J . Phys. Chem. 1991,95, 1786-1789
1786
R3 space group to look like the R3m space group, with respect to the elastic constants. The other elastic constant that is very close to 0 is ~ 1 4 .This suggests that the examined system could be closely approximated by hexagonal ~ y m m e t r y . ’ ~The , ~ elastic constant calculation within hexagonal symmetry was carried out and gave results (in brackets in Table 11) very similar to those for trigonal symmetry, verifying the close approximation of the symmetry here to hexagonal. I f hexagonal symmetry is assumed, the bulk modulus B,, given by
is 7.8 X IO9 N m-2 for the ethanol adduct of Dianin’s compound, and the anisotropy factor A, given by eq 4 is 0.83. A = 2 c 4 4 / ( c I I - c12)
(4)
The elastic constants for the ethanol adduct of Dianin’s compound are almost an order of magnitude larger than very soft hexagonal crystals such as 8-N2 and /3-C0.’s They are, nevertheless, much smaller (by about a factor of 5 ) than trigonal ferric (19) Holuj, P.; Drozdowski, M.; Czajkowski, M. Solid State Commun. 1985, 56, 1019.
( 2 0 ) Ngoepe, P. E.; Comins, J. D. Phys. Reu. Lett. 1988, 61, 978.
systems such as K3Na(Cr04)2,21than the trigonal layered compound Ca(OH)2,19or (by a factor of 10-50) than typical harder crystals such as A1203.22 The elastic constants measured in the present experiment are, in fact, very similar to those of (hexagonal) ice Ih,23the exception being c12,which is larger by a factor of 2 in hexagonal ice. In summary, the main result of the present work is that the complete elastic stiffness tensor of the ethanol adduct of Dianin’s compound has been determined. The crystals may be said to be very similar to ice close to the triple point. From the elastic point of view this material can reliably be approximated by hexagonal symmetry.
Acknowledgment. We thank Professor T. S. Cameron for help in determination of the crystal orientation, Professor K.-H. Brose for providing the Elcon program, Professor M. Jericho for assistance with the ultrasonic measurements, and B. Borecka for help with one figure. The Natural Sciences and Engineering Research Council of Canada supported this work through grants to H.K., M.A.W., and M.J.C. (21) MrBz, B.; Kiefte, H.; Clouter, M. J.; Tuszyfiski, J. A. Phys. Reu. B, in Dress. (22) Watchman, J. B.; Tefft, W. E.; Lam, Jr., D. G.; Stinchfield, R. P. J . Natl. Bur. Std. 1960, 64A, 213. (23) Gammon, P. H.; Kiefte, H.; Clouter, M. J. J . Phys. Chem. 1983,87, 4025.
Behavior of the Rotational Diffusion Tensor of Tetracene under Subslip Conditions M. J. Wirth* and S.-H. Chou Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716 (Received: July 12, 1990; In Final Form: September 7 , 1990)
The fluorescence anisotropy decays of tetracene in 1-butanol, I-octanol,and I-dodecanol were measured at several temperatures by using frequency domain spectroscopy. Subslip rotational diffusion is observed. The double-exponential anisotropy decays were analyzed to determine the components, D,, Dy, and Dz, of the rotational diffusion tensor. The relative values of these componentsvary with temperature, indicating nonhydrodynamicrotational diffusion. Subslip behavior is found to be associated with a value of Dy/D that is significantlylarger than that predicted from hydrodynamics. The subslip phenomenon is interpreted as being a consequence of solvent structure.
