8900
J. Phys. Chem. 1993,97, 8900-8908
A Cross-Correlation Mechanism for the Formation of Spin Polarization Yu. P. Tsentalovich,' A. A. Frantsev, A. B. Doktorov, A. V. Yurkovskaya, and R. Z. Sagdeevt Institute of Chemical Kinetics and Combustion and the International Tomographic Centre, 630090, Novosibirk. Institutskaya str. 3, Russia Received: March 23, 1993; In Final Form: June 2, 1993 Photolysis of acetone in the presence of various hydrogen donors and of 3-hydroxy-3-methyl-2-butanone involves the formation of propan-2-olyl radicals which show both electron and nuclear spin polarization. The electron polarization of the radicals leads to additional nuclear polarization of the reaction products. Transfer of electron to nuclear polarization can occur by cross-relaxation and cross-correlation. The latter is described in detail. Experimentally, the mechanisms lead to formation of net nuclear polarization for symmetrical radical pairs as well as an unusual kinetic behavior of multiplet effects.
Introduction The two principal mechanisms for the formation of spin polarization-radical pair mechanism (RPM) and triplet mechanism (TM)IJ-have been well studied. In the case of RPM, spin polarization is formed during the singlet-triplet evolution of radical pairs, induced by the difference in g-factors of radical partners and hyperfine interaction (hfi) between electrons and nuclei. Chemically induced dynamic nuclear and electron polarizations (CIDNP and CIDEP) can manifest themselves as net emission or enhanced absorption (Ag mechanism) or as a multiplet effect (hfi mechanism). The triplet mechanism of radical polarization formation is realized in reactions of triplet molecules polarized during intramolecular intersystem crossing from theexcited SIstate to theT1state. This kind of polarization is observed in ESR spectra as net emissionor absorption, depending on the sign of the zero field splitting parameter. Until recently, most spin polarization phenomena observed could be well described in terms of RPM and TM. However, not long ago some effects were reported which did not fit in with the traditional mechanisms and called for invoking some new mechanisms of spin polarization formation. The triplet-radical mechanism for CIDEP formation was thus proposed,' and the possibility of the polarization formation due to dipole-dipole interaction4 and due to relaxation of different kinds's6 was considered. Most of these mechanisms (like RPM and TM) lead to the appearance of spin polarization in a spin system which was initially in equilibrium. The kinetics of nuclear and electron polarizations are as a rule analyzed separately; i.e., when the CIDNP is under consideration it is assumed that electron spins are in equilibrium, the effect of CIDEP on CIDNP being disregarded and vice versa. However, the works on the influence of cross-relaxation upon the formation of spin polarization7-15 have shown that CIDNP and CIDEP can significantly affect each other. Cross-relaxation transitions in radicals involving simultaneous electron and nuclear spin flips can result in the transfer of polarization from the nuclear subsystem to the electron one and vice versa. We have studied16a system of equationsdescribing the behavior of a spin system including cross-relaxation transitions in an individual radical as well as accounting for radical encounters in solution. It has been revealed that the equations describing the nuclear polarization kinetics, in addition to the terms related to the CIDNP formation during the singlet-triplet evolution of radical pairs and the polarization transfer from the electron reservoir to the nuclear one via the cross-relaxation mechanism (CRM), involve terms which are also connected to the presence of the CIDEP in radicals and are responsible for the appearance of polarization in the nuclear subsystem. Similar terms were t International Tomographic Centre.
0022-3654/93/2091-8900$04.00/0
obtained in equations for the electron polarization as well. The mechanism responsible for the appearance of these terms is mainly connected with the presence of the multiplet CIDEP of radicals or, in other words, with a correlationbetween electron and nuclear spins. Thus, we call this mechanism cross-correlation(CCM). Unlike the CRM, which implies the transfer of electron polarization to nuclear polarization during free radical diffusion in solution, theCCM implies the formationof CIDNPat encounters. The CCM of CIDNP and CIDEP formation is based only on spin statistics and on the rule of selection according to the total projection of electron spins in a radical pair on radical recombination (the reaction is possible only with antiparallel spins). This work describes various effects occurring in spin polarization, due to the CCM. The kinetics of nuclear polarization were studied experimentallyin the microsecond time scale during the generation of propan-2-olyl radicals in pairs with different partners. It has been shown that the CCM and CRM affect significantly the CIDNP formation.
