for idealized
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D
D
i
e
1
4
microcrystals immobilized on the surface of an electrode. In
order to test the applicability of this model to the solid-state
voltammetry of MOF thin films, we devised a series of
metallocene-doped M-NU-1000 (M = Fe, Ru, Os) thin films on
conductive fluorine-doped tin oxide (FTO) support. A series of
1
-
1-
chronoamperometry experiments in PF
electrolytes was performed with the goal of unravelling the
individual contributions of D and D in MOF thin films. The
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and TFAB
e
i
M-NU-1000 thin film system was chosen based on following
considerations. (1) MOF NU-1000 is robust and chemically
stable. (2) The nodes of NU-1000 have open sites that allow
redox-active centers to be introduced by post-synthetic
modification. (3) Metallocenes including ferrocene,
ruthenocene, and osmocene (denoted as M; M = Fe, Ru, Os), a
class of well-studied redox couples that can undergo reversible
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Figure 1. A) Schematic representation of M-NU-1000 (M = Fe,
Ru, Os) displaying one metallocene per node loading. B) PXRD
patterns of NU-1000 (Black), Fe-NU-1000 (Red), Ru-NU-1000
(Blue), and Os-NU-1000 (Green).
Cyclic voltammetry (CV) of the M-NU-1000 (M = Fe, Ru,
Os) thin films was performed in a three-electrode assembly,
using the M-NU-1000 film as the working electrode, a Pt mesh
2
+
3+ 15, 16
one-electron oxidation reactions from M to M ,
can be
incorporated as redox active centers into the framework. The
use of such isostructural guests with varied self-exchange rates
enables us to probe electron diffusion systematically. (4) Non-
6
as a counter electrode, and either a TBAPF or TBATFAB
dichloromethane solution (0.1 M) as the electrolyte (see SI for
detailed electrochemical procedures). All the cyclic
voltammograms of M-NU-1000 (M = Fe, Ru, Os) thin films
showed a single reversible redox process, characteristic of the
one-electron metallocene-centered redox transit between the
1-
1- 17
coordinating anions such as PF
6
and TFAB , combined with
low donor solvents, such as dichloromethane (DCM), should
facilitate unimpeded ion mobility during the electrochemical
1
5
analysis. Moreover, we can gain insights into how ion
diffusion is affected by counter anions with substantially
different sizes. By applying the theoretical solid state-
voltammetry model to the experimental data, we identified
three key stages in the process of electrochemical
transformation of M-NU-1000 films. To the best of our
2+
3+
M
and M states (M = Fe, Ru, Os) (Figure 2). The counter
-
1-
1-
anion [A ] in the electrolyte solution (PF
6
or TFAB ) acts as a
charge compensator to maintain electroneutrality, according to
the following redox reaction:
0
+1
knowledge, this investigation is the first attempt to quantify D
and D in the redox-hopping process in MOFs. Importantly, the
and D
generally within the same range of Dapp values (10 -10 cm s
e
O
O
Zr
Zr
i
-1
O
Oxi
O
A
(1)
D
e
i
values obtained by applying the theoretical model are
2+
3+
M
Red
M
-14
-9
2
-
1
13, 18, 19
)
of MOFs from literature,
suggesting good feasibility of
applying this model to individually quantify D
e
and D
i
.
In principle, the rate of the MOF redox reaction depends on
both the rate of electron diffusion from one metallocene center
to another (represented by the electron diffusion coefficient,
D ), and the rate of counter anion diffusion through the MOF
e
pores to maintain the charge balance (represented by the ion
2. RESULTS AND DISCUSSION
The incorporation of the metallocene ligands in the structure
of the NU-1000 to obtain M-NU-1000 (M = Fe, Ru, Os) was
achieved through a commonly employed solvent assisted ligand
diffusion coefficient, D ). Specifically, D should be dependent
i
e
2
+
3+
to the homogeneous self-exchange rate (M to M ) of the
metallocene centers (Fe = k, Ru = 2k, Os = 4k).
