J. Phys. Chem. 1995, 99, 14231-14239
14231
Rotational Relaxation of Carbocyanines. Comparative Study with the Isomerization Dynamics Marcia Levitus, R. Martin Negri, and Pedro F. Aramendia" INQUIMAE, Departamento de Quimica Inorgiinica, Analitica y Quimica Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellbn 2, Ciudad Universitaria, I428 Buenos Aires, Argentina Received: April 28, 1995; In Final Form: July 14, 1995@
Steady-state fluorescence anisotropy was measured for a series of carbocyanines in normal primary aliphatic alcohols as a function of temperature. From these values, rotational correlation times (&) were obtained. They were compared with the ones calculated by modeling each molecule by a prolate rotor or an asymmetric rotor, under stick or slip boundary conditions for rotation. The two types of rotor render very similar results. The smaller carbocyanines show a stick rotation regime at low viscosity (7) and a contribution of dielectric friction to the total friction. One dicarbocyanine has a substick behavior at low 7 and reaches the stick limit at high y. The other dicarbocyanines follow the stick regime in the whole viscosity range. The dependence of on y is compared with literature values of the isomerization rate constant's (/cis,,) dependence on 7. Both processes involve large movements of molecular fragments of similar sizes, which are influenced by the solvent viscosity. However, while q5r is proportional to 7, ki,, shows a different behavior. The analysis of the data obtained for different carbocyanines in primary alcohols allows us to conclude that the different viscosity dependencies of ki,, and of r$f arise in the different time scales in which the molecule experiences the solvent friction opposite to the motion.
Introduction
Further extensions and modifications to eq 1 were prop o ~ e d . ' ~ , ~Many ~ - * ~authors found a systematic deviation from Carbocyanines belong to the family of polymethine dyes, Kramers' hydrodynamic equation for c a r b o c y a n i n e ~ ~ ~ ' ~ ~ ~ ~ ~ ~ ~ which have been extensively studied mainly because of their and also for other compound^.^^-^^ The origin of this disagreeability to photosensitise silver halide colloids in photography,' ment has been analyzed on the basis of the breakdown of the and their use as active dye laser media or as mode-lockers of assumptions of the model as follows. (i) The difference between dye lasers.2 the solvent bulk viscosity, y, and the local microscopic friction The photophysics of carbocyanines and other polymethine has been found responsible for the deviations or for part of them dyes, arising upon excitation in the n-n* visible-NIR absorpin some (ii) The frequency dependence of the tion band, is dominated by a very fast isomerization process friction has also been extensively studied as responsible for the which takes place from the first excited singlet ~ t a t e . ~ -The '~ deviation between experiment and theory and various models isomerization begins with a twisting of the molecule around taking into account this non-Markovian friction have been one of the carbon-carbon bonds of the polymethine chain to developed; they provide a very accurate description form a twisted molecule in the excited state hypersurface. This though a number of parameters experimentally difficult to twisted state decays to the ground state hypersurface, where determine have to be added to the description. (iii) Finally, the reaction path branches to yield the ground state photoisomer the contribution of more than one coordinate to the isomerization or return to the thermodynamically stable ground state (N). The has been analyzed for a few cases.28 twisting process competes with fluorescence emission and We see the first explanation as a local difference between intemal conversion from the first excited singlet state to the bulk viscosity and the local friction, whereas the second N.3.8,12,14,19 one is a temporal diyerence between slowly moving molecules Isomerization involves a big molecular movement, and it is and very fast moving molecules, which are the ones that an activated process, which is thus very much influenced by experience photoisomerization. We do not analyze the third temperature and the medium. The activation energy has an possibility, as we think that it plays a minor role, if any, in the electronic contribution and a medium dependent component, isomerization of symmetric carbocyanines, as was previously which can be influenced by viscosity, polarity, or both.4,7,9,11,20,21 discussed.I2 On the other hand, intemal degrees of freedom For symmetric carbocyanines, the medium influence on phodo not have an influence on overall rotation of the molecule. toisomerization is exclusively through the viscosity In a previous paper, when studying the photoisomerization (y).5.9,12,14,15.22,23 The first approach to a quantitative description dynamics of a series of symmetric carbocyanines in n-alcohols of the isomerization rate constant (ki,,) is based on Kramers' as a function of temperature,I2 we found that Kramers behavior, derivation,20which in its hydrodynamic limit adopts the form: as given by eq 1, was obeyed by those molecules having an electronic energy barrier of ca. 10 Idlmol, for which almost the kiso = A ( v / B ) [ ( ~ + (B/v)2) 1/2 - 11 exp(-EdRT) (1) Smoluchowski limit applied and kiso was dependent on y-I. For in which EO is the electronic energy barrier to isomerization, molecules with increasing electronic activation energy, the and A and B are constants related to the curvature of the energy dependence of kiso was surface at the bottom of the well and the top of the barrier, respectively. kiso= Dy-"exp( -EdRT) (2) with 0 5 a 5 1 and D being empirically adjustable constants. * To whom correspondence should be addressed. This behavior was also found in several other cases.7,9,11,14,31,33.35.36 Abstract published in Aduance ACS Abstracrs, September 1, 1995. 14925-27
@
0022-365419512099-14231$09.0010 0 1995 American Chemical Society
14232 J. Phys. Chem., Vol. 99, No. 39, 1995
Levitus et al.
