J. Phys. Chem. 1993,97, 10489-10497
10489
Photobleaching Technique for Measuring Ultraslow Reorientation near and below the Glass Transition: Tetracene in eTerphenyl Marcus T. Cicerone and M. D. Ediger' Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 Received: June 2,I993@
A photobleaching technique for measuring probe rotational diffusion in supercooled and glassy materials is presented. Rotational correlation times from 10-* to 10+4.5s have been obtained for tetracene in o-terphenyl (OTP). Relative to the conventional Tg for OTP (-30 "C),this corresponds to a temperature range of Tg 15 OC to Tg- 5 OC. These results, combined with nanosecond measurements of anthracene rotation in OTP, are compared to OTP viscosity data. We find that, in contrast to translational diffusion measurements of probes in OTP, rotational diffusion follows the temperature dependence of a/Tover the 14 decades of time and viscosity explored. We also explore several possible experimental artifacts associated with the photobleaching technique. We find no evidence that any artifacts influence the results under typical operating conditions.
+
1. Introduction
Though the glass transition has been studied for many years, its underlying nature is still disputed.' There is broad agreement in the field that cooperative dynamics must play an important role in the glass Although no direct experimental evidence supports this view, many indirect lines of evidence point in this direction. For example, the apparent activation energy for viscous flow for a typical glass former near Tgis in the range of 5WkJ/mol. As this figure is comparableto theenergyrequired to break chemical bonds, it seems unlikely that it represents the barrier for a single molecule to change its position or orientation in a field of fixed neighbors. Our understanding of the glass transition is limited by a lack of information about the motion of individual molecules near and below T,. This information has been largely inaccessible due to the very long time scales involved. Single-particle rotational correlation times have been obtained in viscous liquids by transient optical techniques6 and NMR.9J0 However, neither of these techniques can be used to monitor very slow rotational motions in glassy materials. Transient optical experiments (i.e., fluorescence depolarization or triplet anisotropy methods) cannot be performed on time scales long compared to population relaxation times (for the cases above, the singlet or triplet lifetime). Very slow rotation cannot be measured by NMR either because T I is too short or - because the averaging time required is too long. Dielectric methods sometimesallow measurementsof phenomena as slow as lo4 s if conducting impurities can be eliminated from the sample. Nevertheless, because collective rather than singleparticle relaxation is observed,'l the connection to molecular motion is not always straightforward. In this paper we report on a new method for measuring reorientation of molecular probes in glass forming materials near and below T,. The method involves photobleaching a small fraction of the probes and is conceptually similar to transient optical methods of measuring rotation except that the photobleached state is permanent. Thus there is no fundamental limit on the longest rotation time which can be measured. In practice, we have measured rotation times exceeding 10s s, although only results from 10-2to 104.5s are presented here. With the photobleaching technique, the time dependence of the P2 orientation autocorrelation function for an ensemble of probes is measured directly. Only very small probe concentrations (on the order of 10 ppm) are required. Thus, macroscopic properties such as T, and the viscosity are not affected by the presence of
* Abstract published in Advance ACS Abstracts. September 1, 1993.
the probe. Smith et al.Iz were the first to use photobleaching to measure rotational diffusion. They incorporated fluorescent lipid probe moleculesinto biological membranes and reported rotation times in range 0.6-800 s. Velez and Axelrod have described the use of the photobleaching method to measure the rotation of latex particles and proteins in s01ution.I~ The photobleaching technique described in this paper has not previously been applied to the study of molecular reorientation in viscous liquids. We perform measurements of probe reorientation in order to learn about the dynamics of the host material. Studies involving probe molecules have advantages and disadvantages compared to studies of neat materials. The principal disadvantage is that the dynamics of the matrix material are only indirectly observed through the motion of the probe. If specific interactions exist between the probe and the matrix, this will certainly complicate efforts to learn about the matrix dynamics. We have chosen the system studied in this paper to minimize the possibility of specific interactions. Both the probe (tetracene) and the matrix (0terphenyl, OTP) are nonpolar aromatic molecules. Indeed, evidence is presented here indicating that tetracene and OTP reorient at almost identical rates over a very wide range of time scales. The principal advantage of probe studies is that a variety of probes can be used to study a given matrix. If probes of different sizes are chosen, then the matrix dynamics may be examined over a range of length scales. A future publication will present rotation results for a number of probes in OTP.14 We wish to accomplish two goals with this paper. First, we describe the photobleaching technique which we have adapted to measure rotational diffusion of probe molecules in supercooled and glassy systems. In particular, we explore several potential experimentalartifacts which might influence measurements made with this technique. Second,we present new results for the rotation of tetracene inOTP. Rotation times spanning the range 10-zlO4.5 s are presented. The corresponding temperature range is from 15 OC above to 5 O C below the conventional T, for OTP (-30 "C). We have published results of preliminary measurements made on this system.15 In section I1we outline the experimentalprocedures and discuss the details of the photobleaching technique. In section I11 we discuss possible artifacts of the photobleaching method. Experimental results for the tetracene/OTP system are discussed in section IV. A test of the DebyeStokes-Einstein relation using rotational diffusion measurements made over 14 decades in time is presented.
