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Molecular probing of dielectric relaxation in the glass-transition region
Volume 199,number 3,4
CHEMICAL PHYSICS LETTERS
6 November 1992
Molecular probing of dielectric relaxation in the glass-transition region Ranko Richert Fachbereich PhysikalischeChemie, Philipps-Universitiit, Hans-MeerweinStrasse, W-3SSOMarburg, Germany Received 10 August 1992;in final form 1 September 1992
Conventional dielectric s*(w) data and solvation dynamic C( 1) data are recorded simultaneously,assuring perfectcoincidence of experimental conditions for the two relaxation phenomena in the glass-former 2-MTHF doped with quinoxaline. The dynamic MSA theory for dipolar solvation turns out to relate the observed Stokes-shift dynamics to the dielectric data in a quantitative fashion. The agreement between theory and experiment facilitates access to “microscopic” dielectric relaxation via spectroscopy of appropriatemolecular probes in supercooled liquids.
1.
Introduction
Glass-forming liquids in the transition regime to solid-like viscosities, i.e. near their glass transition temperatures To, display complex time and temperature dependences which are no longer reminiscent of simple activated rate processes [ 11. Instead, Kohlrausch-Williams-Watts (KWW) type relaxation patterns and non-Arrhenius activations of the Vogel-Fulcher (VF) form are the rule. With respect to such effects of intrinsic disorder and cooperativity of motion, relaxation experiments arc crucial for the understanding of supercooled liquids. Although sensitive only to the reorientation of permanent dipoles, dielectric relaxation experiments, recorded either in the frequency domain as E*(O) or in the time domain as P(t), serve as a common approach to relaxation phenomena in glassy media. Various examples exist delineating the dielectric features of polar glass-forming liquids [ 2-5 1, which are paralleled by the system studied in this work. At this point it should be emphasized that the externally applied electric field in a conventional dielectric experiment is homogeneous, i.e. macroscopic, and invariant to the progress of polarization responses. Correspondence to: R. Richert, Fachbereich Physikalische Chemie, Philipps-Universitit, Hans-Meerwein Strasse, W-3550 Marburg, Germany.
Recalling that the electronic energy levels of chromophores in matrices are perturbed by the polarization energy of the surrounding medium, spectroscopic features are also sensitive to the dielectric properties of the matrix. This relation between Stokes- or solvent-shift and solvent properties is the basis for empirical polarity scales [ 61, In polar solvents the gas to matrix shift is governed by polarizability effects and by the polarization of permanent dipoles whose response time relates closely to the dielectric relaxation time. The feedback of these dipolar solvation dynamics to the energy levels of a chromophore following its electronic excitation and its subsequent change in dipole moment can be observed as a time-resolved red-shift of emission energies [ 7,8]. In the linear response regime, the relaxation on a solvation coordinate is obtained by normalizing the energy shift y(t), which is the observed quantity in the spectroscopic experiment, a@ cording to the “Stokes-shift correlation function”:
C(t)=[v(f)-v(~)ll[~(O)-~(cx,)l.