other hand, should be directly related to the anion size (PF
0.109 nm , TFAB vol= 0.405 nm ) and the ion-pairing ability
1
0
20, 21
incorporation (SALI) procedure. NMR analysis of the
digested M-NU-1000 samples (Figure S1) revealed that the ratio
i
D on the
1-
6 vol
of Zr
6
to metallocene was 1:1 in all the frameworks, suggesting
3
1-
3 17
=
the presence of one metallocene molecule per zirconium node
(Figure 1A). This type of NMR analysis has been successfully
used in the literature to determine metallocene content in the
of the anion with respect to the metallocenium ion. CV analysis
allowed the determination of the oxidation potentials for the
2+
3+
M /M redox couple for each of the six metallocene-counter
anion combinations (Figure 2). These values (E1/2) were used in
the subsequent potential-step experiments.
1
0, 18
NU-1000 MOF.
It is important to keep this ratio constant
across the series, to ensure that metallocene concentration inside
NU-1000 and the distance between them remains unchanged
during the electrochemical characterization. Additionally,
powder X-ray diffraction (PXRD) patterns of Fe-NU-1000, Ru-
NU-1000, and Os-NU-1000 samples confirmed the expected
NU-1000 structure, which remained consistent after the SALI
procedure (Figure 1B). The deposition of these MOFs as thin
films was achieved by electrophoretic deposition using
To obtain the diffusion coefficients, chronoamperometry
experiments were carried out on the Fe-NU-1000, Ru-NU-
1000, and Os-NU-1000 thin films (see SI for experimental
details). A potential lower than the reduction peak (E
applied for 20 min, followed by a potential E that is higher than
the oxidation peak for 20 min (Figure 3A). The current passed
through the film at E vs. time (I vs. t) plot was obtained (Figure
B). It has been theoretically demonstrated that for solid state
1
) was
2
2
1
0
conductive FTO slides as a support. SEM analysis showed an
average film thickness of 1 µm (Figure S2), and a hexagonal rod
morphology of framework particles across the film surface,
characteristic of NU-1000 microcrystals (Figure S3).
3
voltammetry of electrode-confined collection of microcrystals
in contact with an electrolyte solution, this current-time
response is governed by the electron and ion diffusion
coefficients (D
to quantify the relative contribution of both D
e
and D
i
). A three-dimensional theoretical model
and D was
e
i
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e i
and D
).14 These
developed by Scholz et al. who assumed that the
electrochemical reaction starts at the electrolyte-crystal-
including the diffusion coefficients (D
equations were used to fit the experimental data at each stage,
to obtain the physical values of D and D and their evolution as
the electrochemical reaction progresses.
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electrode three-phase junction (Figure 3D). From this
boundary, a simultaneous injection or removal of electrons and
the corresponding dislocation of ions to maintain
electroneutrality take place, as the reaction zone propagates into
the crystal interior. Electron diffusion is postulated to be
perpendicular to the electrode surface, while ion diffusion is
parallel (Figure 3D). We envisioned that applying this model to
the current-time response obtained for the Fe-NU-1000, Ru-
NU-1000, and Os-NU-1000 thin films in two different
e
i
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electrolytes (Figure 4 A-F), could elucidate the values of D and
D .
i
Figure 3. Schematic representation of A) Time-dependent current
function applied to the M-NU-1000 (M = Fe, Ru, Os) thin films. B)
An example of current response observed in a M-NU-1000 (M =
2
Fe, Ru, Os) thin film at an applied potential (E ) as a function of
time - (I vs. t) plot. C) The I√t vs.√t plot of chronoamperometric
response, depicting the different time stages. D) An illustration of
MOF microcrystals immobilized on an electrode surface, in contact
with an electrolyte solution.
First, the I√t vs.√t curves for the Fe-NU-1000, Ru-NU-1000,
and Os-NU-1000 thin films in the two different electrolytes
were constructed, as shown in Figure 4 G-L. For each of the six
combinations of metallocene-counter anion couples, the
chronoamperometry experiments were repeated four times on
different films, in order to obtain the average D
and the correspondent statistical error (see SI for detailed
electrochemical procedures and step-by-step sample
e i
and D values
a
calculation of the applied model at the three different stages).
