Diffusion of electrically neutral radicals and anion radicals created by photochemical reactions

Article abstract of DOI:10.1039/a706220f

Diffusion processes of the intermediate radicals created by the photochemical reactions of ketones in alcoholic solvents are investigated by using the transient grating (TG) method. The electrically neutral radicals and the anion radicals of acetophenone, benzaldehyde, xanthone, benzophenone and benzil were created selectively by controlling the concentration of sodium hydroxide (NaOH) in alcoholic solvents. The translational diffusion constants (D) of the anion radicals, the neutral radicals, and the parent stable molecules can be successfully measured under the same conditions by this method. It is found that both the neutral and anion radicals diffuse slower than the parent molecules. Values of D of the anion radicals, the neutral radicals and the parent molecules are compared in detail in wide ranges of solvent viscosities, solute sizes and temperatures. Under any conditions, D values of the charged radicals are similar to those of the neutral radicals. A possible origin of such a similarity is discussed in term of the intermolecular charge polarizabilities of the radicals.

Full text of DOI:10.1039/a706220f

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Di†usion of electrically neutral radicals and anion radicals created by
photochemical reactions
Koichi Okamoto, Noboru Hirota and Masahide Terazima*
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto, 606 Japan
Di†usion processes of the intermediate radicals created by the photochemical reactions of ketones in alcoholic solvents are
investigated by using the transient grating (TG) method. The electrically neutral radicals and the anion radicals of acetophenone,
benzaldehyde, xanthone, benzophenone and benzil were created selectively by controlling the concentration of sodium hydroxide
(NaOH) in alcoholic solvents. The translational di†usion constants (D) of the anion radicals, the neutral radicals, and the parent
stable molecules can be successfully measured under the same conditions by this method. It is found that both the neutral and
anion radicals di†use slower than the parent molecules. Values of D of the anion radicals, the neutral radicals and the parent
molecules are compared in detail in wide ranges of solvent viscosities, solute sizes and temperatures. Under any conditions, D
values of the charged radicals are similar to those of the neutral radicals. A possible origin of such a similarity is discussed in term
of the intermolecular charge polarizabilities of the radicals.
The inÑuence of the soluteÈsolvent interaction through
hydrogen bonding was reported recently by Chan and
1
Introduction
Di†usion constants (D) have been measured by several
methods and analyzed based on various theories.1 Values of D
are often described by the equation derived from the hydro-
dynamic theory such as the StokesÈEinstein (SE) equation or
many other empirical modiÐcations of the SE equation.2
Experimentally determined D values for molecules without
any intermolecular interaction can be reproduced reasonably
well based on these equations. Interesting cases arise when
intermolecular interaction plays an important role in the
dynamics. The translational di†usion process of molecules is
sensitive to the environment around the solute molecule, and
information of the intermolecular interaction, the solvation
structure and the existence of microscopic aggregation, etc.,
may be extracted from the studies of the di†usion process.
For example, there are three interesting cases for di†using
species; ionic molecules (atoms), hydrogen bonded systems,
and transient radicals. Mobilities (k) or conductivities (j) of
ions have been measured by several methods to elucidate sol-
vation structures and charge e†ects on mobilities.1,3 The
mobilities of ions can be transformed to the di†usion con-
stants by the Nernst relationship.1,3 Generally, D values of
ions are smaller than those of neutral molecules of similar
sizes in the same solvent and at the same temperature.3 This is
due to the strong intermolecular interaction between the
charge of ions and solvent molecules by Coulombic forces.
With decreasing molecular size, this e†ect becomes stronger
and the di†erence between the D values of ions and stable
molecules will increase. Two models are well known to inter-
pret this size dependence of ionic mobilities. One is the excess
size model,4 which is based on an increase of the molecular
radius by the solvation structure of ions. The other is the
dielectric friction model5 which is based on a friction which
arises when the polarization of solvents follows the movement
of the charges of ions. Both of two models can explain the size
dependence of the D of the ion qualitatively. Boyd,6 Zwanzig7
and HubbardÈOnsager8 proposed equations to estimate the
contribution of the dielectric friction by the continuous Ñuid
theory. These equations can reproduce the experimental D
values qualitatively, but not quantitatively. Recently, Bagchi
and co-workers succeeded in reproducing the experimental D
values quantitatively by a theory based on the dielectric fric-
tion.9
Chan,10 and Tominaga et al.11 They reported that the hydro-
gen bonding between the OH or NH group of a solute mol-
2
ecule and polar solvents makes the di†usion process very
slow. Naturally, this e†ect was not observed in non-polar sol-
vents.
Radicals are another interesting system for di†usion studies
as well as for elucidating the mechanism12 and dynamics13 of
chemical reactions. Unfortunately, until recently, only a few D
values of radicals have been reported14 because of the techni-
cal difficulty. However, recently, we succeeded in measuring
the D values of many intermediate radicals which appear
during photochemical reactions by the transient grating (TG)
method.15h18 It was found that the transient neutral radicals
created by photoinduced hydrogen abstraction reactions of
ketones, quinones and N-heteroaromatic molecules di†use
much slower than their parent molecules.15h18 We further
investigated the viscosity (g) dependence,16 the solute radius
(r) dependence17 and the temperature (T ) dependence18 of the
D values of such radicals. The di†erences in D between the
radicals and the parent molecules become larger with increas-
ing g, 1/r or 1/T . These tendencies are similar to those of
ions.3 We could reproduce such dependences by using the
excess size model with a volume increase of 5È8 ] 102 Ó3.18
This apparent volume expansion was interpreted in that the
radicals interact with surrounding molecules strongly. This
model is similar to that used for D of ions. However, since
these electrically neutral radicals do not have charges, the
source of the radicalÈsolvent interaction is not immediately
clear. Considering that not all of the radicals di†use more
slowly than closed shell molecules [e.g. benzyl radicals,19 2,2,
5,5-tetramethyl-1-piperidinyloxy (TEMPO) or some other
stable radicals20], we cannot attribute the origin of the
radicalÈsolvent interaction to only the presence of the
unpaired electron. Since the slow di†usion of radicals was
observed not only in polar solvents but also in non-polar sol-
vents and in aprotic solvents,16 hydrogen bonding between
the OH or NH group of the radical and the solvents cannot
be the origin of the slow di†usion. Therefore, contrary to ions
or hydrogen bonding systems, the origin of the slow di†usion
remains unclear.
A natural extension of this research is the study of the di†u-
sion of ion radicals, which have an unpaired electron and a
J. Chem. Soc., Faraday T rans., 1998, 94(2), 185È194
185

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charge. In this case, since the motion of the radicals can be
detected as electronic current, experimental measurement is
easier. Indeed, the mobilities of the photochemically produced
intermediate radical cations and anions probed by the time of
Ñight (TOF) technique have been reported by Houser and Jar-
nagin,21 Freeman and co-workers,22 and Albrecht and co-
workers.23 They found that D of the ion radicals are smaller
than those of neutral molecules of similar shapes and sizes.
Freeman and co-workers attributed the origin of the slow dif-
fusion to the electrostrictive drag by the charged species and
dimerization for some compounds.22 Albrecht and co-workers
found that D of the charged radicals can be well reproduced
by the SE equation.23 This result, in good agreement with the
SE relation, is similar to that found for the neutral radicals we
have studied. However, even if one wishes to extract the e†ect
of the charge or the unpaired electron by comparison of D of
the charged radicals determined by this method with those of
closed shell molecules, one has to use D of closed shell mol-
ecules measured by other methods under di†erent conditions.
