Termination of (.)CH2OH/CH2O(.-) Radicals in Aqueous Solution

Article abstract of DOI:10.1021/jp962159x

Hydroxymethyl radical (.)CH2OH and its radical anion (.)CH2O(-) (pK_a 10.7) were generated pulse-radiolytically in N2O-saturated aqueous solutions of methanol.The overall decay is by second-order kinetics.At pH 3 mol^-1 s^-1), one observes ethylene glycol and formaldehyde plus methanol in a disproportionation/recombination ratio of 0.17.At pH >/= 12 ((.)CH2O(-)) the rate constant is 2k = 0.5E9 dm³ mol^-1 s^-1.From the pK_a and the dependence of the rate of bimolecular decay on pH, a mixed-termination rate constant k((.)CH2OH + (.)CH2O(-)) = 1.2E9 dm³ mol^-1 s^-1 is calculated.With increasing pH, the yield of ethylene glycol decreases while that of formaldehyde (plus methanol) shows a corresponding increase.Ethylene glycol is no longer formed at pH >/= 11.3.Quantum-chemical calculations indicate that (.)CH2O(-) possesses considerable spin density also at oxygen (mesomeric structure: (-)CH2O(.)).Since in their bimolecular termination reactions the (.)CH2O(-) radicals can no longer disproportionate by a straightforward H atom transfer, it is concluded either that termination must occur by a C-O type recombination, giving rise to the (unstable) hemiacetal, CH3OCH2OH, or that the disproportionation reaction is water-assisted.The (.)CH2O(-) radical reduces N2O (k = 350 dm³ mol^-1 s^-1); this gives rise to a chain reaction at the low (compared to pulse radiolysis) dose rates of γ-radiolysis (0.02-2 Gy s^-1).

Full text of DOI:10.1021/jp962159x

J. Phys. Chem. 1996, 100, 15843-15847
15843
•
Termination of CH2OH/CH2O•- Radicals in Aqueous Solution
Wen-Feng Wang, Man Nien Schuchmann, Vinzenz Bachler, Heinz-Peter Schuchmann, and
Clemens von Sonntag*
Max-Planck-Institut fu¨r Strahlenchemie, Stiftstrasse 34-36, P.O. Box 101365,
D-45413 Mu¨lheim an der Ruhr, Germany
ReceiVed: July 15, 1996X
Hydroxymethyl radical •CH2OH and its radical anion •CH2O- (pKa 10.7) were generated pulse-radiolytically
in N2O-saturated aqueous solutions of methanol. The overall decay is by second-order kinetics. At pH e 8
(•CH2OH, 2k ) 1.7 × 109 dm3 mol-1 s-1), one observes ethylene glycol and formaldehyde plus methanol in
a disproportionation/recombination ratio of 0.17. At pH g 12 (•CH2O-) the rate constant is 2k ) 0.5 × 109
dm3 mol-1 s-1. From the pKa and the dependence of the rate of bimolecular decay on pH, a mixed-termination
rate constant k(•CH2OH + •CH2O-) ) 1.2 × 109 dm3 mol-1 s-1 is calculated. With increasing pH, the yield
of ethylene glycol decreases while that of formaldehyde (plus methanol) shows a corresponding increase.
•
Ethylene glycol is no longer formed at pH g 11.3. Quantum-chemical calculations indicate that CH2O-
possesses considerable spin density also at oxygen (mesomeric structure: -CH2O•). Since in their bimolecular
termination reactions the •CH2O- radicals can no longer disproportionate by a straightforward H atom transfer,
it is concluded either that termination must occur by a C-O type recombination, giving rise to the (unstable)
hemiacetal, CH3OCH2OH, or that the disproportionation reaction is water-assisted. The •CH2O- radical reduces
N2O (k ) 350 dm3 mol-1 s-1); this gives rise to a chain reaction at the low (compared to pulse radiolysis)
dose rates of γ-radiolysis (0.02-2 Gy s-1).
