- Email: [email protected]
Electron spin relaxation of HCO in liquids
ypiirne
;’
32,number
‘.
3
,CHEMICAL,~YSICS
:
‘.
.-.
._
.:
.’
:
‘_
ti...rAUL .’
:
_‘. -.
;, ‘,
..
CHdOOl~Zurich,
:,
.
E~~ONS~~RELAXATIONOFHCO~LIQULDS .. -FhysiMisch-#~enisches
:._lMay 1975 .:
.,. ._..
‘.
:
; :
,,
:
‘,‘: _.: JXTIERS.., ._ .- ‘. ;
.,
,. :
..
‘.
‘..
-’
,.
Inkhit
der ~tii&siCt
Swinerlmd
Ziirich;
: ..
.: Received 23 January 1975. :
.’
..
The ESR l&&idths of He0 in vtibus s6vents are shown to b% due to spin-roiational ;e&ation; The viscosity dependent;ies of the anguk momentum correlation times TJ folloy relxdonships TJ ~‘I/%T~~wJ + B with,solvent dependent pgameters K arid B. :
‘_ ._ R&ritjy; the,ESR spectra of short-lived’acylradicals RkO in low viscosity solutions have been observed . [ j, i] . Foi R = H or al.@1 hey exhibit linewidths of. sex&
gauss indicating relaxation
rates I/T2
two ol-
.ders of magGtud& faster than those typical qf sm‘allalkyl radica!s,unde’r comparable conditions. Thig paper ,-pr&nts an dialysis of the ESR linewidths of formyl. ’ -- :.(H&) in.& solvents at’different temperatures and viscosi=Ljes:. ,’ Fonnyl &as generated in the BSR’cavity together’ ‘, wi$ f-btityl by‘continuok UWrradiation of oxygen. free solutid~
cont,ai&g
pivalaldehyde,
af@i,ekitation bywleavage
which
by Ost\vkd viscosimetry and density measurements. For, all si$ solvents the low- tid high-field resonances of HCO could be simulated by shape functions of equal widths consisting of sup&-positions Qf 95% (by am+&) lorentzian and 5% gaussian kontributions. ?he pe&:to-peak linewidths Aw of their first derivatives are given as Arrhenius plots Ppor four solvents in fig:l. AwiP FcreaGs with temperature and varies with the solvent. Since the inhompgeneity of the magnetic.field over the sample (AWi* = 3.5 X.105’ Tad s-l) and the deviations frompure lorentzian line shapes
decays
xre small the,relaxation
rates
l/T2
follow
from
[3] _
AU,, 2~ l/T, = 4 &TAw, [4] _!his leads to values .. : intherange 5X IO7 ~-~-<.l/Tz~ 15X lo7 s-l. (CH&HO+ (CH3)&.+ HdO . (1) ,’ !kve.ial met h’anisms foi electroti’spin releation in. liquids hatie been discussed [5,6] .,Of those which could @@ large contributionS to.l/Tz of He0 several During the Ikactisn t&e ESR spectra of both species were observed. r)eta.ils of the expetiknt~ technique .can be excluded immediately: (i), There are no indica-. are given elseprhere [2). ?he ESR’li.ne+d’;hs of HdO tions of a chemic’al exchange prdcess. (ii) .The oxygen ~~.&+det&ninedfor temperatires between:-120°C free solutions,contained radical cdnkentrations of < T 4.-65”C.and for:six ether solvents (dipropylether, : [R-l { 10B6 &Iol~~.Thtis, klaxation by interkolec; .’ dieeylether, methylpropylether, dimethoiymethane, alar spill-spin in&actions is negligible [5]. (iii) The “Zmethyl tetrahydr~fur&i,~propylenk.oxide) all con-. first’excited state offid lies 9294 cm-l above the ‘.. tainibg 5% (by,volume)‘piv&ldehyde. The temperature ground state. [7] so,that’m-Orba& process cannot.’ r_ang: viz+ limited by the melting points of the ‘solutions,, give a n@ticeable contribtition [5] i ,’ I I and the.&itivity of t&spe&rr+ef&. ‘The linewidth Ekcluding unknown i&xation~mechanisms, ,lITz: aha&sk& performed by.cotiputer $imulations of the 1. qf $IdO should thkrefore t+given by’ [S] .. _ .,. ‘: . . ‘2. absorp,tion ,~es.c&rect.ing for‘qverlapping .t-bkt# rese-’ 3. ‘. 1/T2-.=.ft’+,a’: +&I, +.qm[ + Byf , ,. .’ : (2) : knees whercn&essaryt Dyn&ic visc0sities.n of,& . I.solhti@‘as fu&ions of.te~peia@[email protected] determined :: ‘-where of,&-fotational _: in” descritks the:cbikbtit@n :: .I. .I . ‘_. ,. ,, . . ., ...... ,,.. I, ,I_ ; .,’ :-+&
._..-~-y- : ‘,. _.,, ‘... ,’ ., Y’. j.,; ‘, :.:_. ..: ‘_.( ‘._ ,:_:. /. ., .-:... ._I_. .,. r ._ ‘: .. ,. ‘. -. ” .: ‘~.,, : ./ .. ]/ ,., I. ._
1 ‘,
: ‘,
,:, :,
:,
‘. : ,;,,, ,: ,:.,I :-_.:_
,: .:..,+ 1 _:’ ‘,
‘. -.: : _,. .;_ ‘;,::_ “, : ., .- : -, : ,~. ___:- _ ._
,:.. ‘. ,,; .‘.
,. :- .‘. .,: .-.,:,:_,
Volume 32, number 3
ci4EhfIc~~PHYslcs
1m
LETTERS
197s
IlT 55
D
5 Fig,
5.5
6
dependence
1. Tefiperature
nf the
From
the
lo6
linewidth
of
16’
K-l
H&O.
&z; < 3 X 10.6 s- 1. Since this is ne&gibly sma!! cpmpared to the experimentally observed relation rates the relaxation of HCO must be governed by a stochastic modulated spin-rotational interaction (a”), in accord with the observed increase of Awpp with temperature [6] (fig.. 1). For symmetric top mbleculer in the Limits of small
interaction, and the other terms are due to the anisotropic parts of the Zceman and hyperfine.interactions. These terms can b,e estimated as follows: For low temperatures, which correspond to long reorientational correlation times r2., the experimental widths of the. ,‘ r?Q=- + l/2 resonances of HCO are equal within the errorhnit(k IO6 rad s-~).T~us,I~~
ESR
6 5
rad s-r.
anglediffusiontid extrememotional narrowing M&lung [lo] has calculated u Q = (zW3h2) {($ f e$ I, + E,zr,kJ
principal values of the g and hype&me ten-
sors determined ti ref. [8] (table 1) the coefficients a’, P, 7 and 6 can be calculated from known procedures. [9]. For the limit of extreme motional narrow-@, i.e.,
(3)
on the basis of an extended ‘diffusion model. E*, EY, et are the principd values of the spin-rotational cou-
largest’contribution for a given ~2, we find a’ = +3 =. 2 ‘+‘. 4~~XlO~~s-~~y,>~.?hefefore~‘+~~~+~?2~ Table 1 Spechoscopjc constants of HCO [ 7?81 Axi3
Moment of
Spin-rotqion~
Electronic
iiypmfiie
;nar&
&ding
g+Xhle
interacGo.on
CMHd
(lo-4gg cm2) x.
.,
,z a)
19.97 ; .’ 18.77
.Y :
.1.206
(hIHi! a)
,‘
,'.. :
r-207.5 17.1 ,8,‘1203):
Al=
33‘7 AZ=346
2.0037 2.0023
..
1.9948
..
A3=378
Absolute value.
