- Email: [email protected]
Magnetic field effect on the hyperfine-induced triplet formation in systems undergoing donor to radical pair electron transfer
Volume 88. number 6
CHEMICALPHYSICS
MAGNETIC FIELD EFFECT ON THE HYPERFINE-INDUCED IN
28 May I982
LE-I-IERS
TRIPLET FORMATION
SYSTEMSUNDERGOINGDONOR TO RADICAL PAIR ELECTRON TRANSFER
Friedtich
NOLTINC,
Hubert
STAERK
and Albert WELLER
dlaor-Plonck-Ilish’~I Jtir B~opbysikabscbc Cbcrnre, Abtedrrtrg Spekrroshopre. D-3400 Gtithugen. Federal Repubbc o/Germany
Received 30 March 1982
By measuring delayed fluorescence intensities from trtplet-triplet anmhilaton, relative trtplct yields xc dctermrncd a\ a function of external magnetic field strength for photomduccd electron-transfer systems undergoing clcctron ebchangc between donor molecules and the donor radical cations of radical Ion pus Experimental results obtamcd with the system pyrcne/d~merhylanilme in methanol confiim thcorctlcal predictlons
t _ Introduction
field-modulated
Photoinduced electron-transfer processes in polar solvents between electron donor (D) and acceptor (A) molecules produce radical pairs (‘-A’ + 2D’) which either separate into long-lived @s) free radicals or recombme by electron back-transfer to give smglet ground- or triplet excited-state products [l-3). According to the simplified scheme 1(2A:
+ ‘Dt)__,
k&I
3(2A:
+2D+
3A’
+ lD,
(1) radical pairs generated by electron-transfer fluorescence quenching in a singlet electron spin state can recombine to form molecular triplets, 3A*, only after the overall spin multiplicity of the pair has been changed. This spin multiplicity change, occurring with the rate constant k,(B), is based on the hyperfmecoupling-induced coherent spin motion of the unpaired electron spins and can be modulated by weak magnetic fields (B) of the order of magnitude of the hyperfiie interaction Z[akVk, where ak and Ik are the hyperfme cOUphg COflStaIIt and the IIUChI spin of the kth nucleus. ‘llus leads, analogously to the well-known CIDNP effects, to a slowing down of k, and hence to a decrease in triplet yield. As triplet production from singlet exciplexes is not affected by weak magnetic fields, inferences can be drawn from the magnetic
signal about
the relative
participation
of exciplexes and radical pairs in the recombination process [4,5]. Recently, in this laboratory, the theory of hyperfine-induced spm motion of radical pairs has been estended [6] to mclude the exchange reaction (‘Ar+‘D+)+‘D-r’A:+‘D+‘D+
(2)
between donor radical cations and donor molecules in the ground state. The predicted consequence of such a diamagnetic-paramagnetic exchange is a strong effect on the magnetic field dependence of the geminate triplet recombination yield. It is the purpose of the present experimental study to examine the acceptor/donor systems pyrene/dimethylamline (WA), their deuterated analogues, and pyrene/3,5dimethoxyN,Ndimethylaniline (DhfDhtA) in methanol with respect to this effect. Relative tnplet yields are determined by measuring the mtensity, I,,, of the delayed
fluorescence which, being brought about by triplettriplet annthtlation, 3A’ + 3A+ + tA* + tA L
lA+I~~Dr,
(3)
is proportional to the square of the triplet concentration, so that one obtain for an external magnetic field strength B the relative triplet yield
0 009.2614/82/0000-0000/S 02.75 Cl 1982 North-Holland
@-#)/@T(B = 0) = [l,r@)/f,,(B
= o)] ‘I2 . 5’73
Volume 88. number 6
CHEhlICAL PHYSICS LETTERS
28 May 1982
2. Experimental The compounds of the purest quality conunercially available were punlied by zone refming (pyrene), vacuum destrllation (DMA) and vacuum sublimahon (DMDMA). Deuterated pyrene (98% D, Merck, Sharp 8: Dohme) and DMA (99% D, Merck) and methanol spectrograde have been used without further purifcation. The solutions were contained in quartz cuvettes and kept at 19’C. The concentration of pyrene was (2-5) X 10m4 M. The donor concentration, bemg varied by a factor of 100, was (I, 5,10,50,100) X 10-j hf. All samples have been degnsscd by 5-6 freezepump-thaw cycles, The appararus - a magnetic field spectrometer,
