Kinetics of Radlcal Decay
The Journal of Physical Chemistry, Vol. 82, No. 11, 1978 1235
Kinetics of Radical Decay. 6. Radical Pairs in X-Irradiated Polycrystalline n-Alkoxyazoxybenzenes at Low Temperature John J. Trla and Russell H. Johnsen” Department of Chemistty, Florida State University, Tallahassee, Florida 32306 (Received December 27, 1977) Publication costs assisted by the US.Department of Energy
ESR studies indicate that about 70% of the radicals formed by X-radiolysis of polycrystalline samples of n-alkoxyazoxybenzenesat 77 K are produced as closely spaced pairs. Upon warming, the radicals in pairs combine leaving behind a smaller population of chemically different independent radicals. Good correlation between the yield of N2 gas (G(N2)= 0.021) and the yield of radical pairs (G(pairs) i= 0.02) in p-azoxyanisole (PAA), as well as spectral differences in deuterated samples and other considerations, indicate the pairs are probably formed by an intramolecular process involving destruction of the azoxy linkage to leave two substituted phenyl radicals separated by a light gas molecule. Overall radical pair decay is “stepwise”. Plots of fractional decay vs. time for different doses indicate that pair decay is a correlated process; the method of initial rates gives a reaction order of 0.9 and activation energy 2.7 kcal/mol for recombination in p-azoxyphenetole (PAP);and the pair separation distance is constant during decay, all indicating that the decay occurs by a single jump recombination process involving geminate partners.
Introduction The complex decay kinetics frequently observed for free radicals produced in solids by ionizing radiation can arise from the interplay of several factors. The initial damage produced by ionizing radiation is distributed inhomogeneously in tracks and spurs, and may include both independently formed radicals and geminate pairs. Radical pairs may be formed either by inter- or intramolecular processes, but in either case are characterized by a welldefined, small distance between members of a pair. The initial spatial inhomogeneity of damage may at later times be reflected in varying degrees for different radiolysis products due to subsequent reactions and diffusion away from the original damage sites. Since the activation energies for diffusion and rotation of radicals in solids can be large enough to be rate determining, an inhomogeneous spatial distribution can affect the observed decay kinetics in complex ways. Despite the possibilities for complexity, radical decay seems well understood in a number of systems. In previous studies of X-irradiated n-alkoxyazoxybenzenes,172the kinetic behavior of those radicals which decay above room temperature was explained by a model based on a random spatial distribution of radicals and significant activation energies for both diffusion and rotation. However, we reported then that irradiation at 77 K also produces a large population of a different radical which decays rapidly below room temperature. Evidence is presented here that this second population in p,p ’-azoxyanisole (PAA), p,p’-
R = CH, CH,CH, (CH,),CH$
PAA PAP HAB
azoxyphenetole (PAP), and 4,4’-bis(hepty1oxy)azoxybenzene (HAB) is composed of geminate pairs of radicals formed from a single parent molecule by destruction of the azoxy group to liberate a light gas molecule. Thermal decay of the radical pairs appears to occur via a time0022-3654/78/2082-1235$01 .OO/O
dependent first-order process. Experimental Section Sources of PAA, PAP, and HAB as well as purification and sample preparation techniques have been described.ll2 Powder samples were prepared by hand grinding with a Pyrex mortar and pestle. PAA-d6 was obtained from Merck Sharp and Dohme Canada, Ltd. as 90 atom % deuterium and PAA-d14was obtained from Aldrich. These compounds were not recrystallized before use. Samples were irradiated at 77 K with 3-MeV X rays to a typical dose of 16 Mrd at dose rates of 2-5 Mrd/h. ESR data were obtained with a Varian E-12 spectrometer at X-band (-9.5 GHz) using the variable temperature accessory and minicomputer as previously described. The weak signal at “half-field” was best observed under conditions of high microwave power (-196 mW), high gain (2 X lo4),and large modulation amplitude (-10 G) compared to typical settings of 0.15 mW, 2 X lo2gain, and 2.5 G for the signal