Effect of structure on electron transfer reactions between anthracene dyes and TiO2 nanoparticles

Article abstract of DOI:10.1021/jp982740o

Photoinduced electron transfer to TiO₂ nanoparticles has been examined for the 1-, 2-, and 9-isomers of anthracenecarboxylic acid. TiO₂ samples with either anatase or amorphous crystal structures were used for these experiments. The results from time-resolved transient absorption measurements show that the rates of the forward (dye-to-semiconductor) and reverse (semiconductor-to-dye) electron transfer reactions depend on the chemical structure of the dye and the method used to synthesize the particles. These effects arise from differences in both the energetics and the coupling elements for the reactions. Specifically, the reverse electron transfer reactions for the 1- and 2-isomers are significantly faster than that for the 9-isomer due to differences in the oxidation potentials of the dye molecules. In addition, both the forward and reverse electron-transfer times are faster for the anatase TiO₂ particles compared to the amorphous particles. For example, the forward electron transfer time for the anatase particles is ≤200 fs, whereas it is ca. 1.5 ps for the amorphous particles. This is due to a difference in the coupling elements for the forward electron transfer reaction. Finally, all the anthracenecarboxylate dyes examined show red shifts in their UV-vis absorption spectra when they are attached to the semiconductor particles. Experiments with ZrO₂ show that these shifts are not due to a charge-transfer band. The spectra are more strongly perturbed when the dye molecules are attached to the anatase particles, which shows that for this series of compounds there is a correlation between the spectral shifts and the time scale for electron transfer.

Full text of DOI:10.1021/jp982740o

9
508
J. Phys. Chem. B 1998, 102, 9508-9517
Effect of Structure on Electron Transfer Reactions between Anthracene Dyes and TiO2
Nanoparticles
Ignacio Martini, Jos e´ H. Hodak, and Gregory V. Hartland*
Department of Chemistry and Biochemistry, UniVersity of Notre Dame, Notre Dame, Indiana 46556
ReceiVed: June 23, 1998; In Final Form: September 15, 1998
2
Photoinduced electron transfer to TiO nanoparticles has been examined for the 1-, 2-, and 9-isomers of
anthracenecarboxylic acid. TiO samples with either anatase or amorphous crystal structures were used for
2
these experiments. The results from time-resolved transient absorption measurements show that the rates of
the forward (dye-to-semiconductor) and reverse (semiconductor-to-dye) electron transfer reactions depend
on the chemical structure of the dye and the method used to synthesize the particles. These effects arise
from differences in both the energetics and the coupling elements for the reactions. Specifically, the reverse
electron transfer reactions for the 1- and 2-isomers are significantly faster than that for the 9-isomer due to
differences in the oxidation potentials of the dye molecules. In addition, both the forward and reverse electron-
2
transfer times are faster for the anatase TiO particles compared to the amorphous particles. For example,
the forward electron transfer time for the anatase particles is e200 fs, whereas it is ca. 1.5 ps for the amorphous
particles. This is due to a difference in the coupling elements for the forward electron transfer reaction.
Finally, all the anthracenecarboxylate dyes examined show red shifts in their UV-vis absorption spectra
2
when they are attached to the semiconductor particles. Experiments with ZrO show that these shifts are not
due to a charge-transfer band. The spectra are more strongly perturbed when the dye molecules are attached
to the anatase particles, which shows that for this series of compounds there is a correlation between the
spectral shifts and the time scale for electron transfer.
Introduction
In this paper, we report results for a series of carboxy-
anthracene dyes: 9AC, 1-anthracenecarboxylic acid (1AC),
2
(
The demonstration of efficient solar-energy conversion using
dye-sensitized semiconductor electrodes has generated consider-
-anthracenecarboxylic acid (2AC), and 9-anthraceneacetic acid
9AA). Time-resolved experiments were carried out for these
able interest in the electron transfer dynamics of molecules
bound to metal-oxide surfaces.1,2 In general, ultrafast laser
species bound to the two types of TiO2 particles used in our
previous paper (which have anatase or amorphous crystal
structures), as well as particles of ZrO2. The conduction band
of ZrO2 is 1.2 eV higher in energy than that for TiO2,20 which
means that photoinduced electron transfer does not occur to ZrO2
for these systems.
studies show that the forward (dye-to-semiconductor) electron
transfer reaction is extremely fast, usually less than 200 fs.
On the other hand, the back reaction occurs on a range of time
3
-15
scalessvarying from ∼10 ps to microsecondssand often
displays complex, multiexponential decays.5
,6,9-19
Both the
forward and reverse electron-transfer reactions are crucial to
the solar-energy conversion process, therefore, it is important
to understand how the rates of these reactions depend on the
chemical properties of the dye and the semiconductor.
The aim of these experiments is to gain a “chemical”
understanding of the important factors in the dye-sensitization
process. As will be shown below, both the oxidation potential
of the dye and the crystal structure of the semiconductor play
crucial roles in the electron transfer reactions. The experimental
results also show that both the forward and reverse electron
transfer rates are correlated to the shift in the UV-vis absorption
spectra of the dye molecules that occurs when they bind to the
semiconductor particles. However, these spectral changes are
not due to the formation of a charge-transfer band. Analysis
of the rate constants for back electron transfer shows that these
reactions are in the intermediate coupling region (i.e., coupling
In a recent series of papers, we have examined the electron
transfer dynamics of 9-anthracenecarboxylic acid (9AC) bound
9,12
to TiO2 particles.
The TiO2 particles in these studies were
prepared by different techniques, and the time constants
measured for the back electron transfer reaction were found to
be different for the two types of particles.9
,12
The back electron
transfer rate was also found to depend on how the semiconductor
particles were treated after they had been prepared. For
example, adding small amounts of water to the ethanolic dye-
TiO2 solutions produces a red shift in the TiO2 absorption
-
1
elements of 50-200 cm ). Thus, calculations based on the
simple nonadiabatic theory for electron transfer are not adequate
1
2
21-23
spectrum and a decrease in the back electron transfer time.
for these systems.
The red shift implies a lower conduction band energy and,
therefore, a smaller driving force for back electron transfer.