Theory General equations describing the time evolution of CIDNP and CIDEP signals in the presence of cross-relaxationtransitions in radicals are given elsewhere.16 According to the theory of bimolecular encounters in solution,17the time evolution of a onespecies density matrix obeys the equation
where @ ( t ) and ub(t) are the one-species density matrices for species A and B, respectively; &is the Liouviliean describingthe spin evolution of species A without collisions; P(t) is the collision operator including interspecies interactions and describing the effects of the binary encounters; and Cb(0) is the initial concentration of species B. Thus, the first term of eq 1 is determined by processesin the individualradicals. These processes can be of two types: dynamic (with a constant total energy of thesystem) and relaxation. In strongmagnetic fields, thedynamic processes may be neglected16and spin evolution can be described using balance schemes of level populations. This approach was employed13in the description of the cross-relaxationeffect upon CIDEP kinetics in propan-2-olylradicals. However, in describing the kinetic processes in radicals it is more convenient to use equations not for level populations but for average operators of experimentally measured parameters (electron and nuclear polarizations). This approach allows convenient separation of different mechanisms of spin polarization formation and relatively simple analysis of their effects on spin evolution. The second part of eq 1 describesthe recombination of radicals at the bimolecular encounters and the formation of spin polarization in radical pairs. Consider the behavior of spin polarization 0 1993 American Chemical Society
Cross-Correlation Mechanism for Spin Polarization
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 8901
in a system involving radicals of the same kind. Write (S,) = S, - (SA0 (where S, = Sp(@SA), = - (Cl0, (CSz) = qSz- (CS,)o,and = ' Z' - (l'&)o for electron, nuclear, electron-nuclear, and nuclear-nuclear polarizations,respectively; (S2),,, (cS,)o,and are the equilibrium values of the operators. Then the equationsdescribingthe polarization kinetics of radicals and diamagnetic products will be as follows. For radicals:
(Z'x) (l'x)o
(c)o,
(C) C
n and 1 belong to different radicals in eq 8. Here C(0) is the initial concentration of radicals; D is the coefficient of mutual diffusion of partners; N is the number of magnetic nuclei in a radical; R is the reaction radius; and kr is the recombination rate constant of in-cage partners, averaged over all nuclear spin configurations:
'[
d(S,) -= dt
k , ( w = - I+-
N
k
k
+
87rRLl[ 1 + R(
8rRD
-1
:)':.]]
Here k is the rate constant of recombination from the singlet state, w{w is the S-TO conversion frequency for a given {"J configuration of the nuclear spins of partners,
where mf,and m: are the spin projections of the nth nucleus of the first partner and the Ith nucleus of the second partner, respectively. kkT=
1 -
p+'
k
X
1 +k/8xRD
t
r
1
ua
For products:
(7)
where nuclei n and 1 belong to the same radical in eq 7 and nuclei
X is the parameter of the exchange interaction decay, J ( q ) = JO exp[(q - R I P ] . Equations 2-8 were obtained by using the following approximations: (a) binary approximation for collisions, (b) contact approximation for chemical reactions, (c) S-TO approximation (equations were solved for a high magnetic field), (d) strong exchange interaction forbidding singlet-triplet transitions in the zone of radical recombination, and (e) terms proportional to polarization equilibrium values being omitted in equations.16 In eqs 2-5, terms (I) describe the polarization decay in radicals due to electron (k,) and nuclear (k,)spin-lattice relaxation as well as electron-nucleus cross-relaxation transitions. The rate ko corresponds to the scalar cross-relaxation (Am = 0), with kZ corresponding to the dipole cross-relaxation (Am = 2). Terms (11) describethe formation of electron-nuclear (eq4) and nuclearnuclear (eqs 5,7,8) multiplet polarizations in the course of the singlet-triplet evolution of radical pairs formed by the encounters
8902
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993
of radicals in solution. Since the solution contains radicals of the same type, no net polarization is formed in radicals pairs. Term (111) in eq 4 corresponds to the failure of the correlation between electron and nuclear spins due to strong exchange interaction at encounters. Terms (IV) ineqs 3 and 5-7 correspond to the transfer of nuclear polarization from radical to diamagnetic product during radical recombination. Terms (V) in eqs 3, 4, 6, and 8 reflect the influence of statistical effects in homogeneous recombination of radicals upon the spin polarization formation. Consider the physical essence of this phenomenon.
