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The field dependence of CIDNP in gas-phase reactions of biradicals
259
Chemical Physics 112 (1987) 259-264 North-Holland, Amsterdam
THE FIELD DEPENDENCE A.V. YURKOVSKAYA, Novosibirsk
Received
REACTIONS
OF BIRADICALS
R.R. GALIMOV
State University, Novosibirsk-90,
A.A. OBYNOCHNY, Institute
OF CIDNP IN GAS-PHASE
360090, USSR
K.M. SALIKHOV
of Chemical Kinetics and Combustion,
and R.Z. SAGDEEV
Novosibirsk-90,
630090,
USSR
30 June 1986
The field dependence of CIDNP effects in gas-phase biradical reactions is for the first time detected during the photolysis of the homological series of cyclic aliphatic ketones from cyclodecanone to cyclopentadecanone. The influence of magnetic field on nuclear polarization is studied up to 0.47 T. The experimental data are interpreted on the basis of nuclear-spin-selective S-T_ transitions in intermediate biradicals. In contrast to liquid-phase reactions, mainly protons in the y-position are polarized. The relatively weak a-CHz and P-CH, protons in the gas are explained by compensation of various conversion channels in biradicals. The strong spin-rotation interaction in gases excludes polarization transfer observed in solutions. The field dependence of CIDNP effects differs noticeably in gases and liquids. It is associated with the different dynamics of conformational motion in liquids and gases
1. Introduction The CIDNP method holds much promise as applied to studies of the mechanisms of elementary acts in the liquid-phase radical processes. Until recently there were no attempts to observe CIDNP in other phases. Taking into account the high sensitivity of the CIDNP method, a very urgent problem is to extend this method into the field of gas-phase processes involving the shortlived radical particles. During a long time the observation of CIDNP effects in the gas phase has been thought to be impossible. The main reason for this assumption is that the cage effect which is necessary for the CIDNP formation is as a rule negligible in the gas. However, CIDNP effects may arise in gas-phase biradical reactions. The most characteristic feature of these reactions consists in the fact that radical centres cannot freely diffuse far from each other. The first observation of ‘H and 13C CIDNP in gas-phase reactions of biradicals has been made [1,2] in high magnetic fields of NMR spectrometers in the photolysis of cyclic aliphatic ketones. 0301-0104/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
The present investigation is devoted to the field dependence of CIDNP in the gas phase. The results obtained make it possible to understand some peculiarities of the formation of CIDNP effects associated with the character of motion of intermediate biradicals.
2. Experimental We have investigated the photolysis of the homological- series of cyclic aliphatic ketones from cyclodecanone C,,H,,O to cyclopentadecanone C,,H,,O. The samples were sealed inside thinwalled quartz ampoules (5 mm outer diameter, 35 mm long) after five. cycles of freezing in liquid nitrogen, pumping up to low3 mm Hg, and thawing. We have prepared five equal samples at a time each containing the same amount of the substance under study. The reaction occurred in the magnetic field (O-O.476 T) of a small electromagnet fixed above the superconducting magnet of an XL-200 NMR spectrometer (Varian, B, = 4.7 T). A heater for the evaporation of the samples B.V.
260
A. V. Yurkovskaya et al. / Gas-phase reactions of biradicals
inside sealed ampoules was placed in the gap of the electromagnet. The samples were irradiated by the full light of a ultrahigh pressure mercury lamp DRSh-1000 focused with two quartz lenses (KU-l quartz). The irradiation lasted for 5-20 s, then the ampoule was quickly transferred into the probe of the spectrometer and 0.8 s after the irradiation the ‘H CIDNP spectrum was taken. Together with the ketones under study, some low-boiling-point compounds were introduced into the ampoules (pentane, cyclohexane, chloroform and their deuterated analogues C,D,, and CDCl 3), at pressures of lo-30 atm, T = 500 K. This increased Tl of the ketones under study to 3-10 s. In ketone vapours at 350-500 K the longitudinal nuclear relaxation time is within the millisecond range, which makes the transfer method inapplicable to CIDNP studies. After the addition of buffer gases, which increases T,, the transfer does not essentially distort the CIDNP effects. Prior to irradiation, the NMR spectrum of a sample was used to determine the complete evaporation temperature, the position of proton lines of the gas fraction of the ketone, and T,, for every series of the samples. Under heating, the spectrum of ketones with deuterated buffer admixtures showed at first proton signals from molecules condensed on the walls of the ampoule. As the temperature increased further, additional signals from the gas fraction of ketones arose. These signals were some 2.5 ppm shifted towards low fields. Fig. 1 shows the spectrum of C,,H,,O mixed with C,D,, under incomplete evaporation.
