Article pubs.acs.org/JPCA
Volume Increment Effect on the Photoisomerization of Hemicyanine Dyes in Oligo(ethylene glycol)s Youmin Lee and Minyung Lee* Department of Chemistry and Nanoscience, Ewha Womans University, Seoul 120-750, Republic of Korea ABSTRACT: We studied the excited-state dynamics of three hemicyanine dyes that undergo internal twisting from the localized excited state to the twisted intramolecular charge-transfer state. The dyes differ in the length of the alkyl chain in the aniline moiety and, thus, the volume of the motional moiety increases without having much of an effect on the excited-state potential surface. By employing oligo(ethylene glycol)s as a new homologous series of solvents that covers a high viscosity region, we showed that the excited-state lifetime of the hemicyanines gradually increases at any given viscosity when the size of the substituent increases. We describe our results for the solution-phase photoisomerization processes in terms of the breakdown of Stokes’ law, multidimensionality, and the Hubbard relation.
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INTRODUCTION The photophysical and photochemical properties of polymethine dyes have drawn considerable attention, due to their wide applications in various fields such as photographic sensitizers, optical recording medium, nonlinear optical materials, and fluorescence probes.1−20 Polymethines are classified into two distinct classes: cyanines and hemicyanines. Cyanine dyes are constructed with two identical heterocyclic groups at both ends linked by a polymethine. Hemicyanines are modified cyanine dyes that consist of heterocyclic and nonheterocyclic groups. The nonheterocyclic moiety acts as an electron donor (D), and the heterocyclic moiety acts as an electron acceptor (A). Therefore, hemicyanines belong to the group that includes intramolecular charge-transfer species possessing a D−π−A structure in which the D and A moieties are π-electron conjugated. A typical example of such a hemicyanine dye is trans-4-[4-(dimethylamino)styryl]-1-methylpyridinium iodie (4-DASPI) in which the dimethyl amino group and the methyl pyridinium group act as the (electron) donor and acceptor, respectively. One of the common features of hemicyanines as well as cyanines is that they undergo photoisomerization in the excited state. Figure 1 shows the excited-state potential surface of 4DASPI in which the reaction coordinate is the single bond twisting angle ϕ between the dialkylaniline moiety and the alkylpyridylethylene moiety. The initially prepared Franck− Condon state is relaxed to the localized excited (LE) state, which decays to the ground state or undergoes a downhill motion to the twisted intramolecular charge-transfer (TICT) state. The TICT state nonradiatively decays to the ground sate at ϕ = 90°, which further relaxes to a thermodynamically stable form (ϕ = 0° or 180°). The fluorescence of 4-DASPI originates from LE or its charge-transfer form because the TICT state does not fluoresce. A small activation barrier exists for the LE to © 2013 American Chemical Society
Figure 1. One-dimensional potential energy surface of 4-DASPI with respect to the internal twisting angle ϕ. Eb denotes the barrier height.
TICT process. With an isoviscoisty plot, the value has been measured to be 0.86 kJ/mol,16 which is much smaller than the thermal energy at ambient temperature (∼2.5 kJ/mol). The solution-phase photoisomerization is basically a barrier escaping problem that addresses internal motion subjected to friction exerted by the surrounding media. Such photoisomerization processes of 4-DASPI have been widely investigated in various media, including reverse micelles,2,12 layered inorganics,3 polar solvents,5 nanoporous materials,6,11 ionic liquids,8 sol-gels,9,12 Langmuir−Blodgett films,10,15 and polymers.17,20 Unlike cyanines, both ends of a hemicyanine dye consist of different substituents. Due to this unsymmetrical nature, it is possible to chemically modify only one side without affecting the other part. The main purpose of this work is to determine Received: October 11, 2013 Revised: November 13, 2013 Published: November 21, 2013 12878
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with deconvoluting IRF. The fit was performed on the judgment of weighted residuals and the reduced χ2.
how the length of the alkyl chain influences the excited-state processes of the hemicyanines. We chose three hemicyanine dyes possessing different alkyl chain lengths in the aniline moiety (the donor side). The use of a chemically inert alkyl group should allow the volume of the motional moiety to increase without significantly affecting the excited-state potential surface. In addition, we used a homologous series of oligo(ethylene glycol)s to vary the medium viscosity. Previously, n-alkanes and n-alkanols have been employed to tune the viscosity in the medium friction regions.21−25 This work used oligo(ethylene glycol)s as a new homologous solvents that cover the higher viscosity range. By analyzing the fluorescence lifetimes of the hemicyanines measured in oligo(ethylene glycol)s, we attempted to address some unresolved issues for the excited-state rate processes in the condensed phase.
