- Email: [email protected]
Application of chemically induced dynamic nuclear polarization to a kinetic study of phenyl radical reactions
CHEMtCAL PHYSICS
3 (1974)
136-139.Q
NORTH-HOLLAND
PUBLISHINGCOMPANY
APPLICATION OF CHEMICALLY INDUCED DYNAMIC NUCLEAR POLARIZATION TO A KINETIC STUDY OF PHENYL RADICAL REACTIONS L.F. KASUKHIN The L.V. Pisar:hevsky
Insrirwc oJPh_vsiral
and M.P. PONOMARCHUK
of Scietmm ojrhc
C1~errlisrr.v. Academy
b’krairriati
SSR.
Kiev,
USSR
and A.L. BUCHACHENKO lrrsrimre
of ChetnicalPh_vsics,
Academy
of Scietrm
of rife USSR.
,tfoscuw
E-334,
USSR
Rcccivcd 1 July 1973
of P stable pruducr R;Y formed In a free radic;ll rcscrion dcpcnds on nuclear R’ and dccrcrws with 3n mcre3sc of its lifetime, 1~‘. This dcpendcncc was used for evaluation of the liklime of phcnyl radicals gcnemlcd by thcrmolysis of N-nitrosoxrtanilidr (NAA). The . in CCIJ solution al 60’ 1~3s found IO bc 6.9 X lOUs see which corresponds IO ;I rate conskmt k = I .? X IO3 ~~k?p xc-’ for Ihu rcxrion Ph’ + CCI 4 - PhCl t ‘CC13 of which the activation energy equals 8.2 )icJ moic-’ . During Ihc lhcrmolysis of NAA CIDNP arises in 3 geminak radical pair (PIINj ‘ON~PII)~ l’rom which il is wnsfcrrcd lo somatic products through PhN=N’ and the product oi its drsrrucrion, Ph’ rrdical. Comparison ol’ the chpcrimcntal ClDNP enhancement coefficient of the protons in PhN=N’ radical just leaving the radical pair, wvilh !hose calcul3xd fordifferent hktimeS of Ihc inlcrmedistc ~lvcs iIS mean liictime TPhNi = lo-’ see. The CIDNP cnhanccmcnt
relaxation
cocfficicnt
in the pxamagnctic
precursor
The most important quantitative characteristics of the CIDNP (chemically induced dynamic nuclear polarization) is the enhancement coefficient E which is the ratio of nuclear magnetization of the newly formed molecule to the equilibrium one [I 1. The CIDNP which arises as a result of S-TO transitions in a radical pair (R’ ‘R’) (R’ being3 proton bearing radi. cal) is transferred to the combination or disproportionation products RR’. R(-H). R’H, and to the radical R’ escaping the geminate pair by diffusion:
, /RR’. (R’ ‘R ) LR.LRX
R(-H),
R’H (I)
However, during the diffusional motion in solution radical R’ looser part of its initial pclarization @ via nuclear relaxation. Measured in a stable product RX, the CIDNP enhancement coefficient E is determined by E=E”
exp[-rR/Tfi)],
(2)
where rR is the lifetime of the radical R’ and I-i:)
is
the nuclear spin lattice relaxation time of its protons. We used eq. (2) for kinetic studies of the annihilation of free phenyl radicals generated by therrnolysis of N-nitrosoacetanilide radicals and their polarization
(NAA).