Introduction The dynamics of solutes in microscopic media, such as micelles and surface monolayers, is very important to analytical chemistry because dynamics control the performance of liquid chromatography.’ Long-chain, n-alkyl functional groups are used for the most common chromatographic stationary phases and more recently for surfactant modifiers*” and pseudo stationary phases of electrokinetic ~hromatography.~For probing the dynamics of these media, rotational diffusion studies are valuable because fluorescence depolarization measurements can be made with the high sensitivity required for microscopic phases. However, an understanding of the rotational diffusion of solutes in bulk liquids is required in order to understand rotational diffusion of solutes in microscopic media. This understanding has not yet been reached for long-chain alkyl functionalities. The primary difficulty in understanding rotational diffusion for these systems is the description of the coupling between the ( I ) Dynamics of Chromatography; Giddings, J. C., Ed.; Dekker: New York, 1965. (2) Armstrong, D. W.; Henry, S. J. Anal. Chem. 1980, 3, 657. (3) Landy, J. S.;Dorsey, J. G. J . Chromatogr. Sci. 1984, 22, 68. (4) Terabe, S.; Otsuka, K.; Ichikawa, K.; Tsuchiya, A,; Ando, T. Anal. Chem. 1984, 56, 1 I 1 .
0022-3654/91/2095-1786%02.50/0
solute and its environment when the solute molecules are smaller than the solvent molecules. In hydrodynamic rotational diffusion, where the solvent is modeled as a continuum, the reorientation time, T ~ is~linear , in viscosity, 9: Tor
= (?V/kT)f,tickC
(1)
Vis the hydrodynamic volume of the Brownian ellipsoid,f,,ick is a parameter related to the geometric shape of the and Cis the coupling constant between the solute and solvent. In the stick boundary condition, C = 1. In the slip boundary condition, which is applied to nonpolar molecules because their interactions are weak, C < 1. The values for C in the slip boundary condition have been calculated for spheroidss and ellipsoid^.^ Nonpolar solutes in long-chain n-alkanes and n-alcohols reorient faster than that predicted by the slip boundary condition, Le., C < Cdi This subslip behavior was observed by Canonica, Schmid, and &Id for p-terphenyl and p-quaterphenyl in mixtures of pa(5) Polar Molecules, Debye, P., Ed.; Chemical Catalog Company: 1929. (6) Perrin, F. J . Phys. Radium 1936, 7, 1. (7) Deleted in proof. (8) Hu, C.-M.; Zwanzig, R. J. Chem. Phys. 1974, 60, 4354. (9) Youngren, G. K.; Acrivous, A. J . Chem. Phys. 1975, 63, 3846.
0 1991 American Chemical Society
Rotational Diffusion Tensor of Tetracene
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
1787
raffin and dodecane.I0 For these same solutes, Ben-Amotz and Scott showed that C appears to have one value for a series of n-alkanes and a lower value for a series of n-alcohols." Temperature studies of trans-stilbene reorientation by Kim and Fleming showed that C is a property of a given n-alkane and C decreases with increasing chain length.I2 By choosing solutes of differing size, Drake and Ben-Amotz showed that subslip is associated with a small solute size compared to the ~olvent.'~In this same work, the quasi-hydrodynamic model of Dote, Kivelson, and S ~ h w a r t z ,which ' ~ describes C a s the ratio of the solute volume to the total rotational free volume, was found to describe the behavior better than do simple hydrodynamics. However, this model was found to predict the opposite dependence of subslip on the viscosity of the medium, i.e., n-alkanes vs n-alcohols, than was observed experimentally. More detailed information about of the rotational diffusion of solutes is needed to understand subslip behavior. In particular, the components of the diffusion tensor would be valuable to know because these would reveal whether the shape of the rotor is consistent with hydrodynamics predictions. The determination of these components requires that the solute have a double-exponential anisotropy decay. The previous studies of subslip behavior have been made for solutes having single-exponential anisotropy decays: hence, information about the diffusion tensor could not be obtained. In this work, a study of the rotational diffusion behavior of tetracene in 1-butanol, 1-octanol, and 1-dodecanol is undertaken. Tetracene has been shown to exhibit a doubleexponential anisotropy decay.I5 It is similar in shape to the previously studied p-terphenyl, and for interpretation of anisotropy measurements, it is symmetric. Tetracene is also rigid, avoiding any complications from internal rotational motions, and has a small Stokes shift, eliminating possible effects from excess energy added to the environment. Frequency domain experiments are performed to allow quantitation of double-exponential decays to reveal the components of the diffusion tensor D,, Dyrand D, for these three solvents at various temperatures.