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RESULTS AND DISCUSSION In the photoisomerization process, the excited-state population decay becomes a single exponential when the barrier height is significantly higher than the experimental temperature. As shown in Figure 1, the excited-state potential surface of 4DASPI is very low or virtually barrierless at room temperature. Therefore, it is not expected to follow a single exponential function, and all of the measured fluorescence decay curves for DMASPI (4-DASPI), DEASPI, and DBASPI were fitted to a sum of exponentials: N
I(t )/I(0) =
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∑ αi exp[−t /τi] i=1
N
(∑ αi = 1) i=1
(1)
where αi and τi indicate the amplitude and lifetime of the ith component in the exponentials, respectively. We used the amplitude-averaged lifetime as the characteristic time constant that represents the fluorescence decay law:
EXPERIMENTAL SECTION The hemicyanine dyes purchased from Sigma-Aldrich included trans-4-[4-(dimethylamino)styryl]-1-methylpyridinium iodide (DMASPI), trans-4-[4-(diethylamino)styryl]-1-methylpyridinium iodide (DEASPI), and trans-4-[4-(dibutylamino)styryl]1-methylpyridinium iodide (DBASPI). The molecular structures of the three dyes are shown Figure 2. Ethylene glycol
N
⟨τ ⟩ =
∑ αiτi i=1
(2)
The fluorescence decay time can be wavelength specific depending on the nature of the excited-state potential surface. In this experiment, no wavelength selection was made and all of the decay curves were recorded over the entire emission wavelength range. Figure 3 shows the measured fluorescence
Figure 2. Molecular structures of the three hemicyanine dyes where R denotes the alkyl substituents.
(EG), di(ethylene glycol) (2EG), tri(ethylene glycol) (3EG), tetra(ethylene glycol) (4EG), penta(ethylene glycol) (5EG), hexa(ethylene glycol) (6EG), and octa(ethylene glycol) (8EG) were also purchased from Sigma-Aldrich. Hepta(ethylene glycol) (7EG) was obtained from Tokyo Chemical Industry (TCI). All the chemicals were used without further purification. The concentration of the hemicyanine dyes in the solvents was maintained at 1 × 10−5 M for the fluorescence lifetime measurements. The dyes were dissolved in anhydrous ethanol for use as stock solutions. Solvent viscosity values were measured with a Brookfield rheometer (LVDV-IIIU) at 20 °C. The fluorescence lifetimes were measured by using a timecorrelated single photon counting (TCSPC) system. The light source was a picosecond diode laser operating at wavelength of 442 nm (Picoquant) at 20 MHz. The linearly polarized laser beam was converted to a circularly polarized beam by a quarter wave plate, which excites the sample mounted on an inverted confocal microscope (Nikon, TE2000-S). To block the remaining excitation beam, a long pass cutoff filter was placed in front of the detector. The total fluorescence signal was detected by a microchannel plate photomultiplier tube, amplified by a GHz preamplifier, and processed by a fast TCSPC board (Becker-Hickl, SPC-830). The instrument response function (IRF) of our TCSPC system was approximately 90 ps. The fluorescence lifetimes were extracted from the measured decay curves by a nonlinear least-squares fit
Figure 3. Fluorescence decay profiles of DMASPI, DEASPI, and DBASPI in ethylene glycol.
decay curves of the three hemicyanines in EG. The measured viscosity value of EG was 22.2 cP at 20 °C. The data were satisfactorily fitted to a double exponential form and the average lifetimes for the three hemicyanines were 140, 200, and 300 ps in EG. The excited-state lifetime of the hemicyanine dye gradually increased when the size of the substituent increased. The fluorescence lifetimes of the hemicyanines were further measured in glycerol, which provides a highly viscous environment. Figure 4 shows the fluorescence decay curves of the DASPI series in glycerol. The viscosity of glycerol was measured to be 910 cP at 24 °C.16 The data were fitted to a double exponential form and the average lifetimes for DMASPI, DEASPI, and DBASPI were 820 ps, 980 ps, and 1.05 ns, respectively. The viscosity of glycerol is over 40 times larger than that of EG, but the lifetime increased by only 4−6 times. 12879
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The applicability of Stokes’ law can be simply verified by calculating and comparing the solute and solvent sizes. The volume of a nonspherical molecule is V = (4π/3)abc where the three axes values of a, b, and c are not easily determined. Therefore, we used Edward’s method to calculate the van der Waals volume of the solutes and solvents:27 the molecular sizes of DMA, DEA, and DBA were calculated to be 122, 156, and 224 Å3, respectively. The solvent hydrodynamic radii of EG, 2EG, 3EG, 4EG, 5EG, 6EG, 7EG, and 8EG were determined to be 57.8, 81.0, 109.2, 132.4, 155.6, 178.8, 202.0, and 225.2 Å3, respectively. Therefore, the motional moieties of the solute and the solvent sizes are comparable, resulting in the breakdown of Stokes’ law. The breakdown of hydrodynamics has been extensively studied with photoisomerizing molecules such as DODCI,21 trans-stilbene, 2 2 , 2 3 binaphthyl, 2 4 and diphenylbutadienes.25,28−30 To relate the excite-state isomerization process to Kramers theory, the friction coefficient that influences the time scale of the molecular motion must be known. When hydrodynamics break down, the friction coefficient cannot be obtained from the solvent viscosity but can be accessed through the Hubbard relation.31 By measuring the overall rotation time of the molecule, one calculates the friction coefficient through the Hubbard relation:
Figure 4. Fluorescence decay profiles of DMASPI, DEASPI, and DBASPI in glycerol.
