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Decay kinetics of the isothermal luminescence in nonpolar binary mixtures at 77 K
Radial. Phys. Chem. Rinted
in Great
Vol.26,
No. 6, pp. 657-662,
OM-5724185 0 1985
1985
$3.00
+ .OO
Pergamon F’ress Ltd.
Britain.
DECAY KINETICS OF THE ISOTHERMAL LUMINESCENCE IN NONPOLAR BINARY MIXTURES AT 77 K-f A. F’LONKA, J. MAYER, W. LEFIK~~~ J. KROH The Institute of Applied Radiation Chemistry, Technical University, 93-590 Md2, Wr6blewskiego 15, Poland (Received 11 May 1984)$ Abstract-The isothermal luminescence of y-irradiated frozen 3-methylpentane (3MP)-methylcyclohexane (MCH) mixtures (3MP mole fraction from 0 to 0.96) containing naphthalene (Nph) was investigated at 77 K. At high Nph concentration (2.5 x lo-* mol dme3) the luminescence is due to molecular ion recombination by tunnelling. In the soft glass (0.96 mole fraction 3MP) at low Nph concentration (10V3 mol dmm3) electron thermal detrapping seems to contribute to the emission. The experimental decay curves were interpreted based on the Bagdasar’yan relation as well as the continuous-timerandom-walk formalism (assuming a first-order rate equation with a time dependent rate constant of the form /c(t) = B r(n-l)),
INTRODUCTION THE RECOMBINATION of trapped charges formed by y-irradiation of organic solids gives rise to a deferred luminescence which may be observable for several hours at the temperature of irradiation. It has been known for a long time that the decay kinetics of the isothermal luminescence (ITL) can be represented by the Debye-Edwards kinetic law”’
(1)
I, = pt-“,
where Z, is the intensity of the luminescence at time t after the end of irradiation and p, m are constants dependent on charge distribution. Usually the value of m is 1.0 2 0.1, provided the time of irradiation is very short in respect to the time elapsing between the end of y-ray exposure and the beginning of measurements.(2-5) Debye and Edwards”’ derived eqn (1) for spatially, but not Coulombically correlated charge pairs using a diffusion equation. A modification of the above theory within the framework of diffusion model has been proposed by Abel1 and Mozumder.@) Hamill”’ applied eqn (1) to the recombination of Coulombically correlated charge pairs in rigid lowdielectric media and established the validity of the t Dedicated to Professor Schulte-Frohlinde on the occasion of his 60th anniversary. $ Due to a fire at the typesetting facility, this paper had to be replaced causing a delay in its publication.
Debye-Edwards law, extending its range to both shorter and longer irradiation times. Experimental evidence was found that the decay kinetics of ITL in y-irradiated organic solids is independent of temperature from 4.2 K to 77 K.@-‘“) Motivated by these data Tachiya and Mozumder’“’ and Charlesby (I*) formulated phenomenological models for recombination luminescence at low temperature by trapped electron tunnelling. When the recombination takes place by tunnelling the intensity of luminescence is considered to be proportional to tern as given by eqn (1) over a wide time range with m = 1. An interesting modification of the ITL tunnelling model,‘“’ assuming that the frequency factor in the rate reaction is temperature dependent, was derived by Racz.“3’ Equation (1) can be very easily rearranged to the well known empirical Bagdasar’yan relation”4~15’ (2)
IO/Z, = 1 + p (t - to),
where lo and Z, denote intensities of luminescence at the beginning of observation to and at the time of measurement t, respectively; p denotes a constant related to the rate of ITL decay. For a short irradiation time (much less than to) p should be proportional to l/t,. For longer exposures the p-value seems to be a function of irradiation time as well as dose rate.(3*16)It is possible to prove within the framework of the Tachiya and Mozumder model”” that p is dependent on the distribution function of recombining ion ~a&..(~~) 657
