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J. Phys. Chem. 1996, 100, 5182-5187
ARTICLES Solvent Methyl Group Density Dependence of Vibrational Population Relaxation in 1-Methylperylene: Evidence for Short-Range Organization in Branched Alkanes P. K. McCarthy and G. J. Blanchard* Department of Chemistry, Michigan State UniVersity, East Lansing, Michigan 48824-1322 ReceiVed: NoVember 8, 1995; In Final Form: January 8, 1996X
We report on the vibrational population relaxation and rotational diffusion dynamics of 1-methylperylene in a series of branched alkanes with the common formula C7H16. Using the 1370 cm-1 ring breathing resonance of 1-methylperylene as the donor state and the 1378 cm-1 methyl rocking resonance of the solvents as the acceptor state, we have found that the T1 times of 1-methylperylene vary from 10 to 24 ps and the rotational diffusion times in these same solvents range from 10 to 23 ps, but the two relaxation time constants do not correlate directly. For these systems, the time constant for vibrational population relaxation, T1, is directly proportional to solvent CH3 group density, counter to the expected behavior for a statistical orientational distribution of solvent molecules about the solute. The experimental T1 times are also inversely proportional to the boiling point of the solvent, indicating that the ability of the solvent to form organized assemblies around the solute determines the coupling between the solute donor mode coordinate and the solvent acceptor vibrational mode. These data indicate that bath density considerations are less important than intermolecular alignment in determining the efficiency of energy transfer over molecular length scales.
Introduction A significant challenge to both experimental and theoretical chemistry has been understanding how dissimilar molecules interact with one another in solution. Indeed, this is an important problem from a pragmatic standpoint because a significant body of chemical synthesis and separation is performed in the liquid phase. The primary limitation to achieving an understanding of these systems lies in the short persistence times and short lengths of the intermolecular interactions responsible for the observed bulk behavior. We know, as a starting point, that highly specific intermolecular interactions are present in many of these systems because if they were not, all compounds of a given molecular weight would be equally soluble in all solvents. Clearly, this prediction does not match with experiment. Understanding the details of specific intermolecular interactions requires experimental techniques with high time resolution and a well-defined characteristic length scale. Most studies aimed at resolving local organization in liquids have used probe molecules with strong electronic resonances to interrogate their local environments. The chemical identity and optical response of the probe molecule determine, in many cases, the phenomenon observed. For probe molecules with significant electronic absorption and/or emission responses, rotational diffusion1-24 and excitation transport25-29 measurements have been used extensively. For both types of measurements, the interactions between the probe molecule and its local environment that give rise to the response of interest are dominated by dipolar interactions. For rotational diffusion measurements there are two contributions to the mediation of rotational motion: “frictional” or viscous drag30 and dielectric resistance to motion.31-36 Both viscous flow and dielectric * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, March 1, 1996.
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friction arise from dipolar interactions (e.g., dispersion, induced dipole-dipole, and dipole-dipole). Because these intermolecular interaction potential energies all scale as r-6, we expect rotational diffusion measurements, in general, to sense an environment averaged over a ∼10-20 Å radius, depending on the size of the probe molecule and the magnitude of its permanent dipole moment in the state interrogated. Electronic excitation transport measurements sense the strength of dipolar coupling between donor and acceptor molecules directly. The length scale over which these dipolar coupling events can occur depends on the strength of the donor and acceptor transition dipole moments as well as their relative detuning.37-39 In many cases, the critical radius for such energy transfer events is ∼25 Å.40 Thus, while useful for examining average organization over 10-50 Å, dynamical measurements that use electronic states to interrogate the local environment often sense only an average over a large number of solvent configurations. One way to overcome the length scale mismatch between spectroscopic measurements and the solvent local organization of interest is to use molecular