Formation
of the
in faststeps which follow the rate-determining isomerizarionof occurs
NAA to benzene diazoacetate PhN=NOAc [ 2). k PkN(NO)Ac x PhN=NOAc -(PhN=N),O (NAA) -(PbN=NO’ -N2_Ph’
‘N=NPh)S-PhN=N’ Lx’phX
(3)
Decomposition of 0.8 M solutions of NAA in solvents LX (tetralin, carbon tetrachloride, propionitrile and nitroethane) was carried out in the probe of a Varian Ae60A NMR spectrometer (60 MHz) at 60°C and the development of the emission NMR signal from PhX during formation was monitored by automatically repeated sweeping of the 7.2-7.4 ppm region. In table I
,!_I? Kasukhin CI aI.. ClDXPapplicd
Table Kinetic
1 characteristics of rhcrmolysis _.-________--~_
Solvent
Product
LX
PhX
~___
hfsolutions
010.8
at 60°C
and polarization
cocfficicnrs
’ 1) -__ ^_ _. _ ~. IO’
tscc-
kx
IO2
-&
k,,l
9.26
i 0.30
4.54
! 0.24
121.0
i 5.3
cc14
PhCl
4.08
t 0.30
1.09 f 0.06
98.9
f 9.0
1 .O
EKN
PhH
4.97
f 0.15
1.33 i 0.09
82.5
t 5.6
0.37
2.57
44.5 f 3.4
a)
4.60
PhH
.._
_ . I and
PLX 3)
t 0.25
_._
151
(SW-‘) -.. ..----_
PhH
_._
of tic prodocr
-I__
px
___-
of NAA
Tcuahn
EtNOz __
137
IO P kincric srudy ofphcnyf radical reaclions
t 0.24
4.8
0.19
_.__ - .- ._. _~- . _. - --- ___
-__--
Error limits given in rablcs 2 indicate random errors cxprcsscd as the rhc stmdsrd drvirtion of rhc mean v.dur~ ofk and E 2nd from 20 IO 30 mcwuementr of /J. calcuhtcd from 5 IO 8 parallcl mcasurcmcnts
the proton enhancement coefficients E for PhX are presented. ‘Ihey were determined by the following equation [I, 31 log I (I, - I,)/1,
I = log I(Ek - @/0_1- k)l - 0.434 kr ) (4)
where I, and I,
are the NMR signal intensities at some
points of time during the reaction and at the end of the reaction. 6~ (rfi)-’ is the rate of nuclear relasa[ion processes in the diamagnetic product RX. Values fork were evaluated from semilogarithmic plots of CIDNP kinetic curves according to eq. (4) and p’s were determined by radio-frequency saturation recovery of the product absorption NhlR lines [4]. Insertion of the following expression for the phenyl radical lifetime 7R = (k&X])-’
= (k,&@])-’
where k,, = k,,(Ph’
,
t LX)/koh(Ph’+CC14),
kc&
)(I&, [ LX])-
1. (6)
The correlation between the values (k,,, [ LX])-’ and logEl is shown in fig. I and can be described by the equation = 2.11 -
(k
1.?37(kr&q-’
.
ml
40
w
[U])-‘10’.
I hd’
into Fig. 1. Correlation
logEl = IoglEol - (0.434/T{?)
20
IO
(5)
eq. (2) gives
logEl
1.6(r-
(7)
From a comparison of eqs. (6) and (7) the values @ = -128.8 + 2.4 and Tm)k In ccb ~0.351 were found. To our knowledge, the exact value of TIi) for phcnyl radical was not yet determined. Values of TE) for some alkyl and aralkyl radicals, evaluated with the CIDNP technique, fall in the range 8 X 1O-5-4.5 X 10e4 set [6]. Assuming Ti:) * 2.5 X 10e4 set for Ph’, one can estimate the rate constant for the reaction
the data of Fll’ + cc14
of logEl
rablc 1, r
-
kCCLJ
q
and (kr,.llLX))-’
according IJ
0.999.
PhCl + ‘Ccl,
.
(8)
and the IO be kccLI = 1.4 X I03 P rnolc-ls~c-~ sverdge lifetime of Ph’ to bc rR =Z 6.9 X IOm5 scc at 60°C in Ccl,. These conclusions arc based on the assumption that the CIDNP developed in a singlet radical pair (PhN=NO’ ‘N=NPh)S and located in radical PhN=N’ is quantitatively transferred to Ph’ (reaction (3)) where it decays via a relaxation mechanism. The necessary condition for this assumption to be valid is TP~~ 4 rt,,(pwi); in fact, qMN’* = 10-B xc [7] (
7&w>
IO-S-
10-4
SC.
