Radiolysis of Butyl Chloride
The Journal of Physical Chemistry, Vol. 83, No. 3, 1979 337
Mechanism of the Formation of Cationic Species in the Radiolysis of Butyl Chloride. 2 Shigeyoshi Arai" and Masashl Imamura The Institute of Physical and Chemical Research, Wako-Shi, Saitama 351, Japan (Received Ju/y 24, 1978) Publication costs assisted by the Institute of Physical and Chemical Research
Assuming that the cross section for hole scavenging is a function of hole velocity, we present a model for riolute cation formation in irradiated butyl chloride matrices at low temperatures. The model can explain quantitatively the dependence of the cation yields on solute concentration reported recently for matrices containing a single or two different kinds of solutes. Holes with higher velocity are considered to interact preferentially with siolute molecules with a lower ionization potential. The concentration time dependence of cationic species has been examined at low temperatures using a pulse radiolysis technique. Solute cations and trapped holes are produced instantaneously with pulse irradiation and then they decay slowly over 0.1 s or so. Another possible model, i.e., a tunneling model, is inconsistent with the observed behavior. The efficiency of a solute for hole scavenging is proportional to [IP(butyl chloride) - IP(~olute)]~.
Introduction It has been well established that solute cations are produced efficiently upon irradiating low-temperature butyl chloride matrices containing solutes at low concentrations, for example, or M.1-3 The first step is, no doubt, the formation of solvent cations. However, the positive charges must migrate over many solvent molecules and be localized finally on solute molecules. Although a number of papers have been published concerning the optical spectra and kinetic behavior of solute cations,1-8the nature of migrating positive charge carriers or holes has not been understood to an appreciable extent. In a, previous study we have suggested that holes correspond to butyl chloride cations in the Franck-Condon state, i.e., a vibrationally excited state.g The cations in the state rapidly transfer their charges to neighboring neutral molecules and the migration is a succession of such transfers. During migration, the cations transfer the charges to solute molecules on encounters, or decompose into butene cations and HC1, or are stabilized as trapped holes in matrices. Consequently, one can observe absorptions due to butene and trapped butyl chloride cations in irradiated butyl chloride at low temperatures. Kira et al. have recently examined solute cation yields in y-irradiated matrices containing a single or two different kinds of solutes.1° They have obtained an interesting and suggestive relationship between the yields of trapped holes or solute cations and solute concentrations. Developing the concept of holes in our previous paper, we propose a model which can explain satisfactorily the observed relationship in this paper. Experimental Section Most of the data used here are found in ref 9 and 10, although some experiments were carried out in order to obtain additional information of solute cation formation. The experimental details are the same as described previousl~r.~ Model Migrating holes, Le., butyl chloride cations in the Franck-Condon state, are produced by the interaction of fast-moving primary and secondary electrons with neutral butyl chloride molecules. The hole h+ executes zig-zag motion in a rigid matrix and transfers its charge to a solute 0022-365417912083-0337$01 .OO/O
molecule A on encounter. The cross section QA ( u ) may be a function of hole velocity u. The decrease in the number of holes N can be expressed by the following equation -dN/dt = NuaA(u)CA
(1)
where CA is the concentration of A in the matrix. Assuming that the hole velocity decreases according to a simple exponential function of time u = uo exp[-ut]
(2)
we can derive the following equation from eq 1 and 2 In [N(ht+)/N(ho+)]= -(CA/u)J"o~A(u)du = -(CA/u)ZA = In [{Ym-- Y(A+))/Ym] (3)
The decay constant of the velocity is represented by u. The initial hole velocity Vo should be regarded as an average value, because it is probably distributed over a certain range. N(hc) represents the number of holes which escape from scavenging by a solute and should be finally stabilized as either trapped holes or butene cations. Hereafter, the holes are described as trapped holes for simplicity. N(hio+)represents the number of holes produced initially. Y, is the yield of solute cations A+ at infinite concentration of A, where all the holes are converted into A+ due to complete scavenging. Y(A+) is the yield of A+ at the solute concentration CA. The integral in the equation has a constant value EA, which depends only on the nature of the solute and solvent pair used. N(ht+)/N(h,+) is equal to Y(ht+)/Y,, where Y(ht+) is the yield of trapped1 holes. When two different kinds of solute A and B exist in the matrix, a similar treatment leads to the following equation:
-(CAZA+ C B ~ B ) / U = In [Y(ht+)/Yml (4) The symbols with subscript B have a similar meaning as ) those with A. If the distributions of crA(u) and ~ ( uover velocity are widely separated from each other, as shown 0 1979 American Chemical Society
338
The Journal of Physical Chemistry, Vol. 83, No. 3, 1979
z
I-
0
I
S.Arai and M. Imamura
Z
I N I T l A L HOLE!