vibrations to interrogate local structure. In a recent series of papers, we have explored the use of molecular vibrations to sense local organization in solution.41-46 Specifically, we have found that, using the 1375 cm-1 ag mode of perylene to probe local organization in n-alkanes, there is local structure that persists over several angstroms.42 Further investigation, aimed at calibrating this length scale, has served to underscore the importance of understanding the mechanism of the intermolecular coupling responsible for excitation transport.44 Vibrational relaxation processes that involve quadrupole-dipole coupling sense organization over ∼1-3 Å, with the actual length depending on the magnitude of the donor and acceptor transition moments, their detuning, and their alignment. For dipole-dipole vibrational-vibrational (v-v) coupling, there is, again, an uncertainty © 1996 American Chemical Society
Vibrational Population Relaxation in the calibration of the length scale due to uncertainty in the magnitude of the transition moments involved, but we have found that for 1-methylperylene in n-alkanes there is a direct correlation between T1 relaxation dynamics and reorientation dynamics, suggesting a ∼10 Å range for this type of coupling.44 The fact that this length scale is significantly longer than that sensed by the n-alkane-perylene v-v excitation transfer experiments raises the question of whether specific local organization or bulk concentration effects dominate the observed dipolar v-v relaxation for 1-methylperylene. In an attempt to address this question, we have understaken a study of the T1 relaxation behavior of the 1-methylperylene 1370 cm-1 mode in a series of alkanes with the common formula C7H16. The rationale behind these experiments is that, for this series of solvents, the strength of intermolecular interactions is expected to be modest, and there will be little or no long-range organization in these solvents. If these hypotheses are correct, then the measured T1 relaxation times should correlate with the number of CH3 groups per alkane solvent molecule. Our T1 data for 1-methylperylene relaxation in the n-alkanes indicate that there is a discontinuous trend in the methyl group concentration dependence, suggestive of local organization.44 We find that, on the basis of three different CH3 group densities (CH3/total C) for the alkane solvents reported here, there is a measurable solvent structural dependence to the experimental T1 data and that the CH3 density dependence of T1 is the opposite of that predicted on stoichiometric grounds. Our T1 data do demonstrate an inverse correlation with solvent boiling point, indicating that, with decreasing solvent intermolecular interaction strength, there is a corresponding decrease in the probability of the solute transferring energy to the solvent. Taken collectively, these data point to the dominance of intermolecular alignment effects over simple acceptor density considerations in determining the efficiency of intermolecular energy transfer over molecular length scales. Experimental Section Ultrafast Stimulated Spectroscopy. Stimulated vibrational population relaxation and rotational diffusion measurements of 1-methylperylene were made using a pump-probe laser spectrometer that has been described in detail previously.47 Briefly, a mode-locked CW Nd:YAG laser (Coherent Antares 76-S, 30 W average power at 1064 nm, 3 W of second harmonic at 532 nm, 1.1 W of third harmonic at 354.7 nm, 100 ps pulses, 76 MHz repetition rate) was used as the primary light source. The third harmonic output was used to pump two dye lasers (Coherent 701-3) synchronously. Both dye lasers were operated with Stilbene 420 laser dye (Exciton), at 430.5 nm for the pump laser and 457.5 nm for the probe laser. Each dye laser was cavity dumped at 8 MHz and produced ∼5 ps pulses. The cross correlation of the two dye lasers was typically 10 ps FWHM. For both T1 and reorientation measurements, the transient gain signals were detected using a radio and audio frequency triple-modulation, shot noise limited signal encoding scheme with synchronous demodulation detection.48-50 For the rotational diffusion measurements, the transient gain signals were measured for the polarization of the probe laser parallel and perpendicular with respect to the pump laser polarization. For the T1 measurements, the probe laser polarization was set to 54.7° with respect to the pump laser polarization to ensure that only population dynamics contributed to the observed response. Steady State Spectroscopies. The linear response of 1-methylperylene in the branched alkanes was measured with ∼1 nm resolution using a Hitachi U-4001 absorption spectrometer and
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Figure 1. Linear absorption and emission spectra of 1-methylperylene in 3-methylhexane.