These results are consistent with Marcus-inverted behavior for
the back electron transfer reaction.12 Analysis of the data using
the weak coupling limit expression for electron transfer gave a
reorganization energy of 0.75 ( 0.05 eV.12
Experimental Section
The transient absorption apparatus has been described in detail
9
elsewhere. Briefly, the output of a regeneratively amplified
Ti-Sapphire laser system (Clark-MXR CPA-1000; 100-120
1
0.1021/jp982740o CCC: $15.00 © 1998 American Chemical Society
Published on Web 11/03/1998

Effect of Structure on Electron-Transfer Reactions
J. Phys. Chem. B, Vol. 102, No. 47, 1998 9509
CHART 1
for all three anthracenecarboxylic acid isomers in acetonitrile
(Fisher) using ferrocene as the internal reference. The results
from the cyclic voltammetry experiments show that the oxidation
potentials of 1AC and 2AC are 0.1 eV more negative than the
•
+
9
AC oxidation potential. From ref 28, E(9AC/9AC ) ) 1.3
•
+
•+
eV versus NHE, therefore, E(1AC/1AC ) ) E(2AC/2AC )
1.2 eV versus NHE.
)
Results
9-Anthraceneacetic Acid. Both the absorption spectrum and
the transient absorption dynamics of the 9AA-TiO2 solutions
failed to show any differences from the free dye in solution.
Also, no fluorescence quenching was observed for 9AA when
TiO2 was added to the solution. To test whether 9AA binds to
the particles, the stability against flocculation of a solution of
amorphous TiO2 with 9AA and a solution with a greater amount
of 9-methylanthracene (9MA, which is not expected to adsorb
onto TiO2) were compared to as-prepared particles. Both the
fs fwhm; 0.6 mJ/pulse; λ ) 780 nm) was split by a 70/30 beam
splitter (CVI). The 70% portion was doubled in a 1 mm type-I
BBO crystal to supply the pump pulses (390 nm), and the 30%
portion was used as the probe beam, after attenuation by neutral
density filters. White light probe pulses were generated by
focusing into a 6 mm BK-7 window; different wavelengths were
selected by 10 nm band-pass interference filters (Oriel). Cross-
correlations between the pump and probe pulses were measured
by sum frequency generation or parametric amplification in a
9
MA-TiO2 and the straight TiO2 solutions showed significant
turbidity after several hours at room temperature. In contrast,
the solution with 9AA remained clear, indicating that the 9AA
molecules attach to the particles and protect them against
precipitation. The observation of no fluorescence quenching
or change in the transient absorption dynamics implies that the
forward electron transfer time is longer than 10 ns for 9AA
1
mm type-I BBO crystal. The fwhm of the cross-correlation
2
trace was 150-200 fs (sech deconvolution). The polarizations
of the laser pulses were controlled by passing the beams through
λ/2 achromatic waveplates (Special Optics) and Glan-Laser
calcite polarizers (Karl-Lambrecht). The probe beam was split
into signal and reference beams which were detected by matched
photodiodes (Thorlabs) for shot-to-shot normalization. Steady-
state absorption spectra were recorded with a Perkin-Elmer
Lambda 6 UV-vis spectrophotometer, and fluorescence spectra
were obtained with a SLM Instruments MC-320 spectrometer.
The anatase TiO2 nanoparticles were prepared by controlled
(i.e., longer than the estimated lifetime of the excited electronic
state of the dye). This implies that the electronic coupling
element for electron transfer from 9AA to TiO2 (either the
anatase or the amorphous forms) is at least 2 orders of magnitude
smaller than the coupling elements for the other dye molecules
in this study (vide infra).
Note that the sedimentation experiments do not definitively
prove that 9AA adsorbs onto the TiO2 particles, i.e., the
observation of reduced electron-transfer efficiency may simply
mean that the dye molecules are not attached to the particles.
A possible reason why this may occur for 9AA is that adsorption
hydrolysis in water of titanium(IV) isopropoxide (ACROS, 98%)
dissolved in 2-propanol.1
2,24-26
The hydrolysis was carried out
1
1,29
requires deprotonation of the carboxylate group,
which is
under deareated conditions at 1 °C. ZrO2 nanoparticles were
unfavorable for 9AA because the negative charge on the
deprotonated carboxylate cannot be stabilized by resonance with
prepared in a similar way using zirconium(IV) isopropoxide
Aldrich, 99.9%).26 The water was removed by rotatory
(
3
0
the anthracene ring.
evaporation, yielding a white powder that was dried overnight
and redissolved in absolute ethanol. X-ray powder diffraction
and UV-vis absorption spectra confirmed the anatase crystalline
structure. TiO2 nanoparticles were also synthesized by rapid
Steady-State Spectra. When 9AC binds to the surface of
either crystalline form of TiO2, the absorption spectrum of the
9
,12
dye shifts to the red.
Figure 1 shows the absorption spectra
9
,27
of 1AC and 2AC in solution and bound to the anatase and
amorphous TiO2 nanoparticles. There is a pronounced red shift
in the spectra for both isomers, indicating a strong interaction
with the particles. The stoichiometry of this reaction was
studied by recording difference absorption spectra, shown in
Figure 2 for 2AC. In these experiments, the absorption of the
dye-TiO2 system was measured against the same concentration
of dye as a reference. A linear relation of the difference
absorption with the dye concentration (insert of Figure 2) shows
that the dye molecules do not form dimers at the surface of the
hydrolysis of titanium(IV) isopropoxide in absolute ethanol.
In this case, the X-ray powder diffraction patterns failed to show
any peaks, indicating that the particles have an amorphous
crystal structure. The absorption onset for the particles is similar
to that of rutile TiO2 (the amorphous particles have a red-shifted
2
6
absorption spectrum compared to the anatase particles).
Dynamic light scattering measurements (DynaPro-MSDC, Pro-
tein Solutions) show that the anatase particles have an average
hydrodynamic radius between 1.5 and 2.0 nm for samples
prepared on different days. The amorphous particles only
weakly scatter light, which means it was not possible to
accurately record their size via light scattering.
3
1
TiO2 particles. Similar results were obtained for 1AC.
The association constant Ka between the dye molecules and
the semiconductor nanoparticles was calculated using the
9
AC was purchased from Aldrich and was used without
further purification. 1AC and 2AC were purchased from TCI
Tokyo-Kasei) and were also used without further purification.