Introduction
SCHEME 1
2•CH2OH f (CH2OH)2
(1a)
(1b)
The termination reaction of the hydroxymethyl radical
represents an integral part of the free-radical chemistry of
methanol. While in the gas phase and in nonprotic solvents
this radical is restricted to the form •CH2OH, in protic solvents,
its conjugate anion CH2O•- [in water, pKa(•CH2OH) ) 10.7]1,2
must be taken into account as well. One might be tempted to
think of the methanol radical anion as essentially being a carbon-
2•CH2OH f CH2O + CH3OH
•CH2OH + CH2O•- + H2O f (CH2OH)2 + OH- (2a)
•CH2OH + CH2O•- + H2O f CH3O-CH2OH + OH-
•
centered radical, CH2O-. In fact, the ESR g factors of the
(2b)
neutral and the anionic forms are quite similar: g(•CH2OH) )
2.003 17, g(CH2O•-) ) 2.003 67.1 Nevertheless, applying
Hu¨ckel arguments3 to this species which can in principle also
be derived from the formaldehyde molecule by electron addition
into the antibonding π* orbital, one realizes that a non-negligible
spin density should reside at the oxygen atom as well. Indeed,
the oxyl radical mesomeric form -CH2O• plays an important
role in the radiation chemistry of methanol in alkaline aqueous
solution, as will be shown below.
•CH2OH + CH2O•- + H2O f CH2O + CH3OH + OH-
(2c)
2CH2O•- + 2H2O f (CH2OH)2 + 2OH-
(3a)
2CH2O•- + 2H2O f CH3O-CH2OH + 2OH- (3b)
2CH2O•- + 2H2O f CH2O + CH3OH + 2OH- (3c)
There are two aspects to the three possible termination
•
processes (Scheme 1) involving CH2OH and CH2O•-: in
dehyde and methanol. While the disproportionation between a
hydroxymethyl radical and its anion (reaction 2c) is straight-
forward, conceptual difficulties arise when two radical anions
are involved (reaction 3c). In this case, the conventional
notation of the hydroxymethyl radical anion, •CH2O-, does not
allow to formulate a facile H-atom transfer reaction; a carbene
structure would be its improbable result. This difficulty can
be avoided if the involvement of the oxyl-radical mesomeric
form -CH2O• is admitted and water is allowed to participate in
the disproportionation reaction.
principle, each of these has its own rate constant and dispro-
portionation/recombination ratio. It is known that the self-
termination of •CH2OH proceeds by both recombination (reac-
tion 1a) and disproportionation (reaction 1b). It is straightforward
to formulate the latter reaction as an H-atom transfer from
hydroxyl to methyl with the concomitant formation of a carbon-
oxygen double bond. When CH2O•- is involved, one may
envisage two modes of recombination, i.e., the formation of a
C-C as well as of a C-O linkage (reactions 2a, 2b, 3a, and
3b). Product-wise, the latter (reactions 2b and 3b) are impos-
sible to distinguish from disproportionation (reactions 2c and
3c) under the conditions of solution experiments since the
hemiacetal is unstable with respect to solvolysis into formal-
Although some of the questions regarding the termination of
the methanol radical have been addressed in the past,4-16 they
have not been satisfactorily resolved in their entirety. We have
now restudied the termination reactions of hydroxymethyl in
aqueous solution over a wide range of pH.
X Abstract published in AdVance ACS Abstracts, September 1, 1996.
S0022-3654(96)02159-4 CCC: $12.00 © 1996 American Chemical Society

15844 J. Phys. Chem., Vol. 100, No. 39, 1996
Wang et al.
Experimental Section
Aqueous solutions of fractionally distilled methanol (con-
centrations used were 0.2 M for the kinetic experiments and
0.01 M for the product studies) were made up in Milli-Q-filtered
(Millipore) water, which had been saturated with O2-free N2O
by passing the gas through the liquid for 30 min before methanol
addition, then pulse-irradiated (pulse duration, 0.4-2 µs; dose
per pulse, 5-35 Gy) or γ-irradiated in a 60Co panorama γ-source
(Nuclear Engineering Ltd., dose rate range: 0.02-2 Gy s-1).
The pulse radiolysis setup has been described previously.17 The
disappearance of the methanol radicals was monitored by optical
detection at a wavelength of 270 nm.
Formaldehyde was determined spectrophotometrically by the
Hantzsch method.18a Ethylene glycol, after having removed the
radiolytically produced formaldehyde by reduction with NaBH4,
was oxidized with periodate18b to formaldehyde and determined
as such.