0.8
Pyrene-d,,,.oMA-d,,I” MeOH
with features of a phosphoroscope fo measure delayed fluorescence - was in principle the same as that described earlier [7] but with the following improve-
ments: The delayed fluorescence was measured by an XP 2230 photomultiplier (Valve) and a home-made adJustable gated integrator. The intenaty of the repetitive (50 Hz) laser pulses was measured contmuously by means of a beam sphtter and a vacuum photodrode. These signals together with the measured magnetic field strength were fed via an A/D converter into an LSI 1 l/2 computer. This configuration allows setting a discriminating energy window, in width usutiy G% of the nitrogen
laser pulse energy, and averagingover a preselected number of laser shots at discrete levels of magnetic field strength. The resulting values of delayed fluorescence have been corrected for the remaining influence of mtensity variations of the exciting laser (G!S) as well as for a sbght deterioration of the samples due to irreversible photochemistry and have been averaged over 7-10 sweeps of the magnetic field up to 650 G.
3. Results and discussion Fig. 1 shows the relative triplet yield of pyrene as a fun&on of the magnetic field strength for the system pyrene/DhlA (top) and the perdeuterated system pyrene. d,,jDhlAA,, (bottom) in methanol as solvent. One can see that in both systems the relative triplet yield is reduced with mcreasing magnetic field strength gradually reaching a saturation value (above 200 C). At low magnetic field strengths (20-50 G) the triplet yield 524
I 0
I
I
I
I
100
200
..I
‘650
I
B/Gauss Fig. 1. Relative triplet yield of the system pyrencjdimethylan&nc (top) and Ihe deurented analogue (bottom) III methanol as function of the magnetic field strength. Dlmethylamhne concentration (a) 1 X IO-’ hl (Text = 0 0013 ns-‘), (b) 1 X 10-l hl (rexc = 0 13 nPI). The dotted curves (a’, b’) give
the corrected relative triplet yxlds (see text).
drops less rapidly in the case of higher D concentration [(b) curves], at medium fields (=I00 G) the two curves intersect so that at higher field strengths ()I00 G) a stronger magnetic field effect is observed at high donor concentration. The same holds - at lower field strengths - for the perdeuterated pair. __ ln comparing the yields at different donor (D) concentrations one has to keep in mind that the measured yields also comprise pyrene triplets which a! low donor concentrations are formed by normal intersystem crossing due to incomplete quenching of the primarily excited pyrene and at higher D concentrations by triplet energy transfer from injtially_excited p molecules. Both triplet sources give pyrene triplets whose yields are in-
CHEhIICALPHYSICSLETTERS
Volume88. number 6
dependentof the externalmagneticfieldstrength, Making use of the singlet and tripletyrelds from the intermediates (exciplexes and ion pairs) of the system pyrene/DMA in methanol reported in ref. [4,5] and assuming that ail the excited D molecules yield triplet pyrene via energy transfer (see above) a correction has been made (cf. (a’) and (b’) III fig. I) that does not change the relative form of the measured curves very much. For the correctionof the perdeuteratedsystem the samevalues have been used as for the nondeuterated pair. The fiial uncertainty is probably within 2%. The magnetic field effect on the triplet yield can
be characterizedby the fieldstrengthB,p
at whichthe
28 h1.1~1982
fable 1 Hypcrline coupling and mqnelic Acceptor/donor
ZA&llk
pyrcnc/DhlA
field cffccr (all v;liucs rn G) rDlU/lll
B,,,(O)
14.8
57.0
57
4.5
51.0
57
pyrcnc/DhfDhlA
14.8
306
50
pyrenc/DhlAd,‘ pyrencdlO/DhlAd11 --
14.8 4.5
25.3 7-5 3
373’,
pyrcnc+I&DhlA
a)
a) Extrapolated to zero cwhangc raw.