which accounts for the different sensitivities of the optical elements of the spectrofluorimeter to the polarization direction of the light, is given by G = IHVtZHH. The steady-state anisotropy was measured at different combinations of excitation and emission wavelength in the n-n* absorption band. Values with the smallest dispersion were obtained by recording the (3) fluorescence intensity at a fixed wavelength near the emission maximum upon excitation of the sample at a wavelength ca. In eq 3, k is Boltzmann’s constant. If the molecule is not a 30 nm shifted to the blue of this maximum. Measurements were sphere but can be modeled by an ellipsoid of revolution or by performed in the different alcohols at various temperatures an asymmetric ellipsoid, two or three different rotational between 0 and 70 “C (maximum variation range, because correlation times arise, re~pectively.3~-~~ temperature range was dependent on the properties of the In principle, the rotational correlation times can be obtained alcohol). To obtain the maximum fluorescence anisotropy (ro), from fluorescence anisotropy measurements, as molecular measurements in glycerol 87% v/v in water were performed rotation is the main depolarization channel in dilute s o l ~ t i o n . ~ ’ , ~ ~ between 40 and -10 “C. The values of the viscosity of the Furthermore, molecular rotation resembles photoisomerization alcohols at the different temperatures were obtained from the because in the latter, two parts of the molecule, which are similar in size, rotate relative to each other. The spatial domain in c. Fluorescence Lifetimes. The emission decays of DTDCI which the two processes take place is very similar, and the two and HIDCI at 18 “C in MeOH, PeOH, OcOH, and DecOH were processes should experience a similar friction. Rotational obtained by the single-photon timing technique. The samples correlation times should then be a good measure of the local were excited by the output of a cavity-dumped, rhodamine 6 G friction experienced by the molecule during photoisomerization. dye laser (590 nm), synchronously pumped by a mode-locked This was already suggested and measured for some carbocyaargon ion laser. The details of the equipment are given nines’sa and for stilbene and related compound^.^^ Nevertheel~ewhere.4~3~ Each decay had about lo4 counts in the peak less, a systematic comparison between the viscosity dependence channel. The total number of channels was 511. Time of photoisomerization and rotational correlation times has not increments (time calibrations) per channel of 12 and 24 ps were been carried out for carbocyanines. In the present paper, we used. 6 function convolution, using the decay of a monoexanalyze the viscosity dependence of & and compare it with the ponential decaying reference compound (HIDCI in EtOH), viscosity dependence of k,,, (previously measured’2, for five collected at the magic angle, was used in the deconvolution of symmetric carbocyaninesin n-alcohols. We discuss the different the decay^.^^,^^ The fluorescence lifetime of the reference viscosity dependence in terms of what we previously called the compound, zr, was left as a freely adjustable parameter in the local difference and the temporal dzrerence. analyses and the same value of zr was obtained in all cases (zr = 0.85 ns). The solution of HIDCI in EtOH was chosen on Experimental Section the basis of the fact that the reference compound should absorb a. Chemicals. All carbocyanines [3,3’-diethyloxacarbocyaand emit in the same spectral range as the compounds to be nine iodide (DOCI), 3,3’-diethylthiacarbocyanineiodide (DTCI), measured and the value of zr must be shorter than the values of 3,3’-diethyloxadicarbocyanine iodide (DODCI), 3,3’-diethylthithe fluorescence lifetimes. Single-curve analysis was performed, adicarbocyanine iodide (DTDCI), and 1,1’,3,3,3’,3’-hexamethand the decays were fitted by a sum of exponential terms (one ylindodicarbocyanine iodide (HIDCI)] were used as supplied and two). The fitting parameters were determined by minimizby Kodak, Lambda Physik, or Exciton, and their purities were ing the reduced x2. The fits were considered as statistically checked by HPLCI2 (To have the same atom numbering for all satisfactory when x2 I1.3 and Z,2 I3 [Zx2= ( ~ / 2 ) ” ~-&l), ~ carbocyanines, we use the numbering scheme of Figure 2, even where represents the number of degrees of f r e e d ~ m ] . ~ , ~ ~ for HIDCI, which would then be 1,1,1’,1’,3,3’-hexamethylinResults dodicarbocyanine iodide). The alcohols [methanol (MeOH), ethanol (EtOH), pentanol (PeOH), octanol (OcOH), and decanol For HIDCI and DTDCI, at 18 “C in MeOH, PeOH, OcOH, (DecOH)] were analytical grade or freshly distilled. and DecOH, monoexponential fluorescence decays were obb. Absorption and Steady-State Fluorescence Measuretained. The same behavior has been reported for other carbocyanines.