Quantum-Chemical Calculations. Computations were per-
formed by means of the Gaussian 92/DFT suite of ab initio
programs19 and the 6-311G** basis set.20 Spin-density distribu-
tions were computed using the unrestricted Hartree-Fock
(UHF)21 and the restricted open-shell Hartree-Fock (ROSHF)22
method. Spin densities are sensitive to the molecular geom-
etries. These were therefore optimized at the unrestricted
Moeller-Plesset (UMP2) level.23 For these geometries, spin
and charge densities24 were calculated using the UHF and
ROSHF wave functions.
Figure 1. Pulse radiolysis of N2O-saturated aqueous solutions of
•
methanol (0.2 M). Observed termination rate constant of CH2OH/
CH2O•- radicals as a function of pH: O, experiment; line, fit on the
basis of the rate constants given in Table 1 with pKa ) 10.7; i, ionic-
strength effect taken into account. Inset: the inverse of half-lives
observed at pH 5.1, versus initial methanol radical concentration.
TABLE 1: Rate Constants Determined in This Study
rate constant
reaction
(dm3 mol-1 s-1
)
2•CH2OH f products
2k1 ) 1.7 × 109
k2 ) 1.2 × 109
2k3 ) 0.5 × 109
k13 ) 350
•CH2OH + CH2O•- f products
2CH2O•- f products
Results and Discussion
•CH2O•- + N2O + H+ f CH2O + •OH + N2
Hydroxymethyl was generated radiolytically (Scheme 2).25
OH radicals and H atoms formed in the radiolysis of N2O-
saturated water react with the solute methanol predominantly
(>95%) by abstracting a carbon-bound H atom26 (k6 ) 9.7 ×
108 dm3 mol-1 s-1, k7 ) 2.6 × 106 dm3 mol-1 s-1).27
radical concentration [R•]o, which is proportional to the pulse
dose D (varied from 5 to 20 Gy; pulse duration 1 µs): 1/t1/2
)
2kobs[R•]o; [R•]o ) G(R•) D. It is seen in Figure 1 that, in weakly
•
acidic aqueous solution, CH2OH decays with a rate constant
of 2k1 ) 1.7 × 109 dm3 mol-1 s-1.. This is in the lower range
SCHEME 2
of values previously reported in the literature.34
ionizing radiation
8 OH, eaq-, H+, H2O2, H2
(4)
(5)
•
The observed bimolecular decay rate constant stays roughly
the same up to pH 9.5, but in more strongly basic solution, it
drops to a value of about 0.6 × 109 dm3 mol-1 s-1 (see Figure
1). The data in the region below pH 9 show considerable scatter.
H2O
eaq- + N2O f •OH + N2 + OH-
.
One reason for this is that the absorption coefficient of CH2-
CH3OH + •OH f •CH2OH + H2O
CH3OH + H• f •CH2OH + H2
CH3OH + •OH f CH3O• + H2O
CH3O• f •CH2OH
(6)
OH is only about one-half that of CH2O•- at the monitoring
wavelength, and therefore the decay is more difficult to follow.
Moreover, the impression of scatter increases linearly with the
mean which happens to be larger in the acidic range by a factor
of 2 or 3 compared to the alcaline range. No significance is
attached to the apparent slight maximum in the neutral range.
It can be shown that the overall rate constant 2kobs, as a function
of the pH, is given by expression 11. This expression would
(7)
(8)
(9)
•CH2OH a •CH2O- + H+ (pKa ) 10.7)
(10/-10)
2(k1[H+]2 + k2Ka[H+] + k3Ka2)
2kobs
)
(11)
([H+] + Ka)2
Methoxyl CH3O• which is also formed, but in a small propor-
tion,26 is rapidly converted (k9 > 3 × 105 s-1) into additional
•CH2OH.28-31 The system of radicals is thus composed entirely
accommodate a maximum only at a pH near the pKa of the
terminating radicals. By computational modeling, the individual
termination rate constants k1, k2, and k3 compiled in Table 1
are obtained on the basis of the data and a pKa value1,2 of 10.7.