; ’ b) The ‘ hype&x teni& k not diagonal &I the x;& z-frune’ [ 131. _. ‘ ,’ ., : ,._. _. .‘ : ;. .’ : ,’ , ‘ ,,. . _.. -.,, ,’ ., .: ,. ;
,‘ :‘ !.
473 : ,;
,.. ..
.k .,,
:’,.
.. -V&m&
32, numbe;
3.
_.
1 May
CHEMICALPHYSICSLE?TERS
1975
‘.
.. :-p&g tensor, Ir,’=1;1 and 1, the principal moments of inertia, and’?, is the angular momentum correlation time which is assumed to be equalfor ail three angular [lo]. For‘HCO ex, .s,,, eZ, I;, &nL?d I’ (= j,) are known [7] and 1, is obtainable from the molecular structure. [7] (table 1). z is the aXis which nearly cqincides with the C=O bond;y is in the molecular plane and x perpendicular to it [‘il. Table 1 and eq. (3) show that the fast relaxation of He0 is near!, exclusively due to a large spin-rotational cou:, pling fi along the C=O bond. Fdr Se case of large angle-diffusion a” is no longer given by (3) but contains addition4 terms which are.nonlinear in TV-. From the general expression for ry’; [lo] we calculate that for HCO eq. (3) should hold as long as (Y”7 l/r2 < 16 X 10’ s-l. Since this is fulfilled’for all our measurements the angular momentum correlation times TJ can be.detennined from (3). ‘FiGj_2 shows our results for 7~ c-f I-I& as functions ’ momentum components
”
of l/q- for four solvents, The data are well described by Iinear relations between TJ and I/q with solvent dependent slopes,and intercepts. In several investigations it has been pointed out that
experimental data of isotropic andar momentum correlation times TJ can be described as functions of viscosities r) by a modified Stokes-&stein relation [5,6,11-141.
:
I-is the mean moment of inertia of the solute molecule, uo its hydrodynamic ra,dius is determined from tran’slat~,onatdiffusion experiments, and d < K d 1 is a parameter which’should-depend on solute and solvent bui: not on temperature and viscosity. K has
been inierpreted,.on a molecular basis as-being propor-’ tional to the ratjo of the mean square torques to the mean square forces.acting on the solute molecule. It should mcrease with increasing solute and decreasing solvent.dze [ll, lI&14]. Eq. (4) holds for a variety oflarge solute molecules (K.T 1) in different solvents except in alcohols and high viscosity solvents [ 11-141. The appllcabihty of (4) for small solute’molecules (K < 1) leas been tested only for the (7162 radical in different. solvents [14]. Although deviations from (4) were expected to occur for K < 1 the IehtiOn was found td hold in the range 0.02
’
1/8r$jK~ f B ,
(5)
where B’is a solvent dependent parameter. With I = 13.3 X 1O-4u g cm2 and an estimated hydrodynamic radiusoO=1~for~CO(Cl~2:uo=l~1A[14])we have determined.the parameters K and B from ieastsquares’ fits of eq. (5) to our data: The results are @en in tilble 2. The qcalitative .de&ease of the K-values with increasing eize of the solvent molecules is-in agreement with theo:,y [12] and known experimental data [l 1,141. If we compare the K for HdO in diethyli and dipropylether with the values K = 0.360 and K 7 0.133 for (5102 in these.two solvents [14], we fiid the Table values
2 foi
K
nnd E
Solvent
~Xl0j. . 1.06
dipropylether 2-methyl
telrahydrof~ran diethylether methylprop!dether .” :
dimethoxyrr,ethane’
propjlene
oiide’
1.72
’
‘2.61 ; 3,.19
,.
3,53 4s7:.