Because D is very sensitive to environment and experimental
conditions, accurate comparisons are very difficult. However,
if we use the TG method, D values of stable molecules can be
measured simultaneously with those of the transient species.
For example, Terazima et al. have determined D of a cation
radical and its parent molecule, N,N,N@,N@-tetramethyl-p-
phenylenediamine (TMPD), by the TG method under exactly
the same conditions.24 The result showed that the TMPD
cation radical di†uses only half as quickly as the TMPD
parent molecule in ethanol. However, the contribution of the
charge and the unpaired electron could not be separated from
this measurement. It would be very useful, if D values of
closed shell molecules, neutral radicals, and ion radicals of
similar shapes and sizes can be measured under the same con-
dition.
alcoholic solvents by controlling the concentration of sodium
hydroxide (NaOH). Values of D of the anion radicals, the
neutral ketyl radical and the parent stable molecules are mea-
sured under the same conditions and compared. The role of
the charge and unpaired electron in di†usion is discussed on
the basis of the obtained results.
2
Experimental
The experimental arrangement for the TG technique has been
described elsewhere in detail.15h20,24,27 BrieÑy, an excitation
laser pulse from an excimer laser [XeCl (308 nm); Lumonics
Hyper-400] was split into two beams and crossed inside a 10
mm path quartz sample cell. The laser power at the crossing
point was measured by a pyroelectric joulemeter (Molectron
J3-09) and was typically ca. 0.3 mJ cm~2. Solute molecules in
the cell were excited by the interference pattern between these
beams (optical grating). The excited molecules release the heat
by non-radiative relaxation and the temperature of the sample
is modulated (thermal grating). A part of the excited molecules
react and the concentrations of the reactant and product was
also modulated, giving rise to the species grating. The thermal
grating and the species grating disappear by heat conduction
and mass di†usion, respectively. Therefore, these processes can
be measured from the time proÐle of the light intensity of the
di†racted probe beam (TG signal). The TG signal was
detected by a photomultiplier tube (Hamamatsu R-928) after
isolation with a pinhole and a glass Ðlter (Toshiba R-62) and
recorded with a digital oscilloscope (Tektronix 2430A). The
time proÐle of the TG signal was analyzed with a micro-
computer. The signal was averaged by a digital oscilloscope
and a microcomputer to improve the S/N ratio. The fringe
spacing K was roughly estimated from the crossing angle h
and then calibrated from the decay of the thermal grating
signal of a benzene solution containing a trace of Methyl
Red.28 The temperature of the sample solution was controlled
by Ñowing temperature-regulated methanol around a cell
holder with a temperature control system (Lauda RSD6D).
For the transient absorption (TA) measurement, the sample
was excited by the excimer laser (ca. 5 mJ cm~2) and probed
by a 100 W Xe lamp. The probe light was monochromated
with a Spex model 1704 monochromater and detected by the
photomultiplier.
In this work, we performed TG experiments along this line.
Values of D of parent molecules, neutral radicals and anion
radicals of ketones are determined by the TG method under
the same conditions and compared. To create the neutral rad-
icals, we employed hydrogen abstraction reactions. Charged
radicals can be created from the neutral radicals by sub-
sequent reactions. For example, the photochemical process of
acetophenone (AP) is described in Scheme 1.25
The lowest excited triplet (T ) state of AP is created by the
1
intersystem crossing from the lowest excited singlet (S ) state
Spectroscopic grade solvents (methanol, ethanol, propan-2-
ol, butan-1-ol and pentan-1-ol) and solute (acetophenone,
benzaldehyde, xanthone, benzophenone and benzil) were pur-
chased from Nacalai Tesque and used without further puriÐ-
cation. Typical concentrations of the solutes were ca. 10~2 M.
Sample solutions were deoxygenated by the nitrogen bubbling
method and Ñowed by a peristaltic pump (Atto SJ-1211) to
avoid the e†ect of reaction products in the signal.
1
by UV irradiation within an excitation laser pulse width (ca.
10 ns). The neutral radical is created from the T state of AP
1
by hydrogen abstraction (process b). The neutral radical and
the anion radical are in equilibrium (process c). Therefore, one
can create the anion radical or the neutral radical selectively
by controlling the pH (pOH) of the solution. In aqueous solu-
tion such selective creation of the AP anion radical has been
reported and the pK was determined to be 9.9.26 Here we
The van der Waals volumes V of the molecules were
a
w
create the anion radicals or the neutral radicals of acetophe-
obtained from the atomic increments method given by
none, benzaldehyde, xanthone, benzophenone and benzil in
Edward.29 The radii of the molecules, r, were calculated from
V using the relation r \ (3V /4p)1@3.
w
w
3
Results
3.1 Assignment of the TG signal
The time proÐle of the TG signal after the photoexcitation of
AP in ethanol is shown in Fig. 1(a). The time proÐle of the
root square of the TG signal [I (t)1@2] can be Ðtted well with
TG
a sum of three exponential functions.
I
(t)1@2 \ a exp([k t) ] a exp([k t) [ a exp([k t) (1)
TG
1
1
2
2
3
3
where, k [ k [ k are the decay constants and a [ a [
1
2
3
1
3
a [ 0 are the pre-exponential factors. The solid line in Fig.
2
Scheme 1
1(a) is the line Ðtted by using the non-linear least-squares
186
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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by k \ D q2. The obtained value is close to the literature
1
th
values.32
As both the parent molecules and the radicals in this system
have absorption bands at shorter wavelengths than that of the
probe beam, both dn0 and dn0 are expected to be positive
P
R
from KramersÈKronig relationship. Therefore, the sign of the
parent molecule component is negative, which is the same as
the sign of the thermal grating term. On the basis of this reason-
ing, component 2 in the TG signal [Fig. 1(b)] is assigned
to the signal from the parent molecule. On the other hand, the
radicalÏs contribution in the TG signal should be positive.
Component 3 in Fig. 1(b) should be due to the radical. It has
been reported that the electrically neutral radical is created by
photoexcitation of AP in a pure alcoholic solvent.17 In this
reaction system, four chemical species (AP, AP ketyl radical,
ethanol, hydroxyethyl radical) could contribute to the signal.
However, since the absorption coefficient of ethanol and
hydroxyethyl radical are smaller than those of AP and the
ketyl radical, the TG signal due to ethanol and the hydroxy-
ethyl radical could not be detected. Therefore, we assign com-
ponent 2 to the species grating of AP and component 3 to
that of the AP ketyl radical. Then, D and D are the di†usion
P
R
constants of AP and the AP ketyl radical, respectively.
Next, we performed a similar measurement for AP in
ethanol which contains sodium hydroxide. Fig. 2(a) shows the
time proÐle of the TG signal of APÈethanol ] 0.01 M NaOH.
The shape of this signal is slightly di†erent from that given in
Fig. 1(a). This time proÐle can also be Ðtted by eqn. (1) very
well [solid line in Fig. 2(a)]. The three exponential com-
ponents are shown in Fig. 2(b). Comparing Fig. 2(b) with Fig.
