J. Phys. Chem. 1985,89, 1999-2001 individual components. Rather they may be thought of as the weighted average of the components present. Nevettheless the experimental curves could be well fitted with a monoexponential decay law (Figure 6). The errors reported here are not the statistical errors obtained from the fitting process; rather they are the variations encountered with a series of measurements. It is important to note that up to 10% the water content did not influence the lifetime values given in Table I for the pthanolic solutions. The lifetime of component A in ethanol is nearly as long as that observed in the nonprotic solvents. On the other hand, the lifetimes of components B and C show a significantly larger deuterium effect than that of component A.
Discussion The phosphorescence of phenazine in ethanol solutions containing water consists of three components A, B, and C. Component A dominates the spectrum in rigorously dried solutions and is similar to the phosphorescence spectra in nonprotic solvents. On increasing the water content, component B appears qt the cost of A. At higher water concentrations, i.e., at about 3%, ymponent C shows up. These effects may be observed both in phosphorescence and in absorption. In polar but nonprotic solvents only one component could be observed. Thus the appearance of several components is clearly associated with the presence of a proton-donating hydroxy group in the solution. Pr~tonation'~ and ion-pair formationI4 would result in much larger spectral shifts and therefore cannot be responsible for the effects discussed here. The solvent dependence summarized above suggests the following assignments Component A, Free phenazine molecules, Le., molecules that do not have a specific interaction with the solvent. Component B: Phenazine molecules forming one single H bond. This H bond may be either to water or to ethanol. Component C: Phenazine molecules forming two H bonds. At least one of these H bonds involves a water molecule. These assignments are also supported by the lifetime data, in particular the low deuterium effect on the lifetime of A compared to B and C. Furthermore the interpretation given is also in agreement with the spectral features of A, B, and C. In nonpolar media the lowest (14)
Mataga, N.; Ezumi, K. Bull. Chem. Soc. Jpn. 1967,40,
1350.
1999
excited singlet state of phenazine Sl(na*)is known to be about 2800 cm-' below the lowest m* states.15 The phosphorescent state is of AT* type. Upon H-bond formation nr* states generally shift to higher and m*states to lower energy.16 This is exactly what may be observed in the series A B C. The relative maxima (associated with ?r a* transitions) shift to the red both in absorption and in phosphorescence, whereas the broad absorption tail belonging to the n a* transition is only prominent for component A and becomes much shorter and partly covered in the spectrum of the H-bonded species. The appearance of several subspectra due to the formation of different H-bond complexes with protic solvents seems to be a general phenomenon for p-diazines. Although until now no quantitative data are available concerning equilibrium constants, apparently large differences in the degree of complex formation occur. The accessible experimental data for ethanol solutions (96%) at 77 K indicate a rough correlation between the H-bond affinity of a diazine and the pKa value of the conjugated acid. For phenazine (pKa = l.213) and benzo[a]phenanzine (pKa = 1.517) the H-bonded species dominate,6 whereas in the spectra of benzov]quinoxaline (pKa = 0.9'*) and pyrazine (pKa = 0.612) the contribution of the free molecules is larger by about 1 order of m a g r ~ i p d e . ~For , ~ 1,4diazatriphenylene(pK, = 4.419) H-bonded molecules may still be observed in the phosphorescence spectrum although their concentration under these experimental conditions is exceedingly Finally, no evidence for H-bond formation was found in the spectrum of dibenzo[a,c]phenazine (pK, = 0.320). One should notice the qualitative character of this comparison. Neither the temperature dependence of the pKa valuez1 nor the differences in the phosphorescence quantum yield of the various species have been taken into account.