(1)
In contrast to the situation of the conventional dielectric experiment, solvent dipoles in the vicinity of an excited chromophore are subject to a dipole field (or excitation-induced change thereof) arising from a constant charge distribution. This constant charge case alters the polarization time scale from the dielectric time r, in a usual constant field case to the
0009-2614/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
355
Volume 199, number 3,4
CHEMICALPHYSICS LETTERS
longitudinal time zL= ( E,/E, ) SDfor Debye systems [ 9,101. The discrepancy in time scales arises from screening whose effect increases with cI and cannot be ascribed to different molecular motions. From a theoretical point of view, the non-homogeneous field of the solute dipole is the more severe problem and is no longer accounted for appropriately in terms of continuum models. An approach to the microscopic aspect of the polar solvent in terms of individual solvent shells is given by the dynamic mean spherical approximation (MSA), which translates the dielectric function e*(w) into the expected Stokes-shift correlation function C(t) analytically [ 111. The scope of the present paper is to investigate the applicability of solvation dynamics spectroscopy for revealing the dielectric parameters of the bulk material. It will be shown that the MSA theory for dipolar solvation is capable of relating the dynamics of solvation to the dielectric properties for supercaoled liquids. As a conclusion, the solvation dynamic experiment allows microscopic probing of dielectric relaxation in systems of high viscosity, which is expected to complement the results of the macroscopic technique. For the model glass-former investigated here, the two techniques can be related through the dynamic MSA approach. The experimental access to the solvation dynamics in supercooled liquids in the millisecond to second time range using phosphorescent molecular probes has been demonstrated in previous papers [ 12-141. For aprotic molecular glasses it has been shown that (i) the solvation of a dipole reflects bulk properties, (ii) solvation dynamics are related to the primary glass-transition process of the solvent, and (iii) continuum models are inappropriate for rationalizing spectroscopic data. A stringent comparison between the macroscopic dielectric response c*(o) and the solvation response C(t) has so far been hampered by the lack of dielectric data and the need for a temperature coincidence within G 0.1 K for the two experimental techniques. The latter notion derives from the strong and non-Arrhenius like temperature dependences typical for the range TG< T(T,+20 K.
6 November 1992
2. Experiment The model system presently under study is 2methyl tetrahydrofurane (2-MTHF) , considered to represent the class of aprotic and polar glass-farmers involving small and rigid molecules. 2-MTHF was doped with the chromophore quinoxaline (QX) at a concentration of x 2 x lop4 mol/mol. QX has been distilled and 2-MTHF was distilled and further purified over A1203. After purging with dry argon, the solution was transferred into the sample holder and then sealed, both under Ar atmosphere. In order to establish an unambiguous relation between e*(w ) and C(l) data, both the dielectric and the spectroscopic experiments have been carried out simultaneously using a common sample. The vacuum-sealed construction especially designed for this technique is depicted in fig. 1, The plate capacitor is practically free of edge effects with its geometric capacity C,= 10 pF varying less than 1 fF per K temperature change and less than 50 fF per atm pressure difference. A massive brass block minimizes thermal gradients between capacitor and sample volume used for the spectroscopy. A temperature stability of f30 mK long before and throughout the measurement is achieved with a Lake Shore 330 temperature controller with absolute readings within x0.5 K after calibrating with ice-water and the l-N2 temperature corrected for the actual ambient pressure. Dielectric measurements in the range 20 Hz
Fig. I Schematic view of the sample holder desiped for the combined dielectric and spectroscopic experiment.