1(b), we Ðnd that the intensity of component 3 is enhanced
relative to the other components. The enhancement suggests
that the transient in pure ethanol is di†erent from that in
ethanol ] NaOH. In an aqueous solution, it was reported
that the anion radical is created in an alkaline solution, while
the electrically neutral radical is created in pure water.26 In
the next section, we use the transient absorption technique to
identify the intermediates in ethanol and ethanol ] NaOH.
Fig. 1 (a) Time proÐle of the TG signal after the photoexcitation of
AP in ethanol at 20 ¡C (dotted line) and best Ðtted curve (solid line) by
eqn. (1). (b) Three components for the Ðtting in (a) are shown separa-
tely. The assignments of these components are: 1, thermal grating; 2
and 3, species grating of AP and that of the neutral ketyl radical of
AP, respectively.
method with eqn. (1) and the proÐles of the three components
are shown in Fig. 1(b). The method for assignment of each
exponential component of the TG signal to its origin has been
described previously in detail.15,20,24,27 The TG signal inten-
sity is proportional to a sum of the square of the refractive
index change and the absorbance change induced by the
optical grating.30 In this reaction system, absorption bands of
any species are on the far blue side from the probe wavelength
(633 nm).26,31 Thus, the TG intensity is proportional to only
the square of the refractive index change. The thermal e†ect
(thermal grating) and the creation or depletion of chemical
species (species grating) can contribute to the refractive index
change. The time proÐles of the signals due to the thermal
grating and the species grating are given by solving FourierÏs
thermal di†usion equation and FickÏs reactionÈdi†usion equa-
tion, respectively.15 Since in the observation time range of the
TG signal, the creation and termination reaction of the rad-
icals can be neglected as shown later, the time dependence of
the TG signal is given by15h20,24
I
(t)1@2 \ dn0 exp([D q2t)
TG th th
[ ; dn0 exp([D q2t) ] ; dn0 exp([D q2t) (2)
P
P
R
R
P
R
where, q is the grating vector [q \ 2p/K, (K; fringe length)],
the Ðrst term of eqn. (2) represents the thermal grating and
dn0 is the initial refractive index change just after the excita-
th
tion. dn ¡ and dn0 are the initial refractive index changes by
P
R
the species grating of the parent molecules and the radicals,
respectively. D is the thermal di†usion coefficient of the
th
solvent and D , D are the di†usion constants of the parent
P
R
molecules and the radicals, respectively.
Generally, as the refractive index decreases with increasing
Fig. 2 (a) Time proÐle of the TG signal after the photoexcitation of
AP in ethanol ] 0.01 M NaOH (dotted line) and best Ðtted curve
(solid line) by eqn. (1). (b) Three components for the Ðtting in (a) are
shown separately. The assignments of these components are: 1,
thermal grating; 2 and 3, species grating of AP and that of the anion
ketyl radical of AP, respectively.
temperature, dn0 is negative. Because the heat conduction
th
process is a faster process than the mass di†usion process, D
th
is about 100 times larger than D or D . Therefore, com-
ponent 1 in the TG signal obtained [Fig. 1(b)] is assigned to
P
R
thermal grating. Comparing eqn. (2) with eqn. (1), D is given
th
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
187

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3.2 Transient absorption measurements
We examine the intermediates created in pure ethanol and
ethanol ] NaOH by the transient absorption (TA) method.
Fig. 3(a) shows the TA spectra with a 10 ls time delay after
excitation in pure water and in NaOH ] water. The observed
TA spectrum in pure water [Ðlled circles in Fig. 3(a)] is assign-
ed to the AP neutral radical [reported TA spectrum26 is
shown by the solid line in Fig. 3(a)]. Upon adding NaOH to
that solution, the TA spectrum changes and it becomes similar
to the reported spectrum of the AP anion radical [dotted line
in Fig. 3(a)].26 Hayon et al. have reported pK values of AP,
a
benzophenone and benzil as 9.9, 9.25 and 5.5, respectively.26
The TA spectra observed in pure ethanol and
NaOH ] ethanol are shown in Fig. 3(b). The TA spectrum in
pure ethanol [Ðlled circles in Fig. 3(b)] is close to the reported
spectrum of the AP neutral radical in ethanol (solid line).31
The TA spectrum in APÈNaOH ] ethanol [open squares in
Fig. 3(b)] is similar to the spectrum of the AP anion radical in
water26 [dotted line in Fig. 3(a), (b)]. Therefore, we assigned
this spectrum to the AP anion radical.
Based on these observations, we conclude that the electri-
cally neutral radicals and the anion radicals can be created
selectively by controlling the concentration of NaOH in alco-
holic solvents. Fig. 4 shows the intensities of the TA signals at
450 nm and the intensities of the TG signals at various con-
centrations of NaOH in ethanol. Both of the intensities
steeply change at pOH 4 [log [NaOH] \ 3È4. Under dilute
conditions (NaOH \ ca. 10~4 M), the neutral radical is
created. If the concentration of NaOH is [ca. 10~3 M, the
anion radical is dominant in ethanol. Since the spectra do not
depend on the monitoring time (10 ls to a few ms), the neutral
radical and the anion radical of AP are in equilibrium within
10 ls after the creation (Scheme 1) in water and in ethanol.
The pK value of this equilibrium is pK \ 3È4 in ethanol
Fig. 4 Plot of the signal intensity of the transient absorption at 450
nm (top) and that of the transient grating (bottom) at a 100 ls delay
after the excitation against the concentration of NaOH in APÈ
ethanol ] NaOH
(1È5 mJ cm~2). The TA signals show second-order decay
which should be due to the self-termination reaction of the
radicals.26,33 Under a weak excitation laser power for the TG
measurement (ca. 0.3 mJ cm~2), the intensities of the TA
signals are almost constant and the shapes of the TA spectra
do not change within the time range for the TG measurement
(a few milliseconds). Therefore, it is evident that the created
radicals do not react with the solvent or the parent molecules,
and the time proÐle of the TG signal (Fig. 1 and 2) can be
analyzed simply by the di†usion process of each species.
b
b
(pK \ 14 [ 9.9 \ 4.1 in water26). According to this result,
b
component 3 in the TG signal in pure ethanol [Fig. 1(b)] is
assigned to the AP neutral radical and that in ethanol ] 0.01
M NaOH [Fig. 2(b)] to the AP anion radical.
The created radicals are relatively stable and their TA
signals are observable for tens of milliseconds after excitation
3.3 Comparison of values of D for neutral radicals with anion
radicals
The decay rate constants k , k obtained by the Ðtting of the
2
3
TG signals at various fringe spacings are plotted vs. the square
of the grating vector q in Fig. 5. Based on the assignment
given above and from eqn. (1) and (2), the following relation-
ships are obtained.
k \ D q2
(3a)
(3b)
2
P
k \ D q2
3
R
The TG signal decays not only by the di†usion process but
also by any reaction processes. In this case, the decay rate of
the TG signal is accelerated by the reaction, and more
detailed consideration is necessary for the analysis as we have
reported for the benzyl radical case.19 However, the linear
relationship between the decay rate constants and q2 with
small intercepts with the ordinate (Fig. 5) and also the slow
radical decays measured by the TA method ensure that D can
be determined from the slope of the plot. The values obtained
for D of the parent molecule, the neutral radical and the anion
radical in ethanol are listed in Table 1. The value of D for AP
in ethanol is the same as that in ethanol ] NaOH within
experimental error. This suggests that the e†ect of addition of
0.01 M NaOH on di†usion is negligibly small. The main
source of the experimental error comes from the Ðtting error
of the double-exponential function and the fact that the D
values of the parent molecules have large errors.34 Recently,
Donkers and Leaist have reported D of AP by using the
Tayler dispersion (TD) method as 1.24 ] 10~9 and
Fig. 3 (a) Transient absorption spectra at a 10 ls time delay after the
excitation of AP in water (…) and AP in water ] 0.01 M NaOH (K).