Under full evaporation conditions, no signal appeared from the liquid phase in high field. The CIDNP effects in solutions were investigated by the flow technique [ll].
3. Results The CIDNP effects in solutions during the photolysis of aliphatic ketones have been studied in refs. [3,4]. According to refs. [3,4], effects arise in the course of nuclear-spin-selective singlet-triplet transitions in intermediate biradicals as shown in scheme 1. Fig. 2a shows the NMR spectrum of C,,H,,O with CSH,, in the ratio 1: 250 at 470 K in the probe of the spectrometer. Only lines corresponding to the pentane vapour can be seen. Fig. 2b shows the spectrum of the same mixture taken after UV-irradiation in an external field of Ha = 0.08 T. The emission signal pertains to the line of y-, a-, t-CH, protons of cyclododecanone (these protons are designated as y). The polarization of cy-CH, and S-CH, protons in this field is two orders of magnitude weaker. Note for comparison that the photolysis data obtained for these ketones in solutions [3,4] and by means of the flow technique show that the relative intensities of emission lines for the initial ketones correspond to relative intensities of a normal spectrum. Our measurements show a pronounced maximum in the field dependence of CIDNP. The y protons are most strongly polarized. Fig. 3 shows the field dependences of CIDNP for 7 protons of cyclic ketones from cyclopentadecanone to cyclodecanone (except for C,,HZ60). The character of variations in the field dependences of CIDNP for y protons in the homological series of ketones in the gas phase agrees qualitatively with the well-
Fig. 1. NMR spectrum of C12HZ20 mixed with C,D12, T== 370 K PC,D,2 -10 atm, a’, b’, y’ are gas-phase ketone signals. 01, fl, y are signals from liquid on the walls of ampoule. Scheme 1. n = 5-10
A. K Yurkovskayu
261
et al. / Gas-phase reactions of hiradicuis
CIDNP
farbunits)
s
fPPm f
i
i
2
Fig.
3. Field
C,,H@
dependences
(A), C&I&
1
of CIDNP
(a), CUI%O the gas phase.
For C,,H,O (WY GJWJ
(0), (0) in
L
NMR spectra af pentane with cy&dodecanone in the ratio of 250: 1; (a) in the spectrometer cavity, T= 470 K, (b) after irradiation in a Field of 0.08 T.
Fig.
2.
known CIDNP data [3] for aldehyde protons in solutions, As the biradical length grows, the CIDNP m~mum shifts towards low fields and, simultaneously, B,,, decreases {see fig. 3). At the same time, the field dependences of CIDNP do not coincide in gases and liquids for every ketone. Fig. 4 shows the field dependences of CIDNP for y protons af 0.05 ma1 t1 cyclododecanone in CDCl, and also in the gas phase with CDCl, as a buffer gas. In the gas phase, the maximum is seen to be shifted towards high fields; the width B,,2 in the gas exceeds that in the liquid by an order of magnitude. This is typical of all ketones with the exception of cyclop~tad~~on~ which does not show any CIDNP effects in solutions. When the temperature increases from 440 to 530 K and the buffer gas pressure from 5 to 30 atm, bin expe~ent~ error the CIDNP maxi-
mum does not Shift noticeably. Por cycloundecanone the field dependence bends slightly at 0.15 I’, which exceeds experimental error (see fig. 3). Under different experimental conditions fke-
H,@ 3000
4000
_l_--_--l-_
Fig. 4. Field dependences of CIDNP far T-protons of Cx2Hz20 (0) for 0.05 moi 6’ solution in CDCI, , (0) for the gas phase reaction in a mixture with CDCl,; .Q1, is the half-height linewidth.
