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Solvation dynamics studied by ultrafast transient hole burning
ELSEVIER
Journal of h4olecular Liquids. 65/t 56(l99s).3oI-.w
The time-resolved salvation of s-tetraxine in propylene carbonate is studied by ultrafast transient hole burning. In agreement with mode-coupling theory. the temperature dependence of the average t&xation time follows a power law in which the critical temperattne and exponent are the same as in other rektation experiments. Our recenttheory for sob&on by mechanical relaxation provides a unified and quantitative explanation of borh the subpicosectnrd phonon-induced rekxation and the slower stntctursl nJaxa&m. 1. Itttroductloa Becauseof the fundamentaJ impormnce of solvent-solute interactions in chemical reactions, the dynamks of solvation have been widely studied. However. most studies have focused on systems where Charlie tedistribution within the solute is the dominant effect of changing the electronic state.[l.Z] Recendy. Fourhas, Benigno and Berg studied the salvation dynamics of a nonpok solute in a nonpok solvent, whem charge redistribution plays a rni;lor roJe.[3.4) These stndies showed two distinct dynamic components: a s&picosecond viscosity independent reJaxation driven by phonon-Jihe processes, and a slower. viscosity dependeni stmctml rebuation. These resuhs have been expkined qttantitatively by a theory of sokation basedon mechaniealrelaxationoft~eventinresponsecodtangesinIhemdecul;rrs~ofthesdtcteon excitatios[6] Here, we present rest& on the salvation of a nonpo&r solute, s-tetraxine, by a pok sokent, propylene carbonate over the temperature range 300-160 K. In this system, comparisons to severaJ s to salvation are possible. dleomicai 2Tra&entHoJeBuraJJEx@ntenta the sobation dynamics (Big. I).[ 3-5 ] These experiments yield WeuseduansienthoJebumingtomeasure botha~tStokesshift~atime~width,bolhofw~charere~totheEOI~ M!hkeSShik ~~WidttrsWii~bcdiSCUsJtd dynamics. Herewecons*theti~ eiaewhm.191
DemiJedmerwrementpofthe~-tetraxinegps-phasespecuurnweremade. WitJrthesedau,masrPanentof the absohtte Stokes shift S(t) is possible. Because the Stokes shift is xem in the absence of solvent nndear theamountofreJaxtuionwidtin dynatmcs,thema@mdeoftbeStohesshiftattheearBesttimesrepesents the expaittmtal he resohrtion. The s&&y-state abso@on and fhrarrsccace spectmwefe~to provide an itxkpendent value of the equilibrium Stokes shift .L With this data, the absolute s&r&on respomeftJnaion
R(t) = 1 - s(t) S(-)
( 1 )
* Cune~ address: JnstJtutefur MokcuJar Science. Myodaiji. Okraki. 444 Japau + Cm address: lkpmme~ of Chemistry, University of Minncnota. Minneapobs. MN 55455. USA 0167-7322NSBOP.M) Y: 19X E&via SSD/Ol67-7322M)oo82l-7
!kicnce
B.V. All rights resewed.
was cakulated without any normalizing factors. Measurements were made at 13 temperatures between 298, and 160 K. spnnning a viscosity range of 2.6 CP to 3.2~10~~ cP. Comparisons to four different theoretical
3.
Results
A. ModeCorrpling Theory Mude-coupling theories have recently shown great promise for expiaining the microscopic origins of the glass tranaition.(lO.ll] These theories predict ~thrtthedyntunicsatedomituitedbytheexistenceofa critical rempemtnte Tc distinctly above the glass transition tempemtbre. Abnve Tc. the primary (a) smtctnml nlaxation time is predicted to have a
power-law temperature dependence,z = MT-T$y. Tc and T should be the same for all relaxation procases in the same solvent. In Fig. 1. the average solvation time measured by transient hole burning is compared to Du. et al.‘s tneasuretnents of relaxation by depolarixed light scattering.[ 121 These experiments measure relaxation on very different length scales; solvanon on a ntokcular let@ scale, and light scattering on the scale of the wavelength of light. Both sets of data fit with the same exponent of y=2.74 and extrapolate to nearly the same value of Tc, in agmment with mode-ceupling theory.