measurable effect. This behaviour can be correlated with the (sum of the) hyperfme coupling constants of
decrease of +. has reached half the saturation value ob-
pyrene and DMA radical ions (from
tained at high fields above 600 G. It should be noted that the curves (a’) and (b’) in fig. 1, obtained by applying the corrections, yield the sameB1j2 valuesas the uncorrected ones (a) and (b). Comparison of the four deuterated and nondeuterated pyrene/DMA combinations presented m fig. 7, shows that the B112value is obviously governed by the hyperfme coupling properties of DMA-/I and DMA-d. Deuteration of pyrene has no
weighted by the nuclear spin moments (table I). Even for the perdeuterated DMA(t) the sum IShigher than lt is for the normal pyrene(-). A more detailed study of the correlation between B,j2 values and hyperfme coupling constants has been performed and WIIIbe presented elsewhere [8,9] _Comparison of the experimental relative triplet yield curves (fig. I) with the ones calculated on the basis of a somewhat simphfied model (e.g. neglecting Coulomb forces) [6J gives quite reasonable qualitative agreement. In the experiments only a donor concentration variation up to I X low1 M was feasible, corresponding to an exchange rate of less than 1 ns-1, whereas in the theoretical treatment the calculation was executed for exchange rates up to
B’rz
Gauss __--
ESR measurements)
-3
_*--
10 ns-1 and beyond. Takmg the bimolecular rate constant for the electron exchange reaction in solvents like methanol
_*--
ID++ tD+ID+?Dt to be k,,, < 1.3 X IO9 M-l s-l (cf. ref. [ 101) one obtams with a donor concentration of 0.1 M an exns-I. change rate, r_ =k,,,cD,of0.13 At lower field strengths (=I0 C) one observes a small positive magnetic field effect on the triplet yield of the order of 1% (fig. I). Tlus behaviour has , been predicted for the systems investigated here in . ref. [5] where the tnplet probability at 10 G in the I
0005
a01
005 co_dmj mol
I
time range S-15
a1
pair is somewhathrgherthan for zero field.It is interestmg to note that this short-tune behaviour can be monitored
Fig. 2. B,,
values versus donor concentration in methanol*
(0) pYrenel,o/DhlA~tll, (A)pyrenedtO/DhlA-hll, pYrene~lo/DhlDhlA, and (o) pyrene-hlo/DhlAdll, pyrene~&IhIAdll.
(x) (a)
ns after generation
by looking at the delayed
of the radical
fluorescence
in
the far longer m&second region. AU the observations mentioned above have been confirmed recently in this laboratory in a metho&525
Volume 88. number 6
CHEMICAL PHYSICS LETTERS
28 May 1982
tally quite different laser spectroscopic study [8]. There the triplet concentration is measured directly in absorption 50 ns after laser pulse excitation. A rationalization of the observed concentration effects is possible within the framework of the hyperfine mechanism [4-7,121. It is clear that exchange weakens the ZDMA+hyperfme coupling. At very
re,c > 0.1 ns-I, corresponding to residence times in the electron hopping process of typically l-10 ns, the asymptotic value of the triplet probability isp-,. = 3/4 [12]. However, at high magnetic field strength the triplet levels T,, and T_, are well separated from To and only T, and S,, are coupled, provided the exchange interaction in the radical pair is small (GOB7 eV) com-
&II aniline concentrations
pared with the hyperfme
(very high exchange
rates) the magnetic moments of the anilinenuclei averageout and only the (weaker j ‘pyrene- radical hyperfiie coupling remains which results in a smaller
value for the triplet yield curve. This limiting case, however, is not reached in this work. The dlscusslon of the region of low- and mediumexchange rates between, say, 0.1 and 1.Ons-‘, requires a more detailed consideration of the triplet probabdity p-#, B, re,J being a function of tune, magnetic
Bllz
interaction.