(b) Transient absorption spectra of AP in pure ethanol (…) and AP in
ethanol ] 0.01 M NaOH (K). Spectra of the neutral radical of AP
(solid line) and the anion radical of AP (dotted line) from ref. 26 (in
water), 31 (in ethanol) are shown in both Ðgures for comparison.
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J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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similarly strong. Before this study, we expected the values of D
of anion radicals to be smaller than those of neutral radicals
because the anion radical has both charge and an unpaired
electron, both of which can a†ect the di†usion process.
However, this is not the case, although a slight di†erence
between D of neutral radicals and the anion radicals is just
detectable beyond experimental error (Table 1). This slight dif-
ference may be due to the contribution of the charge to the
di†usion process or possible ion pair formation between the
anion and sodium cation. However, previous EPR studies
showed that the ion pairs of ketyls tend to dissociate in
alcohol.39 Another possibility is that the anion radicals are
associatively active and form dimers.40 In this case, D of the
anion radical dimer is expected to be ca. 1.25(\21@3) times
larger than that of monomer,23a since D is inversely pro-
portional to the radius of the solute.
It is interesting that this charge e†ect on D of the anion
radical is much smaller compared with the reported charge
e†ect on D of the ions of similar sizes.1,3 The charge e†ect on
di†usion in the anion radical may be reduced by some factors.
This phenomenon could be related to the origin of the anom-
alously slow di†usion of radicals. In later sections, we discuss
the solvent viscosity, solute size and temperature dependence
of D of neutral and anion radicals to clarify this behavior.
Fig. 5 Relationship between the decay rate constants (k) of each
component of the TG signal and q2. …, L denote the parent molecule
(AP), the neutral radical of AP in ethanol, respectively. =, K denote
the parent molecule (AP), and the anion radical of AP in
ethanol ] 0.01 M NaOH, respectively.
0.76 ] 10~9 m2 s~1 in ethanol and propan-2-ol, respec-
tively.35 Our values from the TG method are close to their
values from the TD method with relative errors of 10 and
17% in ethanol and propan-2-ol, respectively.
The solvent viscosity depends on the concentration of elec-
trolytes. In diluted solution (\1 M), the JonesÈDole equation
describes the concentration dependence of the viscosity well.36
3.4 Solvent viscosity, solute size and temperature dependence
of D
Contrary to our initial expectation, the di†usion of the AP
anion radical is similar to that of the neutral radical. In order
to examine further the cause of the e†ects of the charge and
unpaired electron on the di†usion process, we investigate D
under various conditions. According to the SE equation, D is
proportional to temperature (T ) and inversely proportional to
the viscosity of solvent (g) and radius of solute (r). Depen-
dences of D of these species on solvent viscosity, solute size
and temperature are discussed below.
In order to monitor the e†ect of viscosity, we measured the
TG signal of AP in methanol, propan-2-ol, butan-1-ol and
pentan-1-ol. The time proÐles of the TG signals in various
solvents are similar to that in ethanol and D can be deter-
mined by the same method as before. Values of D of the
parent molecules, the neutral radicals and the anion radicals
in these solvents are listed in Table 1 and plotted vs. g~1 in
Fig. 6.
To monitor the e†ect of molecular size, benzaldehyde,
xanthone, benzophenone and benzil were studied with their
neutral radicals and anion radicals being created by the same
method as for AP. The time proÐles of the TG signals of such
solutes are quite similar to that of AP in both pure ethanol
and ethanol ] 0.01 M NaOH. The obtained D values of these
species are listed in Table 2 and plotted vs. 1/r in Fig. 7.
Values of D of the parent molecules are close to the literature
values [(1.39, 0.90 and 0.95) ] 10~9 m2 s~1 for benzaldehyde,
xanthone and benzophenone, respectively] within ^15%.35
From Fig. 6 and 7, it is evident that the D values of the anion
g/g0 \ 1 ] AC1@2 ] BC
(4)
where g and g0 are the viscosities of the electrolytes solution
and the pure solvent, respectively. Parameter A expresses the
ionÈion interaction and is zero when the solvent is neutral; C
is the concentration (M) of the solute while B is the coefficient
of the solvent viscosity, which indicates the ionÈsolvent inter-
action. Values of B for Na` and OH~ have been reported as
0.086 and 0.112 dm3 mol~1, respectively, in water.37 Gener-
ally, B depends mainly on the ion volume and does not
change much with variation of solvent.38 We estimated the
viscosity change of the solution by the addition of NaOH
from eqn. (4). Using B data in water, we obtained g/g0 \ 1.002
at 0.01 M NaOH. Since, roughly, D is inversely proportional to
the viscosity, this small change of the viscosity is within the
experimental error of this work. Therefore, the viscosity
change upon the addition of NaOH (0.01 M) is negligible and
D of the neutral radical and the anion radical can be com-
pared directly.
Both D of the neutral radical and anion radical of AP are
smaller than that of the parent molecule. Previously, the
reduction of D of neutral radicals relative to the parent mol-
ecules was explained in terms of intermolecular interactions
between the radicals and the solvent molecules. In this case,
we suspect that the intermolecular interactions between both
the neutral and anion radical and the solvent molecules are
Table 1 Di†usion constants (D/10~9 m2 s~1) of acetophenone (AP), the neutral radical of AP in alcoholic solvents and the anion radical of AP
in alcohols ] 0.01 M NaOH obtained by the TG method at 20 ¡C
D in pure solvent
neutral radical
D in solvent ] 0.01 M NaOH
solvent
ethanol
AP
AP
anion radical
1.36 ^ 0.11
1.78 ^ 0.05
0.89 ^ 0.03
0.77 ^ 0.08
0.66 ^ 0.09
0.58 ^ 0.01
1.25 ^ 0.04
0.33 ^ 0.01
0.26 ^ 0.01
0.19 ^ 0.01
1.37 ^ 0.10
1.91 ^ 0.12
0.89 ^ 0.05
0.80 ^ 0.20
0.63 ^ 0.06
0.52 ^ 0.03
1.15 ^ 0.02
0.28 ^ 0.02
0.19 ^ 0.03
0.14 ^ 0.05
methanol
propan-2-ol
butan-1-ol
pentan-1-ol
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
189

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Fig. 8 The temperature dependence of D of AP in ethanol (…), the
neutral radical in ethanol (L), AP in ethanol ] 0.01 M NaOH (=), the
anion radical in ethanol ] 0.01 M NaOH (K). Solid line and dotted
line are D calculated from eqn. (7) and (8), respectively.
Fig. 6 Viscosity dependence of D of AP in alcohols (…), the neutral
radical of AP in alcohols (L), AP in alcohol ] 0.01 M NaOH (=), the
anion radical of AP in alcohol ] 0.01 M NaOH (K). Solvents are 1,
pentan-1-ol; 2, tert-butan-1-ol; 3, propan-2-ol; 4, ethanol and 5, meth-
anol. Solid line and dotted line are D calculated from eqn. (7) and (8),
respectively.