R. Mechanical Rekwtion Theory Berg suggested that a chiMge in the solute size on excitation could produce a significant solvent respome.[6,81He mated the solute as a spherical cavityofmdiuarcanddtesokntasaviscoeiastic continuum with time-dependent compression and shear moduii K(t) and G(t). For a spherically symmetric change in cavity size. two time scales are
, Tph =
0.6
A %
0.2
b ”
Temperature
(K)
Fig. 1 A fit of solvation times to a power law temperature dependence. Depolarized light 1129fit t0 Ihe some scnttering (DPLS) times power and intercept in agreement with modeconpling theoty. Neutron ‘scattering (9%) times [139 match salvation times. suppotting Bagchi’s salvation theory.
m
P
IL+$G,
G(t)
’
where p is the solvent density, and ll is the viscosity. function simplifies to
dt’L-’
dt
(2)
In the nortnal case, where ts >> tph, the response
+2cx-
and
1
The fmpency dependenr modulus is defined by the Laplacelransfofm
2.0
m
&)
=
I&&s)
=
e-+t) I
dt
(4)
1 .5
0
,&uli. andK,andG~aretheitiniteffecpr This model predicts that the salvation WIL(have two distinct comp0nents. The first term of Eq. 3 is a subpicosecond response determined entirely by the high frequency elastic mod&. The moduli, and thaefore t* are only *y temperaturedependent. This term represents’the creation of vibrations (phonons) of the instantaneous structure of the liquid. The second term is a slower, temperature dependent response caused by reorga&atiOn of the in~srmcbm. !Figure 2 shows fits of thii model to the dpamic St&s shift of S-wmzine in propylene wtwnate. A sfmcbed exponential form for G(t) has been used, andthetemperaturedependenceofG,has been e2simedffomli~-gdata.llll Thedetails of the phomzm-componesttme not Observable with current titne-Pesolntioa, but tlie predktions of the ~~~~~Y~~C~~ totheexpriment Aaitical testoftheroawoableness0fthesefitSistheability of the fit pawnews to cow&y predict the solvent’s viscosity. Theviscoaityiswellpre4iictedbythefits . l%evaluesofG,areafactorOf2IPrgerthan expected from light scattering experiments. Ihis diwqwcyc0uldbeexplainfdbyadeviati~fmma ~~l~insine.orbyalocalvatwofG, whichislargathanthl?balkvalua.
0
1
2
3
Log Delay Time (ps)
Fig. 2 A tit of a viscoelastic model of salvation (solid) to transient hole burning data (points). Temperatwes top to botmm: l6OK to 2!%K
C. Bag&i’s Theory Bagchi has presented a molecular theory for solvatioo of spherical nompolar aolutes.[7] It relates the solvatim responsefunction to the intemctioo potential a~d the dynamics saucture facttx. Comp&o k-vecaor .smcamfauor.butsuchrudr neoeonsceoeringexperimerppcen-thed~ are not widely available. Relaxation times from neutr~o scattering at a single k-vectOr are available for Assuming this k-vector is representative of the length scale Of the interaaion propylene c&ooate.[l3,14] patmtial, Bagchi’s theory predicts the solwation times and the neutlon scatwing times would be the same. FigurelshOwsthatthispedictiooisaue. D. Dielectric lta Theory carbaur*hssbemsCudiedbyBsbasad~ Thasolvati0odyniwnics0fCouma4in153inppykne (I51 This solute *as a large ctwge mdistritwiou in the excited byf@!mwwndflgaescenceW. sate. andsolvation isdomimEed by the diiiecfric respoosc of the solvent 10 the new chaogedistribotioo. We
compared the solvatiou times of the Coumarin to our measurementsof the solvation times of s-tetrazine to test whether dielectric salvation is active in our case. At room temperature, the solvation response functions of Coumarin 153 and s-tetrazine are almost ideatical.(Fi~. 3) As the temperature is lowered (267 K and 257 K). the s-tetraziue response function becomes distiucdy slower than the Coumarin response. From this compat’ison, we cooclude that dielecuk solvatiou is relatively unimportant for this nonpolar solute. even though the solvent is strongly p&r. 4.
CQ&KS;Q~~~
These experiments have shown that the slower component, of solvation is linked to the overall structural dynamics of the liquii. aud that mode coupling theory predicts marry of the overall features of thesedynamics. Qieleuric salvation. which is dte most widely studied solvatiorr mechanism. does not play a major role for this nonpolar solute. Two themies of rumpolar solvatkxr give better agreemem with the data, Bag&i’s dteory is more rigorously derived. but our model permits a more detailed aud rigorous comparisou with experimettt.