at g = 2. The g factors are based on pitch in KC1 taken as g = 2.0028. Radical yields and concentrations at 77 K are from comparison of the signal intensities at 77 K with the intensities of the signals from the radicals previously studied at room temperature. The room-temperature concentrations were in turn determined by comparison to a standard sample of pitch in KC1, previously calibrated against serial dilutions of DPPH in benzene. Gas chromatography data were obtained with a Perkin-Elmer 154-B single column instrument having a thermal conductivity detector. A 2 m long by 4 mm i.d. Pyrex glass column packed with 40/60 mesh Linde Molecular Sieve 13X was used at 30 “C. The carrier gas was argon at 20 cm3/min flow rate and 10.5 psi inlet pressure. Samples of 0.5-1 g were degassed via several freezepump-thaw cycles and sealed in Pyrex ampoules for irradiation. After melting the sample to release trapped gas, the headspace gas was analyzed by crushing the ampoule in an “0” ring-sealed device attached to the GC inlet. Retention times and quantitative responses were determined from authentic samples of gases. Peak areas in the chromatograms were measured with an Ott polar planimeter. @ 1978 American Chemical Society
1236
The Journal of Physical Chemistry, Voi. 82, No. 77, 7978
J. J. Tria and R. H. Johnsen
.2 0 ” 70
”
”
” 150
+
’
F,
m, f 310
I
230
,
TEMPERATURE, K Flgure 3. “Warming curve” for HAB irradiated at 77 K. All relative signal intensity (Ill,,) measurements made at 91 K alter about 10 min at specified temperature (except datum at 77 K): (0)total g = 2 signal from radical pairs and independent radicals, by area measurement: (0) radical pair contribution to g = 2 signal, obtained by subtracting independent radical contribution (fraction stable at 323 K) from total signal: (0)height of outermost dipolar peak in g = 2 signal; (+) g = 4 signal area approximated from peak-to-peak height and wldth.
V Flgure 1. ESR spectrum of g = 2 signal from PAA powder sample irradiated at 77 K: (A) at 77 K before warming: (B) at 77 K after warming to room temperature; (C) computed difference, (A) (B).
-
8-
I
PAP
6-
MELT
I
0
183 K
5
10 DOSE, M r a d
15
20
Flgure 4. Radical yield vs. absorbed dose for PAP samples X irradiated at 77 K: (0)g = 2 signal from radical pairs and independent radicals; (0)g = 4 signal from radical pairs. Ordinate scales for ( 0 )and (0) are different and arbitrary.
133 K 91 K HAB
Flgure 2. ESR spectrum of g = 4 signal from HAB powder sample irradiated at 77 K. All spectra recorded at 91 K after warming to temperature noted for about 20 min.
Results The ESR spectrum of X-irradiated PAA at g = 2 before and after warming from 77 K to room temperature is shown in Figure 1. The four lines which disappear on heating are attributed to the AM, = 1 transitions of a radical pair with axial symmetry. The spectrum which remains at room temperature is identical with that of the independent radicals produced by irradiation at room temperature which were previously studied. Figure 2 shows the disappearance on warming of the weak signal in the g = 4 region attributed to the so-called “forbidden” or “AM,= 2” transition of the radical pairs. The ratio of the g = 4 signal intensity to that part of the g = 2 signal due to radical pairs was measured as 12:11,1.9 X €or HAB at 77 K, in fair agreement with the theoretical ratio 3.2 X calculated from the formula of Iwasaki3
Figure 3 is a “warming curve” constructed by raising the sample temperature in steps and measuring the radical concentration after waiting 10 min at each temperature. The intensity of the signal at g is: 4 decreases approximately coincidentally with the decrease of intensity of the features in the g is: 2 region associated with the radical pairs. This experiment indicates that the disappearing peaks in the g = 2 spectrum are correctly associated with
I
I
0
2
6
4 ( mW
8
)1‘*
Flgure 5. Microwave power saturation of ESR signal intensity in PAA measured at 88 K after irradiation at 77 K: (0)height of outermost dipolar peak In g is: 2 signal, immediately after irradiation; (0)integrated signal Intensity of total g = 2 spectrum after warming to room temperature and recooling; (A)peak-to-peak height of g = 4 signal. ( 0 ) and (0)arbitrarily drawn to same scale for comparison of shape; ordinates for g = 2 and g = 4 signals are different and arbitrary.