Once the three stages (A, B, and C) where identified from the
I√t vs.√t plots (Figure 4 G-L), the curve fitting of the
experimental data to the appropriate current-time equation was
carried out as follows:
-1
Figure 2. Cyclic voltammograms (100 mV s ) of the MOF films
in 0.1 M supporting electrolyte in dichloromethane A) Fe-NU-
1
000, TBAPF
TBAPF , D) Ru-NU-1000, TBATFAB, E) Os-NU-1000, TBAPF
F) Os-NU-1000, TBATFAB.
6
, B) Fe-NU-1000, TBATFAB, C) Ru-NU-1000,
6
6
,
Stage A (Figure 3C, and Figure 4 G-L). During Stage A, the
The model suggests the existence of three distinct reaction
stages in the observed I vs. t responses, representing the extent
of redox conversion. When plotting the chronoamperometric
response as a I√t vs.√t plot, these three stages (denoted as A, B,
model assumes that unhindered diffusion of both electrons and
1
4
ions occurred through a quasi-semi-infinite space. The
1
4
resulting current-time function for Stage A is expressed as:
14
and C) become evident (Figure 3C). During Stage A, both
(2)
electron and ion diffusion are unhindered, and the faster process
leads the spread of the initial charge transfer either along the
crystal-solution interface or along the crystal-electrode
boundary. Stage B begins with the maximum of the I√t vs.√t
curve (Figure 3C) that corresponds to the moment when all
redox centers across such interface are oxidized. From this
instant, the further course of the reaction into the crystal bulk is
controlled by the slowest process. The very end of the
conversion is the most characteristic segment (Stage C), where
more than 99% of the crystal is oxidized (Figure 3C). A
schematic illustration of these three stages in the MOF is shown
in Figure S7. The Scholz model provides current-time equations
for each stage, as a function of several physical parameters,
where N is the number of MOF crystallites in the film, F is
Faraday’s constant, u is the length of the three-phase junction
(
perimeter of the electrode-crystal interface), V
molar volume, D is the electron diffusion coefficient, D
ion diffusion coefficient, Δx is the distance an ion travels in one
m
is the MOF
e
i
is the
0
hopping step, Δz
0
is the distance an electron travels in one
hopping step, and
퐹
휑 = (퐸 ― 퐸푓)
(3)
푅푇
where R is the gas constant, T is temperature, E is the applied
potential (E in Figure 3A), and E is the formal potential of
2
f
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2
+
3+
metallocene M /M couple. All of the above parameters can
be empirically obtained from the crystal structure of NU-1000,
e i
case (D > D ) with rapid electron hopping along the crystal
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walls. The D
infra).
i
> D case is also supported in Stage B and C (vide
e
6
SEM images of the films, and the Zr /metallocene ratio
calculated from NMR digestion studies (See SI).
Another important finding is the considerable variation in
the D values for the M-NU-1000 (M = Fe, Ru, Os) series in
Stage A (Figure 5- Stage A). The magnitude of electron
diffusion followed the trend of the self-exchange rates of the
The fitting of Eq. 2 to the current- time response (I vs. t) from
t = 0 s to tref (discussed in Stage B in detail) of all the M-NU-
1000 (M = Fe, Ru, Os) thin films in both electrolytes is shown
e
2
in Figure 4 A-F (blue traces). A generally good fit (R > 96%,
metallocene centers. That is, D
1000 < Ru-NU-1000 < Os-NU-1000 using PF
e
increased in the order Fe-NU-
1
-
see SI) was observed for all the films, evidencing a close
agreement between the experimental data and the theoretical
model. The diffusion coefficients calculated in Stage A are
presented in Figure 5 and summarized in Table 1.
