J. Phys. Chem. 1994, 98, 13083-13092
13083
Effect of Temperature and Viscosity on Rotational Diffusion of Merocyanine 540 in Polar Solvents David R. Bessiret and Edward L. Quitevis" Department of Chemistry and Biochemistry and Institute for Biotechnology, Texas Tech University, Lubbock, Texas 79409 Received: July 12, 1994; In Final Form: August 29, 1994@
The rotational diffusion time, trot, of merocyanine 540 (MC540) in the excited state was inferred from steadystate fluorescence anisotropy measurements as a function of temperature T and viscosity 7 in n-alkyl alcohol and n-alkanenitrile solvents. The rotational diffusion of MC540 is well described by the Debye-Stokesvarying linearly with 7/T. Within experimental error, the slopes of plots Einstein (DSE) equation, with trot vs q/T for solvents in a homologous series are equal. Taking weighted averages, we obtain a slope of of trot 87 f 9 ns WcP for the alcohols and a slope of 117 f 15 ns WcP for the nitriles. These values are greater than the predicted value of 73 ns WcP, based on the assumption that MC540 rotates as a prolate ellipsoid with a volume equal to its van der Waals volume. From the temperature-dependent data, we find that the rotational activation energy is greater than the viscosity activation energy. These results cannot be rationalized by the continuum dielectric friction model. We propose instead a quasi-hydrodynamic model in which the larger slope values are associated either with a local viscosity which is larger than the bulk viscosity or with changing boundary conditions. This quasi-hydrodynamic situation originates from specific solute-solvent interactions with the zwitterionic state of the dye which lead to enhanced solute-solvent coupling in the excited state of the dye. The larger slope in the nitriles is ascribed to greater solvation of MC540 in nitrile solvents than in alcohol solvents, as evidenced by the Stokes shift data.
1. Introduction The rotational diffusion of solute molecules in solution has long been used as a means of probing molecular friction,' typically by using either time-resolved or steady-state fluorescence depolarization techniques. Nonlinear laser spectroscopic techniques, such as transient grating and transient dichroism, have also been used. Through these techniques one obtains a rotational diffusion time, Trot, for the solute molecule. In the absence of dielectric effects, mechanical friction governs the rotational diffusion of a solute molecule in solution. In the simplest case, the mechanical friction is modeled by continuum hydrodynamic equations. This leads to the hydrodynamic model in which the friction coefficient is proportional to the solvent shear viscosity, r. In the hydrodynamic regime, Trot is given by the Debye-Stokes-Einstein (DSE)
where V is the volume of the solute molecule, kB is the Boltzmann constant, Tis the absolute temperature, S is a shape factor which accounts for nonspherical but ellipsoidal symmetry, and F is a friction factor which accounts for different boundary conditions. Under stick boundary conditions, the first layer of solvent sticks to the rotating body. For this boundary condition, F is equal to 1. Under slip boundary conditions, no tangential force is exerted on the body by the solvent. For this boundary condition, F can have values between 0 and 1. For symmetric ellipsoids, the shape factor S depends only on the axial ratio e, which is the ratio of the major axis to minor axis, alb.5 The friction factor in the slip limit for a given value of e can be obtained from the tables of Hu and Zwanzig.6 However, a +
Howard Hughes Medical Institute Undergraduate Fellow.
* To whom correspondence should be addressed.
@
Abstract published in Advance ACS Abstracts, November 15, 1994.
symmetric ellipsoid is a poor approximation for most molecules. It is more convenient to interpret the reorientational data in terms of the hydrodynamic volume, Vhyd, which is equal to VFIS for symmetric ellipsoids. If rotational diffusion is governed solely by hydrodynamics, trot varies linearly with VlT, with the slope being independent of the solvent. Because the solvent is assumed to be a continuum fluid, the DSE equation will be valid for solute molecules that are much larger than the solvent molecules. When the solute molecules approach the solvent molecules in size, a kinetic description must be In polar solvents, dielectric friction can cause deviations from DSE b e h a ~ i o r . ~ -Currently, '~ there is great interest in assessing the possible role of dielectric friction in rotational diffu~ion.'~-'~ It is a nonspecific interaction, arising from the bulk influence of the solvent as a dipolar medium. Briefly, the dipole moment of the solute molecule polarizes the surrounding medium and generates a reaction field. The response of the reaction field to the rotation of the dipole will not be instantaneous because of the frequency dependence of the dielectric constant of the medium. Consequently, the reaction field of the medium will lag behind the dipole, causing a torque to be exerted on the solute molecule which opposes the rotation. There are several ways in which to model the dielectric friction. It can be taken into account by an additional term, Zdf:
where ~ D S Eis the hydrodynamic contribution to the rotational diffusion time which is given by the DSE equation. Although not rigorously correct,10this additive approach provides a simple framework for analyzing the reorientational dynamics in polar solvents. In the dielectric continuum model of Nee and Z ~ a n z i g ,one ~ considers a dipolar solute, with point dipole moment p, slowly rotating in a spherical cavity of radius a,.
