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An empirical equation for dose effect on trapped-electron formation
Volume 60. number I
CHEMICAL
PHYSICS LETTERS
15 December 1978
AN EMI’IRICAL EQUATION FOR DOSE EFFECT ON TRAPPEBELECIRON
FORMATION
Akira KIRA and Masashi lMAMURA T7e Institute of ph3x&l and Chemical Research. Wake-SC. Suitam 351. Japan Received 28 Augy& 1978
An empirical equation is proposed for the dose dependence of the trapped-electron concentration in yirradiated The equation, if suitabk vahxes are given to the parameters, fits the experimental data for organic glasses at 77 K.
glasses
L Introduction ‘Ihe concentration of trapped eIectrons in ‘y-irradiated organic glasses and alkaline ices at Iow temperature increases to a maximum and then decreases with increasing dose [l--8] _ This dose effect has been attributed to eIectron scavenging by radiation-induced radicals [2,9], or to the number of traps in a matrix [ 11, or to the dielectron formation [4] _ The only attempt of formulation for the dose effect has been made by Raitsimring et al. [IO] on the basis of the clielectron formation mechanism. In the present letter we propose an empirical equation for the dose effect which is convenient for practical use. Qualitatively, the equation seems to be consistent with a mechanism that electrons are removed by the tunneling to radiation-induced radicals.
I
OO
I
I
2
4 w x:0-=/(&
g-9
6
F& l_ EIectron concentration as a function of dose in MTHF glass at 77 K: o, OUTdata; 0, ESR data cited from ref- [6] (see text). Solid curve: eq. (1) with the parameter vaIues listed in table I. Broken curve: eq. (2) with A’ = 8.2 X 1O-‘g eT* g cm-’ and Q’ = 5.3 X lo-*’ eV-* g.
2 Data
The dose dependence of the trapped-electron concentration has been measured for alkanes [1,2,5, 681, alcohols [3,7], 2-methyltetrahydrofuran (MTHF) [6], triethylamine [6], and alkaline ices [4,10]_ Some of these data and our new ones are plotted in figs. l-_I, where the optical derrsity per centimeter, OD-!2-1 stands for the trapped-electron concentration_ In our experiments, deaerated samples sealed in 0.1 S- or 1S-mm thick Suprasil cells were irradiated at 77 K with Co-60 7 rays. The dose rate was 1.9 X 1O1* eVg_l min-L for an ethanol glass at 77K. 44
Fig. 2, E&x&on concentration as a function of dose in e-1 glass at 77 K: 0, our data; a, ref. [ 31 (see text). Solid curve: eq (1) with the values in table 1. Broken curve: eq. (2) with A’ = 5.9 X 1O-1g eV_’ g cm-l and d = 5.3 X 101’ eV_’ g_
Volume 60, number 1
CHEMIC_4L PHYSICS LMTERS
IS December 1978
3. EmpiFiml equation The solid curves drawn in the figures express the equation: OD-Q-l = A {I - exp(--ow)j
exp(-@w),
0)
where w denotes the dose in eV g-l; A, EYand 0 are constants to be adjusted and their actual values used for calculation of the curves are listed in table I. The agreemeat of the curves with the d.ata is satisfactory; therefore, eq_ (1) is proposed as an enrpiricat equatiw. Fig. 3. Electron concentrationas a function of dose in isobutanol glassat 77 K. The data are cited from ref. [3]. Solid cwve: eq. (I) with the valuesin table 1_
The broken curves in figs. 1 and 2 express ODCX
= A’w exp(-fz*w),
(2)
where AL*and d are constants. As shown in these examples, eq. (2) fits the data only in part. Mathematicaliy, eq. (2) is au approximation for eq. {I) in case that o! < 6, but actually oz> fl (see table 1). The first order &lacLaurin’s expansion of eq. (1) is OD-Q-l = Am, which is rewritten as [et I = Aon++,
0)
where ee denotes a molar extinction coefficient of trapped electrons. For very low doses the trappedelectron concentration is proportional to the dose, and is given by Fig. 4. Electron concentration as a function of dose: o, methylcyclohexaneat 77 K (our measurement)and o, 3_etbylpentaue at 77 K (ref. [2]). Solid cmvcs: eq. (I) with the valuesin tabk I.