*-’‘ ~ ‘ 5 ~ ’ 6 ~ 2 2 ~ a ~ 4 7The ments. Absorption spectra were recorded with a Shimadzu W~ 4 8 fluorescence lifetimes, zf, of 160 spectrophotometer. Steady-state fluorescence spectra were the above mentioned solutions were used to calculate the recorded using a Perkin Elmer LS5 spectrofluorimeter equipped radiative rate constant, kf = &/zf,where & is the fluorescence with polarizers. The instrument has a 90” configuration for quantum yield, measured previously under the same condiexcitation and emission directions. The sample was contained tions.I2 The values of kf are, for both carbocyanines, indepenin a 10 mm excitation path, 4 mm emission path quartz cuvette dent of the solvent. Furthermore, these values are in excellent provided with a thermostatization jacket. The temperature was agreement with those calculated by the Strickler and Berg controlled by a Lauda RCS 6 thermostat-cryostat and measured equation.49 They are also independent of the temperature in in the cuvette with a PtlOO thermometer. In all cases absorbance the range considered.l2 Therefore, it is very well established was kept lower than 0.05 in 1 cm to minimize depolarization that the value of kf of HIDCI and DTDCI is a constant effects due to reabsorption or energy transfer. independent of solvent and temperature. For DOCI and DTCI The steady-state fluorescence anisotropy, (r), is defined as it was not possible to measure the values of zf because of the (r) = (IVV - GZVH)/(ZVV f ~ G I v H )where , I stands for the unfavorable spectral conditions for excitation with the output fluorescence intensity and the first and second subscript refer of a rhodamine laser. Then, the kf values for DOCI and DTCI to the settings of the excitation and emission polarizers, were calculated using the Strickler and Berg equation. For respectively. The vertical orientation (V) denotes the direction DODCI we used the value of ref 16. These values are constant perpendicular to the plane of the excitation and emission beams, for each compound and, for DOCI and DTCI, have been and the horizontal orientation (H) is perpendicular to V and to successfully used in a previous workI2 for the calculation of photoisomerization rate constants. the direction of the propagation of the beam. The factor G, On the other hand, molecular rotation is also influenced by solvent viscosity, as described by the Stokes-Einstein equation for the rotational correlation time (&) of a spherical molecule of volume V (eq 3):37
Rotational Relaxation of Carbocyanines
J. Phys. Chem., Vol. 99, No. 39, 1995 14233
5
3 2
'y
2' 3' 8
9
k
k Ir
0.1
0.3
0.0
0.2
4'
R
I+++++-+ 19
In plane
DODCI
= I*
Out or plane
bc
DOCI
0
Figure 1. Steady-state fluorescence anisotropy in different solvents as a function of temperature. Solvents: (0)methanol; (0)ethanol; (V) pentanol; (v)octanol; and (0)decanol.
The steady-state anisotropy ((r))was independent of excitation and emission wavelengths for d l compounds, within the visible n-n* transition. No difference could be detected in ( r ) at a certain temperature, when it was reached in upward or downward directions. For DOCI, DTCI, and HIDCI in methanol and ethanol, and for the other compounds in methanol, an increase in ( r ) was observed upon raising the temperature. In all other cases, the normal behavior of a decreasing (r) with temperature was observed. The temperature dependence of (r) in different alcohols is shown in Figure 1 for DOCI, DODCI, and HIDCI, the three examples chosen for illustration of results in this work. The values of ro were derived from the measurements in 87% v/v glycerol, as listed in Table 1. The values of ro are very near the maximum expected for an isotropic medium, which is 0.4.50 From ro, the angle between the absorption and emission dipoles @) is calculated according to eq 4.50
ro = (3 cos2 /?- 1)/5
(4)
They are all around 1 2 O , as shown in Table 1. In order to calculate the rotational dynamics of the carbocyanines, the molecules were modeled by an ellipsoid. The molecular structure of a carbocyanine and the axes choice for the modeling are described in Figure 2 (axis 3 is perpendicular to the plane of the paper, with the positive direction pointing
0 Figure 2. Top: Molecular structure of a carbocyanine showing atom numbering and orientation of two of the principal axes of rotation (For practical reasons we will use this numbering scheme also for HIDCI, which would then be 1,1,1',1',3,3'-hexamethylindodicarbocyanine iodide). The third axis, number 3, is perpendicular to the plane of the molecule and pointing in the upward direction. Middle and bottom: molecular model of DOCI and HIDCI superimposed on the in plane projection of the ellipsoid used to model the molecule. To the right the projection of the ellipsoid in a plane perpendicular to the plane of the molecule is shown. The asymmetric rotor is shown in the upper diagram, and the prolate rotor, in the lower one of each molecule.
upward). The general expression for the time dependent fluorescence anisotropy, r(t), is the sum of five exponentials for a general ellipsoid with arbitrary orientations of the absorption and emission transition dipole The carbocyanines studied in this work are molecules with CzV symmetry, with an all-trans conformation in s o l ~ t i o n , 5 ~ and -~~ according to the small Stokes shift of the fluorescence emission,
TABLE 1: Photophysical Parameters of the Excited State of Carbocyanines substance ro P t P (ns) 4P kf (lo8s-') &rmaxc DOCI 0.376 11.5 0.3 0.12' 4.6 1.00 DTCI 0.370 12.9 0.3 0.071' 2.7 1.00 DODCI 0.375 11.8 1.2 0.42'f 4.0 0.90 DTDCI 0.370 12.9 1.5 0.35c,g 2.4 0.65 HIDCI 0.377 11.3 0.6 0.14' 2.4 0.60 in
AXIS I
8'
Dd
a
Eo (H-mol-I)
2.0 x 10" 2.3 x 10" 8.0 x 10" e 5.6 x lo'*' 4.1 x lo'*'
0.92' 0.82' 0.43' 0.51' 0.72'
1o c 10' 11.3' 24' 20'
Angle between absorption and emission dipoles, calculated according to eq 6. In ethanol at 25 OC. From ref 12. Values for 7 in CP and k,,, see eq 2. e From ref 14.'From ref 47. 8 From ref 79.