Einstein estimated f by assuming the solvent to be a contin-
uous Ñuid.1
radicals of all solutes in all solvents in this work are close to
those of the neutral radicals. Therefore the reduction of the
charge e†ect on D seems to be general for the intermediate
ketyl radicals created by the hydrogen abstraction reaction.
We compare the experimental D values of these species with
theoretical calculations where D is described by the Stokes
law1
f
\ apgr
(7)
SE
Eqn. (6) and (7) are well known as the StokesÈEinstein (SE)
formula, which gives one of the most fundamental equations
for D. Constant a in eqn. (7) indicates the boundary condition
of the friction between the solute and solvent. For the stick
boundary condition, a \ 6, and for the slip boundary condi-
tion, a \ 4. The calculated D of the SE equation (D ) gener-
ally reproduce experimental D well when the sizes of solute
molecules are sufficiency large. However, if the volume of a
solute molecule is small or close to the solvent volume, D
SE
D \ k T /f
(6)
B
where f is the friction of the solute molecules in the solvent.
SE
underestimates the experimentally observed D because the
continuous Ñuid approximation for the solvent is no longer
valid.
Some modiÐcations of the SE equation have been pro-
posed.2 Evans and co-workers proposed an empirical equa-
tion, which is given by41
g(c@rA`d)
f
\
(8)
EV
k exp(a/r ] b)
B
A
where a, b, c and d are constants, which were determined by
Evans and co-workers as a \ 5.973 Ó, b \ [7.3401,
c \ [0.863 65 Ó and d \ 1.0741.42 In a series of our previous
studies, we have shown that the calculated D values from this
equation (D ) agree very well with the D values of the parent
EV
molecules.18,19 On the other hand, the D values of radicals are
closer to D under the stick condition.15h18 Fig. 6 and 7
SE
show plots of D and D (stick boundary). As can be seen, D
EV
SE
values of the parent molecules are close to D and D of both
EV
the neutral and anion radicals are close to D . It is inter-
SE
Fig. 7 The solute size dependence of D of parent molecules in
ethanol (…), neutral radicals in ethanol (L), AP in alcohol ] 0.01 M
NaOH (=), the anion radical of AP in alcohol ] 0.01 M NaOH (K).
Solute ketones are 1, benzil; 2, benzophenone; 3, xanthone; 4, aceto-
phenone and 5, benzaldehyde. Solid line and dotted line are D calcu-
lated from eqn. (7) and (8), respectively.
esting that the experimental data indicate that the di†erence
in D between the parent molecules and the anion radicals
increases with increasing g and/or decreasing r. This tendency
is what we observed before in neutral radicals.
Table 2 Size dependence of the di†usion constants (D/10~9 m2 s~1) of the parent molecules, the neutral radicals and the anion radicals in
ethanol and ethanol ] 0.01 M NaOH
D in ethanol
D in ethanol ] 0.01 M NaOH
solute
parent molecule
neutral radical
parent molecule
anion radical
benzaldehyde
xanthone
benzophenone
benzil
1.60 ^ 0.05
0.90 ^ 0.05
0.80 ^ 0.05
0.77 ^ 0.05
0.58 ^ 0.01
0.50 ^ 0.01
0.49 ^ 0.03
0.50 ^ 0.03
1.52 ^ 0.02
0.87 ^ 0.04
0.80 ^ 0.10
0.70 ^ 0.10
0.48 ^ 0.02
0.46 ^ 0.01
0.43 ^ 0.02
0.45 ^ 0.01
190
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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Table 3 Activation energy for di†usion (E ) and the pre-exponential
where f is the hydrodynamic friction and the R/r3 term is the
D
0
factor (D ) [D \ D exp ( [ E /k T )] of AP, the neutral radical and
dielectric friction. Generally, f is calculated from the Ein-
0
0
D B
0
the anion radical obtained by the Arrhenius plot of D (Fig. 8) in
ethanol and ethanol ] 0.01 M NaOH
steinÏs formula [eqn. (7)]. According to the theory by Zwanzig,
R is given by7
D /10~7 m2 s~1
E a/kcal mol~1
0
D
Ae2(e [ e )q
0
= D
R \
(12)
parent molecule
in ethanol
Z
e (2e ] e )
0
0
=
2.0 ^ 0.1
1.7 ^ 0.2
2.97 ^ 0.04
2.88 ^ 0.05
Based on the HubbardÈOnsager (HO) theory, R is written as8
in ethanol ] 0.01 M NaOH
neutral radical
Ae2(e [ e )q
in ethanol
anion radical
in ethanol ] 0.01 M NaOH
2.3 ^ 0.2
1.9 ^ 0.1
3.52 ^ 0.06
3.56 ^ 0.03
0
= D
R
\
(13)
HO
e2
0
where, e and e are the static and optical dielectric constants,
0
=
a 1 cal \ 4.184 J.
respectively, e is the charge of the proton and q is DebyeÏs
D
relaxation time. Constant A has a value of 3/8 for the stick
boundary condition and 3/4 for the slip boundary condition
of eqn. (12), 17/280 for the stick boundary condition and 1/15
for the slip boundary condition of eqn. (13).
The temperature dependence of D in pure ethanol and
ethanol ] NaOH between 50 and [50 ¡C is shown in Fig. 8.
The temperature dependence of D in various solutions can
generally be expressed by the following Arrhenius-type equa-
tion.1
Evans and co-workers3 experimentally determined R of
some tetraalkylammonium ions in several solvents by com-
parison of D of non-ionic molecules. The experimentally
obtained values of D of the ionic molecules studied by Evans
and co-workers3 are plotted vs. 1/r and 1/g in Fig. 9 along
with our data. Both D and D calculated from eqn. (7) and
D \ D exp([E /k T )
(9)
0
D B
SE
EV
(8) are plotted. It is evident from the Ðgures that values of D of
where E is the di†usion activation energy and D is the pre-
D
0
the ions are close to D under the stick condition, similarly to
exponential factor. The log D vs. 1/T plots of Fig. 7 indicate
that an Arrhenius-type relation holds for this system. Deter-
mined E and D values are listed in Table 3. It is of note that,
SE
D
0
although D of the parent molecules and neutral (or anion)
radicals are very di†erent, D of these species are very similar.
0
On the other hand, E of both types of radical are larger than
D
those of the parent molecules. This behavior can be again
reproduced by calculation from eqn. (7) and (8), both qualit-
atively and quantitatively (Fig. 8). Again this is similar to the
case of the neutral radicals reported before.18 In that paper,
we explained the temperature dependence by the excess size
model. The activation energy of the anion radical is almost
the same as that of the neutral radical. The charge in the
radical does not change the activation energy of di†usion. We
consider a possible origin of this fact below.