356
6 November 1992
CHEMICALPHYSICS LETTERS
Volume 199, number 3,4
curves was conducted as previously described [ 141.
extrapolates to zero at infinite temperatures as re quired. The characteristic relaxation times tcD follow the VF-type temperature dependence
3. Results ln(z&s)= Dielectric relaxation results. Fig. 2 displays the di-
electiic relaxation data E’and 6”for the QX/ZMTHF sample. The analogous experiment prior to doping with QX yielded identical results, thereby assuring that QX at the present concentration does nbt affect the bulk dielectric signal. The obvious decrease in susceptibility at 106 K is due to partial crystallization, which affects es, but without a significant impact on the relaxation time data. The data set is well described by the Cole-Davidson (CD) function E*(W)=t,+
1151 (~,-&.¶)(2~,+~,) t,(E,+2)2
-
0
+B,
(4)
with A=792.5 K, B=- 36.6 and T,=71.7 K. The result 8~0.49 indicates marked deviations from exponentiality regarding P(t). The CD type E*(W) possesses no simple analogous function in the time domain. However, apart from the short-time/highfrequency behaviour not resolved here, the KWW pattern can serve as an estimate for the polarization decay corresponding to a CD-type E*(W) [ 161. The time domain function thus reads
JYt)=exp[-WkwwYY,
(l~i?&s=‘.-ic”,
as represented by the solid lines in fig. 2. Within the range92-102Ktbeparametersj?=0.49andt,=3.05 are virtually independent of temperature while the static dielectric constant obeys Onsager’s equation
P2 z&F=
&
’
(3)
where V= 150 A3and p= 1.38 D quantify the volume and dipole moment of 2-MTHF. The applicability of eq. (3) is approved by the notion that the expression (t,-~m)(2s+Cm)/s(~m+2)2 in eq. (3)
where the KWW parameters (?xw, a) matching the CD values (Tag, /3) can be obtained on a leastsquafe basis [ 171. The validity of this approximation has been checked via KWW analysis of the numerical transformations of the t*(a) fits. For the polarization response P(t) an exponent a=0.62 is obtained. The mean decay time (r) Kwwof P(t) is then given by (r>x~+zK~a-‘r(a-‘). The experimental results for ( r>xWWas a function of temperature are shown in fig. 3. Sohtion dynamic results. Average T, -+So (O-O) emission energies v(t) have been measured in the range 88-98 K fir times 20 ms < t< 0.8 s. At 88 and 98 K the energies are time invariant, thereby reflect-
0.8
log,, (f/Hz)
Fig 2. Dielectric relaxation date (. .) and Cole-Davidson fit (-) (to f’) for QX/Z-MTHF. The temperatures are 92 to 106 K in 2 K steps in the order of increasingf-. See text for the fit parameters and details.
(5)
09
1.0
Fig. 3. Temperature dependence of the mean dielectric and solvation relaxation time ( r)and VF fit to the dielectric data in a In(s) versus To/T representation. Defining To via (~)~(T~)=100syicldsT~=90.7Kfor2-~F.Theslope at To defines a fragility index of Me79.5. (0) Dielectric data; (r)solvationdata;(-)VFfit;(---)slopcatT,
357
Volume 199,number 3,4
CHEMICALPHYSICS LElTERS
1 .Y
90
-_ h
-TT_ ,..
zu
.T-_ 92
‘....,
-. -_
--1
5’
g( .(
.’ .ii -2
-__9J
OO
0.1 time Is
.., 5-‘.
,.
0.8
Fig. 4. Experimental (-) and predicted (. . ) (MSA) Stokesshin correlation function C(t). The data is recorded simultaneously with that of fig. 2 at the temperatures indicated as T (K) for QX/s-MTHF. Bars indicate the experimental time windows of 20 ms length.
ing the Franck-Condon solvent state energy Y(0) = 21285 cm-’ and the completely solvated state energy v(m)=21043 cm-‘, which are used to obtain C(Z) according to eq. ( 1). Fig. 4 portrays the time-resolved solvation process at intermediate temperatures, indicative of highly non-exponential response patterns. For other details of the phosphorescence analysis regarding QX/2-MTHF, the reader is referred to refs. [ 1l-l 31. Anticipating that the dispersion of the KWW-type C( t ) patterns in terms of (Yis not expected to alter significantly within 10 K, the solvation dynamic data is best reproduced by cr=O.49 for 909 T<98 K. The resulting values for the solvation times in terms of ( r) kwwas a function of Tare included in fig. 3.