262
A. V. Yurkovskaya
et al. / Gas-phuse reactions of biradicals
tone vapour pressure, buffer gas pressure, TX) cycl~~e~anone and cy~loundecanone show maximum CIDNP effects in the homological series of ketones from C,,H,,O to C,,H,,O. Taking into account T,, we have estimated the CIDNP enhancement coefficient (E) on the basis of photometric data on benzpinacol yields in benzophenone photoreaction with isopropanol f17] in CDCl,, and by comparing the polarized signals from 7 protons with a signal from a known amount of pentane gas in the probe of the spectrometer. The value E z lo5 agrees with that obtained in ref. [14] by qualitative E measurements for C,,H,O by NMR relaxation in low fields. 4. Discussion The exchange interaction of unpaired electrons is known to be of importance for the formation of the CIDNP effects in biradical reactions [4,5,16]. The interaction splits singlet (S) and triplet (T) terms of biradicals by 2J. An external magnetic field B splits the triplet levels into T,, T, and T . If B=B* = 2 1J f/y, the resonance between S and T_ is attained (J < 0). Under the resonance condition, the hyperfine interaction (hfi) effeetively mixes the S and T_ states. In this case, the nuclear spins flip simultaneously with the electron spins. As a result, the nuclear spins in the singlet biradical recombination products are polarized. This explains the m~mum in the field dependence of CIDNP for biradical reactions [4,16]. A biradical may be of various conformations with various J. The conformational transitions in the biradical modulate randomly the exchange interaction J(r). The manifestation of exchange interactions in CIDNP is determined, on one hand, by the possible configurations (set of possible J) and, on the other hand, by the rate of conformational transitions. In the limit of sufficiently fast conformational changes J(t) is averaged, and therefore only a certain effective J shows up. The model of m~festations of the polymethylene chain dynamics in the CIDNP has been calculated by de Kanter et al. [5,6]. The set of biradical configurations is the same in liquids and gases. However, the rate of conformational transitions may be substantially different
in liquids and gases. We think this is the cause of the different field dependences of CIDNP observed experimentally in liquids and gases (fig. 4). In solutions the frequency of conformational transitions of biradical is 10-‘“-lO-” s-* [6]. A conformational transition [7] is an example of monomolecular isomerization of a polyatomic molecule [S]. We assume that in the molecule under study the conformational transitions in the gas phase occur more slowly than in liquids. This assumption is confirmed by experimental data from measurements of conformational transition rates in cyclohexane by the NMR method [lo]. The type of confo~ation~ tr~sition in cyclohexane is similar to that of the biradical under study. It has been shown IlO] that for cyclohexane the conformational transition rate increases by an order of magnitude (twenty times) when pressure increases from 5 to 4000 Torr. Even at 4000 Torr this rate does not reach the value of the rate in liquids (three times smaller). It is not possible to take directly into account the quantitative results of ref. [lo] because in ref. [lo] molecules and buffer gases were used which certainly have encounter efficiencies different from the molecules in the present study. But one can qualitatively compare these two systems. An average lifetime of a triplet biradical is 10e7 s (41. We suppose that in liquids the conformational transitions effectively average the exchange interaction, which does not occur in gases. In the gas phase there may arise practically static distribution of J values. Therefore (B,,,),, % (q&i,ui,~ In principle, studies of the field dependence of CIDNP open up a way of determining the biradical dist~bution as a function of J, as well as the rate and character of conformational transitions. To determine the biradical distribution as a function J, it is more convenient to measure CIDNP in the gas phase, because the gas phase is characterized by comparatively slow conformational transitions. Let rp(B, J) be the field dependence of CIDNP for a biradical with a fixed J. Until now we do not know its exact form. Its asymptotes are cp(B, J) -+ 0 at J + 0 and cp(B, J) -+ a, at J -+ 00 and have maxima near the resonance 2 1J I/y at sufficiently high J.
For the set of J with the density f(J) the field dependence of CIDNP is determined by the average magnitude J
cp(B, J)
f(J)
dJJ=x(B).
