- Email: [email protected]
Resonance effect of a high-frequency magnetic field on the recombination probability of radical pairs in a liquid
Volume 73, number
2
RESONANCE EFFECT OF A HIGH-FREQUENCY ON THE RECOMBINATION S I. KUBARFW,
15 July 1980
CHEMICAL PHYSICS LETTERS
PROBABILITY
S.V. SHEBERSTOV
MAGNEnC
FIELD
OF RADICAL PAIRS iN A LIQUID
and A.S. SHUSTOV
Insrzhte of Chemrcal Physics. Academy of Scrences of the USSR, Moscow I I 7334. USSR
Received 8 Apnl 1980
ExpressIons for a resonance dependence of gemmate recombmation probabhty of radical pairs on the intensity of an external steady magnetic field m the presence of a tigh-frequency magnetic field normal to it have been obtamed Numeral calculations of the above dependence have been performed for the cases mvolvmg Ag and hyperfme coupling mechanisms of spm convewon
The posslbfity of a resonance effect of a high-frequency magnetic field H,(r) on the probabihty of reactlons taking place between paramagnetic particles in condensed medra in the presence of an external steady magnetic field H(assummg that HI I H) was fast predicted in refs. [I ,2 1. The sLmplest case of radical paus (RP) with various g factors and non-magnetic nuclei was consIdered. Shortly afterwards the abovementioned effect was expenmentally found by Frankevich et al. [3-S] m reactions involvmg triplet excltons and doublet particles (electrons and holes) m crystalline aromatic compounds, and later by Molm and co-workers m neutralisatlon reactions of ion-radical pairs in a liquid [6] _ These papers [3-5 ] contained studies of reaction rate dependence on the strength n of a steady magnetic field in the presence of a high-frequency magnetic field of fued frequency w and strength HI. These dependences were of a resonance nature and were denoted by the authors as RYDMR spectra (reactron yield detected magnetic resonance). These spectra, m view of the Hugh sensrtrvIty of recording techniques, make it possible to obtam mformation concerning lughly reactive short-lived intermediate reaction products. These products are usually present m concentrations so small as to be undetectabIe by other techmques such as the ESR method (see for example refs. [4,6]). The present work IS aimed at formulatmg a general approach to the calculation of RYDMR spectra in the case of an arbitrary interaction between radicals as well as at studying the mfluence of radical structure and the character of their motion in a medium on the shapes of the spectra. The studies are conducted by using as an example the Rp geminate recombmatron in a hquid within the framework of the approximation of a single radical encounter [2] _ It is assumed that radicals can recombine only m the singlet state IS). Then it follows that the probability PC23 of a recombination of radicals R, and k, formed III a spin state Ii> can be represented as [7]
(1) where OLis the probability of a singlet RP recombination during an encounter of the ra&cals 171; C(t) = (S]*(t)) where I*(r)> is the RP spm state, with I*(O)> = Ii> (m the present paper we assume that i= S);f(t) is the probability density of the first encounter of the radicals at the recombination radius. The value IC~)(t)l* can be expressed III the form lC’~)(r)l* 370
= Tr E(t)3(s)]
,
(2)
Volume 73, number 2
CHEMICAL
15 Jury 29Stp
PHY SlCS LETTERS
where Tr apphes to all electron and nuclear RP spin states; ii(t) is the spin density matrix of RP at time z after its creation in lS);~~@) = lS)(sl is the singlet projection operator_ The RP spin hamiltonian with the spin-dependent inter-radical interaction disregarded, has the form & = 5%1 + 6i2, where (3) Here n = 1,s G$) = g&?lti, WY) = g,QHIIA, ~$‘n = -y&Z; $ is the electron spin operator of the nth ra&& of the pair, In1 is the operator of the ith nuclear spin of RP n, yni is its gyromagnetic ratio; Ani is the corresponding hyperfme constant; the z axis coincides with the directron of the steady magnetic field. In this work the intensity of the steady magnetic field is assumed to be fairly hrgh (He LO3 Oe) whereas the value hAlgp for most organic radicals does not exceed a few tens of oersted. Thus, the non-secular terms inducing transitions between the states wrth different nuclear spm projections of radicals can be neglected in the spin ham& tonian (3). In this case it can easily be shown that the third term in (3) describing the Zeeman nuclear interaction does not affect the value lC~)(r)12. By neglecting the non-secular terms in the spin hamiltonian (3) we can obtain an exact solution of the quantum Liouvrlle equation for the RP spin density matrix s(f) and represent [C$)(r)I* in the form
