14592
J. Phys. Chem. 1996, 100, 14592-14597
An Experimental Examination of the Competition between Polar Coupling and Local Organization in Determining Vibrational Population Relaxation P. K. McCarthy and G. J. Blanchard* Department of Chemistry, Michigan State UniVersity, East Lansing, Michigan 48824-1322 ReceiVed: April 24, 1996; In Final Form: June 18, 1996X
We report on the vibrational population relaxation and rotational diffusion dynamics of perylene and 1-methylperylene in benzene and toluene. For these experiments, the naphthalene-like ring distortion modes of both perylene (1375 cm-1) and 1-methylperylene (1370 cm-1) were excited selectively using a stimulated emission population scheme, and the efficiency of depopulation of these modes was measured in each solvent. For these systems, there is an IR-active acceptor vibrational mode at the same frequency and the order of the dominant intermolecular vibrational energy transfer process depends on the identity of the solute. For 1-methylperylene, dipole-dipole coupling is operative, and for perylene, quadrupole-dipole coupling mediates the transfer. The importance of solvent organization about the solute can be evaluated by comparing solute T1 times in the two solvents. In the limit of fast solvent cage exchange, the solute T1 relaxation times should increase with increasing order of the polar coupling process and decrease with increasing intermolecular alignment. Our experimental data indicate that the T1 times are similar for all systems studied, implying the importance of persistent intermolecular interactions in determining the efficiency of vibrational population exchange in solution.
Introduction Understanding how dissimilar molecules exchange energy and the extent to which solutes induce local organization in solvents is imperative for developing predictive power over chemical processes performed in solution. A critical step in developing this understanding is characterizing the extent and form of such local organization. Of the three states of matter, two are comparatively well understood. The gas phase is characterized by a random distribution of species, and intermolecular interactions can, for the most part, be treated statistically. Solids possess persistent, if complex structure, which is amenable to examination by a well-developed family of steady-state measurements. Liquids are the least well understood phase, and it is important to characterize intermolecular interactions in this medium since many industrially important chemical reactions are carried out in solution. Two significant difficulties exist in our ability to achieve an understanding of intermolecular interactions in the liquid phase. These are (i) the associative nature of the solvent and solute molecules and (ii) the short characteristic interaction time scales, which diminish the utility of steady-state spectroscopies for this application. There are a range of transient spectroscopies that have been applied to understanding the interactions between a chromophore and its immediate environment.1-40 We have focused our recent efforts on vibrational population relaxation41-52 because it is a physical process that is exquisitely sensitive to local organization in liquids.53-58 Initial experiments on perylene in n-alkanes revealed the presence of orientationally biased interactions between the chromophore and certain solvent molecules,54 but these results did not correlate with other dynamical responses sensitive to intermolecular interactions, such as rotational diffusion.24 The reason for the apparent absence of correlation between T1 and τOR for the perylene/n-alkane system lies in the mechanism of vibrational energy transfer operating for these systems. For perylene, the 1375 cm-1 ν7 vibrational mode is * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)01192-6 CCC: $12.00
Raman-active and IR-inactive, and the lowest order multipole moment to be modulated by ν7 excitation is the quadrupole moment. The solvent alkane terminal CH3 group rocking motion at 1378 cm-1 (∆νDA ) 0 cm-1) is both IR- and Ramanactive and represents a modulation of the alkane dipole moment on excitation. Such induced quadrupole-induced dipole coupling operates over a shorter length scale than induced dipoleinduced dipole coupling (vide infra). To verify that polar coupling is the dominant mechanism for liquid-phase T1 relaxation, we measured the vibrational population relaxation dynamics of 1-methylperylene in the same n-alkane solvents, where induced dipole-induced dipole coupling is expected to dominate, and indeed, these T1 data correlate directly with reorientation results.56 We have also measured 1-methylperylene 1370 cm-1 mode relaxation in a homologous series of branched and linear C7H16 solvents to determine whether the dominant factor in determining the probability of vibrational population relaxation is acceptor density or donor-acceptor intermolecular alignment.57 Contrary to expectations based on a statistical model of solute-solvent interactions, the