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Slowing down of oxygen migration in the processes of radical oxidation and of phenanthrene phosphorescence quenching in methanol glasses at 90 K
373
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 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. / Slowing 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.
2. Experimental The reagents used: CH,OD, D,O (deuterated isotope contents were 99% and 99.8%, respectively), phenanthrene. Phenanthrene was doubledistilled in vacuum. The deuterated reagents were supplied by Isotop. To obtain the glassy matrix, 9.1 vol.% D20 was added to methanol. We used
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 luminescence was excited by the 313 nm line of the mercury lamp. The samples were frozen to glass in liquid nitrogen. The matrix annealing, the oxidation reaction and the phosphorescence intensity measurements were carried out at liquid oxygen temperature (90 K). The effect of 0, mobility on
375
E.L Zapadinsky et al. / Slowing down of oxygen migration
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. Kinetic measurements reaction
on the radical oxidation
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 saturated at over 1 atm showed appreciable amounts of 0; radical ions and of peroxide radicals, their concentrations increasing with pressure. At the 0, concentration corresponding to 5 atm the proportion of 0; was 40 f 8% of the total concentration of paramagnetic centres, whilst the peroxide radicals formed by radiolysis made up 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 on the amount of perioxide radicals arising under radiolysis. The CH,OD oxidation kinetics in glassy CH,OD at 90 K and the annealing effect proved to be similar to those observed for ethyl radicals in glassy CD,OD at 87 K [4]. Let us consider the method of processing experimental data proposed
131.
Let the oxidation kinetics be written as
d[R]/dt
= -ak,(t
+ r)“-‘ta-‘[R][O,].
(2)
-1.0 -
I
I
I
I
Fig. 1. (a),‘(b) CH,OD radical oxidation kinetics at various annealing times and various oxygen saturation pressures. Solid lines are calculated curves. For T = 30 min the curve is calculated by eq. (8); in the other cases: by eq. (4) for non-annealed samples, and by eq. (5) for annealed one, with a= 0.56, B = 0.74. The curves are arbitrarily shifted along the time axis.
If 7 = 0 (non-annealed
NWP01)
samples), then
= --kP21t”.
In the case of non-annealed samples, eq. (4) agrees with experiment (e.g., see fig. 1). The exponent a determined by the least-squares method is 0.56-0.60 for oxygen saturation of l-5 atm. At 0.21 atm the accuracy is worse, a = 0.54-0.65. If 7 B t (long annealing times), the (t + 7)*-p variations during the observation time can be neglected. In this case, eq. (3) is reduced to
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)
(4
ks = (a//3)
k,+--B.
(5)
(6)
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E. L. Zapadinsky et al. / Slowing down of oxygen migration
Formula (5) fairly well describes experiment for annealing samples also at r > t (see fig. l), when j3 is within 0.70-0.75 at a saturation pressure of l-5 atm, and within 0.73-0.80 at 0.21 atm. In the above (Y and p ranges, the error associated with (t + T)“-~ variations at t = 7 is less than 5%. As shown by measurements at various oxygen pressures, the experimental slope in coordinates ln[R]/R,] a tY (y = a, p) is proportional to oxygen concentrations in both annealed and non-annealed samples. This agrees with dependences (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,,])
= -0.74k,,,,r0.74[02]
dy
z
X
/0
(1
+
y)0.‘8y0.26
(8)
’
We fitted the experimental data at small r by eq. (8) with varying k,,,,. The approximation curves fairly well describe experiment (fig. la). Fig. 2 shows the k,,, values obtained. Thus, our experimental results are described satisfactorily by eq. (2) within wide ranges of annealing times and of oxygen concentrations. This conclusion agrees with results obtained [3-51 for other systems. Under our conditions eq. (2) assumes the form d[R]/dt
= -0.56k,.,,[R][O,]/(t
+ .)“‘18t0.26.
