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Influence of self-quenching of the benzene triplet state on estimates of naphthalene T2→T1 internal conversion rates
CHEMICAL
Volume 53. number 1
INFLUENCE
OF SELF-QUENCHING
OF NAPHTHALENE
‘J+-
PHYSICS
OF THE BENZENE
T, INTERNAL
1 January 1978
UZITERS
TRIPLET
CONVERSION
STATE ON ESTJMATES
RATES
Vicente G. TOSCANO and Frank H. QUINA
Received 20 September 1977
Selfquenching of the benzene triplet state is shown to be important under the conditions employed by Ladwig and Liu to estimate the Tg lifetime of naphthalene derivatives. The appropriate kinetic expressions, which reinforce the validity of their experimental approach, are presented and their data corrected for the self-quenching process. The corrected data indicate a slightly larger deuterium effect and somewhat shorter Ta lifetimes than previously estimated.
Tn a recent series of papers, Ladwig and Liu [I-3] have reported the results of an elegant technique for the interception of the second triplet state of naphthalene @+I&), perdeutero~~phth~ene (Np-dg), and l~~oronaphth~e~e (I-CiNp). The naph~~ene Ta state transferred excitation to an energy carrier benzene (B), which in turn sensitized the internal cycloaddition of endo-dicyclopentadiene (E). On the basis of a corresponding kinetic scheme [33 and the assumption that exothermic energy transfer steps occur at the diffusion controlled rate, they derived the following equation for the dependence of the product qu~tum yield on the concentration of I3
SIope/~tercept ratios of plots of @;l versus [B]-” were then employed to obtain vahres of k2/kl, where k2 is the naphthalene T2TX internal conversion rate and k, the rate of energy transfer (presumably diffusion controlled) from the naphthalene T2 state to B. Inherent in the de~va~on of eq. (1) is the assump tion that the benzene triplet state (BTr ) is completely trapped by transfer to E and N [3]. However, 91 the concentration range employed (I- 10 M B), the benzene triplet lifetime is known to be relatively short [4-S] and to depend on the benzene concentration
in a manner which can be kinetically represented as a seifquenching process BTr f BSu 5
2BSo .
(2)
A value of about 2 X 107 M-l s-1 for kc is consistent with data for the lifetime of BTr in neat benzene (3-7 ns [4-71, kg = (1.4 -3) X 107 M-l s-l) and for energy transfer from BT1 to anthracene (kg = 1.8 X 107 M-1 s-1 for [B] < 1.1 M [6]) or trms-2-octene (ks* t 1.7 X 107 M-l s-l for [B] < 6 M [7]) in cyclohexane solution. Incorporating the self-quenching step in the kinetic scheme of J_adwig and Liu [3], and retaining their other assumptions, one obtains the following expression for the product quantum yield, where k, is the presumably diffusion contralied rate (6-2 X 109 M-l s-1) for energy transfer from BT, to E and N
tEl+INl+k2k6~ 1
1 -=-
[El
QiP
k,
+~[El+N+k6’ k,
CBIEI
kd
WI
1
fB1 _ kd
Fl
(3)
From the apprOpr&ite magnitudes of &jr and kd and the experimental concentrations of B, E and N [l--3], it can be shown that the fourth term on the right hand side of eq_(3) is small relative to the third, in agreement 65
Volume 53, number 1
CHEMICAL PHYSICS LETTERS
with the observed linearity of plots of #F’ versus [B] -l_ Thus, neglecting the last term, eq- (3) pr&icts that the siope/intercept ratio of such plots should be a function of [E] and [NJ slope
intercept
kl c----f
C k2
k6’
1
kc&El + Ir?rl)
-1
-
(4)
Indeed, the observed ratios for Np-A8 (2 X 10e3 M) are 9.7 M for [El = 0.05 M and 13.9 + 2.3 M for [E] = O-10 M [I-3] _ Using these data in eq- (4) we fmd k-,/k1=25M for Np-hS and k6-/kd=0.0033. From t&e fatter we obtain k6’ = 2 X f07 M-1 s-1, a value in excellent agreement with the literature values cited above, pointing to the appropriateness of eqs. (3) and (4) under the conditions employed by Xadwig and i&l*. Recalculatfon of *Sledata of JLadwigand L.iu [l-3], taking into account the self-quenching of the benzene triplet state via eq. (4) and using the value of ks./kd (which is a property of e1 alone) obtained above, provides vahxes of k2[kl of 13.7 M for Np-d8 and 20 M for I-ClNp- The effect of perdeuteration on the TzT, internal conversion rate of naph~~ene, k2(Np-~8)/k~~p-d*), is therefore calculated to be somewhat Iarger (1.8 versus I-4) than that estimated by Ladwig and Liu. For k, = k,, we estimate T2 iifetimes of 6.5 ps for Np-h,, 12 ps for Np-ds. and 8 ps for lClNp, values which are about a factor of two shorter than those estimated on the basis of eq. (I). The real significance of eqs. (3) and (4) lies not so *
Althougheq. (1) is muchmore appealingfrom an experimentaI point of view, seIfquenchiugseemsto be a commonprop-
erty of simple methy&enze~es [8-l 1 ]_ T&X littie would be gained by using a GmpIe substituted benzene as the energy carrier.