SKI,
14234 J. Phys. Chem., Vol. 99, No. 39, 1995
Levitus et al.
+ c2> = 3(b2Q+ c2R)
TABLE 2: Geometric Parameters of the Carbocyanines,
16vn(b2
Obtained According to the Texta van der waals substance
volume(A3)
DOC1 DTCI DODCI DTDCI HIDCI
303 326 33 1 354 386
prolate rotor a(& b(A) 8.4 8.1 9.1
10.0 9.6
asymmetric rotor a @ ) b(A) c(A)
2.9 3.0 2.9 2.9 3.1
8.4 8.1 9.1 10.0 9.6
4.3 4.5 4.1 4.2 3.1
a The semiaxis length a is taken along the longest molecular axis; c is the semiaxis length in the out of plane direction (see Figure 2).
the geometries of the excited and the ground states should be very similar. The n-n* transition moment is oriented along the longest axis of the m o l e ~ u l e(axis ~ , ~ 1~in Figure 2), and in this case r(t) reduces to a double exponential:
+
+
r(r) = 0.3{(B + A ) exp[-(6D 2A)tl ( B - A ) exp[-(6D
- 2A)tl) ( 5 )
where B, A, D, and A depend on the director cosines of the absorption and emission dipole moments ( y r and qr , i = 1, 2, 3, respectively) with respect to the principal axes of rotation of the molecule (these are axes 1, 2, and 3 taking into account the symmetry of the molecule). According to Figure 2 and the above discussion, yl = 1 and the other two y r values vanish. To determine the values of the three qr, we have to consider the angle p formed between the absorption and emission dipoles as calculated above: this angle defines only the surface of a cone where the emission dipole lays and this fixes the value q1 = cos p. For the other two values, we consider two limiting cases: case I, where the emission dipole is in the plane defined by axes 1 and 3, or case 11, where the emission dipole is in the plane defined by the axes 1 and 2. In case I, q 2 = 0 and q3 = sin p; and in case II the values are exchanged, so q 2 = sin /3 and q3 = 0. Considering these orientations of the transition moments, the parameters B, D, and A in eq 5 have the expressions given by eqs 6, which are identical for the two cases, and A is given by eqs 7 and 8 for cases I and 11, respectively, which have axes 2 and 3 exchanged, as expected.
COS^^ - -31
(64
+ D22 + D32 - DID2 - D2D3 - D3D1)1/2
(6b)
B=
A = (D12
1 D = 3(DI
+ D2 + D3)
=
16vz(a2
+ c2)
+ c2R) 16rp(a2 + b2) f3 = 3(a2P + b2Q)
2.0 2.0 2.0 2.0 2.6
f2
3(a2P
where P, Q, and R are elliptical integrals as follows:
P = J(Q2
+ x)-'[(a2+ x)(b2+ x)(c2+
X ) p 2
dx
Q = ~ ( b 2 + ~ ) - ' [ ( ~ 2 + ~ ) ( b 2 + ~ ) ( ~ 2 + (11) ~)]-112dx R=
hm(c2+ x)-'[(a2+ x)(b2+ x)(c2+ x)]-'I2 dx
For the expression describing the three Di's (eq 9), another correction factor should be added arising from the boundary condition for rotation. This factor is unity for the stick regime (when the molecule rotates with solvent molecules attached to its surface) but differs from unity in the case of the slip regime (when the molecule rotates with no solvent attached). For the latter case, the appropriate values of the correction factor (dependent on the ratio of the semiaxes lengths) were taken from the l i t e r a t ~ r e ~ (see ~ - ~ below). ' The value of B in eq 5 can be readily calculated taking into account the value of ro and eqs 4 and 6a:
The integrals of eqs 11 were numerically solved in order to calculate the other parameters. For the prolate rotor, the integrals P,Q, and R are tabulated;39the numerical integration method that was used could reproduce them in all cases. The values of the axes lengths were obtained by molecular models using the following criteria. The van der Waals volumes (Vvdw) were calculated for the carbocyanine cations by the addition method suggested by Edward and B ~ n d i . ~This ~ , method ~~ renders molecular volumes which are comparable to those obtained by other methods, when used for carbocyanines.4°,64 The semiaxis length Q was taken as fixed and equal to the distance between the hydrogens bonded to carbons 5 and 5' of the benzene moieties (see Figure 2 ) plus two times the van der Waals radius of a hydrogen atom. From these two criteria, the value of the other molecular axis b was calculated for a prolate rotor according to eq 13:
(7)
The Di's are the three principal diffusion constants, given bys7 D j = kT&,
(9)
where fi are the friction coefficients, dependent on the length of the axes of the ellipsoid and on viscosity. The ellipsoid which models the molecule is characterized in general by three different semiaxis lenghts, named a, b, and c with respect to axes 1, 2, and 3 of the molecule, respectively (see Figure 2). The fi's have the expression^^^-^^
with b = c. Using the asymmetric rotor model, the length of the shortest molecular axis, c (the one giving the thickness of the molecule out of the plane), was fixed at 2.0 A for all the molecules except HIDCI,for which the value was 2.6 A, in view of the presence of the four methyl groups bonded to carbons 1 and 1'. The semiaxis length b was calculated using eq 13. The way the molecules can be represented by the prolate and asymmetric rotor is depicted in Figure 2, where a molecular model is superimposed on the in plane and out of plane projections of the ellipsoids. All geometrical parameters of the carbocyanines, obtained using these criteria, are listed in Table 2. Using these values