@(t) 12= [
v
(*llZ
+
1)C21~j+1)]-1
f/l
lCg(t)12,
where Inniis the value of the zth spin of the nth radical of the pair; the summation extends over all nuclear [email protected]. The quantity @A( equals lCcs) @)I2 = AR sm
+ BE) cos [(aim)
ap
a)2
+ a(m) 2 ) t] + cg
cos [(ac;n) -
a(m)) t] + 0%
[cos (a$mlm’t)f cos (aa(,m
)
where = [‘(a$’
-
+ (&Jy)2]
112 )
n = 1,2;
0:)
s UP)
+ CA i
.m nt ni
9
where mnl IS the value of nth radical’s rth nuclear spin projectron onto the z axis. If we introduce the notation sin ap)
= o(;)/$n),
cos tip’
= (A-z:’ - w)/cp’
,
the coefficients A, B, Cand D, dependent on the nuclear-spin state lm)= lmI)lm2)are B(S) = ; sin4 [f(a\m) - $N)],
cf$ = $ cos4 [I
m
~(9 = p k2($m) m Thus
_ g(m) 2)’
A@) = @ m
+ C$
_ $mQ
,
_
the calculatron of the recombination probability PCs) is actually reduced to the evaluation of irate-
of
the form F(SL)
= jcos(Rt)f(t)dt
_
0
Let us assume that the relative motion of radicals in a liquid outside the region of their immediate contact can be regarded as an isotropic continual diffusion. Then the functronf(r) is expressed in accordance with ref. [71 as f(t) = 4n&
ac(r, fyari,,,
,
c-9
where a is the RP recombination rarhus; D is the coefficient of their relative diffusion in a medium; G(r, t) is tfre probabihty density for a pair of radicals to be separated by the distance r in time t after their creation. If the interaction of the radicals outside the recombination region does not depend on their spins and is descriied by a spheri371
Volume
73,
tally symmetrical
15 July 1980
CHEMICAL PHYSICS LETTERS
number 2 potentiai
U(r), then G(r, t) satrsfies the Smoluchowski
equation
(6) with boundary condrtions [7] G(a. t) = 0, G(r, t += -) -+ 0. Here T is the hfetrme of the radicals. If are separated by a distance r = ro (r > a) at the moment of their creation r = 0, the rmtial conditions G(r, 0) = 6(r - ro)/4nr;. It is readrIy seen from eq. (4) that the functton F(a) is expressed by the real part of the Laplace the functron G(r, t)_ Applying the Laplace transformatron to eqs. (5) and (6) and performmg a few tions, F(Q)
= Wo)
Re
where y(r) 1s the solution y”-{[(l+iQr)/o7]
the radicals of eq. (6) are transform of simple opera-
Iv(qJ~@)l ewC-_(1/2kT) W(a) - WoNI , vanishing
(7)
at r +-m of the equation
+(U’/2kT)2-(l/2kT)(U”+2U’/r)}y=0.
(8)
In the present work a case of non-mteracting radicals is constdered, when we can assume that U(r) = 0. The case of ion-radica1 pans w~vlllbe considered elsewhere. If U(r) = 0, from the solution of eq. (8) and m accordance with (7) we find that [2] F(Q)
= (fr/ro) exp {-(rD/r)‘/2
{[ I+ (a~)~ ] U2 + 1}1/2) cos {(TD/T)L/~ {[l + (a~)~]
U2 -
1}*i2} ,
where rD = (r. - a)2/20. We have made a numerical calculation of the shape of a RYDMR bne for various kinds of RP. Generally speakmg, the RR recombinatron probabrhty P@ depends on the following parameters. T, rD, Ag, hyperfiie constants, Q, ro. It turns out that the shape of a RYDMR spectrum is strongly affected only by r and by the values of the parameters Ag and the constants A, which are determined by the magnetic properties of the radrcals and their structure. Figs. 1-4 show the dependence of the value W(H) = [P@(H, 0) - @)(H, HL)]/o (the difference of normalized r
WlcP
3
3550
2
3555
H,Oe
00
1
3550
3560
3570
H, Oersted Fig. 1. WeU resolved RYDMR spectra. The case of the Ag mechanism of spur conversion in the absence of magnetic nuclei. (1) Ag= 1o-2 , (2) Ag = 4 X 10-3, (3) Ag' 1.5 X 11T3.