the radical pair interaction. I t should also be noted that the concentration of radicals stable at room temperature (independent radicals) is only 25-35’30 of the initial total radical concentration at 77 K for the materials studied, hence the number of radicals formed in pairs at 77 K is 2 to 3 times the number of independent radicals. The dose dependence of the yields of radical pairs and independent radicals at 77 K was studied at doses up to 16 Mrd for PAP. As seen in Figure 4,the yields increase linearly and maintain a constant ratio. Microwave power saturation effects on the ESR signal intensity in PAA irradiated at 77 K are shown in Figure 5. The g is: 4 signal shows no evidence of power saturation up to 200 mW, the maximum available. The g = 2 radical
The Journal of Physical Chemistry, Vol. 82, No. 11, 1978
Kinetics of Radical Decay
1237
TABLE I: ESR Parameters and Pair Separations
3’ *2
Compd PAA PAA-dE, PAA-d,, PAP HAB
95 139 130 117 167
Dl9
G
rlija
rLa
* 0,0004 aisb
* 0.0004
112
8.37 7.38 7.55 8.02 6.92
8.04 7.20 7.33 7.28 6.29
2.0036 2.0034 2.0025 2.0022 2.0026
2.0037 2.0040 2.0049 2.0024 2.0028
*
2 54 75 71 72
A
A
f
C
giso 0.0004
d &enter (room
Peak-peak
i: temp) 0.0004
gwidth = 4, at G
2.0045 2.0049 2.0043 2.0047 2.0052
27 i: 2 29i: 2 12t 1 26* 3 33 * 3
2.0036 2.0038 2.0031 2.0024 2.0027
rll and r l from formulae in text. gli and g l from centers of Dil and Dl splittings, respectively. */3gl. gcenkrat room temperature taken where derivative curve goes through zero.
giso= 1/3g11-t
a
’f
I
I
1
(IC
0
120
40 80 TIME ,MINUTES
Figure 7. Fractional decay at 195 K for radical pair population (independent radical signal subtracted) in PAP irradiated at 77 K to different doses: (0)3.9 Mrd; (A)7.3 Mrd; (0) 16 Mrd; (U) 24 Mrd. Signal at time 0 equals concentration stable at 77 K.
. *. 0
.2
0
I
I
40
I
.
I
80
I
1
120
TIME ,MINUTES
Flgure 8. First-order decay plot for radical pairs in same PAP sample Irradiated to 3.9 Mrd shown in Figure 7.
due entirely to the radical pairs. Figure 6 shows the rapid initial decay followed by a great reduction in decay rate to leave a relatively stable population of radicals which occurs when a cold sample is placed in a dewar preheated to a higher temperature. Raising the temperature results in another rapid initial decay followed by a dramatic reduction of decay rate to leave a new, smaller population of relatively stable radicals (so-called “stepwise” decay). As one might expect, the decay data do not fit simple firstor second-order kinetic plots, as seen from Figures 6 and 8. When fractional decay vs. time was plotted for different doses, as suggested by Willards to test for correlated decay of geminate pairs, the decay curves for four samples irradiated to doses between 3.9 and 24 Mrd coincided within the scatter of the data, as shown in Figure 7. Although the time required for temperature equilibration of the sample and spectrometer adjustment makes the earliest part of the decay data hardest to obtain reliably, a version of the method of initial rates6 was used to obtain an ac-
1238
J. J. Tria and R. H. Johnsen
The Journal of Physical Chemistry, Vol. 82, No. 11, 1978
tivation energy of 2.7 kcal/mol and a reaction order of 0.9 for radical pair decay in PAP.