A. PLONKAet ul.
658
Equation (2) was reported(“) to be very useful for representation of ITL decay in v-irradiated organic solids at 77 K. A few years ago Hamill et ~f.(‘~,~‘)proposed applying the continuous-time-random-walk (CTRW) formalism of Scher-Montroll(2’) to the interpretation of trapped electron, e; decay. Plonka et ~1.‘~~)using CTRW formalism with a time dependent rate constant of the form (3)
k(t) = B t(='-'),
where B and 0 < a < 1 are constants that satisfactorily describe the radioluminescence kinetics of yirradiated frozen LiCl solutions. It has been found”” that for e,- tunnelling reaction with scavenger at 77 K (Yequals ca 0.1, whereas for a diffusion assisted process a much higher a-value, -0.6, is required. The purpose of the present work is: (i) to find out how the type of recombining pairs (electroncation or anion-cation) can influence the ITL decay kinetics at 77 K as described by either eqn (2) or CTRW formalism; (ii) to analyse the ITL decay at 77K in nonpolar binary matrices of different viscosities (q). It is knownc3’ that for a “hard” glass, eg. methylcyclohexane (q - 1O”P at 77 K’23’), eqns (1) and (2) were found to be valid whereas for a “softer” matrix, eg. 3-methylpentane (q - 1012P at 77 K(23)), these relations do not always give satisfactory results. In the latter system ITL decay was suggested to correspond to the electron thermal detrapping(3.‘7.24.*“.
EXPERIMENTAL The solvents, 3-methylpentane (3MP) and methylcyclohexane (MCH), both Fluka pure grade, were chromatographed through a freshly activated silica gel column and kept under argon. Naphthalene (Nph), analytical grade, was used as received. The solution was deaerated by bubbling the pure argon (or helium) through it. The matrix disc samples (about 2 mm thick, 10 mm in diameter) supported in washerlike rings without optical windows were prepared under the surface of liquid nitrogen. The samples before irradiation were kept for 600 s at 77 K. The irradiations with 6oCo y-rays were carried out in liquid nitrogen at a dose rate of ca 0.25 Gy s-l. The dose used equalled 37.5 Gy. The total light from y-irradiated samples was analysed at 77 K using radioluminescence equipment described previously. (26)During all the procedure the samples were kept in the dark. The emission
measurements started 180 s after the end of y-irradiation. The ITL decay was observed in most cases over 1800 s.
RESULTS AND DISCUSSION In the course of our study the ITL decay was measured at 77 K in the 3MP-MCH mixtures containing Nph as a scavenger. 3MP content in the matrix varied from 0 to 0.96 mole fraction (m.f.), whereas only two Nph concentrations were applied, i.e. 10m3mol dme3 and 2.5 x low2 mol dm-“. The decay of ITL can be expressed by a linear Badgasar’yan relationship [eqn (2)] up to 1800 s although sometimes slight deviations were observed, particularly in the case of “softer” glasses containing low Nph concentration (Fig. 1). Then the pparameter was calculated taking into account the linear part of the curve. In order to check the influence of matrix composition on ITL decay two parameters were chosen, i.e. lo and B [see eqn (2)]. The intensity of emission is proportional to the rate of charge recombination. The dependencies of IO and p on the matrix composition for two Nph concentrations are shown in Fig. 2. Each point is an average value of at least three independent measurements. The data presented in Fig. 2 lead to the following conclusions: (i) There is no significant influence of matrix composition on both IO and B values for mixtures containing higher Nph concentration ([Nph] = 2.5 x lo-‘mol dmm3). In these cases one may expect that all trapped electrons e; produced by the irradiation are scavenged by Nph’27-29’ and that ITL is due to the recombination of solute ion pairs by electron tunnelling.07*30*31’ (ii) At low Nph concentration lo slightly increases with 3MP content in the matrix, whereas p values seem to be constant up to ca 0.80 m.f. of 3MP. In the presence of 10e3 mol dme3 Nph the e;-cation recombination contributes to the ITL.07,30*3” The 3MP concentration effect on the IO value may result from two reasons. First, the yield of e; in 3MP at 77 K is higher that that for MCH.‘32’ Second, the rate of e; reaction should be viscosity dependent, assuming that the e; thermal detrapping may contribute to ITL in particular at high 3MP content.‘3*24*25’The latter effect may be responsible for the sudden decrease of p in the case of matrix containing 0.96 m.f. of 3MP. As was mentioned before, the p change suggests a different distance distribution of ion pairs in the softest mixture compared with harder glasses.“” One might expect such an effect because the temperature of irradiation and examination in this case ought to be very
Decay kinetics of isothermal luminescence
659
close to the glass transition point of the matrix under consideration.‘23) It is worth mentioning that the glass transition temperature of pure 3MP is equal to -77 K. (23)Taking into account data shown in Fig. 2 we decided to apply CTRW formalism’1921)to ITL decay for MCH glasses and matrices containing O.% m.f. of 3MP. Following the calculations given in Ref. (22) the intensity of ITL at time t, Z, should be proportional to the rate of charge recombination, -dn(,jdt
Fig. 1. The ITL decays at 77 K in hydrocarbon matrices as represented by Bagdasar’yan relation (2) 0-MCH glass in the presence of 10Y3 mol dmm3 Nph [curve (I)]. X-MCH3MP (0.96 m.f. of 3MP) in the presence of lo-‘mol dm-’ Nph [curve (3)]. l -MCH glass in the presence of 2.5 x 10-2mol dmm3 Nph (curve (2)). OMCH3MP (0.96 m.f. of 3MP) in the presence of 2.5 x lo-‘mol dmW3 Nph [curve (4)].
