373 zyxwvutsr
Chemical Physics 108 (1986) 373-379
North-Holland,
Amsterdam
SLOWING DOWN OF OXYGEN MIGRATION IN THE PROCESSES
OF RADICAL OXIDATION AND OF PHENANTHRENE
PHOSPHORESCENCE
QUENCHING IN METHANOL GLASSES AT 90 K zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM
E.L. ZAPADINSKY,
V.V. KOROLEV,
N.P. GRITSAN,
Institute of Chemical Kinetics and Combustion, Novosibirsk
N.M. BAZHIN
and V.A. TOLKATCHEV
630090, USSR
Received 10 February 1986; in final form 11 June 1986
The hydroxymethyl radical oxidation kinetics follows the second-order equation with a time-dependent rate constant, K(t).
The annealing effect is described by way of dividing K(t) into two factors, one of them depending on the preliminary
annealing time (7): K(t) = K,(r + 7)K2(t). The time dependence of both factors is fairly well approximated by the power
follows an
functions: K,(t + 7) = (t + T)-‘,” and K,(t) = t-o.26. The oxygen quenching of phenanthrene phosphorescence
exchange mechanism, with the static conditions setting in at 77 K. At 90 K oxygen diffusion adds to the quenching efficiency.
The time of oxygen jumps (TV) and its time dependence under the matrix annealing at 90 K are determined by comparing the
theoretical 1,‘~~ dependence of the quenching volume with experiment. The l/rj(r)
is well described by the power function
7 -(0rs*0.02). The annealing time functions of the oxidation rate constant and of the inverse jumping time are similar. The
oxidation rate constant and the diffusion constant coincide in the order of magnitude. Consequently, the slowing down of
oxygen migration contributes essentially to the time dependence of the rate constant.
1. Introduction
The hydrocarbon radical oxidation kinetics in
small molecular glassy alcohols at 77-W K obeys
the equation
d[R]/ dt
= -K(r)[R][G,],
where [R] is the radical concentration, [0,] the
oxygen concentration and K(t) the time-dependent rate constant [l-5]. The function K(t) can
be approximated as
K(t)
= &,tQ-‘,
(1)
where (Y and k, are constants, the exponent (Y
depends on the particular system and varies within
0.45-0.78 [l-5]. The reaction stage does not limit
the process [4].
The time dependence of the rate constant describes the additional retardation of reaction with
decreasing reagent concentrations. The solid phase
reaction can also be described in terms of reactivity distribution. For example, similar experimental
data on H-abstraction by free radicals from matrix molecules are described in both ways (cf. refs.
[6,7]). In the case of small molecular glasses we
prefer the time dependence of rate constant, since
this formalism interpretes not only the time dependence of radical concentrations, but also the
radical kinetic behaviour against the other reagent
concentration [2].
The matrix annealing at the reaction temperature (87 K), performed prior to radical generation,
changes the kinetics [3-51. The reaction is slower
in annealed than in non-annealed samples; the
kinetic curves differ in annealed and non-annealed
samples.. The annealing effect can be taken into
account by dividing K(t) into two factors, K(t)
=K,(t +7)K2(t)
[3]. Here 7 is the annealing
time prior to the reaction, t is reckoned from the
starting moment of the chemical reaction. The
former factor allows for the overall time during
which the matrix is at the reaction temperature;
the latter one takes into account the time after
starting the oxidation reaction. The time dependence of both factors is approximated by a power
function similar to eq. (1) [3].
In all experiments the concentrations of radicals and of oxygen are small in magnitude (under
0301-0104/ 86/ $03.50
0 Elsevier Science Publishers B.V.
(North-Holland Physics Publishing Division)
374
E.L. Zapadinsky et al. / Slow ing down of oxygen migration
1% of the overall particle concentration,
in most
cases = lo-*%). Therefore, if their relative distribution is uncorrelated,
the reaction obviously includes the stage of mutual approach of the reagents. As a result, the annealing
effect may reduce to changes in the oxygen migration rate. For
example, the phenanthrene
luminescence
quenching was investigated
[8,9] at 64-90 K in various
small molecular glasses; the phosphorescence
was
quenched under static and under migration-accelerated
conditions.
In experiments
on oxygen
quenching
of phenanthrene
phosphorescence
in
ethanol under migration-accelerated
conditions
at
77-90 K, the phosphorescence
quantum yield increased with the annealing
time. Yet the static
quenching
efficiency
(at 64 K) remained
unchanged [9]. The fall in the quenching
efficiency
under migration-accelerated
conditions
at 77-90
K was associated
[9] with the deceleration
of
migration in time.