Rotational Relaxation of Carbocyanines
J. Phys. Chem., Vol. 99, No. 39, 1995 14235
TABLE 3: Values of the Parameters Determining the Time Dependent Anisotropy, According to Eq 14, Calculated for the Two Models of Rotor As Described in the Text, Compared with Experimental Value# DOCI
DTCI
DODCI
DTDCI
HIDCI
1.5 x 107 2.9 x 107
1.4 107 2.6 x 107
1.5 x 107 3.2 x 107
1.4 3.4 x 3.0 x 1.2 x
1.3 x 3.2 x 2.8 x 1.1 x
1.4 107 3.5 x 107 3.8 x 107 5.9 x 108
Prolate Rotor ClSUck (cP/(sK)) ClsllP(cP/(sK))
2.1 107 3.6 x 107
1.9 x 107 4.3 x 107
CI"Ick (cP/(sK))
1.9 x 107
C2S"Ck (cP/(sK)) Cis"P(cP/(s*K)) C2s"P(cP/(s*K))
3.7 x 107 4.4 x 107 9.1 x 107
1.7 x 107 3.3 x 107 4.1 107 8.5 x 107
6, stick
2.6 x 10-4 0.058
Asymmetric Rotor
6, slip
6, stick 6, slip
107 107 107 108
107 107 107 108
Emission Dipole on the (a,c) Plane
-1.2 x 10-4
0.049
3.4 x 10-4
3.0 x 10-4
0.003 0.059 Emission Dipole on the (a,b) Plane -1.8 x 10-4 0.047
-1.3 10-4 0.001
3.8 10-4 0.003 -1.8 7.7
10-4 10-4
1.1 x 10-4 1.0 x 10-4 -7.3 x 10-5
-8 x
ExDerimental Cexp (cP/(pK))
1.10 x 107
1.40
107~
1.37 x 107
1.36
107
1.48 x 107
For ro see Table 1. the integrals in eqs 11 can be evaluated and the three Di's can be obtained. This renders A, B, D, and A for r(t) in eq 5, which we will rewrite as
where 4r1,2 are the two rotational correlation times. Equation 12 relates ro and B. The other parameters in eqs 5 and 14 are related by
6 = 0.3(8 - A )
each other, the two orientations considered for the emission dipole yield practically the same results. When the anisotropy decay is represented by a sum of two exponentials, (r) is given by eq 1738
and the two rotational correlation times 4 r ~=, (C1,2)-l(q/T) ~ (see eq 15) cannot be obtained from the single value of (r).For this reason, we calculate the function 4, defined by eq 18:
( 15a)
(15b) The values of 6 , CI, and CZ were calculated for all the carbocyanines, modeled by a prolate and an asymmetric rotor, considering the two orientations of the emission dipole described above, and for the stick and the slip rotation boundary conditions (see Table 3). For the later rotation regime, the values of Di were obtained using the slip to stick coefficient ratios of Youngren and A c r i v ~ sas~ corrected ~ by Sension and Hochstrassep for the asymmetric rotor. The corresponding values of the prolate rotor were obtained from the table calculated by Hu and Zwanzig.61 For the prolate rotor, a single-exponential decay is always obtained for r(r), for symmetry reasons, and consequently always 6 = 0 in eq 14 for both stick and slip boundary conditions. The symmetry also explains the equivalence between the two orientations of the emission dipole for this rotor. When only one rotational correlation time is present, & can be easily calculated from (r), considering ro and zfusing eq 16:
For the asymmetric rotor, r(t) is a sum of two exponentials. For the stick regime, the values of Table 3 show that one component accounts for more than 99% of the anisotropy decay. Under the slip boundary conditions, the weight of the second exponential term increases up to 15% for DOCI and DTCI, but it is still very small for the other cases. As the two smaller dimensions in the asymmetric rotor do not differ much from
which coincides with Cpr in the case of a monoexponential anisotropy decay. Since rf is temperature and viscosity dependent for the carbocyanines, its value should be calculated using values of 4f determined under similar conditions as those for the measurements of ( I ) :
where kic is the intemal conversion rate constant. The necessary values to compute Tf from eq 20 are given in Table 1.
where the maximum fluorescence quantum yield is q5f max = M(kf + k c ) . The function 4 of eq 18 is used to compare models that predict a sum of two exponentials with monoexponential decays. In order to do this, we calculate ( r ) from eq 17 using the values of Table 3, and finally, we obtain 4 with eq 18. In all cases, the difference between 4 and &I is negligible. This is so even for DOCI and DTCI under slip conditions, because for 412 the smaller amplitude corresponds to a shorter rotational correlation time, which according to eq 17 lowers even more the contribution to (r). Straight lines are used to represent 4 as a function of v/T for the different models and the different boundary conditions in Figure 3. The experimental values of the constant Cexp,obtained with eq 21, are also listed in Table 3, and the
Levitus et al.
14236 J. Phys. Chem., Vol. 99, No. 39, 1995
6E
'
'
'
I .
0
3
1
DOC1
1
HlDCl
0.6
0.4 2
m
In
c W
C
U
0
c
4
L
4
1
I
0.00
0.0
J
HlDCl
8
n
0.2
0.6 0.4
0.02
0.04
0.06
0.08
1
I
-I
/ '
.....