The results obtained confirm experimentally the dependence of the CIDNP enhancement coefficients
138
L. F. Kasukldn er al.. CIDNPapplied
ro a kineric srudy ofphenyl
radica! rcacrions
Table 2 Kinelic paramcferr of thcrm31 decomposition ol NAA in CC],(0.8 hl) and polarization coefficients of the product PhCl3)
kx 10~
Temper-
px
3turc Pa
bet-’
10’
43.4 48.5 53.6 57.3
3.10 3.44 4.06 4.35
63.0 --_-
4.09 t 0.3 __
Y. 0.1 -c 0.1 i 0.2 f 0.2
3) See footnote
-E
‘~~QF
51.0 r 1.6 62.0 * 3.4 15.1 f 5.9
0.104 0.132 0.182
(SW-‘)
1
0.21 0.32 0.60 0.82
+ 0.03 *- 0.02 c 0.04 f 0.02
78.1 + 5.1
0.193
1.31 2 0.03
90.5 f 3.5
0.273
of rablc 1.
products on the lifetime of their paramag netic precursors. Shortening of rR with increase of solvent reactivity reduces nuclear depolarization in a radical and provides for a mom complete transfer of CIDNP from the radical to molecule. An analogous dependence should also hold with increase of temperature, i.e., the shorter the lifetime of a radical the higher the E value. In table 2 the E values are presented for protons in PhCl formed during the thetmolysis of 0.8 M solutions of NAA in CC14 over a temperature range from 43 to 63°C and also kCCbT1!) values calculated from eq. (6) where LX f
of stable
CCI,
and krcl = 1. In accordance
prediction the
E
with
values rise in absolute
the temperature increase. The dependence of kCcL and TE) has an exponential character, i.e., &l,jTln (R) =k&(T(:b”
the previous magnitude on
with
temperature
exp[-(~+~rot)/fWl
,
(9)
where E is an activation energy of reaction (8) and Erot is an activation barrier of rotation of radical Ph’ which modulates anisotropic hyperfine interactions with ortho-protons and induces their relaxation. The correlation between the experimental values log[kccbTg)] and T1 (fig. 2) can be expressed by the following equation log[kCQ
TE)) = 6.09 - 2.24 X IO3 T-1 ,
(10)
from which E + E et = (10.3 + 1.5) kcal mole-t and log[I~~~ (Tii))$ = 6.09 were found. The estimation of erOt from 7 rot = &
exP]erotlW
I
01)
in which the period of rotation rrot of Ph’ is determined
?.O
3.1
T-l. 103, % Fig. 2. Corfcl~lion of log(k CCb#)) the data of table 2. r = 0.993.
end T-’
accordiq
IO
from the expression
l/TE’ = 2nb’ 0 r IOI’
(12)
(bu: constant of anisotropic hyperfine interactions of ortho-protons in Ph’. equals 2.5 G [S], 7:” = 5 X lO-13 set) gives erOt = 2. I kcal mole- 1. Thus, the activation energy of reaction (8) is 8.2 + 1.5 kcal mole-t. The enhancement coefficient of the phenyldiazenyl radical PhN=N’ at the moment of its escape from the radical pair (PhN=NO’ ‘N=NPh)S the following equation [9] fl
= (pub - pa’b’)/(&
is determined
by
(13)
- @b’) 9
where (Pub - P,‘b’) is the nonequilibrium population difference of the nuclear spin statesob and o’b’, and (&
- e$)
is their equilibrium
population difference.
POb - Pa’b’ = @r+12fl*,
(14)
where Q is the probability of recombination per one radical encounter in a singlet radical pair, m = 0.1rD-i12 (r; radius of PhN=N*; D: diffusion coefficient), x=
[(2r&)’
t r-2]‘14
cos[~arctg(2l~,b[7)]
- [(2JC0*~)2 + rm2]lj4 where
7 is the lifetime
and
cos[larctg(2l~~,,.ls)l,
of the PhN=N’
radical
(15) with
L.F. Kamkhin
respect to decomposition, Jc,b = CSIJC~TO)a~ is the matrix element of S-T,, mixing in the nuclear spin state ob of the radical pair.