6
as the counter
anion. This result highlights the interdependence of electron
diffusion and the self-exchange rate of the redox centers,
presenting the strategy to control the rate of electron transport
0
1
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1
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0
1-
in MOFs. A similar behavior was observed using TFAB as the
Theoretically, two different cases can occur during Stage A,
as the reaction zone spreads from the three-phase boundary: (1)
counter anion, however the trend was weaker, the D
varied in the order of Fe-NU-1000 ≈ Ru-NU-1000 < Os-NU-
000.
Stage B. The moment when all the redox centers at the
e
values
e i
If D < D , this period is characterized by the rapid migration of
1
ions along the electrode-crystal interface, where the redox
14
active centers along this boundary are quickly converted. (2)
If D > D , the reaction zone rapidly spreads away from the
e
i
electrolyte-crystal interface are oxidized, corresponds to the
maximum of the I√t vs.√t curve (Figure 3C, and Figure 4 G-L).
At this point, Eq. 2 loses its validity as diffusion is no longer
assumed unhindered and ion diffusion into the crystallite
electrode in a perpendicular direction, along the electrolyte-
crystal interface (the crystal surface).
Application of the model to Stage A data reveals that the
1
4
-15
-18
becomes rate determining. Therefore, the theoretical model
i
values of D (10 - 10 ) across all the M-NU-1000 (M = Fe,
1
4
developed by Scholz et al. defined this maximum of the I√t
vs.√t curves (Figure 3C), as a characteristic time tref, that follows
the mathematical expression:
Ru, Os) thin films, regardless of the counter ion size, are
significantly lower than those reported in literature for typical
-5
-6
through-solution diffusion of ions (10 - 10 ), Figure 5, Table
2
2
1
.
Prior to applying a potential, the MOF microcrystals are
(4)
surrounded by a bath of counter ions (0.1 M), including ions
located proximal to the crystal-electrolyte interface. As a result,
ion diffusion is almost negligible during this initial stage and
where H is the thickness of the MOF particles (1 µm,
according to SEM images, Figure S2). As a result, the current
i
thus, the D calculated are small. That said, the mechanism of
1
4
detected at this time (Iref) can be expressed as:
electron/ion transport in Stage A is believed to follow the latter
Figure 4. Left: The current - time response (I vs. t) at an applied potential E, measured in 0.1 M supporting electrolyte for the films of A)
6
Fe-NU-1000, TBAPF , B) Fe-NU-1000, TBATFAB, C) Ru-NU-1000, TBAPF , D) Ru-NU-1000, TBATFAB, E) Os-NU-1000, TBAPF ,
6
6
F) Os-NU-1000, TBATFAB. Black: Experimental response, Blue: Model fitting Stage A Equation (2), Red: Model fitting Stage C Equation
(6). Right: Chronoamperometric response expressed as a I√t vs.√t plot at an applied potential E, measured in 0.1 M supporting electrolyte
for the films of G) Fe-NU-1000, TBAPF
6 6
, H) Fe-NU-1000, TBATFAB, I) Ru-NU-1000, TBAPF , J) Ru-NU-1000, TBATFAB, K) Os-
NU-1000, TBAPF , L) Os-NU-1000, TBATFAB.
6
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(
5)
D
e
and D
i
in Stage B were calculated using Eq.4 and Eq.5 and
are summarized in Figure 5 and Table 1. Since the process is
-9
-10
limited by ion movement, the values of D
again found to be higher than those of D (≈ 10 - 10 ) for all
the metallocenes in both electrolytes. Importantly, the D values
e
(≈ 10 - 10 ) were
-11
-14
i
e
in Stage B are lower than those obtained in Stage A. As
mentioned above, electrons predominantly hop along the
crystal-electrolyte boundary that is perpendicular to the
substrate in Stage A. In contrast, electrons in Stage B (beginning
from tref ) are gradually diffusing deep into the MOF crystals.