B -.(10-‘4
s)
1.56 1.04’ d-82 0.74
1.18 : 0.,83
:
;
Volume 32, number 3
CHE?dCAL
PHYSICS
L _hfsy 1975
mLE;Rs
,‘
ratios ‘of thti two K-values to be nearly the same for Cl& (2.7) and He0 (2.5). However K of I$0 is two orders, of magnitude loiter-than that of Cl02 :Since both radicals have about equal sizes their translational .&fusion coefficients ina given solvent. and hence the mean square forces acting on them should be sitiar 1121. Thus, because the spin-rotational relaxation of He0 comes mainly from the rotation around the C=O direction our data indicates, that in a given solvent the components of the torques in this direction are
considerably
smaller
than
thqse
for the
responsible
spin-rotational relaxation of ClO2. This may be due to the fact that in contrast to HdO the main_contributioti to the spin-rotational relaxation of Cl02 conies. from the rotation around an axis which is perpendicular to the molecule’s electric dipole moment. The existence of the intercepts B indicates that relation (4) with a temperature and viscosity independent K really
may break
down
for vex-y sm&
values
of K. as
was expected from assumptions made in the theoietical derivation of (4) [12,14]. It is not clear if in such a case an extension of (4) to (5) is meaningful. For the small temperature (and viscosity) range where the ESR spectra of He0 could be observed an exponential [ 151 with energies E lower law TJ = I, exp(-E/NJ than those of the viscosities of the solutions describes our data equally well. But it is interesting to note that an empirical
relationship
TV = T’v/T(Q
+Q’),
7’ and 77’
being soluta and solvent dependent parameters, has been found to represent.the viscosity Bependence of dielectrkrelaxation times rl in a variety of systems over the ‘range 0.3cP ,< 17< 2OOcP [I 61. According to the Hubbard relation TiTl= I/2kT [ 171 this corresponds to,a dependence of 7J on n of the form (5). Thus, it may be expected that relation (5) holds for other systems also.
I would like to thank kofeuor H. Fischer for helpful discussions and the Swiss National Foundation for financial support.
References [l],P.J. KrusicandT.A. 722. [2]
El. Pad
ad
Ret@, I. .&n.C’hem.
Sac. 92 (1973)
H. Fischer, Helv. C%im. Acta 56 CL973)
1535.
[3] B. Blank,
A.
Henne
and H. Fischer, Hetv. chim- Acta 57
(1974) 920. ] [4] C.P. Poole Jr., Electron spin resonance (Interscienn, New York, 1967). D. Xiv&on, i11:Electron spi-r mta~ation in Liquids,. eds. L.T. hluus and P.W. Atkins (bnum PreSs, New York 1972) p. 213, and references therein. [6] P.W. Atkins, in: Electron spin relaxation in liquids, ed:. L.T. Muus and P.W. Atkins (Elenum Press, Neiv York, 1972) p. 279, and references thercicr. [‘I].J.A. Austin, D.H. Levy,C.A. Gotttieb and HE. Radford,
15]
J. Chsm. Fhys. 60 (1974)
207.
[8].R.W. Holmberg, J. Chem. PIys 51 (1969) 3255. [9] R. Wilson and D. Kivelson, J. Chem. Phys. 44 (1966) 154. [IO] R.E.D. h¶cC!ung. J. Chem. Fhys. 57 (1972) 5478. [ll] 1. Hwang, D. Kivelson and W. Piachy, I. Chem. Phys. 58 (1973) 1753. [121 D. Kivelson, hf. Kivelson and I. Oppenheim. 1. Chem. fiys. 52 (1972) 1810. [ 131 R. Huang and D. Kivelson. Pure AppI. Chem. 32 (1972) 207. (141 R.E.D. MeClung and D. Kivelsan. I. Cnem. Phys. 49 (1968)
3380.
[I51 D.E. O’ReiU!!, Ber. Bunsenges. physik. aem. 75 (1971) 208.’ [16] MD. Magee, J. Chem. Sot. Faraday Trans. II 70 (1974)
929. [17] P.S. Hubbard, whys. Rev. L31(1963)
1155.