AA was synthesized by treating 9-(chloromethyl)anthracene
Aldrich, 98%) with magnesium turnings (1 equiv) in dry THF
3
2
Langmuir adsorption isotherm
(
9
(
Θ
K )
(1)
a
[
D] (1 - Θ)
f
under reflux overnight. The resulting Grignard reagent was
reacted with dry ice to produce 9AA. The product was
recrystallized from toluene/ethanol and identified by IR, NMR,
and mass spectroscopy. Cyclic voltammetry was performed
where [D]f is the concentration of free dye and Θ is the fraction
of occupied sites at the particle surface. The fraction of
occupied sites is given by Θ ) [D]b/[S]0, where [D]b is the

9510 J. Phys. Chem. B, Vol. 102, No. 47, 1998
Martini et al.
Figure 3. Absorption spectra for 2AC bound to anatase TiO
amorphous TiO (‚‚‚), ZrO (- - -), 2AC in ethanol (-‚‚-), and 2AC in
an acidic ethanolic solution with an excess of Al (-‚-).
2
(s),
2
2
3+
the following effective association constants were obtained for
AC, 2AC, and 9AC, respectively, Kaγ ) 6000 ( 1000, 4300
800, and 1400 ( 200. These results show that 1AC and
AC have a significantly stronger chemical interaction with the
1
(
2
semiconductor particles than 9AC.
For the amorphous TiO2 particles, the smaller perturbation
of the absorption spectra does not allow for an accurate
determination of Kaγ by this method. Thus, the association
constants for the different dye molecules bound to the amor-
phous TiO2 particles were determined using the fluorescence
quenching method described in ref 9. The effective association
constants were found to be within experimental error of the
values obtained for the anatase TiO2 particles. For ZrO2, the
effective association constants are approximately one-half of
those for anatase TiO2.
Figure 1. Top: Absorption spectra for 1AC in ethanol (‚‚‚) and bound
to anatase (s) and amorphous (- - -) TiO . Bottom: Absorption spectra
for 2AC in ethanol (‚‚‚) and bound to anatase (s) and amorphous
- - -) TiO
2
(
2
.
In Figure 3, absorption spectra are presented for 2AC in
ethanol, bound to anatase TiO2, amorphous TiO2 and ZrO2
3+
particles, and in an acidified ethanol solution with excess Al .
This figure shows that 2AC interacts with ZrO2 and anatase
TiO2 in a similar way, but the perturbation of the spectrum for
the amorphous TiO2 particles is much weaker. This can be
clearly seen in the λ > 400 nm spectral region. Also note that
the red shift in the absorption spectrum of the dye induced by
3
+
complexation with Al is nearly identical to the shift induced
by the amorphous particles. A red shift due to the formation
of a dye-metal ion complex has been previously observed for
a variety of dye molecules, see for example ref 10. It is
important to note that the spectral shifts for the anatase TiO2
and ZrO2 particles are larger than that caused by complexation
2
Figure 2. Absorption spectra of 2AC bound to anatase-TiO minus
the absorbance of an equimolar solution of free 2AC. The concentration
of 2AC increases from bottom-to-top at 410 nm. The inset shows the
linear dependence of the absorbance difference at 410 nm on the
concentration of 2AC.
3
+
with Al . 1AC and 9AC show qualitatively similar results.
Fluorescence quenching measurements show that the fluo-
rescence quantum yield for 1AC and 2AC bound to ZrO2 is ca.
90% of that for the free dye molecules in solution. For 9AC-
ZrO2, the relative fluorescence quantum yield is ca. 70%. This
shows that photoinduced electron transfer to ZrO2 is not
significant for the anthracenecarboxylate dye molecules. These
results are in agreements with recent fluorescence measurements
performed by Levinger and co-workers for coumarin 343 bound
concentration of bound dye and [S]0 is the total concentration
of sites. The total concentration of dye is D0 ) [D]f + [D]b
and [S]0 ) γ[TiO2], where γ is a proportionality constant that
is related to the average number of binding sites per particle.
Using the last two relationships in eq 1 yields
[
TiO2]
1
Kaγ
- K )
(2)
a
A/ꢀl
(D - A/ꢀl)
0
3
3
to ZrO2. For the dye molecules bound to TiO2, the fluores-
cence quantum yields are ca. 5% of those for the free dye in
solution. Fluorescence excitation spectra show that the emission
from the dye-TiO2 solutions is due to free dye in solution. In
contrast, for the dye-ZrO2 solutions, the fluorescence excitation
spectra show that the majority of the fluorescence (>90%) arises
from bound dye molecules. These results are consistent with
fast photoinduced electron transfer to TiO2 but not to ZrO2.
Transient Absorption and Time-Resolved Anisotropy
Measurements. In our previous studies, we compared the
where A ) ꢀl[D]b is the absorbance of the bound dye molecules.
The effective association constant Kaγ was calculated using data
from a range of wavelengths. In these calculations the values
of the ꢀl were initially estimated from a solution with a high
concentration of TiO2. Kaγ was then obtained from the slope
of a plot of 1/(D0 - A/ꢀl) versus [TiO2]/(A/ꢀl). The percentage
of bound dye was then calculated, and the values of ꢀl were
reevaluated. This series of calculations was performed itera-
tively until the answers were self-consistent. For anatase TiO2

Effect of Structure on Electron-Transfer Reactions
J. Phys. Chem. B, Vol. 102, No. 47, 1998 9511
Figure 4. Magic-angle transient absorption data for 9AC bound to
anatase TiO
to the experimental data, the results of which are summarized in Table
. The experiments were performed with 390 nm pump and 780 nm
2 2 2
, amorphous TiO , and ZrO . The dashed lines are the fits
1
probe pulses. The experiments for amorphous TiO
over a 200 ps total delay time.
2
were performed
transient absorption dynamics and time-resolved anisotropy of
9,12
9AC-TiO2 to the free dye in solution.
In this paper, we
introduce the results for 9AC bound to ZrO2 nanoparticles.
Figure 4 compares the dynamics of 9AC bound to the anatase
and amorphous TiO2 particles and the ZrO2 nanoparticles. The
best fits to the data using a sum of exponentials convoluted
with a Gaussian instrument response function are also shown.