In this case the
triplet probability can at the most reach the valuepT = l/Z, independent of the magnitude of the exchange rate. These arguments lead to relative triplet yields of I#.,.(B)/eT (B = 0) = 4/$ = i for no electron exchange and a more than 10% lower value of $q-(B)/q+(B = 0) = i/a = s for high exchange rates. A decrease of the
relative triplet yield of roughly this order of magmtude is indeed experimentally observed (fig. 1).
field strength, and exchange rate. In the theoretical treatment [6] this is accomplished by averaging the electron spin correlation tensor over all possible sequences of exchange events. The plot ofpT versus time far short times and a magnetic field strength of the order of the sum of the hyperfme couplmg con-
We thank B. Frederichs, H. Meyer and R. Mitzkus for valuable technical assistance. We also thank Professor K. Schulten for severaldiscussions.This work has been
stants, show a slower increase of the triplet probabll-
supported
ity with tune at highexchangeratesthan at r,,, = 0. Thisis because thelifetImeof a fucednuclearspin
through
Acknowledgement
by the Deutsche Forschungsgemeinschaft
Sonderforschungsbereich SFB93,“Photo-
chemistrywith lasers”.
environment decreaseswith increasingandine concentration (mcreasing exchange rate). It has been shown in ref. [ 121 that the short lifetime of a certain nuclear spin configuration requires larger fields for a modulation of the triplet yield and reaches the saturation value more slowly. An alternative view adopting
the uncertamty pnnciple demands an energy broadening of the states involved by AE S=re,.c?i. As a consequence the B,lz values must increase correspondingly. In our experiments the B112 valueschange by 43-52% at the highest exchange rate of 0.13 ns-I. The larger increase is observed with the system, where DMA is
deuterated (seefig,2), Unfortunately, a detailedtheeretical treatment of hyperfme modulatmn ofdeuterated systems at low magnetic field strength is not yet available. At high magnetic field strengths (X00 G) the fmal relative triplet yield assumes a lower value for exchange rates other than zero (e.g. fe,c = 0.1-l ns-l). This is
explained as follows: At zero magnetic field strength and for an exchange rate rtXc= 0 the triplet probability approaches the value pT = 2/3, for an exchange rate
References [l] H Leonhardt and A.
Weller, Ber Bunsenges. Phynk. Chem. 67 (1963) 791, A. Weller. tn: Fast Reactions and Pnmary Processes in Chemical Ktnetlcs, ed. S. Claesson, Nobel Symposium 5 (1967); D. Rehm and A. Weller. Z. Physik. Chem. NF 69 (1970) 183; H. Schomburg, H. Staerk and A. WeUer,Chem. Phys. Letters 21 (1973) 433: 56 (1978) 399. [2] M Schulz, Dissertation, University of GBttingen (1974); H. Schomburg, Dissertation, University of Giittingen (1975): F. Nolting, Dissertxtton, University ofCottingen (1977). [ 31 N. Ma@a, T. Okada and K. Ezumi, Mol. Phys. 9 (1966) 201. (41 K. Schulten, H. Staerk, A. Weller, H.-J. Werner and 8. Ntckcl, Z. Physik. Chem. NF 101 (1976) 371. [5] H.-J. Werner, 2. Schulten and K. Schulten, J. Chem. Phys. 67 (1977) 646; H.-J. Werner, Dissertation, University of Cdttingen (1977). [6] E.-W. Knapp and K. Schulten, J. Chem. Phys. 71(1979) 1878.
Volume 88, number 6
CHEMICALPHYSICS
28 May 1982
LETTERS
to
[ 71 H.-J. Werner, H. Staerk and A. Weller, J. Chem. Phys.
[IO]
I-. Nolting, H. Staerk and A. \VcUer.
68 (1978) 2419. [S] D. Rehm and A. Weller, Ber. Bunscnges. Phyak. Chem.
[ ll]
Z. Schulten and K. Schulten, I. Chem. Phys 66 (1977)
73 (1969) 834. [ 91 R. Treichel, Diplomarbeit,
[ 121K. Schulten and University of Ciittmgen (1982).
bc pubhshed.