0022-365419412098-13083$04.50/0 0 1994 American Chemical Society
Bessire and Quitevis
13084 J. Phys. Chem., Vol. 98, No. 49, 1994 The radius a, is usually estimated from the molecular volume of the solute. The contribution of dielectric friction to rotational diffusion is then given by
zdf = P ,
E,
-1
T(2e, i- l)2zD
(3)
where P1 = p 2 / ( a $ k ~ ZD ) , is the Debye relaxation time, and E , is the static dielectric constant of the solvent. Thus, dielectric friction effects should be most prominent for small molecules with large dipole moments. Strictly speaking, the dipolar solute model is not appropriate for all solutes, in particular for ionic solutes. Alavi and W a l d e ~ k lhave ~ ~ recently calculated the dielectric friction for an arbitrary charge distribution in a spherical cavity and found that zdf retains the same form as eq 3 with P1 being given by a more complex expression that depends on the actual charge distribution of the solute molecule. Short-range solute-solvent interactions of sufficient strength can give rise to solvent attachment.20-22 For example, a recent study of the rotational diffusion of the dye coumarin 102 ((2102) in trifluoroethanol (TFE) strongly points to the rotating species as being a 1:l (2102-TFE complex.22 Thus, deviations from DSE behavior can occur not only because of dielectric friction effects but also because the effective volume is that of a solutesolvent complex and not just the solute molecule itself. Previous studies have indicated the difficulty in being able to unambiguously distinguish dielectric friction effects from solvent attachment because of the uncertainty in the size and/or shape of the rotating s p e ~ i e s . 1 2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ To understand the effect of solvent on the reorientational dynamics of the solute molecule in polar solvents, one must unravel the effects of mechanical friction, dielectric friction, and specific short-range solute-solvent interactions. To date, emphasis has been placed on the rotational diffusion of mediumsized solute molecules (a few hundred cubic angstroms) in order to probe molecular relaxation in the transition region between the molecular regime to the continuum regime for the sol~ e n t . ' ~However, .~~ there is also a need to understand the role of hydrodynamics and dielectric interactions in the rotational diffusion of large molecules in the continuum regime.24 In a preliminary study from our lab0ratory,2~Trot values for merocyanine 540 (MC540) in polar solvents were measured by using picosecond polarized pump-probe spectroscopy. In this earlier study of MC540, we found that trot varied linearly with 7 at room temperature, with the slope being independent of the solvent. Because the pump-probe technique is an absorption technique, it provides information about the reorientational dynamics of the ground state. These results suggested that the ground-state rotational diffusion of MC540 is mainly controlled by mechanical friction and not by dielectric friction. MC540 is a fairly large anionic lipophilic dye (Figure 1) that has been used extensively as a fluorescent probe of the transmembrane potential of cell and organelle membra ne^^^-^^ and in the photochemotherapeutic treatment of leukemia and certain v i r u ~ e s . ~ Merocyanine ~*~~ dyes are of particular interest because their spectral properties are very sensitive to both specific and nonspecific solute-solvent interactions?2-34 MC540 is a negative solvatochromatic dye and therefore exhibits a blue shift in its absorption maximum with increasing polarity. The ground-state dipole moment in this case is greater than the excited-state dipole moment. The chromophore in MC540 is a resonance hybrid (Figure 1) of a weakly polar structure (resonance structure a) and a highly polar or zwitterionic structure (resonance structure b). Increasing the solvent polarity increases the zwitterionic character of the molecule. The
t
I R2
R2
Figure 1. Resonance structures of merocyanine 540. R1 = (CH&S03-Na+; Rz = (CH2)3CHs. Not shown is the equivalent
zwitterionic structure with the negative charge on the other carbonyl oxygen. zwitterion will be further stabilized by protic solvents through hydrogen-bonding interactions with the oxygen atoms on the thiobarbituric acid moiety. These interactions are present in most merocyanine dyes. In the case of MC540, one must consider additional interactions of the solvent with the sulfonate group which is attached to the chromophore by the propyl side chain on the benzoxazole subunit. Because the negative charge remains localized, solute-solvent interactions at this site should play less of a role in influencing the electronic properties of the chromophore than solute-solvent interactions at the carbonyl groups. In this paper, we present new data on the temperature and viscosity dependence of the reorientational dynamics of MC540 in nitrile solvents (nonassociating solvents) and in alcohol solvents (associating solvents). The goal of this study is to further understand the solute-solvent interactions that influence the rotational diffusion of MC540. Specifically, we wish to examine more carefully the role of dielectric friction and specific solute-solvent interactions. The paper is organized as follows. In section 2, the method used to obtain the values of Trot from steady-statefluorescence anisotropy data is described. In section 3, we use steady-state spectral data to obtain estimates of the dipole moment in the ground state and the excited state. The results from solvent-dependent and temperature-dependent rotational diffusion studies are then given. In section 4, we show that the behavior of Trot is well described by the DSE equation, with the hydrodynamic volume in the excited state being larger than in the ground state. This state dependence however cannot be rationalized by the continuum dielectric friction model and spectroscopically derived dipole moments. On the basis of the temperature-dependent studies, we postulate that the larger hydrodynamic volume is a manifestation of a local microviscosity effect or changing boundary conditions, which arise because of specific solvent interactions with the zwitterionic state of the dye.
2. Experimental Section A. Sample Preparation. MC540 (Molecular Probes or Sigma) and rhodamine 101 (RhlOl) (Exciton, laser grade) showed single spots on thin-layer chromatography plates and were used without further purification. MC540 was stored in the dark as a concentrated stock solution (1 mM) in an ethanol/ carbon tetrachloride mixture (1:l v/v). Solvents of the highest commercial purity were used. The solvents were further purified by distillation over CaH2 and stored over molecular sieve in tightly capped flasks prior to use. Solvent shear viscosities and