In high fields, X(B) 2: B/2, the field dependence of CIDNP for cycloundecanone shows two maxima (fig. 3). We associate this with an additional maximum observed in the biradical distribution as a function of J for this system. Note that for biradicals involving ten or more CH, groups in the chain (the ketones under study), the statistical weight of #nformations with a negligible exchange integral is substantial. Therefore, the averaging of J shifts the CIDNP maximum to lower fields in liquids than in gases (fig. 4). The shift of the CIDNP maximum and the change in B,,, observed in gas-phase reactions as compared to liquid phase, can thus be explained by a substanti~ fall in the conformational transition rate in gases as compared to the liquids. In the range of CIDNP mechanism, F protons are mainly polarized, although their hfi constant (A = 0.07 mT [13]) is much smaller than those for ol-CH; (A = 2.198 mT) and for P-CH; protons (A = 2.985 mT (131). According to the CIDNP theory for radical pair reactions in higb magnetic fields, in the S-T, appro~mation [15] CfDNP passes via a maximum with an increase of hfi constant. Therefore, the fact that protons with lower hfi constants are more polarized is neither strange nor impossible in itself. However, in the range of the maximum of CIDNP the polarization in biradicals is associated with Sj3-T_(w rather than with S-T, transitions ((w and p are spin states of the proton). Taking into account only S-T_, transitions results in that as the hfi constant increases, the transition efficiency and the CIDNP associated with this transition also increase, saturate and become constant. Therefore, in order to explain the experiment under discussion, we assume that in gas phase biradicals, even in fields of one or several kG, Sg-T_,o( transitions occur together with the Sot-T+iP associated with proton flips with sufficiently large hfi constant. As a rule, Se+T+tP transitions are neglected, since the energy gap between S and T+l
states,AEs_T+,,is much less than the hfi energy (= A), and therefore S-T+1 mixing occurs at a small parameter value (A/AEs_=+,)* +x 1 [16]. However, the situation changes dramatically for sufficiently long times. If one takes into account that during the pass to the S state the biradicals r~ombine, then it becomes clear that during the lifetime all the T, r biradicals may convert to the S state. Let K be the singlet biradical recombination rate constant, r the lifetime of a triplet biradical. In this case, the S-T,, efficiency transition can be estimated by the formula [16] P = K( A/AEs_r+,)21.
2: ( A,‘B)2Kr.
Let us assume that K = lo’*-lOI3 s-r, B 2: 0.3 lo3 mT, r= 10F7 s-l. In this case, P = (lo-‘-10-*)A*. Obviously, if A = 1.0 mT, hfi transfers all the Ti biradicals to the singlet state. If A ,< 0.1 mT, P +Z 1. It is possible to suppose that under our experimental conditions the weak proton polarizations of (Y- and P-CH, groups result from the fact that various channels of Se--?; p and S&-T_ to1conversions can essentially compensate each other within the biradical lifetime. In the case of v-CH, protons, the efficiency of the Sol-T+,j3 conversion is negligible and therefore the abovementioned compensation does not occur. That is why the y-CH, protons are polarized stronger (with a pronounced resonant character) than ol-CH, and l3-CH, ones. As it has been mentioned above, in cycloketone photolysis in solutions the relative signal intensities for polarized protons correspond to the relative signal intensities of a standard ketone spectrum, irrespective of the hfi constant in the intermediate biradical. This has been attributed [12] to the nuclear polarization transfer by spin-spin coupling of a cycloketone molecuIe. In gases this proton coupling is not important in comparison to the coupling of every spin with the rotational momentum of the molecule which forms the basic contribution to nuclear relaxation 191. In the presence of such a strong relaxation channel in gases the effect of proton coupling does not show up, neither are polarizations redistributed among ketone protons. X
264
A. V. Yurkwskaya et ai.
The authors are very thankful to Dr. Yu.A. Grishin and Dr. E.G. Bagryanskaya for help in flow technique experiments.
References 111A.V. Y~rk~~aya~
GA. U~~~~u~ and R.Z. Sagdeev, Doki, Akad. Nauk SSSR 2?1(1983) 136. [Z] A.V. Dushkin, A.V. Yurkovskaya and R.Z. Sagdeev, Chem. Phys. Letters 61 (1979) 524. [3] CL. Gloss and C.E. Doubleday, J. Am. Chem. Sue. 195 (2973) 2736. [4] CL. Gloss and O.D. Redvine, J. Am. Chem. SW. 107 (2985) 4547. [5] FJJ. de Kanter, R. Kaptein and R.A. van Santen, Cbem. Phys. Letters 45 (1977) 575. [6] F.J.I. de Kanter, R. Kaptein, S.A. den ~~~~~der and A.R. Huizer, Mol. Pbys. 34 (1977) 857.