4616. (1978)
P.G. Wolynes, J. Chem. Phyb 68
3292.
527
CHEMICALPHYSICS
MAGNETIC FIELD EFFECT ON THE HYPERFINE-INDUCED IN
28 May I982
LE-I-IERS
TRIPLET FORMATION
SYSTEMSUNDERGOINGDONOR TO RADICAL PAIR ELECTRON TRANSFER
Friedtich
NOLTINC,
Hubert
STAERK
and Albert WELLER
dlaor-Plonck-Ilish’~I Jtir B~opbysikabscbc Cbcrnre, Abtedrrtrg Spekrroshopre. D-3400 Gtithugen. Federal Repubbc o/Germany
Received 30 March 1982
By measuring delayed fluorescence intensities from trtplet-triplet anmhilaton, relative trtplct yields xc dctermrncd a\ a function of external magnetic field strength for photomduccd electron-transfer systems undergoing clcctron ebchangc between donor molecules and the donor radical cations of radical Ion pus Experimental results obtamcd with the system pyrcne/d~merhylanilme in methanol confiim thcorctlcal predictlons
t _ Introduction
field-modulated
Photoinduced electron-transfer processes in polar solvents between electron donor (D) and acceptor (A) molecules produce radical pairs (‘-A’ + 2D’) which either separate into long-lived @s) free radicals or recombme by electron back-transfer to give smglet ground- or triplet excited-state products [l-3). According to the simplified scheme 1(2A:
+ ‘Dt)__,
k&I
3(2A:
+2D+
3A’
+ lD,
(1) radical pairs generated by electron-transfer fluorescence quenching in a singlet electron spin state can recombine to form molecular triplets, 3A*, only after the overall spin multiplicity of the pair has been changed. This spin multiplicity change, occurring with the rate constant k,(B), is based on the hyperfmecoupling-induced coherent spin motion of the unpaired electron spins and can be modulated by weak magnetic fields (B) of the order of magnitude of the hyperfiie interaction Z[akVk, where ak and Ik are the hyperfme cOUphg COflStaIIt and the IIUChI spin of the kth nucleus. ‘llus leads, analogously to the well-known CIDNP effects, to a slowing down of k, and hence to a decrease in triplet yield. As triplet production from singlet exciplexes is not affected by weak magnetic fields, inferences can be drawn from the magnetic
signal about
the relative
participation
of exciplexes and radical pairs in the recombination process [4,5]. Recently, in this laboratory, the theory of hyperfine-induced spm motion of radical pairs has been estended [6] to mclude the exchange reaction (‘Ar+‘D+)+‘D-r’A:+‘D+‘D+
(2)
between donor radical cations and donor molecules in the ground state. The predicted consequence of such a diamagnetic-paramagnetic exchange is a strong effect on the magnetic field dependence of the geminate triplet recombination yield. It is the purpose of the present experimental study to examine the acceptor/donor systems pyrene/dimethylamline (WA), their deuterated analogues, and pyrene/3,5dimethoxyN,Ndimethylaniline (DhfDhtA) in methanol with respect to this effect. Relative tnplet yields are determined by measuring the mtensity, I,,, of the delayed
fluorescence which, being brought about by triplettriplet annthtlation, 3A’ + 3A+ + tA* + tA L
lA+I~~Dr,
(3)
is proportional to the square of the triplet concentration, so that one obtain for an external magnetic field strength B the relative triplet yield
0 009.2614/82/0000-0000/S 02.75 Cl 1982 North-Holland
@-#)/@T(B = 0) = [l,r@)/f,,(B
= o)] ‘I2 . 5’73
Volume 88. number 6
CHEhlICAL PHYSICS LETTERS
28 May 1982
2. Experimental The compounds of the purest quality conunercially available were punlied by zone refming (pyrene), vacuum destrllation (DMA) and vacuum sublimahon (DMDMA). Deuterated pyrene (98% D, Merck, Sharp 8: Dohme) and DMA (99% D, Merck) and methanol spectrograde have been used without further purifcation. The solutions were contained in quartz cuvettes and kept at 19’C. The concentration of pyrene was (2-5) X 10m4 M. The donor concentration, bemg varied by a factor of 100, was (I, 5,10,50,100) X 10-j hf. All samples have been degnsscd by 5-6 freezepump-thaw cycles, The appararus - a magnetic field spectrometer,