All the scans presented in Figure 4 were measured at the magic
angle (54.7°) to eliminate effects due to rotation.34 In the ZrO2
experiments, the 780 nm probe pulse interrogates the electroni-
cally excited dye molecules that are bound to the surface of the
semiconductor particles (particle concentrations used are such
that over 95% of the molecules are bound). The 9AC-ZrO2
signal has a biexponential decay with time constants of 44 ps
Figure 5. (a) Time-resolved anisotropy data for 9AC-anatase TiO
and 9AC-ZrO . The dashed line for 9AC-anatase TiO is a calculation
of the time-dependent anisotropy using a 33 ps back-electron-transfer
time. The dashed line for 9AC-ZrO is a fit to the data using a sum
of exponentials. See text for details. (b) Time-resolved anisotropy data
for 1AC-anatase TiO and 1AC-ZrO
2
2
2
2
2
2
.
the time-resolved anisotropy in our experiments is given by r(t)
3
6
) nD(t)rD(t) + nRC(t)rRC(t), where nD(t) and nRC(t) are the
relative populations of the electronically excited dye and the
radical cation, respectively, and rD(t) and rRC(t) are the corre-
sponding anisotropies (which are time dependent due to
rotation).
(
28%) and 7 ps (22%) with a 50% offset. For the TiO2 particles,
the fluorescence quenching studies show that most of the excited
AC molecules undergo electron transfer, creating trapped
9
•+
electrons in the TiO2 particles and the 9AC radical cation that
A simulation based on the above equation for r(t) assuming
that the offset in the transient absorption signal (13% of the
signal) is only due to free dye is included in Figure 5. In this
calculation, the time-dependent anisotropy of the free dye rD(t)
was taken from ref 12 and that for the radical cation rRC(t) was
assumed to have the same form as the anisotropy for ZrO2 but
with a different sign. (The anisotropy for 9AC-ZrO2 decays
with time constants of 40 (63%) and 10 ps (23%), with a 14%
offset.) These calculations show that the decay in the anisotropy
arises from a combination of rotation, and the decrease in the
population of the radical cation compared to free dye due to
the back electron transfer reaction. The agreement between the
calculations and the experimental results supports the assignment
of the 33 ps decay time to back electron transfer. Figure 5b
shows time-resolved anisotropy data for 1AC bound to anatase
TiO2 and ZrO2. The anisotropy signals for 1AC-TiO2 and
1AC-ZrO2 are significantly different, indicating that electron
transfer occurs for 1AC-TiO2. However, in this case, the
anisotropy is negative for both the radical cation and the
electronically excited dye molecules. This makes it difficult
to quantitatively analyze the results for 1AC. 2AC shows a
similar behavior to 1AC.
strongly absorb the 780 nm probe light.9
,10,12,35
The decay in
the signal for 9AC-TiO2 is assigned to the back electron transfer
reaction.9 This reaction destroys both the electrons localized
in the TiO2 particles and the dye radical cation. The data in
Figure 4 for the TiO2 particles can be fitted using a single-
exponential decay plus an offset. For anatase TiO2 the decay
time is 33ps (87% of the decay), and for amorphous TiO2 the
decay time is 54 ps (72% of the decay). The constant
,12
•
+
background that remains after the 9AC signal has decayed is
due either to bound 9AC molecules that do not transfer an
9
electron or (more likely) to free dye molecules in solution. It
is important to note that the back electron transfer time is faster
for anatase TiO2 compared to the amorphous particles.
Figure 5a shows time-resolved anisotropy measurements for
9AC bound to anatase TiO2 and ZrO2. The positive anisotropy
shown by the 9AC-ZrO2 system is a signature of the excited
electronic state of the neutral dyesthe anisotropy of the free
dye is also positive.9 The negative anisotropy indicates the
presence of the radical cation in the 9AC-TiO2 system. The
difference in the sign of the anisotropy arises because the radical
cation and the dye have different electronic structures. This
causes the transition dipole moment for absorption at 780 nm
to have a different alignment with respect to the molecular axis
for the radical cation compared to the electronically excited dye
molecules.1 The decay in the negative anisotropy signal occurs
because two different species contribute to the transient absorp-
tion signal that have different anisotropy signals (electronically
excited dye molecules and the dye radical cation). Specifically,
Magic-angle transient absorption data for 1AC bound to ZrO2
and TiO2 are presented in Figure 6a, and data for 2AC are shown
in Figure 6b. These species have very similar dynamics, i.e.,
there is almost no decay in the signal for ZrO2, and the decay
for anatase TiO2 is faster than that for amorphous TiO2. These
results are similar to what was observed for 9AC, except that
the 9AC-ZrO2 data showed a significant decay on a 100 ps
2

9512 J. Phys. Chem. B, Vol. 102, No. 47, 1998
Martini et al.
consistent with either transfer of population from high to low
3
7
vibrational levels (vibrational relaxation), stabilization of the
3
8
ground state of the radical cation via solvation, or a blue shift
in the absorption spectrum of the electrons in the TiO2
3
9
particles. At present we cannot determine which of these
possibilities is primarily responsible for the short time dynamics
in Figure 8. For 1AC and 2AC bound to amorphous TiO2, the
time scales for the spectral shifts for the radical cation are 2.3
(
0.3 and 2.2 ( 0.5 ps, respectively.
Short time scans for 1AC and 2AC adsorbed at the surface
of the amorphous TiO2 particles are presented in Figure 9. The
rise in this signal is much slower than that for anatase TiO2
(see Figure 8 and Table 1: τ3). As discussed in the next section,
this slow rise is tentatively assigned to the forward electron
transfer process. The short time anisotropy for 9AC bound to
amorphous TiO2 is shown in Figure 10, along with the
corresponding anisotropy for anatase TiO2. For the 9AC-
amorphous TiO2 system, the anisotropy becomes negative at
ca. 1.5 ps, whereas for anatase TiO2 the anisotropy is negative
within the laser pulse. These results also suggest that the
forward electron transfer reaction is slower for amorphous TiO2
compared to anatase TiO2.
Figure 6. Magic-angle transient absorption data for (a) 1AC and (b)
AC bound to anatase TiO , amorphous TiO , and ZrO . The dashed
Discussion
2
2
2
2
An energy-level diagram for the forward electron transfer
process, based on the Gerischer model for electron transfer at
lines are the best fits to the experimental data; the results from these
fits are summarized in Table 1.