;’
32,number
‘.
3
,CHEMICAL,~YSICS
:
‘.
.-.
._
.:
.’
:
‘_
ti...rAUL .’
:
_‘. -.
;, ‘,
..
CHdOOl~Zurich,
:,
.
E~~ONS~~RELAXATIONOFHCO~LIQULDS .. -FhysiMisch-#~enisches
:._lMay 1975 .:
.,. ._..
‘.
:
; :
,,
:
‘,‘: _.: JXTIERS.., ._ .- ‘. ;
.,
,. :
..
‘.
‘..
-’
,.
Inkhit
der ~tii&siCt
Swinerlmd
Ziirich;
: ..
.: Received 23 January 1975. :
.’
..
The ESR l&&idths of He0 in vtibus s6vents are shown to b% due to spin-roiational ;e&ation; The viscosity dependent;ies of the anguk momentum correlation times TJ folloy relxdonships TJ ~‘I/%T~~wJ + B with,solvent dependent pgameters K arid B. :
‘_ ._ R&ritjy; the,ESR spectra of short-lived’acylradicals RkO in low viscosity solutions have been observed . [ j, i] . Foi R = H or al.@1 hey exhibit linewidths of. sex&
gauss indicating relaxation
rates I/T2
two ol-
.ders of magGtud& faster than those typical qf sm‘allalkyl radica!s,unde’r comparable conditions. Thig paper ,-pr&nts an dialysis of the ESR linewidths of formyl. ’ -- :.(H&) in.& solvents at’different temperatures and viscosi=Ljes:. ,’ Fonnyl &as generated in the BSR’cavity together’ ‘, wi$ f-btityl by‘continuok UWrradiation of oxygen. free solutid~
cont,ai&g
pivalaldehyde,
af@i,ekitation bywleavage
which
by Ost\vkd viscosimetry and density measurements. For, all si$ solvents the low- tid high-field resonances of HCO could be simulated by shape functions of equal widths consisting of sup&-positions Qf 95% (by am+&) lorentzian and 5% gaussian kontributions. ?he pe&:to-peak linewidths Aw of their first derivatives are given as Arrhenius plots Ppor four solvents in fig:l. AwiP FcreaGs with temperature and varies with the solvent. Since the inhompgeneity of the magnetic.field over the sample (AWi* = 3.5 X.105’ Tad s-l) and the deviations frompure lorentzian line shapes
decays
xre small the,relaxation
rates
l/T2
follow
from
[3] _
AU,, 2~ l/T, = 4 &TAw, [4] _!his leads to values .. : intherange 5X IO7 ~-~-<.l/Tz~ 15X lo7 s-l. (CH&HO+ (CH3)&.+ HdO . (1) ,’ !kve.ial met h’anisms foi electroti’spin releation in. liquids hatie been discussed [5,6] .,Of those which could @@ large contributionS to.l/Tz of He0 several During the Ikactisn t&e ESR spectra of both species were observed. r)eta.ils of the expetiknt~ technique .can be excluded immediately: (i), There are no indica-. are given elseprhere [2). ?he ESR’li.ne+d’;hs of HdO tions of a chemic’al exchange prdcess. (ii) .The oxygen ~~.&+det&ninedfor temperatires between:-120°C free solutions,contained radical cdnkentrations of < T 4.-65”C.and for:six ether solvents (dipropylether, : [R-l { 10B6 &Iol~~.Thtis, klaxation by interkolec; .’ dieeylether, methylpropylether, dimethoiymethane, alar spill-spin in&actions is negligible [5]. (iii) The “Zmethyl tetrahydr~fur&i,~propylenk.oxide) all con-. first’excited state offid lies 9294 cm-l above the ‘.. tainibg 5% (by,volume)‘piv&ldehyde. The temperature ground state. [7] so,that’m-Orba& process cannot.’ r_ang: viz+ limited by the melting points of the ‘solutions,, give a n@ticeable contribtition [5] i ,’ I I and the.&itivity of t&spe&rr+ef&. ‘The linewidth Ekcluding unknown i&xation~mechanisms, ,lITz: aha&sk& performed by.cotiputer $imulations of the 1. qf $IdO should thkrefore t+given by’ [S] .. _ .,. ‘: . . ‘2. absorp,tion ,~es.c&rect.ing for‘qverlapping .t-bkt# rese-’ 3. ‘. 1/T2-.=.ft’+,a’: +&I, +.qm[ + Byf , ,. .’ : (2) : knees whercn&essaryt Dyn&ic visc0sities.n of,& . I.solhti@‘as fu&ions of.te~peia@[email protected] determined :: ‘-where of,&-fotational _: in” descritks the:cbikbtit@n :: .I. .I . ‘_. ,. ,, . . ., ...... ,,.. I, ,I_ ; .,’ :-+&
._..-~-y- : ‘,. _.,, ‘... ,’ ., Y’. j.,; ‘, :.:_. ..: ‘_.( ‘._ ,:_:. /. ., .-:... ._I_. .,. r ._ ‘: .. ,. ‘. -. ” .: ‘~.,, : ./ .. ]/ ,., I. ._
1 ‘,
: ‘,
,:, :,
:,
‘. : ,;,,, ,: ,:.,I :-_.:_
,: .:..,+ 1 _:’ ‘,
‘. -.: : _,. .;_ ‘;,::_ “, : ., .- : -, : ,~. ___:- _ ._
,:.. ‘. ,,; .‘.
,. :- .‘. .,: .-.,:,:_,
Volume 32, number 3
ci4EhfIc~~PHYslcs
1m
LETTERS
197s
IlT 55
D
5 Fig,
5.5
6
dependence
1. Tefiperature
nf the
From
the
lo6
linewidth
of
16’
K-l
H&O.
&z; < 3 X 10.6 s- 1. Since this is ne&gibly sma!! cpmpared to the experimentally observed relation rates the relaxation of HCO must be governed by a stochastic modulated spin-rotational interaction (a”), in accord with the observed increase of Awpp with temperature [6] (fig.. 1). For symmetric top mbleculer in the Limits of small
interaction, and the other terms are due to the anisotropic parts of the Zceman and hyperfine.interactions. These terms can b,e estimated as follows: For low temperatures, which correspond to long reorientational correlation times r2., the experimental widths of the. ,‘ r?Q=- + l/2 resonances of HCO are equal within the errorhnit(k IO6 rad s-~).T~us,I~~
ESR
6 5
rad s-r.
anglediffusiontid extrememotional narrowing M&lung [lo] has calculated u Q = (zW3h2) {($ f e$ I, + E,zr,kJ
principal values of the g and hype&me ten-
sors determined ti ref. [8] (table 1) the coefficients a’, P, 7 and 6 can be calculated from known procedures. [9]. For the limit of extreme motional narrow-@, i.e.,
(3)
on the basis of an extended ‘diffusion model. E*, EY, et are the principd values of the spin-rotational cou-
largest’contribution for a given ~2, we find a’ = +3 =. 2 ‘+‘. 4~~XlO~~s-~~y,>~.?hefefore~‘+~~~+~?2~ Table 1 Spechoscopjc constants of HCO [ 7?81 Axi3
Moment of
Spin-rotqion~
Electronic
iiypmfiie
;nar&
&ding
g+Xhle
interacGo.on
CMHd
(lo-4gg cm2) x.
.,
,z a)
19.97 ; .’ 18.77
.Y :
.1.206
(hIHi! a)
,‘
,'.. :
r-207.5 17.1 ,8,‘1203):
Al=
33‘7 AZ=346
2.0037 2.0023
..
1.9948
..
A3=378
Absolute value.