-
(5)
!!!Q = k(t)*rq,,, dt
where k(t) denotes the time dependent rate constant given by eqn (3). Integration eqn (5) one obtains
I(j0.u.)
xd
where K denotes the proportionality factor, whereas n(,, represents the concentration of charge pairs. The charge recombination rate is assumed to be a first order reaction
or xl0
9
n(,)
=
nco exp
B - a P
( > .
It is worth mentioning that (6) describes quite well the decay of e; in aqueous glasses.(33S34)Combining eqns (4)-(6) one obtains
E
IsI 0.009
0
Q
-.+___--~
(a)
0
(7)
Z, = a t@-‘) exp
B - -P ci (
, >
0
where a = robin is a constant proportional to the concentration of charge pairs at lo. The solid lines in Fig. 3 correspond to the values calculated according to (7) with a, B and a parameters given in Table 1. At first one can conclude that a parameters are almost the same except for the 0.96 m.f. 3MP matrix in the presence of 10e3 mol drne3 Nph, where e; a5 thermal detrapping may contribute to ITL. X3MP The numerical values of the B and a parameters allow us to rind the distribution of reaction conFig. 2. The influence of matrix composition on the p parameter (a) and luminescence intensity la (b) at time to = stants. The lower the numerical value of a the wider 180 s after the end of y-irradiation at 77 K. O-2.5 X the distribution function f(k); for a = 1 one gets 10-Zmol drne3 Noh (x lo-* luminescence scale). Omonoexponential decay and B corresponds to the 10-3mol dm-3 Nph (X low9 luminescence scale). For time-independent rate constant known in classical comparison the semilogarithmic dependence of the viscosity reciprocal on matrix composition is shown - - -.(23) kinetics. 73
f
I
I
L
A. PLONKA et al.
660
TABLE ~.THEINFLUENCEOFMATRIXCOMPOSITIONONTHE RATEPARAMETERS ACCORDINGTOEQ. (7)
No. (1)
(2) (3) (4)
MCH, Nph (10m3 mol dm-‘) MCH, Nph (2.5 x lo-* mol dme3) MCH3MP (x = 0.96), Nph (10m3 mol dm-‘) MCHJMP (x = O.%), Nph (2.5 x IO-’ mol dmm3)
In order to find the distribution function f(k) one should regard relation (6) as the result of superposition of many first order decays (8)
l-
f(k) exp( - kt) dk = exp
In this way, one obtains the distribution of decay constants f(k) as the inverse Laplace a transform of the right-hand side of (8). Using the simple saddle point method’2’,35’ one obtained the normalized function f(k) in the analytical form r( l/a) f(k) =
(91
V[Tr(P-
cu)][
x t exp{ -(l
ho
CY
a
Matrix
1
a/2(1-cd
- a) [~]““-a’},
OFITL
DECAY
(SF-)
2)
340.6 4204.2
0.339 0.330
0.1522 0.1029
3.593 12.192
241.4
0.677
0.0869
1.626
0.309
0.1261
8.857
5478
,ro =
lffit (- $$qojdt
= (;)“a
I (d)
denotes the average lifetime of electron in the matrix (Table 1) and I (l/o&-the gamma function. Average lifetimes of electron 7. in the matrices containing high Nph concentration are quite long, suggesting multiple electron trapping by scavenger before recombination with the cation takes place. The distribution functions of f(k) calculated from ITL decay data (Table 1) are shown in Fig. 4. It is clearly seen that ITL in 0.96 m.f. of 3MP matrix containing 10m3 mol drne3 Nph corresponds to much higher rate constants than in the other three systems. The above results can be explained, assuming some contribution of the electron thermal detrap-
Fig. 3. The ITL decays at 77 K in hydrocarbon matrices as represented by eqn (7), the kinetic parameters are listed in Table 1 (see Fig. 1 or Table 1 for key to the curves).