Rotational Diffusion of Merocyanine 540 in Polar Solvents dielectric parameters for these solvents were obtained from the literat~re.~~-~~ B. Spectroscopic and Photophysical Measurements. Absorption spectra were obtained on a Shimadzu 265 UV-vis spectrophotometer. Corrected fluorescence spectra were recorded on an SLM Aminco 4800C fluorometer. The samples were contained in 1-cm cuvettes in the fluorometer. The temperature of the sample was controlled to f l “C with a temperature-controlled water circulator (Neslab RTE-4). The temperature in the cuvette was measured with a thermometer. The temperature of the sample was varied between 288 and 333 K. The fluorescence quantum yield and anisotropy measurements were carried out with the excitation and emission monochromators set respectively at 520 and 575 nm. The steady-state fluorescence anisotropy was obtained in the usual way in order to correct for the polarization bias of the emission monochromator in the fluorometer.@ The intensities IVV and IVH were measured, where IWrepresents the vertically polarized emission with vertically polarized excitation and IVH represents the horizontally polarized emission with vertically polarized excitation. To correct for the polarization bias of fluorometer, the intensities Iw and Im were measured, where Iw represents the vertically polarized emission with horizontally polarized excitation and Im represents the horizontally polarized emission with horizontally polarized excitation. In terms of these experimentally measured intensities, the steady-state fluorescence anisotropy is calculated from the relationship
rs =
‘VV - GzVH IVV
+ 2GzVH
(4)
where G = IW/IHH. Based on previous time-resolved fluorescence anisotropy measurement~,4~.~~ the reorientational dynamics of MC540 is well described by a single-exponential time correlation function. For single-exponential decay, the steady-state fluorescence anisotropy is related to the fluorescence lifetime, zf, and trot through the equation
J. Phys. Chem., Vol. 98, No. 49, 1994 13085
TABLE 1: Dielectric Parameters and Steady-State Spectral Data for Merocyanine 540 in n-Alkyl Alcohol and n-Alkanenitrile Solvents at 298 K solvent csn n” nm nm Stokes shift,‘ cm-l methanol 32.7 1.327 555 581 806 ethanol
24.5 20.3 1-butanol 17.5 1-pentanol 13.9 1-hexanol 13.3 1-heptanol 11.6 acetonitrile 37.5 propionitrile 27.9 butanenitrile 23.3 pentanenitrile 19.7 hexanenitrile 19.7 heptanenitrile 15.4 octanenitrile 13.9 nonanenitrile 12.6
1-propanol
1.360 1.381 1.397 1.409 1.418 1.422 1.342 1.366 1.384 1.395 1.406 1.410 1.418 1.426
560 562 564 565 565 566 559 561 562 563 564 565 566 566
583 586 587 589 588 588 587 587 589 589 590 591 591 590
704 729 695 721 692 66 1 853 790 816 784 781 779 747 719
Static dielectric constant, cs, and refractive index, n, obtained from refs 35, 36, and 38. Absorption maximum, 1,. Fluorescence maximum, &. Uncertainity f1 nm. e Calculated from difference in absorption and fluorescence maxima; uncertainty f 3 0 cm-I. description of the solvent, the absorption energy is given by the Bayliss-McRae equation48
hc5, = hcv; - [2f(n2)/uc31(D,2- p;)
+
{ ~ H E-A~~)IIU,~I(D; J - pfle
3. Results A. Determination of Dipole Moments from Steady-State Spectroscopy. The ground- and excited-state dipole moments can be estimated from the solvent-induced shifts in the absorption and fluorescence maxima. Within the dielectric continuum
4) (6)
and the Stokes shift is given by the Lippert-Mataga equation@
where Pa and Vf are the maxima of the absorption and fluorescence spectra, respectively. In the above expressions, P: is the absorption maximum of the isolated molecule, pg is the ground-state dipole moment, pe is the excited-state dipole moment, Ap is the difference in the dipole moments (pg- pJ, and 4 is the angle between the ground- and excited-state dipole moments. The quantitiesflg) andfln2) are the Onsager reaction field functions49 defined by f l x ) = (x - 1)/(2x l), with x equal to the static dielectric constant 6, or the square of the refractive index n2. The second and third terms in eq 6 give the solvent’s contribution to the solute free energy. The quantity 2fln2)/uc3is the optical response function associated with the solvent electronic degrees of freedom. The quantity ( 2 m 4 An2)]/uc3) is the orientational response function associated with the rotation of the solvent dipole moments. If the optical response term is neglected in eq 6 and we assume that the ground- and excited-state dipoles are parallel, a plot of Va as function of Af = WE,) - fin2)] should be linear with the slope proportional to pg&. Similarly, a LippertMataga plot of Va - i+ as a function of Af should be linear with slope, proportional to (Ap)2. Using the spectral data and solvent parameters listed in Table 1, the plots in Figure 2 were constructed. For MC540 in nitriles solvents both the absorption maximum and the Stokes shift show reasonably linear correlations with Af. However, in alcohols the absorption maximum and Stokes shift clearly do not vary linearly with Af. This is consistent with the fact that the continuum model is not valid in hydrogen-bonding solvents.50 The nitrile plots should give more reliable estimates of the dipole moments. Using the slopes from the nitrile plots, the molecular volume as determined by the method of van der Waals radii increments (485 A3),51 and the relationship pg = p e Ap, we estimate the ground- and the excited-state dipole moments to be 9.6 and 5.2 D, respectively. Our value of the ground-state dipole moment agrees
+
where ro is the initial anisotropy. The initial anisotropy is obtained by measuring the steady-state fluorescent anisotropy in a highly viscous liquid. Under these conditions Trot >> zf, and r, is equal to ro. In this work, the measurement of r, in ethylene glycol at 273 K gave a value of 0.36, which is consistent with values of ro (0.31 -0.34) obtained in timeresolved fluorescence anisotropy measurement^.^^ The fluorescence lifetime was inferred from quantum yield data that were previously rep0rted.4~ Briefly, zf is equal to @f/ k,, where @f is the fluorescence quantum yield and kr is the radiative rate constant. The Strickler-Berg equation4 was used to calculate the value of kr from the steady-state spectra. In the fluorescence quantum yield measurements a polarizer placed between the sample and the emission monochromator was set at 54.7” (“magic angle”) to remove reorientational effects. RhlOl in ethanol (@f w 1)45-47was used as the reference for the quantum yield measurements.
COS
+
13086 J. Phys. Chem., Vol. 98, No. 49, 1994
A
t
'E
2
17900
f
.-E 17800
U
TABLE 2: Comparison of Experimentally Measured and Calculated Rotational Diffusion Times in n-Alkyl Alcohol and n-Alkanenitrile Solvents at 298 K
Alcohols
18000 L
r
Bessire and Quitevis
0 Nitriles
' -
17700
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. t 0.24
. . .
!
.
.
.
I
.
0.28
0.26
.
.
#
.
.
v:
solvent methanol ethanol 1-propanol 1-butand 1-pentanol 1-hexanol 1-heptanol acetonitrile propionitrile butanenitrile pentanenitri1e hexanenitrile heptanenitrile octanenitrile nonanenitrile
]
0.30
Af
cp 0.55 1.14 1.95 2.60 3.57 4.54 5.81 0.348 0.416 0.542 0.678 0.917 1.19 1.55 1.95
tmt!ns 0.18 f 0.05 0.33 f 0.10 0.57 f 0.18 0.78 f 0.24 1.2 f 0.4 1.1 f 0.3 1.7 f 0.5 0.12 f 0.03 0.14 f 0.04 0.18 f 0.05 0.23 f 0.07 0.35 f 0.1 1 0.41 f 0.12 0.52 f 0.16 0.81 f 0.26
~ D S E , Cns
0.120 0.249 0.425 0.567 0.779 0.990 1.267 0.076
0.097 0.118 0.148 0.200 0.260 0.338 0.425
P c
Solvent shear viscosity, 7. obtained from ref 39. Rotational correlation time, tmt, determined from steady-state fluorescence anisotropy. Rotational correlation time, ~ D S E , calculated from DSE equation (eq 1) for stick boundary conditions with V = 485 A3,and S = 0.480; see text for further details.