4. Discussion The C(t) prediction based on the MSA formalism for dipolar solvation refers only to the t*(w) data as input parameter and assumes equal van der Waals radii for the solvent and solute molecules, which is approximately fulfiied by the QX/Z-MTHF system. On comparing the theoretical C(t) cuNes derived from the E*(W)data with the simultaneously acquired C(t) data, one observes that the predicted C(t) relaxes faster by a common factor of 3, irrespective of temperature. Inserting 3r, instead of 7, into the MSA calculation results in the theoretical C(t) decays in fig. 4 (dotted lines). In excellent agreement with the KWW exponent cr=O.49 found [ 111
358
6 November 1992
to tit the experimental C( t ) data, a KWW analysis of the calculated C(t) cuNes again yields (~~0.49. Therefore, the observed incease in dispersion of event times for the C(t) relaxation (~~~0.49) relative to a!=O.62 for P(t) is a direct consequence of differently acting solvent shells and justifies the need for a microscopic model. From fig. 4 it is obvious that the solvation relaxation pattern is reproduced by the MSA theory, albeit with the absolute time scale of the solvation being slower than expected on the basis of E*(W)data. According to r( T) as shown in fig. 3, the factor of 3 on the time scale relates to a temperature variation of 0.55 K, thereby significantly exceeding the expected temperature mismatch of the two simultaneous experiments. Therefore, experimental uncertainty cannot account for the observed discrepancy in time scales. Other solvation models also covered by the MSA formalism like the ionic solvation and the continuum approach result in even faster C(t) decays. A straightforwardexplanation for the discrepancy cannot by given at present. A previous [ 141 comparison of the temperature dependence of solvation with that of other relaxation phenomena (by extrapolating relaxation times in the vicinity of the glass transition) indicated an excess activation energy of in;50% for the solvation process, thereby violating any theoretical picture relating C(t) to e(w). In contrast, an unambiguous coincidence of experimental conditions as presently achieved reveals identical activation parameters for the two processes as seen in fig. 3. For liquids of low viscosity solvation dynamic data resulting from fluorescent probes in the picosecond and nanosecond time range are notorious for severe controversies relative to the MSAtheory [ 181, probably due to translational and inertia effects not accounted for within the MSA model. Apart from the well-understood coincidence of dielectric and dipole solvation phenomena, combining the data has extended the experimentally accessed time/temperature range for dipolar relaxation in 2MTHF to below TG.Therefore, an unambiguous identification of T,=90.7 K via (T&Z (7) ( Tc) = 100 s and of the departure from an Arrhenius-like behaviour in terms of the fragility index M= 79.5 is possible. The gauge for non-exponentiality regarding the P(t) relaxation patterns is the KWW value (~~0.62 for 2-MTHF. In agreement with 2-MTHF
Volume 199,number 3,4
CHEMICAL PHYSICSLETTERS
being a molecular glass-former without intramolecular motional freedom, the present material displays very low TG and TG- To values compared to other molecular glasses.However, the expected correlation between Q!and M noted for a large class of glass-formers [ 19-211 is well reproduced for 2-MTHF. In summary, a theoretically founded relation between bulk dielectric relaxation in a macroscopic field and local dielectric relaxation in a dipole field has been verified experimentally. The simultaneous experiments undoubtedly reveal identical temperature dependences of c’(w) and C(t) data and the applicability of the MSA formalism to such systems. The results validate the spectroscopic technique for molecularly probing dielectric relaxation in supercooled liquids. Possible applications are spatially selective experiments near interfaces, dielectric relaxation studies in confined geometries and in inhomogeneously mixed systems.
Acknowledgement Financial support by the Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie is gratefully acknowledged. References [ I] J. Wong and C.A. Angell, Glass structure by spectroscopy (Marcel Dekker, New York, 1976).