To further verify the viscosity dependence, the fluorescence decay curves were measured in oligo(ethylene glycol)s. We chose seven oligo(ethylene glycol)s, which are structured as H−[O−CH2−CH2−]n−OH (n = 2, 3, 4, 5, 6, 7, 8). The measured viscosity values were in the range 37.2 cP (2EG) to 117.8 cP (8EG) at 20 °C. The higher oligo(ethylene glycol)s could not be used because they exist as solidified forms at room temperature. All of the average lifetimes obtained from the double exponential fit are shown in Table 1. When the molecular size was varied in the aniline moiety (the donor side), the fluorescence lifetimes of the hemicyanines were always in the order of DMASPI < DEASPI < DBASPI at any given viscosity. It has been previously reported that the excitedstate dynamics of the hemicyanines are independent of the length of the alkyl chain attached to the pyridinium ring (the acceptor side).6 Therefore, our results clearly indicate that the time scale of the internal rotation of DASPI is dominated by the aniline moiety not the stilbazolium moiety. Hydrodynamics has been widely employed to describe the internal rotation of photoisomerizing molecules in the condensed phase. Solvent friction slows down the photoisomerization reaction. The friction coefficient (ς) is obtained from the macroscopic solvent viscosity (η) through Stokes’ law: ς = 6πηr, where r is the radius of the solute. The original Stokes’ law was developed for a spherical solute under stick boundary condition. Hu and Zwanzig have suggested a modified form of Stokes’ law to accommodate different boundary conditions.26 Hydrodynamics is suitable when the solute (isomerizing species) is much larger than the solvent. A serious problem arises when the solute and solvent sizes are comparable. In this case, the medium cannot be regarded as a continuum, the Stokes’ law breaks down, and the time scale of the motion is not linearly dependent on the solvent viscosity.
ς = 6kBTτor
(3)
where kB is the Boltzmann constant, T is the absolute temperature, and τor is the rotational reorientation time. Anna and Kubarych employed 2D IR chemical exchange spectroscopy to investigate the ground-state isomerization of Co2(CO)8.32 The Hubbard relation was successfully applied when the isomerization rate process was compared to Kramers theory. Recently, Bain and co-workers revisited the Hubbard relation and explained their observations on the excited-state dynamics of NADH and NADPH in terms of the overall rotation.33 The rotational reorientation time of excited-state chromophores is typically obtained by fluorescence anisotropy and has been described by the following phenomenological equation: τor =
Vη fC + τo kBT
(4)
where C is the bounadary condition parameter, f is the Perrin shape factor, and τo is the free rotor correlation time.34 Equation 4 simply states that the rotation time is linearly proportional to the viscosity with an intercept. The boundary condition sets the upper limit to C = 1 for stick and the lower limit to C = 2/3 for slip. The rotational motion of hydrophilic DASPI in OEGs may follow the stick boundary condition more closely rather than the slip. In addition, the dialkylaniline
Table 1. Average Fluorescence Lifetimes ⟨τ⟩ of DMASPI, DEASPI, and DBASPI as a Function of Solvent Viscosity at 20 °C with the χ2 Values solvent
viscosity (cP)
DMASPI ⟨τ⟩ (ns)
χ2
DEASPI ⟨τ⟩ (ns)
χ2
DBASPI ⟨τ⟩ (ns)
χ2
EG 2EG 3EG 4EG 5EG 6EG 7EG 8EG
22.2 37.2 50.1 61.2 73.3 87.5 99.5 117.8
0.16 0.22 0.31 0.35 0.42 0.47 0.51 0.65
1.22 1.39 1.22 1.31 1.33 1.13 1.63 1.10
0.22 0.31 0.39 0.41 0.49 0.52 0.62 0.71
1.15 1.30 1.12 1.05 1.18 1.34 1.09 1.40
0.31 0.36 0.53 0.55 0.60 0.67 0.73 0.80
1.47 1.51 1.07 1.18 1.20 1.24 1.23 1.06
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solution has been well described by an angle−dependent Langevin equation based on the Fokker−Planck theory. According to the Kramer’s theory, the reactive mode coupling is divided into inertial and diffusive regimes.36 The energy diffusion controls the inertial regime that typically occurs in the gas phase. The spatial diffusion controls the diffusive regime that occurs in the liquid phase. In this region, the Kramers’ equation is given by
moiety of DASPI can be approximated as a prolate rotor. The Perrin factor for a prolate ellipsoid is given by f = 2(p2 − 1)/3p{p − (p2 − 1)−1/2 ln[p + (p2 − 1)1/2 ]} (5)
where p is the axial ratio of the long axis relative to the short axis (p = a/b).35 The free rotor correlation time is defined as
⎛ IR ⎞1/2 τo = ⎜ ⎟ ⎝ kBT ⎠
1/2 ⎧ ⎫ ⎛ 2ω b ⎞2 ⎤ ⎪ ωa γ ⎪⎡⎢ ⎥ ⎨ 1+⎜ A= − 1⎬ ⎟ ⎢ ⎥ 2πω b 2 ⎪⎣ ⎝ γ ⎠⎦ ⎪ ⎩ ⎭
(6)
where IR is the moment of inertia.34 We calculated the moment of inertia for DMA, DEA, and DBA along the molecular axis because it is related to internal twisting. The IR values are 1.9 × 10−45, 2.7 × 10−45, and 4.2 × 10−45 kg m2, from which the free rotor correlation times of DMA, DEA, and DBA are calculated to be 0.68, 0.82, and 1.02 ps, respectively. The excited state of a photoisomerizing molecule is deactivated as a result of the internal rotation. Therefore, the excited-state lifetime is a direct measure of the time scale of the internal rotation which is dependent on solvent viscosity. The fluorescence lifetimes of the hemicyanines were plotted in Figure 5 as a function of solvent viscosity. The data show nearly
where ωa and ωb are the well and barrier frequencies, respectively. At high friction, the Kramers theory is simplified to the Smoluchowski limit: ωω k = a b exp( −E b /kBT ) 2πγ (10) Applying the Stokes−Einstein equation under the stick boundary condition gives the internal rotation time (τir) as τir =