Tsentalovich et al. One more example of the realization of CCM is the formation of net nuclear polarization in a system with multiplet electronnuclear and net electron polarizations.
Statistical Effects of Radical Recombination in a Homogeneous Solution The averaging of the kinetic equation for a pair density matrix over all possible encounters of radicals in solution yields statistical effects which are absent in radical recombination in geminate pairs. It should be noted that these effects are not associated with the singlet-triplet conversion of a radical pair. To demonstrate the mechanism of the statistical effects, consider some systems involving several one-nucleus radicals. Radicals are indicated by arrows, the arrow direction denoting the direction of the nuclear spin of the radical. The formation of the multiplet CIDNP of products in the presence of the multiplet polarization of radicals is the simplest case of CCM. Let the configurations with antiparallel electron and nuclear spins prevail in radicals:
s,
= 112
s,
escaped radicals:
= -112
= 112
s,
= -112
This spin system exhibits net electron and nuclear polarizations and no multiplet electron-nuclear polarization. Due to spin exchange, encounters are followed by coordinated ‘flip-flops” of RP electron spins. Since both the ensembles contain the same radicals, the electron exchange means radical transfer from one ensemble to another. Let each radical of the second ensemble, when encountering radicals of the first ensemble, be involved in one electron exchange. The statistically most probable set of nuclear spin orientationsof the first ensemble radicals encountered with the second ensemble radicals is enclosed in a frame. Thus:
s, = 112
(1 )
s,
diamagnetic product: set of spins
t t t t t t l l t t t t ttrrl
Only the radicals with antiparallel electron spins recombine in encounters, the nuclear spins of resulting products being also antiparallel. This corresponds to the multiplet CIDNP (term (V) in eq 8). Consider the situation when radicals in solution show net electron and nuclear polarizations. Break a system of 12 radicals down into two ensembles by electron spin direction:
s,
This spin system has no net nuclear polarization (the numbers of nuclei with spins oriented along and across the field being equal) and shows multiplet electron-nuclear (electron and nuclear spins are mainly parallel) and net electron polarization (most electron spinsare oriented along the magneticfield). Only radicals belonging to different ensembles can recombine. Let all radicals of the second ensemble, (2) recombine. The statistically most probable set of nuclear spin orientations of recombined radicals of the first ensemble (1) is indicated in the scheme.
= -112
(2)
The spin system shows now the multiplet electron-nuclear polarization, with the net polarization being unchanged (term (V) in eq 4). The recombination results in the same effect.
transferred into
As a result, unrecombined radicals and the diamagnetic reaction product (terms (V) in eqs 3 and 6) show net nuclear polarizations of different signs. In addition, the multiplet nuclear-nuclear polarization can be formed in the recombination products of radicals with net nuclear polarization (term (V) in eq 8). It should be noted that, in experiment, the effects described do not always manifest themselves significantly. Thus, crossrelaxationand cross-correlationeffects should manifest themselves in CIDNP more strongly than in CIDEP. Owing to the large differencein Boltzmann factors of electrons and nuclei, the CIDEP kinetics change noticeably only given a high nuclear polarization; at the same time, even a small CIDEP can result in appreciable departure from equilibrium in a nuclear subsystem.
Experimental Section CIDNP spectra were obtained using an AM-250 NMR spectrometer (“Bruker”). A sample under study was placed in the probe of the spectrometer and irradiated by an EMG 101 MSC excimer laser (‘Lambda Physik”, 308 nm, power up to 150 mJ). The laser light was supplied on the side of a standard Pyrex tube using an optical system consisting of two quartz lenses, a prism, and a light guide. The optical length in the sample was 4 mm. The optical density of solutions used in photochemical experiments was below 0.3. The energy of laser radiation impinging on the sample, determined by the photodecomposition of dibenzyl ketone in benzene,l*J9was 15-20% of the laser output power. Time-resolvedCIDNP spectra weredetected using a standardM pulse sequence: saturation-laser pulse-delay-detection. The minimum duration of the detecting rf pulse employed in obtaining CIDNP kinetics with submicrosecond time resolution was 300 ns. The sample temperature was monitored by the spectrometer
Cross-Correlation Mechanism for Spin Polarization computer, accurate to 1 degree. Prior to irradiation, samples were bubbled with pure argon for 5 min. The deuterated solventsacetonitriled3 and 2-propanol-dg(v/o “Izotop”), as well as acetone and 2-propanol (“Reakhim”), were used as received. Triethylamine was distilled over zinc powder. 3-Hydroxy-3-methyl-2-butanone(HMB) was prepared as describedz1and purified by distillation (bp 140 “C).