Line i in Figure 1 is obtained when the ionic-strength effect
(cf. ref 39) on 2k3 is taken into account. It is seen that the
cross-termination rate constant k2 is the largest of the three (cf.
also ref 12: 2.25 × 109 dm3 mol-1 s-1); this trend is in
agreement with that observed in the nonaqueous system 100%
methanol.11,12 Further values for the rate constant 2k3 are
reported in the literature.40
•
of CH2OH and/or its anion. Both show a relatively weak but
characteristic absorption2 in the UV. Taking G(•CH2OH/
CH2O•-) at 6.9 × 10-7 mol-1 J-1 [G(•OH) ) 6.4 × 10-7 mol-1
•
J-1, G(•H) ) 0.5 × 10-7 mol-1 J-1] in N2O-saturated 0.2 M
methanol solution,32 we obtain for ꢀ(260 nm) the values of 540
and 1060 dm3 mol-1 s-1, respectively, which are in good
agreement with those reported in ref 33. The second-order rate
constants 2kobs at various pH (Figure 1) have been determined
from the slopes of plots (cf. Figure 1, inset) of the first half-life
of the decay of the radicals, monitored as a function of the initial

•
Termination of CH2OH/CH2O•- Radicals
J. Phys. Chem., Vol. 100, No. 39, 1996 15845
with CH2O•-, such an H-transfer may still operate, with the
former as the H donor. With regard to reaction 3, however, it
•
is difficult to conceive how CH2O- could undergo dispropor-
tionation with its own kind since this would require the
intermediacy of a carbene structure. One suggestion would be
that these radicals react with one another head-to-tail, (reaction
3b, Scheme 1) where a hemiacetal is formed that is ultimately
detected as formaldehyde. Thus, an apparent “disproportion-
ation” would in fact be the result of a recombination reaction.
The hypothesis of head-to-tail reaction is supported by quantum-
chemical calculations which show that the hydroxymethyl
radical anion carries a spin density of 0.73 (by UHF) or 0.69
(by ROSHF) at the carbon atom, while a considerable spin
density of 0.34 (by UHF) or 0.27 (by ROSHF) is localized also
at the oxygen atom. These values are in general accord with
those reported previously,45 i.e., 0.79 at carbon and 0.34 at
oxygen. Thus, spin density at carbon is markedly below unity
while it is very significantly aboVe zero at oxygen, in contrast
to the situation of the neutral species where practically the total
spin density is localized at carbon, as is of course expected.
The significant presence of spin at the oxygen atom in the
hydroxymethyl radical anion implies a fair chance of hemiacetal
vs glycol formation.
Figure 2. Pulse irradiation (3 Gy per pulse) of N2O-saturated aqueous
solutions of methanol (0.01 M). Radiation-chemical yields (G values,
in units of 10-7 mol J-1) of the formation of ethylene glycol (b) and
formaldehyde (O) as a function of pH: lines, fit obtained using the
low- and high-pH data together with the rate constants in Table 1,
assuming that cross-termination does not furnish ethylene glycol.
In addition, the finding11,43 that the ethylene glycol yield in
nonaqueous methanol is not affected by the degree of alkalinity
up to 0.01 M base, in contrast to the present case where the
effect becomes visible already between pH 8 and 9 (Figure 2),
seems to indicate a particular influence of the medium. In
Baxendale and Mellows’ experiments,43 in 0.01 M methanolic
methoxide solution, the methanol radical species exist in a ratio
of 0.86 for [CH2O•-]/[•CH2OH] (as one estimates from their
equilibrium constant in methanol11), i.e. if the rate constants
and the disproportionation/recombination ratios found in the
present work (Figures 1 and 2; Table 1) were to apply to theirs,
the ethylene glycol yield in the alkaline should be considerably
lowered relative to that observed by them under acidic and near-
neutral conditions. Therefore as an alternative to the foregoing
hypothesis of recombination by C-O bond formation, a
“solvent-assisted disproportionation” (reaction 12) may be
formulated.
Chemical diversity may arise through a variation in the
relative importance of the disproportionation vs recombination
•
reactions as the pH is varied. It is known that the CH2OH
radical as such mainly recombines to give rise to ethylene glycol,
while disproportionation into formaldehyde and methanol is of
minor importance41 (reactions 1a and 1b). The ratio k1b/k1a has
been reported near or below 0.2.42 The situation has remained
unresolved for the reactions involving the radical anion, apart
from an indication that in the alkaline nonaqueous system (100%
methanol containing 10-2 mol dm-3 sodium methoxide) the
formaldehyde-to-ethylene-glycol yield ratio remains essentially
unchanged compared to what it is in the absence of alkali.14,43
Our own results concerning the ethylene glycol and formalde-
hyde yields in aqueous medium over a wide pH range are shown
in Figure 2, where the radiation-chemical yields of ethylene
glycol and formaldehyde are plotted vs the pH.