4. 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 quencher. The quencher (0,) influence on the donor 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],
5.0
-‘1
\I I
2
1
I
4
LogT
(minl
Fig. 2. Plot of log k,,, versus log 7. The intercept of the Y axis is lop[(0.56/0.74)k0,,,]. The values of k0,74 obtained by eq. (8) are circles. In the other cases k,, is calculated by eq. (5)> km,
by eq. (4).
(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 to oxygen migration is more convenient to consider in terms of jumping migration [lo]. Under migration eq. (9) holds, however, (rl) depends on both the static quenching parameters (PO, L) and the characteristic jumping time (TV). This depen-
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
et al. / Slowing down of oxygen migration 6
t)]/~j
-n(r,
t)/To+
2
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), where R, is determined from the condition K( R,) = l/+rO.In our case (R, - R) = 5 A. Under stationary conditions eq. (11) is solved as n(r)
= n,/(I
+fx),
(12)
where x = K(~)T~, f= T~/(T + Q) and nrn = WT,,. The quenching volume can be determined as follows 1 00 Lx, = -w R n(r) /
K(r)
4nr* dr.
(13)
The expression for (Y,,can be derived analytically [ll]: (1) p=P,?)f
f+=$ [
+2/3 5 (-1).$ n=l
(14)
. I
(2) p=P,7(Jf>l;
+ h*(ln +2p
P + P) + 8* ln[(l + PI/PI
E (-1)” n=l
n2pn
2
f
n=l
1
(-1)” . n3pn
(15)
0
0.1
0.2
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.
Fig. 3 shows the calculated dependence of (Y,, versus 1/TV. As in the case of the ethanol matrix [9], phenanthrene phosphorescence intensity in the presence of oxygen in glassy methanol increases in time at 90 K. In contrast to the phosphorescence, the fluorescence intensity, also quenched by oxygen, does not change with time of preliminary matrix annealing within experimental accuracy ( f 2%). Moreover, a preliminary aging of samples at 90 K does not affect quenching parameters determined at 77 K. Consequently, the phosphorescence intensity changes observed at 90 K cannot result from changes in the spatial distribution of dissolved oxygen or the relative distribution of phenanthrene-O2 pairs but arise due to changes in oxygen mobility in the process of annealing the glassy matrix. Fig. 4 shows experimental dependence of the quenching volume under 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 the equation l/Tj = AT-=‘,
(16)
E. L. Zapadinsky et al. / Slowing down of oxygen 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. Discussion
100
%(min
1
Fig. 4. The annealing time dependence of quenching volume under migration (a,) and static quenching volume (ar) difference.
in. order to determine the exponent (Y’. Fig. 5 shows the processing of our experimental data by eq. (16). Eq. (16) holds well within rather a wide time range, with (Y’= 0.18 f 0.02. The CX’value coincides with /3 - a in eq. (2). Note that eq. (11) was solved under stationary conditions. In the jumping migration mechanism all non-stationary processes occur within about a single jump time, which in our case is = 30 s. The
1
c
I
7
9
\Y . - -1.3 0” 1
-1.5
-1.7 0
2
1 LogZimin)
Fig. 5. The annealing time dependence of the inverse time of jumps in logarithmic coordinates.
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 s-l (fig. 5) to be the initial value. In this case, setting the cage radius to be 5 A, we have Vu = (3.5 f 1.5) x 1O-23 cm3/s. Let us estimate the oxidation rate constant by the initial slope of ln([R]/[R,]) a [02]t. The result is (9 f 4) x 1O-23 cm3/s. The same procedure carried out for a longer time, say 100 min, gives Vu = (1 + 0.5) X 1O-23 cm3/s, whilst the experimental constant is (1.3 + 0.5) x 1O-23 cm3/s. Thus, the oxidation rate constant observed corresponds to the diffusion constant by the order of magnitude. The main experimental result of the present work is that the 0, jump frequency, obtained 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 constant. This means that the slowing down of oxygen migration in time leads to a reduction of the oxidation rate constant. Note in this connection that once the rate constant is represented as Vu, the cage volume must be time dependent in our case. This means that V is an effective parameter characterizing an elementary chemical act in a solid. Let us consider possible interpretations of 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 + r> -O.‘* arises due to the matrix structure relaxation that affects the 0, jump frequency. The term t-0.26 results from the environmental relaxation around a radical just after its formation, which influences also the chemical reaction rate. The
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]).