for which
661
Decay kinetics of isothermal luminescence
The rate constant of electron tunnelling through a rectangular barrier of the height LE (eV) and width r (A) may be written asc3@: k = v exp[ - 1.035 AZ?‘*rl.
(10)
1 l6'
66
Ki3
n-4
lo-3
1.
(o-2 m-l k,,'
Fig. 4. Distribution of electron reactivities f(k) deduced from ITL decay curves found for hydrocarbon matrices. (see Fig. 1 or Table 1 for key to the curves).
Assuming the frequency factor v = 1013s-’ and AE = 0.5 eV , the distribution of distances, P(r) can be found for a given f(k) (Fig. 5). Again for the above mentioned three matrices, the distance distribution is very similar, whereas in the case of the softest glass the exceptionally narrow distribution function was obtained. Comparing both ITL decay kinetic equations one can conclude that the p-value [eqn (2)] and Bparameter [eqn (7)] show similar dependence on the matrix composition or reaction mechanism (Fig. 1, Table 1). Certainly the interpretation based on CTRW formalism gives a deeper insight into the mechanism involved than does the Bagdasar’yan relation.
ping in the former
matrix whereas in the latter one pure electron tunnelling should be the most probable mechanism of charge transfer. In these three glasses ITL is due either to the reaction of molecular ions or to the e; - cation recombination in “hard” matrix (MCH).
REFERENCES 1. P. DEBYE and J. 0. EDWARDS,J. Chem. Phys. 1952,
20, 236. 2.
F . KIEFFER,J . KLEIN, C . LAPERSONNE-MEYER and M. MAGAT, J. Chem. Sot. Faraday Discuss. 1977,63,55. 3. P. CONNER, F. KIEFFER, C. LAPERSONNE-MEYER and J. RIGAUT, in Radiation Research (Edited by 0. F. Nygard, H. I. Adler and W. K. Sinclair), p. 426. Academic Press, New York, 1975. 4. J. BULLOTand A. C. ALBRECHT,J. Chem. Phys. 1969, 51, 2220. 5. M. BAZIN, M. AUBAILLY and R. SANTAS, J. Chem. Phys. 1977, 67, 5070. 6. G. C. ABELLand A. MOZUMDER,J. Chem. Phys. 1972,
46,4079. 7. W. H. HAMILL, J. Chem. Phys. 1979, 71, 140. 8. F. KIEFFER, C. MEYER and J. RIGAUT, Chem. Phys. Lett. 1971, 11, 359. 9. F. KIEFFER, C. LAPERSONNE-MEYERand J. RIGALJT, In?. J. Radial. Phys. Chem. 1974, 6, 79. 10. M. WYP~CH and R. LESZCZ~~SKI, Radiochem. Ra-
dioanal. Lett. 1978, 36, 309.
;::: (4)
!t 2)
60
r,A
Fig. 5. Distribution of electron recombination distances P(r) deduced from ITL decay curves found for hydrocarbon matrices (see Fig. 1 or Table 1 for key to the curves).
11. M. TACHIYA and A. MOZUMDER. Chem. Phvs. Lett. 1975, 34, 77. 12. A. CHARLESBY,Radiat. Phys. Chem. 1981, 17, 399. 13. 2. RAcz, J. Luminescence 1981. 23. 255. 14. KH. S. BAGDASAR’YAN,R. I. M~UT&KAYA and YA. V. KOVALEV, Khim. Vysok, Energii 1967, 1, 127. 15. KH. S. BAGDASAR’YAN,Dokl. Acad. NaukSSSR 1980,
255, 1150. 16. B. G. ERSHOVand F. KIEFFER. Chem. Phvs. Left. 1974, 25, 576. 17. J. MAYER, M. SZADKOWSKA-NICZE and J. KROH, Radiat. Phys. Chem. 1980, 15, 643. 18. J. KRO~ and J. MAYER,. Ini J. Radiat. Phys. Chem. 1974, 6, 423. 19. W. H. HAMILL~I~~K. FUNABASHI,Phys. Rev. B 1977, 16, 5523.