the same slope with the value of 50 ± 2 ps/cP. However, eq 4 indicates that the slope should increase as the volume of the rotating moiety increases, which means that the hydrodynamic eq 4 does not adequately describe our observations. The reason for the discrepancy may arise from the difference between the internal rotation and overall rotation. Although both depend on solvent friction, the internal motion is distinguished from the overall rotation in that the internal motion experiences forces that arise from the potential surface. When there exists a barrier in the potential surface, the rate process for photoisomerization is a friction-dependent unimolecular reaction.21
k iso =
(11)
1 − kr ⟨τ ⟩
(12)
where kr is the radiative rate constant. If kr is known, the fluorescence lifetime measurements provide information on kiso through eq 12. The radiative rate constants for three hemicyanies were calculated from the Strikler−Berg formula.37 The values of kr in EG were calculated to be 1.48 × 108, 1.50 × 108, and 1.75 × 108 s−1 for DMASPI, DEASPI, and DBASPI, respectively. One of the rigorous requirements for the application of Kramers theory is that the potential surface must be onedimensional. Most photoisomerizing molecules including
(7)
where γ is the reduced friction coefficient and Eb is the potential barrier. For internal rotation, the reduced friction coefficient is defined as γ = ς /Iϕ
12π 2 V η exp(E b /kBT ) ωaω b Iϕ
The slope in the equation contains the V/Iϕ term. At constant temperature, the main difference between eqs 4 and 11 is the treatment of the slope where τor is proportional to V but τir is proportional to V/Iϕ. In the DASPI series, the ratio of V/Iϕ for the moving moiety of the three dyes is nearly the same (i.e., DMA:DEA:DBA = 1.0:1.0:0.9). Therefore, eq 11 correctly describes our observations. In fact, the Hubbard relation (eq 3) implies that the friction coefficient should be proportional to V/Iϕ because the overall rotation time is proportional to the hydrodynamic volume at a constant temperature (Iϕ = IR). The data in Figure 4 produce the same slope but yield different intercepts, being 30, 95, and 200 ps for DMA, DEA, and DBA. These values are much larger than the free rotor correlation time. In the Kramers theory, the photoisomerization approaches to the Kramers turnover regime prior to reaching to the inertial regime. Therefore, the intercept does not contain any useful information because the use of eq 11 is only limited to the diffusive regime. The fluorescence lifetime is determined by the combination of the radiative decay and many nonradiative decay processes such as internal conversion, intersystem crossing, and photoisomerizion. If the photoisomerization process dominates other nonradiative rate processes, then the rate constant for the isomerization, kiso, can be calculated using
Figure 5. Average fluorescence lifetime ⟨τ⟩ of DMASPI, DEASPI, and DBASPI as a function of solvent viscosity. The solid lines are a leastsquares fit to the data.
k = A(γ ) exp[−E b /kBT ]
(9)
(8)
where Iϕ is the moment of inertia corresponding to the isomerizing coordinate.22 The internal twisting motion in 12881
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Notes
hemicyanines do not satisfy the requirement because some of the low frequency vibrations are usually coupled to the reactive mode. As an alternative, a power-law function that represents the fractional dependence has been used to fit the isomerization data:34
k iso = αη−β
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
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REFERENCES
This research was supported by the Basic Science Program through the National Research Foundation funded by the Ministry of Education 2013R1A1A2A10004510) and the Global Top 5 Program of Ewha Womans University.
(13)
where α and β are empirical parameters. The α value is associated with the time scale of the internal motion. The β value is related to the medium heterogeneity and the multidimensionality of the potential surface. The comparability of the solvent and solute sizes is also responsible for the fractional dependence. In Figure 6, the isomerization rate
Research of Korea (NRFResearch
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Figure 6. Isomerization rate constant of DMASPI, DEASPI, and DBASPI as a function of viscosity. The solid curves are a nonlinear least-squares fit to the data.
constant was plotted as a function of viscosity (from EG to 8EG) and our data were fitted to eq 13. The β values for DMASPI, DEASPI, and DBASPI are 0.94, 0.79, and 0.68, respectively, which clearly demonstrates a decrease as the length of the alkyl chain increases due to the incremental effect of multidimensionality.
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CONCLUSION Electronically excited hemicyanines undergo internal twisting from a localized excited state to a twisted intramolecular charge-transfer state. We have measured the fluorescence lifetimes of three hemicyanine dyes (DMASPI, DEASPI, and DBASPI) to investigate the photoisomerization processes in highly viscous solvents. By using the dyes that differ in the length of the alkyl chain length in the aniline moiety, we expect that the volume of the motional moiety would increase without significantly affecting the excited-state potential surface. In addition, we explored oligo(ethylene glycol)s as a new homologous series that covers a high viscosity region and showed that the excited-state lifetime of the hemicyanines gradually increases in oligo(ethylene glycol)s when the size of the substituent increases. Finally, we attempted to address some important issues of the condensed-phase photoisomerization processes, such as the breakdown of Stokes’ law, multidimensionality, and the Hubbard relation.