vibrational relaxation time constants of the 1-methylperylene 1370 cm-1 mode increased in proportion to acceptor density. Comparison of the solvent-dependent T1 times to bulk measures of the ability of the solvent to organize with itself, such as boiling point, indicated that the dominant factor in determining the efficiency of vibrational energy transfer for these systems was intermolecular alignment and not simple acceptor density. A significant basis for this finding lies in the modest length scale over which resonant dipolar coupling processes operate (∼10 Å) for vibrational transitions. In this work, we are interested in determining the dependence of perylene and 1-methylperylene T1 times on the interactive distance of the solute and solvent and whether or not the solvent orientational distribution about the solute can be treated as a random distribution for solvents other than the n-alkanes. We use the ring breathing modes of both 1-methylperylene (1370 cm-1) and perylene (1375 cm-1) as donor resonances and the vibrational modes of benzene and toluene as the acceptor © 1996 American Chemical Society
Vibrational Population Relaxation
J. Phys. Chem., Vol. 100, No. 35, 1996 14593
resonances. For benzene, all Raman-active modes are infraredinactive, and there are several IR-active modes in close energetic proximity to 1370 cm-1. The lower symmetry of toluene increases the number of IR-active acceptor modes available to the donor species. By choosing donor and acceptor resonances appropriately, we can examine induced dipole-induced dipole D-A coupling (1-methylperylene/toluene and 1-methylperylene/ benzene) and induced quadrupole-induced dipole D-A coupling (perylene/toluene and perylene/benzene). Due to the different intermolecular distance dependencies of these coupling processes, in the limit of fast molecule exchange between the bulk solvent and the solute “cage”, T1(1-methylperylene) is expected to be less than T1(perylene). Experimentally, we observe T1(1-methylperylene) = T1(perylene), underscoring the importance of intermolecular alignment and detuning effects in determining the efficiency of vibrational energy transfer. We do find that the T1 relaxation behavior of 1-methylperylene in benzene is anomalous compared to that of the other systems we report here, and rotational diffusion measurements of these systems reveal the anomalous reorientation behavior of this same system. These data point collectively to persistent and apparently cooperative interactions between 1-methylperylene and benzene. Experimental Section Ultrafast Stimulated Spectroscopy. The spectrometer used here for T1 and τOR measurements has been described in detail before,59 and we provide only a brief outline here. The third harmonic of the output of a mode-locked CW Nd:YAG laser (Coherent Antares 76-S) was used to excite synchronously two cavity dumped dye lasers (Coherent 701-3). Both dye lasers were operated with Stilbene 420 laser dye (Exciton). Due to small solvent-dependent shifts of the probe molecule absorption and emission spectra, the pump dye laser, set to excite the S0V)0 T S1V)0 transition, was operated at fixed wavelengths between 435.8 and 442.2 nm. The probe dye laser was operated within the wavelength range 463.5-470.9 nm. For the 1-methylperylene and perylene measurements νpump - νprobe ) 1370 and 1375 cm-1, respectively. Both dye lasers produced secondorder autocorrelation traces of ∼5 ps with a cavity dumping repetition rate of 8 MHz. The cross correlation of the two dye lasers is ∼10 ps fwhm. For the rotational diffusion measurements, the probe dye laser polarization was set parallel and perpendicular with respect to the pump dye laser for collection of the quantities I|(t) and I⊥(t), respectively. For T1 measurements, the probe laser polarization was set to 54.7°with respect to the pump laser polarization to recover only a populationdependent response. Detection of the transients is accomplished using a triple-modulation, shot noise limited scheme.60-62 Steady-State Spectroscopies. The linear responses of all solutions used here were recorded using a Hitachi U-4001 absorption spectrometer and a Hitachi F-4500 emission spectrometer, each operating at 1 nm resolution. We present the linear responses of 1-methylperylene in toluene in Figure 1a and of perylene in toluene in Figure 1b. To ensure that no photoreaction or photodegradation occurred during the laserexcited measurements, absorption spectra of each sample were recorded before and after laser excitation. Chemicals and Sample Handling. Perylene, benzene, and toluene were purchased from Aldrich Chemical Co. at the highest purity available and were used as received. 1-Methylperylene was synthesized according to a literature preparation from perylene and CH3Li.63 This reaction methylates perylene at the 1 position with >95% selectivity. Methyllithium and 10% Pd on C catalyst were purchased from Aldrich and used
Figure 1. Absorption and emission spectra of (a) 1-methylperylene in toluene and (b) perylene in toluene.