662
A. PLONKAet al.
20. W. H. HAMILL, J. Phys. Chem. 1978, 82, 2073. 21. H. SCHER and E. W. MONTROLL.Phvs. Rev. B 1975, 12, 2455. 22. A. PLONKA, M. WYPYCH, W. LEFIKand J. KROH, Rudiat. Phys. Chem. 1984, 23, 715. 23. A. C. LING and J. E. WILLARD, .I. Phys. Chem. 1968, 72, 3349; 1968, 72, 1918. 24. D. CECCALDIand J. BULLOT, Chew Phys. Lett. 1971, 9, 551. 25. J. BULLOT, D. CECCALDIand 0. GALLAIS, Can. J. Chem. 1973, 51, 3428. 26. J. KROH and M. WYPYCH, Nukleonika 1971, 16, 521. 27. W. H. HAMILLin Radical Ions (Edited by E. T. Kaiser and L. Kevan), John Wiley, New York, 1968. 28. J. B. GALIVAN and W. H. HAMILL, J. Chem. Phys. 1966, 44, 1279, 2378.
29. K. OKA, H. YAMAZAKIand S. SHIDA,Bull. Chem. Sot. Japan 1973, 46, 2347. 30. J. MAYER, M. SZADKOWSKAand J. KROH, Faraday Discus. Chem. Sot. 1977, 63, 91. 31. F. KIEFFER, N. V. KLASSEN and C. LAPERSONNEMEYER, J. Luminescence 1979. 20. 17. 32. T. KIMURA, N. BREMERand J. E. WILLARD, J. Chem. Phys. 1977, 66, 1127. 33. A. P~ONKA,W. LEFlKand J. KROH, Chc~tn.Phys. Lett. 1979, 62, 271. 34. A. PLONKA,T. S. KOWALSKI,W. LEFIK and J. KROH. Radiut. Phys. Chem. 1981, 17, 375. 35. C. K. MAJUMDAR,Solid State Comm. 1971, 9, 1087. 36. Cz. STRADOWSKIand J. KROH. Radial. Phys. Chem. 1978, 12, 17.5.
in Great
Vol.26,
No. 6, pp. 657-662,
OM-5724185 0 1985
1985
$3.00
+ .OO
Pergamon F’ress Ltd.
Britain.
DECAY KINETICS OF THE ISOTHERMAL LUMINESCENCE IN NONPOLAR BINARY MIXTURES AT 77 K-f A. F’LONKA, J. MAYER, W. LEFIK~~~ J. KROH The Institute of Applied Radiation Chemistry, Technical University, 93-590 Md2, Wr6blewskiego 15, Poland (Received 11 May 1984)$ Abstract-The isothermal luminescence of y-irradiated frozen 3-methylpentane (3MP)-methylcyclohexane (MCH) mixtures (3MP mole fraction from 0 to 0.96) containing naphthalene (Nph) was investigated at 77 K. At high Nph concentration (2.5 x lo-* mol dme3) the luminescence is due to molecular ion recombination by tunnelling. In the soft glass (0.96 mole fraction 3MP) at low Nph concentration (10V3 mol dmm3) electron thermal detrapping seems to contribute to the emission. The experimental decay curves were interpreted based on the Bagdasar’yan relation as well as the continuous-timerandom-walk formalism (assuming a first-order rate equation with a time dependent rate constant of the form /c(t) = B r(n-l)),
INTRODUCTION THE RECOMBINATION of trapped charges formed by y-irradiation of organic solids gives rise to a deferred luminescence which may be observable for several hours at the temperature of irradiation. It has been known for a long time that the decay kinetics of the isothermal luminescence (ITL) can be represented by the Debye-Edwards kinetic law”’
(1)
I, = pt-“,
where Z, is the intensity of the luminescence at time t after the end of irradiation and p, m are constants dependent on charge distribution. Usually the value of m is 1.0 2 0.1, provided the time of irradiation is very short in respect to the time elapsing between the end of y-ray exposure and the beginning of measurements.(2-5) Debye and Edwards”’ derived eqn (1) for spatially, but not Coulombically correlated charge pairs using a diffusion equation. A modification of the above theory within the framework of diffusion model has been proposed by Abel1 and Mozumder.@) Hamill”’ applied eqn (1) to the recombination of Coulombically correlated charge pairs in rigid lowdielectric media and established the validity of the t Dedicated to Professor Schulte-Frohlinde on the occasion of his 60th anniversary. $ Due to a fire at the typesetting facility, this paper had to be replaced causing a delay in its publication.