: .oo 298
0.75
K
050
. 025 025 l.
e
COO :.a0~
257 K
0.75 0.54
l
* . .
0
25
000
.
:1:
00
. 05
10
. 1.5
1.0
Log Delay iimc
(ps)
2.5
Fip. 3 A comparison of the salvation of steKazine (points) and Coumarin 153 (solid) [2] in propylene carbonate. Dfferent solvation mechanisms appear to operate for different soluK?s.
5. References 1. M. Maroncelli. J. Mol. Liq. 57, 1 (1993). 2. P. F. Barbara and W. Jarzeba. Adv. Photo&em. 15 , 1 (1990). 3. J. T. Fourkas and M. Berg. J. Chem. Phys. 98 , 7773 (1993). 4. J. T. Fourkas, A. Benign0 and M. Berg, J. Chem. Phys. 99 , 8552 (1993). 5. H. Murakami, S. Kinoshita, Y. Hiram, T. Okada and N. Mataga, J. Chem. Phys. 97.7881 (1992). 6. M. Berg. Chem. Phys. Lett. 228 , 317 (1994). 7. B. Bagchi. J. Chem. Phys. 199 . 6658 Wm. 8. M. Berg. in preparation. 9. J. Ma, D. Vanden Bout and M. Berg, in prepamiQn. 10. W. G&e. in Liq&!s. Freezing ad the Glass Trodion. edited by J.P. Hansen. D. Levesque, and J. Zinn-Justin (North-Holland, Amsterdam, 1990). p. 287. 11. W. G&z and L. ;;i%en. Rep. Prog. Pbys. 55. 241 (1992). 12.W. M. Du. G. Li. H. Z. Cummins. M. Fuchs, J. Toulouse and L. A. Knauss. Phys. Rev. E. 49. 2192 (1994). 13 L. B&jesson and W. S. Howells, J. Nonctyst. Solids. 131i133 , 53 (1991). 14 L. B&jesson , M. Elmworth, L. M.’ Torell, Chem. Phys. 149. 209 (1990). 15. W. Jaezeba. G. C. Waker. A. E. Johnson and P. F. Barbara, Chem. Phys. 152.57 (1991).
Journal of h4olecular Liquids. 65/t 56(l99s).3oI-.w
The time-resolved salvation of s-tetraxine in propylene carbonate is studied by ultrafast transient hole burning. In agreement with mode-coupling theory. the temperature dependence of the average t&xation time follows a power law in which the critical temperattne and exponent are the same as in other rektation experiments. Our recenttheory for sob&on by mechanical relaxation provides a unified and quantitative explanation of borh the subpicosectnrd phonon-induced rekxation and the slower stntctursl nJaxa&m. 1. Itttroductloa Becauseof the fundamentaJ impormnce of solvent-solute interactions in chemical reactions, the dynamks of solvation have been widely studied. However. most studies have focused on systems where Charlie tedistribution within the solute is the dominant effect of changing the electronic state.[l.Z] Recendy. Fourhas, Benigno and Berg studied the salvation dynamics of a nonpok solute in a nonpok solvent, whem charge redistribution plays a rni;lor roJe.[3.4) These stndies showed two distinct dynamic components: a s&picosecond viscosity independent reJaxation driven by phonon-Jihe processes, and a slower. viscosity dependeni stmctml rebuation. These resuhs have been expkined qttantitatively by a theory of sokation basedon mechaniealrelaxationoft~eventinresponsecodtangesinIhemdecul;rrs~ofthesdtcteon excitatios[6] Here, we present rest& on the salvation of a nonpo&r solute, s-tetraxine, by a pok sokent, propylene carbonate over the temperature range 300-160 K. In this system, comparisons to severaJ s to salvation are possible. dleomicai 2Tra&entHoJeBuraJJEx@ntenta the sobation dynamics (Big. I).[ 3-5 ] These experiments yield WeuseduansienthoJebumingtomeasure botha~tStokesshift~atime~width,bolhofw~charere~totheEOI~ M!hkeSShik ~~WidttrsWii~bcdiSCUsJtd dynamics. Herewecons*theti~ eiaewhm.191
DemiJedmerwrementpofthe~-tetraxinegps-phasespecuurnweremade. WitJrthesedau,masrPanentof the absohtte Stokes shift S(t) is possible. Because the Stokes shift is xem in the absence of solvent nndear theamountofreJaxtuionwidtin dynatmcs,thema@mdeoftbeStohesshiftattheearBesttimesrepesents the expaittmtal he resohrtion. The s&&y-state abso@on and fhrarrsccace spectmwefe~to provide an itxkpendent value of the equilibrium Stokes shift .L With this data, the absolute s&r&on respomeftJnaion
R(t) = 1 - s(t) S(-)
( 1 )
* Cune~ address: JnstJtutefur MokcuJar Science. Myodaiji. Okraki. 444 Japau + Cm address: lkpmme~ of Chemistry, University of Minncnota. Minneapobs. MN 55455. USA 0167-7322NSBOP.M) Y: 19X E&via SSD/Ol67-7322M)oo82l-7
!kicnce
B.V. All rights resewed.