Jc,, =$(&$.W +C upa i
C i
ajnrb),
(1’5)
where Ag is the g-factor difference of the radicals in the pair; IQ 111, and ai, “lb are hyperfiie coupling constants and nuclear spins respectively for both radicals in the p3ir. The INDO calculation of hyperline coupling constants for the PhN=N’ radical has been carried out by Abronin. T’he structure of the radical was assumed to be planar, the angle between the N-N and Cl -CA axis was assumed to be equal to 60”. The hyperfine coupling constants were found to be: o(Nt ) = 13.62 G, a(N,) = 6.19 G,u(cis-Hz) = 0.12 C,a(frarls-I-12) = I .69 G, o(cis-H3) = 0.90 G. o(trurrs-Hj) = 0.0 I G, a(H4) = 0.30 C. For the sake of simplicity the pair (PhN=NO’ ‘N=NPh) can be trealed 3s a one-proton pair with hypcrfine coupling constant a = 2 G.Thcn the matrix
10
20
139
cl al, CIDIVPappliedto a kinetic study of plrcnyiradical rcactiuns
50
40
a.G Fig. 3. Plots of X for the phcnyldiazenyl radial versus the hypclfiic coupling conswnt of its orthwprofon at different lifetimes of PhN=N’; curves I- 11 correspond to TR = 4 x lo-‘. 2 x lo-‘. lo-‘, 8 X 1O-8, 6 X 10-a, 5 X 10-8, 4 x lo-*, 3 x lOmE, 2 X IO-a, IOw8, and 6 X 10m9 see, xspectively.
elements arc Jc,, = f(LgW + $a) and 3Ca*,* = f (AggpH - $7,. Dependence of X on a for different lifetimes of PhN=N’ is shown in fig. 3. A broken straight line corresponds to X = -0.32 X IO3 sec-ti2 calculated from the expcrimcntal I?’ value with Q = 0.75, & = . -g ,,N ,.=,.0010-7,.0017=-7x1O-4 f;y?&$b -%$bV = IO- 5, r = 3&D = 10m6 cn~~scc-~. Assuming a value of ZC for the hypcrfinc coupling constant, the experimental enhanccmcnt coefficient corresponds to a lifetime of the PhN=N’ radical of 10m7 sec. This value should be considered only as an order of magnitude estimation because of uncertainties in the choice of some parameters, especially of tht hyperfine coupling constant. The results reported illustrate the possibilities of the CIDNP method for the determination of lifetimes and rate constants of active short living radicals.
References
[ 11A.1,.Buchxhcnko
and GM
Zhidomirov.
Usp. Khim. 40
(1971) 1729. A.L. Buchachcnko, A.V. Kcsscnllih and S.V. Rykov. Zh. Eksp. Tcor. Fiz. 58 (1970) 766. 121 L.F. Kasukhin, h1.P. Ponomarchuk and S.D. Rudcnko. Zh. Org. Ehim., in press. 131 A.L. Buchachenko and Sh.A. hlarkarim, Inlcrn. 1. Chcm. KineIics4 (1971) 513. 141 W.A. Anderton. in: NhlR and EPR sprct~oscopy (Pergaman Press, Nrw York, 1960) 01. 8. 151 R.F. Bridger and G.A. Russell, 1. Am. Chem. Sot. 85 (1963) 3754. 161 G.L. Gloss and A.D. Trifunac, 1. Am.Chem. Sot. 92 (1970) 7227; hf. Lehnig and H. Fisher, i. Naturforsch. 2% (1970) 1963; C. Walling and R.A. Lcplcy. J. Am. Chem. Sac. 94 (1972) 2007. 171 N.A. Porter. L.J. Marnett. C.H. LochmiiUer.G.L.Closs and hlasako Shobaraki. J. Am. Chem. Sot. 94 (1972) 3664. 181 P.H. Kasai, E. Hcdsya and E.B. Whipple. J. Am. Chcm. sot. 91 (1969) 4364. [ 91 A.L. Buchachenko. Chemical polarization of clccrrons and nuclei (Science Publisher. Moscow), in press; A. Buchachcnko and Sh.A. Mukari.~. Org. hlagn. Res., in pnss; A. Buchachenko and Sh.A. hlarkarian, The CIDNPand ClDEP Symposium (Tallinn, 1972) p. 24. [ 101 J.I. Cadogan, R.M. Paton and C. Thomson, J. Chern. Sot. B (1971) 583.