4
0,41
semiconductor surfaces,
is shown in Figure 11. In this
time scale. The results from fitting the data to the convolution
of the function S(t) ) A0 + A1e-t/τ
-t/τ
-t/τ
model, the distribution of energies for the ground-state oxidation
of the dye is represented by a Gaussian function that is separated
from the standard redox potential by the reorganization energy
1
+ A2e
2
+ A3e
3
with
a Gaussian instrument response function are summarized in
Table 1 for all the samples. It is important to note that the
back electron transfer time (τ1) for the anatase TiO2 particles is
much faster for 1AC and 2AC than for 9AC. However, for
amorphous TiO2, 9AC presents the faster decay. Experiments
performed with degenerate 390 nm pump/probe pulses are
presented in Figure 7 for 1AC anatase-TiO2. This signal has
two components: a transient bleach that is maximized for
parallel pump and probe polarizations and a transient absorption
signal that is maximized for perpendicular polarizations. Ex-
periments with ZrO2 show that the transient absorption signal
has an anisotropy of r(0) ) -0.18 ( 0.01 (which is close to
the minimum allowed value). The transient absorption contri-
bution in Figure 7 is due to free dye molecules in solution. The
time scale for the bleach recovery is 23 ( 2 ps, which is
consistent with the decay time in the 390 nm pump/780 nm
probe experiments. Note that the bleach recovery can be seen
in both the parallel and perpendicular polarization experiments.
The combination of the bleach recovery and time-resolved
anisotropy experiments confirm that the decays in Figures 4
and 6 for the TiO2 particles are due to the back electron transfer
reaction.
(Λ). The curve shown in Figure 11 was calculated using a redox
potential of 1.3 eV versus NHE (appropriate for 9AC) and a
reorganization energy of 0.7 eV (vide infra). Note that the
relative energy levels are not significantly different for 1AC
and 2AC. The distribution of energies for the excited-state
reaction was obtained by simply adding the S1 r S0 frequency
to the ground-state distribution. Figure 11 shows that the excited
state of the dye is significantly above the conduction-band
minimum (CBM) of TiO2 but below the CBM of ZrO2. The
conduction band minima for anatase TiO2 and ZrO2 were taken
from ref 20 and corrected for the pH of the solution.32 Thus,
electron transfer into the conduction band is energetically
possible for TiO2 but not for ZrO2. This energy-level picture
agrees with the fluorescence quenching results for the different
dye molecules.
Steady-State Spectra. Figure 3 shows that there is a
considerable shift in the absorption spectrum of the dye
molecules upon binding to the nanoparticles that is not simply
1
0
due to metal-ion complexation. There are several possible
mechanisms for producing this shift. One possibility is a charge-
transfer band. Coupling between the wave functions of the
excited electronic state of the dye Ψ(D*) and the charge-
Finally, as shown in Table 1, 1AC and 2AC have a fast decay
component (τ2) whereas 9AC only shows a single-exponential
decay when bound to TiO2. To assign the process that gives
rise to the faster decay, experiments were performed at different
probe wavelengths. Figure 8 shows the short time dynamics
for 1AC-TiO2 recorded with 780 and 600 nm probe pulses.
The instrument response function is also presented. The fast
+
•
-
separated state Ψ(D + e ) can give mixed states with energies
2
1
1
E( ≈ Em (
x
∆+|V| , where Em ) /2(E1 + E2), ∆ ) /2(E1 -
E2), V is the coupling constant for interaction between the states,
and E1 and E2 are the energies of the unperturbed levels.4
Optical transitions to E- give a red-shifted absorption spectrum.
2,43
+
•
-
850 fs decay at 780 nm (28%) shows up in the 600 nm scan as
For TiO2, the energy of the charge-separated state E(D + e )
is less than the energy of the excited electronic state of the dye
E(D*). Thus, the lower energy state for TiO2 would be assigned
to a charge-transfer state (the wave function for the lower energy
mixed state is predominantly made up of the lower energy zero-
order state). In contrast, for ZrO2 E(D*) < E(D + e ), which
means that the lower state for ZrO2 would be mostly Ψ(D*).
a fast 900 fs rise (15%). As discussed below, the forward
electron transfer time for anatase TiO2 is ca. 200 fs (i.e., within
the instrument response time). Thus, the ∼900 fs process is
due to a blue shift or a decrease in the width of the absorption
spectrum of the radical cation. For 2AC, the corresponding
relaxation time is 650 ( 100 fs. These spectral changes are
+•
-

Effect of Structure on Electron-Transfer Reactions
TABLE 1: Best-Fit Values for the Transient Absorption Data Presented in Figures 4, 6, 8, and 9a
compoundb
(ps) (ps)
-Anthracenecarboxylic Acid
J. Phys. Chem. B, Vol. 102, No. 47, 1998 9513
A
0
A
1
τ
1
A
2
τ
2
A
3
3
τ (ps)
1
TiO
TiO
TiO
2
2
2
(a) (780 nm)
(a) (600 nm)
(b)
0.14 ( 0.02
0.58 ( 0.04
0.55 ( 0.1
0.3 ( 0.1
18 ( 1
19 ( 1
73 ( 5
0.28 ( 0.05
0.85 ( 0.2
0.3 ( 0.1
-0.15 ( 0.1
-0.5
-0.3 ( 0.1
0.9 ( 0.2
1.6 ( 0.2
0.35 ( 0.1
0.07 ( 0.03
0.7 ( 0.1
0.15 ( 0.1
2.3 ( 0.3
ZrO
2
2
-Anthracenecarboxylic Acid
TiO
TiO
ZrO
2
(a)
(b)
0.02 ( 0.02
0.08 ( 0.06
0.5
0.11 ( 0.03
0.25 ( 0.1
14 ( 1
0.37 ( 0.03
0.15 ( 0.1
0.65 ( 0.2
2.2 ( 0.5
-0.5
-0.5
-0.5
0.45 ( 0.2
1.7 ( 0.3
0.35 ( 0.1
2
55 ( 5
2
9
-Anthracenecarboxylic Acid
TiO
TiO
ZrO
2
(a)
(b)
0.11 ( 0.02
0.14 ( 0.03
0.25 ( 0.1
0.72 ( 0.02
0.36 ( 0.03
0.14 ( 0.11
33 ( 2
-0.17
-0.5
-0.5
2.3 ( 0.3
0.3 ( 0.1
0.3 ( 0.1
2
54 ( 2
44 ( 4
2
0.11 ( 0.1
7 ( 1
a
e-t/τ
e-t/τ
e-t/τ
The fitting function used was S(t) ) A
0
+ A
1
1
+ A
2
2
+ A
3
3
3
. The negative A coefficients indicate that this component corresponds
b
to a rise in the transient absorption signal. The short and long time components were determined from separate experiments. TiO
crystal structure; TiO (b) ) amorphous crystal structure.