; ’ b) The ‘ hype&x teni& k not diagonal &I the x;& z-frune’ [ 131. _. ‘ ,’ ., : ,._. _. .‘ : ;. .’ : ,’ , ‘ ,,. . _.. -.,, ,’ ., .: ,. ;
,‘ :‘ !.
473 : ,;
,.. ..
.k .,,
:’,.
.. -V&m&
32, numbe;
3.
_.
1 May
CHEMICALPHYSICSLE?TERS
1975
‘.
.. :-p&g tensor, Ir,’=1;1 and 1, the principal moments of inertia, and’?, is the angular momentum correlation time which is assumed to be equalfor ail three angular [lo]. For‘HCO ex, .s,,, eZ, I;, &nL?d I’ (= j,) are known [7] and 1, is obtainable from the molecular structure. [7] (table 1). z is the aXis which nearly cqincides with the C=O bond;y is in the molecular plane and x perpendicular to it [‘il. Table 1 and eq. (3) show that the fast relaxation of He0 is near!, exclusively due to a large spin-rotational cou:, pling fi along the C=O bond. Fdr Se case of large angle-diffusion a” is no longer given by (3) but contains addition4 terms which are.nonlinear in TV-. From the general expression for ry’; [lo] we calculate that for HCO eq. (3) should hold as long as (Y”7 l/r2 < 16 X 10’ s-l. Since this is fulfilled’for all our measurements the angular momentum correlation times TJ can be.detennined from (3). ‘FiGj_2 shows our results for 7~ c-f I-I& as functions ’ momentum components
”
of l/q- for four solvents, The data are well described by Iinear relations between TJ and I/q with solvent dependent slopes,and intercepts. In several investigations it has been pointed out that
experimental data of isotropic andar momentum correlation times TJ can be described as functions of viscosities r) by a modified Stokes-&stein relation [5,6,11-141.
:
I-is the mean moment of inertia of the solute molecule, uo its hydrodynamic ra,dius is determined from tran’slat~,onatdiffusion experiments, and d < K d 1 is a parameter which’should-depend on solute and solvent bui: not on temperature and viscosity. K has
been inierpreted,.on a molecular basis as-being propor-’ tional to the ratjo of the mean square torques to the mean square forces.acting on the solute molecule. It should mcrease with increasing solute and decreasing solvent.dze [ll, lI&14]. Eq. (4) holds for a variety oflarge solute molecules (K.T 1) in different solvents except in alcohols and high viscosity solvents [ 11-141. The appllcabihty of (4) for small solute’molecules (K < 1) leas been tested only for the (7162 radical in different. solvents [14]. Although deviations from (4) were expected to occur for K < 1 the IehtiOn was found td hold in the range 0.02
’
1/8r$jK~ f B ,
(5)
where B’is a solvent dependent parameter. With I = 13.3 X 1O-4u g cm2 and an estimated hydrodynamic radiusoO=1~for~CO(Cl~2:uo=l~1A[14])we have determined.the parameters K and B from ieastsquares’ fits of eq. (5) to our data: The results are @en in tilble 2. The qcalitative .de&ease of the K-values with increasing eize of the solvent molecules is-in agreement with theo:,y [12] and known experimental data [l 1,141. If we compare the K for HdO in diethyli and dipropylether with the values K = 0.360 and K 7 0.133 for (5102 in these.two solvents [14], we fiid the Table values
2 foi
K
nnd E
Solvent
~Xl0j. . 1.06
dipropylether 2-methyl
telrahydrof~ran diethylether methylprop!dether .” :
dimethoxyrr,ethane’
propjlene
oiide’
1.72
’
‘2.61 ; 3,.19
,.
3,53 4s7:.