c xa
m
\
;D
o W m
I
/IZrnMDEA+BP
0 -rl
ul D m
u,
m
0
-
0
LT
o
m
VI
VELOCITY Flgure 1. Hole scavenging by solute A and B (see text). Curves A and B represent the cross section distributions over the hole velocity for solute A and E, respectively. No is the number of holes produced initially. N,', N,', and Nh+ are the number of A+, E+, and, :h respectively. The symbol v,, is the initial hole velocity. -1 5
1
7
1
D E A t 24mM BP IZrnMDEA+BP
D E A a l o n e \ \ . C
0
5
10
15
h I+ 20
[DEAI/ mM
Figure 2. Relation between solute cation yield and solute concentration (see ref 10 and text): DEA alone, A, Y = 0.60 - D(DEA+); A , Y = D(h:); BP alone, V, Y = 0.95 - D(BP+); 12 mM DEA 4- BP, 9, Y = D(DEA+); V, Y = 0.28 - D(BP+); DEA 24 mM BP; 0, Y = 0.66 D(DEA+); 0 , Y = D(BP+). Scales for each line are indicated by the arrows.
+
The definition of Y , is the same as described above. Namely, Y , equals the yield of A+ or B+ at infinite concentration when either A or B exists as a solute, and hence corresponds to the yield of the holes produced initially.
Results and Discussion The elementary process of hole migration is the transfer of positive charge from a solvent cation to a neighboring neutral solvent molecule. The hole velocity of eq 1 is, therefore, the product of a transfer frequency and an average transfer distance. The cross section is related to the reaction probability between the hole and the solute molecule added. Although the physical meanings of the velocity and cross section are different from those used in a gas kinetic theory, eq 1 is still sufficiently accurate. The hole velocity has been assumed to decrease exponentially with time. In such a case where the decrease is complex, ZA/u of eq 3 must be replaced by a more complicated function. However, the basic semilogarithmic relationship still holds between the cation yield and the solute concentration. Kira et al. have recently made measurements of solute cation yields in y-irradiated butyl chloride matrices containing a single or two different kinds of aromatic solutes.1° Figure 2 shows the results obtained with N,N'-diethylaniline (DEA), biphenyl (BP), and diethylaniline-biphenyl (DEA-BP) systems, where cation yields are represented by their optical densities D(DEA+), D(BP+),and D(ht+). In the simple case of DEA or BP alone eq 3 can satisfactorily explain the observed dependence of D(DEA+), D(BP+), and D(ht+) on the solute concentration. The slopes in the figure give the values of & ) E A / U and ZBP/u, which are identical with n(DEA) and n(BP) of ref 10, respectively. For the DEA-BP (24 mM) system, both the log (0.66 - D(DEA+))vs. [DEA] plot and the log D(BP+)vs. [DEA] plot give straight lines with the same slope, as shown in Figure 2. The slope is also the same as that of the log 10.60 - D(DEA+)]vs. [DEA] plot or that of the log D(h,+) vs. [DEA] plot for DEA alone. In addition, the slopes of the log (0.28 - D(BP+))vs. [BPI plot for DEA (12 mM)-BP and the log (0.95 - D(BP+))vs. [BPI plot for B P alone are equal to each other. D(DEA+) is almost constant independent of [BPI for DEA (12 mM)-BP. All these experimental facts can be explained completely by