The Journal of Physical Chemistry, Vol. 97,No. 35, I993 8903
1’50-
*v 0 ,*
1.00
H 7
Results and Discussion &
1. Photolysis of Acetone in 2-Propanol. The reaction of the photolysisof acetone in 2-propanol is well-known~2-~~ and involves the abstraction of a hydrogen atom from solvent by an excited triplet acetone molecule to form the initial RP of two similar propan-2-olyl radicals. The main recombination and disproportionation products are the initial compounds, enol and pinacol, which show CIDNP effects
z 5
0.50
V
0.00
m 1 ‘00
Time (us) Figure 1. Kinetics of the net CIDNP of CH3 protons of 2-propanol at T = 318 K: solid line, calculations in accordance with eqs 2-8; 0,
2(CH3)$OH
-
(CH3),eOH (CH3),eOH
experiment; broken line, calculations without statistical effects. 0 00
(CH&COHCOH(CH3)2, CH3COCH3, (CH&CHOH, CH2 =COHCH3
Unfortunately,the investigationof CIDNP effectsin protonated solvents involves certain experimental problems. Therefore, we used 2-propanol-dsas a solvent and observed CIDNPin the PMR spectra. The main differences of this mixture from the solution of acetone-hb in 2-propanol-ha are the following: (i) the CIDNP spectra exhibit no in-cage multiplet polarizationof methyl protons of 2-propanol as the latter is represented by its isomer CH3CDODCH3 or CD3CHODCD3 l 5 and (ii) the velocity of deuterium atom transfer is lower than that of hydrogen atom transfer.z6 Experiments on the photolysis of acetonein the mixture 2-propanol-ha/acetonitrile-d3= 1/10 have shown that theeffects to be discussed in this,work take place in both deuterated and protonated 2-propanol. Therefore, for simplicity, below, in qualitative models, deuterated and protonated radicals will be considered to be the same. CIDNP spectra detected on the photolysis of acetone in 2-propanol-ds are shown in ref 15. According to the reaction scheme, the polarization is observed in 2-propanol (CH3 group 1.15ppm,CHgroup3.93ppm),enol(CH3group 1.73 ppm,CHz group 3.66 and 3.98ppm), acetone (2.14 ppm), and pinacol(l.22 ppm). In addition, the polarizationis also detected in the products of the minor reaction of Norrish type I a-cleavage of a C-C bond following the two-photon m e c h a n i ~ m . ~In~ -this ~ ~ case, the polarization is formed in methane (0.19ppm) and ethane (0.85 ppm), and the reaction of triplet acetone with the ground-state acetone yields methyl ethyl ketone (1.01 ppm). Multiplet and net polarization kinetics of various products are shown in Figures 1-4. 1.a. Net Polarization. It is known that, in terms of the RPM, no net CIDNP and CIDEP are formed in a symmetrical RP in S-To transitions at high magnetic fields. Nevertheless, for the photolysis of acetone in 2-propanol, CIDEP spectra at room temperature exhibit absorptionwhich decreases with temperature, and at T < -45 OC the net polarization reverses its ~ign.~,29-3~ The traditional interpretation of net contributions to CIDEP (the triplet mechanism at high temperatures and the ST- transitions at low temperatures) is currently do~bted.~J5.2~ At the same time, net CIDNP effects are observed in the spectra of the diamagnetic products of this reaction, and the temperature dependence of net CIDNP effects is almost identical with the same dependence for net CIDEP.1S The assumption about the connection of CIDEP and CIDNP effects via the cross-relaxation
*0 -2.00 *
7-
A
-2 OHN
--4.00
PI
zn -600
- - -4
0
-8.00 U
&
0
5
Time (us) 10
15
1 00
F w e 2 . Kineticsof the multiplet CIDNPof CH3 protonsof enol (broken
line, calculations;A,experiment)and 2-propanol (solidline. calculations: T = 263 K.