as received. Following purification by plate chromatography, the identity of 1-methylperylene was confirmed by mass spectrometry, 1H NMR, UV-visible, and infrared absorption measurements. The sample concentrations were ∼1 × 10-5 M in the probe molecule to minimize the possibility of aggregation effects, concentration quenching, and excited-state donor-donor energy transfer. The sample handling system used a flow cell with a path length of 1 mm and a temperature control system set at 300 ( 0.1 K. Results and Discussion The primary focus of this work is on determining whether intermolecular alignment or a type of intermolecular coupling dominates T1 relaxation. In a series of previous papers, we have discussed the foundations of the measurement scheme we use to obtain ground-state T1 relaxation information,53-58 and a detailed discussion of the information content of our method is presented elsewhere.64 For our technique to yield information on the ground-state vibrational resonance of interest, the probe laser pulse senses both S1V)0 T S0V)V stimulated absorptive and emissive transitions during the time that the probe pulse is present. The time-resolved data we show in Figure 2 for perylene in benzene demonstrate the probe laser intensity independence of the signal, demonstrating that both stimulated emission and absorption contribute to the measured response.64 We understand the temporal evolution of the experimental signal and can model these data quantitatively in the context of the probe molecule behaving as a strongly coupled three-level system. A first consideration is whether the dominant process for exchange of vibrational energy is collisional or by noncollisional resonant coupling processes. Our work on perylene in the n-alkanes54 demonstrated that intermolecular collisions could not be the dominant relaxation pathway, consistent with a discussion of this point for gas-phase V-V energy transfer by Yardley.65 In that work, Yardley concluded that resonant (µµ) coupling was ∼103 more efficient than collisions at exact resonance and that collisional interactions in gases did not dominate until a D-A detuning of ∆νDA ∼ 250 cm-1. While the D-A detuning for which this crossover occurs may be
14594 J. Phys. Chem., Vol. 100, No. 35, 1996
McCarthy and Blanchard TABLE 1: Vibrational Population Relaxation Time Constants (T1), Zero-Time Anisotropies (R(0)), and Reorientation Time Constants (τOR) for Perylene and 1-Methylperylene in Toluene and Benzenea solute/solvent system
T1 ( 1σ (ps)
1-methylperylene/toluene 1-methylperylene/benzene
15 ( 3 35 ( 3
perylene/toluene perylene/benzene
16 ( 4 11 ( 2
R(0) ( 1σ
τOR ( 1σ (ps)
0.29 ( 0.014 0.28 ( 0.024 0.035 ( 0.0017 0.26 ( 0.029 0.27 ( 0.017
18 ( 1 15 ( 1 281 ( 16 16 ( 1 15 ( 1
a T times for perylene are for the ν mode at 1375 cm-1 and for 1 7 1-methylperylene are for the 1370 cm-1 mode.
Figure 2. Experimental pump-probe signal intensity dependence for 2 × 10-5 M perylene in benzene. The probed vibrational resonance is 1375 cm-1. The instrumental response function is shown with the data. Individual traces have been offset from ∆T/T ) 0 for clarity of presentation only. Top trace: Iprobe ) Ipump ∼ 10 mW average power. Second trace from the top: Ipump ) 0.1 Iprobe. Third trace: Ipump ) 0.01 Iprobe. Fourth (bottom) trace: Ipump ) 0.001 Iprobe. While the ∆T/T scale is arbitrary, the signals have not been normalized and are of the same magnitude for all conditions.
slightly different for liquid-phase systems, we work under conditions of ∆νDA ∼ 0 cm-1, ensuring the dominance of longrange resonant coupling. Our earlier comparison of the T1 relaxation dynamics of perylene in n-C8H18 and n-C8D18 indicates that, for significant D-A detuning, there is a background relaxation process that limits T1 for the perylene ν7 mode to ∼350 ps.54 The mechanism of this background relaxation is likely off-resonance polar coupling but could also have contributions from intramolecular anharmonic coupling to lowfrequency modes or direct collisional interactions with the solvent. For the systems we have investigated here, the donor multipole moment we sense is induced by the incident laser electric field(s) and the modulation of the acceptor moment(s) are induced by energy transfer from the donor. Thus, despite any permanent polar interactions operating in these systems, it is the induced moments in the donor and acceptor that are of consequence to these measurements, and therefore, we treat these processes in the context of dispersion interactions. As discussed above, we control the order of the longest range V-V coupling process through judicious choice of the donor and acceptor molecules. We need, therefore, to consider the length scale over which these processes operate. For dispersion interactions involving induced dipole-induced dipole coupling the relative interaction energy may be written in the following manner:66
(
µ-µ udis ≈-
-3ED
)( ) RDRA
4(4π0)
2
r6
(1)
where ED is the ionization energy of the donor molecule, RD and RA are the dipole-dipole polarizability tensors for the donor and acceptor species, and r is the intermolecular distance. The second term on the right-hand side of eq 1 is of consequence here, with the first term acting as a scaling constant. For quadrupole-dipole interactions we approximate the interaction energy dependence on polar coupling θ-µ ∝udis
ADRA r7
(2)
where AD is the quadrupole-dipole polarizability tensor for the donor and, as before, RA is the dipole-dipole polarizability tensor for the acceptor. The terms A and R depend, necessarily, on the symmetry of the donor and acceptor species, and eqs 1 and 2 represent the general cases for these interactions. For molecules possessing a center of inversion, such as perylene, the A term will vanish and the next higher order terms are the longest range processes θ-µ udis ∝-