0.8
Pyrene-d,,,.oMA-d,,I” MeOH
with features of a phosphoroscope fo measure delayed fluorescence - was in principle the same as that described earlier [7] but with the following improve-
ments: The delayed fluorescence was measured by an XP 2230 photomultiplier (Valve) and a home-made adJustable gated integrator. The intenaty of the repetitive (50 Hz) laser pulses was measured contmuously by means of a beam sphtter and a vacuum photodrode. These signals together with the measured magnetic field strength were fed via an A/D converter into an LSI 1 l/2 computer. This configuration allows setting a discriminating energy window, in width usutiy G% of the nitrogen
laser pulse energy, and averagingover a preselected number of laser shots at discrete levels of magnetic field strength. The resulting values of delayed fluorescence have been corrected for the remaining influence of mtensity variations of the exciting laser (G!S) as well as for a sbght deterioration of the samples due to irreversible photochemistry and have been averaged over 7-10 sweeps of the magnetic field up to 650 G.
3. Results and discussion Fig. 1 shows the relative triplet yield of pyrene as a fun&on of the magnetic field strength for the system pyrene/DhlA (top) and the perdeuterated system pyrene. d,,jDhlAA,, (bottom) in methanol as solvent. One can see that in both systems the relative triplet yield is reduced with mcreasing magnetic field strength gradually reaching a saturation value (above 200 C). At low magnetic field strengths (20-50 G) the triplet yield 524
I 0
I
I
I
I
100
200
..I
‘650
I
B/Gauss Fig. 1. Relative triplet yield of the system pyrencjdimethylan&nc (top) and Ihe deurented analogue (bottom) III methanol as function of the magnetic field strength. Dlmethylamhne concentration (a) 1 X IO-’ hl (Text = 0 0013 ns-‘), (b) 1 X 10-l hl (rexc = 0 13 nPI). The dotted curves (a’, b’) give
the corrected relative triplet yxlds (see text).
drops less rapidly in the case of higher D concentration [(b) curves], at medium fields (=I00 G) the two curves intersect so that at higher field strengths ()I00 G) a stronger magnetic field effect is observed at high donor concentration. The same holds - at lower field strengths - for the perdeuterated pair. __ ln comparing the yields at different donor (D) concentrations one has to keep in mind that the measured yields also comprise pyrene triplets which a! low donor concentrations are formed by normal intersystem crossing due to incomplete quenching of the primarily excited pyrene and at higher D concentrations by triplet energy transfer from injtially_excited p molecules. Both triplet sources give pyrene triplets whose yields are in-
CHEhIICALPHYSICSLETTERS
Volume88. number 6
dependentof the externalmagneticfieldstrength, Making use of the singlet and tripletyrelds from the intermediates (exciplexes and ion pairs) of the system pyrene/DMA in methanol reported in ref. [4,5] and assuming that ail the excited D molecules yield triplet pyrene via energy transfer (see above) a correction has been made (cf. (a’) and (b’) III fig. I) that does not change the relative form of the measured curves very much. For the correctionof the perdeuteratedsystem the samevalues have been used as for the nondeuterated pair. The fiial uncertainty is probably within 2%. The magnetic field effect on the triplet yield can
be characterizedby the fieldstrengthB,p
at whichthe
28 h1.1~1982
fable 1 Hypcrline coupling and mqnelic Acceptor/donor
ZA&llk
pyrcnc/DhlA
field cffccr (all v;liucs rn G) rDlU/lll
B,,,(O)
14.8
57.0
57
4.5
51.0
57
pyrcnc/DhfDhlA
14.8
306
50
pyrenc/DhlAd,‘ pyrencdlO/DhlAd11 --
14.8 4.5
25.3 7-5 3
373’,
pyrcnc+I&DhlA
a)
a) Extrapolated to zero cwhangc raw.