Debye-Edwards law, extending its range to both shorter and longer irradiation times. Experimental evidence was found that the decay kinetics of ITL in y-irradiated organic solids is independent of temperature from 4.2 K to 77 K.@-‘“) Motivated by these data Tachiya and Mozumder’“’ and Charlesby (I*) formulated phenomenological models for recombination luminescence at low temperature by trapped electron tunnelling. When the recombination takes place by tunnelling the intensity of luminescence is considered to be proportional to tern as given by eqn (1) over a wide time range with m = 1. An interesting modification of the ITL tunnelling model,‘“’ assuming that the frequency factor in the rate reaction is temperature dependent, was derived by Racz.“3’ Equation (1) can be very easily rearranged to the well known empirical Bagdasar’yan relation”4~15’ (2)
IO/Z, = 1 + p (t - to),
where lo and Z, denote intensities of luminescence at the beginning of observation to and at the time of measurement t, respectively; p denotes a constant related to the rate of ITL decay. For a short irradiation time (much less than to) p should be proportional to l/t,. For longer exposures the p-value seems to be a function of irradiation time as well as dose rate.(3*16)It is possible to prove within the framework of the Tachiya and Mozumder model”” that p is dependent on the distribution function of recombining ion ~a&..(~~) 657
A. PLONKAet ul.
658
Equation (2) was reported(“) to be very useful for representation of ITL decay in v-irradiated organic solids at 77 K. A few years ago Hamill et ~f.(‘~,~‘)proposed applying the continuous-time-random-walk (CTRW) formalism of Scher-Montroll(2’) to the interpretation of trapped electron, e; decay. Plonka et ~1.‘~~)using CTRW formalism with a time dependent rate constant of the form (3)
k(t) = B t(='-'),
where B and 0 < a < 1 are constants that satisfactorily describe the radioluminescence kinetics of yirradiated frozen LiCl solutions. It has been found”” that for e,- tunnelling reaction with scavenger at 77 K (Yequals ca 0.1, whereas for a diffusion assisted process a much higher a-value, -0.6, is required. The purpose of the present work is: (i) to find out how the type of recombining pairs (electroncation or anion-cation) can influence the ITL decay kinetics at 77 K as described by either eqn (2) or CTRW formalism; (ii) to analyse the ITL decay at 77K in nonpolar binary matrices of different viscosities (q). It is knownc3’ that for a “hard” glass, eg. methylcyclohexane (q - 1O”P at 77 K’23’), eqns (1) and (2) were found to be valid whereas for a “softer” matrix, eg. 3-methylpentane (q - 1012P at 77 K(23)), these relations do not always give satisfactory results. In the latter system ITL decay was suggested to correspond to the electron thermal detrapping(3.‘7.24.*“.
EXPERIMENTAL The solvents, 3-methylpentane (3MP) and methylcyclohexane (MCH), both Fluka pure grade, were chromatographed through a freshly activated silica gel column and kept under argon. Naphthalene (Nph), analytical grade, was used as received. The solution was deaerated by bubbling the pure argon (or helium) through it. The matrix disc samples (about 2 mm thick, 10 mm in diameter) supported in washerlike rings without optical windows were prepared under the surface of liquid nitrogen. The samples before irradiation were kept for 600 s at 77 K. The irradiations with 6oCo y-rays were carried out in liquid nitrogen at a dose rate of ca 0.25 Gy s-l. The dose used equalled 37.5 Gy. The total light from y-irradiated samples was analysed at 77 K using radioluminescence equipment described previously. (26)During all the procedure the samples were kept in the dark. The emission
measurements started 180 s after the end of y-irradiation. The ITL decay was observed in most cases over 1800 s.