was cakulated without any normalizing factors. Measurements were made at 13 temperatures between 298, and 160 K. spnnning a viscosity range of 2.6 CP to 3.2~10~~ cP. Comparisons to four different theoretical
3.
Results
A. ModeCorrpling Theory Mude-coupling theories have recently shown great promise for expiaining the microscopic origins of the glass tranaition.(lO.ll] These theories predict ~thrtthedyntunicsatedomituitedbytheexistenceofa critical rempemtnte Tc distinctly above the glass transition tempemtbre. Abnve Tc. the primary (a) smtctnml nlaxation time is predicted to have a
power-law temperature dependence,z = MT-T$y. Tc and T should be the same for all relaxation procases in the same solvent. In Fig. 1. the average solvation time measured by transient hole burning is compared to Du. et al.‘s tneasuretnents of relaxation by depolarixed light scattering.[ 121 These experiments measure relaxation on very different length scales; solvanon on a ntokcular let@ scale, and light scattering on the scale of the wavelength of light. Both sets of data fit with the same exponent of y=2.74 and extrapolate to nearly the same value of Tc, in agmment with mode-ceupling theory.
R. Mechanical Rekwtion Theory Berg suggested that a chiMge in the solute size on excitation could produce a significant solvent respome.[6,81He mated the solute as a spherical cavityofmdiuarcanddtesokntasaviscoeiastic continuum with time-dependent compression and shear moduii K(t) and G(t). For a spherically symmetric change in cavity size. two time scales are
, Tph =
0.6
A %
0.2
b ”
Temperature
(K)
Fig. 1 A fit of solvation times to a power law temperature dependence. Depolarized light 1129fit t0 Ihe some scnttering (DPLS) times power and intercept in agreement with modeconpling theoty. Neutron ‘scattering (9%) times [139 match salvation times. suppotting Bagchi’s salvation theory.
m
P
IL+$G,
G(t)
’
where p is the solvent density, and ll is the viscosity. function simplifies to
dt’L-’
dt
(2)
In the nortnal case, where ts >> tph, the response
+2cx-
and
1
The fmpency dependenr modulus is defined by the Laplacelransfofm
2.0
m
&)
=
I&&s)
=
e-+t) I
dt
(4)
1 .5
0
,&uli. andK,andG~aretheitiniteffecpr This model predicts that the salvation WIL(have two distinct comp0nents. The first term of Eq. 3 is a subpicosecond response determined entirely by the high frequency elastic mod&. The moduli, and thaefore t* are only *y temperaturedependent. This term represents’the creation of vibrations (phonons) of the instantaneous structure of the liquid. The second term is a slower, temperature dependent response caused by reorga&atiOn of the in~srmcbm. !Figure 2 shows fits of thii model to the dpamic St&s shift of S-wmzine in propylene wtwnate. A sfmcbed exponential form for G(t) has been used, andthetemperaturedependenceofG,has been e2simedffomli~-gdata.llll Thedetails of the phomzm-componesttme not Observable with current titne-Pesolntioa, but tlie predktions of the ~~~~~Y~~C~~ totheexpriment Aaitical testoftheroawoableness0fthesefitSistheability of the fit pawnews to cow&y predict the solvent’s viscosity. Theviscoaityiswellpre4iictedbythefits . l%evaluesofG,areafactorOf2IPrgerthan expected from light scattering experiments. Ihis diwqwcyc0uldbeexplainfdbyadeviati~fmma ~~l~insine.orbyalocalvatwofG, whichislargathanthl?balkvalua.