0, experiment) at
mechanism allowed the interpretation of some unusual effects observed in spin polarization kineti~s.~.8J~-*S In this work, we shall give no consideration to the mechanisms of net CIDEP formationin this radical pair and discuss in moredetail the transfer of the net CIDEP to CIDNP. Analysis of CIDNP kinetics obtained for the photolysis of acetone in 2-propanol shows that the net emission of the main reaction products (acetone, enol, 2-propanol) is formed in the bulk processes. As stated above, due to the minor reaction of Norrish type I cleavage of acetone, the solution involves methyl and acyl radicals in addition to ketyl ones. However, the presence of these radicals cannot lead to the formation of net emission in enol and 2-propanol since by Kaptein’s rules the methyl protons of enol .form+ in the F pairs ((CH3)zCOH CHp] and [(CH3)2COH COCHp) must show absorption (Ag > 0, hfi constant > 0). Thus, the transfer of net polarization from electron subsystem to the nuclear one can be the only reason for the emission exhibited by enol and propanol protons. An additional support of this conclusion is the fact that temperature decrease changes the sign of net polarization for both CIDEP and CIDNP.15 As follows from eqs 3 and 6, the polarization transfer can occur by both CRM and CCM, the sign of resulting nuclear
8904 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993
-7
OOOr------
j
I
*0 -1.00 O N
--2.00
-4.00
0
5
10
15
1000
Time ( u s )
Figure 3. Kinetics of the multiplet CIDNP of CH3 protons of enol at T = 318 K: solid line, calculations; 0, experiment.
0
-0.50
*
c A
0-N OHN
--1.00
PI
R
n -1.50
--J Time (us)
Figure4. Kinetics of the multiplet CIDNPof CHI protons of 2-propanol at T = 318 K: solid line, calculations in accordance with eqs 2-8; 0 , experiment; broken line, calculations without statistic effects. polarizations being the same in both cases. However, there are some differences. Thus, in the case of CRM, polarization is transferred from the electron subsystem to the nuclear one and then, in recombination of radicals in the bulk, appears in the CIDNP spectrum of the diamagnetic reaction products. Thus, at t = 0 the derivative of the time dependence of the nuclear polarization intensity dZ/dt equals zero and the kinetic curve should be u-shaped, with a latent period of the order of the longitudinal electron relaxation time q. In the case of CCM, the electron polarization formed in a geminate pair is transferred to the CIDNP of products immediately in radical recombination in the bulk, and at t = 0 dZ/dt differs from zero. Hence, the contribution of CCM can be isolated by analyzing CIDNP behavior in the initial section of the kinetic curve. It can be seen from Figure 1 that the kineticcurveof thenet nuclear polarization of isopropanol increases monotonously with no bends; hence, the net polarization in the initial section is determined by CCM. The derivative of the initial section of this curve allows estimation of CIDEP intensity at a field of 5.9 T (see below). Consider the pecularitiesof the CIDNP kinetics at longer times. Equations 2-8 suggest that the CCM induces no nuclear spin flips and involves only the statistical selection by nuclear spins. Thus, the formation of net emission of the reaction products by CCM is followed by theappearance of the net nuclear polarization
Tsentalovich et al. of opposite sign in radicals. In the subsequent recombination of radicals in the bulk, this polarization is transferred into the products, and the net CIDNP kinetics should pass its maximum and then, with relaxation absent, go to zero (behavior similar to that of the kinetics of CIDNP formed by RPM in cyclic reactions).33J4 Experiments, however, demonstrate the monotonous decrease of net CIDNP for all reaction products. In our opinion, this may be caused by CRM responsible for the transfer of the net electron polarization (A type) to the nuclear polarization (E type). As a result, the radical recombination products always show net absorption. Thus, both mechanisms, CCM and CRM, effectively participate in the formation of the net CIDNP of ketyl radical recombination products. 1 .b. Multiplet Polarization. Consider the formation of the multiplet nuclear polarization of the main reaction products, enol and 2-propanol. (Acetone cannot show the multiplet polarization by reason of magnetic equivalence of all six protons.) The geminate A/E polarization of enol results from the singlet-triplet evolution of initial RP of two ketyl radicals (Figures 2 and 3). The kinetics of geminate polarization in this case depend on the rate of formation of initial RP. Indeed, the rate of deuterium atom abstraction by triplet acetone from 2-propanol in pure 2-propanol-ds26is 5.8 X 106 s-1, which is consistent with the rate of multiplet CIDNP increase in the enol at the initial interval of the kinetic curve. The nuclear polarization of 2-propanol and enol continues formation in the encounters of escape radicals in the bulk. The polarization of the products can be formed via four channels: 1. The CIDNP formation by RPM mechanism in F pairs, like in geminate pairs, occurs due to nuclear-spin-dependent intersystem crossing. By Kaptein’s rules, the A/E polarization is formed in both enol (nuclei belong to the same radical, the spinspin interaction constant J < 0) and 2-propanol (nuclei belong to different radicals, J > 0). 2. CRM results only in the polarization of enol. This fact has a simple physical interpretation. When the electron polarization is transferred into nuclear polarization by CRM, intercorrelation of nuclear spin projections of six equivalent nuclei of the same radical appears. On disproportionation, the proton is transferred from one radical to another. All ”ordered” protons in 2-propanol remain equivalent, and multiplet polarization is still unobserved. In contrast, in enol, the formation of a double bond makes the protons unequivalent, and the “hidden” polarization manifests itself as a multiplet effect. 