9001
'"I
0.8
a
c8
I1
I 0.24
0.26
0.28
0.30
Af
Figure 2. Plots of the (a) absorption maximum and the (b) Stokes shift versus Af = Ne6) - An2)] for merocyanine 540. The quantity
Ax) is the reaction field function, ( x - 1)@
+
l), with x equal to the static dielectric constant, es, or the square of the refractive index, n2. Lines through points are linear least-squares fits of data with the following values of the slopes: (a) alcohols, 4498 cm-'; nitriles, 3325 cm-'. (b) alcohols, 1417 cm-'; nitriles, 1639 cm-'.
well with the dipole moments of closely related merocyanine These dipole moments are considerably smaller than the dipole moment value of m35 D, which is estimated from molecular mechanics calculations of the ~ w i t t e r i o n . ~The ~-~~ smaller dipole moments are attributed to the fact that the electronic state of dye is more accurately characterized by the weakly polar resonance structure than by the zwitterionic resonance structure.53 B. DSE Analysis. Solvent-Dependent Study. For the alcohols, we find quite good agreement between the values of zmtinferred from our steady-state fluorescence depolarization measurements and those obtained by using time-resolved techniques. The steady-state fluorescence anisotropy data yielded values of 0.33,0.78, and 1.68 ns for MC540 respectively in ethanol, 1-butanol, and 1-heptanol at 298 K, which compare well with the values of 0.326, 0.750, and 1.678 ns obtained in the same solvents at 294 K by using picosecond time-correlated single-photon counting.42 Table 2 summarizes representative reorientational data at 298 K for MC540 in both n-alkyl alcohol and n-alkanenitrile solvents. Figure 3 shows that the dependence of zmton ylT at 298 K for MC540 in nitrile and alcohol solvents is linear. The lines are linear least-squares fits to a modified form of eq 1
2.0 -
f
1.5
Y
0.5
[
t 5
10
15
20
q r r (10-3 CPIK) Figure 3. Debye-Stokes-Einstein plots for merocyanine 540 in (a) nitriles and (b) alcohols at 298 K. The points are labeled by the number of carbons (C.) in the alkyl chain. Linear least-squares fit parameters: for alcohols, slope = 0.080 f 0.006,intercept = 0.036 f 0.011, correlation coefficient = 0.978; for nitriles, slope = 0.110 f 0.015, intercept = -0.014 f 0.017, correlation coefficient = 0.984. The
dashed lines were calculated from the Debye-Stokes-Einstein equation (eq 1) for stick boundary conditions using V = 485 A' and S = 0.48. See text for further details.
where zo is the zero-viscosity intercept and C is the slope. Pecora and c o - ~ o r k e r first s ~ ~showed that the rotational diffusion times of small molecules in liquids are well described by an equation of this form. The values of the slope and intercept for these linear fits are 80 f 6 ns KIcP and 0.036 f 0.01 1 ns
J. Phys. Chem., Vol. 98,No. 49,1994 13087
Rotational Diffusion of Merocyanine 540 in Polar Solvents
-E
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0.20
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3.5
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4.5
5
5.0
10
15
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q r r (10-3 CPIK)
q r r (10-3 CPIK)
Figure 4. Representative Debye-Stokes-Einstein plots obtained by varying the temperature for merocyanine 540 in (a) propionitrile, (b) heptanenitrile, (c) ethanol, and (d) hexanol. The solid lines through points are linear least-squares fits of data. See Table 3 for fit parameters.
TABLE 3: Fit Parameters for Rotational Difkion in n-Alkyl Alcohol and n-Alkanenitrile Solvents solvent
slope," ns WcP
intercept," ns
solvent
slope," ns WcP
methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol
114 f 37 67 f 23 94 f 27 107 f 24 99 f 27 72 f 20 a7 f 20
-0.016 f 0.022 0.103 f 0.017 -0.027 f 0.022 -0.069 f 0.025 0.016 f 0.024 -0.026 f 0.023 0.023 f 0.027
acetonitrile propionitrile butanenitrile pentanenitrile hexanenitrile heptanenitrile octanenitrile nonanenitrile
122 f 54 128 f 47 104 f 42 123 f 43 116 f 42 112 f 39 109 f 37 128 f43
" Slope and intercept of
linear fits of plots of
trot vs
intercept: ns -0.017 -0.021 -0.010 -0.052 -0.003 -0.025 -0.038 -0.013
f 0.021 f 0.023 f 0.024 f0.025 f 0.022 f 0.022 f 0.027 f 0.025
v/T. See Figure 4 for representative plots.
for the alcohols and 110 f 15 ns WcP and -0.014 f 0.017 ns for the nitriles. Temperature-Dependent Study. Figure 4a-d shows singlesolvent DSE plots in which the solvent is kept constant while the temperature is varied. This temperature-dependent study also shows that zrotvaries linearly with qIT. The solid lines through the experimental points are linear least-squares fits of eq 8. The fit parameters are summarized in Table 3. The temperature-dependent study provides a more stringent test of the hydrodynamic model. If hydrodynamics is valid, the same rotational diffusion time should be obtained for a particular value of qIT, regardless of whether the solvent or the temperature is changed. Because the plots of Trot vs qlT are obtained by varying the temperature and not the solvent, differences in solvent properties should not play a role in determining the variation of trot with q/T. Furthemore, the slopes of these plots should be independent of solvent and in fact should be equal to the slopes obtained in the solvent-dependent study. This appears to be true if one compares the slope values for solvents within a homologous series. However, just as we had found in the
solvent-dependent study, the slope for the alcohols is different than the slope for the nitriles. Taking weighted averages?' one obtains slope values of 87 zk 9 ns WcP for the alcohols and 117 f 15 ns WcP for the nitriles. As can be seen in Figure 5 , the data for all the solvents within a homologous series can be well overlapped and fitted by a single line with nearly the same slope values as above: 81 f 20 ns WcP for the alcohols and 123 k 31 ns WcP for the nitriles.