measurable effect. This behaviour can be correlated with the (sum of the) hyperfme coupling constants of
decrease of +. has reached half the saturation value ob-
pyrene and DMA radical ions (from
tained at high fields above 600 G. It should be noted that the curves (a’) and (b’) in fig. 1, obtained by applying the corrections, yield the sameB1j2 valuesas the uncorrected ones (a) and (b). Comparison of the four deuterated and nondeuterated pyrene/DMA combinations presented m fig. 7, shows that the B112value is obviously governed by the hyperfme coupling properties of DMA-/I and DMA-d. Deuteration of pyrene has no
weighted by the nuclear spin moments (table I). Even for the perdeuterated DMA(t) the sum IShigher than lt is for the normal pyrene(-). A more detailed study of the correlation between B,j2 values and hyperfme coupling constants has been performed and WIIIbe presented elsewhere [8,9] _Comparison of the experimental relative triplet yield curves (fig. I) with the ones calculated on the basis of a somewhat simphfied model (e.g. neglecting Coulomb forces) [6J gives quite reasonable qualitative agreement. In the experiments only a donor concentration variation up to I X low1 M was feasible, corresponding to an exchange rate of less than 1 ns-1, whereas in the theoretical treatment the calculation was executed for exchange rates up to
B’rz
Gauss __--
ESR measurements)
-3
_*--
10 ns-1 and beyond. Takmg the bimolecular rate constant for the electron exchange reaction in solvents like methanol
_*--
ID++ tD+ID+?Dt to be k,,, < 1.3 X IO9 M-l s-l (cf. ref. [ 101) one obtams with a donor concentration of 0.1 M an exns-I. change rate, r_ =k,,,cD,of0.13 At lower field strengths (=I0 C) one observes a small positive magnetic field effect on the triplet yield of the order of 1% (fig. I). Tlus behaviour has , been predicted for the systems investigated here in . ref. [5] where the tnplet probability at 10 G in the I
0005
a01
005 co_dmj mol
I
time range S-15
a1
pair is somewhathrgherthan for zero field.It is interestmg to note that this short-tune behaviour can be monitored
Fig. 2. B,,
values versus donor concentration in methanol*
(0) pYrenel,o/DhlA~tll, (A)pyrenedtO/DhlA-hll, pYrene~lo/DhlDhlA, and (o) pyrene-hlo/DhlAdll, pyrene~&IhIAdll.
(x) (a)
ns after generation
by looking at the delayed
of the radical
fluorescence
in
the far longer m&second region. AU the observations mentioned above have been confirmed recently in this laboratory in a metho&525
Volume 88. number 6
CHEMICAL PHYSICS LETTERS
28 May 1982
tally quite different laser spectroscopic study [8]. There the triplet concentration is measured directly in absorption 50 ns after laser pulse excitation. A rationalization of the observed concentration effects is possible within the framework of the hyperfine mechanism [4-7,121. It is clear that exchange weakens the ZDMA+hyperfme coupling. At very
re,c > 0.1 ns-I, corresponding to residence times in the electron hopping process of typically l-10 ns, the asymptotic value of the triplet probability isp-,. = 3/4 [12]. However, at high magnetic field strength the triplet levels T,, and T_, are well separated from To and only T, and S,, are coupled, provided the exchange interaction in the radical pair is small (GOB7 eV) com-
&II aniline concentrations
pared with the hyperfme
(very high exchange
rates) the magnetic moments of the anilinenuclei averageout and only the (weaker j ‘pyrene- radical hyperfiie coupling remains which results in a smaller
value for the triplet yield curve. This limiting case, however, is not reached in this work. The dlscusslon of the region of low- and mediumexchange rates between, say, 0.1 and 1.Ons-‘, requires a more detailed consideration of the triplet probabdity p-#, B, re,J being a function of tune, magnetic
Bllz
interaction.