TABLE I: Anisotropy Decay Parameters for Tetracene in 1-Butanol (BuOH). 1-Octanol (OcOH), and 1-Dodecanol (DoOH)
(10) Canonica, S.;Schmid, A. A.; Wild, U. P. Chem. Phys. Lett. 1985, 122, 529. (1 I ) Ben-Amotz, D.; Scott, T. W. J . Chem. Phys. 1987, 3799. (12) Kim, S.K.; Fleming, G. R.J. Phys. Chem. 1988, 92, 2168. (13) Ben-Amotz, D.; Drake, J. M. J . Chem. Phys. 1988, 89, 1019. (14) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J . Phys. Chem. 1981,85, 2169. (15) Wirth, M. J.; Chou, S.-H. I n Laser Techniques in Luminescence Spectroscopy: Vo-Dinh, T., Eastwood, D., Eds.; ATSM: Philadelphia, PA, 1990. (16) Chuang, T. J.; Eisenthal, K. D. J. Chem. Phys. 1972, 57, 5094.
Results and Discussion
BuOH (mp = -90 " C ) OcOH (mp = -16 "C)
DoOH (mp = 23 "C)
7 7 15 25 34 25 35 46
4.3 13.2 10.4 7.2 5.5 17.1 11.6 7.9
97 216 178 133 98 124 85 65
1.0 0.76 0.86 0.92 0.94 0.70 0.74 0.83
578 537 512 535 447 304 249
0.24 0.26 0.26 0.26 0.26 0.31 0.31 0.31
0.6 0.7 0.8 0.9 1.2 0.9 0.7 0.6
From the experimental determination of T2, 72, r(O), and F, the values of D,, Dy, and D, are calculated. For y-axis excitation, 0,and D, appear in a almost indistinguishably. A separate experiment employing UV excitation to an x-axis polarized band and emission at 476 nm makes a = (D - D , ) / A and is thus used to distinguish D, from D,. Experimental Section
The determination of anisotropy decays by frequency domain spectroscopy involves the measurement of the differential phase shifts and amplitude ratios for the parallel and perpendicular polarizations of the emission intensity for each modulation frequency."*18 The frequency domain spectrometer is a modification of the one used previously;19 the modifications allow measurements at higher frequencies. In this work, the mode beats of an argon ion laser include 82, 164,328, 574, and 738 MHz. The frequency domain electronics now employ a high-frequency lock-in amplifier to allow the use of mechanical chopping as a means of eliminating radio-frequency background. This is necessary for use of the mode beats at 574 and 738 MHz. .The phase response of the highfrequency lock-in amplifier was calibrated by using an optical delay line. The in-phase and out-of-phase outputs, which contain the phase and amplitude information, were measured by calibrated low-frequency lock-in amplifiers tuned to the chopping frequency. Nonlinearities in the photomultiplier response were made negligible Theory by using average currents 2 orders of magnitude below the maximum linear currents. Diagnostics verified that nonlinearities The relation between the parameters of the fluorescence anwere negligible. The calibration variances were smaller than the isotropy decay and the components of the diffusion tensor was noise in the experimental data and were combined to express the derived by Chuang and Eisenthal.I6 For tetracene, the short axis total variance used in regression of the data. is denoted y, the long axis, x, and the normal to the molecular Optically, the mode-locked argon ion laser was tuned to its plane, z. Excitation into the 0-0 band of the first excited singlet 476-nm line and 10 mW of power was focused to approximately state creates a transition dipole oriented along t h e y axis of tet50 pm into the sample cell. The beam was highly