3 (1974)
136-139.Q
NORTH-HOLLAND
PUBLISHINGCOMPANY
APPLICATION OF CHEMICALLY INDUCED DYNAMIC NUCLEAR POLARIZATION TO A KINETIC STUDY OF PHENYL RADICAL REACTIONS L.F. KASUKHIN The L.V. Pisar:hevsky
Insrirwc oJPh_vsiral
and M.P. PONOMARCHUK
of Scietmm ojrhc
C1~errlisrr.v. Academy
b’krairriati
SSR.
Kiev,
USSR
and A.L. BUCHACHENKO lrrsrimre
of ChetnicalPh_vsics,
Academy
of Scietrm
of rife USSR.
,tfoscuw
E-334,
USSR
Rcccivcd 1 July 1973
of P stable pruducr R;Y formed In a free radic;ll rcscrion dcpcnds on nuclear R’ and dccrcrws with 3n mcre3sc of its lifetime, 1~‘. This dcpendcncc was used for evaluation of the liklime of phcnyl radicals gcnemlcd by thcrmolysis of N-nitrosoxrtanilidr (NAA). The . in CCIJ solution al 60’ 1~3s found IO bc 6.9 X lOUs see which corresponds IO ;I rate conskmt k = I .? X IO3 ~~k?p xc-’ for Ihu rcxrion Ph’ + CCI 4 - PhCl t ‘CC13 of which the activation energy equals 8.2 )icJ moic-’ . During Ihc lhcrmolysis of NAA CIDNP arises in 3 geminak radical pair (PIINj ‘ON~PII)~ l’rom which il is wnsfcrrcd lo somatic products through PhN=N’ and the product oi its drsrrucrion, Ph’ rrdical. Comparison ol’ the chpcrimcntal ClDNP enhancement coefficient of the protons in PhN=N’ radical just leaving the radical pair, wvilh !hose calcul3xd fordifferent hktimeS of Ihc inlcrmedistc ~lvcs iIS mean liictime TPhNi = lo-’ see. The CIDNP cnhanccmcnt
relaxation
cocfficicnt
in the pxamagnctic
precursor
The most important quantitative characteristics of the CIDNP (chemically induced dynamic nuclear polarization) is the enhancement coefficient E which is the ratio of nuclear magnetization of the newly formed molecule to the equilibrium one [I 1. The CIDNP which arises as a result of S-TO transitions in a radical pair (R’ ‘R’) (R’ being3 proton bearing radi. cal) is transferred to the combination or disproportionation products RR’. R(-H). R’H, and to the radical R’ escaping the geminate pair by diffusion:
, /RR’. (R’ ‘R ) LR.LRX
R(-H),
R’H (I)
However, during the diffusional motion in solution radical R’ looser part of its initial pclarization @ via nuclear relaxation. Measured in a stable product RX, the CIDNP enhancement coefficient E is determined by E=E”
exp[-rR/Tfi)],
(2)
where rR is the lifetime of the radical R’ and I-i:)
is
the nuclear spin lattice relaxation time of its protons. We used eq. (2) for kinetic studies of the annihilation of free phenyl radicals generated by therrnolysis of N-nitrosoacetanilide radicals and their polarization
(NAA).