The dependence
of the reaction rate on the
preliminary
annealing
time may result from the
relaxation of matrix physical parameters (such as
viscosity, density), which affects the rate of migration. It is also possible that the annealing effect is
as follows. While migrating
about a disordered
structure, oxygen is redistributed
amongst deeper
traps, which also slows down the diffusion. In this
case, the reaction rate in an annealed sample may
be lower than in a non-annealed
one, the matrix
structure remaining unchanged.
We have investigated comparatively
the annealing effects on radical oxidation kinetics and on the
efficiency of oxygen quenching
of phenanthrene
phosphorescence
in methanol glasses under similar conditions.
The aim was to compare the annealing effects on the constant oxidation rate and
on the oxygen migration.
5 X 10-j M phenanthrene
as a phosphorescent
compound.
The radicals were produced under yirradiation from 6oCo. Thereafter the samples were
irradiated by the visible light from a high-pressure
DRSh-500 mercury lamp for 30 min to photoanneal the captured electrons.
In oxidation reaction studies we employed the
method of saturating the samples at oxygen pressures of l-5 atm [2]. The oxygen concentration
corresponding
to a saturation pressure of 0.21 atm
was attained by saturating the samples with air at
atmospheric pressure. The presence of nitrogen in
the samples did not affect the kinetic curves [2].
Experiments
on the phosphorescence
quenching efficiency required higher oxygen concentrations (saturation
pressure up to 50 atm). Such
pressures
were obtained
by freezing a certain
amount
of oxygen gas into a cylindric
quartz
ampoule - 2-3 mm i.d., 1 mm thick walls, = 1 ml
volume - using a vacuum system. The ampoule
was then sealed, shaken and frozen repeatedly
until an equilibrium
oxygen concentration
was
obtained,
which was checked by the stationary
level of the luminescence
intensity attained for the
frozen sample. The Henry law was verified to hold
for oxygen dissolved at saturation
pressures of
O-15 atm [2] and O-80 atm [9]. The oxygen solubility at room temperature is (4 + 0.8) X 10’s cme3
atm-’ [2]. The validity of the Henry law allowed
the saturation
pressure to be assumed as a measure of 0, concentration.
In calculating
the concentration in a frozen sample, we took into account
a 23% decrease of the sample volume due to
freezing.
The oxidation kinetics was investigated
by the
ESR method using a RE-1306 radiospectrometer.
The luminescence
spectra were taken on a setup
consisting of a DRSh-500 mercury lamp, a highradiance
monochromator,
a sample chamber,
a
prismatic
scanning
monochromator,
a PMT-79,
and an Endim X-Y recorder. The phenanthrene
2. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Experimental
luminescence
was excited by the 313 nm line of
the mercury lamp.
The reagents used: CH,OD,
D,O (deuterated
The samples were frozen to glass in liquid
isotope contents
were 99% and 99.8%, respecnitrogen. The matrix annealing,
the oxidation retively), phenanthrene.
Phenanthrene
was doubleaction and the phosphorescence
intensity
meadistilled in vacuum. The deuterated reagents were
surements were carried out at liquid oxygen temsupplied by Isotop. To obtain the glassy matrix,
perature (90 K). The effect of 0, mobility
on
9.1 vol.% D20 was added to methanol. We used
E.L Zapadinsky et al. / Slowing down of oxygen migration
375 zyxwvuts
quantum yield was investigated under continuous
irradiation. The measurements of static quenching
parameters, the photoannealing of trapped electrons, and the detection of ESR spectra were
performed in liquid nitrogen. At 77 K the radical
oxidation reaction is much slower.
3. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Kinetic measurements on the radical oxidation
reaction
The CH,OD
oxidation kinetics was investigated at 90 K. The oxygen concentration was
9.6 x 10” -2.4 x lOI cmP3; the radical concentration was 3 x 1016-2.7 X. 10” cmP3. The concentration of oxygen was always over 30 times as high as
that of radicals.
The ESR spectra variations were as described
in ref. [5]. A fall in the concentration of hydroxymethyl radicals corresponded to a rise in that of
peroxide radicals, the total concentration
of
paramagnetic centres remaining constant. Note
that after gamma-irradiation samples which were
-1.0 saturated at over 1 atm showed appreciable
amounts of 0; radical ions and of peroxide radiI
I
cals, their concentrations increasing with pressure.