polarized by racene. This simplifies the anisotropy decay to a double expoa Glan laser prism, and its polarization was controlled electronnential: ically by the use of a wide-bore Pockels cell, resulting in a por(r) = 0.3(8 + a) exp[-(6D + 2A)tl + larization extinction of 1OOO. The emission was collected at a right 0.3(8 - a) exp[-(6D - 2A)tl (2) angle from the excitation, collimated, and passed through a fixed polaroid, followed by a monochromator tuned to 508 nm and was D is the average of the components of the diffusion tensor: D = finally focused onto the photocathode of a Hamamatsu 1635 (D, + Dy + D,)/3. A is a measure of the asymmetry of the photomultiplier. : + D: - DXDy - D,D, - D,Dz)1/2. Tetracene was obtained from Aldrich, and its purity was tested diffusion tensor: A = (0: + D For excitation along the y axis of the solute and emission along by high-performance liquid chromatography and was found to angle 6 with respect to the y axis, a = (D - Dy cos2 6 - D, sin2 need no further purification. 1-Butanol, 1-octanol, and l-dode@/A and 6 = cos2#Knowledge of the preexponential factors canol were obtained from Fisher, Aldrich, and Alfa, respectively, and time constants allows calculation of the components of the and used without further purification. Temperature was controlled diffusion tensor, D,, Dy, and D,. by flowing the solution through a heat exchanger and reservoir, To calculate the diffusion parameters, the experimental data which were kept in a temperature bath. The temperature of the are regressed to fit a double-exponential decay: sample was monitored with a calibrated thermocouple that sensed the temperature within several millimeters of the probed region with an accuracy of * O S O C . The raw frequency domain data for tetracene in the various solvents are shown graphically in Figure 1. Higher temperatures and lower viscosities generally show a smaller phase shift and lower (17) Klein, U. K. A.; Haar, H.-P. Chem. Phys. Lett. 1978, 58, 531. (18) Lakowicz, J. R.; Cherek, H.; Maliwal, B. P.; Gratton, E. Biochemistry
1985, 24, 376.
(19) Chou, S.-H.; Wirth, M. J. J. Phys. Chem. 1989, 93, 7694.
1788 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
Wirth and Chou TABLE 11: R o f P t i ~ Diffusion ~l Parameters for Tetracene"
T,
18.0
BuOH OcOH 14.0 s
0
DoOH
P)
z 10.0 L
c
OC
DnlT
7 7 15 25 34 25 35 46
0.0152 0.0250 0.0224 0.0192 0.0181 0.0495 0.21 0.0471 0.25 0.0400 0.34
a 0.40 0.23 0.31 0.36 0.38
D, GHz D J D D J D D J D AID 0.53 0.62 0.79 1.0 0.86 1.3 1.6
1.9 2.0 2.2 2.4 2.1 2.1 2.2
0.81 0.57 0.32 0.12 0.73 0.64 0.40
0.32 0.43 0.51 0.51 0.18 0.26 0.43
1.4 1.5 1.8 2.1 1.7 1.7 1.8
"The sensitivity of the regression for D and its components is typically 0.01 for octanol and 0.02 for dodecanol for a 0.1 change in x2.
a
3 6.00
TABLE III: Tbeoretical Solute Dimensions ( y , x, z ) and Their Corresmndine Diffusion Coefficients for the Slip Boundarv Condition" y , x,
2.00
140.
280.
420.
560.
700.
Frequency IHHz)
21.47
D,lD
DylD
D,lD
DTIT
1.44 1.39 2.25 1.25 2.37
0.34 0.33 0.24 0.34 0.21
1.22 1.28 0.51 1.41 0.42
0.005 0.005 0.008 0.006 0.015
14.2, 3.0 14.2, 2.8 14.2, 3.0 13.2, 3.0 11.5, 3.0
D is in units of GHz.
r 1.61
7.3, 7.3, 5.7, 7.3, 4.9,
t i-
,,/
?lt
4J
a a
0
4J
21.33
P
4
1.19
1.05
140.
280. 420. 560. Frequency (MHz)
700.