3. On radical recombination in the bulk, the multiplet CIDNP carried away from the primary cage (as well as from F pairs) also exhibits polarization signals only in enol. This is associated with the fact that the in-cage multiplet polarization of 2-propanol is formed due to the selection according to the mutual projections of the nuclear spins which belong to two different radicals. In diffusion separation, the nuclear spin correlation of RP partners is lost, and the correlation of nuclear spins belonging to the same radical results only in the appearance of E/A CIDNP of enol.’3 4. Multiplet CIDNP formation by a cross-relaxation mechanism is based on two phenomena: First, due to the multiplet electron polarization, the electron spin is correlated with spins of nuclei belonging to the same radical. Second, hydrogen atom transfer goes by rule of spin selection for radical recombination: the reaction proceeds from the singlet state of RP. As a result, on the hydrogen transfer from one ketyl radical to another, the correlation of six equivalent protons of the radical relative to electron is transformed into the correlation of CHs protons of 2-propanol relative to the “arrived” CH proton, and the CIDNP spectrum shows the multiplet effect. In enol, the additionalproton, relative to the radical from which it is formed, does not appear, and the multiplet CIDNP does not form (see Table I). The above qualitative analysis shows that the formation of in-bulk polarization of enol involves three mechanisms: the
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 8905
Cross-Correlation Mechanism for Spin Polarization
TABLE I: Mechanisms of Multiplet Nuclear Polarization Formation enol
2-propanol
F pairs
escape polarization
CRM
CCM
AJE A/E
E/A
AJE
no
no
AJE
no
polarization transfer from the initial cage and F pairs, the F pair mechanism, and the cross-relaxation mechanism. The former mechanism yields the E/A polarization, and the two latter give the A/E polarization. It is evident that nuclear polarization kinetics are affected by electron and nuclear paramagnetic relaxations which tend to bring the spin populations to the Boltzmann equilibrium. The competition of different channels of the formation of multiplet polarization of enol manifests itself appreciably in the temperature dependence of CIDNP kinetics. At T = 263 K, nuclear relaxation pl and CRM suppress the A/E polarization of radicals, transferred from the initial cage and from F pairs, and the CIDNP kinetics of enol show a monotonously increasing A/E polarization (Figure 2). Rising temperature leads, on the one hand, to decreasing rate of nuclear relaxation and, on the other hand (due to increasing diffusion coefficient), to increasing rate constant of radical decay in the bulk. As a result, at T = 318 K, the kinetic curve passes its maximum at 2 ps, and the subsequent decrease in CIDNP intensity indicates that the E/A polarization in radicals becomes predominant (Figure 3). The quantitative relationship between the contributions of different mechanismsof CIDNP seemsto be of interest. Consider the multiplet polarization of the methyl protons of 2-propanol. The escape multiplet polarization of 2-propanol is formed by two mechanisms: F pair mechanism and CCM. Both mechanisms lead to the formation of the A/E polarization; hence, the CIDNP of 2-propanol always monotonously increases (Figures 2 and 4). Since the polarization carried away from the primary cage and from F pairs makes no contribution to the polarization of 2-propanol (vide supra), the value of stationary polarization depends on the three mechanisms: in-cage CIDNP F pair CIDNP CCM. As has been sh0wn,3~.35the value of polarization formed in F pairs cannot be higher than the 3-fold value of geminate CIDNP in the case of triplet precursor. Thus, the CCM contribution can be estimated from below by means of comparison between the in-cage, I,, and stationary, I,, polarizations. The measurementswere performed for the photolysisof acetone in the mixture acetonitrile-d3/2-propanol-hs(3/ 1) (as indicated above,when deuterated 2-propanol is used as a solvent, 2-propanol exhibits no geminate multiplet polarization). The best plan to be followed in this case is to measure the intensity of the multiplet CIDNP of 2-propanol immediately after the laser pulse and after the completion of the CIDNP formation. However, owing to the high concentration of protonated 2-propanol in solution (4 M), we failed to suppress completely the dark signals of CH3 protons occurring in a random phase. The intensity of these incompletely suppressed signals was below 10% of 1,; however, the error of measurementsof the geminate polarizationintensityof 2-propanol was 50%. Thus, the contribution of geminate polarization to the signal was measured using the radical pair symmetry. In a geminate pair of two ketyl radicals, all the 12 methyl protons are equivalent and, hence, have the same geminate polarization. In CH disproportionation,the observed polarization of enol CH3 protons should be half as large as that of 2-propanol methyl protons. Therefore, we measured the relationshipbetween the stationary multiplet polarization 1, of 2-propanol and double the value of the geminate CIDNP of enol (21,). In the absence of CCM, 1, should not be higher than 81,.34.35 Experiment, however, showed that I, = 121,. This means that thecontribution of CCM to the multiplet CIDNP of 2-propanol is at least twice as large as the in-cage polarization, which is significant.