M.V. Volke~t~i~, ~o~fig~at~ou~ statistics of polymer chains (Izv. Akad. Nank SSSR, Moscow-Leningrad, 1958) [in Russian], P.J. Robinson and kA. FKolbrook, Monomolec~ar reaetions (Mir, Moscow, 1975) [in Russian]. R.G. Gordon, J. Chem. Phys. 44 (1966) 229. B. Ross and N.S. True, J. Am. Chem. Sot. 105 (1983) 4871. EC. Bagryanskaya, Yu.A. G&bin and R.Z. Sagdeev, Chem, Phys. Letters 113 (ZSS5) 234. F.J.J. de Kanter, Ph.D. Thesis, Leyden Unive~~t~~ The hIether$ands j197X). H. Fisher and K. Helwege, eds., ~ndolt-3~mstei~ New Series, Group II, Vol. 9, Part C2 (Springer, Berlin, 1979). A.V. Dud&in, Yu.A. Gristin and R.Z. Sagdeev, Chem. Phys. Letters 55 (1977) 174. KM. Salikhov and P.S. Sarvarov, Teoret. Eksp. Khim 2 (1982) 146. K.M. Salikhov, Yu.N. M&r, R.Z. Sagdeev and AL. Buchade~o, Spin po~~ation and magnetic effects in radical reactions (Elsevier, Amsterdam, 1984). 3.G. Calvert and J.N. Pit&, Phot~bem~st~ @fir, Moscow, 2968) fin Russian].
Chemical Physics 112 (1987) 259-264 North-Holland, Amsterdam
THE FIELD DEPENDENCE A.V. YURKOVSKAYA, Novosibirsk
Received
REACTIONS
OF BIRADICALS
R.R. GALIMOV
State University, Novosibirsk-90,
A.A. OBYNOCHNY, Institute
OF CIDNP IN GAS-PHASE
360090, USSR
K.M. SALIKHOV
of Chemical Kinetics and Combustion,
and R.Z. SAGDEEV
Novosibirsk-90,
630090,
USSR
30 June 1986
The field dependence of CIDNP effects in gas-phase biradical reactions is for the first time detected during the photolysis of the homological series of cyclic aliphatic ketones from cyclodecanone to cyclopentadecanone. The influence of magnetic field on nuclear polarization is studied up to 0.47 T. The experimental data are interpreted on the basis of nuclear-spin-selective S-T_ transitions in intermediate biradicals. In contrast to liquid-phase reactions, mainly protons in the y-position are polarized. The relatively weak a-CHz and P-CH, protons in the gas are explained by compensation of various conversion channels in biradicals. The strong spin-rotation interaction in gases excludes polarization transfer observed in solutions. The field dependence of CIDNP effects differs noticeably in gases and liquids. It is associated with the different dynamics of conformational motion in liquids and gases
1. Introduction The CIDNP method holds much promise as applied to studies of the mechanisms of elementary acts in the liquid-phase radical processes. Until recently there were no attempts to observe CIDNP in other phases. Taking into account the high sensitivity of the CIDNP method, a very urgent problem is to extend this method into the field of gas-phase processes involving the shortlived radical particles. During a long time the observation of CIDNP effects in the gas phase has been thought to be impossible. The main reason for this assumption is that the cage effect which is necessary for the CIDNP formation is as a rule negligible in the gas. However, CIDNP effects may arise in gas-phase biradical reactions. The most characteristic feature of these reactions consists in the fact that radical centres cannot freely diffuse far from each other. The first observation of ‘H and 13C CIDNP in gas-phase reactions of biradicals has been made [1,2] in high magnetic fields of NMR spectrometers in the photolysis of cyclic aliphatic ketones. 0301-0104/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
The present investigation is devoted to the field dependence of CIDNP in the gas phase. The results obtained make it possible to understand some peculiarities of the formation of CIDNP effects associated with the character of motion of intermediate biradicals.
2. Experimental We have investigated the photolysis of the homological- series of cyclic aliphatic ketones from cyclodecanone C,,H,,O to cyclopentadecanone C,,H,,O. The samples were sealed inside thinwalled quartz ampoules (5 mm outer diameter, 35 mm long) after five. cycles of freezing in liquid nitrogen, pumping up to low3 mm Hg, and thawing. We have prepared five equal samples at a time each containing the same amount of the substance under study. The reaction occurred in the magnetic field (O-O.476 T) of a small electromagnet fixed above the superconducting magnet of an XL-200 NMR spectrometer (Varian, B, = 4.7 T). A heater for the evaporation of the samples B.V.