Figure 1. Raw frequency domain data: (top) differential phase shifts and (bottom) amplitude ratios vs modulation frequency. The solvents and temperatures are (A) I-butanol at 7 OC,(BI-4) I-octanol at 7, 15, 25, and 34 OC,respectively, and (CI-3) I-dodecanol at 25, 35, and 46 OC,respectively. Typical 95% confidence intervals are indicated by the error bars for the dodecanol solution at 25 OC.
amplitude ratio, as expected. While it is difficult to draw conclusions from raw frequency domain data, one can discern from the dependence of the phase shifts upon frequency that the solvents behave differently from one another. Analysis of the frequency domain data yielded the decay parameters summarized in Table I. For a given solvent, r(0) is a constant; however, this parameter was found to be dependent upon solvent. The value of r(0) is less than 0.4 because the first vibronic band of the emission was used rather than the 0-0 band of the emission. As an independent confirmation of the lower symmetry of the vibronic band, the polarization dependence of the fluorescence spectrum of tetracene in a stretched polyethylene film shows that the polarization ratio for the first vibronic is lower than that for the 0-0 band.*O All data fit very well to a double-exponential decay except for the c a s of 1 -butanol, which fits best to a single-exponential decay: the maximum fractional contribution of a second exponential is 0.6%. Qualitatively, the viscosity and the time constants decrease (20) Dekkers, J. J.; Hoornweg, G. Ph.; Maclean, C.; Velthorst, N. H. Chem. Phys. 1974, 5, 393.
with temperature, as expected. The m a t obviously unusual feature of the decay data is that the fractional contributions of the exponentials change with temperature for a given solvent. The data do not fit to a set of decay parameters having fixed preexponentials. For a fixed value of r(O), the changes in the values of the preexponentials reveal a change in the relative values of D,, Dy, and D,. The diffusion coefficients were calculated from the decay parameters. A UV experiment for tetracene in dodecanol at room temperature revealed D, to be faster than D,, which is consistent with hydrodynamic predictions. The diffusion parameters calculated from the experimental data are summarized in Table 11. There are three salient features of the diffusion data. (1) The values of Dq/ T show strong subslip behavior: tetracene reorients nearly twice as fast in dodecanol as it does in octanol for the same value of q / T . For hydrodynamic rotational diffusion, Dq/T would be a constant. ( 2 ) The parameter Dq/T varies even for a given solvent, showing a decrease with temperature. (3) The relative values of the components of the diffusion tensor vary with temperature: Dx/D and D,/D increase and D y / D decreases with temperature. For hydrodynamic behavior, D,/D, Dy/D,and DJD would be constant. The diffusion components cannot be calculated from butanol because it has a single-exponential decay. The decay constant, 7,.for butanol is virtually the same as for octanol at 34 OC,and the values of t)/ T are within 20% of one another. This is consistent with nearly hydrodynamic behavior for octanol at 34 OC. If one uses eq 2, a decrease in r(0) would cause F to increase if Dx, D and D,were constant. The increase in F for butanol corresponl; well to the decrease in r(0) if the rotor shape were the same as for octanol as 34 OC,which further supports the conclusion of nearly hydrodynamic behavior for octanol at 34 OC. The values of D v / T decrease with temperature, showing that the subslip effect decreases with temperature for octanol and dodecanol. Further insight into how the rotation is changing can be obtained by comparing the slip hydrodynamic predictions with the experimental values. The hydrodynamic predictions for D,/D, D ID,and DJD are given in Table 111 for various approximations ofthe dimensions of the Brownian ellipsoid, using the method of Small and Isenberg.2' The first set of dimensions corresponds to the van der Waals dimensions of tetracene, and the following three sets indicate how sensitive the components are to slight changes in the dimensions. The last set is based upon exponential results for the tetracene dianion in liquid argon.22 In all cases, (21) Small, E. W.; Isenberg, I. Biopolymers 1977, 16, 1907. (22) Huppert, D.; Douglass, D. C.; Rentzepis, P. M. J . Chem. Phys. 1980, 72, 2841.