+
+
I .c. Comparison between Experimental Results and Calculation. The next step of our investigation is the theoretical modeling of the processes proceeding in the solution of acetone in 2-propanol under flash photolysis. Equations 2-8 for spin polarizations of radicals and diamagnetic products involve many parameters: the rateconstantsof various processes, characteristics of the medium, radii and magnetic resonance parameters of radicals, initial concentrations of radicals, etc. The values for some of these parameters were taken from the literature. The parameters whose values are unavailable or ambiguous were used as fitting (naturally, within certain limits) parameters. We aimed at finding such a set of parameters which provided a good fit between the calculation and experiment for the following kinetic curves simultaneously: multiplet polarization of enol and 2-propanol at different temperatures and net polarization of 2-propanol. Equations 2-8 describe the spin polarization kinetics in homogeneousreactions; Le., it is assumed that at t = 0 the solution is characterized by an initial concentration of polarized radicals. In fact, owing to the finite rate of abstraction of a deuterium atom by an excited acetone molecule from 2-propanol,the process of geminate pair formation is extended in time. The formation rate of propan-2-olyl radicals on the photolysis of acetone in isopropanol-ds26 is kcc = 5 X 106 s-1. In our experiments, this manifests itself, in particular, as prolonged formation of geminate multiplet polarization of enol (Figures 2 and 3). The rate of geminate pair formation was accounted for using the convolution of expressions for nuclear polarization kinetics with the function kcc exp(k,t). Thus, the calculated curves represented in Figures 1-4 were obtained at the following parameters. The parameters taken from the literature or set by experimental conditions:
H, = 5.875 X lo4 Oe, ahfi= 19.5 Oe36 at T = 318 K D = 1.1 X l O - ’ ~ m ~ / s ; ~C,~ = 8 X lo-’ M D = 3 X 10“ cm’/~;~’ C, = 5 X lo-’ M
at T = 263 K
Fitting parameters:
R = 5 A, X = 0.5 A, k, = 2.5 X lo5 s-’, k, = 0,
(.Iz),= 0 at T = 318 K k,= 3 x 103 s-1 ko = 5 x 103 s-1 k,=SX106~-~ (sz)o= 9.5 x 10-3 (P#z)o -1.15 X (G&, = 3 x 10-4
at T = 263 K k,= 5 x 103 s-1 ko = 3 x 103 s-1 k, = 3.3 x 106 s-1 (P#z)o=-l.8 X 10-2
(G&)o= 3.8 X 10-4
Note that for most parameters the fitted values are in good agreement with the literature data.13.26.32J7 The exception is the rate constant of scalar cross-relaxation ko,whose value is an order of magnitude lower than that proposed by Paul.13 Perhaps such a discrepancy can be accounted for by the fact that the value ko = 4 X lo4 s-l was obtained in experiments with CIDEP at a magnetic field of 3.3 X 103 Oe. The expression for ko involves the term ~ ~ / ( 1~ , 2 0 , 2 ) , where T~ is the correlation time of relaxation-inducing perturbation and oeis the Larmour frequency. At ESR magnetic fields, as a rule, T.+~