RESULTS AND DISCUSSION In the course of our study the ITL decay was measured at 77 K in the 3MP-MCH mixtures containing Nph as a scavenger. 3MP content in the matrix varied from 0 to 0.96 mole fraction (m.f.), whereas only two Nph concentrations were applied, i.e. 10m3mol dme3 and 2.5 x low2 mol dm-“. The decay of ITL can be expressed by a linear Badgasar’yan relationship [eqn (2)] up to 1800 s although sometimes slight deviations were observed, particularly in the case of “softer” glasses containing low Nph concentration (Fig. 1). Then the pparameter was calculated taking into account the linear part of the curve. In order to check the influence of matrix composition on ITL decay two parameters were chosen, i.e. lo and B [see eqn (2)]. The intensity of emission is proportional to the rate of charge recombination. The dependencies of IO and p on the matrix composition for two Nph concentrations are shown in Fig. 2. Each point is an average value of at least three independent measurements. The data presented in Fig. 2 lead to the following conclusions: (i) There is no significant influence of matrix composition on both IO and B values for mixtures containing higher Nph concentration ([Nph] = 2.5 x lo-‘mol dmm3). In these cases one may expect that all trapped electrons e; produced by the irradiation are scavenged by Nph’27-29’ and that ITL is due to the recombination of solute ion pairs by electron tunnelling.07*30*31’ (ii) At low Nph concentration lo slightly increases with 3MP content in the matrix, whereas p values seem to be constant up to ca 0.80 m.f. of 3MP. In the presence of 10e3 mol dme3 Nph the e;-cation recombination contributes to the ITL.07,30*3” The 3MP concentration effect on the IO value may result from two reasons. First, the yield of e; in 3MP at 77 K is higher that that for MCH.‘32’ Second, the rate of e; reaction should be viscosity dependent, assuming that the e; thermal detrapping may contribute to ITL in particular at high 3MP content.‘3*24*25’The latter effect may be responsible for the sudden decrease of p in the case of matrix containing 0.96 m.f. of 3MP. As was mentioned before, the p change suggests a different distance distribution of ion pairs in the softest mixture compared with harder glasses.“” One might expect such an effect because the temperature of irradiation and examination in this case ought to be very
Decay kinetics of isothermal luminescence
659
close to the glass transition point of the matrix under consideration.‘23) It is worth mentioning that the glass transition temperature of pure 3MP is equal to -77 K. (23)Taking into account data shown in Fig. 2 we decided to apply CTRW formalism’1921)to ITL decay for MCH glasses and matrices containing O.% m.f. of 3MP. Following the calculations given in Ref. (22) the intensity of ITL at time t, Z, should be proportional to the rate of charge recombination, -dn(,jdt
Fig. 1. The ITL decays at 77 K in hydrocarbon matrices as represented by Bagdasar’yan relation (2) 0-MCH glass in the presence of 10Y3 mol dmm3 Nph [curve (I)]. X-MCH3MP (0.96 m.f. of 3MP) in the presence of lo-‘mol dm-’ Nph [curve (3)]. l -MCH glass in the presence of 2.5 x 10-2mol dmm3 Nph (curve (2)). OMCH3MP (0.96 m.f. of 3MP) in the presence of 2.5 x lo-‘mol dmW3 Nph [curve (4)].
-
(5)
!!!Q = k(t)*rq,,, dt
where k(t) denotes the time dependent rate constant given by eqn (3). Integration eqn (5) one obtains
I(j0.u.)
xd
where K denotes the proportionality factor, whereas n(,, represents the concentration of charge pairs. The charge recombination rate is assumed to be a first order reaction
or xl0
9
n(,)
=
nco exp
B - a P
( > .
It is worth mentioning that (6) describes quite well the decay of e; in aqueous glasses.(33S34)Combining eqns (4)-(6) one obtains
E
IsI 0.009
0
Q
-.+___--~
(a)
0
(7)
Z, = a t@-‘) exp
B - -P ci (
, >
0
where a = robin is a constant proportional to the concentration of charge pairs at lo. The solid lines in Fig. 3 correspond to the values calculated according to (7) with a, B and a parameters given in Table 1. At first one can conclude that a parameters are almost the same except for the 0.96 m.f. 3MP matrix in the presence of 10e3 mol drne3 Nph, where e; a5 thermal detrapping may contribute to ITL. X3MP The numerical values of the B and a parameters allow us to rind the distribution of reaction conFig. 2. The influence of matrix composition on the p parameter (a) and luminescence intensity la (b) at time to = stants. The lower the numerical value of a the wider 180 s after the end of y-irradiation at 77 K. O-2.5 X the distribution function f(k); for a = 1 one gets 10-Zmol drne3 Noh (x lo-* luminescence scale). Omonoexponential decay and B corresponds to the 10-3mol dm-3 Nph (X low9 luminescence scale). For time-independent rate constant known in classical comparison the semilogarithmic dependence of the viscosity reciprocal on matrix composition is shown - - -.(23) kinetics. 73