372
Frg. 2 Spin reversion
effect of a RYDMR .&MI for the Ag spm conversion. (1) Ag= 8 5 X 104, (2) Ag= 7.0 mechanismof X 104, (3) Ag = 5 X 104, (4) Ag = lOa'.
Volume 73. number 2
CHEMICAL
PHYSICS LETTERS
15 July 1980
J I
3540
I
3550
1
3560
-I
H,CJe
Rg. 3. Dependenceof the shapeof a RYDMR spectral hne on RP Wetime. HyperFme couphng mechamsm of_spinconversion, one magnetic nucleus(f = l/2) on the radical R 1; the ra&cal Rz does not contam any magnetic nuclei. ~0 = 1O”t s. (1) s = 10” s. (2) t = 5 X 10’s~. (3) T = 2 X lOma s. Hyperfme constant fiA/p = 15 Oe.
Jwo
s3sa
3560
Q*
F%g.4. Examples of well-resolved RYDMR spectra_ T = iW7s. (1) 5g= 8 X 10e3,r~= lo-r*s,one~gneticnuc~uswith RA 1/P= 10 Oe, (2) Ag = 0, two identical nucIei on the mdical kt ~thfiA&?=fiA#= lOOe,one msgneticnucleuson $
withltA&=100e,rD=5
X 10'10s.(3)Ag= O,onemag-
netic nucleus on each of the radicaIs,fiA~/g = 100e,EAz/@= 20 Oe, w = lo-* 1 s.
RP recombination probabrhties in the presence and the absence of a high-frequency magnetic field) on the intensity of an external steady magnetic field. The calculatrons were made on the assumption that the intensity of the h&h.frequency magnetic field H, = 1 Oe and rts frequency o = 6.24 X lOIos-1 @w/2.002/3 = 35SOOe). The RYQMR spectra of radical pairs wrth non-magnetic nuclei and different g factors of radicals with r = 10-T s are given in figs. 1 and 2. It was assumed that D = 1O-5 cm2/s (which is equivalent to rD = 1O-IL s). It should be noted that caIcuIations involving various other values of rD (IO-” s =GrD G IOP7 s) were also made with the result that the shape of the RYDMR spectrum was found to be weakly dependent on TV, whereas the amphtude of the RYDMR signal decreases by one order of magnitude as rD decreases by two orders. Well resolved RYDMR spectra correspond to the positive value of W(fY) in the centre of the spectrum and to a very small (in absolute magnitude) negative value of ?V(%r)at its wings and constitute sets of individual peaks. The positions of maxima in them correspond to the alIowec transitions between the magnetic spin sublevels of a pair of non-interacting radicals (see fig. 1; fig. 3, curves (I) and (2); fig. 4). However, as seen from the results obtained, when individual peaks come close together or move apart, fust occurs the smking of the wings and then the center of the curve also sinks. The sign of the effect changes too (see figs. I and 2). The negative RYDMR effect (W(H) < 0) 1s due to spin-conversion slowdown in RP caused by a ~~-frequency magnetic field. The mechanism of such slo~gdo~ is made clearer by resorting to the simpIe example of a pure Ag effect at
Consider a new coordinate system (x’,~‘, z) rotating around the axis J with the frequency o of tb~ field HE _ Let RI be parallel to the x’ axis. Then, in the field H = If9 (Ho = 3550 Oe), the spin S, of the radical Rg will precess around the direction of an effective field, which practicaIIy comcides in this case with E&(t) at the frequency approx imately equal to CQ~“.The s in S, wilI also precess with frequency close to c@ around Hi. Therefore the S-to-T transrtion time will be n/lo~ ?) - o(12”l whr c h considerably exceeds the time of ‘such a transition in the case of the Ag effect m a steady magnetic field (H,
Volume 73, number 2
CHEMICAL PHYSICS LETTERS
15 July 1980
Rough estimations indicate that in the case of the Ag effect of a high-frequency field, the vahtity of the inequality IAwl Z+gpSlfi, where 6 = t2/gar3f4s$4 1s the spectral line width, can serve as a criterion of a good resolution
of the RYDMR spectrum. Summing up, we point out that the study of RYDMR spectra yields the folIowing information: (1) For well resolved spectra, the posItIons of resonance peaks in the case of a pure Ag effect can be used to determme the g factors of short-lived rack?&. Besides, the measurement of hnewidths makes it possrble to determme the hfetimes of radicals in a mechum. (2) Well resolved spectra of RP containing magnetrc nucIei make it possible to determine through the posrtions of peaks the hyperfme constants of highly reactive radicals. (3) The shapes of poorly resolved spectra in the case of the Ag effect (see fig. 2) strongIy depend on the drfference of Rpg factors and on therr hfetnnes T, which m turn allows us to estimate the vahres of Ag and 7. Thus, the study of RYDMR spectra seems extremely promising for the rnvestigation of the mechanism of elementary stages of radrcal reactlons.