66
l-January 1978
much in the correction of estimates based OR eq_ (1) as in the mechanistic insight prkided_ The excellent agreement between literature values of kg’ and that
obtained from the data-of Ladwig and L.iu via eq. (4) clearly indicates the intermediacy of the benzene triplet state in _thetransfer process and thus reinforces the
validity of their experimental approach. The Laboratorio de Fotoquimica is supported by funds from the Brazilian Conselho Naciond de Desenvolvimento Cientifico e TecnoK@co (CNPq) and the U-S. National Academy of Sciences (NASj- FHQ is a CNPq-NAS Fellow_
References 111CC. Ladwig and RS.R Liu, I_ Am. Chem. Sot 96 (1974) 6210.
121CC_ Ladwig and R.S.H. Lia, Chem, Phys. Letters 35 (1975) 563.
PI CC. Ladwigand R.S.H. Liu, J. Am_ Chem. Sot. 98<1976)
8093. E4I K_J_Thomas, Ann. Rev_Phys. Chem_21 (1970) 17, and references therein.
151RR. Hentz and L-M_ PerIcey,J_ Phys. Chem. 74 C1970) 3047. 161RV_ Bensasson,J.T. Richards and I.K. Thomas, Chem. Phys. Letters 9 (1971) 13.
171R.R Hentz and RM. ‘Ihiiauit, J. Phys. Chem. 77 (1973) 1105. 181RB. Cundali and W. Tippett, Trans. Faraday Sot. 66 (1970) 350. t91 RB. Cundall and W_ Tippett, Advan Chem_Ser_82 (1968) 387. I101 R.B. CundaU and A.3.R Voss, Chem. Commun. (1969) ll&_ fill RB. CundaI!, D.A. Robinson and A.J.R. VOSS,1.Photo_ them. 2 <1973/74)231.
Volume 53. number 1
INFLUENCE
OF SELF-QUENCHING
OF NAPHTHALENE
‘J+-
PHYSICS
OF THE BENZENE
T, INTERNAL
1 January 1978
UZITERS
TRIPLET
CONVERSION
STATE ON ESTJMATES
RATES
Vicente G. TOSCANO and Frank H. QUINA
Received 20 September 1977
Selfquenching of the benzene triplet state is shown to be important under the conditions employed by Ladwig and Liu to estimate the Tg lifetime of naphthalene derivatives. The appropriate kinetic expressions, which reinforce the validity of their experimental approach, are presented and their data corrected for the self-quenching process. The corrected data indicate a slightly larger deuterium effect and somewhat shorter Ta lifetimes than previously estimated.
Tn a recent series of papers, Ladwig and Liu [I-3] have reported the results of an elegant technique for the interception of the second triplet state of naphthalene @+I&), perdeutero~~phth~ene (Np-dg), and l~~oronaphth~e~e (I-CiNp). The naph~~ene Ta state transferred excitation to an energy carrier benzene (B), which in turn sensitized the internal cycloaddition of endo-dicyclopentadiene (E). On the basis of a corresponding kinetic scheme [33 and the assumption that exothermic energy transfer steps occur at the diffusion controlled rate, they derived the following equation for the dependence of the product qu~tum yield on the concentration of I3
SIope/~tercept ratios of plots of @;l versus [B]-” were then employed to obtain vahres of k2/kl, where k2 is the naphthalene T2TX internal conversion rate and k, the rate of energy transfer (presumably diffusion controlled) from the naphthalene T2 state to B. Inherent in the de~va~on of eq. (1) is the assump tion that the benzene triplet state (BTr ) is completely trapped by transfer to E and N [3]. However, 91 the concentration range employed (I- 10 M B), the benzene triplet lifetime is known to be relatively short [4-S] and to depend on the benzene concentration
in a manner which can be kinetically represented as a seifquenching process BTr f BSu 5
2BSo .