4. Discussion A. Hydrodynamic Model. For a given shape, the hydrodynamic contribution to Trot can be calculated by using the DSE equation. We will assume that the molecule rotates under stick boundary conditions (F = 1) as if it were a prolate symmetric ellipsoid with the major axis lying along the polymethine chain. By using CPK space-filling models, we estimate the lengths of the major and minor axes (a and b) to be 9-10 and 3.4-3.6 A, respectively. The values of a and b were chosen to be consistent with the van der Waals molecular volume (i.e., V = 4zab2/3 = 485 A3). With the ellipsoidal dimensions of a = 9.5 and b
a
Bessire and Quitevis
13088 J. Phys. Chem., Vol. 98, No. 49, 1994 a
1'4[ 1.2
0.6
0.4
o.2 0.0
. I 2
8
6
4
?/T (10-3 CPIK)
P Y
8
be neglected when compared to the hydrodynamic part of the rotational diffusion time. B. Continuum Dielectric Friction Model. In our earlier study,25 we were able to account adequately for the groundstate values of tmtfor MC540, without having to invoke dielectric interactions, by using the molecular dimensions determined from space-filling models and the DSE equation. The values of trotobtained by using fluorescence techniques are associated with the reorientational dynamics of the molecule in the first excited-singlet state. The measured values of trot obtained here could therefore be larger than the values predicted by the DSE equation, because the rotational diffusion of MC540 is state-dependent. Let us consider the possibility that the state dependence is caused by dielectric friction effects. Based on the Nee-Zwanzig dielectric continuum model, the difference Az = trot- ZDSE should vary linearly with the quantity ( E , - 1)zd[T(2cS with slope equal to P1 = pe2/ ( a c 3 k ~ )In. principle, it should be possible to c o n f i i this by using the estimated value of the excited-state dipole moment and the molecular volume. However, the experimental errors in zmtare much too large (Table 2) to examine dielectric friction effects in this way. Instead, we follow the approach of Alavi and W a l d e ~ k "by ~ making use of an empirical relationship for the dielectric friction:
2.5
-
2.0
-
1.5
-
1.0
-
0.5
-
+
o.ot,-, , 0
5
,
, 10
.
,
15
,
,
20
, 25
,
,
1
30
[(E,
- l)t,]/[T(2~,
+ 1)2] = K,v/T i- K2
(9)
q r r (10-3 CPIK)
Figure 5. Debye-Stokes-Einstein plots obtained by combining all the temperature-dependent data for a homologous series of solvents in a single plot for (a) nitriles and (b) alcohols. Representative error bars are given. Linear least-squares fit parameters: for alcohols, slope = 0.0814 f 0.020, intercept = 0.059 f 0.034, correlation coefficient = 0.979; for nitriles, slope = 0.123 f 0.031, intercept = -0.034 f 0.026, correlation coefficient = 0.987.
= 3.5 A, we calculate that S = 0.480 by using the Pemn equation for the shape factor. This gives a slope of 73.2 ns WcP. As shown in Table 2, the values of tmt calculated on the basis of this molecular shape and the DSE equation are less than the measured values of zrot. This difference is apparent when one compares the fit lines in Figure 3 to the predicted DSE lines for a slope of 73.2 ns WcP. Within experimental error, the intercept is negligible in comparison to the hydrodynamic term. Originally, the zeroviscosity intercept was interpreted as the free rotor time of the molecule, ~ F R Obviously, . ~ ~ the free rotor interpretation breaks down for a negative zero-viscosity intercept. There is currently no clear consensus on the physical significance of the zeroviscosity intercept. As pointed out by Evans and Kivelson?8 the intercept does not describe the dynamics at low viscosities but is associated with behavior at high viscosities, extrapolated to zero viscosity. Alavi and W a l d e ~ k " ~have rationalized negative zero-viscosity intercepts in temperature-dependent studies as being a reflection of changing boundary conditions that could occur because the attractive solute-solvent interactions become less important at higher temperatures. For large molecules, the free rotor time does not contribute significantly to the rotational diffusion time. The free rotor time is given by (2n/9)(I/k~J')~'~, where I is the moment of inertia. To estimate the moment of inertia, we will assume that the molecule rotates about the minor axis as if it were a prolate ellipsoid with uniform mass density. For this rotating body, I = Muz/ 10, where M is the mass of the molecule. Using this simple model for the rotor, we find that the free rotor time for MC540 is constant to within few a percent over the temperature range of our measurements and is roughly equal to 3 ps. Clearly, ~ F R is much less than ZDSE (Table 2). Therefore, free rotation can
where K1 and K2 are parameters obtained from fits of plots of [(es - l)~D]/[T(2€s 1)2] vs q/T. The justification for this relationship is the observation that the Debye dielectric relaxation time correlates linearly with vi~cosity.~No physical significance should be assigned to the fit parameters K1 and K2. In fact, on the basis of eq 9, one would arrive at the nonphysical conclusion that the rotational dielectric friction becomes constant at high temperatures. Combining eqs 1-3 and 9 yields the equation
+