4
0.0 0.000 0 . 0 0 2 0.004 0.006 0.008 0.010
7)/T (cP/K) Figure 3. Function 4, as defined by eqs 18 and 21 of the text, plotted against q/T for the carbocyanines in all solvents. Experimental values of (r): (V) methanol; (A) ethanol; (0)pentanol; (0)octanol; and ( 0 ) decanol. The dotted lines were calculated for the prolate rotor, and the full lines, for the asymmetric rotor with the geometric parameters of Table 2. The two upper lines represent the stick condition, and the two lower lines correspond to the slip regime.
values of q5exp are represented as dots in Figure 3.
Discussion Influence of the Excited-State Isomerization Rate Constant on the Temperature Dependence of (r). The anomalous increase in ( r ) with temperature observed in methanol, and in some cases, also in ethanol, can be interpreted on the basis of the shortening of zf upon temperature increase in these carbocyanines. As isomerization competes with fluorescence emission, the increase in kiso (k,,, = 17-O exp(-EdRT), according to eq 2) lowers zf. The polarization state of the emission depends on the competition between rotational correlation time (proportional to v/T) and excited state lifetime (see for example eq 16 for the case of only one rotational correlation time). When the decrease is greater for zf than for &, ( r ) is expected to show the behavior described, opposite to the normal one. This effect is only observed when ki,, >> kf k,,, because in these cases the influence of k,,, on zf is at its maximum. For other conditions, zf does not decrease so fast because h,, is comparable to the sum kf k,, or much smaller than this sum. The results obtained for the different cyanines are discussed separately in the next sections. HIDCI: Stick or Slip Boundary Conditions? The agreement between experiment and modeling is very good for HIDCI. It is not possible to distinguish between a prolate rotor and an asymmetric rotor, but the value of CIStlckfor either of them
+
+
Figure 4. Same plot and symbols as for Figure 3, but in a more restricted viscosity range.
reproduces the values of (r) very well. This rotation regime was also found for other carbocyanines.@ The anisotropy decay of HIDCI is predicted to be monoexponential. However, the fitting of the experimental data to the stick limit is a misleading conclusion of the type of representation in Figure 3, as we demonstrate in what follows, because it overweighs the importance of the higher viscosity range values. Figure 4 shows the same data from Figure 3 in the low viscosity range. In this range, the slope of 4 vs q/T is smaller than the mean value obtained considering all experimental data. Although the same is found for DODCI and DTDCI, the changes of the slopes are not so pronounced as for HIDCI and are discussed separately in the next section. If we consider, on the basis of the previous experimental evidence and calculations, that the molecules are well represented by a prolate rotor and that only one & is present, then eq 22 holds:
where vh = Vvdwfig) is called the hydrodynamic volume of the molecule, f i g ) is a shape factor depending on the ratio of the axis lengths alb, which is tabulated for symmetric r ~ t o r ~ , ~ ~ , ~ ~ and g ( g ) depends on the rotation regime, being unity for stick boundary conditions and having the values calculated by Hu and Zwanzig6' for the slip regime. Considering that zf = &/kf and taking into account eq 22, eq 16 can be rearranged to eq 23
A plot of ((r)-I - r0-I) against &T/v gives more weight to the low viscosity range values and consequently shows differ-
Rotational Relaxation of Carbocyanines 0
0
t c
20
-
15
-
20
10
30
J. Phys. Chem., Vol. 99, No. 39, 1995 14237 40
50
DODCI
I
/?
-
V
\ 50
0
0
100
150
200
I
1
I
I
I
10
20
30
40
50
250 / I
60
Figure 5. Plot according to eq 23 of the text. Dots are experimental
values, and the line is the least-squares best fit to the data. ences with the results of Figure 3. The same experimental values as in Figure 3 are represented in Figure 5 according to eq 23. For HIDCI we obtain Vhg(@) = 589 A3. For the axial ratio a/b = 3.10, fle) = 2.5 and g(g) = 0.50 for slip conditions; consequently VvdW = 470 A 3 if we consider the slip regime and 235 A3 for the stick regime. The actual volume is intermediate between these two values. The negative intercept obtained for this compound suggests that ro would be 0.44, which is unexpected in solution. We obtain such a result for this representation because there is a change in rotation regime. From the above discussion we can conclude that HIDCI shows a change in the rotation regime from slip condition to stick condition as q increases. This compound reaches the slip limit at low q more clearly than the others, showing a lower interaction with the solvent, probably because the four methyl groups in carbons 1 and 1' prevent hydrogen bridging to the solvents. DODCI and DTDCI. Equation 23 was used for the case of DODCI and DTDCI also. We obtain Vhg(g) of 836 and 977 A3 from the plots of ((I-)-' - r0-I) against &T/V, for DODCI and DTDCI, respectively (plot shown in Figure 5 only for DODCI). Considering the axial ratios obtained from Table 2, the values of fle) are 2.8 and 2.9, respectively, giving VvdW of 300 A3 for BODCI and 340 A3 for DTDCI, both for the stick regime. The regime change is much milder for DODCI than it is for HIDCI, in the viscosity range in which we worked, but a closer approach to the slip limit cannot be discarded at lower viscosity (the lowest viscosity we worked at is 0.38 CPfor this
compound). In the viscosity range of our measurements, DTDCI stays in the stick regime for rotation. DOCI and DTCI: Influence of Dielectric Friction. For DOCI and DTCI the agreement between modeling and experiment is not good, being much worse for DOCI. Both of them show rotational correlation times larger than predicted by the models. This is the principal difference between the dicarbocyanines HIDCI, DODCI, and DTDCI and the smallest cyanines, DOCI and DTCI. Of course modeling the rotation by an ellipsoid is an oversimplification, but it rendered good results for c a r b ~ c y a n i n e sand , ~ ~many ~ ~ ~other ~ example^.