4
Discussion
4.1 Comparison of D between ionic radicals and stable ions
In the previous section, we compared D of charged radicals
with those of neutral radicals. This comparison will provide
information of the charge e†ect on the radicals. In order to
discuss the charge e†ect on the radicals and also that on the
closed shell molecules, D of stable ions are compared with
those of the closed shell molecules. A large number of studies
have been made on the di†usion process of metal ions.1 As the
metal ions become small, the e†ect of the Coulombic force
becomes remarkably large and values of D of metal ions
become much smaller than D . This e†ect has been explained
SE
by the formation of a complex with a large number of solvent
molecules.4 Since the sizes of the metal ions are too small for
the hydrodynamic theory based on the continuous Ñuid
model, it would not be appropriate to use such data for com-
parison with our samples. Values of D of larger non-metallic
ions have been measured by the ionic conductance method for
some tetraalkylammonium ions and the values are compared
with values of D of some tetraalkyltins by the Trylor disper-
sion technique.3 The results show that the ionic mobility is
slower than that of non-ionic molecules and such di†erences
were analyzed by the dielectric friction model.
Fig. 9 The reported D of the tetraalkyltins (>) and D calculated
from the reported j of the tetraalkylammonium ions (|) from ref. 3
with our data. (a) The solvent viscosity dependence of D of Me Sn,
4
Me N` (radii are 3.06 and 2.84 Ó, respectively) in 1, butan-1-ol; 2,
4
propan-2-ol; 3, ethanol; 4, methanol; 5, acetonitrile and 6, acetone. (b)
The solute size dependence of D of the stable molecules 1, Bu Sn; 2,
4
Et Sn; 3, Me Sn; 4, CCl and the ions 5, Bu N`; 6, Pr N`; 7,
4
4
4
4
4
Et N`; 8, Mt N` in ethanol. The curved solid line, straight solid line,
4
4
dotted line, and broken line are D calculated by eqn. (8), the SE equa-
tion [eqn. (7)], the excess volume model [eqn. (14)], and the dielectric
model corrected by the HubbardÈOnsager equation (ref. 43), respec-
tively.
The e†ect of the dielectric friction is given by
f \ f ] R/r3
(11)
0
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
191

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radicals. This agreement indicates that the di†usion of the
stable ions is expressed by the stick boundary condition of the
hydrodynamic model rather than the dielectric model. (The
neutral radicals and ionic radicals are close to D under the
stick boundary condition under a variety of conditions of
solvent, temperature and molecular size (although slight di†er-
SE
agreement of D of the non-ionic molecule with D is expected
since eqn. (8) was empirically determined from these data.)
ences are apparent). This fact may suggest that D at the stick
boundary condition could be the lowest limit of D. If the
EV
SE
boundary condition is already completely stick-like for the
neutral radicals and ions, the condition cannot be “more stick-
likeÏ even if a charge is attached to the neutral radical or if an
unpaired electron is attached to the ion. Another possible
explanation for the similar D values of neutral and ionic rad-
icals may be related to the origin of the slow di†usion of the
neutral radicals. We will come back to this point later in this
section.
What is the origin of the slow di†usion of the neutral rad-
icals? To answer this the fact that D of the neutral radicals
and that of the stable ions are very similar over wide ranges of
viscosities and molecular sizes (Fig. 9) may be a clue. It sug-
gests that the soluteÈsolvent intermolecular interaction of ions
and neutral radicals could be similar, more speciÐcally, similar
to the electrostatic interaction. Of course, neutral radicals
have no overall charge, but if the charge densities of the rad-
icals are polarized signiÐcantly and/or the radicals have large
dipole moments, they can interact with the solvent molecules
by electrostatic interaction. This e†ect may be the origin of the
slow di†usion of the radicals.
4.2 Models for slow di†usion
For a detailed comparison of D values of neutral radicals,
anion radicals and stable ions, the size dependence of di†usion
of the three types of species are plotted in Fig. 9(b). Although
D
[straight solid line in Fig. 9(b)] reproduce D of three
SE
species, some di†erences are notable; D decreases in the order:
stable ions, neutral radicals, anion radicals.
We have explained the di†usion process of the neutral rad-
icals based on the excess volume model.17,18 In this model,
the equation derived by Evans and co-workers41,42 was modi-
Ðed as if the molecular volume of the radical was expanded.
An equation from this model is given by18
C
[a
D
f \ k~1 exp
[ b g@*c@(r3`3V0@4p)1@3+`d@ (14)
V
B
(r3 ] 3V /4p)1@3
0
where V is the apparent excess volume of the radical. In a
0
series of investigations on radical di†usion, we have succeeded
in reproducing the size, viscosity and temperature depen-
Nee and Zwanzig proposed a theory of the dielectric fric-
tion for a dipolar molecule,45 and subsequently, many theories
have been proposed to account for the dielectric friction to the
rotation of polar solutes in polar solvents46 or reorientation
of polar solute molecules interacting with polar solvents.47 No
theory to explain the dielectric friction e†ect of a polar solute
to the translational di†usion have been reported. However, by
analogy with the rotation process, it is natural to consider
that the di†usion process of the polar solute should be inÑu-
enced by the dielectric friction. In fact from the dynamic
Stokes shift measurement, Maroncelli and co-workers con-
cluded that, even in non-polar solvents, the dielectric friction
can be notable by the interaction with the quadrupole
moment of the solvent.48 Moreover, Okazaki et al. found that
a merocyanine form of a benzospiropyran, which has a large
dipole moment (ca. 12 D¤) di†uses slower than the non-
charge-separated spiro-form not only in ethanol but also in
cyclohexane.49 These observations suggest that the dielectric
friction is not so small as predicted from eqn. (12), (13), and
the corrected HO equations even in non-polar solvents.
If electrostatic interaction is the main origin of the slow dif-
fusion of the radicals (such as due to dielectric friction), the
radicals should be more polar than the parent molecules. We
calculated and compared the polarizabilities and the dipole
moments of the radicals and the parent molecules by using a
semi-empirical molecular orbital (MO) calculation with modi-
Ðed neglect of diatomic overlap (MNDO) method.19 However,
the calculated dipole moments of the ketyl radicals of AP and
benzophenone (1.6, 1.4 D, respectively) are smaller than those
of the parent molecules of AP and benzophenone (2.7 and 2.5
D, respectively). Furthermore, the polarizabilities of the rad-
icals and the parent molecules are found to be similar.19
Therefore, we could not Ðnd any signiÐcant di†erences in the
molecular orbital character between the radicals and their
parent molecules by simple MO calculations.
dences of D of the radical by this model with V \ 5È8 ] 102
0
Ó3. Although values of D calculated from this model (D ) are
V
close to D , the size dependence of the di†usion activation
SE
energies of radicals agrees better with the calculation based on
this model rather than on the SE equation.18 Values of D
SE
are proportional to 1/r [straight line in Fig. 9(b)] while the
slope of D on 1/r is gentler [dotted line in Fig. 9(b)]. Values
V
of D are close to D of the neutral and anion radicals but
V
those of the stable ions are slightly larger than D .
Felderhof showed that the HO theory for ionic mobility
V
needs to be corrected and performed more careful numerical
studies based on dielectric friction theory.43 In a similar
manner, Ibuki and Nakahara tested the dielectric friction
theory for ion mobility in polar solvents. They found that the
HO theory is better than the Zwanzig theory to describe D of
an ionic species and proposed an approximate HO equa-
tion.44 We calculated values of D from their approximated
equation and compared them with the experimental D values.
However, the calculated D values are very di†erent from the
experimental values. For example, D for Et N` in ethanol is
4
0.72 ] 10~9 m2 s~1, while the calculated D is 0.47 ] 10~9 m2
s~1. A similar result has been reported by Terazima et al. for
the TMPD cation radical.24 The disagreement is expected
because Ibuki and Nakahara used the Einstein equation [eqn.