0022-3654/93/2097-10489$04.00/0 0 1993 American Chemical Society
Cicerone and Ediger
10490 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 11. Experimental Section
BS1
Sample Preparation. o-Terphenyl (OTP, obtained from Eastman) was distilled three times and then passed through a 0.2-pm filter. Tetracene (Aldrich) was used as received. Tetracene was added to the purified OTP, typically to produce a concentration of 10 ppm (determined by visible absorption). Sample equilibration near TBdepended sensitively on the cell used to hold the sample. Cell design is discussed in section 111. The onset of TB for the distilled and filtered OTP sample with and without probe wasdetermined by DSC (10 OC/min.) to be-30 OC, in agreement with values found in the literature.16 Samples which were left at room temperature remained in the supercooled state for several months (Tm= 57 "C). TemperatureControl. A home-builtcryogenicdewar was used to contain thesample during measurements. Thedewar consisted of a cold-bathchamber which was thermally contacted to a copper cold finger and sample holder. The cold finger and sample holder were in a vacuum chamber for insulation purposes. The cold bathconsistedofethanol kept at-50 OCwitha NeslabInstruments Model CC-6511 cooler. Sample temperature was kept constant towithinf0.05 "C by heatingagainst thecold bath witharesistive heater controlled by a Lake Shore Model 330 temperature controller. A calibrated platinum RTD was used to measure the temperature of the copper sample holder. This RTD was calibrated to within f0.06 OC against standards supplied by Lake Shore and traceable to a NIST standard. The temperature of the sample was measured directly in several experiments by placing a second RTD in the sample cell. We have corrected for a temperature dependent thermal gradient (0.5 OC at Tg)between the position of the RTD in the copper sample holder and the sample. For all data presented here the temperature is known to within 0.2 OC absolute accuracy. The primary contribution to uncertainty in the temperature is the presence of a thermal gradient across the sample itself. This thermal gradient was due to radiative heating and has subsequentlybeen largely eliminated with better radiation shielding. Technique. The conceptual idea behind the photobleaching experimentis most easily understood in terms of the more familiar fluorescence depolarization technique. In that e~periment,'~J* a short pulse of linearly polarized light photoselects an oriented set of chromophores from an initially isotropic distribution. The probability of a given chromophore being excited depends upon the square of the cosine of the angle between the chromophore's transition dipole and the excitinglight's polarizationvector. Since chromophoresemit light polarized along their transition dipoles, the time-dependent fluorescencepolarization is a measure of the orientation remaining among the excited chromophoresat a given time. This experimentcannot be used to determine rotation times which are significantly longer than the fluorescencelifetime since very few fluorescence photons are emitted at such long times. The photobleachingexperiment circumventsthe limitations of fluorescence depolarization experiments by photoselecting to a state with an essentially infinite lifetime.19 This state is the photoproduct of a reaction which can occur only from the excited state. (The mechanism of this reaction is discussed below.) Each time a probe molecule is excited there is a small probability (typically 10-4)that a photobleachingreaction will occur. During the bleaching pulse probe molecules are cycled through the excited state 102-103 times, creating a substantially anisotropic distribution of unbleached ground-state probe molecules. The photobleaching reaction is orientationally anisotropic because the distribution of excited molecules is anisotropic. In time the anisotropicdistribution of ground-state probe molecules becomes isotropic again through rotational diffusion. We monitor the time-dependent anisotropyby comparingthe fluorescence induced by a weak reading beam (attenuated 106comparedto the bleach beam) polarized either parallel or perpendicular to the polarization of the bleach beam.
-
P S
BS3
1JZ
SAMPLE
Figure 1. Schematicof photobleaching apparatus: BS,beam splitter;P, polarizer; S, shutter; M, mirror; ND, neutral densityfilter; PD, photodiode; A/D,analog/digital converter;PEM, photoelastic modulator; PP, partial polarizer; h / 2 (X/4), half- (quarter-) wave retarder. The components encompassed by a dotted line are necessary only for measuring T. < 5 s (see text).
