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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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. 6. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Conclusion 20 (1982) 281. 1151 J.M. McBride, Accounts Chem. Res. 16 (1983) 304. The oxygen quenching of phenanthrene phosI161 G. Pfister and H. Sher, Advan. Phys. 27 (1978) 747. phorescence has been employed to show the timeW.R. Schneider and R. 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. and of the inverse jumping time of oxygen moleI191 W.P. Helman and K. Funabashi, J. Chem. Phys. 71(1979) cule on the preliminary annealing time are the 2458. same. The rate constant coincides with the diffuI201 G. Zumofen, J. KIafter and A. Blumen, J. Chem. Phys. 79 (1983) 5131. sion constant in order of magnitude. Thus, the