-
-
--
Registry No. Phenazine, 92-82-0; ethanol, 64-17-5. ( 1 9 Narva. D. L.:McClure. D. S.J. Chem. Phvs. 1981. 56. 167. (16) W e h j , E. L.'h "Fluore&ence";Guibault, 6.G., Ed:; Dkkker: New York, 1967; p 255. (17) Mordzinski, A.; Grabowska, A. J. Lumin. 1981, 23, 393. (18) Waluk, J.: Grabowska. A.: Pakula. B. J . Lumin. 1980, 21. 277. (19) Bulska, H.; Chodkowska, A.; Grabowska, A.; Pakula, B.; Slanina, 2. J. Lumin. 1975, 10, 39. (20) Markgraf, J. H.;Katt, R. J. J. Org. Chem. 1972.37, 717. (21) Perrin, D. D. Aust. J . Chem. 1964, 17,484.
Dielectric Friction as a Source of Rotatlonai Drag on Charged Noncentrosymmetric Molecules Daniel Kivelson* Department of Chemistry, University of California, Los Angeles, California 90024
and Kenneth G. Spears Department of Chemistry, Northwestern University, Evanston, Illinois 60201 (Received: September 24, 1984; In Final Form: January 2, 1985) Although dielectric friction is small for uncharged rotating molecules in solution, for asymmetrically charged ions dielectric friction can cause appreciable slowing of the reorientational motions. Therefore, in order to use rotational data to obtain information concerning the short-range nearest-neighbor interactions and structural rearrangements for asymmetrically charged ions, one must first substract off the significant dielectric friction effects. We have presented a simple theory of dielectric friction for such ions and have compared it with existing experimental data.
Introduction There have been a number of experimental observations of rotational correlation times for anions in solutions1 which yield times that are appreciably longer than those of corresponding (1) K. G. Spears and L. E. Cramer, Chem. Phys., 30, 1 (1978); K. G. Spears and K. M. Steinmetz, to be submitted for publication.
0022-3654/85/2~89-1999$01.50/0
uncharged probe molecules. One can conceive of numerous mechanisms associated with the charge which could contribute to this observed drag. One class of such mechanisms involves short-range or nearest-neighbor interactions and in this category are solvation and other structural rearrangements about the probe molecule. These may well be the dominant effects, but unfortunately they are difficult to evaluate. A second class of mechanisms involve long-range interactions with the bulk continuum 0 1985 American Chemical Society
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The Journal of Physical Chemistry, Vol. 89, No. 10, 1985
properties of the fluids; in this category one can place dielectric friction.* We shall investigate the possibility that dielectric friction can account in large part for the observed rotational drag of noncentrosymmetric ions. Both the experiments and theory that we discuss have appeared elsewhere, but the application of the theory to the problem of the rotational retardation of noncentrosymmetrically charged particles is, we believe, new and represents a situation which is qualitativery different from those previously considered. Dielectric friction comes about when a rotating dipole interacts with the surrounding dielectric medium. The dipole polarizes the medium and the polarized medium acts back on the probe dipole. If, then, the probe dipole rotates, the medium must readjust so that its polarization conforms to the new orientation of the probe, but the solvent reorientation is not instantaneous; this lag inhibits the probe rotation, thereby giving rise to rotational dielectric frictions2 The dielectric friction is affected by numerous relaxation processes: the longitudinal and transverse dielectric relaxation of the medium,)~~ the translational motions of both probe and solvent dipoles,) and the rotational motions of the probe itself.5 The zero-frequency dielectric friction tlDD is related to the rotational correlation time T I associated with the 1-rank orientational tensor of the rotating probe ion by the expression3 where 7: is the rotational correlation time for the probe molecule in the absence of dielectric friction, I is the molecular moment of inertia, kBis the Boltzmann constant, and Tis the temperature. Expressions for the ratio in eq 1 which include translational effects have been obtained by a number of author^.