As shown in fig. 1, the previous ESR data for MTHF [6], where the concentration is given in the spin number per gram, agree with our optical-absorption data if the former are multiplied by 2.3 X IO” g cm-l, which corresponds to a value of 1.3 X lo4 MSi cm-l for the molar extinction coefficient. The optical densities at 700 run in ethanol glass [3] were converted to the ones at 525 nrn by multiplying a v&ue of 4.04 for 0DSu/OD700 measured at a dose of 2.3 X FfIzO eV g-l , and joined to our data as shown in fig. 2. There are three sets of the data for methylcyclohexane &sses (refs. [1,8] and ours), but those do not agree one another; only ours are plotted in fig_ 4,
let]
= ~oPGeW/~~,
(4)
where G, is the intrinsic, not apparent, G value of the trapped electron, NA is the Avogadro number, and p is the density of the glass. Comparison of eq. (3) with eq. (4) leads to Table 1 The corMants in c+ (I) and GcEeestimatedusing e+ (5) Glass F-1 h%THF EtOH i-BuOH INCH 3EP
1300 525 555
1600
1600
a) P and B are in IO*’
A (Cm’)
a a)
83
Geee b)
117 108 16.1 10.1 6.1
6.2 5.2 6.7 14 22
L-8 o-2 1.7 5.5 7.0
A0 3-5 O-69 0.90 0.92
eV_’ g.
b) GeEei.5in 104&I-’ cm-l. 45
VoIurne60, number I
CHEhlICAL PHYSICS LETTERS
Geee= AoN~fl0~.
(5)
The values for Geee estimated using eq. (5) are also listed in table 1. Eq. (5) enables us to determine the value for Geee without measurement at extreme low doses and is considered to be useful for estimation of G, for h&b-LET irradiation; we found it difficuit to measure the trappedelectron concentration for lowdose irradiation with ion beams of high LET [I I]. In the high dose region the graph for eq. (1) shows a tailing decay, but the or% for the equation of Raits&ring et al. [lo] shows a descending decay. it should be remarked that not orily the data in the present paper but also those by Mtsimring et al. are featured by the tailing decay. For some glasses (e.g. methylcyclohexane [I] and alkaline ices {6] ) the descending decay had been reported, but the tailing decay was observed for the same gasses in later ex-
4. Possible mechanism The mathematical form of eq. (1) suggests that the equation can be reIated to the exponential relation for electron scavenging in matrices 1121: = wG-nI!Sl),
WI
where [et ] and [e; ] r, are the trapped-electron concentrations in the presence and absence of a scavenger S, respectively. and n is a capture constant specific to the soIute. Eq. (6) is compatibIe with both electrontunneling [ 12 ] and mobileelectroncapture models.
[ 131
Fust we wiI! consider a process that electrons freshIy produced during a very small increase in the dose are scavenged by products which have been accumufated during the preceding irradiation. The products can be either neutral or cation radicals. Combining eq. (6)witha differential expression for eIectron concentrations: d[e;]o one dfet
= 10pG~~ldw,
Gt&%ins I
idw = IOPG, exFf-np
IPI )/NA,
01
where nP is the capture constant of the product P. U it is assumed that 46
PI = ~OPG~W/N~~
03)
where GP Is the G vahre of the product, then eq. (7) is
integrated to give [et]
= (G&,G,)fl
-
exp(-lO~npGpw~N~)J.
(9)
The right-hand side of eq. (9) multiplied by ee equals in eq. (1) if a = 10p~zpGr$V~. It A II - exp(.-M] should be noted that A = lOpG,e,/~V~from eqs. (3) and (4). Eq. (8) is a very crude approximation for a presumption that the product concentration increases with the dose. It has been reported that the concentration of some radicals increases with the dose even in the dose region where the trappedelectron concentration decreases with increasing dose [3]. Since the product is removed by the reaction with electrons, eq. (8) does not hold rigorously; however, it can be a good approximation if Gp is larger than G,.
periments.
Zetl/fe&
15 December 1978
Eq. (9) indicates that the trappedefectron concentration continues to increase with the dose and converges on Ge/rzpGP. Qualitatively, the behavior wiil be the same even if a better approximation for the product concentration is used instead of eq. (8). Thus the process considered above is not sufficient to explain the decrease in the trapped-electron concentration in the high dose region. Eq. (7) which deals with a short time corresponding to dw, is pertinent to the mobileelectron capture where the reaction terminates within an apparent life time of the mobile electron, but incomplete for the electron tunneling, for which the following factors should also be taken into account. (1) T&e tunneling radius increases with time [12]; therefore, the tunneling may occur even long time after the electron formation. (2) The electron surviving the capture as expressed by eq. (7) can be scavenged by the product which appears within the tunneling radius on subequent irradiation. We consider that the second factor is mainly responsible for the decrease in the trapped-electron concentration. We have not succeeded yet in formulating this process, though eq. (1) suggests that exp(--gw) could represent it. Thus, our empiricai equation seems to be consistent qualitatively with the tunneling model. The possibility of partial contniution of the mobile. electron capture cannot be ruled out; however, it shouId be noted that the mobiLelectron capture
Volume 60, number
1
CHEMICAL
PHYSICS
cannot explab singly the decrease in the trappedelectron concentration. Tachiya 1141 has recently derived a theoretial equation for the electron tunneling to a radiation-induced product on the assumption that the product concentration is proportional to the dose. This theoretical equation indicates thar the trappedelectron concentration should increase and then decrease with increasing dose, though it is too complicated to compare directly with our empirical equation_
Adcnowkdgement We thank Dr. M. Tachiya for his deriving the theoretical equation for the tunneling model at our request.