References [I i S-1. Kubarev and E.A. Pshemchnov, Chem. Phys. Letters 28 (1974) 66. [2] S-1. Kubarev. E.A. Pshemchnov and AS. Shustov. Tear. Ekspernn. Wurn. 12 (1976) 435. [3] E.L. Frankevich and A-1. Pnstupa, Zh. Eksp. Teor. Fiz, Pls’ma Red. 24 (1976) L397. 141 V-L L.esm, V-P- Sakun, A.I. F’ristupaand E.L. Frankewch, Phys. Stat. SOL 84b (1977) 513. [S] E-L. Frankevrch, V.I. Lesin and A.I. Pristupa, Zh. Eksperun. I Teor. FiL 75 (1978) 415. (61 0.k AnLumov. V.M. Grygoryants, V.K. Molchanov and Yu.N. Mobn, Chem Phys Letters 66 (1979) [7j J.M. Deutch. J. Chem. Phys. 56 (1972) 6076.
374
265.
2
RESONANCE EFFECT OF A HIGH-FREQUENCY ON THE RECOMBINATION S I. KUBARFW,
15 July 1980
CHEMICAL PHYSICS LETTERS
PROBABILITY
S.V. SHEBERSTOV
MAGNEnC
FIELD
OF RADICAL PAIRS iN A LIQUID
and A.S. SHUSTOV
Insrzhte of Chemrcal Physics. Academy of Scrences of the USSR, Moscow I I 7334. USSR
Received 8 Apnl 1980
ExpressIons for a resonance dependence of gemmate recombmation probabhty of radical pairs on the intensity of an external steady magnetic field m the presence of a tigh-frequency magnetic field normal to it have been obtamed Numeral calculations of the above dependence have been performed for the cases mvolvmg Ag and hyperfme coupling mechanisms of spm convewon
The posslbfity of a resonance effect of a high-frequency magnetic field H,(r) on the probabihty of reactlons taking place between paramagnetic particles in condensed medra in the presence of an external steady magnetic field H(assummg that HI I H) was fast predicted in refs. [I ,2 1. The sLmplest case of radical paus (RP) with various g factors and non-magnetic nuclei was consIdered. Shortly afterwards the abovementioned effect was expenmentally found by Frankevich et al. [3-S] m reactions involvmg triplet excltons and doublet particles (electrons and holes) m crystalline aromatic compounds, and later by Molm and co-workers m neutralisatlon reactions of ion-radical pairs in a liquid [6] _ These papers [3-5 ] contained studies of reaction rate dependence on the strength n of a steady magnetic field in the presence of a high-frequency magnetic field of fued frequency w and strength HI. These dependences were of a resonance nature and were denoted by the authors as RYDMR spectra (reactron yield detected magnetic resonance). These spectra, m view of the Hugh sensrtrvIty of recording techniques, make it possible to obtam mformation concerning lughly reactive short-lived intermediate reaction products. These products are usually present m concentrations so small as to be undetectabIe by other techmques such as the ESR method (see for example refs. [4,6]). The present work IS aimed at formulatmg a general approach to the calculation of RYDMR spectra in the case of an arbitrary interaction between radicals as well as at studying the mfluence of radical structure and the character of their motion in a medium on the shapes of the spectra. The studies are conducted by using as an example the Rp geminate recombmatron in a hquid within the framework of the approximation of a single radical encounter [2] _ It is assumed that radicals can recombine only m the singlet state IS). Then it follows that the probability PC23 of a recombination of radicals R, and k, formed III a spin state Ii> can be represented as [7]
(1) where OLis the probability of a singlet RP recombination during an encounter of the ra&cals 171; C(t) = (S]*(t)) where I*(r)> is the RP spm state, with I*(O)> = Ii> (m the present paper we assume that i= S);f(t) is the probability density of the first encounter of the radicals at the recombination radius. The value IC~)(t)l* can be expressed III the form lC’~)(r)l* 370
= Tr E(t)3(s)]
,