6 November 1992
[2] J.G. Berberian and R.H. Cole, J. Chem. Phys. 84 (1987) 6921. [3]G.P. JohariandC.P.Smyth,J.Chem.Phys.56(1972)4411. [4] G.P. Johari and M. Goldstein, J. Chem. Phys. 53 (1970) 2372. [S] G. Williams, J. Non+%. Solids 131-133 (1991) 1. [6] M.J. Kamlet, J.L.M. Abboud and R.W. Taft, Progr. Phys. Org. Chem. 13 (1981) 485. [ 71 W.R. Ware, P. Chow and S.K. Lee, Chem. Phys. Letters 2 (1968) 356. [ 81 M. Mamncelliand G.R. Flemin8,J. Chem. Phys. 86 1987) 6221. [9] I-LFtihlich, Theory of dielectrics (Oxford Univ Oxford, 1958). [ lo] D. Kivelson and H. Friedman, J. Phys. Chem. 93 ( 1989) 7026. [ 111I. Rips, J. Klafter and J. Jortner, J. Chem. Phys. 88 1988) 3246;89 (1988) 4288. [ 121R. Richert, Chem. Phys. Letters 171 (1990) 222. [ 13] A. Wagenerand R. Richert, Chem. Phys. Letters 176 ( 1991) 329. [ 141R. Richert and A. Wagener, J. Phys. Chem. 95 (1991) 10115. [ 151C.J.F. Biittcher, Theory of electric polarization, Vol. 1 (Elsevier, Amsterdam, 1973) p. 178. [ 161G. Williams, D.C. Watts, S.B. Dev and A.M. North, Trans. Faraday Sot. 67 (1971) 1323. [ 171C.P. Lindsey and G.D. Patterson, J. Chem. Phys. 73 (1980) 3348. [ 181M. Marconcelli,J. MacInnis and G.R. Fleming, Science 243 (1989) 1674. [ 191J.T. Bendler and M.F. Shlesinger, Macmmolecules 18 (1985) 591. [20] CA. Aqell, J. Non-Cryst. Solids 131-133 (1991) 13. [ 2 1 ] KL. Ngai, R.W. Rendell and D.J. Plazek, J. Chem. Phys. 94 (1991) 3018.
359
CHEMICAL PHYSICS LETTERS
6 November 1992
Molecular probing of dielectric relaxation in the glass-transition region Ranko Richert Fachbereich PhysikalischeChemie, Philipps-Universitiit, Hans-MeerweinStrasse, W-3SSOMarburg, Germany Received 10 August 1992;in final form 1 September 1992
Conventional dielectric s*(w) data and solvation dynamic C( 1) data are recorded simultaneously,assuring perfectcoincidence of experimental conditions for the two relaxation phenomena in the glass-former 2-MTHF doped with quinoxaline. The dynamic MSA theory for dipolar solvation turns out to relate the observed Stokes-shift dynamics to the dielectric data in a quantitative fashion. The agreement between theory and experiment facilitates access to “microscopic” dielectric relaxation via spectroscopy of appropriatemolecular probes in supercooled liquids.
1.
Introduction
Glass-forming liquids in the transition regime to solid-like viscosities, i.e. near their glass transition temperatures To, display complex time and temperature dependences which are no longer reminiscent of simple activated rate processes [ 11. Instead, Kohlrausch-Williams-Watts (KWW) type relaxation patterns and non-Arrhenius activations of the Vogel-Fulcher (VF) form are the rule. With respect to such effects of intrinsic disorder and cooperativity of motion, relaxation experiments arc crucial for the understanding of supercooled liquids. Although sensitive only to the reorientation of permanent dipoles, dielectric relaxation experiments, recorded either in the frequency domain as E*(O) or in the time domain as P(t), serve as a common approach to relaxation phenomena in glassy media. Various examples exist delineating the dielectric features of polar glass-forming liquids [ 2-5 1, which are paralleled by the system studied in this work. At this point it should be emphasized that the externally applied electric field in a conventional dielectric experiment is homogeneous, i.e. macroscopic, and invariant to the progress of polarization responses. Correspondence to: R. Richert, Fachbereich Physikalische Chemie, Philipps-Universitit, Hans-Meerwein Strasse, W-3550 Marburg, Germany.
Recalling that the electronic energy levels of chromophores in matrices are perturbed by the polarization energy of the surrounding medium, spectroscopic features are also sensitive to the dielectric properties of the matrix. This relation between Stokes- or solvent-shift and solvent properties is the basis for empirical polarity scales [ 61, In polar solvents the gas to matrix shift is governed by polarizability effects and by the polarization of permanent dipoles whose response time relates closely to the dielectric relaxation time. The feedback of these dipolar solvation dynamics to the energy levels of a chromophore following its electronic excitation and its subsequent change in dipole moment can be observed as a time-resolved red-shift of emission energies [ 7,8]. In the linear response regime, the relaxation on a solvation coordinate is obtained by normalizing the energy shift y(t), which is the observed quantity in the spectroscopic experiment, a@ cording to the “Stokes-shift correlation function”:
C(t)=[v(f)-v(~)ll[~(O)-~(cx,)l.