LETTERS
15 Deazmber 1978
[2]
A. Ekstrom. R Suexuam and J.E. ‘Willard, J. Phys Chcm 74 (1970) 1888. 131 S. Fujii and J.E. Wild, 3. Phys Chem. 74 (1970) 4313. [4] J, Zinzbrick and L Kevan, J. Am Chem. Sot 89 (1967) 2483. [S] J. Lin, K. Tsuji and F. Williams, J. Am. Chem. Sot 90 (1968) 2766. [61 D-p- Olinand L, Kevan, J. Chem. Phys 55 (1971) 2696. [7] T. Sasaki, S. Ohno and K. Kawatsrira, Chem. Letters (1972) 91. [S] G. Dolivo and T. Gzuman, Radiit. Phys Chem. 10 (1977) 207. [9] D-P. Lin and J-E. Wiid, J. Phys Chem. 78 (1974) 1135. [lo] A.M. Raitsimring, R-1. Samilova and Yu.D. Tsvetkov, Radiat. Phys. Chem. 10 (1977) 177. [llj A. Kira, M. Matsui and M. Lmamura, ICPR Cyclotron progr. Rept- 11 (1977) 124. [12] 3. Miller, J- Chem. Phys 56 (1972) 5173. [ 131 R.K. Wolff, MJ. Bronskill and J-W. Hunt, 3. Chem. Phys 53 (1970) 4211. [ 141 M. Tachiya, private communication_
References [ 11 Ed. !3hirom and J-E_ Wi, (1968) 2184.
J. Am. Chem. Sot 90
47
CHEMICAL
PHYSICS LETTERS
15 December 1978
AN EMI’IRICAL EQUATION FOR DOSE EFFECT ON TRAPPEBELECIRON
FORMATION
Akira KIRA and Masashi lMAMURA T7e Institute of ph3x&l and Chemical Research. Wake-SC. Suitam 351. Japan Received 28 Augy& 1978
An empirical equation is proposed for the dose dependence of the trapped-electron concentration in yirradiated The equation, if suitabk vahxes are given to the parameters, fits the experimental data for organic glasses at 77 K.
glasses
L Introduction ‘Ihe concentration of trapped eIectrons in ‘y-irradiated organic glasses and alkaline ices at Iow temperature increases to a maximum and then decreases with increasing dose [l--8] _ This dose effect has been attributed to eIectron scavenging by radiation-induced radicals [2,9], or to the number of traps in a matrix [ 11, or to the dielectron formation [4] _ The only attempt of formulation for the dose effect has been made by Raitsimring et al. [IO] on the basis of the clielectron formation mechanism. In the present letter we propose an empirical equation for the dose effect which is convenient for practical use. Qualitatively, the equation seems to be consistent with a mechanism that electrons are removed by the tunneling to radiation-induced radicals.
I
OO
I
I
2
4 w x:0-=/(&
g-9
6
F& l_ EIectron concentration as a function of dose in MTHF glass at 77 K: o, OUTdata; 0, ESR data cited from ref- [6] (see text). Solid curve: eq. (1) with the parameter vaIues listed in table I. Broken curve: eq. (2) with A’ = 8.2 X 1O-‘g eT* g cm-’ and Q’ = 5.3 X lo-*’ eV-* g.