(2)
Volume 73, number 2
CHEMICAL
15 Jury 29Stp
PHY SlCS LETTERS
where Tr apphes to all electron and nuclear RP spin states; ii(t) is the spin density matrix of RP at time z after its creation in lS);~~@) = lS)(sl is the singlet projection operator_ The RP spin hamiltonian with the spin-dependent inter-radical interaction disregarded, has the form & = 5%1 + 6i2, where (3) Here n = 1,s G$) = g&?lti, WY) = g,QHIIA, ~$‘n = -y&Z; $ is the electron spin operator of the nth ra&& of the pair, In1 is the operator of the ith nuclear spin of RP n, yni is its gyromagnetic ratio; Ani is the corresponding hyperfme constant; the z axis coincides with the directron of the steady magnetic field. In this work the intensity of the steady magnetic field is assumed to be fairly hrgh (He LO3 Oe) whereas the value hAlgp for most organic radicals does not exceed a few tens of oersted. Thus, the non-secular terms inducing transitions between the states wrth different nuclear spm projections of radicals can be neglected in the spin ham& tonian (3). In this case it can easily be shown that the third term in (3) describing the Zeeman nuclear interaction does not affect the value lC~)(r)12. By neglecting the non-secular terms in the spin hamiltonian (3) we can obtain an exact solution of the quantum Liouvrlle equation for the RP spin density matrix s(f) and represent [C$)(r)I* in the form
@(t) 12= [
v
(*llZ
+
1)C21~j+1)]-1
f/l
lCg(t)12,
where Inniis the value of the zth spin of the nth radical of the pair; the summation extends over all nuclear [email protected]. The quantity @A( equals lCcs) @)I2 = AR sm
+ BE) cos [(aim)
ap
a)2
+ a(m) 2 ) t] + cg
cos [(ac;n) -
a(m)) t] + 0%
[cos (a$mlm’t)f cos (aa(,m
)
where = [‘(a$’
-
+ (&Jy)2]
112 )
n = 1,2;
0:)
s UP)
+ CA i
.m nt ni
9
where mnl IS the value of nth radical’s rth nuclear spin projectron onto the z axis. If we introduce the notation sin ap)
= o(;)/$n),
cos tip’
= (A-z:’ - w)/cp’
,
the coefficients A, B, Cand D, dependent on the nuclear-spin state lm)= lmI)lm2)are B(S) = ; sin4 [f(a\m) - $N)],
cf$ = $ cos4 [I
m
~(9 = p k2($m) m Thus
_ g(m) 2)’
A@) = @ m
+ C$
_ $mQ
,
_
the calculatron of the recombination probability PCs) is actually reduced to the evaluation of irate-
of
the form F(SL)
= jcos(Rt)f(t)dt
_
0
Let us assume that the relative motion of radicals in a liquid outside the region of their immediate contact can be regarded as an isotropic continual diffusion. Then the functronf(r) is expressed in accordance with ref. [71 as f(t) = 4n&
ac(r, fyari,,,
,
c-9
where a is the RP recombination rarhus; D is the coefficient of their relative diffusion in a medium; G(r, t) is tfre probabihty density for a pair of radicals to be separated by the distance r in time t after their creation. If the interaction of the radicals outside the recombination region does not depend on their spins and is descriied by a spheri371
Volume
73,
tally symmetrical
15 July 1980
CHEMICAL PHYSICS LETTERS
number 2 potentiai
U(r), then G(r, t) satrsfies the Smoluchowski
equation
(6) with boundary condrtions [7] G(a. t) = 0, G(r, t += -) -+ 0. Here T is the hfetrme of the radicals. If are separated by a distance r = ro (r > a) at the moment of their creation r = 0, the rmtial conditions G(r, 0) = 6(r - ro)/4nr;. It is readrIy seen from eq. (4) that the functton F(a) is expressed by the real part of the Laplace the functron G(r, t)_ Applying the Laplace transformatron to eqs. (5) and (6) and performmg a few tions, F(Q)
= Wo)
Re
where y(r) 1s the solution y”-{[(l+iQr)/o7]
the radicals of eq. (6) are transform of simple opera-
Iv(qJ~@)l ewC-_(1/2kT) W(a) - WoNI , vanishing
(7)
at r +-m of the equation
+(U’/2kT)2-(l/2kT)(U”+2U’/r)}y=0.