In this case the
triplet probability can at the most reach the valuepT = l/Z, independent of the magnitude of the exchange rate. These arguments lead to relative triplet yields of I#.,.(B)/eT (B = 0) = 4/$ = i for no electron exchange and a more than 10% lower value of $q-(B)/q+(B = 0) = i/a = s for high exchange rates. A decrease of the
relative triplet yield of roughly this order of magmtude is indeed experimentally observed (fig. 1).
field strength, and exchange rate. In the theoretical treatment [6] this is accomplished by averaging the electron spin correlation tensor over all possible sequences of exchange events. The plot ofpT versus time far short times and a magnetic field strength of the order of the sum of the hyperfme couplmg con-
We thank B. Frederichs, H. Meyer and R. Mitzkus for valuable technical assistance. We also thank Professor K. Schulten for severaldiscussions.This work has been
stants, show a slower increase of the triplet probabll-
supported
ity with tune at highexchangeratesthan at r,,, = 0. Thisis because thelifetImeof a fucednuclearspin
through
Acknowledgement
by the Deutsche Forschungsgemeinschaft
Sonderforschungsbereich SFB93,“Photo-
chemistrywith lasers”.
environment decreaseswith increasingandine concentration (mcreasing exchange rate). It has been shown in ref. [ 121 that the short lifetime of a certain nuclear spin configuration requires larger fields for a modulation of the triplet yield and reaches the saturation value more slowly. An alternative view adopting
the uncertamty pnnciple demands an energy broadening of the states involved by AE S=re,.c?i. As a consequence the B,lz values must increase correspondingly. In our experiments the B112 valueschange by 43-52% at the highest exchange rate of 0.13 ns-I. The larger increase is observed with the system, where DMA is
deuterated (seefig,2), Unfortunately, a detailedtheeretical treatment of hyperfme modulatmn ofdeuterated systems at low magnetic field strength is not yet available. At high magnetic field strengths (X00 G) the fmal relative triplet yield assumes a lower value for exchange rates other than zero (e.g. fe,c = 0.1-l ns-l). This is
explained as follows: At zero magnetic field strength and for an exchange rate rtXc= 0 the triplet probability approaches the value pT = 2/3, for an exchange rate
References [l] H Leonhardt and A.
Weller, Ber Bunsenges. Phynk. Chem. 67 (1963) 791, A. Weller. tn: Fast Reactions and Pnmary Processes in Chemical Ktnetlcs, ed. S. Claesson, Nobel Symposium 5 (1967); D. Rehm and A. Weller. Z. Physik. Chem. NF 69 (1970) 183; H. Schomburg, H. Staerk and A. WeUer,Chem. Phys. Letters 21 (1973) 433: 56 (1978) 399. [2] M Schulz, Dissertation, University of GBttingen (1974); H. Schomburg, Dissertation, University of Giittingen (1975): F. Nolting, Dissertxtton, University ofCottingen (1977). [ 31 N. Ma@a, T. Okada and K. Ezumi, Mol. Phys. 9 (1966) 201. (41 K. Schulten, H. Staerk, A. Weller, H.-J. Werner and 8. Ntckcl, Z. Physik. Chem. NF 101 (1976) 371. [5] H.-J. Werner, 2. Schulten and K. Schulten, J. Chem. Phys. 67 (1977) 646; H.-J. Werner, Dissertation, University of Cdttingen (1977). [6] E.-W. Knapp and K. Schulten, J. Chem. Phys. 71(1979) 1878.
Volume 88, number 6
CHEMICALPHYSICS
28 May 1982
LETTERS
to
[ 71 H.-J. Werner, H. Staerk and A. Weller, J. Chem. Phys.
[IO]
I-. Nolting, H. Staerk and A. \VcUer.
68 (1978) 2419. [S] D. Rehm and A. Weller, Ber. Bunscnges. Phyak. Chem.
[ ll]
Z. Schulten and K. Schulten, I. Chem. Phys 66 (1977)
73 (1969) 834. [ 91 R. Treichel, Diplomarbeit,
[ 121K. Schulten and University of Ciittmgen (1982).
bc pubhshed.
4616. (1978)
P.G. Wolynes, J. Chem. Phyb 68
3292.
527