(RO),CO
+
RO.(CO).OR
(3)
(RO),CO
+
RO*(CO,).R
(4)
Discussion The features of the ESR signal at g = 2 and their irreversible change upon warming, the position and intensity of the “half-field” signal at g = 4 and the coincidence of its thermal decay with the changes in the g = 2 spectrum, and the power saturation effects all indicate that a large fraction of the radicals produced by X irradiation at 77 K are closely spaced pairs. The constant ratio of radical pairs to independent radicals with increasing dose indicates that the radical pairs are not being formed by overlap of spurs containing independently produced radicals, but rather that the radicals in pairs are formed as geminate partners in some yet unspecified process. Data presented in Table I show radical-radical separation distances ranging from 6.5 to 8.2 A for pairs in the is not different compounds studied. The fact that D,, exactly twice D, may be partly due to the overlap of the radical pair and independent radical spectra. Another possibility is that the central feature of the radical pair spectrum obtained by difference in Figure 1represents the unresolved dipolar splitting of a second type of radical pair with a larger separation distance and that overlap with this signal further distorts the measured splittings. Except for the deuterated samples, as the size and mass of the molecule (and therefore the difficulty of displacing it from its lattice position) increase, the radical pair separation decreases. The small quantities of the deuterated compounds which were available were used as received from the manufacturers without benefit of recrystallization from toluene. It is known from X-ray diffraction studies that PAA798 and PAP8i9grown from toluene solution have quite similar structures (HAB is unreported). However, PAP and some other members of this homologous series are known to exist in several different crystalline forms2J0-13depending on the mode of crystallization and thermal history of the sample, so that one cannot be certain the lattice effects in the deuterated samples are comparable to those in the protonated material. In Table I giso values for the radical pairs are seen to differ significantly from the g values for the independent radicals stable at room temperature, indicating that the radicals in pairs are a different species from the independent radicals. Examination of the peak-to-peak width of the half-field signal for PAA and its d6 (deuterated only in the methoxy groups) and dI4 (completely deuterated) analogues indicates that the radical sites in the pairs are on a benzene ring. The high ratio (-51) of N2 yield (G(N2)= 0.021) to H2 yield (G(H2)= 0.0043) determined by GC indicates that a large part of the chemical damage resulting from irradiation of PAA is manifested in attack on the azoxy group. Since the “warming curves” show the ratio of radicals formed in pairs at 77 K to independent radicals is ~ 2 . 3 to 1 in PAA, and since the previously reported G(independent radicals) at room temperature is 0.018, we can estimate 2.3 X 0.018 = 0.042 as the approximate G(radicals formed in pairs). This is just the yield predicted from G(N2)if formation of each N2molecule is associated with formation of a radical pair. Similar agreement between radical pair concentrations and gas yields has been observed for a number of organic solids of similar molecular structure irradiated at 77 K: diphenyl carbonate and di-p-tolyl carbonate have been reported to eliminate C02 and/or CO to yield radical pairs separated by 5.7 and 6.8 A in the former and 5.9 A in the latter14-18
benzoyl peroxide eliminates two molecules of C 0 2 to give a pair of phenyl radicalslg (RCO,),
+
R*2(C02)*R
(5)
and azobenzene eliminates N2 to give a pair of phenyl radicals18 RN=NR+ R * ( N , ) . R
(6 1
The important factors in these examples are that the samples were exposed to ionizing radiation, either 6oCo y rays or high-energy X rays, and that the radical pairs formed were either the predominant radical products or were comparable in concentration to any other radicals formed. Symons20has noted that the similarity of this process to photolysis may indicate that it involves the decomposition of an electronically excited molecule. In view of the above examples, it seems plausible that in the alkoxyazoxybenzenes studied here the major chemical result of radiolysis at 77 K is the destruction of the azoxy group to produce a pair of closely spaced radicals and a small gas molecule. Whether this intramolecular process initially produces N2 or N20 is not clear because of the complicated interactions of nitrogen oxides, nitrogen, and oxygen possible on a molecular sieve column, and because of the difficulty in detecting the small quantities of gases produced at the dosages employed. Consequently, we are at present unsure whether RN,OR+ R * ( N , O ) * R