where the free rotor time has been included. It is evident from this equation that the slope of a DSE plot will have contributions from both the mechanical friction and the dielectric friction. This equation predicts that, due to dielectric friction, the slope and intercept in DSE plots will vary with solvent through the parameters K1 and Kz, respectively. Deviations from DSE behavior due to dielectric friction can therefore be quantified in terms of the parameter P1K1. The extent to which dielectric friction affects the slope is largely determined by the electrical properties and molecular dimensions of the solute molecule, as reflected in the parameter PI. Figure 6 is a plot of eq 9 for alcohols using the data in Table 4. With the exception of I-hexanol, eq 9 is a reasonable fit of the data. (The curvature in the plot of the data for 1-hexanol can be partly attributed to a deviation from linearity for ZD vs 7 at low 7.) Using the spectroscopically derived excited-state dipole moment and a cavity radius of 4.8 A, we calculate a value of 1772 K for PI. Table 5 lists calculated values of PlKl for several alcohols. The calculations show that on the basis of the Nee-Zwanzig model the contribution of dielectric friction to the slope varies from -3% for methanol to 18% for 1-hexanol. This variation is much less than the error in the experimental slope values. Nonetheless, greater than 85% of the actual slope for the alcohols can be accounted for by mechanical and dielectric friction. As an aside, negative zeroviscosity intercepts can arise if the term P1K2 is negative and
J. Phys. Chem., Vol. 98, No. 49, 1994 13089
Rotational Diffusion of Merocyanine 540 in Polar Solvents
TABLE 4: Viscosity and Dielectric Parameters for the Alcohols as a Function of Temperature Methanol Ethanol Propanol Butanol Pentanol Hexanol
5
temp, K
10
15
20
qrr (10-3 CP/K) Figure 6. Plot of the dielectric friction parameter [(es - l)t~]/[T(2e~ 1)2]vs v/T for alcohols using data given in Table 4. The solid lines
+
II." cp
+
+
tDIb
ps
288 293 298 308 323 333
125 111 100 81 60 50
288 293 298 308 323 333
(b) Ethanol 1!355 1.218 1.098 0.903 0.688 0.582
25.4 24.6 23.8 22.3 20.2 19.0
163 147 134 112 87 74
288 293 298 308 323 333
(c) 1-Propanol 2.477 21.6 2.183 21.o 1.932 20.3 1.531 19.1 1.110 17.3 0.910 16.3
308 266 230 175 120 95
288 293 298 308 323 333
(d) l-Butanol 3.348 2.920 2.558 1.989 1.404 1.133
17.9 17.4 16.8 15.8 14.4 13.5
503 415 344 24 1 148 109
288 293 298 308 323 333
(e) 1-Pentanol 4.988 15.0 4.235 14.5 3.615 14.1 2.675 13.1 1.764 11.9 1.364 11.1
1070 847 677 442 245 171
288 293 298 308 323 333
6.540 5.581 4.787 3.576 2.389 1.862
are linear least-squares fits. Fit parameters are given in Table 5.
has an absolute value greater than tm. As can be seen in Table 5 , K2 becomes more negative in going from the lower to higher alcohols. For the lower alcohols (methanol through butanol), zm is greater than or equal to zero. For the higher P1K2 alcohols, P1K2 ZFR is negative. Although the slopes in the DSE plots for the excited-state rotational diffusion of MC540 in alcohols seem to be consistent with the estimates based on dielectric friction and hydrodynamics, similar agreement cannot be found for the excited-state rotational diffusion in nitriles or for ground-state rotational diffusion. Moreover, because the spectroscopically derived dipole moment is greater in the ground state than the excited state, rotational diffusion times should be longer in the ground state than in the excited state, based on the continuum dielectric friction model, which is contrary to what is actually observed. In trying to link the spectroscopy of MC540 to its rotational dynamics, we are making the implicit assumption that the solute-solvent interactions that are the origin of the solventinduced spectral shifts are the same interactions that affect the reorientation of the molecule and that the continuum perspective is valid for this molecule. The discrepancies may indicate that the actual charge distribution of the dye cannot be accurately represented by the spectroscopically derived dipole moment. Alavi and W a l d e ~ k "have ~ previously pointed out that the dipole moment of a charged solute is not well-defined because it depends on the origin of the coordinate system, which is arbitrary. In the Nee-Zwanzig model,9 the point dipole field falls off as rP3,whereas the field for a charge falls off as r-*. Because of this difference in the distance dependence of the fields, the dielectric friction will not necessarily be the same for ions and point dipoles. In fact, Alavi and W a l d e ~ k "have ~ recently shown that using a more realistic charge distribution can change the dielectric friction by several orders of magnitude. C. Quasi-Hydrodynamic Model. The above analysis indicates that the state dependence of the rotational dynamics cannot be explained by the simple continuum model for dielectric friction. A more consistent explanation can be obtained by taking a quasi-hydrodynamic approach which incorporates some of the microscopic aspects of rotational diffusion. Based on the DSE equation, differences in the hydrodynamic volume could be attributed to differences in the friction factor F, the shape factor S, or the molecular volume
esb
(a) Methanol 0.640 34.8 0.590 33.9 0.545 33.0 0.469 31.2 0.381 28.8 0.335 27.2
(0 1-Hexanol 10.6 10.2 9.8 9.0 7.9 7.2
2450 1760 1280 70 1 304 181
a Obtained from ref 39. Values at these temperatures were obtained by exponential extrapolation of data in ref 37.
TABLE 5: Rotational Diffusion Parameters for Continuum Dielectric Friction Model
+
Ki )(1 ps/cP
10-3ps/K
PlKl,b ns WcP
methanol 1.354 ethanol 0.833 l - p ~ p ~ o 1.255 l 1-butanol 2.013 1-pentanol 3.710 1-hexanol 8.710
-0.083 1.25 0.472 -1.85 -6.87 -42.5
2.4 1.5 2.2 3.6 6.6 15.4
solvent
a
K2,"
PlK2+ tmICps
3 5 4
0 -9 -70
DSE DF slope," ns WcP 76 75 75 77 80 87
Slope, K1, and intercept, K2, from fit of eq 9 to data in Table 4.
P1 = 1772 K. Free rotor time, tm. Sum of DSE slope and dielectric friction contribution, P I K ~ .