6. Conclusion The oxygen quenching of phenanthrene phosphorescence has been employed to show the timedeceleration 0, migration in the methanol matrix. The dependences of the oxidation rate constant and of the inverse jumping time of oxygen molecule on the preliminary annealing time are the same. The rate constant coincides with the diffusion constant in order of magnitude. Thus, the
ofoxygenmigration
379
slowed down 0, migration contributes importantly to the time dependence of the rate constant.
References 111 V.M. Zaskul’nikov and V.A. Tolkatchev,Kinet. i Katahz 20 (1979) 263; React. Kinet. Catal. Letters 14 (1980) 435. 121V.M. Zaskul’nikov, V.L. Vyazovkin, B.V. Bol’shakov and V.A. Tolkatchev, Intern. J. Chem. Kinetics 13 (1981) 707. 131 V.M. Zaskul’nikov and V.A. ToIkatchev, Kinet. i Katahz 23 (1982) 1063. I41 V.A. Bagryansky, V.M. Zaskul’nikov and V.A. ToIkatchev, Chem. Phys. 78 (1983) 41. V.M. Zaskul’nikov, V.A. Tolkatchev, [51 E.L. Zapadinsky, Kinet. i KataIiz 26 (1985) 809. I61 T. Doba, K.U. Ingold, W. Siebrand and T.A. Wildman, J. Phys. Chem. 88 (1984) 3165; Chem. Phys. Letters 115 (1985) 51; T. Doba, K.U. Ingold and W. Siebrand Chem. Phys. Letters 103 (1984) 339. 171 V.L. Vyazovkin, B.V. Bol’shakov and V.A. ToIkatchev, Chem. Phys. 95 (1985) 93. [81 N.M. Bazhin, N.P. Gritsan, V.V. Korolev and S.V. Kamyshan, Khim. Fiz., to be published. I91 V.V. Korolev, N.P. Gritsan and N.M. Bazhin, Khim. Fiz. 5 (1986) 730. 1101 A.I. Burshtein, A.B. Doktorov, A.A. Kipriyanov, V.A. Morozov and S.G. Fedorenko, Zh. Eksp. Tear. Fiz. 88 (1985) 878. Ill1 N.M. Bazhin, B.I. Yakobson and AI. Burshtein, Intern. J. Quantum. Chem. 16 (1979) 931. 1121 Ya.S. Lebedev, Kinet. i Kataliz 8 (1967) 245. and Ya.S. Lebedev, Usp. Khim. 47 I131 O.E. Yakimchenko (1978) 1018. 1141 V.M. Syutkin and V.A. Tolkatchev, Radiat. Phys. Chem. 20 (1982) 281. 1151 J.M. McBride, Accounts Chem. Res. 16 (1983) 304. I161 G. Pfister and H. Sher, Advan. Phys. 27 (1978) 747. W.R. Schneider and R. I171 S. Alexander, J. Bemansoni, Orbach, Rev. Mod. Phys. 53 (1981) 175. I181 W.P. Helman and K. Funabashi, J. Chem. Phys. 66 (1977) 5790. I191 W.P. Helman and K. Funabashi, J. Chem. Phys. 71(1979) 2458. I201 G. Zumofen, J. KIafter and A. Blumen, J. Chem. Phys. 79 (1983) 5131.
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 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. / Slowing 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.