eq 5-7, if A is DEA and B is BP. The ratio of the intercept for the log (0.28- D(BP+)]vs. [BPI plot to that for the log (0.95 - D(BP+)) vs. [BPI plot should be equal to e x p [ - . ( C ~ ~ ~ & , ~ ~according )/u] to eq 6. The observed ratio 0.29 is, in fact, close to exp[-92 M-' X 12 mM] N 0.33, where 92 M-l is the experimental value for ZDEA/u.Kira et a1.I' have suggested the following mechanism based on the selective capture of a different state of holes hl+ and h2+ by each solute: hi+
+ DEA
+ -
hl+
h2+ BP h2+
+
DEA'
hz+ BPS
h,+
This scheme is essentially the same as the present model, if the different state arises from the difference in hole velocity. It is generally accepted that the cross section for the charge transfer in a gas phase is a function of relative velocity11J2
-
x++ Y x + Y+ + m
m = IP(X) - IP(Y)
where IP(X) and IP(Y) are ionization potentials for X and Y. The larger the energy discrepancy AE, the greater is the velocity at which the maximum of the cross section occurs. This relationship may be written semiquantitatively in the formula (aaE)/(hutn) 1 (8) The symbol u, is the relative velocity of the colliding pair when the cross section has the maximum value. The symbol a is the range of interaction. Hasted has shown that the equation fits a large number of experimental data within an error of 10-209'0 when 2xa is 7 A or so.12 If the same relationship is applicable to interactions in a condensed phase, the maximum of the cross section for hole scavenging shifts to a lower velocity side as the ionization potential of the solute increases. The solute A in eq 5-7 is, therefore, expected to be DEA (IP = 6.99 eV) and the
Radiolysis of Butyl Chloride
0
The Journal of Physical Chemistry, Vol. 83, No. 3, 197:9 339
--
2.0
=
1.9
-
1.8
-
#-
z
W v ~
1.7
0 II
1
1.6
BP* (700 nm) 1.5
01.4
H -
in sec-butyl chloride containing 10 mM DEA and 16 mM BP. One small division in the vertical scale corresponds to 5.0% absorption and one small division in the horizontal scale to 20 ps. Zero lines for absorptrons are indicated by the arrows. The pulse duration used was 1 ps.
o/
-
-
0.3
Flgure 3. Decay curves of DEA' and BP' produced at about 90 K
DEA
NA
Pap
slope = 2
0.4
0.5
0.6
Log A E
Figure 4. Plots of log TZlul vs. log A€ (see text): DEA, N,N'diethylaniline; PY, ipyrenei BA, benzanthracene; NA, naphthalene; BP, biphenyl.
two-step tunneling process.l9 However, we could not observe any significant increase or decrease in the DEA+ and BP+ absorptions after pulse irradiation, as shown in Figure 3. Both solute cations are produced completely in a rapid process. Trapped holes and DEA and B P cations produced in DEA, BP, and DEA-BP systems were found to disaplpear in 0.1 s or so under the experimental conditions used here. Their decay may be due to the softness of matrices because the temperature was about 90 K. The efficiency of solute cation formation is related to Z A / u in eq 3; the concentration necessary for producing solute cations ait one half of the limiting yield Y , is equal to 0.69 u/ZA. Solute cations tend to be produced more efficiently when the ionization potentials of the solutes are lower. Figure 4 shows the log [ E / u ]vs. log AE plot for various solutes, where AE is the difference of the ionization potential between butyl chloride and a solute. Z is proportional to AB2,although its theoretical estimation has not yet been made.