V. From the weighted average of the slopes, we calculate values of 1490 f 200 and 1200 f 110 A3 for the hydrodynamic volume of MC540 in nitriles and alcohols, respectively. These values are clearly greater than the predicted hydrodynamic volume of 1010 A3,which is based on the assumption that the molecule rotates as a prolate ellipsoid with major and minor axes of 9.5 and 3.5 A. However, it does not seem plausible to us that the difference between Vhyd in the ground state and in
Bessire and Quitevis
13090 J. Phys. Chem., Vol. 98, No. 49, 1994
;
L
P
-
5.0
"
,
"
"
,
"
"
l
"
"
l
'
"
'
,
,
,
"
'
"
has been observed previously for the dye DODCI rotating in alcohol solvents.60 If Em, were equal to E,, all the points would fall on a line of unit slope and zero intercept. Figure 8 clearly shows that this does not occur. Although the slopes of the lines in Figure 8 are close to unity, the intercepts are nonzero. The intercept is equal to 0.72 f 0.33 kcal/mol for nitriles and 0.41 f 0.31 kcaVmol for the alcohols. We interpret the nonzero intercept as being due to an additional interaction energy, M i n t :
.
;:a/
4.5
8
rL
t c
-
4.0
3.5
7/:
; . ,
,l, 3.0
,
,
,
,
,
3.1
,
,
3.2
,
,
,
,
,
,
,
,
3.3
~,
,
,
Erot
,,
b
rmicro
3.1
3.2
3.3
3.4
Figure 7. Representative Arrhenius plots of Tt,, for merocyanine 540 in (a) nitriles and (b) alcohols. The lines are linear least-squares fit to the data. Lines are identified by the number of carbon atoms in the alkyl chain of the solvent molecule. Activation energies obtained from fits are given in Table 6.
the excited state is due solely to a change in the intrinsic shape of the dye upon excitation. The temperature-dependent data suggest instead that the larger value of Vhyd is due to enhanced solute-solvent coupling that affects the local viscosity and/or boundary conditions. It is well-known that 7 can be expressed by the empirical equation59 (1 1)
where E, is the viscosity activation energy. Combining eqs 1 and 11 gives the following expression for the temperature dependence of Trot: Trot = (v0VF/kJs)
exp(EJRT)
(14)
= 7 exP(minJRT)
(15)
This would be consistent with Blanchard's explanation for the state dependence of the rotational diffusion time for oxazine 725 in normal alcohols.16b The microviscosity concept is useful because it allows us to retain the form of the DSE equation for describing the rotational diffusion of MC540. Clearly, if 7 in the DSE equation is replaced by this expression for qmicro,the slope in the plots of Trot vs q/T will be given by
lOOO/T (K-')
v = 70 e x ~ (JRT) E
+ mint
From the values of the intercepts, we would therefore conclude that the interaction energy is nearly twice as large for the nitriles as for the alcohols. This additional term could be a reflection of the fact that the mechanical friction is not simply proportional to the solvent shear viscosity, as given by hydrodynamics, but is instead proportional to the local viscosity or microviscosity, Vmicro, with
3.4
lOOOlT (K-')
3.0
=7'
(12)
The validity of eq 1 can therefore be verified by constructing plots of 1n(TrIot)vs UT, as shown in Figure 7 . The plots are linear, indicating that Tz,, can be well described empirically by the relation
where Erotis the rotational activation energy. Note that because relaxation time data and not rate constant data are used, the Arrhenius temperature dependence leads to a positive exponential. If the viscosity and temperature dependence of the reorientational dynamics of MC540 are governed by hydrodynamics, the values of Erotand E, for a given solute should be the same. A comparison of these activation energies (Table 6) shows that E,, tends to be greater than Ell. This is made more apparent in a plot of Erotvs E, in Figure 8. A similar pattern
c = (vF/kbs)exp(AEi,JRT)
(16)
On the basis of this interpretation, it not surprising then that Vhyd can be larger than the value calculated from the molecular size of the solute (i.e., the quantity VF/S). The factor exp(AEht/ RT) accounts for anomalies in vhyd. Positive values of AEht would indicate attractive solute-solvent interactions. Equation 16 predicts that DSE plots will not be linear. However, because the actual value of AEht is less than RT over the temperature range of our measurements, the slope is essentially constant. Alternatively, we can associate AEht with changing boundary c o n d i t i o n ~ ~ lby - ~giving ~ the friction factor F an exponential functional dependence of the form exp(AEht/RT). Such a functional dependence is intuitively appealing. The normal stick boundary condition, F = 1, is obtained when AEh, = 0. Positive values of AEh, would then lead to "superstick" boundary conditions. Moreover, superstick boundary conditions are expected to be more important at lower temperatures than at higher temperatures (e.g., exp(AEh4RT) increases with decreasing temperature). The magnitude of AEht determines the rate at which the boundary conditions change with temperature. For large positive values of Mint,the boundary condition changes rapidly with temperature. In the normal hydrodynamic model under stick boundary conditions, the f i s t solvent layer sticks to the rotating body because of surface drag due to collisions of solvent molecules with the molecular "bumps" on the solute.% In principle, frictional drag can therefore occur in the absence of any specific solute/solvent interactions, as long as the surface of the rotating solute body has sufficient roughness. In this case, only the banier to solvent flow (i.e., the viscosity activation energy) governs the rotational motion of the solute molecule. These conditions are obviously achieved for large solute molecules rotating in a solvent consisting of smaller molecules. We think that the enhanced solute-solvent coupling present in excited-state rotational diffusion is due to specific interactions
Rotational Diffusion of Merocyanine 540 in Polar Solvents
J. Phys. Chem., Vol. 98, No. 49, 1994 13091
TABLE 6: Comparison of Viscosity Activation Energies and Rotational Activation Energies Et,,,rb kcal mol-' solvent solvent E,,," kcal mol-' E,,," kcal mol-' 2.53 f 0.10 3.07 f 0.35 acetonitrile 1.70 f 0.16 methanol 3.37 f 0.10 3.40 f 0.37 propionitrile 1.86 f 0.10 ethanol 4.62 f 0.29 2.33 f 0.20 butanenitrile 4.29 f 0.10 1-propanol l-butanol 5.39 f 0.44 2.50 f 0.10 pentanenitrile 4.60 f 0.10 1-pentanol 5.01 f 0.52 2.63 f 0.20 5.22 f 0.24 hexanenitrile 5.42 f 0.53 3.02 f 0.20 heptanenitrile 1-hexanol 5.25 f 0.12 6.03 f 0.43 3.43 f 0.32 5.66 f 0.41 1-heptanol octanenitxile 3.76 f 0.44 nonanenitrile
ErOt,b kcal mol-'
2.15 f 0.39 2.31 f 0.61 2.45 f 0.18 3.48 f 0.25 3.14 f 0.51 3.36 f 0.22 3.83 f 0.44 3.89 f 0.62
Viscosity activation energy, E,,, obtained from ref 39 or by fitting viscosities at different temperatures to eq 11. Rotational activation energy, E,,, obtained by linear least-squares fit of semilogarithmic plots of Tt,, versus 1/T over temperature range 288-333 K.