Fig. 1. (a),‘(b) zyxwvutsrqponmlkjihgfedcbaZYXWVUT
CH,OD radical oxidation kinetics at various
At the 0, concentration corresponding to 5 atm
annealing times and various oxygen saturation pressures. Solid
lines are calculated curves. For T = 30 min the curve is calcuthe proportion of 0;
was 40 f 8% of the total
lated by eq. (8); in the other cases: by eq. (4) for non-annealed
concentration of paramagnetic centres, whilst the
samples, and by eq. (5) for annealed one, with a= 0.56,
peroxide radicals formed by radiolysis made up
B = 0.74. The curves are arbitrarily shifted along the time axis.
6 f 2%. In the course of oxidation, the 0; concentration was constant, as it was observed earlier
(41. The shape of the kinetic curve did not depend
If 7 = 0 (non-annealed samples), then
on the amount of perioxide radicals arising under
radiolysis.
NWP01) = --kP21t”.
(4
The CH,OD
oxidation
kinetics in glassy
In the case of non-annealed samples, eq. (4) agrees
CH,OD at 90 K and the annealing effect proved
with experiment (e.g., see fig. 1). The exponent a
to be similar to those observed for ethyl radicals
determined
by the least-squares
method
is
in glassy CD,OD at 87 K [4]. Let us consider the
0.56-0.60
for oxygen saturation of l-5 atm. At
method of processing experimental data proposed zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF
0.21 atm the accuracy is worse, a = 0.54-0.65.
131.
If 7 B t (long annealing times), the (t + 7)*-p
Let the oxidation kinetics be written as
variations during the observation time can be neglected. In this case, eq. (3) is reduced to
d[R]/ dt = -ak,(t
+ r)“ -‘ta-‘[R][O,].
(2)
I
I
If [O,] B [RI, [O,] 5: constant eq. (2) is solved as
ln([Rl/[%l) = -k&MtB.
ln([R]/ [%])
Here
= -ak[Or]
x
/
cl(” + T) a-flXfl-i
dx.
(3)
ks = (a//3)
k,+--B.
(5)
(6)
376
E. L. Zapadinsky et al. / Slowing down of oxygen migration
We fitted the experimental
data at small r by
Formula (5) fairly well describes experiment
for
eq.
(8)
with
varying
k,,,,.
The
approximation
annealing samples also at r > zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
t (see fig. l), when
curves fairly well describe experiment
(fig. la).
j3 is within 0.70-0.75 at a saturation
pressure of
Fig. 2 shows the k,,, values obtained.
l-5 atm, and within 0.73-0.80 at 0.21 atm. In the
Thus, our experimental
results are described
above (Y and p ranges, the error associated with
satisfactorily
by eq. (2) within wide ranges of
(t + T)“-~ variations at t = 7 is less than 5%. As
annealing
times and of oxygen concentrations.
shown
by measurements
at various
oxygen
This conclusion agrees with results obtained [3-51
pressures, the experimental
slope in coordinates
for other systems. Under our conditions
eq. (2)
ln[R]/R,]
a tY (y = a, p) is proportional
to
assumes the form
oxygen concentrations
in both annealed
and
non-annealed
samples. This agrees with depend[R]/dt
= -0.56k,.,,[R][O,]/(t
+ .)“‘18t0.26.
dences (4) and (5).
Let us write eq. (6) in the form
log kp=log(cr//?)k,+(cX-/3)
log 7.
(7)
Taking into account the allowable cx and fi values,
the best fit of eq. (7) to experiment is for OL= 0.56
and p = 0.74 (fig. 2).
The applicability
of eq. (2) was verified also for
small r, when (t + ~)“-fl variations could not be
neglected. Based on the (Yand /3 values obtained,
eq. (3) can be written in the form
ln([R]/[R,,])
4. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ
Determination
of the oxygen
migration
efficiency
by phenanthrene
phosphorescence
quenching
The method proposed recently [9] to study 0,
mobility by oxygen quenching of organic molecule
phosphorescence
in glassy matrices at low temperatures is based on a rise in the excited state
quenching
efficiency due to diffusion of O2 as a
= -0.74k,,,,r0.74[02]
quencher.
z
dy zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
The quencher
(0,)
influence
on the donor
X
(8)
/ 0 (1 + y)0.‘8y0.26
’
phosphorescence
quantum yield (77) without diffusion is described by the expression
where z = t/r.
ln(9/90)
= -~~[021.
(9)
The exchange quenching
constant
in a donoracceptor pair depends on the separation
(r) between the partners as follows
o-
0.21&n
0
1.l
.