2 Data
The dose dependence of the trapped-electron concentration has been measured for alkanes [1,2,5, 681, alcohols [3,7], 2-methyltetrahydrofuran (MTHF) [6], triethylamine [6], and alkaline ices [4,10]_ Some of these data and our new ones are plotted in figs. l-_I, where the optical derrsity per centimeter, OD-!2-1 stands for the trapped-electron concentration_ In our experiments, deaerated samples sealed in 0.1 S- or 1S-mm thick Suprasil cells were irradiated at 77 K with Co-60 7 rays. The dose rate was 1.9 X 1O1* eVg_l min-L for an ethanol glass at 77K. 44
Fig. 2, E&x&on concentration as a function of dose in e-1 glass at 77 K: 0, our data; a, ref. [ 31 (see text). Solid curve: eq (1) with the values in table 1. Broken curve: eq. (2) with A’ = 5.9 X 1O-1g eV_’ g cm-l and d = 5.3 X 101’ eV_’ g_
Volume 60, number 1
CHEMIC_4L PHYSICS LMTERS
IS December 1978
3. EmpiFiml equation The solid curves drawn in the figures express the equation: OD-Q-l = A {I - exp(--ow)j
exp(-@w),
0)
where w denotes the dose in eV g-l; A, EYand 0 are constants to be adjusted and their actual values used for calculation of the curves are listed in table I. The agreemeat of the curves with the d.ata is satisfactory; therefore, eq_ (1) is proposed as an enrpiricat equatiw. Fig. 3. Electron concentrationas a function of dose in isobutanol glassat 77 K. The data are cited from ref. [3]. Solid cwve: eq. (I) with the valuesin table 1_
The broken curves in figs. 1 and 2 express ODCX
= A’w exp(-fz*w),
(2)
where AL*and d are constants. As shown in these examples, eq. (2) fits the data only in part. Mathematicaliy, eq. (2) is au approximation for eq. {I) in case that o! < 6, but actually oz> fl (see table 1). The first order &lacLaurin’s expansion of eq. (1) is OD-Q-l = Am, which is rewritten as [et I = Aon++,
0)
where ee denotes a molar extinction coefficient of trapped electrons. For very low doses the trappedelectron concentration is proportional to the dose, and is given by Fig. 4. Electron concentration as a function of dose: o, methylcyclohexaneat 77 K (our measurement)and o, 3_etbylpentaue at 77 K (ref. [2]). Solid cmvcs: eq. (I) with the valuesin tabk I.
As shown in fig. 1, the previous ESR data for MTHF [6], where the concentration is given in the spin number per gram, agree with our optical-absorption data if the former are multiplied by 2.3 X IO” g cm-l, which corresponds to a value of 1.3 X lo4 MSi cm-l for the molar extinction coefficient. The optical densities at 700 run in ethanol glass [3] were converted to the ones at 525 nrn by multiplying a v&ue of 4.04 for 0DSu/OD700 measured at a dose of 2.3 X FfIzO eV g-l , and joined to our data as shown in fig. 2. There are three sets of the data for methylcyclohexane &sses (refs. [1,8] and ours), but those do not agree one another; only ours are plotted in fig_ 4,
let]
= ~oPGeW/~~,
(4)
where G, is the intrinsic, not apparent, G value of the trapped electron, NA is the Avogadro number, and p is the density of the glass. Comparison of eq. (3) with eq. (4) leads to Table 1 The corMants in c+ (I) and GcEeestimatedusing e+ (5) Glass F-1 h%THF EtOH i-BuOH INCH 3EP
1300 525 555
1600
1600
a) P and B are in IO*’
A (Cm’)
a a)
83
Geee b)
117 108 16.1 10.1 6.1
6.2 5.2 6.7 14 22
L-8 o-2 1.7 5.5 7.0
A0 3-5 O-69 0.90 0.92
eV_’ g.
b) GeEei.5in 104&I-’ cm-l. 45
VoIurne60, number I
CHEhlICAL PHYSICS LETTERS
Geee= AoN~fl0~.
(5)
The values for Geee estimated using eq. (5) are also listed in table 1. Eq. (5) enables us to determine the value for Geee without measurement at extreme low doses and is considered to be useful for estimation of G, for h&b-LET irradiation; we found it difficuit to measure the trappedelectron concentration for lowdose irradiation with ion beams of high LET [I I]. In the high dose region the graph for eq. (1) shows a tailing decay, but the or% for the equation of Raits&ring et al. [lo] shows a descending decay. it should be remarked that not orily the data in the present paper but also those by Mtsimring et al. are featured by the tailing decay. For some glasses (e.g. methylcyclohexane [I] and alkaline ices {6] ) the descending decay had been reported, but the tailing decay was observed for the same gasses in later ex-
4. Possible mechanism The mathematical form of eq. (1) suggests that the equation can be reIated to the exponential relation for electron scavenging in matrices 1121: = wG-nI!Sl),
WI
where [et ] and [e; ] r, are the trapped-electron concentrations in the presence and absence of a scavenger S, respectively. and n is a capture constant specific to the soIute. Eq. (6) is compatibIe with both electrontunneling [ 12 ] and mobileelectroncapture models.