2
(a) ) anatase
2
Figure 9. Short-time transient absorption data for 1AC-amorphous
TiO and 2AC-amorphous TiO . The dashed lines are fits to the
experimental data.
2
2
Figure 7. Degenerate 390 nm pump/probe experiments for 1AC-
anatase TiO performed with parallel and perpendicular pump and probe
2
laser polarizations. The transient absorption signal that dominates the
perpendicular polarization experiments is due to free dye molecules in
solution.
Figure 10. Short-time time-resolved anisotropy data for 9AC bound
to anatase and amorphous TiO . The dashed lines are exponential decays
2
that estimate the experimental decays.
is unclear. One possible explanation for this effect is that
electronic excitation of the dye molecules produces a change
in their dipole moment, which creates an image dipole in the
Figure 8. Short-time transient absorption data for 1AC-anatase TiO
2
measured at two different probe wavelengths. The solid lines are the
experimental data, the dashed lines are the best fits to the experimental
results, and the dotted line is the cross-correlation between the 390 nm
pump and the 600 nm probe pulses.
4
4
semiconductor. The image dipole lowers the energy of the
excited state, producing a red shift in the absorption spectrum
compared to the free dye in solution. This effect should be
essentially instantaneous. With this interpretation we would
expect that all molecules that have a substantial change in dipole
moment upon electronic excitation should have red-shifted
absorption spectra. A second possibility is that the large charge
density at the surface of the anatase TiO2 and ZrO2 particles
creates a strong electric field which causes a Stark shift in the
Assuming that the coupling elements for TiO2 and ZrO2 are
similar, the red shift should be larger for TiO2 than for ZrO2
because the conduction band of TiO2 is lower in energy. Thus,
the fact that the spectra are nearly identical for anatase TiO2
and ZrO2 implies that the spectral red shift for these particles
is not due to a charge-transfer band.
4
5
At present, the exact mechanism for the larger red shift
observed upon binding to the anatase TiO2 and ZrO2 particles
spectra of the bound dye molecules. This effect would not
occur for the amorphous particles because they have a signifi-

9514 J. Phys. Chem. B, Vol. 102, No. 47, 1998
Martini et al.
they are attached to the ZrO2 surface.33 Note that for free 9AC,
rt he fe 9a .n isotropy is essentially zero after ∼30 ps, see Figure 9 of
Electron Transfer Dynamics. A. Forward Electron
Transfer. We previously reported that the negative anisotropy
9,12
for 9AC is a signature of the radical cation.
This assignment
was based on a comparison of the anisotropies of the free dye
and the dye bound to amorphous TiO2. The results presented
in Figure 5a for 9AC-ZrO2 show that this assignment is
correctsthe negative anisotropy signal is not a consequence of
the interaction of the excited dye molecules with the surface.
Furthermore, as shown in Figure 5b, the different isomers of
anthracenecarboxylic acid show a change in anisotropy when
the radical cation is formed. Thus, polarized light experiments
appear to be a general way of probing the forward electron
transfer reaction in these systems. In contrast, the magic angle
transient absorption experiments are more difficult to interpret
Figure 11. Energy-level diagram for photoinduced electron transfer
for 9AC bound to anatase TiO and ZrO particles. The lower Gaussian
represents the distribution function for the ground-state reaction of the
dye, and the upper Gaussian represents that for the electronically excited
2
2
c 2 c 2
dye molecules. E (TiO ) and E (ZrO ) are the conduction band minima
+
+•
for the two nanoparticles (assuming a sample pH of 3), E° (D/D ) is
the redox potential for 9AC (1.3 eV), and Λ is the total reorganization
energy (assumed to be 0.7 eV).
for two reasons. (i) D* and D absorb in the same spectral
region (a pathological problem in these experiments). Thus,
+•
the increase in the signal due to formation of D is masked by
the decay due to destruction of D*. (ii) Vibrational relaxation,
solvation dynamics, and intramolecular vibrational energy
redistribution (IVR) also contribute to the short-time transient
absorption signal.
cantly lower surface charge density. The pH of the amorphous
TiO2 solutions is pH ≈ 6, which is very close to the point of
26
zero charge (pH ≈ 5.0) for TiO2.
Reorientation at the ZrO2 Surface. Figures 4-6 show that
the different dye molecules have different dynamics at the
surface of ZrO2. The transient absorption signal for 9AC decays
with double-exponential kinetics (44 and 7 ps representing 28%
and 22% of the decay, respectively), while the signals for 1AC
and 2AC remain constant over the time scale of our experiments.
The decay for 9AC-ZrO2 also shows up in the time-resolved
anisotropy data. We discard vibrational relaxation as the reason
for the 9AC dynamics because the pump laser excites molecules
very close to the origin of the absorption band. Experiments
performed at different concentrations of 9AC give essentially
equivalent results, which shows that resonant energy transfer
between adsorbed dye molecules is not important in this
system.46
Figure 10 shows that the negative anisotropy signal appears
instantaneously when the dye molecules are bound to the anatase
TiO2 particles, suggesting that the forward electron-transfer
process occurs within the time response of our laser system (τf
e 200 fs). However, for amorphous TiO2, the dynamics are
quite different: in this case, the negative anisotropy signal
appears in ca. 1.5 ps. Figure 9 shows that the transient
absorption signals for 1AC and 2AC bound to amorphous TiO2
also have slow rise components of 1.6 ( 0.2 and 1.7 ( 0.2 ps,
respectively, that are not observed when the dye molecules are
bound to the anatase particles. These results indicate that the
forward electron transfer process is much faster for the anatase
particles (e200 fs) compared to the amorphous particles (ca.
1
.5 ps).
We believe that the decay for 9AC-ZrO2 is due to reorienta-
tion of the bound dye molecules after electronic excitation. This
motion must change both the orientation of the transition dipole
moment with respect to the polarization of the pump laser (to
give a decay in the anisotropy signal) as well as the energy of
the first excited electronic state relative to the higher electronic
states (to give a decay in the transient absorption signal). For
free 9AC, the time-resolved anisotropy has a biexponential decay
with time constants of 1 and 10 ps. In our previous paper, the
The current understanding of the forward electron transfer
process is that the rate is proportional to the square of the
electronic coupling element times the density of states in the
4
1,47
conduction band of the semiconductor.