Rotational Diffusion Tensor of Tetracene
Figure 2. Time-averaged solvation structure upon lengthwise solvent/ solute alignment and rapid rotation about the solute x axis. The shape of the free volume would enhance D,/D because it increases the angle of free rotation about t h e y axis.
slip hydrodynamics predict D x / D to be the largest and D y / D to be the smallest. In the experimental data of Table 11, the subslip effect is associated with an anomalously large value of D J D . The data further show that normal slip hydrodynamics are approached for octanol and dodecanol as temperature is increased. Both the subslip effect and the anomalously large D y / D decrease with temperature. The changes in D J D , D y / D , and D , / D suggest that the shape of the free volume is a factor in the subslip behavior of tetracene. A plausible explanation for the larger increase in D y / D compared to D , / D and D J D can be made if the liquid is taken to be a partially disordered version of the crystal. A lengthwise alignment of the alkyl chains and the long axis of tetracene gives a roughly cylindrical solvation structure, as illustrated in Figure 2. The cylinder is used to represent qualitatively the ensemble average of orientations of tetracene about its x axis. It is shown in Figure 2 that this geometry allows a greater angular displacement about the solute y axis than its z axis. The structural order of the solvent thus places the free volume in a region favoring Dy, explaining why D y / D would be anomalously fast. Following this logic, as the temperature is raised and the liquid becomes increasingly disordered, Du/D returns to its hydrodynamic value and the subslip effect diminishes. The behavior of D J D , D y / D , and D J D is therefore consistent with the lengthwise alignment of the tetracene and the alkyl chains.
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991 1789 The existence of short-range structure in liquidn-alkanes has been demonstrated from light scattering measurement^^^ and thermodynamic measurements."" Both of these measurements show increasing structural order with increasing chain length. For 1-dodecanol, a phase change 6 "C above the melting point has been observed by using 13C N M R techniques,26 indicating structural order of the alkyl chains exists in the liquid phase. Solutes in n-hexadecane show evidence of solute/solvent alignment from excess enthalpies and heat capacitie~.~'A shape-selective contribution to the chemical potential for the set of dimethylnaphthalenes in n-dodecane provides further evidence of the lengthwise alignment of aromatic solutes and n-alkane solvent molecules.** Picosecond spectroscopic studies by Blanchard revealed a change in the rotor shape of cresyl violet from oblate to prolate as the temperature of the solvent dodecanol approached its freezing point.29 Interpreting subslip behavior as a consequence of structural order is consistent with these previous observations. To probe the viscosities of microscopic media containing n-alkyl functionalities, it is important to know whether subslip behavior is occurring. A calculation of the viscosity based upon slip hydrodynamics would be in error is subslip were occurring. The behavior of tetracene in these alcohols shows that a determination of the values of D J D , D J D , and D J D can be used to assess the presence of subslip. Such a study provides the additional information about structural ordering in these phases, which may ultimately be an even more important factor than viscosity in chromatographic applications. Acknowledgment. This work was supported by the National Science Foundation under Grant CHE-8814602. Registry No. Tetracene, 92-24-0; 1-butanol, 7 1-36-3; 1-octanol, 1 1 1-87-5; I-dodecanol, 112-53-8.
(23) Nagai, K. J . Chem. Phys. 1967,47,4690. (24) Delmas, G.; Turrell, S. J. Chem. Soc., Faraday Trans. I 1974, 70,
c7*
JIL.
(25) Lam, V. T.; Picker, P.; Patterson, D.; Tancrede, P., J . Chem. Soc., Faraday Trans. 2 1974, 70, 1465. (26) Blanchard, G . J.; Wirth, M. J. J . Phys. Chem. 1986, 90, 2521. (27) Ali, J.; Andreoli-Ball, L.; Bhattacharya,N.; Knonberg, B.; Patterson, D.J . Chem. SOC.,Faraday Trans. I 1985, 81, 3037. (28) Wirth, M. J.; Hahn, D. A. J . Phys. Chem. 1987, 91, 3099. (29) Blanchard, G. J. J . Chem. Phys. 1987,87,6802.