In the pH range where •CH2OH is the only methanol radical
species extant, the formaldehyde-to-ethylene-glycol yield ratio
of 0.17 falls close to the value given in ref 5, but in the alkaline
range, in contrast to the findings in pure methanol, the ethylene
glycol yield tends toward zero at high pH where only the radical
anion is present while the formaldehyde yield reaches the full
complement, i.e., a G value of 3 × 10-7 mol-1 J-1 that one
expects if half of the hydroxymethyl radicals are converted into
formaldehyde while the other half revert to methanol (at a
methanol concentration of 0.01 M, G(•CH2OH) ) 6 × 10-7
mol-1 J-1); these results were obtained with the relatively high-
dose-rate (compared to γ-radiolysis) electron pulse which favors
the termination reaction over a side reaction with N2O, see
below. This outcome indicates termination by disproportion-
ation (reactions 3c) and/or recombination under C-O bond
formation (reaction 3b), with essentially the complete absence
of reaction 3a. The disproportionation/recombination ratio of
the cross-termination process (reactions 2a-c) cannot be directly
determined, but a computational fit of the experimental points
in Figure 2 with the Gear algorithm,44 using the low- and the
high-pH data as well as the appropriate rate constants from Table
1, indicates that cross-termination also proceeds practically
exclusively by disproportionation (reaction 2c) and/or recom-
bination by C-O bond formation (reaction 2b).
2(CH2O•-)aq f CH2(OH)2 + CH3OH + 2OH- (12)
Two potential mechanisms of the “solvent-assisted dispro-
portionation” are illustrated in Scheme 3 (A, characterized by
electron transfer; B, by H-atom transfer).
SCHEME 3
Formaldehyde hydrate in water is more stable than formal-
dehyde itself. So is formaldehyde methyl hemiacetal in
methanol. But if the transition state in the aqueous medium is
such that the hydrate can be instantly formed while the
analogous option is not available in methanol, then the
thermodynamic bias in favor of the recombination reaction is
much stronger in methanol than in water, as can be estimated
from the heats of formation of the products,46,47 and so would
parallel the contrast between our results and those of ref 43.
In the case of the neutral •CH2OH, disproportionation
proceeds by the transfer of the oxygen-bound hydrogen to a
•
•
second CH2OH radical. In the cross-termination of CH2OH

15846 J. Phys. Chem., Vol. 100, No. 39, 1996
Wang et al.
(The evaluation of the data of ref 8 from 100% methanol yields
410 dm3 mol-1 s-1 for k13.) A similar chain reaction is observed
with the formate radical CO2•-, where the propagation rate
constant is about 5 times larger than in the present case.49 The
inset of Figure 3 demonstrates the rise of G(CH2O) beyond the
1
nonchain value of /2G(CH2O•-) ) 3 × 10-7 mol J-1 at a
methanol concentration of 0.01 M, under γ-radiolysis conditions
at high pH.
References and Notes
(1) Laroff, G. P.; Fessenden, R. W. J. Phys. Chem. 1973, 77, 1283.
(2) Asmus, K.-D.; Henglein, A.; Wigger, A.; Beck, G. Ber. Bunsen-
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(3) See, for instance: Heilbronner, E.; Bock, H. Das HMO-Modell
und seine Anwendung; Verlag Chemie: Weinheim, Germany, 1968.
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Soc. 1966, 88, 2851.
(8) Sherman, W. V. J. Phys. Chem. 1967, 71, 4245.
(9) Seki, H.; Nagai, R.; Imamura, M. Bull. Chem. Soc. Jpn. 1968, 41,
2877.
(10) Dainton, F. S.; Salmon, G. A.; Wardman, P. Proc. R. Soc. London
1969, 313A, 1.
(11) Johnson, D. W.; Salmon, G. A. J. Chem. Soc., Faraday Trans. 1
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(12) Johnson, D. W.; Salmon, G. A. Can. J. Chem. 1976, 55, 2030.
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(14) Johnson, D. W.; Salmon, G. A. J. Chem. Soc., Faraday Trans. 1
1979, 446.