^^^^^ We are interested in rather large probe ions for which the modulation of tPDby both translational (DA) and rotational (D,) diffusion of the probe molecule (A) can be neglected; the latter because, relative to the dielectric relaxation time ( T D ) of the solvent, the probe rotates slowly, and the former because it translates slowly. For these large ions the modulation of FlDD by the translational diffusion (De) of the solvent molecules (B) is also negligible because movement over distances comparable to the dimensions (ro)of the probe are slow. (These conclusions are implicit both in the work of Madden and Kivelson3 and of Van der Zwan and Hynes6). If we let v be the volume of the probe molecule (u = 4wO3/3) and t the zero-frequency dielectric constant of the solvent, then, in the notation of ref 3 , these conditions lead to ~ D > B DA, TD-’ > (tDe/ro2),and 7D-l > D,.In this limit, for dilute solutions the dielectric friction can be obtained from eq 58, 59ab, 64, 65ab, and 54 of ref 3 : It2DD 4 r ( p ) 2 [ t - c ( m ) 1 ( T D / T 2 0 ) -6kBT~20 3ukBT[2e t ( m ) I 2
+
(2)
where t(m) is the dielectric constant of the solvent at infinite frequency, and jt is the magnitude of the dipole moment of the probe molecule. (In obtaining eq 2 from ref 3 , we have set DA = DB = D, = 0, and since we are using esu units, we have set 4nro = 1.) Dipole The interaction of a molecule with an external field can be written as a multipole expansion. If the molecule has a charge, the dipole and higher multipoles depend upon the choice of origin. If one is concerned with rotational motion one conveniently chooses an origin which simplifies the discussion of rotations; for gases the origin should be taken at the center of mass while for solutions it should be taken at the center of hydrodynamic strew8 A charged molecule that lacks a center of symmetry is likely to have (2) T. W. Nee and R. Zwanzig, J. Chem. Phys., 52, 6353 (1970). (3) P. A. Madden and D. Kivelson, J . Phys. Chem., 86, 4244 (1982). (4) P. A. Madden and D. Kivelson, Adv. Chem. Phys., 56, 467 (1984). (5) J. B. Hubbard and P. G. Wolynes, J. Chem. Phys., 69, 998 (1978). (6) G. Van der Zwan and J. T. Hynes, Chem. Phys. Lert., 101,367 (1983). (7) P. J. Stiles and J. B. Hubbard, Chem. Phys., 84, 431 (1984). (8) J. Dote and D. Kivelson, J. Phys. Chem., 87, 3889 (1983).
Kivelson and Spears a large dipole moment about its rotational center. It is the dielectric friction of this charge-related dipole that we study. It should be noted that the quadrupole and higher moments taken about the rotational center may be large and may also contribute to the dielectric friction. We shall neglect these multipole effects. If the charge Ze on an ion is located along a principal rotational axis at a distance a from the origin, the dipole moment has magnitude p: p = Zea (3) For noncentrosymmetric ions these dipole moments can be quite large: if Z = 1 and a = 5 A, p is almost 25 D.
Magnitudes and Trends In many cases, where dielectric friction is negligible, one can write T? % Uh?lK/kgT (4) where 3 is the coefficient of shear viscosity of the solvent, uh is a hydrodynamic molecular volume, and K is a dimensionless parameter which is reasonably independent of temperature. The hydrodynamic volume u h is equal to the actual molecular volume v for spherical molecules, and for nonspherical molecules uh > v; Perrin8,’ has given an explicit formula for the ratio (uh/u) for ellipsoidal molecules. For stick boundary conditions, K = 1 while for slip boundary conditions 0 C K C 1.l0 We expect stick boundary conditions if u is large compared to the volume of a solvent molecule and if the solvent interacts strongly with the solute.8*11We neglect local coordination effects since these must be classified with the short-range effects we are not considering. In the stick limit ( K = 1) and with the molecules approximated by ellipsoids, eq 4 represents the “stick” Debye-Stokes-Einstein-Perrin (DSEP) model; in the slip limit eq 4 represents the “slip”-DSEP model. We shall assume that the molecules can be approximated by spheroids. The factor [ & D D / 6 k B T ~ 2 appearing 0] in eq 1 and 2 is the fractional increase in the rotational correlation time due to dielectric friction. From the discussion above we expect this factor to be proportional to ( a 2 / u ) and to [t - t(m)] [2t + For t(m) = 1, the latter factor increases up to a value of t = 2.5 and decreases for increasing values o f t > 2.5. At low t the increase of 5 corresponds to an increase in the dipoles of the solvent, but at high t an increase in c is accompanied by the effective screening of the dipole-dipole interactions. For a = 6 A, t = 30, v 200 A), Z = 1, T D = 5 ps, T? = 25 ps, eq 2 yields
ItZDD = 0.6 6kBT7?