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AUTHOR INFORMATION
Corresponding Author
*M. Lee: e-mail, [email protected]. 12882
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Volume Increment Effect on the Photoisomerization of Hemicyanine Dyes in Oligo(ethylene glycol)s Youmin Lee and Minyung Lee* Department of Chemistry and Nanoscience, Ewha Womans University, Seoul 120-750, Republic of Korea ABSTRACT: We studied the excited-state dynamics of three hemicyanine dyes that undergo internal twisting from the localized excited state to the twisted intramolecular charge-transfer state. The dyes differ in the length of the alkyl chain in the aniline moiety and, thus, the volume of the motional moiety increases without having much of an effect on the excited-state potential surface. By employing oligo(ethylene glycol)s as a new homologous series of solvents that covers a high viscosity region, we showed that the excited-state lifetime of the hemicyanines gradually increases at any given viscosity when the size of the substituent increases. We describe our results for the solution-phase photoisomerization processes in terms of the breakdown of Stokes’ law, multidimensionality, and the Hubbard relation.
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INTRODUCTION The photophysical and photochemical properties of polymethine dyes have drawn considerable attention, due to their wide applications in various fields such as photographic sensitizers, optical recording medium, nonlinear optical materials, and fluorescence probes.1−20 Polymethines are classified into two distinct classes: cyanines and hemicyanines. Cyanine dyes are constructed with two identical heterocyclic groups at both ends linked by a polymethine. Hemicyanines are modified cyanine dyes that consist of heterocyclic and nonheterocyclic groups. The nonheterocyclic moiety acts as an electron donor (D), and the heterocyclic moiety acts as an electron acceptor (A). Therefore, hemicyanines belong to the group that includes intramolecular charge-transfer species possessing a D−π−A structure in which the D and A moieties are π-electron conjugated. A typical example of such a hemicyanine dye is trans-4-[4-(dimethylamino)styryl]-1-methylpyridinium iodie (4-DASPI) in which the dimethyl amino group and the methyl pyridinium group act as the (electron) donor and acceptor, respectively. One of the common features of hemicyanines as well as cyanines is that they undergo photoisomerization in the excited state. Figure 1 shows the excited-state potential surface of 4DASPI in which the reaction coordinate is the single bond twisting angle ϕ between the dialkylaniline moiety and the alkylpyridylethylene moiety. The initially prepared Franck− Condon state is relaxed to the localized excited (LE) state, which decays to the ground state or undergoes a downhill motion to the twisted intramolecular charge-transfer (TICT) state. The TICT state nonradiatively decays to the ground sate at ϕ = 90°, which further relaxes to a thermodynamically stable form (ϕ = 0° or 180°). The fluorescence of 4-DASPI originates from LE or its charge-transfer form because the TICT state does not fluoresce. A small activation barrier exists for the LE to © 2013 American Chemical Society
Figure 1. One-dimensional potential energy surface of 4-DASPI with respect to the internal twisting angle ϕ. Eb denotes the barrier height.
TICT process. With an isoviscoisty plot, the value has been measured to be 0.86 kJ/mol,16 which is much smaller than the thermal energy at ambient temperature (∼2.5 kJ/mol). The solution-phase photoisomerization is basically a barrier escaping problem that addresses internal motion subjected to friction exerted by the surrounding media. Such photoisomerization processes of 4-DASPI have been widely investigated in various media, including reverse micelles,2,12 layered inorganics,3 polar solvents,5 nanoporous materials,6,11 ionic liquids,8 sol-gels,9,12 Langmuir−Blodgett films,10,15 and polymers.17,20 Unlike cyanines, both ends of a hemicyanine dye consist of different substituents. Due to this unsymmetrical nature, it is possible to chemically modify only one side without affecting the other part. The main purpose of this work is to determine Received: October 11, 2013 Revised: November 13, 2013 Published: November 21, 2013 12878
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with deconvoluting IRF. The fit was performed on the judgment of weighted residuals and the reduced χ2.
how the length of the alkyl chain influences the excited-state processes of the hemicyanines. We chose three hemicyanine dyes possessing different alkyl chain lengths in the aniline moiety (the donor side). The use of a chemically inert alkyl group should allow the volume of the motional moiety to increase without significantly affecting the excited-state potential surface. In addition, we used a homologous series of oligo(ethylene glycol)s to vary the medium viscosity. Previously, n-alkanes and n-alkanols have been employed to tune the viscosity in the medium friction regions.21−25 This work used oligo(ethylene glycol)s as a new homologous solvents that cover the higher viscosity range. By analyzing the fluorescence lifetimes of the hemicyanines measured in oligo(ethylene glycol)s, we attempted to address some unresolved issues for the excited-state rate processes in the condensed phase.