Figure 1 illustrates the experimental apparatus. The bleach beam follows the direct path from BSI to BS3, while the reading beam follows the indirect pathvia BS2. At the sample, the bleach and reading beams are collinear and have identical spot sizes (=l mm). A computer controls shutters which gate the beams on and off and also controls a shutter which protects the PMT from fluorescence during the intense bleaching pulse. A photodiode is used to correct for laser fluctuations. We use 0.5 W cm-2 of 476-nm light from a continuous-wave (cw) Ar+ laser to bleach tetracene, with the duration of the bleaching pulse ranging from 1 to 100 ms. The polarization of the various beams used in the experiment are chosen so that the absorption dipole autocorrelation function is measured (see eq 5).*0 The bleaching beam is polarized at 45O from vertical. The polarization of the reading beam is modulated between this polarization and the orthogonal one. Fluorescence from the reading beam is detected at 90° through a polarizer set at 54.7' from horizontal. This fluorescence signal is directly proportional to the number of ground-state molecules excited by the reading beam.zoJ Other correlationfunctions (e.g. absorption dipoleemission dipole cross correlation) can be measured by properly arranging the polarization and direction of the bleach and reading beams and the angle of observation.20 Modulation of the polarization of the reading beam is accomplished in one of two ways. In one scheme, we pass the reading beam through a half-wave plate which is mounted on a motorized rotational stage. The half-wave plate is rotated to give the desired polarizationof the reading beam, and fluorescence intensity induced by the reading beam is measured. With this scheme we can acquire anisotropy decay data at a rate of 0.5 Hz or slower. We can therefore measure rotational correlation times T~ 1 5 s using this method. In an alternate procedure we pass the reading beam through a quarter-wave plate and a photoelastic modulator (PEM). This combination modulates the polarization of the reading beam between horizontal and vertical at 50 kHz. The half-wave plate has a fixed orientation in this schemeand rotates the polarizations of the beam to f45O. Clearly the PEM offers an advantage in time resolution; anisotropy data can be obtained at 50 kHz, allowing measurements of 7, 2 0.5 ms. Using the PEM, the output signal from the PMT looks roughly like a damped square wave with a time-dependent dc component. For all the results reported in this paper ( T > ~ 10 ms), a lock-in analyzer was used to determine the amplitude of the square wave while a low-pass filter was used to determine the dc offset of the signal. This procedure produces anisotropydecay curveswith thecorrect time dependence and shape. Because the PMT signal is not sinusoidal but has a rather wide frequency spectrum, the amplitude of the anisotropy obtained from the lock-in has been corrected by
Ultraslow Reorientation at the Glass Transition
The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10491
comparison with the first modulation scheme. For anisotropy decays with T~ < 10 ms (not reported in this paper), the lock-in cannot be used to obtain the anisotropy since the "dc" part of the signal changes significantly during one cycle of the polarization modulation. A custom built demodulator has been constructed in order to interpret the signal correctly over all anisotropy decay times which are measurable using the PEM. The components in Figure 1 which are encompassed by a dotted line are necessary only if the PEM is used. The partial polarizer is used to compensate for the difference in reflected intensity of the s and p polarization from the beam splitter BS3. We used a partial polarizer composed of six stacked plates oriented at about 61 O to the beam. A micrometer and a 6-in. lever arm were necessary to make fine angle adjustments to the partial polarizer. Photobleaching Mechanism. For these experiments on the tetracene/OTP system,the precise mechanismof photobleaching is unimportant since only the rotation of unbleached molecules is observed. Some qualifications to the above statement may be necessary for other probe/matrix combinations. These qualifications are discussed in section 111. The exact photobleaching reaction for tetracene has not been established. Studies of similar aromatic molecules indicate that photoperoxidation is responsiblefor photobleaching.22-" We have observed that the photobleaching efficiency of tetracene is directly proportional to 02 concentration over the range of 0.2 to 2 atm. Given these results, it is reasonable to assume that for tetracene (and the other unsaturated hydrocarbon probes which we use), the photobleaching reaction is a photoperoxidation which takes place as follows:*2
+ + + lo2*S + hv
S*
M
3
~
+S 2
S*
.-
E
" '
0
"
" '
.'" 100
"
'
'
' ' .
'
' .' ...'
200
'
' ' '
1
Ec, O
1.1
.
.
.
.
I
.
.
.
.
1
I . . . . ,
,..
100
0
~1
300
, I . . . .
200
Time
[SI
8
.
.
,.I
3 00
Figure 2. Photobleaching measurements of the reorientationof tetracene in OTP at -26.5 O C . The reading beam polarization was modulated either by rotating the half wave plate (a) or by using the PEM (b). See text for discussion of these two methods of data acqdsition. In (a), the fluorescence intensity i n d u d by the reading beam is shown as a function oftime. The topcurvein (b) is theaverageintensityA(t),and thebottom curve is the intensity differenceD(t). Tetracene is pictured in (a) along with its S, SIabsorption dipole.