f
I
I
L
A. PLONKA et al.
660
TABLE ~.THEINFLUENCEOFMATRIXCOMPOSITIONONTHE RATEPARAMETERS ACCORDINGTOEQ. (7)
No. (1)
(2) (3) (4)
MCH, Nph (10m3 mol dm-‘) MCH, Nph (2.5 x lo-* mol dme3) MCH3MP (x = 0.96), Nph (10m3 mol dm-‘) MCHJMP (x = O.%), Nph (2.5 x IO-’ mol dmm3)
In order to find the distribution function f(k) one should regard relation (6) as the result of superposition of many first order decays (8)
l-
f(k) exp( - kt) dk = exp
In this way, one obtains the distribution of decay constants f(k) as the inverse Laplace a transform of the right-hand side of (8). Using the simple saddle point method’2’,35’ one obtained the normalized function f(k) in the analytical form r( l/a) f(k) =
(91
V[Tr(P-
cu)][
x t exp{ -(l
ho
CY
a
Matrix
1
a/2(1-cd
- a) [~]““-a’},
OFITL
DECAY
(SF-)
2)
340.6 4204.2
0.339 0.330
0.1522 0.1029
3.593 12.192
241.4
0.677
0.0869
1.626
0.309
0.1261
8.857
5478
,ro =
lffit (- $$qojdt
= (;)“a
I (d)
denotes the average lifetime of electron in the matrix (Table 1) and I (l/o&-the gamma function. Average lifetimes of electron 7. in the matrices containing high Nph concentration are quite long, suggesting multiple electron trapping by scavenger before recombination with the cation takes place. The distribution functions of f(k) calculated from ITL decay data (Table 1) are shown in Fig. 4. It is clearly seen that ITL in 0.96 m.f. of 3MP matrix containing 10m3 mol drne3 Nph corresponds to much higher rate constants than in the other three systems. The above results can be explained, assuming some contribution of the electron thermal detrap-
Fig. 3. The ITL decays at 77 K in hydrocarbon matrices as represented by eqn (7), the kinetic parameters are listed in Table 1 (see Fig. 1 or Table 1 for key to the curves).
for which
661
Decay kinetics of isothermal luminescence
The rate constant of electron tunnelling through a rectangular barrier of the height LE (eV) and width r (A) may be written asc3@: k = v exp[ - 1.035 AZ?‘*rl.
(10)
1 l6'
66
Ki3
n-4
lo-3
1.
(o-2 m-l k,,'
Fig. 4. Distribution of electron reactivities f(k) deduced from ITL decay curves found for hydrocarbon matrices. (see Fig. 1 or Table 1 for key to the curves).
Assuming the frequency factor v = 1013s-’ and AE = 0.5 eV , the distribution of distances, P(r) can be found for a given f(k) (Fig. 5). Again for the above mentioned three matrices, the distance distribution is very similar, whereas in the case of the softest glass the exceptionally narrow distribution function was obtained. Comparing both ITL decay kinetic equations one can conclude that the p-value [eqn (2)] and Bparameter [eqn (7)] show similar dependence on the matrix composition or reaction mechanism (Fig. 1, Table 1). Certainly the interpretation based on CTRW formalism gives a deeper insight into the mechanism involved than does the Bagdasar’yan relation.
ping in the former
matrix whereas in the latter one pure electron tunnelling should be the most probable mechanism of charge transfer. In these three glasses ITL is due either to the reaction of molecular ions or to the e; - cation recombination in “hard” matrix (MCH).
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;::: (4)
!t 2)
60
r,A
Fig. 5. Distribution of electron recombination distances P(r) deduced from ITL decay curves found for hydrocarbon matrices (see Fig. 1 or Table 1 for key to the curves).
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