(1)
In contrast to the situation of the conventional dielectric experiment, solvent dipoles in the vicinity of an excited chromophore are subject to a dipole field (or excitation-induced change thereof) arising from a constant charge distribution. This constant charge case alters the polarization time scale from the dielectric time r, in a usual constant field case to the
0009-2614/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
355
Volume 199, number 3,4
CHEMICALPHYSICS LETTERS
longitudinal time zL= ( E,/E, ) SDfor Debye systems [ 9,101. The discrepancy in time scales arises from screening whose effect increases with cI and cannot be ascribed to different molecular motions. From a theoretical point of view, the non-homogeneous field of the solute dipole is the more severe problem and is no longer accounted for appropriately in terms of continuum models. An approach to the microscopic aspect of the polar solvent in terms of individual solvent shells is given by the dynamic mean spherical approximation (MSA), which translates the dielectric function e*(w) into the expected Stokes-shift correlation function C(t) analytically [ 111. The scope of the present paper is to investigate the applicability of solvation dynamics spectroscopy for revealing the dielectric parameters of the bulk material. It will be shown that the MSA theory for dipolar solvation is capable of relating the dynamics of solvation to the dielectric properties for supercaoled liquids. As a conclusion, the solvation dynamic experiment allows microscopic probing of dielectric relaxation in systems of high viscosity, which is expected to complement the results of the macroscopic technique. For the model glass-former investigated here, the two techniques can be related through the dynamic MSA approach. The experimental access to the solvation dynamics in supercooled liquids in the millisecond to second time range using phosphorescent molecular probes has been demonstrated in previous papers [ 12-141. For aprotic molecular glasses it has been shown that (i) the solvation of a dipole reflects bulk properties, (ii) solvation dynamics are related to the primary glass-transition process of the solvent, and (iii) continuum models are inappropriate for rationalizing spectroscopic data. A stringent comparison between the macroscopic dielectric response c*(o) and the solvation response C(t) has so far been hampered by the lack of dielectric data and the need for a temperature coincidence within G 0.1 K for the two experimental techniques. The latter notion derives from the strong and non-Arrhenius like temperature dependences typical for the range TG< T(T,+20 K.
6 November 1992
2. Experiment The model system presently under study is 2methyl tetrahydrofurane (2-MTHF) , considered to represent the class of aprotic and polar glass-farmers involving small and rigid molecules. 2-MTHF was doped with the chromophore quinoxaline (QX) at a concentration of x 2 x lop4 mol/mol. QX has been distilled and 2-MTHF was distilled and further purified over A1203. After purging with dry argon, the solution was transferred into the sample holder and then sealed, both under Ar atmosphere. In order to establish an unambiguous relation between e*(w ) and C(l) data, both the dielectric and the spectroscopic experiments have been carried out simultaneously using a common sample. The vacuum-sealed construction especially designed for this technique is depicted in fig. 1, The plate capacitor is practically free of edge effects with its geometric capacity C,= 10 pF varying less than 1 fF per K temperature change and less than 50 fF per atm pressure difference. A massive brass block minimizes thermal gradients between capacitor and sample volume used for the spectroscopy. A temperature stability of f30 mK long before and throughout the measurement is achieved with a Lake Shore 330 temperature controller with absolute readings within x0.5 K after calibrating with ice-water and the l-N2 temperature corrected for the actual ambient pressure. Dielectric measurements in the range 20 Hz
Fig. I Schematic view of the sample holder desiped for the combined dielectric and spectroscopic experiment.