-
(1)
lo2*
MO,
Here S is a sensitizer molecule (tetracene in this case), M is the unsaturated substrate molecule (also tetracene), and an asterisk denotes an electronically excited state. We have performed successful preliminary experiments on rubrene, anthracene, anthracene derivatives, stilbenes, and other conjugated and aromatic molecules. Thus we expect that the photobleaching technique will be applicable to a wide range of chromophores. Data Analysis. Typical results from the photobleaching experiment are shown in Figure 2. The sample is tetracene in OTP at -26.5 OC (Tg 3.5'). Tetracene is depicted in Figure 2a, along with the orientation of the SO S1 transition dipole which is monitored with this experiment. Figure 2a also shows time dependent fluorescence intensities for reading beam polarization parallel (Ill) and perpendicular (ZJ to the bleach polarization (Le. at f45O to vertical). Note that only 10%of the probe molecules were bleached. Immediately after photobleaching (t = 0), the two fluorescence signals differ. Probe molecules with absorption dipoles parallel to the bleach polarization have been bleached preferentially. Therefore, 41is weaker than I*. In time, molecular reorientation randomizes the transition dipoles and identical signals are again obtained from both polarizations of the reading beam. The time dependent anisotropy of the ground-state molecules is extracted from these data by the following equation:
+
2.1L
-
-
Here AZ(t) is the difference between the fluorescenceintensities before bleaching and at time t after bleaching. If the detection scheme involving the PEM is used, then the signalsdetected will be a time dependent difference, D(t) = Z l ( t )
1 o-'
10''
1 OO
10'
10'
1 o3
10'
Time [SI Figure 3. Anisotropy decays for tetracene in OTP at the temperatures indicated. The solid lines are KWW fits to the data. The bleach depth was 10% for these experiments.
- I l ( t ) ,and a time-dependent average fluorescenceintensity,A ( t ) = O.S[Z,(t) + Zll(t)], as shown in Figure 2b. In this case the anisotropy is given by
D(t) (3) 3B - 0.5D(t) - 3A(t) Here B is the fluorescence intensity before the bleach. The denominators in eqs 2 and 3 are proportional to the fraction of probe molecules which have been bleached (bleach depth). The points in Figure 3 represent anisotropydecays for tetracene rotation in OTP at the temperatures indicated. The orientation autocorrelation function CF(t) can be obtained from the anisotropy by r(t) =
CF(t) = r(t)/r(O) (4) The autocorrelation function is related to molecular reorientation
10492 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993
Cicerone and Ediger
1-81 L
Here iirepresents the absorption transition dipole for the probe, P2 is the second Legendre polynomial, and the brackets represent an ensemble average. A model independent average correlation time T, can be defined as T, E
J
1.61 1.4
K C F ( t ) dt
The data can be approximately fit with the KohlrauschWilliams-Watts (KWW) function: C F ( ~ )= e+/T)' (7) The solid lines in Figure 3 are KWW fits to the data. Within this approximation, 'I,is given by the relationship where r is the gamma function. Expressions other than eq 7 also fit the data well. The KWW function is an extremely flexible two parameter function and is used for this reason.
O a 0.4
-
i 1 oo
1 0'
Irradiation During Bleach [J crn-*] Figure 4. Rotational correlation times for tetracene in OTP obtained as a function of the energy flux of the bleaching beam. The error bars are calculated from replicate determinations. These results indicate that local heating is unlikely to distort the observed rotational dynamics.
III. Exploration of Possible Experimental Artifacts Because the photobleaching technique has not previously been applied to the study of molecular rotation in glass-forming liquids, we have performed a number of experiments to test for possible experimental artifacts. These tests are reported in this section. They give us considerable confidence that no artifacts associated with the photobleaching measurement have significantly distorted the results presented in section IV. Local Heating. Because of the inefficiency of the photobleaching reaction, the average probe molecule will be cycled through the excited state many times during the bleaching pulse. Depending on the photophysics of the particular probe, a significant amount of the energy absorbed by the probe molecules could be radiationlessly dissipated into the matrix as vibrational energy. This could conceivably cause significant local heating of the matrix, resulting in artificially fast rotational diffusion. For tetracene, roughly half of the light energy absorbed by the molecule will be dissipated as heat in the matrix. We varied the energy of the bleach pulse over nearly 2 orders of magnitude without varying the depth of the bleach in order to determine whether local heating influences the observed reorientation. This could be done by adjusting the 02 concentration ( [ O , ] )in one sample since photobleaching efficiency scales linearly with [02] over a wide range of [02]. The results of this experiment are shown in Figure 4. No change in T , was observed even though we changed the number of times the average tetracene molecule was excited during the bleach pulse by a factor of 100. Since we typically bleach tetracene with