(8)
In the present work a case of non-mteracting radicals is constdered, when we can assume that U(r) = 0. The case of ion-radica1 pans w~vlllbe considered elsewhere. If U(r) = 0, from the solution of eq. (8) and m accordance with (7) we find that [2] F(Q)
= (fr/ro) exp {-(rD/r)‘/2
{[ I+ (a~)~ ] U2 + 1}1/2) cos {(TD/T)L/~ {[l + (a~)~]
U2 -
1}*i2} ,
where rD = (r. - a)2/20. We have made a numerical calculation of the shape of a RYDMR bne for various kinds of RP. Generally speakmg, the RR recombinatron probabrhty P@ depends on the following parameters. T, rD, Ag, hyperfiie constants, Q, ro. It turns out that the shape of a RYDMR spectrum is strongly affected only by r and by the values of the parameters Ag and the constants A, which are determined by the magnetic properties of the radrcals and their structure. Figs. 1-4 show the dependence of the value W(H) = [P@(H, 0) - @)(H, HL)]/o (the difference of normalized r
WlcP
3
3550
2
3555
H,Oe
00
1
3550
3560
3570
H, Oersted Fig. 1. WeU resolved RYDMR spectra. The case of the Ag mechanism of spur conversion in the absence of magnetic nuclei. (1) Ag= 1o-2 , (2) Ag = 4 X 10-3, (3) Ag' 1.5 X 11T3.
372
Frg. 2 Spin reversion
effect of a RYDMR .&MI for the Ag spm conversion. (1) Ag= 8 5 X 104, (2) Ag= 7.0 mechanismof X 104, (3) Ag = 5 X 104, (4) Ag = lOa'.
Volume 73. number 2
CHEMICAL
PHYSICS LETTERS
15 July 1980
J I
3540
I
3550
1
3560
-I
H,CJe
Rg. 3. Dependenceof the shapeof a RYDMR spectral hne on RP Wetime. HyperFme couphng mechamsm of_spinconversion, one magnetic nucleus(f = l/2) on the radical R 1; the ra&cal Rz does not contam any magnetic nuclei. ~0 = 1O”t s. (1) s = 10” s. (2) t = 5 X 10’s~. (3) T = 2 X lOma s. Hyperfme constant fiA/p = 15 Oe.
Jwo
s3sa
3560
Q*
F%g.4. Examples of well-resolved RYDMR spectra_ T = iW7s. (1) 5g= 8 X 10e3,r~= lo-r*s,one~gneticnuc~uswith RA 1/P= 10 Oe, (2) Ag = 0, two identical nucIei on the mdical kt ~thfiA&?=fiA#= lOOe,one msgneticnucleuson $
withltA&=100e,rD=5
X 10'10s.(3)Ag= O,onemag-
netic nucleus on each of the radicaIs,fiA~/g = 100e,EAz/@= 20 Oe, w = lo-* 1 s.