(6)] for f in eqn. (11), yet D cannot reproduce the experi-
0
SE
mental D values. In order to improve f , we used f [eqn. (8)]
0
EV
instead of f . The calculated values by the corrected HO
equations with the slip boundary constants (D ) are plotted
in Fig. 9 (broken line) and compared with the experimental D
SE
HO
values of these species. We Ðnd that D reproduce D of the
HO
stable ions well rather than those of the radicals in region of
r~1 \ 0.3 Ó~1. From Fig. 9, it is evident that D increases
HO
exponentially with 1/r. This deviation becomes larger with
increasing 1/r of ions. In this region, the corrected HO equa-
tions can no longer reproduce the experimental D, therefore,
in a wide range of 1/r, the experimental D values are better
A possible explanation of the slow di†usion of radicals was
given very recently by Morita and Kato.50 They investigated
electric properties of radicals created by the hydrogen
abstraction reactions by ab initio MO calculations, and found
that the sensitivities of the intramolecular charge polarization
induced by an external electrostatic Ðeld are remarkably
enhanced in the some radicals, though this sensitivity does not
reproduced by D rather than D
.
SE
HO
4.3 Intermolecular interactions of neutral and anion radicals
One of main interesting Ðndings in this research is that D
values of neutral radicals are quite close to those of the anion
radicals and ions. This fact indicates that the friction of the
neutral radicals (whatever its origin), and the dielectric friction
of ions are not additive. It is interesting that D values of ions,
¤ 1 D B 3.335 64 ] 10~30 C m.
192
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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appear in the usual polarizability calculated by the MO calcu-
lation we used.50 According to their analysis, such an
enhancement is due to the rÈp mixing that facilitates the
deformation of the p-electron orbital of aromatic radicals.
They suggested that this particular sensitivity of aromatic rad-
icals could be the origin of the anomalous slow di†usion of
the radicals. Their theoretical suggestion seems to be consis-
tent with our Ðnding that the friction of neutral radicals is
similar to that of ions.
Their calculations show that the charge sensitivity depends
on the molecular structure. When a charge is attached to the
neutral radical, the structure should be changed and the rÈp
mixing, which is the origin of the enhanced charge sensitivity,
could diminish. In that case, only the intermolecular inter-
action by the electric charge (not the charge sensitivity) causes
the slow di†usion of the ionic radicals like that of stable ions.
This exclusive mechanism of the slow di†usion of neutral and
ionic radicals may answer to the question as to why the e†ect
of the charge and the unpaired electron is not additive.
References
1
(a) E. L. Cussler, Di†usion, Cambridge University Press, Cam-
bridge, 1984; (b) H. J. V. Tyrrell and K. R. Harris, Di†usion in
L iquid, Butterworths, London, 1984; (c) L andolt-Bornstein T abel-
len, Springer, Berlin, 1961, 6 AuÑ., Bd. II.
(a) F. Perrin, J. Phys. Radium., 1931, 7, 1; (b) A. Spernol and K.
Z. Wirtz, Z Naturforsch., T eil A, 1953, 8a, 352; 522; (c) E. G.
Scheibel, Ind. Eng. Chem., 1954, 46, 2007; (d) C. R. Wilke and P.
C. Chang, Am. Inst. Chem. Eng. J., 1995, 1, 264; (e) C. J. King, L.
Hsueh and K. W. Mao, J. Chem. Eng. Data, 1965, 10, 348.
(a) F. D. Evans, C. Chan and B. C. Lamartine, J. Am. Chem. Soc.,
1977, 28, 6492; (b) D. F. Evans, T. Tominaga and C. Chan, J.
Solution Chem., 1979, 8, 461.
(a) H. S. Frank and W. Y. Wen, Discuss. Faraday Soc., 1957, 24,
133; (b) O. Ya. Samoilov, Discuss. Faraday Soc., 1957, 24, 141; (c)
E. Waisman and J. L. Lebowitz, J. Phys. Chem., 1970, 52, 4307.
(a) H. Sadek and R. M. Fuoss, J. Am. Chem. Phys., 1959, 81,
4507; (b) D. S. Berns and R. M. Fuoss, J. Am. Chem. Phys., 1960,
82, 5585.
2
3
4
5
6
7
8
R. H. Boyd, J. Chem. Phys., 1961, 35, 1281; 1963, 39, 2376.
R. Zwanzig, J. Chem. Phys., 1963, 38, 1603; 1970, 52, 3625.Ï
(a) J. B. Hubbard and L. Onsager, J. Chem. Phys., 1977, 67, 4850;
(b) J. B. Hubbard, J. Chem. Phys., 1978, 68, 1649.
9
R. Biswas, S. Roy and B. Bagchi, Phys. Rev. L ett., 1995, 75, 1098.
5
Conclusion
10 M. L. Chan and T. C. Chan, J. Phys. Chem., 1995, 99, 5765.
11 T. Tominaga, S. Tenma and H. Watanabe, J. Chem. Soc.,
Faraday T rans., 1996, 92, 1863.
12 (a) H-H. Schuh and H. Fischer, Helv. Chim. Acta, 1978, 61, 2130;
Int. J. Chem. Kinet., 1976, 8, 341; (b) M. Lehni, H. Schuh and H.
Fischer, Int. J. Chem. Kinet., 1979, 11, 705; (c) M. Sitarski, Int. J.
Chem. Kinet., 1981, 13, 125; (d) M. Lehni and H. Fischer, Int. J.
Chem. Kinet., 1983, 15, 733.
13 (a) F. J. Adrian, J. Chem. Phys., 1971, 54, 3918; (b) J. B. Pedersen
and J. H. Freed, J. Chem. Phys., 1973, 58, 2746; (c) H. J. Werner,
Z. Schulten and K. Schulten, J. Chem. Phys., 1977, 67, 646; (d) R.
Kaptein, J. Am. Chem. Soc., 1972, 94, 6251.
14 (a) R. D. Burkhart, J. Phys. Chem., 1969, 73, 2703; (b) R. D. Burk-
hart, R. F. Boynton and J. C. Merrill, J. Am. Chem. Soc., 1971, 93,
5013; (c) R. D. Burkhart and R. J. Wong, J. Am. Chem. Soc.,
1973, 95, 7203; (d) P. P. Levin, I. V. Khudyakov and V. A.
Kuzumin, J. Phys. Chem., 1989, 93, 208.
The translational di†usion constants (D) of electrically neutral
ketyl radicals, anion radicals and parent molecules were mea-
sured by the transient grating (TG) method in alcoholic solu-
tions. The neutral radicals and the anion radicals could be
created selectively by controlling the concentration of sodium
hydroxide not only in aqueous solution but also in alcoholic
solutions. The presence and the decay kinetics are examined
by transient absorption and the time proÐle of the TG signal
is interpreted in terms of the mass di†usion of these species. It
was found that both the neutral and anion radicals di†use
more slowly than the parent molecules. Values of D of the
anion radicals are compared to those of the neutral radicals
for studying the e†ect of the charge and the unpaired electron
on the di†usion process. We measured the solvent viscosity
dependence, the solute size dependence and the temperature
dependence of D. These D values are compared with the
15 (a) M. Terazima and N. Hirota, J. Chem. Phys., 1993, 98, 6257;
(b) M. Terazima, K. Okamoto and N. Hirota, L aser Chem., 1994,
13, 169.
values calculated based on the StokesÈEinstein equation (D )
16 M. Terazima, K. Okamoto and N. Hirota, J. Phys. Chem., 1993,
97, 13387.