(15) Grotheer, H. H.; Riekert, G.; Walter, D.; Just, T. Chem. Phys. Lett.
1988, 148, 530.
(16) Pagsberg, P.; Munk, J.; Sillesen, A. Chem. Phys. Lett. 1988, 146,
375.
(17) von Sonntag, C.; Schuchmann, H.-P. Methods Enzymol. 1994, 233,
3.
Figure 3. γ-Radiolysis of N2O-saturated aqueous solutions of methanol
(0.01 M) at pH 11.6; G(CH2O) as a function of the inverse of the square
root of the dose rate. The value obtained at the high dose rate of pulse
radiolysis (3 Gy µs-1) is indicated by the symbol 4. Inset: G(CH2O)
at the dose rate of 0.18 Gy s-1 as a function of pH.
The behavior of another simple radical anion, superoxide
O2•-, comes to mind which does not show a similar propensity
toward disproportionation. Its self-reaction is immeasurably
slow48 because there is no disproportionation while recombina-
tion is reversible on account of the very low strength of the
-O2-O2 bond.
-
Since the formation of hydroxymethyl takes place in the
presence of N2O, any possible interaction with this additive must
be taken into account. It is well-known that reducing radicals
can transfer an electron to N2O, albeit reacting much more
slowly than the solvated electron itself.8,49,50 The reducing
power of the •CH2OH radical is not strong enough to make this
reaction proceed at a noticeable rate under the present conditions,
but with the CH2O•- radical, a chain reaction (reactions 13 and
14)
(18) Kakac, B.; Vejdelek, Z. J. Handbuch der photometrischen Analyse;
Verlag Chemie: Weinheim, Germany, 1974; Vol. 1, (a) p 257, (b) p 67.
(19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon,
M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.;
Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, ReVision G.4; Gaussian
Inc.: Pittsburgh, PA, 1993.
CH2O•- + N2O f CH2O + N2 + O•-
(13)
(20) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys.
1980, 72, 650.
O
•- + CH3OH f •CH2OH + OH-
(14)
(21) Pople, J. A.; Nesbet, R. K. J. Chem. Phys. 1959, 22, 571.
(22) Roothaan, C. C. J. ReV. Mod. Phys. 1960, 32, 179.
(23) Moeller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618.
(24) Mulliken, R. S. (a) J. Chem. Phys. 1955, 23, 1833. (b) Ibid. 1955,
23, 1841. (c) Ibid. 1955, 23, 2338. (d) Ibid. 1955, 23, 2343. (e) Ibid. 1962,
36, 3428.
(25) von Sonntag, C. The Chemical Basis of Radiation Biology; Taylor
and Francis: London, 1987.
(26) Asmus, K.-D.; Mo¨ckel, H.; Henglein, A. J. Phys. Chem. 1973, 77,
1218.
(27) Buxton, G. V.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. J.
Phys. Chem. Ref. Data 1988, 17, 513.
(28) Schuchmann, H.-P.; von Sonntag, C. J. Photochem. 1981, 16, 289.
(29) Gilbert, B. C.; Holmes, R. G. G.; Laue, H. A. H.; Norman, R. O.
C. J. Chem. Soc., Perkin Trans. 2 1976, 1047.
is clearly observable (cf. ref 8). O•- is the deprotonated form
of the OH radical (pKa ) 11.9) and is about equally reactive in
this system (cf. ref 27), so that reaction 13 represents the rate-
determining step.
In Figure 3, G(CH2O) in N2O-saturated aqueous solutions at
pH 11.6 has been plotted against the inverse of the square root
of the dose rate, according to expression 15, which relates the
rates of radical initiation, propagation, and termination under
the steady-state approximation (D′, dose rate in units of W
dm-3).
(30) Gilbert, B. C.; Holmes, R. G. G.; Norman, R. O. C. J. Chem. Res.
(S) 1977, 1.
(31) Berdnikov, V. M.; Bazhin, N. M.; Fedorov, V. K.; Polyakov, O.
V. Kinet. Catal. (Engl. Transl.) 1972, 13, 986.
1/2
G(CH2O•-)
G(CH2O) ) k13[N2O]
(15)
(
)
2k3D′
(32) Buxton, G. V. In Radiation Chemistry; Farhataziz, Rodgers, M.