1
'
'
0
0
'
'
'
'
'
'
'
'
'
'
'
'
Alcohols Nitriles
'
'
'
'
'
I
'
'
/
' '1
v 'I
'
5-
4 -
3-
2-
2
3
4
5
6
E,, (kcal mol'')
Figure 8. Correlation of rotational activation energy, E,,,, to viscosity activation energy, E,,. Values of E,, were obtained from the slopes of Arrhenius plots of Trrat. See Table 6 for list of activation energies.
The solid line is a line of unit slope and zero intercept. The dashed lines through the points are linear least-squares fits of data with the following parameters: for nitriles, slope = 0.89 f 0.18, intercept = 0.72 f 0.33, correlation coefficient = 0.928; for alcohols, slope = 0.97 f 0.20, intercept = 0.41 f 0.31, correlation coefficient = 0.973. of the solvent molecules with the zwitterionic state of the dye. In the excited-state, the dye not only rotates but also undergoes trans-cis photoisomerization about the central C-C bond of the polymethine chain.43 During isomerization the bond must go from being a double bond to a single bond. As the resonance structures show (Figure 1), single bond formation must be accompanied by intramolecular charge transfer. Isomerization about the central C-C bond is accompanied by the acquisition of significant zwitterionic character, which tends to favor stronger interaction with the solvent. In contrast, because of the large activation barrier in the ground state ( ~ 3 kcal/mol 9 in 95% ethanol),@isomerization does not occur during rotational diffusion. Dielectric interactions in the ground-state rotational diffusion would therefore only involve the solvent and the dye molecule in mainly the weakly polar state. Regardless of whether one characterizes the reorientational dynamics in terms of a local viscosity or changing boundary conditions, the quasi-hydrodynamic approach leads to the slope in a DSE plot being a function of the solute-solvent interactions. As our studies indeed show, the slopes are not the same for the nitriles and alcohols. This difference must be a manifestation of the fact that alcohols are strongly associated solvents, whereas nitriles are not. However, the trend is not what one would have expected from a simple consideration of the usual specific solute-solvent interactions. In alcohols, solute-solvent and solvent-solvent interactions are dominated by hydrogen bonding, which is stronger than the dipole-dipole force that mainly governs the interactions in nitrile solvents. This picture would imply that the slope should be greater for
the alcohols than for the nitriles, which is opposite to what is actually found experimentally for MC540 in these solvents. Furthermore, if one views Mintas being related to the energy of these specific solute-solvent interactions, Mintshould be greater for the alcohols than for the nitriles, which is contrary to the data. These discrepancies can be resolved if we realize the local solvent structure is perturbed by the solute. The rotational diffusion time can be then viewed as a measure of the relaxation of the solute-perturbed local solvent structure. Because ions exert strong forces on solvent molecules, the local solvent structure around a charged dye molecule, such as MC540, should be more highly perturbed than around an uncharged dye molecule.65 The degree of the perturbation will depend on the relative strength of solute-solvent vs solvent-solvent interactions. In order to accommodate the charged solute, reorganization of the local solvent structure must occur. For alcohols, this reorganization inevitably involves the breaking up of the hydrogen-bonded network around the solute. Because the molecules in nitrile solvents are not strongly associated, reorganization of the solvent molecules around the charged solute should occur more readily. If the Stokes shift is a measure of the solvation energy of the solute molecule, the spectral data (Figure 2 ) would indicate that MC540 is more highly solvated in nitriles than in alcohols. We envision that in nitriles MC540 is surrounded by the polar cyano groups of the solvent molecules, with the alkyl chains pointing away. This would lead to an effective hydrodynamic volume which is larger in nitriles than in alcohols. A more highly solvated solute molecule would also be consistent with the higher value of Mint for the nitriles than for the alcohols. Indeed, Vauthey,66 in a recent transient grating study, noticed that the rotational diffusion time for the dye, nile red, in alkanenitriles is anomalously longer for the higher members of the series than for the lower members. The longer times were attributed to the formation of a micellelike solvent structure around the dye molecule.
4. Conclusions This work lends further credence to our previous result that the rotational diffusion of MC540 in polar solvents is well described by hydrodynamics and that dielectric friction does not play much of a role. We attribute deviations from DSE behavior to specific interactions of the solvent with the zwitterionic state of the dye. These interactions lead to enhancement of the solute-solvent coupling in the excited state and therefore to values of zrOtwhich are greater in the excited state than in the ground state. The temperature-dependent data indicate that the local viscosity can be represented by the product of the solvent shear viscosity and an exponential factor exp(AEint/RT), where AEintis the energy of these specific solutesolvent interactions that give rise to the enhanced solute-solvent coupling. The larger values of zmtcan also be taken into account by invoking changing boundary conditions, where the friction
13092 J. Phys. Chem., Vol. 98, No. 49, 1994 factor F is replaced by exp(AEht/RT). Surprisingly, the value of A&, is greater in nitriles than in alcohols. We think this difference is a consequence of greater solvation in nitriles than in alcohols. This would be consistent with the Stokes shift data and the larger hydrodynamic volume which is found for MC540 in the nitriles. Finally, these studies point to the importance of using appropriate solute molecules to test the various models for rotational diffusion. In order to further confirm these conclusions, the reorientational dynamics of an uncharged merocyanine dye must be investigated. Because such a dye would be soluble in nonpolar as well as in polar solvents, the dye’s reorientational dynamics can be studied in the absence of dielectric interactions. Lastly, electronic structure calculations on charged and neutral merocyanine dyes must be performed in order to obtain a more realistic representation of the charge distribution for use in dielectric friction models. These studies are currently in progress in our laboratory.
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