356
6 November 1992
CHEMICALPHYSICS LETTERS
Volume 199, number 3,4
curves was conducted as previously described [ 141.
extrapolates to zero at infinite temperatures as re quired. The characteristic relaxation times tcD follow the VF-type temperature dependence
3. Results ln(z&s)= Dielectric relaxation results. Fig. 2 displays the di-
electiic relaxation data E’and 6”for the QX/ZMTHF sample. The analogous experiment prior to doping with QX yielded identical results, thereby assuring that QX at the present concentration does nbt affect the bulk dielectric signal. The obvious decrease in susceptibility at 106 K is due to partial crystallization, which affects es, but without a significant impact on the relaxation time data. The data set is well described by the Cole-Davidson (CD) function E*(W)=t,+
1151 (~,-&.¶)(2~,+~,) t,(E,+2)2
-
0
+B,
(4)
with A=792.5 K, B=- 36.6 and T,=71.7 K. The result 8~0.49 indicates marked deviations from exponentiality regarding P(t). The CD type E*(W) possesses no simple analogous function in the time domain. However, apart from the short-time/highfrequency behaviour not resolved here, the KWW pattern can serve as an estimate for the polarization decay corresponding to a CD-type E*(W) [ 161. The time domain function thus reads
JYt)=exp[-WkwwYY,
(l~i?&s=‘.-ic”,
as represented by the solid lines in fig. 2. Within the range92-102Ktbeparametersj?=0.49andt,=3.05 are virtually independent of temperature while the static dielectric constant obeys Onsager’s equation
P2 z&F=
&
’
(3)
where V= 150 A3and p= 1.38 D quantify the volume and dipole moment of 2-MTHF. The applicability of eq. (3) is approved by the notion that the expression (t,-~m)(2s+Cm)/s(~m+2)2 in eq. (3)
where the KWW parameters (?xw, a) matching the CD values (Tag, /3) can be obtained on a leastsquafe basis [ 171. The validity of this approximation has been checked via KWW analysis of the numerical transformations of the t*(a) fits. For the polarization response P(t) an exponent a=0.62 is obtained. The mean decay time (r) Kwwof P(t) is then given by (r>x~+zK~a-‘r(a-‘). The experimental results for ( r>xWWas a function of temperature are shown in fig. 3. Sohtion dynamic results. Average T, -+So (O-O) emission energies v(t) have been measured in the range 88-98 K fir times 20 ms < t< 0.8 s. At 88 and 98 K the energies are time invariant, thereby reflect-
0.8
log,, (f/Hz)
Fig 2. Dielectric relaxation date (. .) and Cole-Davidson fit (-) (to f’) for QX/Z-MTHF. The temperatures are 92 to 106 K in 2 K steps in the order of increasingf-. See text for the fit parameters and details.
(5)
09
1.0
Fig. 3. Temperature dependence of the mean dielectric and solvation relaxation time ( r)and VF fit to the dielectric data in a In(s) versus To/T representation. Defining To via (~)~(T~)=100syicldsT~=90.7Kfor2-~F.Theslope at To defines a fragility index of Me79.5. (0) Dielectric data; (r)solvationdata;(-)VFfit;(---)slopcatT,
357
Volume 199,number 3,4
CHEMICALPHYSICS LElTERS
1 .Y
90
-_ h
-TT_ ,..
zu
.T-_ 92
‘....,
-. -_
--1
5’
g( .(
.’ .ii -2
-__9J
OO
0.1 time Is
.., 5-‘.
,.
0.8
Fig. 4. Experimental (-) and predicted (. . ) (MSA) Stokesshin correlation function C(t). The data is recorded simultaneously with that of fig. 2 at the temperatures indicated as T (K) for QX/s-MTHF. Bars indicate the experimental time windows of 20 ms length.
ing the Franck-Condon solvent state energy Y(0) = 21285 cm-’ and the completely solvated state energy v(m)=21043 cm-‘, which are used to obtain C(Z) according to eq. ( 1). Fig. 4 portrays the time-resolved solvation process at intermediate temperatures, indicative of highly non-exponential response patterns. For other details of the phosphorescence analysis regarding QX/2-MTHF, the reader is referred to refs. [ 1l-l 31. Anticipating that the dispersion of the KWW-type C( t ) patterns in terms of (Yis not expected to alter significantly within 10 K, the solvation dynamic data is best reproduced by cr=O.49 for 909 T<98 K. The resulting values for the solvation times in terms of ( r) kwwas a function of Tare included in fig. 3.