(5)
this suggests that dielectric friction increases the rotational correlation time by about 60%. Comparison with Experiment The rigorous experimental verification of the contribution of dielectric friction to the rotational correlation time requires a comparison of the behavior of the same molecule with and without a displaced charge. Data on such systems are not now available, but numerous measurements have been made on charged prolate dye molecules, some of which are thought to have displaced charges and some centrosymmetrically distributed charges; comparison of these dyes with each other and with uncharged molecules with comparable sizes and shapes has provided some understanding of the putative contribution of dielectric friction to the rotational correlation time. The work of Fleming et al.Iz showed that a neutral molecule such as 2,5-bis( 5’-tert-butyl-2-benzoxazolyl)thiophene(BBOT) can rotate faster than predicted by calculations based on the (9) F. Perrin, J. Phys. Radium,5 , 497 (1934). (10) C. M. Hu and R. Zwanzig, J . Chem. Phys., 60,4354 (1974). (11) J. Dote, D. Kivelson, and R. Schwartz, J . Phys. Chem., 85, 2169 (1981). (12) G. R. Fleming, A. E. W. Knight, J. M. Morris, R. J. Robbins, and G. W. Robinson, Chem. Phys. Le??.,51, 399 (1977).
Dielectric Friction as a Source of Rotational Drag
“stick”-Debye-Stokes-Einstein-Perrin(DSEP) model, while rotational correlation times of singly charged molecules are often comparable to or larger than those predicted in this “stick limit”. Large frictional effects have been attributed to hydrogenbonding between solvent and probe molecules, and in studying rotational diffusion one must distinguish between dielectric and hydrogen-bonding contributions. It has long been known13 that protic solvents solvate anions more effectively than cations, and, indeed, the work by Fleming et a1.,12 Spears et al.,’ and Von Jena and Lessing14have established that, in hydrogen-bonding solvents, anions without steric hindrance to solvent hydrogen bonding can have correlation times several times larger than predicted by the “stick”-DSEP model, while in dipolar aprotic solvents these same anions have correlation times comparable to that predicted by “stick”-DSEP. Since the hydrogen-bonding effect is generally less for cations, we focus our attention on positively charged dyes. The most structurally symmetric cations, such as pyronine G, acridine orange, and oxazines have symmetric electronic systems which yield resonance sharing of a single cation charge with both ends of the long axis. Thus these symmetric cations should not exhibit appreciable dielectric friction. These molecules have rotational correlation times which are slightly faster than those expected on the basis of “stick”-DSEP, even in alcohol s01vents.l~ We believe that these data are compatible with a model in which there is no dielectric friction and in which hydrogen bonding to the solvent is sterically hindered. Structurally asymmetric dianions which have both a localized and a delocalized charge may have reasonably small effective rotational dipole moments and, consequently, little dielectric friction. This seems to be the case for fl~orescein’~ and rose bengal’ dianions which have rotational correlation times in DMF and dimethyl sulfoxide which are comparable to those predicted by “stick”-DSEP theory. The “stick”-DSEP calculations are made on the assumption that the highly asymmetrical rotor can be modeled as an oblate spheroid, and since the observed values do in fact lie close to the “stick”-DSEP values, we assume that this assumption is reasonable. Since the prolate, symmetric monoanion, resorufin, shows DSEP behavior with boundary conditions close to slip in dipolar aprotic solvents,’ one might have to be more cautions about using the “stick”-DSEP calculations for prolate systems. Although there is as yet some uncertainty concerning its rotational correlation times, the cresyl violet dye molecule appears to be the best cation for which data are available that can be used for examining the dielectric friction h y p o t h e ~ i s . ’ ~Even ’ ~ though (13) A. J. Parker, Q. Rev. Chem. Soc., 16, 163 (1962); L. Salem, ‘Electrons in Chemical Reactions”, Wiley, New York, 1982. (14) A. Von Jena and H. E. Lessing, Chem. Phys. Let?.,78, 187 (1981); Chem. Phys., 40, 245 (1979). (15) D. P. Millar, R. Shah, and A. H. Zewail, Chem. Phys. Lett., 66,435 (1979). (16) D. Waldeck, A. J. Cross, D. B. McDonald, and G. R. Fleming, J . Chem. Phys., 74, 3381 (1981).