Formation
of the
in faststeps which follow the rate-determining isomerizarionof occurs
NAA to benzene diazoacetate PhN=NOAc [ 2). k PkN(NO)Ac x PhN=NOAc -(PhN=N),O (NAA) -(PbN=NO’ -N2_Ph’
‘N=NPh)S-PhN=N’ Lx’phX
(3)
Decomposition of 0.8 M solutions of NAA in solvents LX (tetralin, carbon tetrachloride, propionitrile and nitroethane) was carried out in the probe of a Varian Ae60A NMR spectrometer (60 MHz) at 60°C and the development of the emission NMR signal from PhX during formation was monitored by automatically repeated sweeping of the 7.2-7.4 ppm region. In table I
,!_I? Kasukhin CI aI.. ClDXPapplicd
Table Kinetic
1 characteristics of rhcrmolysis _.-________--~_
Solvent
Product
LX
PhX
~___
hfsolutions
010.8
at 60°C
and polarization
cocfficicnrs
’ 1) -__ ^_ _. _ ~. IO’
tscc-
kx
IO2
-&
k,,l
9.26
i 0.30
4.54
! 0.24
121.0
i 5.3
cc14
PhCl
4.08
t 0.30
1.09 f 0.06
98.9
f 9.0
1 .O
EKN
PhH
4.97
f 0.15
1.33 i 0.09
82.5
t 5.6
0.37
2.57
44.5 f 3.4
a)
4.60
PhH
.._
_ . I and
PLX 3)
t 0.25
_._
151
(SW-‘) -.. ..----_
PhH
_._
of tic prodocr
-I__
px
___-
of NAA
Tcuahn
EtNOz __
137
IO P kincric srudy ofphcnyf radical reaclions
t 0.24
4.8
0.19
_.__ - .- ._. _~- . _. - --- ___
-__--
Error limits given in rablcs 2 indicate random errors cxprcsscd as the rhc stmdsrd drvirtion of rhc mean v.dur~ ofk and E 2nd from 20 IO 30 mcwuementr of /J. calcuhtcd from 5 IO 8 parallcl mcasurcmcnts
the proton enhancement coefficients E for PhX are presented. ‘Ihey were determined by the following equation [I, 31 log I (I, - I,)/1,
I = log I(Ek - @/0_1- k)l - 0.434 kr ) (4)
where I, and I,
are the NMR signal intensities at some
points of time during the reaction and at the end of the reaction. 6~ (rfi)-’ is the rate of nuclear relasa[ion processes in the diamagnetic product RX. Values fork were evaluated from semilogarithmic plots of CIDNP kinetic curves according to eq. (4) and p’s were determined by radio-frequency saturation recovery of the product absorption NhlR lines [4]. Insertion of the following expression for the phenyl radical lifetime 7R = (k&X])-’
= (k,&@])-’
where k,, = k,,(Ph’
,
t LX)/koh(Ph’+CC14),
kc&
)(I&, [ LX])-
1. (6)
The correlation between the values (k,,, [ LX])-’ and logEl is shown in fig. I and can be described by the equation = 2.11 -
(k
1.?37(kr&q-’
.
ml
40
w
[U])-‘10’.
I hd’
into Fig. 1. Correlation
logEl = IoglEol - (0.434/T{?)
20
IO
(5)
eq. (2) gives
logEl
1.6(r-
(7)
From a comparison of eqs. (6) and (7) the values @ = -128.8 + 2.4 and Tm)k In ccb ~0.351 were found. To our knowledge, the exact value of TIi) for phcnyl radical was not yet determined. Values of TE) for some alkyl and aralkyl radicals, evaluated with the CIDNP technique, fall in the range 8 X 1O-5-4.5 X 10e4 set [6]. Assuming Ti:) * 2.5 X 10e4 set for Ph’, one can estimate the rate constant for the reaction
the data of Fll’ + cc14
of logEl
rablc 1, r
-
kCCLJ
q
and (kr,.llLX))-’
according IJ
0.999.
PhCl + ‘Ccl,
.
(8)
and the IO be kccLI = 1.4 X I03 P rnolc-ls~c-~ sverdge lifetime of Ph’ to bc rR =Z 6.9 X IOm5 scc at 60°C in Ccl,. These conclusions arc based on the assumption that the CIDNP developed in a singlet radical pair (PhN=NO’ ‘N=NPh)S and located in radical PhN=N’ is quantitatively transferred to Ph’ (reaction (3)) where it decays via a relaxation mechanism. The necessary condition for this assumption to be valid is TP~~ 4 rt,,(pwi); in fact, qMN’* = 10-B xc [7] (
7&w>
IO-S-
10-4
SC.