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RESULTS AND DISCUSSION In the photoisomerization process, the excited-state population decay becomes a single exponential when the barrier height is significantly higher than the experimental temperature. As shown in Figure 1, the excited-state potential surface of 4DASPI is very low or virtually barrierless at room temperature. Therefore, it is not expected to follow a single exponential function, and all of the measured fluorescence decay curves for DMASPI (4-DASPI), DEASPI, and DBASPI were fitted to a sum of exponentials: N
I(t )/I(0) =
■
∑ αi exp[−t /τi] i=1
N
(∑ αi = 1) i=1
(1)
where αi and τi indicate the amplitude and lifetime of the ith component in the exponentials, respectively. We used the amplitude-averaged lifetime as the characteristic time constant that represents the fluorescence decay law:
EXPERIMENTAL SECTION The hemicyanine dyes purchased from Sigma-Aldrich included trans-4-[4-(dimethylamino)styryl]-1-methylpyridinium iodide (DMASPI), trans-4-[4-(diethylamino)styryl]-1-methylpyridinium iodide (DEASPI), and trans-4-[4-(dibutylamino)styryl]1-methylpyridinium iodide (DBASPI). The molecular structures of the three dyes are shown Figure 2. Ethylene glycol
N
⟨τ ⟩ =
∑ αiτi i=1
(2)
The fluorescence decay time can be wavelength specific depending on the nature of the excited-state potential surface. In this experiment, no wavelength selection was made and all of the decay curves were recorded over the entire emission wavelength range. Figure 3 shows the measured fluorescence
Figure 2. Molecular structures of the three hemicyanine dyes where R denotes the alkyl substituents.
(EG), di(ethylene glycol) (2EG), tri(ethylene glycol) (3EG), tetra(ethylene glycol) (4EG), penta(ethylene glycol) (5EG), hexa(ethylene glycol) (6EG), and octa(ethylene glycol) (8EG) were also purchased from Sigma-Aldrich. Hepta(ethylene glycol) (7EG) was obtained from Tokyo Chemical Industry (TCI). All the chemicals were used without further purification. The concentration of the hemicyanine dyes in the solvents was maintained at 1 × 10−5 M for the fluorescence lifetime measurements. The dyes were dissolved in anhydrous ethanol for use as stock solutions. Solvent viscosity values were measured with a Brookfield rheometer (LVDV-IIIU) at 20 °C. The fluorescence lifetimes were measured by using a timecorrelated single photon counting (TCSPC) system. The light source was a picosecond diode laser operating at wavelength of 442 nm (Picoquant) at 20 MHz. The linearly polarized laser beam was converted to a circularly polarized beam by a quarter wave plate, which excites the sample mounted on an inverted confocal microscope (Nikon, TE2000-S). To block the remaining excitation beam, a long pass cutoff filter was placed in front of the detector. The total fluorescence signal was detected by a microchannel plate photomultiplier tube, amplified by a GHz preamplifier, and processed by a fast TCSPC board (Becker-Hickl, SPC-830). The instrument response function (IRF) of our TCSPC system was approximately 90 ps. The fluorescence lifetimes were extracted from the measured decay curves by a nonlinear least-squares fit
Figure 3. Fluorescence decay profiles of DMASPI, DEASPI, and DBASPI in ethylene glycol.
decay curves of the three hemicyanines in EG. The measured viscosity value of EG was 22.2 cP at 20 °C. The data were satisfactorily fitted to a double exponential form and the average lifetimes for the three hemicyanines were 140, 200, and 300 ps in EG. The excited-state lifetime of the hemicyanine dye gradually increased when the size of the substituent increased. The fluorescence lifetimes of the hemicyanines were further measured in glycerol, which provides a highly viscous environment. Figure 4 shows the fluorescence decay curves of the DASPI series in glycerol. The viscosity of glycerol was measured to be 910 cP at 24 °C.16 The data were fitted to a double exponential form and the average lifetimes for DMASPI, DEASPI, and DBASPI were 820 ps, 980 ps, and 1.05 ns, respectively. The viscosity of glycerol is over 40 times larger than that of EG, but the lifetime increased by only 4−6 times. 12879
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The applicability of Stokes’ law can be simply verified by calculating and comparing the solute and solvent sizes. The volume of a nonspherical molecule is V = (4π/3)abc where the three axes values of a, b, and c are not easily determined. Therefore, we used Edward’s method to calculate the van der Waals volume of the solutes and solvents:27 the molecular sizes of DMA, DEA, and DBA were calculated to be 122, 156, and 224 Å3, respectively. The solvent hydrodynamic radii of EG, 2EG, 3EG, 4EG, 5EG, 6EG, 7EG, and 8EG were determined to be 57.8, 81.0, 109.2, 132.4, 155.6, 178.8, 202.0, and 225.2 Å3, respectively. Therefore, the motional moieties of the solute and the solvent sizes are comparable, resulting in the breakdown of Stokes’ law. The breakdown of hydrodynamics has been extensively studied with photoisomerizing molecules such as DODCI,21 trans-stilbene, 2 2 , 2 3 binaphthyl, 2 4 and diphenylbutadienes.25,28−30 To relate the excite-state isomerization process to Kramers theory, the friction coefficient that influences the time scale of the molecular motion must be known. When hydrodynamics break down, the friction coefficient cannot be obtained from the solvent viscosity but can be accessed through the Hubbard relation.31 By measuring the overall rotation time of the molecule, one calculates the friction coefficient through the Hubbard relation:
Figure 4. Fluorescence decay profiles of DMASPI, DEASPI, and DBASPI in glycerol.