^^*^^-^' To analyze the flexibility of the model, we shall take the prolate rotor under the stick boundary conditions as an example (this is also applicable to the asymmetric rotor in view of the similar results it gives in these cases, but calculations are more difficult for the latter rotor). For DOCI, in order to reproduce a Cexpof 1.1 x 1O7 cP/sK, v h = 1250 A3 would be required under the stick boundary conditions. Taking into account the value of VvdW from Table 2,fle) = 4.1 means e = 4.5. Consequently b = 2.5 and a = 11.4 A. The greatest variation in CIStick is obtained by varying the semiaxis length a. A change from 8.4 to 9.0 A lowers CIStLCk from 1.9 x lo7 to 1.8 x lo7 cP/sK (b = 2.8 A). To fit the experimental value requires a length greater than the axis length of the dicarbocyanines, and the molecular shape would be greatly distorted. If we assume that the molecule rotates as an ion pair and we add the ionic volume of the iodide ion (45A3), CIStiCk would only decrease by 5% (this is the case also for the other substances). Finally, we can assume that DOCI rotates with attached solvent molecules. As the plots of Figures 3 and 4 are linear, the total hydrodynamic volume of the rotating fragment should be constant, but this would mean that different numbers of solvent molecules participate in the cluster in the different alcohols, depending on solvent size, or that the shape factor changes in order to keep the value of v h . We have no evidence to discard this explanation, but it seems rather fortuitous that it can be responsible for the behavior observed. For DTCI, the divergence is not so large and an increase in the semiaxis length a from 8.7 to 9.5 8, lowers CISflCk to 1.6 x lo7 cP/s*K,very near the experimental value of 1.4 x lo7 cP/ s*K. Nevertheless, this value of a is almost the length of the dicarbocyanines, and still the agreement is not so good as for the dicarbocyanines DODCI, DTDCI, and HIDCI. As shown in Figure 4 for DOCI (it is also the case for DTCI), the compounds approach the stick regime at low viscosity. The plots in Figure 5 for these compounds give vhg(@)= 854 A3 for DOCI and 994 A3 for DTCI (data not shown), which, taking into account the axial ratio e = 2.9, give VvdW = 368 A3 for DOCI and 428 A3 for DTCI under the stick regime, ca. 25% bigger than calculated. Furthermore, for DOCI, the plot gives a negative intercept. As values of anisotropy greater than ro cannot be expected in solution, the negative intercept of the plot could indicate that ro = 0.376 is wrong and that its value should be bigger or that there is an additional contribution to the friction other than viscosity. Increasing ro to 0.4 (its maximum possible value) does not significantly improve the fit, as the value of 0.44 is needed to fit the data for DOCI. The values of ro obtained for the other carbocyanines in glycerol fit well into the set of ( r ) values measured in n-alcohols. For these compounds a possible explanation for the greater & obtained at higher viscosity, compared to the model, can be the influence of dielectric friction. In this case, the frictions can be added to give eq 24:67-69.72-75
14238 J. Phys. Chem., Vol. 99, No. 39, 1995
where p is the dipole moment of the carbocyanine, Vo is the volume of the cavity in which the solute rotates, E is the static dielectric constant of the solvent, and ZD is the dielectric relaxation time of the solvent. In our experiments, generally higher q is associated with lower E and higher ZD,which makes the two terms in eq 24 increase with q. A plot of q$kT/v against TD(E- 1 ) / ( 2 ~ 1)2 should be linear, according to eq 24, and have an intercept equal to Vhg(g). Aliphatic alcohols have more than one dielectric relaxation time, corresponding to different motions of a cluster of molecules, of a whole molecule or of part of it, taking place in very different time scale^.^^-^* For our calculations, we considered the longest ZD,which corresponds to the reorientation of molecular aggregates of solvent. The amount to which each motion contributes to the dielectric constant of the solvent is not clear for all the alcohols so no quantitative conclusion can be drawn from the value of the slope (see ref 78). The values of the dielectric relaxation times of the solvents were taken from the l i t e r a t ~ r e . ~The ~ . ~plot ~ for DOCI gives Vg(g) = 878 A3, in excellent agreement with the representation of eq 24 (854 A3) and with the predictions for a prolate rotor of VvdW = 303 A3 and g = 3.5 under stick conditions. This value of g is somewhat greater than the value of 2.9 obtained from Table 2, yielding a = 9.6 A (if we conserve VvdW), very near the size of the dicarbocyanines but this time with a good explanation of the results. Similar results are obtained for DTCI (Vhg(g) = 834 A3, g = 3.5, and a = 9.6 A). On the basis of the above discussion it seems reasonable to conclude that DOCI and DTCI attach to the stick regime with an important contribution of dielectric friction to the total friction of rotation. Finally, we explore the possibility of dielectric friction for HIDCI, DODCI, and DTDCI. For HIDCI, the plot according to eq 24 shows a positive slope, comparable to the slope for DTCI and DOCI, but the value of the intercept (Vhg(g) = 414 A3) indicates a slip limit for rotation (with g = 3.1, VvdW = 344 As). The regime change can also account for a positive slope of the mentioned plot, and we prefer this explanation. The plots according to eq 24 for DODCI and DTDCI are horizontal within experimental error and the intercepts coincide with the hydrodynamic volume of the molecules under the stick regime. The conclusion is that dielectric friction does not seem to play a role in the rotation of these compounds. At the present state of the investigations we do not have an explanation for the fact that dielectric friction has an important contribution to the total friction for the case of the smallest cyanines but not for the larger dicarbocyanines. Comparison of Rotation and Isomerization Dynamics. First, we shall analyze the cases of DODCI, DTDCI, and HIDCI, for which rotational correlation times present proportionality with the bulk viscosity of the solvent and the agreement between experiment and modeling is excellent, taking into account only viscosity as responsible for the observed friction. This indicates either that viscosity accounts for the real total local microscopic friction opposite to rotation or that it is proportional to the microscopic friction in all cases studied. The two possibilities are mathematically indistinguishable, as the difference would only affect the proportionality constants multiplying q (for example the volume in eq 3). Strong support for the proposal that the microscopic friction can be described by bulk viscosity arises from the good reproduction of the Cexpvalues from modeling of the rotors with molecular parameters (see Figures 3 and 4).