The Journal of Physical Chemistry, Vol. 89, No. 10, 1985 2001 its amino group is not as sterically hindered as those of some other cations, it has the important feature of a single, asymmetrically placed positive charge. The “stick”-DSEP value for (72’/v) has been estimated variously as 80,14 1 and 180 p ~ / c P ; we, ’ ~ too, obtain the value of 110 ps/cP proposed by Waldeck et a1.,I6 and this in turn yields “stick”-DSEP rZovalues of 65 ps in methanol, 140 ps in ethanol, 95 ps in dimethylformamide (DMF), and 238 ps in dimethyl sulfoxide (Me2SO).’s With these values of the “stick”-DSEP 72, we findi7that for cresyl violet ( T ~ / T ? )is between 1.2 and 1.5 in methanol, between 1.6 and 1.9 in ethanol, 1.6 in DMF, and 1.7 in Me2S0.I8 The similarity between the data in alcohols and in aprotic solvents suggests that little or no slowing of the cresyl violet rotations is attributable to hydrogen bonding. We, therefore, assume that the slowing in D M F is in large part due to dielectric friction, and we seek to compare the calculated with the “measured” ( 7 2 / 7 2 ’ ) in this solvent. To calculate ( 7 2 / 7 2 ) we take16 the molecular volume as v = 218 A3,the hydrodynamic volume as vh = v/0.445, the dielectric c ~ n s t a n t of ’ ~D M F as t = 37 and t(m) = 2,20the distance of the charge from the rotational center as a = 7 A, the dielectric relaxation time for D M F as 7 D = 15 PS,~’ and the rotational correlation time in the absence of dielectric friction (which we take to be the time obtained by the “stick”-DSEP calculation) as approximately 72’ = 95 ps. With the aid of eq 1-3 we calculate a ratio [ ( T 2 / 7 2 ) - 11 = 0.5, which accounts for nearly all the “experimentally” determined value of 0.6. Conclusions Although dielectric friction is small for uncharged rotors in solution, for asymmetrically charged ions dielectric friction can cause appreciable slowing of the rotational motion. Although it is the short-range or nearest-neighbor interactions that are usually of most interest, it is not possible to obtain much insight concerning these interactions from the rotational data unless one can first subtract off the long-range dielectric friction contributions. Acknowledgment. This work was supported in part by the National Science Foundation (Grant CH-8 1-09068 for D.K. and Grant CHE-7714668 for K.G.S.). (17) Several different values have been reported for +2 of cresyl violet at temperatures near 297 K. In methanol the values are lOOI3 and 80 ps;I2 in ethanol the values are 22013.’4and 270 ps;I2 in DMF the value is 150 ps;I2in Me2S0 the value is 420 ps.I2 (18) G. S.Beddard, T. Doust, and J. Herdales, Nature (London),294, 145 (1981). By means of fluorescence measurements on cresyl violet, these authors = 330 ps in ethanol and T~ = 150 ps in water; these correspond obtained i2 to an anomalously large (r2/+?)= 2.3 in ethanol and a somewhat small value of 1.34 in water. We have not used these data because the measurements probe excited states. (19) G. Leader, J . Am. Chem. Soc., 73, 856 (1951). (20) “Handbook of Chemistry and Physics” R. Weast, Ed.,63rd ed, CRC Press, Boca Raton, FL, 1983. Used valie of refractive index squared. (21) S. J. Bass, W. I. Nathan, R. M. Meighan, and R. H. Cole, J . Phys. Chem., 68, 509 (1964). The frequency dependent conductance was observed. The relaxation time at 300 K was obtained by interpolation.