(7)
or RN,OR+ R.(N,).OR
or possibly both occur. Yet another indication that the radical pair formation process is associated with the loss of N2or N20 comes from examination of the g values in Table I. The gisovalues for the radical pairs are noticeably lower than the g values for the independent radicals stable at room temperature, which were previously1>2 attributed to loss of a hydrogen atom from a ring or alkyl chain carbon. These lower values of gisowould be expected if the radicals in the pairs did not contain the higher atomic number atoms oxygen and nitrogen, which are retained in the hydrogen-lossradicals. The plot of fractional decay vs. time, Figure 7, indicates a decay process which is independent of bulk concentration, i.e., a correlated recombination of geminate pairs according to a “time dependent” first-order process. Likewise, the results of the initial rate method gave a reaction order of 0.9 and an activation energy of 2.7 kcal/mol for PAP, also consistent with a pairwise decay process. The activation energy is too low for a bulk diffusion process but seems reasonable for a defect-assisted jump or a rotation. All the experimental evidence thus rules against a diffusion-limited recombination process such as was found for the independent radicals above room temperature.lI2 The 6-8-A separation of radicals in pairs is several angstroms greater than would result from a simple removal of N20 with the remaining fragments held in place. There must obviously be a spatial rearrangement of the radical fragments. This rearrangement could consist in part of some rotational movement of the radical fragments away from their original orientations, as well as a simple linear displacement. Since the absence of noticeable change in the dipolar splittings during decay indicates that no gradual change is occurring in the distribution of separation distances, it is inferred that decay occurs in a single
The Journal of Physical Chemistty, Vol. 82, No. 11, 1978
Thermodynamics of Electrolytes
1239
tainties in the decay mechanism may be clarified by future experiments in which the better spectral resolution anticipated from properly oriented single crystals may allow unambiguous separation of the radical pair and independent radical contributions to the g = 2 signal.
step process. We use the term “jump” somewhat loosely to describe this step since there may well be a rotational as well as a translational component of the motion which results in the two radicals achieving a suitable orientation for recombination. For radical pairs produced in di-p-tolyl carbonate other workers14have recently reported simple first-order decay kinetics. A number of reasons are possible for the more complicated kinetics observed in our experiments. As pointed out by an anonymous reviewer, if the energy deposited at the site of radical production disorganizes the immediate environment or displaces the radicals by varying small amounts, or if the stable gas molecule separating the radicals can be in various positions, then one might expect time dependent rather than simple first-order kinetics. If more than one type of radical pair is present, as the central area of the difference spectrum in Figure 1indicates is possible, then the overall kinetics might well be more complicated than simple first order. Another possibility is that this feature in the difference spectrum is the unresolved dipolar splitting of radical pairs which have diffused farther apart rather than recombining. However, since the 6-8-A separation distances measured are only about one-half a molecular length or less, and since the radical pair and stable gas molecule must constitute a significant local disturbance in the lattice, there is no reason to suspect that the probability of escape is as large as the probability of combination. If the probabilities were equal, one would predict only half the observed signal loss in the g = 2 region when samples are warmed to room temperature, and the signal stable at room temperature would be 0.6510 (0.3 from the independently formed radicals and 0.35 from the pairs which separate). Some smaller fraction of the paired radicals may diffuse apart during warming, possibly followed by conversion to the type of radical formed independently. This would account for the discrepancy between the decay rates of the g = 4 radical pair signal and the g = 2 radical pair signal observed in the warming curve experiment. These uncer-
Note Added in Proof. PAA-d6 and -d14 samples recrystallized from toluene showed only small differences from unpurified samples: Dll = 135,138 G; D , = 68,70 G; gll = 2.0023, 2.0032; g, = 2.0032, 2.0030; gi,, 5 2.0029, 2.0031 for PAA-d6 and -d14, respectively. Acknowledgment. The authors acknowledge the support of the D.O.E.This is O R 0 document 2001-39.