3.0
K(r)=P,exp[-2(r-R)/L],
(10)
where PO is the quenching constant at a contact,
R the closest approach and L is the characteristic
parameter
of exchange
interaction
decay. The
static quenching parameters have been determined
earlier [8] in methanol at 77 K: PO = 106-lo9 s-’
and L = 0.55 k 0.05 A.
Mathematically,
the enhancement
of oxygen
quenching
of
phenanthrene
phosphorescence
due
I
1
1
to
oxygen
migration
is
more
convenient
to
con2
4 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
LogT (minl
sider in terms of jumping
migration
[lo]. Under
Fig. 2. Plot of log k,,, versus log 7. The intercept of the Y
migration eq. (9) holds, however, (rl) depends on
axis is lop[(0.56/0.74)k0,,,].
The values of k0,74 obtained by
both the static quenching parameters (PO, L) and
eq. (8) are circles. In the other cases k,,
is calculated by eq.
the characteristic
jumping
time (TV). This depen(5)> km, by eq. (4).
5.0
-‘-
\I
I
E.L Zapadinsky
dence can be calculated theoretically. To this end,
it is sufficient to consider the situation with one
acceptor molecule in a solution with donor molecules. The relationship between the excited donor
concentration (n) and the distance to an acceptor
molecule (r) migrating by jump [lo] is expressed
by an equation, the simplest form of which is
an(r,
t)/ at=
--[n(r,
t)-n(oo,
-k(r)n(r,
2)
311 zyxwvutsr
et al. / Slowing down of oxygen migration
6
t)]/~j
-n(r,
t)/To+
2 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON
w.
(11)
Here 7,, is the natural lifetime of an excited donor,
W the donor excitation rate, K(r) is defined by
eq. (10) and n(cc, t) is the excited donor concentration at infinite distance from the acceptor.
Eq. (11) holds when the jump lengths exceed the
characteristic size of the range of concentration
variations of excited donors. This size is (R, - R),
is determined
from the condition
where R,
0
0.2
0.1
0.3
lKj(S-‘I
Fig. 3. Calculated dependence of quenching volume under
migration (a,,) and static quencbiag volume ($)
difference
on time ofjumps (TV)_
(11: L = 0.6 A, <,, =12 A, (2): L = 0.55
A, R, =11.5 A, (3): L = 0.5 A, R, =11 A.
K( R,) = l/ +rO.In our case (R, - R) = 5 A.
Under stationary conditions eq. (11) is solved
as
Fig. 3 shows the calculated dependence of (Y,,
versus 1/ TV.
n(r) = n,/ (I +fx),
(12)
As in the case of the ethanol matrix [9],
where x = K(~)T~, f= T~/ (T + Q) and nrn = WT,,.
phenanthrene phosphorescence intensity in the
The quenching volume can be determined as
presence of oxygen in glassy methanol increases in
follows
time at 90 K. In contrast to the phosphorescence,
the fluorescence
intensity, also quenched by
1
00
Lx, = -w R n(r) K(r) 4nr* dr.
(13)
oxygen,
does
not
change
with time of preliminary
/
matrix annealing within experimental accuracy
The expression for (Y,,can be derived analytically
( f 2%). Moreover, a preliminary aging of samples
[ll]:
at 90 K does not affect quenching parameters
(1) p=P,?)f<l;
determined at 77 K. Consequently, the phosphorescence intensity changes observed at 90 K
m zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
P”
f+=$
/ 3* ln(l+p)+2nF12(-l)‘+l
cannot result from changes in the spatial distribu[
tion of dissolved oxygen or the relative distribution of phenanthrene-O2
pairs but arise due to
+2/ 3 5 (-1).$
.
(14) changes in oxygen mobility in the process of ann=l
I
nealing the glassy matrix. Fig. 4 shows experimental dependence of the quenching volume under
(2) p=P,7(Jf>l;
migration (a,) and the static quenching volume
(a,“ ‘) difference versus annealing time (7).
To compare the dependences l/ ~~(7) and K( +r),
the measured 1/ 7j values have been analyzed by
+ h* (ln
P + P) + 8* ln[(l + PI/ PI
the equation
+2p
E (-1)”
n=l
n2pn
2
f
n=l
1
(-1)” .
(15)
l/ Tj = AT-=‘,
(16)
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
n3pn
E. L. Zapadinsky et al. / Slow ing down of oxy gen migration
378
characteristic
time of the matrix heating from 77
to 90 K is also = 30 s. That is why we began the
registration of phosphorescence
intensity from this
moment. Therefore the transient,
non-stationary,
processes may be neglected.
5. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ
Discussion
It is interesting
to compare quantitatively
the
absolute
values of the oxidation
and diffusion
constants.
For migration
by jumps the diffusion
constant is naturally estimated as I/V [12], where V
is a cage volume and Y is the frequency of oxygen
molecule jumps, v = l/r,. Assume v = 6.3 x 1O-2
100 %(min 1
s-l (fig. 5) to be the initial value. In this case,
Fig. 4. The annealing time dependence of quenching volume
setting the cage radius to be 5 A, we have Vu =
under migration (a,) and static quenching volume (ar) dif(3.5 f 1.5) x 1O-23 cm3/s.
Let us estimate
the
ference.
oxidation
rate constant
by the initial slope of
ln([R]/[R,])
a [02]t. The result is (9 f 4) x 1O-23
in. order to determine
the exponent
(Y’. Fig. 5
cm3/s. The same procedure carried out for a longer
shows the processing of our experimental
data by
time, say 100 min, gives Vu = (1 + 0.5) X 1O-23
eq. (16). Eq. (16) holds well within rather a wide
cm3/s, whilst the experimental
constant is (1.3 +
time range, with (Y’= 0.18 f 0.02. The CX’value
0.5) x 1O-23 cm3/s. Thus, the oxidation rate concoincides with /3 - a in eq. (2).
stant observed corresponds
to the diffusion conNote that eq. (11) was solved under stationary
stant by the order of magnitude.
conditions.
In the jumping migration
mechanism
The main experimental
result of the present
all non-stationary
processes occur within about a
work is that the 0, jump frequency,
obtained
single jump time, which in our case is = 30 s. The
from phosphorescence
quenching
data, depends
on the matrix lifetime at the reaction temperature
in the same way as one of the factors in the rate
c zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
constant.
This means that the slowing down of
7
oxygen
migration
in time leads to a reduction of
9
\Y
the
oxidation
rate
constant. Note in this connec.
tion
that
once
the
rate constant is represented
as
- - 1.3
0”
Vu,
the
cage
volume
must
be
time
dependent
in
1
our case. This means that V is an effective parameter characterizing
an elementary chemical act in a
solid. Let us consider possible interpretations
of
- 1.5
the K(t) structure.
Let us assume that the dividing of K(t) into
two time terms is justified by the existence of two
independent
processes. The time dependence (t +
- 1.7
r> -O.‘* arises due to the matrix structure relaxation that affects the 0, jump frequency. The term
1
2
0
LogZimin)
t-0.26 results from the environmental
relaxation
around a radical just after its formation,
which
Fig. 5. The annealing time dependence of the inverse time of
jumps in logarithmic coordinates.
influences
also the chemical reaction rate. The
1
I
E.L Zapadinsb
et al. / Slowing down
surrounding structure may differ from equilibrium
[13-151. If the radical surroundings relax in the
course of chemical reaction, this may affect the
time dependence of the rate constant. Note that
we do not discuss the possibility of CH,OD diffusion, because CH,OD does not recombine under
similar experimental conditions, but in the absence of oxygen [5]. This means that CH,OD may
be assumed immobile in our conditions.
The time deceleration of 0, migration can be
interpreted in another way. The hole and electron
mobilities in disordered systems are often described under the assumption that the transition
probabilities
of neighbours experience strong
fluctuations due to weak fluctuations of distances
between them, or of transition activation energies
(see refs. [16,17]). This model describes the slowing down of migration in time. In some cases it is
possible to introduce a time-dependent rate constant for the chemical reaction [18,19]. Let us
assume a substantial spread of the 0, transition
probability
resulting, e.g., from the transition
activation energy spread [4]. It seems to be possible that this model can ascribe the two time terms
of the rate constant to a single cause without
additional assumptions, because within this model,
the particle decay rate constant is related to
migration characteristics in a complicated way (cf.
refs. [18,20]).
ofoxygenmigration
379 zyxwvutsr
slowed down 0, migration contributes importantly to the time dependence of the rate constant.
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Conclusion
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I171 S. Alexander, J. Bemansoni,
Orbach, Rev. Mod. Phys. 53 (1981) 175.
deceleration 0, migration in the methanol matrix.
I181 W.P. Helman and K. Funabashi, J. Chem. Phys. 66 (1977)
The dependences of the oxidation rate constant
5790.
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cule on the preliminary annealing time are the
2458.
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sion constant in order of magnitude. Thus, the