0
1
2
3
Log Delay Time (ps)
Fig. 2 A tit of a viscoelastic model of salvation (solid) to transient hole burning data (points). Temperatwes top to botmm: l6OK to 2!%K
C. Bag&i’s Theory Bagchi has presented a molecular theory for solvatioo of spherical nompolar aolutes.[7] It relates the solvatim responsefunction to the intemctioo potential a~d the dynamics saucture facttx. Comp&o k-vecaor .smcamfauor.butsuchrudr neoeonsceoeringexperimerppcen-thed~ are not widely available. Relaxation times from neutr~o scattering at a single k-vectOr are available for Assuming this k-vector is representative of the length scale Of the interaaion propylene c&ooate.[l3,14] patmtial, Bagchi’s theory predicts the solwation times and the neutlon scatwing times would be the same. FigurelshOwsthatthispedictiooisaue. D. Dielectric lta Theory carbaur*hssbemsCudiedbyBsbasad~ Thasolvati0odyniwnics0fCouma4in153inppykne (I51 This solute *as a large ctwge mdistritwiou in the excited byf@!mwwndflgaescenceW. sate. andsolvation isdomimEed by the diiiecfric respoosc of the solvent 10 the new chaogedistribotioo. We
compared the solvatiou times of the Coumarin to our measurementsof the solvation times of s-tetrazine to test whether dielectric salvation is active in our case. At room temperature, the solvation response functions of Coumarin 153 and s-tetrazine are almost ideatical.(Fi~. 3) As the temperature is lowered (267 K and 257 K). the s-tetraziue response function becomes distiucdy slower than the Coumarin response. From this compat’ison, we cooclude that dielecuk solvatiou is relatively unimportant for this nonpolar solute. even though the solvent is strongly p&r. 4.
CQ&KS;Q~~~
These experiments have shown that the slower component, of solvation is linked to the overall structural dynamics of the liquii. aud that mode coupling theory predicts marry of the overall features of thesedynamics. Qieleuric salvation. which is dte most widely studied solvatiorr mechanism. does not play a major role for this nonpolar solute. Two themies of rumpolar solvatkxr give better agreemem with the data, Bag&i’s dteory is more rigorously derived. but our model permits a more detailed aud rigorous comparisou with experimettt.
: .oo 298
0.75
K
050
. 025 025 l.
e
COO :.a0~
257 K
0.75 0.54
l
* . .
0
25
000
.
:1:
00
. 05
10
. 1.5
1.0
Log Delay iimc
(ps)
2.5
Fip. 3 A comparison of the salvation of steKazine (points) and Coumarin 153 (solid) [2] in propylene carbonate. Dfferent solvation mechanisms appear to operate for different soluK?s.
5. References 1. M. Maroncelli. J. Mol. Liq. 57, 1 (1993). 2. P. F. Barbara and W. Jarzeba. Adv. Photo&em. 15 , 1 (1990). 3. J. T. Fourkas and M. Berg. J. Chem. Phys. 98 , 7773 (1993). 4. J. T. Fourkas, A. Benign0 and M. Berg, J. Chem. Phys. 99 , 8552 (1993). 5. H. Murakami, S. Kinoshita, Y. Hiram, T. Okada and N. Mataga, J. Chem. Phys. 97.7881 (1992). 6. M. Berg. Chem. Phys. Lett. 228 , 317 (1994). 7. B. Bagchi. J. Chem. Phys. 199 . 6658 Wm. 8. M. Berg. in preparation. 9. J. Ma, D. Vanden Bout and M. Berg, in prepamiQn. 10. W. G&e. in Liq&!s. Freezing ad the Glass Trodion. edited by J.P. Hansen. D. Levesque, and J. Zinn-Justin (North-Holland, Amsterdam, 1990). p. 287. 11. W. G&z and L. ;;i%en. Rep. Prog. Pbys. 55. 241 (1992). 12.W. M. Du. G. Li. H. Z. Cummins. M. Fuchs, J. Toulouse and L. A. Knauss. Phys. Rev. E. 49. 2192 (1994). 13 L. B&jesson and W. S. Howells, J. Nonctyst. Solids. 131i133 , 53 (1991). 14 L. B&jesson , M. Elmworth, L. M.’ Torell, Chem. Phys. 149. 209 (1990). 15. W. Jaezeba. G. C. Waker. A. E. Johnson and P. F. Barbara, Chem. Phys. 152.57 (1991).