B -.(10-‘4
s)
1.56 1.04’ d-82 0.74
1.18 : 0.,83
:
;
Volume 32, number 3
CHE?dCAL
PHYSICS
L _hfsy 1975
mLE;Rs
,‘
ratios ‘of thti two K-values to be nearly the same for Cl& (2.7) and He0 (2.5). However K of I$0 is two orders, of magnitude loiter-than that of Cl02 :Since both radicals have about equal sizes their translational .&fusion coefficients ina given solvent. and hence the mean square forces acting on them should be sitiar 1121. Thus, because the spin-rotational relaxation of He0 comes mainly from the rotation around the C=O direction our data indicates, that in a given solvent the components of the torques in this direction are
considerably
smaller
than
thqse
for the
responsible
spin-rotational relaxation of ClO2. This may be due to the fact that in contrast to HdO the main_contributioti to the spin-rotational relaxation of Cl02 conies. from the rotation around an axis which is perpendicular to the molecule’s electric dipole moment. The existence of the intercepts B indicates that relation (4) with a temperature and viscosity independent K really
may break
down
for vex-y sm&
values
of K. as
was expected from assumptions made in the theoietical derivation of (4) [12,14]. It is not clear if in such a case an extension of (4) to (5) is meaningful. For the small temperature (and viscosity) range where the ESR spectra of He0 could be observed an exponential [ 151 with energies E lower law TJ = I, exp(-E/NJ than those of the viscosities of the solutions describes our data equally well. But it is interesting to note that an empirical
relationship
TV = T’v/T(Q
+Q’),
7’ and 77’
being soluta and solvent dependent parameters, has been found to represent.the viscosity Bependence of dielectrkrelaxation times rl in a variety of systems over the ‘range 0.3cP ,< 17< 2OOcP [I 61. According to the Hubbard relation TiTl= I/2kT [ 171 this corresponds to,a dependence of 7J on n of the form (5). Thus, it may be expected that relation (5) holds for other systems also.
I would like to thank kofeuor H. Fischer for helpful discussions and the Swiss National Foundation for financial support.
References [l],P.J. KrusicandT.A. 722. [2]
El. Pad
ad
Ret@, I. .&n.C’hem.
Sac. 92 (1973)
H. Fischer, Helv. C%im. Acta 56 CL973)
1535.
[3] B. Blank,
A.
Henne
and H. Fischer, Hetv. chim- Acta 57
(1974) 920. ] [4] C.P. Poole Jr., Electron spin resonance (Interscienn, New York, 1967). D. Xiv&on, i11:Electron spi-r mta~ation in Liquids,. eds. L.T. hluus and P.W. Atkins (bnum PreSs, New York 1972) p. 213, and references therein. [6] P.W. Atkins, in: Electron spin relaxation in liquids, ed:. L.T. Muus and P.W. Atkins (Elenum Press, Neiv York, 1972) p. 279, and references thercicr. [‘I].J.A. Austin, D.H. Levy,C.A. Gotttieb and HE. Radford,
15]
J. Chsm. Fhys. 60 (1974)
207.
[8].R.W. Holmberg, J. Chem. PIys 51 (1969) 3255. [9] R. Wilson and D. Kivelson, J. Chem. Phys. 44 (1966) 154. [IO] R.E.D. h¶cC!ung. J. Chem. Fhys. 57 (1972) 5478. [ll] 1. Hwang, D. Kivelson and W. Piachy, I. Chem. Phys. 58 (1973) 1753. [121 D. Kivelson, hf. Kivelson and I. Oppenheim. 1. Chem. fiys. 52 (1972) 1810. [ 131 R. Huang and D. Kivelson. Pure AppI. Chem. 32 (1972) 207. (141 R.E.D. MeClung and D. Kivelsan. I. Cnem. Phys. 49 (1968)
3380.
[I51 D.E. O’ReiU!!, Ber. Bunsenges. physik. aem. 75 (1971) 208.’ [16] MD. Magee, J. Chem. Sot. Faraday Trans. II 70 (1974)
929. [17] P.S. Hubbard, whys. Rev. L31(1963)
1155.