+
Levitus et al. For DOCI and DTCI there is a contribution of dielectric friction to rotation, but the total friction still remains proportional to q in the solvents studied. Now we consider the isomerizationprocess. Equation 1 fails to describe the photoisomerization from the first excited singlet state of the dicarbocyanines, while this process follows eq 2 with exponents a of 0.43 for DODCI,I4 0.51 for DTDCI,I2 and 0.72 for HIDCI.I2 The most important aspect is that, as was shown in previous works, excited state isomerization and ground state isomerization present different viscosity dependences for all the compounds, while it is evident that the moving fragments have the same size for each p r o c e ~ s . ~ * ' ~ ~ ' ~ The above discussion also points out that rotation and isomerization have different viscosity dependences (+r = q,ks0-' a qa) and, again, the size of the moving fragments is similar in both processes. These facts would discard the size factor or local diyerence as responsible for the departure of isomerization rates from the hydrodynamic limit of Kramers' theory, as expressed in the Introduction. We will focus now our attention on the temporal difference as responsible for the appointed disagreement. For this, we should compare the time scales of rotation and isomerization. The characteristic time for rotation is &, which at room temperature and 1 CPis on the order of 100 ps. Isomerization has an activation energy between 10 and 70 W/mol, depending on the compound and solvent. During the isomerization process, the fate of the molecule is determined by the motion around a very small twisting angle range in the neighborhood of the barrier top. Out of this small space, the thermal bath very rapidly thermalizes the molecule, either to the departure state or forward to the isomer conformation. The amount of time the molecule stays in this space is given by the value of the preexponential factor of k,,,, i.e., (D/q")-',the frequency factor. This value is in the range 0.2-5 ps at 1 CP for the different carbocyanines,as calculated from the parameters listed in Table 1 (see also ref 12). There are two orders of magnitude in the time scale in which the molecule experiences the solvent drag opposite to the motion. In other words, isomer buildup and molecular rotation take place in comparable time scales but the molecule is influenced by friction during the whole rotational motion. On the other hand, during the process leading to isomerization, the motion depends on the friction only in the very small fraction of time the molecule spends in the surroundings of the barrier top. This statement follows from the fact that the reactant (in this case the excited singlet state of the carbocyanine) is in thermal equilibrium and very rapidly goes up and down the vibrational ladder on the twisting coordinate, compared to the isomerization rate. If this were not the case, a wavelength dependent isomerization yield, fluorescence quantum yield, and fluorescence emission spectral distribution should be observed. DOCI and DTCI follow eq 1 for photoi~omerization~~'~ in the excited state, but their departure from this behavior of the isomerization in the ground state is the greatest of all cases discussed.I2 The influence of dielectric friction is not noticed in isomerization as long as the total friction remains proportional to the viscosity. On the other hand, as the dipolar moment of the substances is expected to be quite similar in the ground and excited states, the friction should be the same in both cases. For these compounds, the frequency dependent friction also provides a coherent explanation of the different behaviors observed for rotation and isomerization.
Acknowledgment. This project was supported by research grants from the University of Buenos Aires (UBA), Fundacih Antorchas (Argentina), and Stiftung Volkswagenwerk and GTZ
Rotational Relaxation of Carbocyanines (Germany). M.L. and R.M.N. are student and postdoctoral fellows of UBA, respectively. P.F.A. is a member of the Carrera del Investigador Cientifico y TecnoMgico from Consejo Nacional de Investigaciones Cientificas y Ttcnicas (CONICET, Argentina). We thank Professor Franz C. De Schryver (Katholieke Universiteit, Leuven, Belgium) for providing the facilities to measure time-resolved fluorescence emission. We are indebted to Professor Silvia E. Braslavsky (Max-Planck-Institut fiir Strahlenchemie, Mulheim Ruhr, Germany) for her constant support and encouragement.
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