solute B to be BP (IP = 8.27 eV). The concentration necessary for scavenging half of total holes is about 8 mM for DEA. This concentration means that the hole migrates over about 1000 solvent molecules before solute cation formation. Since migrating holes are vibrationally excited butyl chloride cations, their decay time may be considered s. These data lead to a hole velocity to be around of 10:' cm/s using a molecular dimension of 5 A for butyl chloride. On the other hand, we can estimate the hole velocity to be lo7cm/s, assuming tentatively that eq 8 is valid in a condensed phase. The value of 2aa was taken to be 7 A and aE to be 3.6 eV. Although a crude assumption has been made, the agreement between both estimations is support for the model. Several studies of trapped electrons in rigid matrices have shown that trapped electron yields also decrease exponentially with increasing scavenger con~entration.l~-~~References arid Notes (1) T. Shida and W. H. Hamill, J . Chem. Phys., 44, 4372 (1966). In addition, trapped electrons were found to disappear over (2) T. Shida and S. Iwata, J. Am. Chem. Soc., 95, 3473 (1973). a wide time range of s to minutes after irradiation. (3) W.H. Hamill, "Radical Ions", E. T. Kaiser and L. Kevan, Ed., InPlots of [e;] against log t give a relatively good straight terscience, Mew York, N.Y., 1968, pp 321-416. line. Miller has suggested that these results are consistent (4) S. Arai, H. Usda, R. F. Firestone, and L. M. Dorfrnan, J. Chem. phys., 50, 1072 (1969). with a model based on tunneling of trapped electrons.13-15 (5) N. E. Shank and L. M. Dorfman, J. Chem. Phys., 52, 4441 (1970). If similar tunneling between trapped holes and solute (6) (a) B. Badger and B. Brocklehurst, Trans. Faraday SOC., 65, 2576 molecules occurs in butyl chloride matrices, the observed (1969); (b) bid., 65, 2578 (1969); (c) bid., 65, 2588 (1969). (7) A. Kira, S. Ariai, and M. Imamura, J . Chem. Phys., 54, 4890 (1971). semilogarithmic relationship may be explained equally well (8) A. Kira, S. Ani, and M. Imamura, J. Phys. Chem., 76, 11 19 (1972). in terms of the model. The previous low-temperature pulse (9) S. Arai, A. Kira, and M.Imamura, J . Phys. Chem,, 80, 1968 (1976). radiolysis study has demonstrated that both trapped holes (10) A. Kira, T. Nakamura, and M. Imamura, J . Phys. Chem., to be published. and solute cations are formed instantaneously with pulse (11) H. S. W.Mastjey, E. H. S. Burhop, and H. B. Gilbody, "Electronic and irradiation in n-butyl chloride glass containing 5 X M Ionic Impact Phenomena", 2nd ed., Voi. 3, Oxford University Press, b i ~ h e n y l . ~Similar results have been obtained in the London, 197'1. (12) J. B. Hasted, "Physics of Atomic Collisions", Butterworths, London, present study also. If positive charges transfer from 1972, pp 61:!-658. trapped holes to biphenyl via tunneling, a certain portion (13) J. R. Miller, J'. Chem. Phys., 56, 5173 (1972). of the 700-rim absorption due to biphenyl cations must (14) J. R. Miller, &em. Phys. Lett., 22, 180 (1973). grow gradually after the pulses in contrast with the ob(15) J. R. Miller, J . Phys. Chem., 79, 1070 (1975). (16) M. Tachiya and A. Mozumuder, Chem. Phys. Lett., 28, 87 (1974). servation. Tachiya has recently applied the tunneling (17) F. Kieffer, C. Meyer, and J. Rigant, Chem. phys. Lett., 11, 369 (1971). model to the results obtained with the DEA-BP system, (18) A. Kira and M. Imamura, J . Phys Chem., to be published where DEA cations were considered t o be produced by a (19) M. Tachiya, private communication.