2. Experimental The reagents used: CH,OD, D,O (deuterated isotope contents were 99% and 99.8%, respectively), phenanthrene. Phenanthrene was doubledistilled in vacuum. The deuterated reagents were supplied by Isotop. To obtain the glassy matrix, 9.1 vol.% D20 was added to methanol. We used
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 luminescence was excited by the 313 nm line of the mercury lamp. The samples were frozen to glass in liquid nitrogen. The matrix annealing, the oxidation reaction and the phosphorescence intensity measurements were carried out at liquid oxygen temperature (90 K). The effect of 0, mobility on
375
E.L Zapadinsky et al. / Slowing down of oxygen migration
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. Kinetic measurements reaction
on the radical oxidation
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 saturated at over 1 atm showed appreciable amounts of 0; radical ions and of peroxide radicals, their concentrations increasing with pressure. At the 0, concentration corresponding to 5 atm the proportion of 0; was 40 f 8% of the total concentration of paramagnetic centres, whilst the peroxide radicals formed by radiolysis made up 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 on the amount of perioxide radicals arising under radiolysis. The CH,OD oxidation kinetics in glassy CH,OD at 90 K and the annealing effect proved to be similar to those observed for ethyl radicals in glassy CD,OD at 87 K [4]. Let us consider the method of processing experimental data proposed
131.
Let the oxidation kinetics be written as
d[R]/dt
= -ak,(t
+ r)“-‘ta-‘[R][O,].
(2)
-1.0 -
I
I
I
I
Fig. 1. (a),‘(b) CH,OD radical oxidation kinetics at various annealing times and various oxygen saturation pressures. Solid lines are calculated curves. For T = 30 min the curve is calculated by eq. (8); in the other cases: by eq. (4) for non-annealed samples, and by eq. (5) for annealed one, with a= 0.56, B = 0.74. The curves are arbitrarily shifted along the time axis.
If 7 = 0 (non-annealed
NWP01)
samples), then
= --kP21t”.
In the case of non-annealed samples, eq. (4) agrees with experiment (e.g., see fig. 1). The exponent a determined by the least-squares method is 0.56-0.60 for oxygen saturation of l-5 atm. At 0.21 atm the accuracy is worse, a = 0.54-0.65. If 7 B t (long annealing times), the (t + 7)*-p variations during the observation time can be neglected. In this case, eq. (3) is reduced to
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)
(4
ks = (a//3)
k,+--B.
(5)
(6)
376
E. L. Zapadinsky et al. / Slowing down of oxygen migration
Formula (5) fairly well describes experiment for annealing samples also at r > t (see fig. l), when j3 is within 0.70-0.75 at a saturation pressure of l-5 atm, and within 0.73-0.80 at 0.21 atm. In the above (Y and p ranges, the error associated with (t + T)“-~ variations at t = 7 is less than 5%. As shown by measurements at various oxygen pressures, the experimental slope in coordinates ln[R]/R,] a tY (y = a, p) is proportional to oxygen concentrations in both annealed and non-annealed samples. This agrees with dependences (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,,])
= -0.74k,,,,r0.74[02]
dy
z
X
/0
(1
+
y)0.‘8y0.26
(8)
’
We fitted the experimental data at small r by eq. (8) with varying k,,,,. The approximation curves fairly well describe experiment (fig. la). Fig. 2 shows the k,,, values obtained. Thus, our experimental results are described satisfactorily by eq. (2) within wide ranges of annealing times and of oxygen concentrations. This conclusion agrees with results obtained [3-51 for other systems. Under our conditions eq. (2) assumes the form d[R]/dt
= -0.56k,.,,[R][O,]/(t
+ .)“‘18t0.26.
4. 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 quencher. The quencher (0,) influence on the donor 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],
5.0
-‘1
\I I
2
1
I
4
LogT
(minl
Fig. 2. Plot of log k,,, versus log 7. The intercept of the Y axis is lop[(0.56/0.74)k0,,,]. The values of k0,74 obtained by eq. (8) are circles. In the other cases k,, is calculated by eq. (5)> km,
by eq. (4).
(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 to oxygen migration is more convenient to consider in terms of jumping migration [lo]. Under migration eq. (9) holds, however, (rl) depends on both the static quenching parameters (PO, L) and the characteristic jumping time (TV). This depen-
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
et al. / Slowing down of oxygen migration 6
t)]/~j
-n(r,
t)/To+
2
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), where R, is determined from the condition K( R,) = l/+rO.In our case (R, - R) = 5 A. Under stationary conditions eq. (11) is solved as n(r)
= n,/(I
+fx),
(12)
where x = K(~)T~, f= T~/(T + Q) and nrn = WT,,. The quenching volume can be determined as follows 1 00 Lx, = -w R n(r) /
K(r)
4nr* dr.