RP recombination probabrhties in the presence and the absence of a high-frequency magnetic field) on the intensity of an external steady magnetic field. The calculatrons were made on the assumption that the intensity of the h&h.frequency magnetic field H, = 1 Oe and rts frequency o = 6.24 X lOIos-1 @w/2.002/3 = 35SOOe). The RYQMR spectra of radical pairs wrth non-magnetic nuclei and different g factors of radicals with r = 10-T s are given in figs. 1 and 2. It was assumed that D = 1O-5 cm2/s (which is equivalent to rD = 1O-IL s). It should be noted that caIcuIations involving various other values of rD (IO-” s =GrD G IOP7 s) were also made with the result that the shape of the RYDMR spectrum was found to be weakly dependent on TV, whereas the amphtude of the RYDMR signal decreases by one order of magnitude as rD decreases by two orders. Well resolved RYDMR spectra correspond to the positive value of W(fY) in the centre of the spectrum and to a very small (in absolute magnitude) negative value of ?V(%r)at its wings and constitute sets of individual peaks. The positions of maxima in them correspond to the alIowec transitions between the magnetic spin sublevels of a pair of non-interacting radicals (see fig. 1; fig. 3, curves (I) and (2); fig. 4). However, as seen from the results obtained, when individual peaks come close together or move apart, fust occurs the smking of the wings and then the center of the curve also sinks. The sign of the effect changes too (see figs. I and 2). The negative RYDMR effect (W(H) < 0) 1s due to spin-conversion slowdown in RP caused by a ~~-frequency magnetic field. The mechanism of such slo~gdo~ is made clearer by resorting to the simpIe example of a pure Ag effect at
Consider a new coordinate system (x’,~‘, z) rotating around the axis J with the frequency o of tb~ field HE _ Let RI be parallel to the x’ axis. Then, in the field H = If9 (Ho = 3550 Oe), the spin S, of the radical Rg will precess around the direction of an effective field, which practicaIIy comcides in this case with E&(t) at the frequency approx imately equal to CQ~“.The s in S, wilI also precess with frequency close to c@ around Hi. Therefore the S-to-T transrtion time will be n/lo~ ?) - o(12”l whr c h considerably exceeds the time of ‘such a transition in the case of the Ag effect m a steady magnetic field (H,
Volume 73, number 2
CHEMICAL PHYSICS LETTERS
15 July 1980
Rough estimations indicate that in the case of the Ag effect of a high-frequency field, the vahtity of the inequality IAwl Z+gpSlfi, where 6 = t2/gar3f4s$4 1s the spectral line width, can serve as a criterion of a good resolution
of the RYDMR spectrum. Summing up, we point out that the study of RYDMR spectra yields the folIowing information: (1) For well resolved spectra, the posItIons of resonance peaks in the case of a pure Ag effect can be used to determme the g factors of short-lived rack?&. Besides, the measurement of hnewidths makes it possrble to determme the hfetimes of radicals in a mechum. (2) Well resolved spectra of RP containing magnetrc nucIei make it possible to determine through the posrtions of peaks the hyperfme constants of highly reactive radicals. (3) The shapes of poorly resolved spectra in the case of the Ag effect (see fig. 2) strongIy depend on the drfference of Rpg factors and on therr hfetnnes T, which m turn allows us to estimate the vahres of Ag and 7. Thus, the study of RYDMR spectra seems extremely promising for the rnvestigation of the mechanism of elementary stages of radrcal reactlons.
References [I i S-1. Kubarev and E.A. Pshemchnov, Chem. Phys. Letters 28 (1974) 66. [2] S-1. Kubarev. E.A. Pshemchnov and AS. Shustov. Tear. Ekspernn. Wurn. 12 (1976) 435. [3] E.L. Frankevich and A-1. Pnstupa, Zh. Eksp. Teor. Fiz, Pls’ma Red. 24 (1976) L397. 141 V-L L.esm, V-P- Sakun, A.I. F’ristupaand E.L. Frankewch, Phys. Stat. SOL 84b (1977) 513. [S] E-L. Frankevrch, V.I. Lesin and A.I. Pristupa, Zh. Eksperun. I Teor. FiL 75 (1978) 415. (61 0.k AnLumov. V.M. Grygoryants, V.K. Molchanov and Yu.N. Mobn, Chem Phys Letters 66 (1979) [7j J.M. Deutch. J. Chem. Phys. 56 (1972) 6076.
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