The results obtained confirm experimentally the dependence of the CIDNP enhancement coefficients
138
L. F. Kasukldn er al.. CIDNPapplied
ro a kineric srudy ofphenyl
radica! rcacrions
Table 2 Kinelic paramcferr of thcrm31 decomposition ol NAA in CC],(0.8 hl) and polarization coefficients of the product PhCl3)
kx 10~
Temper-
px
3turc Pa
bet-’
10’
43.4 48.5 53.6 57.3
3.10 3.44 4.06 4.35
63.0 --_-
4.09 t 0.3 __
Y. 0.1 -c 0.1 i 0.2 f 0.2
3) See footnote
-E
‘~~QF
51.0 r 1.6 62.0 * 3.4 15.1 f 5.9
0.104 0.132 0.182
(SW-‘)
1
0.21 0.32 0.60 0.82
+ 0.03 *- 0.02 c 0.04 f 0.02
78.1 + 5.1
0.193
1.31 2 0.03
90.5 f 3.5
0.273
of rablc 1.
products on the lifetime of their paramag netic precursors. Shortening of rR with increase of solvent reactivity reduces nuclear depolarization in a radical and provides for a mom complete transfer of CIDNP from the radical to molecule. An analogous dependence should also hold with increase of temperature, i.e., the shorter the lifetime of a radical the higher the E value. In table 2 the E values are presented for protons in PhCl formed during the thetmolysis of 0.8 M solutions of NAA in CC14 over a temperature range from 43 to 63°C and also kCCbT1!) values calculated from eq. (6) where LX f
of stable
CCI,
and krcl = 1. In accordance
prediction the
E
with
values rise in absolute
the temperature increase. The dependence of kCcL and TE) has an exponential character, i.e., &l,jTln (R) =k&(T(:b”
the previous magnitude on
with
temperature
exp[-(~+~rot)/fWl
,
(9)
where E is an activation energy of reaction (8) and Erot is an activation barrier of rotation of radical Ph’ which modulates anisotropic hyperfine interactions with ortho-protons and induces their relaxation. The correlation between the experimental values log[kccbTg)] and T1 (fig. 2) can be expressed by the following equation log[kCQ
TE)) = 6.09 - 2.24 X IO3 T-1 ,
(10)
from which E + E et = (10.3 + 1.5) kcal mole-t and log[I~~~ (Tii))$ = 6.09 were found. The estimation of erOt from 7 rot = &
exP]erotlW
I
01)
in which the period of rotation rrot of Ph’ is determined
?.O
3.1
T-l. 103, % Fig. 2. Corfcl~lion of log(k CCb#)) the data of table 2. r = 0.993.
end T-’
accordiq
IO
from the expression
l/TE’ = 2nb’ 0 r IOI’
(12)
(bu: constant of anisotropic hyperfine interactions of ortho-protons in Ph’. equals 2.5 G [S], 7:” = 5 X lO-13 set) gives erOt = 2. I kcal mole- 1. Thus, the activation energy of reaction (8) is 8.2 + 1.5 kcal mole-t. The enhancement coefficient of the phenyldiazenyl radical PhN=N’ at the moment of its escape from the radical pair (PhN=NO’ ‘N=NPh)S the following equation [9] fl
= (pub - pa’b’)/(&
is determined
by
(13)
- @b’) 9
where (Pub - P,‘b’) is the nonequilibrium population difference of the nuclear spin statesob and o’b’, and (&
- e$)
is their equilibrium
population difference.
POb - Pa’b’ = @r+12fl*,
(14)
where Q is the probability of recombination per one radical encounter in a singlet radical pair, m = 0.1rD-i12 (r; radius of PhN=N*; D: diffusion coefficient), x=
[(2r&)’
t r-2]‘14
cos[~arctg(2l~,b[7)]
- [(2JC0*~)2 + rm2]lj4 where
7 is the lifetime
and
cos[larctg(2l~~,,.ls)l,
of the PhN=N’
radical
(15) with
L.F. Kamkhin
respect to decomposition, Jc,b = CSIJC~TO)a~ is the matrix element of S-T,, mixing in the nuclear spin state ob of the radical pair.