(2)
A value of about 2 X 107 M-l s-1 for kc is consistent with data for the lifetime of BTr in neat benzene (3-7 ns [4-71, kg = (1.4 -3) X 107 M-l s-l) and for energy transfer from BT1 to anthracene (kg = 1.8 X 107 M-1 s-1 for [B] < 1.1 M [6]) or trms-2-octene (ks* t 1.7 X 107 M-l s-l for [B] < 6 M [7]) in cyclohexane solution. Incorporating the self-quenching step in the kinetic scheme of J_adwig and Liu [3], and retaining their other assumptions, one obtains the following expression for the product quantum yield, where k, is the presumably diffusion contralied rate (6-2 X 109 M-l s-1) for energy transfer from BT, to E and N
tEl+INl+k2k6~ 1
1 -=-
[El
QiP
k,
+~[El+N+k6’ k,
CBIEI
kd
WI
1
fB1 _ kd
Fl
(3)
From the apprOpr&ite magnitudes of &jr and kd and the experimental concentrations of B, E and N [l--3], it can be shown that the fourth term on the right hand side of eq_(3) is small relative to the third, in agreement 65
Volume 53, number 1
CHEMICAL PHYSICS LETTERS
with the observed linearity of plots of #F’ versus [B] -l_ Thus, neglecting the last term, eq- (3) pr&icts that the siope/intercept ratio of such plots should be a function of [E] and [NJ slope
intercept
kl c----f
C k2
k6’
1
kc&El + Ir?rl)
-1
-
(4)
Indeed, the observed ratios for Np-A8 (2 X 10e3 M) are 9.7 M for [El = 0.05 M and 13.9 + 2.3 M for [E] = O-10 M [I-3] _ Using these data in eq- (4) we fmd k-,/k1=25M for Np-hS and k6-/kd=0.0033. From t&e fatter we obtain k6’ = 2 X f07 M-1 s-1, a value in excellent agreement with the literature values cited above, pointing to the appropriateness of eqs. (3) and (4) under the conditions employed by Xadwig and i&l*. Recalculatfon of *Sledata of JLadwigand L.iu [l-3], taking into account the self-quenching of the benzene triplet state via eq. (4) and using the value of ks./kd (which is a property of e1 alone) obtained above, provides vahxes of k2[kl of 13.7 M for Np-d8 and 20 M for I-ClNp- The effect of perdeuteration on the TzT, internal conversion rate of naph~~ene, k2(Np-~8)/k~~p-d*), is therefore calculated to be somewhat Iarger (1.8 versus I-4) than that estimated by Ladwig and Liu. For k, = k,, we estimate T2 iifetimes of 6.5 ps for Np-h,, 12 ps for Np-ds. and 8 ps for lClNp, values which are about a factor of two shorter than those estimated on the basis of eq. (I). The real significance of eqs. (3) and (4) lies not so *
Althougheq. (1) is muchmore appealingfrom an experimentaI point of view, seIfquenchiugseemsto be a commonprop-
erty of simple methy&enze~es [8-l 1 ]_ T&X littie would be gained by using a GmpIe substituted benzene as the energy carrier.
66
l-January 1978
much in the correction of estimates based OR eq_ (1) as in the mechanistic insight prkided_ The excellent agreement between literature values of kg’ and that
obtained from the data-of Ladwig and L.iu via eq. (4) clearly indicates the intermediacy of the benzene triplet state in _thetransfer process and thus reinforces the
validity of their experimental approach. The Laboratorio de Fotoquimica is supported by funds from the Brazilian Conselho Naciond de Desenvolvimento Cientifico e TecnoK@co (CNPq) and the U-S. National Academy of Sciences (NASj- FHQ is a CNPq-NAS Fellow_
References 111CC. Ladwig and RS.R Liu, I_ Am. Chem. Sot 96 (1974) 6210.
121CC_ Ladwig and R.S.H. Lia, Chem, Phys. Letters 35 (1975) 563.
PI CC. Ladwigand R.S.H. Liu, J. Am_ Chem. Sot. 98<1976)
8093. E4I K_J_Thomas, Ann. Rev_Phys. Chem_21 (1970) 17, and references therein.
151RR. Hentz and L-M_ PerIcey,J_ Phys. Chem. 74 C1970) 3047. 161RV_ Bensasson,J.T. Richards and I.K. Thomas, Chem. Phys. Letters 9 (1971) 13.
171R.R Hentz and RM. ‘Ihiiauit, J. Phys. Chem. 77 (1973) 1105. 181RB. Cundali and W. Tippett, Trans. Faraday Sot. 66 (1970) 350. t91 RB. Cundall and W_ Tippett, Advan Chem_Ser_82 (1968) 387. I101 R.B. CundaU and A.3.R Voss, Chem. Commun. (1969) ll&_ fill RB. CundaI!, D.A. Robinson and A.J.R. VOSS,1.Photo_ them. 2 <1973/74)231.