To further verify the viscosity dependence, the fluorescence decay curves were measured in oligo(ethylene glycol)s. We chose seven oligo(ethylene glycol)s, which are structured as H−[O−CH2−CH2−]n−OH (n = 2, 3, 4, 5, 6, 7, 8). The measured viscosity values were in the range 37.2 cP (2EG) to 117.8 cP (8EG) at 20 °C. The higher oligo(ethylene glycol)s could not be used because they exist as solidified forms at room temperature. All of the average lifetimes obtained from the double exponential fit are shown in Table 1. When the molecular size was varied in the aniline moiety (the donor side), the fluorescence lifetimes of the hemicyanines were always in the order of DMASPI < DEASPI < DBASPI at any given viscosity. It has been previously reported that the excitedstate dynamics of the hemicyanines are independent of the length of the alkyl chain attached to the pyridinium ring (the acceptor side).6 Therefore, our results clearly indicate that the time scale of the internal rotation of DASPI is dominated by the aniline moiety not the stilbazolium moiety. Hydrodynamics has been widely employed to describe the internal rotation of photoisomerizing molecules in the condensed phase. Solvent friction slows down the photoisomerization reaction. The friction coefficient (ς) is obtained from the macroscopic solvent viscosity (η) through Stokes’ law: ς = 6πηr, where r is the radius of the solute. The original Stokes’ law was developed for a spherical solute under stick boundary condition. Hu and Zwanzig have suggested a modified form of Stokes’ law to accommodate different boundary conditions.26 Hydrodynamics is suitable when the solute (isomerizing species) is much larger than the solvent. A serious problem arises when the solute and solvent sizes are comparable. In this case, the medium cannot be regarded as a continuum, the Stokes’ law breaks down, and the time scale of the motion is not linearly dependent on the solvent viscosity.
ς = 6kBTτor
(3)
where kB is the Boltzmann constant, T is the absolute temperature, and τor is the rotational reorientation time. Anna and Kubarych employed 2D IR chemical exchange spectroscopy to investigate the ground-state isomerization of Co2(CO)8.32 The Hubbard relation was successfully applied when the isomerization rate process was compared to Kramers theory. Recently, Bain and co-workers revisited the Hubbard relation and explained their observations on the excited-state dynamics of NADH and NADPH in terms of the overall rotation.33 The rotational reorientation time of excited-state chromophores is typically obtained by fluorescence anisotropy and has been described by the following phenomenological equation: τor =
Vη fC + τo kBT
(4)
where C is the bounadary condition parameter, f is the Perrin shape factor, and τo is the free rotor correlation time.34 Equation 4 simply states that the rotation time is linearly proportional to the viscosity with an intercept. The boundary condition sets the upper limit to C = 1 for stick and the lower limit to C = 2/3 for slip. The rotational motion of hydrophilic DASPI in OEGs may follow the stick boundary condition more closely rather than the slip. In addition, the dialkylaniline
Table 1. Average Fluorescence Lifetimes ⟨τ⟩ of DMASPI, DEASPI, and DBASPI as a Function of Solvent Viscosity at 20 °C with the χ2 Values solvent
viscosity (cP)
DMASPI ⟨τ⟩ (ns)
χ2
DEASPI ⟨τ⟩ (ns)
χ2
DBASPI ⟨τ⟩ (ns)
χ2
EG 2EG 3EG 4EG 5EG 6EG 7EG 8EG
22.2 37.2 50.1 61.2 73.3 87.5 99.5 117.8
0.16 0.22 0.31 0.35 0.42 0.47 0.51 0.65
1.22 1.39 1.22 1.31 1.33 1.13 1.63 1.10
0.22 0.31 0.39 0.41 0.49 0.52 0.62 0.71
1.15 1.30 1.12 1.05 1.18 1.34 1.09 1.40
0.31 0.36 0.53 0.55 0.60 0.67 0.73 0.80
1.47 1.51 1.07 1.18 1.20 1.24 1.23 1.06
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solution has been well described by an angle−dependent Langevin equation based on the Fokker−Planck theory. According to the Kramer’s theory, the reactive mode coupling is divided into inertial and diffusive regimes.36 The energy diffusion controls the inertial regime that typically occurs in the gas phase. The spatial diffusion controls the diffusive regime that occurs in the liquid phase. In this region, the Kramers’ equation is given by
moiety of DASPI can be approximated as a prolate rotor. The Perrin factor for a prolate ellipsoid is given by f = 2(p2 − 1)/3p{p − (p2 − 1)−1/2 ln[p + (p2 − 1)1/2 ]} (5)
where p is the axial ratio of the long axis relative to the short axis (p = a/b).35 The free rotor correlation time is defined as
⎛ IR ⎞1/2 τo = ⎜ ⎟ ⎝ kBT ⎠
1/2 ⎧ ⎫ ⎛ 2ω b ⎞2 ⎤ ⎪ ωa γ ⎪⎡⎢ ⎥ ⎨ 1+⎜ A= − 1⎬ ⎟ ⎢ ⎥ 2πω b 2 ⎪⎣ ⎝ γ ⎠⎦ ⎪ ⎩ ⎭
(6)
where IR is the moment of inertia.34 We calculated the moment of inertia for DMA, DEA, and DBA along the molecular axis because it is related to internal twisting. The IR values are 1.9 × 10−45, 2.7 × 10−45, and 4.2 × 10−45 kg m2, from which the free rotor correlation times of DMA, DEA, and DBA are calculated to be 0.68, 0.82, and 1.02 ps, respectively. The excited state of a photoisomerizing molecule is deactivated as a result of the internal rotation. Therefore, the excited-state lifetime is a direct measure of the time scale of the internal rotation which is dependent on solvent viscosity. The fluorescence lifetimes of the hemicyanines were plotted in Figure 5 as a function of solvent viscosity. The data show nearly
where ωa and ωb are the well and barrier frequencies, respectively. At high friction, the Kramers theory is simplified to the Smoluchowski limit: ωω k = a b exp( −E b /kBT ) 2πγ (10) Applying the Stokes−Einstein equation under the stick boundary condition gives the internal rotation time (τir) as τir =