4. Discussion The C(t) prediction based on the MSA formalism for dipolar solvation refers only to the t*(w) data as input parameter and assumes equal van der Waals radii for the solvent and solute molecules, which is approximately fulfiied by the QX/Z-MTHF system. On comparing the theoretical C(t) cuNes derived from the E*(W)data with the simultaneously acquired C(t) data, one observes that the predicted C(t) relaxes faster by a common factor of 3, irrespective of temperature. Inserting 3r, instead of 7, into the MSA calculation results in the theoretical C(t) decays in fig. 4 (dotted lines). In excellent agreement with the KWW exponent cr=O.49 found [ 111
358
6 November 1992
to tit the experimental C( t ) data, a KWW analysis of the calculated C(t) cuNes again yields (~~0.49. Therefore, the observed incease in dispersion of event times for the C(t) relaxation (~~~0.49) relative to a!=O.62 for P(t) is a direct consequence of differently acting solvent shells and justifies the need for a microscopic model. From fig. 4 it is obvious that the solvation relaxation pattern is reproduced by the MSA theory, albeit with the absolute time scale of the solvation being slower than expected on the basis of E*(W)data. According to r( T) as shown in fig. 3, the factor of 3 on the time scale relates to a temperature variation of 0.55 K, thereby significantly exceeding the expected temperature mismatch of the two simultaneous experiments. Therefore, experimental uncertainty cannot account for the observed discrepancy in time scales. Other solvation models also covered by the MSA formalism like the ionic solvation and the continuum approach result in even faster C(t) decays. A straightforwardexplanation for the discrepancy cannot by given at present. A previous [ 141 comparison of the temperature dependence of solvation with that of other relaxation phenomena (by extrapolating relaxation times in the vicinity of the glass transition) indicated an excess activation energy of in;50% for the solvation process, thereby violating any theoretical picture relating C(t) to e(w). In contrast, an unambiguous coincidence of experimental conditions as presently achieved reveals identical activation parameters for the two processes as seen in fig. 3. For liquids of low viscosity solvation dynamic data resulting from fluorescent probes in the picosecond and nanosecond time range are notorious for severe controversies relative to the MSAtheory [ 181, probably due to translational and inertia effects not accounted for within the MSA model. Apart from the well-understood coincidence of dielectric and dipole solvation phenomena, combining the data has extended the experimentally accessed time/temperature range for dipolar relaxation in 2MTHF to below TG.Therefore, an unambiguous identification of T,=90.7 K via (T&Z (7) ( Tc) = 100 s and of the departure from an Arrhenius-like behaviour in terms of the fragility index M= 79.5 is possible. The gauge for non-exponentiality regarding the P(t) relaxation patterns is the KWW value (~~0.62 for 2-MTHF. In agreement with 2-MTHF
Volume 199,number 3,4
CHEMICAL PHYSICSLETTERS
being a molecular glass-former without intramolecular motional freedom, the present material displays very low TG and TG- To values compared to other molecular glasses.However, the expected correlation between Q!and M noted for a large class of glass-formers [ 19-211 is well reproduced for 2-MTHF. In summary, a theoretically founded relation between bulk dielectric relaxation in a macroscopic field and local dielectric relaxation in a dipole field has been verified experimentally. The simultaneous experiments undoubtedly reveal identical temperature dependences of c’(w) and C(t) data and the applicability of the MSA formalism to such systems. The results validate the spectroscopic technique for molecularly probing dielectric relaxation in supercooled liquids. Possible applications are spatially selective experiments near interfaces, dielectric relaxation studies in confined geometries and in inhomogeneously mixed systems.
Acknowledgement Financial support by the Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie is gratefully acknowledged. References [ I] J. Wong and C.A. Angell, Glass structure by spectroscopy (Marcel Dekker, New York, 1976).
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