260
A. V. Yurkovskaya et al. / Gas-phase reactions of biradicals
inside sealed ampoules was placed in the gap of the electromagnet. The samples were irradiated by the full light of a ultrahigh pressure mercury lamp DRSh-1000 focused with two quartz lenses (KU-l quartz). The irradiation lasted for 5-20 s, then the ampoule was quickly transferred into the probe of the spectrometer and 0.8 s after the irradiation the ‘H CIDNP spectrum was taken. Together with the ketones under study, some low-boiling-point compounds were introduced into the ampoules (pentane, cyclohexane, chloroform and their deuterated analogues C,D,, and CDCl 3), at pressures of lo-30 atm, T = 500 K. This increased Tl of the ketones under study to 3-10 s. In ketone vapours at 350-500 K the longitudinal nuclear relaxation time is within the millisecond range, which makes the transfer method inapplicable to CIDNP studies. After the addition of buffer gases, which increases T,, the transfer does not essentially distort the CIDNP effects. Prior to irradiation, the NMR spectrum of a sample was used to determine the complete evaporation temperature, the position of proton lines of the gas fraction of the ketone, and T,, for every series of the samples. Under heating, the spectrum of ketones with deuterated buffer admixtures showed at first proton signals from molecules condensed on the walls of the ampoule. As the temperature increased further, additional signals from the gas fraction of ketones arose. These signals were some 2.5 ppm shifted towards low fields. Fig. 1 shows the spectrum of C,,H,,O mixed with C,D,, under incomplete evaporation.
Under full evaporation conditions, no signal appeared from the liquid phase in high field. The CIDNP effects in solutions were investigated by the flow technique [ll].
3. Results The CIDNP effects in solutions during the photolysis of aliphatic ketones have been studied in refs. [3,4]. According to refs. [3,4], effects arise in the course of nuclear-spin-selective singlet-triplet transitions in intermediate biradicals as shown in scheme 1. Fig. 2a shows the NMR spectrum of C,,H,,O with CSH,, in the ratio 1: 250 at 470 K in the probe of the spectrometer. Only lines corresponding to the pentane vapour can be seen. Fig. 2b shows the spectrum of the same mixture taken after UV-irradiation in an external field of Ha = 0.08 T. The emission signal pertains to the line of y-, a-, t-CH, protons of cyclododecanone (these protons are designated as y). The polarization of cy-CH, and S-CH, protons in this field is two orders of magnitude weaker. Note for comparison that the photolysis data obtained for these ketones in solutions [3,4] and by means of the flow technique show that the relative intensities of emission lines for the initial ketones correspond to relative intensities of a normal spectrum. Our measurements show a pronounced maximum in the field dependence of CIDNP. The y protons are most strongly polarized. Fig. 3 shows the field dependences of CIDNP for 7 protons of cyclic ketones from cyclopentadecanone to cyclodecanone (except for C,,HZ60). The character of variations in the field dependences of CIDNP for y protons in the homological series of ketones in the gas phase agrees qualitatively with the well-
Fig. 1. NMR spectrum of C12HZ20 mixed with C,D12, T== 370 K PC,D,2 -10 atm, a’, b’, y’ are gas-phase ketone signals. 01, fl, y are signals from liquid on the walls of ampoule. Scheme 1. n = 5-10
A. K Yurkovskayu
261
et al. / Gas-phase reactions of hiradicuis
CIDNP
farbunits)
s
fPPm f
i
i
2
Fig.
3. Field
C,,H@
dependences
(A), C&I&
1
of CIDNP
(a), CUI%O the gas phase.
For C,,H,O (WY GJWJ
(0), (0) in
L
NMR spectra af pentane with cy&dodecanone in the ratio of 250: 1; (a) in the spectrometer cavity, T= 470 K, (b) after irradiation in a Field of 0.08 T.
Fig.