the same slope with the value of 50 ± 2 ps/cP. However, eq 4 indicates that the slope should increase as the volume of the rotating moiety increases, which means that the hydrodynamic eq 4 does not adequately describe our observations. The reason for the discrepancy may arise from the difference between the internal rotation and overall rotation. Although both depend on solvent friction, the internal motion is distinguished from the overall rotation in that the internal motion experiences forces that arise from the potential surface. When there exists a barrier in the potential surface, the rate process for photoisomerization is a friction-dependent unimolecular reaction.21
k iso =
(11)
1 − kr ⟨τ ⟩
(12)
where kr is the radiative rate constant. If kr is known, the fluorescence lifetime measurements provide information on kiso through eq 12. The radiative rate constants for three hemicyanies were calculated from the Strikler−Berg formula.37 The values of kr in EG were calculated to be 1.48 × 108, 1.50 × 108, and 1.75 × 108 s−1 for DMASPI, DEASPI, and DBASPI, respectively. One of the rigorous requirements for the application of Kramers theory is that the potential surface must be onedimensional. Most photoisomerizing molecules including
(7)
where γ is the reduced friction coefficient and Eb is the potential barrier. For internal rotation, the reduced friction coefficient is defined as γ = ς /Iϕ
12π 2 V η exp(E b /kBT ) ωaω b Iϕ
The slope in the equation contains the V/Iϕ term. At constant temperature, the main difference between eqs 4 and 11 is the treatment of the slope where τor is proportional to V but τir is proportional to V/Iϕ. In the DASPI series, the ratio of V/Iϕ for the moving moiety of the three dyes is nearly the same (i.e., DMA:DEA:DBA = 1.0:1.0:0.9). Therefore, eq 11 correctly describes our observations. In fact, the Hubbard relation (eq 3) implies that the friction coefficient should be proportional to V/Iϕ because the overall rotation time is proportional to the hydrodynamic volume at a constant temperature (Iϕ = IR). The data in Figure 4 produce the same slope but yield different intercepts, being 30, 95, and 200 ps for DMA, DEA, and DBA. These values are much larger than the free rotor correlation time. In the Kramers theory, the photoisomerization approaches to the Kramers turnover regime prior to reaching to the inertial regime. Therefore, the intercept does not contain any useful information because the use of eq 11 is only limited to the diffusive regime. The fluorescence lifetime is determined by the combination of the radiative decay and many nonradiative decay processes such as internal conversion, intersystem crossing, and photoisomerizion. If the photoisomerization process dominates other nonradiative rate processes, then the rate constant for the isomerization, kiso, can be calculated using
Figure 5. Average fluorescence lifetime ⟨τ⟩ of DMASPI, DEASPI, and DBASPI as a function of solvent viscosity. The solid lines are a leastsquares fit to the data.
k = A(γ ) exp[−E b /kBT ]
(9)
(8)
where Iϕ is the moment of inertia corresponding to the isomerizing coordinate.22 The internal twisting motion in 12881
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Notes
hemicyanines do not satisfy the requirement because some of the low frequency vibrations are usually coupled to the reactive mode. As an alternative, a power-law function that represents the fractional dependence has been used to fit the isomerization data:34
k iso = αη−β
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
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REFERENCES
This research was supported by the Basic Science Program through the National Research Foundation funded by the Ministry of Education 2013R1A1A2A10004510) and the Global Top 5 Program of Ewha Womans University.
(13)
where α and β are empirical parameters. The α value is associated with the time scale of the internal motion. The β value is related to the medium heterogeneity and the multidimensionality of the potential surface. The comparability of the solvent and solute sizes is also responsible for the fractional dependence. In Figure 6, the isomerization rate
Research of Korea (NRFResearch
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Figure 6. Isomerization rate constant of DMASPI, DEASPI, and DBASPI as a function of viscosity. The solid curves are a nonlinear least-squares fit to the data.
constant was plotted as a function of viscosity (from EG to 8EG) and our data were fitted to eq 13. The β values for DMASPI, DEASPI, and DBASPI are 0.94, 0.79, and 0.68, respectively, which clearly demonstrates a decrease as the length of the alkyl chain increases due to the incremental effect of multidimensionality.
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CONCLUSION Electronically excited hemicyanines undergo internal twisting from a localized excited state to a twisted intramolecular charge-transfer state. We have measured the fluorescence lifetimes of three hemicyanine dyes (DMASPI, DEASPI, and DBASPI) to investigate the photoisomerization processes in highly viscous solvents. By using the dyes that differ in the length of the alkyl chain length in the aniline moiety, we expect that the volume of the motional moiety would increase without significantly affecting the excited-state potential surface. In addition, we explored oligo(ethylene glycol)s as a new homologous series that covers a high viscosity region and showed that the excited-state lifetime of the hemicyanines gradually increases in oligo(ethylene glycol)s when the size of the substituent increases. Finally, we attempted to address some important issues of the condensed-phase photoisomerization processes, such as the breakdown of Stokes’ law, multidimensionality, and the Hubbard relation.
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AUTHOR INFORMATION
Corresponding Author
*M. Lee: e-mail, [email protected]. 12882
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