(13)
The expression for (Y,,can be derived analytically [ll]: (1) p=P,?)f
f+=$ [
+2/3 5 (-1).$ n=l
(14)
. I
(2) p=P,7(Jf>l;
+ h*(ln +2p
P + P) + 8* ln[(l + PI/PI
E (-1)” n=l
n2pn
2
f
n=l
1
(-1)” . n3pn
(15)
0
0.1
0.2
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.
Fig. 3 shows the calculated dependence of (Y,, versus 1/TV. As in the case of the ethanol matrix [9], phenanthrene phosphorescence intensity in the presence of oxygen in glassy methanol increases in time at 90 K. In contrast to the phosphorescence, the fluorescence intensity, also quenched by oxygen, does not change with time of preliminary matrix annealing within experimental accuracy ( f 2%). Moreover, a preliminary aging of samples at 90 K does not affect quenching parameters determined at 77 K. Consequently, the phosphorescence intensity changes observed at 90 K cannot result from changes in the spatial distribution of dissolved oxygen or the relative distribution of phenanthrene-O2 pairs but arise due to changes in oxygen mobility in the process of annealing the glassy matrix. Fig. 4 shows experimental dependence of the quenching volume under 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 the equation l/Tj = AT-=‘,
(16)
E. L. Zapadinsky et al. / Slowing down of oxygen 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. Discussion
100
%(min
1
Fig. 4. The annealing time dependence of quenching volume under migration (a,) and static quenching volume (ar) difference.
in. order to determine the exponent (Y’. Fig. 5 shows the processing of our experimental data by eq. (16). Eq. (16) holds well within rather a wide time range, with (Y’= 0.18 f 0.02. The CX’value coincides with /3 - a in eq. (2). Note that eq. (11) was solved under stationary conditions. In the jumping migration mechanism all non-stationary processes occur within about a single jump time, which in our case is = 30 s. The
1
c
I
7
9
\Y . - -1.3 0” 1
-1.5
-1.7 0
2
1 LogZimin)
Fig. 5. The annealing time dependence of the inverse time of jumps in logarithmic coordinates.
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 s-l (fig. 5) to be the initial value. In this case, setting the cage radius to be 5 A, we have Vu = (3.5 f 1.5) x 1O-23 cm3/s. Let us estimate the oxidation rate constant by the initial slope of ln([R]/[R,]) a [02]t. The result is (9 f 4) x 1O-23 cm3/s. The same procedure carried out for a longer time, say 100 min, gives Vu = (1 + 0.5) X 1O-23 cm3/s, whilst the experimental constant is (1.3 + 0.5) x 1O-23 cm3/s. Thus, the oxidation rate constant observed corresponds to the diffusion constant by the order of magnitude. The main experimental result of the present work is that the 0, jump frequency, obtained 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 constant. This means that the slowing down of oxygen migration in time leads to a reduction of the oxidation rate constant. Note in this connection that once the rate constant is represented as Vu, the cage volume must be time dependent in our case. This means that V is an effective parameter characterizing an elementary chemical act in a solid. Let us consider possible interpretations of 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 + r> -O.‘* arises due to the matrix structure relaxation that affects the 0, jump frequency. The term t-0.26 results from the environmental relaxation around a radical just after its formation, which influences also the chemical reaction rate. The
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]).
6. Conclusion The oxygen quenching of phenanthrene phosphorescence has been employed to show the timedeceleration 0, migration in the methanol matrix. The dependences of the oxidation rate constant and of the inverse jumping time of oxygen molecule on the preliminary annealing time are the same. The rate constant coincides with the diffusion constant in order of magnitude. Thus, the
ofoxygenmigration
379
slowed down 0, migration contributes importantly to the time dependence of the rate constant.
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