A. J., Eds.; VCH Publishers: New York, 1987; p 321.
(33) Simic, M.; Neta, P.; Hayon, E. J. Phys. Chem. 1969, 73, 3794.
Expression 15 allows determination of k13, hitherto apparently
unknown.51 The intercept which corresponds to an “infinitely
high” steady-state concentration of CH2O•- radicals, directly
reflects the nonchain yield [G(CH2O) ) 3 × 10-7 mol J-1].
Essentially the same, nonchain value can be obtained directly,
applying the ionizing radiation at the relatively high (compared
to γ-radiolysis) dose rate of pulse radiolysis (3 Gy per 1 µs
pulse, triangle (4) in Figure 3). The slope of 2.9 × 10-7 mol
dm-3/2 s-1/2 J-1/2, upon appropriate substitution (i.e., [N2O] )
2.4 × 10-2 mol dm-3 and 2k3 ) 0.5 × 109 dm3 mol-1 s-1),
(34) Values previously reported: 2.4 × 109 dm3 mol-1 s-1 33
dm3 mol-1 s-1 in 100% methanol;11 1.44 × 109 dm3 mol-1 s-1 in 100%
methanol;12 2.8 × 109 dm3 mol-1 s-1 in 100% methanol;36 5.3 × 109 dm3
mol-1 s-1 in 100% di-tert-butylperoxide;37 5.5 × 109 dm3 mol-1 s-1 in
100% methanol.38
;
3.0 × 109
dm3 mol-1 s-1 35
;
1.4 × 109 dm3 mol-1 s-1 in 100% methanol;13 2.7 × 109
(35) Rabani, J.; Mulac, W. A.; Matheson, M. S. J. Phys. Chem. 1977,
81, 99.
(36) Getoff, N.; Ritter, A.; Schwo¨rer, F. J. Chem. Soc., Faraday Trans.
1 1983, 79, 2389.
(37) Paul, H.; Small, R. D.; Scaiano, J. C. J. Am. Chem. Soc. 1978,
100, 4520.
gives a propagation rate constant k13 of 350 dm3 mol-1 s-1
.

•
Termination of CH2OH/CH2O•- Radicals
J. Phys. Chem., Vol. 100, No. 39, 1996 15847
(38) Wu, J. Q.; Fischer, H. Int. J. Chem. Kinet. 1995, 27, 167.
(39) Lin, S. H.; Li, K. P.; Eyring, H. In Physical Chemistry. An AdVanced
Treatise; Eyring, H., Ed.; Academic Press: New York, 1975; p 1.
(46) Benson, S. W.; Cruickshank, F. R.; Golden, D. M.; Haugen, G.
R.; O’Neal, H. E.; Rodgers, A. S.; Shaw, R.; Walsh, R. Chem. ReV. 1969,
69, 279.
(47) Benson, S. W. J. Chem. Ed. 1965, 42, 502.
(48) Bielski, B. H. J.; Cabelli, D. E.; Arudi, R. L.; Ross, A. B. J. Phys.
Chem. Ref. Data 1985, 14, 1041.
(49) Al-Sheikhly, M. I.; Schuchmann, H.-P.; von Sonntag, C. Int. J.
Radiat. Biol. 1985, 47, 457.
(50) Sherman, W. V. J. Phys. Chem. 1967, 71, 1695.
(40) Values previously reported: 0.9 × 109 dm3 mol-1 s-1 33
;
0.4 × 109
dm3 mol-1 s-1 in 100% methanol;11 0.16 × 109 dm3 mol-1 s-1 in 100%
methanol.12
(41) Schuchmann, H.-P.; Wagner, R.; von Sonntag, C. Int. J. Radiat.
Biol. 1986, 50, 1051.
(42) Previously reported ratios are as follows: 0.18;5 0.15;41 about 0.1;10
0.09.9
(43) Baxendale, J. H.; Mellows, F. W. J. Am. Chem. Soc. 1961, 83,
4720.
(44) Stabler, R. N.; Chesick, J. P. Int. J. Chem. Kinet. 1978, 10, 461.
(45) Barone, V.; Cristenziano, P. L.; Lelj, F.; Pastore, A. Theochem.
1982, 90, 59 (Table 1).
(51) Neta, P.; Grodkowski, J.; Ross, A. B. J. Phys. Chem. Ref. Data
1996, 25, 709.
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