[ 131
Fust we wiI! consider a process that electrons freshIy produced during a very small increase in the dose are scavenged by products which have been accumufated during the preceding irradiation. The products can be either neutral or cation radicals. Combining eq. (6)witha differential expression for eIectron concentrations: d[e;]o one dfet
= 10pG~~ldw,
Gt&%ins I
idw = IOPG, exFf-np
IPI )/NA,
01
where nP is the capture constant of the product P. U it is assumed that 46
PI = ~OPG~W/N~~
03)
where GP Is the G vahre of the product, then eq. (7) is
integrated to give [et]
= (G&,G,)fl
-
exp(-lO~npGpw~N~)J.
(9)
The right-hand side of eq. (9) multiplied by ee equals in eq. (1) if a = 10p~zpGr$V~. It A II - exp(.-M] should be noted that A = lOpG,e,/~V~from eqs. (3) and (4). Eq. (8) is a very crude approximation for a presumption that the product concentration increases with the dose. It has been reported that the concentration of some radicals increases with the dose even in the dose region where the trappedelectron concentration decreases with increasing dose [3]. Since the product is removed by the reaction with electrons, eq. (8) does not hold rigorously; however, it can be a good approximation if Gp is larger than G,.
periments.
Zetl/fe&
15 December 1978
Eq. (9) indicates that the trappedefectron concentration continues to increase with the dose and converges on Ge/rzpGP. Qualitatively, the behavior wiil be the same even if a better approximation for the product concentration is used instead of eq. (8). Thus the process considered above is not sufficient to explain the decrease in the trapped-electron concentration in the high dose region. Eq. (7) which deals with a short time corresponding to dw, is pertinent to the mobileelectron capture where the reaction terminates within an apparent life time of the mobile electron, but incomplete for the electron tunneling, for which the following factors should also be taken into account. (1) T&e tunneling radius increases with time [12]; therefore, the tunneling may occur even long time after the electron formation. (2) The electron surviving the capture as expressed by eq. (7) can be scavenged by the product which appears within the tunneling radius on subequent irradiation. We consider that the second factor is mainly responsible for the decrease in the trapped-electron concentration. We have not succeeded yet in formulating this process, though eq. (1) suggests that exp(--gw) could represent it. Thus, our empiricai equation seems to be consistent qualitatively with the tunneling model. The possibility of partial contniution of the mobile. electron capture cannot be ruled out; however, it shouId be noted that the mobiLelectron capture
Volume 60, number
1
CHEMICAL
PHYSICS
cannot explab singly the decrease in the trappedelectron concentration. Tachiya 1141 has recently derived a theoretial equation for the electron tunneling to a radiation-induced product on the assumption that the product concentration is proportional to the dose. This theoretical equation indicates thar the trappedelectron concentration should increase and then decrease with increasing dose, though it is too complicated to compare directly with our empirical equation_
Adcnowkdgement We thank Dr. M. Tachiya for his deriving the theoretical equation for the tunneling model at our request.
LETTERS
15 Deazmber 1978
[2]
A. Ekstrom. R Suexuam and J.E. ‘Willard, J. Phys Chcm 74 (1970) 1888. 131 S. Fujii and J.E. Wild, 3. Phys Chem. 74 (1970) 4313. [4] J, Zinzbrick and L Kevan, J. Am Chem. Sot 89 (1967) 2483. [S] J. Lin, K. Tsuji and F. Williams, J. Am. Chem. Sot 90 (1968) 2766. [61 D-p- Olinand L, Kevan, J. Chem. Phys 55 (1971) 2696. [7] T. Sasaki, S. Ohno and K. Kawatsrira, Chem. Letters (1972) 91. [S] G. Dolivo and T. Gzuman, Radiit. Phys Chem. 10 (1977) 207. [9] D-P. Lin and J-E. Wiid, J. Phys Chem. 78 (1974) 1135. [lo] A.M. Raitsimring, R-1. Samilova and Yu.D. Tsvetkov, Radiat. Phys. Chem. 10 (1977) 177. [llj A. Kira, M. Matsui and M. Lmamura, ICPR Cyclotron progr. Rept- 11 (1977) 124. [12] 3. Miller, J- Chem. Phys 56 (1972) 5173. [ 131 R.K. Wolff, MJ. Bronskill and J-W. Hunt, 3. Chem. Phys 53 (1970) 4211. [ 141 M. Tachiya, private communication_
References [ 11 Ed. !3hirom and J-E_ Wi, (1968) 2184.
J. Am. Chem. Sot 90
47