References and Notes (1) J. J. Tria and R. H. Johnsen, J. Phys. Chem., 81, 1274 (1977). (2) J. J. Tria and R. H. Johnsen, J. Phys. Chem., 81, 1279 (1977). (3) M. Iwasaki, T. Ichikawa, and T. Ohmori, J. Chem. Phys., 50, 1984 (1969). (4) Y. Kurita, J. Chem. Phys., 41,3926 (1964). (5) W. G. French and J. E. Willard, J. Phys. Chem., 72, 4604 (1968). (6) K. J. Hall, T. I. Quickenden, and D. W. Watts, J . Chem. Educ., 53, 493 (1976). (7) F. Wurstlln, 2. Kristallogr.,88, 185 (1934). (8) J. D. Bernal and D. Crowfoot, Trans. Faraday Soc., 29, 1032 (1933). (9) P. Chatelain, C . R . Acad. Scl., 203, 266 (1936);Bull. SOC. Fr. Mineral., Crlstallogr.,80, 280 (1937). (10) H. Arnold, 2. Phys. Chem. (Lelpzig),225, 146 (1964). (11) H. Arnold and H. Sackmann, 2.Phys. Chem. (Leiprig), 213, 145 (1960). (12) H. Llppmann and K.-H. Weber, Ann. Phys., 8, 265 (1957). (13) R. Kohler, Ann. Phys., 7 , 241 (1960). (14) R. Lembke and L. Kevan, Int. J. Radkt. Phys. Chem., 7, 547 (1975). (15) A. Davis, J. H. Golden, J. A. McRae, and M. C . R. Symons, Chem. Commun., 398 (1967). (16) A. Davis and J. H. Golden, J. Chem. SOC. 6 , 425 (1968). (17) J. A. McRae and M. C. R. Svmons. J . Chem. SOC.6 . 428 (1968). . . (l8j A. R. Lyons, M. C . R. Symdns, and J. K. Yandell, J. Chem. SOC., Faraday Trans. 2 , 88, 495 (1972). (19) . . I. I. Chkheidze, V. I. Trofimov, and A. T. Koritskii, Kinet. Kafal., 8, 453 (1967). (20) M. C. R. Symons, Magn. Reson. Relat. Phenom., Proc. Congr. AMPERE 78th, 1974, 2, 505-506 (1975).
Thermodynamics of Electrolytes. 11, Properties of 3:2, 4 2 , and Other High-Valence Types Kenneth S. Piker” and Leonard F. Silvester Department of Chemlstry and Lawrence Berkeley Laboratory, Unlversity of Callfornla, Berkeley, California 94720 (Recelved January 11, 1978) Publlcatlon costs asslsted by the U.S. Department of Energy
Various thermodynamic properties are considered for very high-valence 3:2 and 4:2 electrolytes in water at room temperature. These solutions show the behavior described by Davies in which ion pairing arises as the concentration increases followed by redissociation at still higher concentrations. Heat of dilution data, which extend below M, are interpreted with the same form of equation used earlier for 2:2 electrolytes. Activity and osmotic coefficient data do not extend to low enough concentration for independent interpretation, but they are treated with the aid of conductancedata in the more dilute range. Parameters are reported for Al,(S04)8, La2(SO4I3,III~(SO~)~, and several cyanoferrates. High-valence electrolytes show a special behavior at very low concentrations which was recognized by Bjerrum’ who showed in 1926 that purely electrostatic forces would yield an ion association. Davies2 showed that this association 0022-3654/78/2082-1239$01 .OO/O
commonly reached a maximum at an intermediate concentration above which there was a redissociation. From one viewpoint, this ion association is an artifact of the linearization approximation in the Debye-Huckel theory 0 1978 American Chemical Society