Jc,, =$(&$.W +C upa i
C i
ajnrb),
(1’5)
where Ag is the g-factor difference of the radicals in the pair; IQ 111, and ai, “lb are hyperfiie coupling constants and nuclear spins respectively for both radicals in the p3ir. The INDO calculation of hyperline coupling constants for the PhN=N’ radical has been carried out by Abronin. T’he structure of the radical was assumed to be planar, the angle between the N-N and Cl -CA axis was assumed to be equal to 60”. The hyperfine coupling constants were found to be: o(Nt ) = 13.62 G, a(N,) = 6.19 G,u(cis-Hz) = 0.12 C,a(frarls-I-12) = I .69 G, o(cis-H3) = 0.90 G. o(trurrs-Hj) = 0.0 I G, a(H4) = 0.30 C. For the sake of simplicity the pair (PhN=NO’ ‘N=NPh) can be trealed 3s a one-proton pair with hypcrfine coupling constant a = 2 G.Thcn the matrix
10
20
139
cl al, CIDIVPappliedto a kinetic study of plrcnyiradical rcactiuns
50
40
a.G Fig. 3. Plots of X for the phcnyldiazenyl radial versus the hypclfiic coupling conswnt of its orthwprofon at different lifetimes of PhN=N’; curves I- 11 correspond to TR = 4 x lo-‘. 2 x lo-‘. lo-‘, 8 X 1O-8, 6 X 10-a, 5 X 10-8, 4 x lo-*, 3 x lOmE, 2 X IO-a, IOw8, and 6 X 10m9 see, xspectively.
elements arc Jc,, = f(LgW + $a) and 3Ca*,* = f (AggpH - $7,. Dependence of X on a for different lifetimes of PhN=N’ is shown in fig. 3. A broken straight line corresponds to X = -0.32 X IO3 sec-ti2 calculated from the expcrimcntal I?’ value with Q = 0.75, & = . -g ,,N ,.=,.0010-7,.0017=-7x1O-4 f;y?&$b -%$bV = IO- 5, r = 3&D = 10m6 cn~~scc-~. Assuming a value of ZC for the hypcrfinc coupling constant, the experimental enhanccmcnt coefficient corresponds to a lifetime of the PhN=N’ radical of 10m7 sec. This value should be considered only as an order of magnitude estimation because of uncertainties in the choice of some parameters, especially of tht hyperfine coupling constant. The results reported illustrate the possibilities of the CIDNP method for the determination of lifetimes and rate constants of active short living radicals.
References
[ 11A.1,.Buchxhcnko
and GM
Zhidomirov.
Usp. Khim. 40
(1971) 1729. A.L. Buchachcnko, A.V. Kcsscnllih and S.V. Rykov. Zh. Eksp. Tcor. Fiz. 58 (1970) 766. 121 L.F. Kasukhin, h1.P. Ponomarchuk and S.D. Rudcnko. Zh. Org. Ehim., in press. 131 A.L. Buchachenko and Sh.A. hlarkarim, Inlcrn. 1. Chcm. KineIics4 (1971) 513. 141 W.A. Anderton. in: NhlR and EPR sprct~oscopy (Pergaman Press, Nrw York, 1960) 01. 8. 151 R.F. Bridger and G.A. Russell, 1. Am. Chem. Sot. 85 (1963) 3754. 161 G.L. Gloss and A.D. Trifunac, 1. Am.Chem. Sot. 92 (1970) 7227; hf. Lehnig and H. Fisher, i. Naturforsch. 2% (1970) 1963; C. Walling and R.A. Lcplcy. J. Am. Chem. Sac. 94 (1972) 2007. 171 N.A. Porter. L.J. Marnett. C.H. LochmiiUer.G.L.Closs and hlasako Shobaraki. J. Am. Chem. Sot. 94 (1972) 3664. 181 P.H. Kasai, E. Hcdsya and E.B. Whipple. J. Am. Chcm. sot. 91 (1969) 4364. [ 91 A.L. Buchachenko. Chemical polarization of clccrrons and nuclei (Science Publisher. Moscow), in press; A. Buchachcnko and Sh.A. Mukari.~. Org. hlagn. Res., in pnss; A. Buchachenko and Sh.A. hlarkarian, The CIDNPand ClDEP Symposium (Tallinn, 1972) p. 24. [ 101 J.I. Cadogan, R.M. Paton and C. Thomson, J. Chern. Sot. B (1971) 583.