Metallocenes inside MOF pores tend to have lower degrees of
freedom compared to those anchored on the outer surface of
MOF crystals. As a result, redox centers at the crystal-
electrolyte interface can orient more efficiently, allowing for
faster electron diffusion in Stage A. Similarly, the overall ion
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i
diffusion (D ) has increased across the series in Stage B
compared to the negligible values obtained in Stage A. This fact
illustrates that only ions that were initially at the electrolyte-
crystal interface were satisfying the electroneutrality
requirement in Stage A, while from tref, ion diffusion occurred
from the crystal-electrolyte interface to the bulk of the particle
through the MOF channels (Stage B).
One of the key conclusions of this modelling was that the
principal trends in diffusion coefficients observed for the M-
NU-1000 (M = Fe, Ru, Os) thin films in Stage A remained
e
increased generally
following the order Fe-NU-1000 < Ru-NU-1000 < Os-NU-
or TFAB as the counter anion.
This result reconfirms the dependence of electron diffusion on
the self-exchange rate of the redox centers. Essentially, the
largely unchanged in Stage B (Figure 5). D
1-
-
1
000 when using either PF
6
Figure 5. Summary of the diffusion coefficients for M-NU-1000
1
-
1-
(M = Fe, Ru, Os) thin films in PF
at the three reaction stages. Stage A: Electron diffusion coefficient
(Top left), ion diffusion coefficient D (Top right). Stage B:
Electron diffusion coefficient D (Middle left), ion diffusion
coefficient D (Middle right). Stage C: Ion diffusion coefficient D
Bottom right).
6
and TFAB based electrolytes
D
e
i
e i
similarities in the diffusion coefficient trends (D and D ) for the
e
M-NU-1000 (M = Fe, Ru, Os) thin films at both Stage A and
Stage B, suggest that the redox hopping rate can be
straightforwardly modulated (and potentially maximized)
through the incorporation of molecular moieties with rapid self-
exchange rates into a MOF structure containing large channels,
as well as employing electrolytes based on smaller counter ions.
i
i
(
Stage C. After the rapid exhaustion of the metallocene
centers at the electrolyte-crystal interface (Stage A), the further
course of the reaction into the crystal bulk (Stage B, starting
from maximum of the I√t vs.√t curve) is controlled by the ability
of ions to propagate into the MOF interior and provide the
charge balance. As the majority of the MOF is oxidized (Figure
3
C and Figure 4 G-L), ion migration through the framework
channels becomes extremely important, and the last period of
the electrochemical conversion is determined by the dimensions
of the MOF crystallites. As
chronoamperometric curves for Stage C can be modeled
exclusively in terms of the ion diffusion coefficients (D ), and
a
consequence, the
i
1
4
the crystal dimensions:
(6)
where L and B are the average length and the average width of
the MOF particles, respectively (according to SEM images,
Figure S3). It is important to note that Eq. 6 has been developed
for the very last segment of Stage C, where the total conversion
1
4
of the crystal is higher than 99% (Figure 3C).
Table 1. Summary of the electron (D ) and ion (D ) diffusion
e
i
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coefficients for M-NU-1000 (M = Fe, Ru, Os) thin films in PF
and TFAB based electrolytes
6
but will also reduce the reorganization energy of the system
facilitating the electron transport.