Specifically, a
2
Fermi’s Golden Rule treatment yields kf ) 2π/p|V| F(E) where
4
8
F(E) is the density of states. Thus, differences in kf could be
due to differences in V or F(E). In our experiments, the
conduction-band minimum is approximately the same for the
anatase and rutile particles (see eq 4 below). Thus, their density
of states should be similar, which means that differences in kf
1
ps process was assigned to vibrational energy exchange
between levels with different vibronic symmetry and the 10 ps
process was assigned to overall rotation.9 The fact that the 1
ps component does not appear for 9AC-ZrO2 is surprising and
indicates that our original assignment is not correct. An
improved assignment is that the 1 ps anisotropy decay for the
free dye is due to internal rotation of the carboxylate group.
This motion would be severely hindered when the dye molecules
are bound to the metal oxide surface. The fact that the decay
in the anisotropy is much slower for 9AC bound to ZrO2
compared to free 9AC could be due to the following effects:
must be due to the coupling element. For bulk rutile TiO ,
2
-
1
-1 49
F(E) ) 2 eV atom . Using this value for F(E) yields V g
-1
-1
1
30 cm for anatase-TiO2 and V ≈ 50 cm for the amorphous-
TiO2 particles. Note that in this calculation we have assumed
that each dye molecule primarily interacts with one Ti atom
and that quantum size effects (which drastically affect F(E))
2
4
are unimportant for TiO2.
The conclusion that the coupling element for the forward
electron transfer reaction is larger for the anatase particles
compared to the amorphous particles is the major result of this
section. The coupling element is related to the degree of wave
function overlap between the excited electronic state of the dye
and the delocalized conduction-band levels of the semiconduc-
(i) the environment at the surface of the particles is restricted
compared to bulk solution and/or (ii) the internal rotation
involves movement of the bulky anthracene ring when the
carboxylate group is bound to the surface of the particle. The
anisotropy does not decay to zero for the dye molecules bound
to ZrO2 on the time scale of our experiments. This is expected
since the molecules are not free to rotate about all 3 axes when
5
0
tor. This quantity is strongly distance dependent. The larger
coupling element for anatase TiO2 compared to amorphous TiO2
implies that the chromophore is closer to the surface for the

Effect of Structure on Electron-Transfer Reactions
J. Phys. Chem. B, Vol. 102, No. 47, 1998 9515
anatase particles. The dye molecules used in this study bind
through interaction between the carboxylate group and surface
Ti atoms. For the amorphous TiO2 particles, the geometry
around the surface Ti atoms must force the dye molecules to
be further away from the surface than for the anatase particles.
This picture is consistent with the larger perturbation of the
UV-vis absorption spectra when the dye molecules are bound
to the anatase particles compared to the amorphous particles.
B. Back Electron Transfer. The transient absorption
measurements show that the time constants for back electron
transfer for the anatase and amorphous TiO2 particles, respec-
tively, are 18 and 73 ps for 1AC, 14 and 55 ps for 2AC, and 33
and 54 ps for 9AC. Thus, the general trend is that the back
electron-transfer times are much faster for anatase TiO2 than
for amorphous TiO2. In terms of Marcus theory, this could be
due to changes in the driving force, the reorganization energy,
or the coupling element. The aim of this section is to determine
whether we can separate these different contributions to the
experimental data.
reasonable to use the flatband potential of rutile TiO2 to calculate
the conduction-band energy of the amorphous particles. Thus,
the pH dependence of the conduction bands of the two types of
2
0,53,54
particles are taken as
Ecb(anatase) ) -0.12 - 0.059pH
Ecb(amorphous) ) 0.06 - 0.059pH
(4)
We have previously used eq 3 to show that the back electron
transfer reaction for 9AC bound to anatase TiO2 lies in the
Marcus-inverted region with a reorganization energy of Λ )
12
0.75 ( 0.05 eV. For this calculation, we used a value of ∆G°
) -1.8 eV for the driving force. This value does not properly
include the effect of pH on the flatband potential. If we take
into account that the anatase synthesis yields water solutions at
pH 3 and assume the same proton activity for the ethanolic
solutions, then the total reorganization energy is 0.7 ( 0.1 eV.
Thus, correction for the proton activity of the solution does not
have a large effect on the value of Λ derived in our previous
A classical formulation for the back electron transfer rate
5
0
12
constant kb is
paper. In these calculations, only ratios of rate constants were
calculated, i.e., we did not directly determine the coupling
element. Attempts to use eq 3 to calculate a coupling element
yield unrealistically large values of V, implying that the weak
coupling limit used to derive eq 3 is not valid for these systems.
Equation 3 is a classical derivation for the electron transfer
rate constant. It underestimates the rate for reactions that have
a large ∆G° because it does not account for tunneling through
2
2
p
π
2
1
(∆G° + Λ)
4ΛkT
kb )
|V|
exp -
(3)
( )
{
}
x
4πΛkT
where Λ is the total reorganization energy, V is the coupling
element, and ∆G° is the overall free energy of reaction. The
existence of electron-trap sites at the surface of the semiconduc-
tor particles makes it difficult to determine accurate values for
21-23,50
the barrier.
Therefore, direct calculations of the coupling
element using eq 3 result in an overestimate of V. A more
∆
G°. Recent spectroelectrochemistry measurements by Gr a¨ tzel
suitable expression for the rate of electron transfer in the inverted
region is
2
2,50
and co-workers show that the majority of trap sites for ca. 15
nm diameter anatase-TiO2 particles cast in a film are within
.3 eV of the conduction-band minimum.5 In addition, the
1
0
SV′
2
π
1
2
observation of single exponential decays in our experiments for
the back electron transfer reaction implies a narrow energy
distribution of sites for the trapped electrons. Specifically, a
kb )
|V|
exp(-S)
×
∑
(
)
p
V′
V′!
4
x
πλ kT
s
2
wide distribution of trap sites should produce distributed kinetics
-(λ + V′pω + ∆G°)
s
and complex, multiexponential decays.1
2,15-19,52,53
This is not
exp
(5)
{
}
4
λskT
observed in the 100-200 ps time scale of our experiments when
absolute ethanol is used as the solvent.12,52 Note that on longer
time scales the back reaction may become nonsingle exponential.