2.
known CIDNP data [3] for aldehyde protons in solutions, As the biradical length grows, the CIDNP m~mum shifts towards low fields and, simultaneously, B,,, decreases {see fig. 3). At the same time, the field dependences of CIDNP do not coincide in gases and liquids for every ketone. Fig. 4 shows the field dependences of CIDNP for y protons af 0.05 ma1 t1 cyclododecanone in CDCl, and also in the gas phase with CDCl, as a buffer gas. In the gas phase, the maximum is seen to be shifted towards high fields; the width B,,2 in the gas exceeds that in the liquid by an order of magnitude. This is typical of all ketones with the exception of cyclop~tad~~on~ which does not show any CIDNP effects in solutions. When the temperature increases from 440 to 530 K and the buffer gas pressure from 5 to 30 atm, bin expe~ent~ error the CIDNP maxi-
mum does not Shift noticeably. Por cycloundecanone the field dependence bends slightly at 0.15 I’, which exceeds experimental error (see fig. 3). Under different experimental conditions fke-
H,@ 3000
4000
_l_--_--l-_
Fig. 4. Field dependences of CIDNP far T-protons of Cx2Hz20 (0) for 0.05 moi 6’ solution in CDCI, , (0) for the gas phase reaction in a mixture with CDCl,; .Q1, is the half-height linewidth.
262
A. V. Yurkovskaya
et al. / Gas-phuse reactions of biradicals
tone vapour pressure, buffer gas pressure, TX) cycl~~e~anone and cy~loundecanone show maximum CIDNP effects in the homological series of ketones from C,,H,,O to C,,H,,O. Taking into account T,, we have estimated the CIDNP enhancement coefficient (E) on the basis of photometric data on benzpinacol yields in benzophenone photoreaction with isopropanol f17] in CDCl,, and by comparing the polarized signals from 7 protons with a signal from a known amount of pentane gas in the probe of the spectrometer. The value E z lo5 agrees with that obtained in ref. [14] by qualitative E measurements for C,,H,O by NMR relaxation in low fields. 4. Discussion The exchange interaction of unpaired electrons is known to be of importance for the formation of the CIDNP effects in biradical reactions [4,5,16]. The interaction splits singlet (S) and triplet (T) terms of biradicals by 2J. An external magnetic field B splits the triplet levels into T,, T, and T . If B=B* = 2 1J f/y, the resonance between S and T_ is attained (J < 0). Under the resonance condition, the hyperfine interaction (hfi) effeetively mixes the S and T_ states. In this case, the nuclear spins flip simultaneously with the electron spins. As a result, the nuclear spins in the singlet biradical recombination products are polarized. This explains the m~mum in the field dependence of CIDNP for biradical reactions [4,16]. A biradical may be of various conformations with various J. The conformational transitions in the biradical modulate randomly the exchange interaction J(r). The manifestation of exchange interactions in CIDNP is determined, on one hand, by the possible configurations (set of possible J) and, on the other hand, by the rate of conformational transitions. In the limit of sufficiently fast conformational changes J(t) is averaged, and therefore only a certain effective J shows up. The model of m~festations of the polymethylene chain dynamics in the CIDNP has been calculated by de Kanter et al. [5,6]. The set of biradical configurations is the same in liquids and gases. However, the rate of conformational transitions may be substantially different
in liquids and gases. We think this is the cause of the different field dependences of CIDNP observed experimentally in liquids and gases (fig. 4). In solutions the frequency of conformational transitions of biradical is 10-‘“-lO-” s-* [6]. A conformational transition [7] is an example of monomolecular isomerization of a polyatomic molecule [S]. We assume that in the molecule under study the conformational transitions in the gas phase occur more slowly than in liquids. This assumption is confirmed by experimental data from measurements of conformational transition rates in cyclohexane by the NMR method [lo]. The type of confo~ation~ tr~sition in cyclohexane is similar to that of the biradical under study. It has been shown IlO] that for cyclohexane the conformational transition rate increases by an order of magnitude (twenty times) when pressure increases from 5 to 4000 Torr. Even at 4000 Torr this rate does not reach the value of the rate in liquids (three times smaller). It is not possible to take directly into account the quantitative results of ref. [lo] because in ref. [lo] molecules and buffer gases were used which certainly have encounter efficiencies different from the molecules in the present study. But one can qualitatively compare these two systems. An average lifetime of a triplet biradical is 10e7 s (41. We suppose that in liquids the conformational transitions effectively average the exchange interaction, which does not occur in gases. In the gas phase there may arise practically static distribution of J values. Therefore (B,,,),, % (q&i,ui,~ In principle, studies of the field dependence of CIDNP open up a way of determining the biradical dist~bution as a function of J, as well as the rate and character of conformational transitions. To determine the biradical distribution as a function J, it is more convenient to measure CIDNP in the gas phase, because the gas phase is characterized by comparatively slow conformational transitions. Let rp(B, J) be the field dependence of CIDNP for a biradical with a fixed J. Until now we do not know its exact form. Its asymptotes are cp(B, J) -+ 0 at J + 0 and cp(B, J) -+ a, at J -+ 00 and have maxima near the resonance 2 1J I/y at sufficiently high J.