1
-
25
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Stage A
2
-1
2
-1
3. CONCLUSION
D
e
(cm s )
D
i
(cm s )
TFAB1-
1
-
TFAB1-
1-
PF
6
PF
6
In summary, the systematic variation of metallocene redox
center and counter anions in a series of chronoamperometry
experiments allowed the elucidation of the relative contribution
of electron and ion diffusion in metallocene-doped NU-MOF
(9.99 ± 7.75) × 10-7
(1.52 ± 1.13) × 10-5
(3.94 ± 1.64) × 10-7
(8.22 ± 2.33) × 10-8
(4.01 ± 1.88) × 10-17 (1.47 ± 1.23) × 10-17
(9.92 ± 7.03) × 10-15 (1.88 ± 2.76) × 10-18
Fe
Ru
Os
(2.34 ± 1.33) × 10-5 (1.75 ± 1.37) × 10-5 (8.40 ± 4.62) × 10-18 (1.00 ± 1.01) × 10-17
e
thin films. The electron diffusion coefficient D in both Stages
Stage B
A and B was found to increase in the order of Fe-NU-1000 <
Ru-NU-1000 < Os-NU-1000, in parallel to the self-exchange
0
1
2
3
4
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2
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0
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4
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9
0
1
2
3
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0
1
2
3
4
5
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9
0
2
-1
2
-1
D
e
(cm s )
TFAB1-
D
i
(cm s )
TFAB1-
2
+
3+
rates of the M / M couples (M = Fe, Ru, Os). Ion diffusion
1
-
1-
1-
1-
PF
6
PF
6
i 6
(D ) of TFAB was generally faster compared to PF ,
highlighting the easier ion mobility due to lower ion-pairing
association. During all stages, ion diffusion is the limiting
process in redox hopping. The trends observed in the diffusion
(1.08 ± 0.56) × 10-9 (4.34 ± 1.50) × 10-10 (3.72 ± 3.23) × 10-13 (1.42 ± 1.11) × 10-13
Fe
Ru
Os
(1.83 ± 0.38) × 10-9
(4.05 ± 1.02) × 10-9 (3.88 ± 2.36) × 10-11 (1.32 ± 0.21) × 10-14
1-
(3.88 ± 0.73) × 10-9 (3.67 ± 1.01) × 10-9 (3.21 ± 2.54) × 10-12 (2.72 ± 1.59) × 10-12
e i 6
coefficients (D and D ) of these systems obtained in PF and
1-
TFAB based electrolytes at the different stages of the
electrochemical reaction, demonstrated that the electron redox
hopping rates inside frameworks can be controlled through the
modifications of the self-exchange rates of redox centers and
proper selection of counter anions. The successful application
of a solid state-voltammetry theoretical model to the
experimental chronoamperometry data of MOF thin films, is a
significant advancement to the understanding of electron and
ion mobility in the context of electrochemical experiments, and
can be used to guide further research into other redox-active
MOFs.
Stage C
2
-1
D
i
(cm s )
TFAB1-
1
-
PF
6
Fe (1.44 ± 0.55) × 10-11 (1.64 ± 0.30) × 10-11
Ru (5.08 ± 0.12) × 10-12 (1.22 ± 0.12) × 10-11
-
1
2
-
1
2
Os
(
5
.
1
2
±
0
.
1
3
)
×
1
0
(
5
.
2
3
±
0
.
2
4
)
×
1
0
The fitting of Eq. 6 to the current-time response (I vs. t) from
the moment where 99% charge has passed to the end of all the
M-NU-1000 (M = Fe, Ru, Os) thin films in both electrolytes is
shown in Figures 4 A-F (red traces) (see SI for detail). A
ASSOCIATED CONTENT
2
generally good fit (R > 90%, see SI) was achieved, evidencing
a good agreement between the experimental data and the
theoretical model. The diffusion coefficients obtained in Stage
C are presented in Figure 5 and summarized in Table 1. As
Supporting Information. Detailed experimental procedures,
NMR, SEM images, detailed electrochemical procedures, step by
step sample calculation of the model applied. This material is
available free of charge via the Internet at http://pubs.acs.org
calculated, the D
obtained in both Stage A and Stage B, for all the M-NU-1000
M = Fe, Ru, Os) thin films. In fact, the last segment of Stage C
i
values in this final stage are higher than those
AUTHOR INFORMATION
(
represents the moment of 99% of conversion. Thus, instead of
transport from solution to crystal interior, ion diffusion in this
last stage is dominated by short-distance metallocene-to-
metallocene hopping since the electroneutrality requirement is
almost totally satisfied across the particle. Therefore, the values
Corresponding Author
*E-mail: ajmorris@vt.edu
ACKNOWLEDGMENTS
This material is based upon work supported by the National
Science Foundation under Grant No. 1551964
obtained for D
i
describe an instant where the diffusion
conditions are similar to a typical twin-electrode thin film cell.
1
4
1
-
Interestingly, ion diffusion of TFAB was generally faster
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Table of Contents Figure
7
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