However, the majority of the back electron transfer process
where S ) λi/pω, λi is the reorganization energy of the single
high-frequency mode of the dye, ω is the frequency of this
mode, λs is the reorganization energy of the solvent, and V′ are
all the possible final vibrational states. Complications in the
calculation of V from eq 5 arise from the uncertainty in the
values of ∆G°, λi, λs, and ω. However, the ratio Vanat/Vamorph
is relatively invariant to the above-mentioned variables. Our
calculations show that the ratio of the electronic coupling
elements for the two different crystalline structures of TiO2 are
Vanat/Vamorph ) 2 ( 0.5 for 1AC and 2AC and Vanat/Vamorph )
1.3 ( 0.2 for 9AC for Λ ) λi + λs ) 0.7 eV. For all three
isomers the square of Vanat/Vamorph is very close to the ratio of
the back electron-transfer rate constants, i.e., for a specific dye
the difference in the back electron transfer times for the anatase
and amorphous TiO2 particles is due to the coupling elements.
Furthermore, the different values of Vanat/Vamorph for 1AC/2AC
compared to 9AC explain why the back electron transfer times
for 1AC and 2AC are faster than that for 9AC for anatase-TiO2
and slower for amorphous-TiO2. These calculations were
performed using the same values of λi, λs, and ω for the two
semiconductor samples and calculating ∆G° from eq 4 and the
redox potential of the dye molecules. Note that the calculated
ratios of the coupling elements are relatively insensitive to
changes in ∆G° of e0.2 eV.
(
>75%) occurs within 100 ps for the anatase TiO2 particles and
within 200 ps for the amorphous particles. These observations
imply that in our experiments the energy levels for back electron
transfer are narrowly distributed within 0.3 eV of the conduc-
tion-band minimum. Because we do not know the exact energy
of the trap sites, we will assume that ∆G° is given by the
difference between the conduction-band minimum and the redox
potential of the ground state of the dye. This assumption means
that the coupling elements derived in the following analysis are
upper limits.
In our systems we expect that Λ should be the same for the
different particles, as Λ is determined by the internal modes of
the dye and the reorganization of the solvent.2
2,50
On the other
hand, both V and ∆G° could be different for the anatase and
amorphous TiO2 particles. For semiconductor nanoparticles,
band bending effects are negligible, so that the energy of the
conduction band can be equated to the flatband potential of the
semiconductor.2 For TiO2, the flatband potential depends on
the pH and the crystal structure of the sample. For anatase TiO2,
the flatband potential is well-known.2
0,53,54
No measurements
are available for the amorphous particles. However, because
the band gap of these particles is similar to rutile TiO2, it is

9516 J. Phys. Chem. B, Vol. 102, No. 47, 1998
Martini et al.
Equation 5 provides more realistic values for the coupling
semiconductor. In this case, differences were principally
observed in the back (semiconductor-to-dye) electron transfer
reaction. For anatase TiO2, the data can be satisfactorily
explained by the different redox potentials for the three
anthracenecarboxylic acid isomers. Specifically, 1AC and 2AC
have smaller (less positive) oxidation potentials compared to
9AC and, therefore, smaller driving forces for the back electron
transfer reaction. This produces faster back electron transfer
times for 1AC and 2AC compared to 9AC because the back
reaction is in the Marcus-inverted region. For the amorphous
TiO2 samples, the differences in the back electron transfer times
for the three dye molecules arise from differences in both the
driving force and the coupling elements.
element than eq 3, however, the problem is severely underde-
termined. For example, if we choose ω ) 1500 cm- and λi )
λs ) 0.35 eV, then the rate constants for 1AC, 2AC, and 9AC
bound to anatase TiO2 can be reproduced with a value of V )
1
-
1
6
0 cm . On the other hand, using λs ) 0.6 eV and λi ) 0.1
-
1
eV requires V ) 100-200 cm . Although at present it is
impossible to quantitatively determine all the parameters in eq
5
, we can conclude that reasonable values of λi and λs (i.e., λi,
-1
λs ) 0.2-0.6 eV) require coupling elements in the 50-200 cm
range for the anatase TiO2 particles and correspondingly smaller
values for the amorphous particles. These values are on the
verge of the strong coupling limit for electron transfer. Note
that if the back electron transfer reaction occurs from trap sites
below the conduction band, the driving force for the reaction
would be smaller than that calculated by eq 4. In this case, the
values of V needed to reproduce the rate constants would be
smaller than those reported above.
Finally, all the dye molecules examined show a red shift in
their steady-state absorption spectrum when they are attached
to the particles. The perturbations of the absorption spectra of
2
the bound dye molecules are larger for the anatase TiO particles
compared to the amorphous TiO particles. Comparison of the
2
The above analysis shows how the back electron transfer
reaction for a specific dye molecule depends on the identity of
the semiconductor. Equation 5 can also be used to investigate
how the back electron transfer time for a specific semiconductor
particle depends on the chemical structure of the dye. For
anatase TiO2, the differences in the rate constants observed for
spectra of dye molecules bound to TiO2 and ZrO2 show that
the spectral shifts are not due to the formation of a charge-
transfer band, i.e., the steady-state spectra do not provide direct
information about the forward (dye-to-semiconductor) electron
transfer process. However, our experimental results suggest that
for anthracene dyes attached to TiO2, stronger perturbations in
the absorption spectra are correlated to faster electron transfer
timessfor both the forward and reverse reaction.
1AC, 2AC, and 9AC are due to differences in the redox
potentials of the dye molecules. Specifically, the calculated
coupling elements for the three dye molecules vary by only
∼
10%. This means that the factor of 2 difference in the time
scales for back electron transfer is due to differences in ∆G°:
AC and 2AC have smaller ∆G° values than 9AC and,
Acknowledgment is made to the donors of the Petroleum
Research Fund, administered by the American Chemical Society.
We also thank Dr. Steve Patterson for synthesizing the 9-an-
thraceneacetic acid, Prof. Marya Lieberman for help with the
cyclic voltammetry experiments, Prof. Paul McGinn for record-
ing the X-ray powder diffraction data, and Prof. Nancy Levinger
for performing the dynamic light scattering measurements.
1
therefore, faster back electron transfer times because of Marcus-
inverted behavior. This conclusion is unaffected by the presence
of surface states that change ∆G°. (In these calculations we
have assumed that λi, λs, and ω are the same for the three dye
molecules.) For the amorphous TiO2 particles, the different rate
constants for the three dye molecules arise from differences in
both the coupling elements and the redox potential.
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(
(
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(
(
The experimental data can also be analyzed to compare the
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(

Effect of Structure on Electron-Transfer Reactions
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