For the set of J with the density f(J) the field dependence of CIDNP is determined by the average magnitude J
cp(B, J)
f(J)
dJJ=x(B).
In high fields, X(B) 2: B/2, the field dependence of CIDNP for cycloundecanone shows two maxima (fig. 3). We associate this with an additional maximum observed in the biradical distribution as a function of J for this system. Note that for biradicals involving ten or more CH, groups in the chain (the ketones under study), the statistical weight of #nformations with a negligible exchange integral is substantial. Therefore, the averaging of J shifts the CIDNP maximum to lower fields in liquids than in gases (fig. 4). The shift of the CIDNP maximum and the change in B,,, observed in gas-phase reactions as compared to liquid phase, can thus be explained by a substanti~ fall in the conformational transition rate in gases as compared to the liquids. In the range of CIDNP mechanism, F protons are mainly polarized, although their hfi constant (A = 0.07 mT [13]) is much smaller than those for ol-CH; (A = 2.198 mT) and for P-CH; protons (A = 2.985 mT (131). According to the CIDNP theory for radical pair reactions in higb magnetic fields, in the S-T, appro~mation [15] CfDNP passes via a maximum with an increase of hfi constant. Therefore, the fact that protons with lower hfi constants are more polarized is neither strange nor impossible in itself. However, in the range of the maximum of CIDNP the polarization in biradicals is associated with Sj3-T_(w rather than with S-T, transitions ((w and p are spin states of the proton). Taking into account only S-T_, transitions results in that as the hfi constant increases, the transition efficiency and the CIDNP associated with this transition also increase, saturate and become constant. Therefore, in order to explain the experiment under discussion, we assume that in gas phase biradicals, even in fields of one or several kG, Sg-T_,o( transitions occur together with the Sot-T+iP associated with proton flips with sufficiently large hfi constant. As a rule, Se+T+tP transitions are neglected, since the energy gap between S and T+l
states,AEs_T+,,is much less than the hfi energy (= A), and therefore S-T+1 mixing occurs at a small parameter value (A/AEs_=+,)* +x 1 [16]. However, the situation changes dramatically for sufficiently long times. If one takes into account that during the pass to the S state the biradicals r~ombine, then it becomes clear that during the lifetime all the T, r biradicals may convert to the S state. Let K be the singlet biradical recombination rate constant, r the lifetime of a triplet biradical. In this case, the S-T,, efficiency transition can be estimated by the formula [16] P = K( A/AEs_r+,)21.
2: ( A,‘B)2Kr.
Let us assume that K = lo’*-lOI3 s-r, B 2: 0.3 lo3 mT, r= 10F7 s-l. In this case, P = (lo-‘-10-*)A*. Obviously, if A = 1.0 mT, hfi transfers all the Ti biradicals to the singlet state. If A ,< 0.1 mT, P +Z 1. It is possible to suppose that under our experimental conditions the weak proton polarizations of (Y- and P-CH, groups result from the fact that various channels of Se--?; p and S&-T_ to1conversions can essentially compensate each other within the biradical lifetime. In the case of v-CH, protons, the efficiency of the Sol-T+,j3 conversion is negligible and therefore the abovementioned compensation does not occur. That is why the y-CH, protons are polarized stronger (with a pronounced resonant character) than ol-CH, and l3-CH, ones. As it has been mentioned above, in cycloketone photolysis in solutions the relative signal intensities for polarized protons correspond to the relative signal intensities of a standard ketone spectrum, irrespective of the hfi constant in the intermediate biradical. This has been attributed [12] to the nuclear polarization transfer by spin-spin coupling of a cycloketone molecuIe. In gases this proton coupling is not important in comparison to the coupling of every spin with the rotational momentum of the molecule which forms the basic contribution to nuclear relaxation 191. In the presence of such a strong relaxation channel in gases the effect of proton coupling does not show up, neither are polarizations redistributed among ketone protons. X
264
A. V. Yurkwskaya et ai.
The authors are very thankful to Dr. Yu.A. Grishin and Dr. E.G. Bagryanskaya for help in flow technique experiments.
References 111A.V. Y~rk~~aya~
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