SE
EV
and the equation proposed by Evans and co-workers (D ).
17 M. Terazima, K. Okamoto and N. Hirota, J. Chem. Phys., 1995,
102, 2506.
Values of D of the parent molecules are close to D , while D
EV
of both types of radicals are close to D , D values of anion
SE
18 K. Okamoto, M. Terazima and N. Hirota, J. Chem. Phys., 1995,
103, 10445.
radicals are close to that of the neutral radicals over a wide
range of solvent viscosity, solute size and temperatures. Com-
paring this result with reported D values of stable ions, we
found that the di†usion of neutral radicals, ionic radicals and
ions are similar. For a more careful comparison, we calculated
D values using the excess volume model based on D (D )
19 K. Okamoto, N. Hirota and M. Terazima, J. Phys. Chem. A,
1997, 101, 5269.
20 M. Terazima, S. Tenma, H. Watanabe and T. Tominaga, J.
Chem. Soc., Faraday T rans., 1996, 92, 3057.
21 N. Houser and R. C. Jarnagin, J. Chem. Phys., 1970, 52, 1069.
22 (a) S. S. Sam and G. R. Freeman, J. Chem. Phys., 1979, 70, 1538;
1980, 72, 1989; (b) J. P. Dodelet and G. R. Freeman, Can. J.
Chem., 1975, 53, 1263.
EV
V
and the dielectric friction model, which is corrected by the
HubbardÈOnsager equation (D ). The D values of the radical
HO
are close to D . On the other hand, the D values of ions are
23 (a) S. K. Lim, M. E. Burba and A. C. Albrecht, J. Phys. Chem.,
1994, 98, 9665; (b) K. S. Haber and A. C. Albrecht, J. Phys.
Chem., 1984, 88, 6025; (c) D. Roy and A. C. Albrecht, J. Phys.
Chem., 1989, 93, 2475; (d) S. K. Lim, M. E. Burba and A. C.
Albrecht, Chem. Phys. L ett., 1993, 216, 405.
24 M. Terazima, T. Okazaki and N. Hirota, J. Photochem. Photo-
biol., 1995, 92, 7.
25 J. I. G. Cadogan, Principles of Free Radical Chemistry, The
Chemical Society Monographs For Teachers No. 24, 1973.
26 (a) E. Hayon, T. Ibata, N. N. Lichtin and M. Simic, J. Phys.
Chem., 1972, 76, 2072; (b) A. Beckett, A. D. Osborne and G.
Porter, T rans. Faraday Soc., 1964, 60, 873.
V
closer to D than D . At present, we think that the slow
HO
V
di†usion of the radicals and ions may be due to a similar
origin, which may be soluteÈsolvent electrostatic interaction.
Recently, Morita and Kato reported that the sensitivities of
the intramolecular charge polarization of the radicals are
enhanced remarkably by an external electrostatic Ðeld. They
proposed that such an enhancement is the origin of the anom-
alously slow di†usion of radicals. Their proposal is consistent
with our explanation.
27 M. Terazima and N. Hirota, J. Chem. Phys., 1991, 95, 6490.
28 M. Terazima, K. Okamoto and N. Hirota, J. Phys. Chem., 1993,
97, 5188.
We thank Dr A. Morita and Prof. S. Kato (Kyoto University)
for the discussion on the origin of the anomalous slow di†u-
sion of radicals and showing us the results of ab initio MO
calculations before publication. This work is supported by
ScientiÐc Research Grant-in-Aid (No. 08554021) and on
Priority-Area-Research “Photoreaction DynamicsÏ (No.
08218230) from the Ministry of Education, Science Sports and
Culture of Japan.
29 J. T. Edward, J. Chem. Educ., 1970, 47, 261.
30 H. J. Eichler, P. Gunter and D. W. Pohl, L aser-Induced Dynamic
Grating, Springer, Berlin, 1986.
31 H. Lutz, E. Breheret and L. Lindquist, J. Phys. Chem., 1973, 77,
1753.
32 (a) Y. S. Touloukian, T hermophysical Properties of Matter,
Plenum, New York, 1970, vol. III; (b) International Critical
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
193

View Article Online
T ables, McGraw-Hill, New York, 1928, vol. III; (c) L andolt-
Bornstein T abellen, Springer, Berlin, 1972, 6 AuÑ., Bd. IV.
33 I. V. Khudyakov and L. L. Koroli, Chem. Phys. L ett., 1984, 103,
383.
43 B. U. Felderhof, Mol. Phys., 1983, 49, 449.
44 K. Ibuki and M. Nakahara, J. Chem. Phys., 1986, 84, 2776.
45 T. W. Nee and R. Zwanzig, J. Chem. Phys., 1970, 52, 6353.
46 (a) J. B. Hubbard and P. G. Wolynes, J. Chem. Phys., 1978, 69,
998; (b) J. B. Hubbard, J. Chem. Phys., 1978, 69, 1007; (c) P.
Madden and D. Klveison, J. Chem. Phys., 1978, 86, 4244; (d) B.
U. Felderhof, Mol. Phys., 1983, 48, 1269; (e) E. Nowak, J. Chem.
Phys., 1983, 79, 976.
34 K. Okamoto, N. Hirota and M. Terazima, J. Phys. Chem. A,
1997, 101, 5380.
35 L. R. Donkers and G. Leaist, J. Phys. Chem. B, 1997, 101, 304.
36 G. Jones and M. Dole, J. Am. Chem. Soc., 1932, 51, 2950.
37 R. Shimha, J. Phys. Chem., 1940, 44, 25.
38 A. Einstein, Ann. Phys., 1966, 19, 289; 1967, 34, 591.
39 K. Nakamura, B. F. Wong and N. Hirota, J. Am. Chem. Soc.,
1973, 95, 6919.
47 (a) G. Zwan and J. H. Hynes, J. Phys. Chem., 1985, 89, 4181; (b)
M. Maroncelli and G. R. Fleming, J. Chem. Phys., 1987, 86, 6221.
48 L. Reynolds, J. A. Gradecki, J. V. Frankland, M. L. Horng and
M. Maroncelli, J. Phys. Chem., 1996, 100, 10337; (b) M. Maro-
ncelli and G. R. Fleming, J. Chem. Phys., 1997, 106, 1545.
49 T. Okazaki, N. Hirota and M. Terazima, J. Photochem. Photo-
biol., 1996, 99, 155.
40 M. Chanon, M. Rajzmann and F. Chanon, T etrahedron, 1990, 46,
6193.
41 (a) H. T. Davis, T. Tominaga and D. F. Evans, AIChE J., 1980,
26, 313; (b) D. F. Evans, H. T. Davis and T. Tominaga, J. Chem.
Phys., 1981, 74, 1298.
42 S. H. Chen, H. T. Davis and D. F. Evans, J. Chem. Phys., 1982,
77, 2540.
50 A. Morita and S. Kato, J. Am. Chem. Soc., 1997, 119, 4021.
Paper 7/06220F; Received 26th August, 1997
194
J. Chem. Soc., Faraday T rans., 1998, V ol. 94