a Hitachi F-4500 emission spectrometer. We show in Figure 1 the absorption and emission spectra of 1-methylperylene in 3-methylhexane. The linear response of 1-methylperylene is independent of the identity of the alkane solvent for the measurements reported here. Chemicals and Sample Handling. The alkanes used here (n-heptane, 2-methylhexane, 3-methylhexane, 2,3-dimethylpentane, and 2,4-dimethylpentane) were purchased from Aldrich Chemical Company at the highest available purity and were used without further purification. 1-Methylperylene was synthesized according to a published procedure. The identity and purity of 1-methylperylene were verified using 1H NMR, mass spectrometry, and UV-visible spectrometry. All 1-methylperylene solutions used for dynamical measurements were ∼10 µM. The samples were held in a sealed 1 cm path length cuvette and stirred to minimize thermal lensing contributions to the experimental signal. The sample cuvette was supported in a jacketed mount (brass block) with the temperature of the brass block maintained at 300 ( 0.2 K. Results and Discussion A significant motivation for doing this research is to understand local organization in liquid and fluid media and to determine the length scales over which polar coupling processes operate to mediate intermolecular vibrational energy transfer in solution.51 An important advantage of our experimental approach to this problem is that we can perform v-v relaxation measurements on systems where the donor and acceptor resonance frequencies are degenerate by virtue of the Ramanbased excitation scheme we use. Initially, we focused on degenerate vibrational energy transfer between perylene and n-alkanes42 because of the apparent structural simplicity of the constituents. For this work, using the perylene 1375 cm-1 ν7 Raman-active ag mode as the donor species and the solvent terminal CH3 group rocking vibration as the acceptor moiety, we found that there is indeed organization in room temperature n-alkanes, with a characteristic persistence length of several angstroms. To verify that the efficiency of vibrational energy transport in solution depends on the order of the polar modulation imposed on the donor and acceptor molecules by the vibrational motion of the modes involved, we demonstrated that the analogous v-v energy transfer process between 1-methylperylene and the same n-alkanes operated over a significantly longer (∼10 Å) range.44 For 1-methylperylene, we demonstrated that there is a discontinuous dependence of the T1 relaxation time constant for the 1370 cm-1 vibration in the same n-alkanes. Further, this T1 behavior correlated directly
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McCarthy and Blanchard
Figure 2. Schematic coupled three level used to describe the experimental signal. The dashed arrow indicates the fourth wave in the four-wave mixing process. The stimulated process indicated by this arrow is not important for these measurements because the experimental conditions do not approach saturation of this transition.
with rotational diffusion dynamics, in contrast to the results for perylene.24 We believe that the dynamical data for 1-methylperylene in the n-alkanes are consistent with local organization of the solvent about the solute molecule and, specifically, for the longer n-alkanes (gC10), that the 1-methylperylene solute resides in quasi-lamellar solvent cages. We are interested in achieving a more detailed understanding of local organization in these comparatively simple systems, and accordingly, it is important to determine whether or not the T1 relaxation dynamics of the 1-methylperylene 1370 cm-1 mode can be explained simply in stoichiometric terms for cases where the solvent is not expected to form well-organized local environments. We have investigated the T1 relaxation behavior of 1-methylperylene in a series of C7 alkanes, where we can both control the density of CH3 groups and, at the same time, introduce sufficient structural irregularity to the system to minimize the possibility of forming significantly structured local environments. In order to estimate the length scale over which these relaxation processes operate, we have examined the rotational diffusion dynamics of 1-methylperylene in these same solvents. We discuss the results of these two bodies of experimental data separately. Vibrational Population Relaxation Measurements. The details of how we measure T1 have been presented before,41-43 and we recap only the salient aspects of these measurements here. Briefly, the pump dye laser is tuned to the 1-methylperylene 0-0 transition so that there is no contribution to the stimulated response from excited state vibrational relaxation.43 The probe dye laser is tuned to couple the vibrationless excited electronic state with the ground state vibrational resonance of interest (the 1370 cm-1 mode here). The experimental stimulated signal is modeled in the context of the four-wave mixing response of a strongly coupled three-level system (Figure 2). The form of the stimulated response, S(t), detected in these experiments is
S(t) ) A exp(-k1t) - B exp(-k3t)
(1)
where the prefactors A and B are functions of the rate constants indicated in Figure 2, k1 is the sum of the spontaneous and stimulated emission rate constants, and k3 is the vibrational population relaxation rate constant for the mode of interest. As discussed previously, the form of the experimental signal is the difference between two exponential functions and not the sum of the two functions because of the way the detection system applies modulations to the electronic and vibrational state populations.42 The dependence of T1 on solvent identity is shown in Figure 3a and Table 1. There are several important points to note regarding these data. The first is that the T1 times are comparatively fast, consistent with our earlier report on the T1 relaxation dynamics of 1-methylperylene in n-alkanes.44 The reason that relaxation from the 1370 cm-1 mode of 1-methylperylene is fast compared to relaxation of the perylene ν7 mode in the same solvents is that the intermolecular coupling
Figure 3. (a) T1 relaxation times of 1-methylperylene in the C7 alkane homologous series as a function of solvent methyl carbon density. (b) Boiling points of solvents as a function of solvent methyl carbon density. Boiling point data taken from ref 53.
TABLE 1: Vibrational Relaxation and Rotational Diffusion for the 1-Methylperylene 1370 cm-1 Mode in Alkane Solvents solvent n-heptane 2-methylhexane 3-methylhexane 2,3-dimethylpentane 2,4-dimethylpentane
viscosity (η) T1 ( 1σ (ps) (cP) 0.38a 0.35a 0.34a 0.44b 0.36b