ODRA r8
(3)
where the term OD is the octupole-dipole polarizability tensor for the donor. From eqs 1-3, it is clear that the operative length scale of the coupling process sensitively on the order of the the polar interaction. Despite this significant r dependence, we expect that intermolecular alignment can also play a role in our measurements. For example, in dipole-dipole interactions, the Fo¨rster treatment67 shows that the probability of an excitation transport event is related to D-A alignment:68
()
kD-A ) K′κ2
R0 R
6
(4) 2 κµ-µ ) {sin θD sin θA cos φ - 2 cos θD cos θA}2
The terms θD and θA are the angles that the D and A dipole moments make with respect to the vector connecting them, and φ is the azimuthal angle between the D and A dipole moments. For the higher order multipolar interactions, such as quadrupole-dipole interactions, the orientation dependence of kDA may be described as68 2 κθ-µ ) {3/2[cos θD(3 cos2 θA - 1) -
2 sin θD sin θA cos θA cos φ]}2 (5) For higher order coupling, the form of κ2 is slightly different, but the general result is the same, and the essential symmetry elements of the interaction are represented in eq 5. We expect, in general, that intermolecular distance, r, order of polar coupling, D-A alignment, and detuning effects all play a role in determining the T1 times we measure experimentally. We can determine the order of the polar coupling process and ∆νDA, leaving the quantities r and κ2 to be inferred by experiment. We have reported previously on the dominance of intermolecular alignment over simple acceptor chromophore density.57 In this work, the density of the acceptor chromophore is held nominally constant and the order of the coupling process is the variable. We expect, in the limit of fast exchange of solvent molecules in the cage surrounding the solute, 1-methylperylene to exhibit T1 times faster than those of perylene. We do not realize this expectation experimentally (Table 1), and there are
Vibrational Population Relaxation
Figure 3. IR spectra of (a) benzene and (b) toluene. Boxed region indicates perylene and 1-methylperylene resonances.
four possible reasons for the discrepancy between experiment and expectation. It is possible that there is density augmentation of the solvent about the solute or that the relative strengths of the donor and acceptor vibrational transition moments vary widely and in such a way as to compensate for variations in polar coupling effects. It is also possible that contributions from nonresonant (∆ν > 0 cm-1) coupling processes serve to make energy transfer efficient for all systems we have studied, or in connection with our earlier work, vibrational energy transfer could be mediated primarily by intermolecular alignment effects.57 We consider each of these possibilities below. The data we report here could potentially be accounted for in terms of local density augmentation, analogous to what has been observed for supercritical fluids near their critical points.69-77 Several factors, however, argue against this possibility. These are, first, that local density augmentation effects have not been observed previously for liquids and this effect is not seen for supercritical fluids under conditions well away from the critical temperature and pressure. In addition, we should observe a solvent-dependent trend, independent of the solute for both T1 and reorientation measurements if augmentation were operative, and we do not see this experimentally (Vide infra). A second possibility that could account for the experimental T1 data is that the D and A transition moments vary widely enough and in such a way as to compensate for differences in the r dependence of the coupling processes. Again, this is not likely based on a comparative examination of perylene and 1-methylperylene T1 relaxation dynamics in n-alkanes.54,56 In that work, the differences in T1 for the two solutes could be explained in terms of the r dependence of the coupling processes. In addition, for the solvents we use here, the Ramanactive transitions we use have similar Raman scattering cross sections, to within a factor of 5, based on measurements made in our laboratory.78 The IR spectra of benzene and toluene have essentially the same absorption cross sections for the 1375 cm-1 resonance (Figures 3). Thus the transition moments for the solute-solvent permutations we examine are uniform enough that they cannot account for the similarities in the T1 times for all systems.
J. Phys. Chem., Vol. 100, No. 35, 1996 14595
Figure 4. Raman spectra of (a) benzene and (b) toluene.
The third factor that may influence the vibrational relaxation times are the presence of additional acceptor vibrations at |∆νDA| > 0 cm-1. Specifically, both toluene and benzene have several additional IR-active (Figure 3) and Raman-active vibrations (Figure 4) in the vicinity of the dominant acceptor vibration (∼1380 cm-1). The presence of these competing acceptor modes, even for |∆νDA| ∼ 200 cm-1, can substantially increase the probability of an energy transfer event. Previous measurements in our laboratory indicate that the order of D-A polar coupling does affect the efficiency of vibrational energy transfer. For perylene/n-hexane54 and 1-methylperylene/n-hexane56 the T1 times were 300 and 20 ps, respectively. Since, in that work, the solvent molecules are similar in size to the solute species, changes in the donor-acceptor interactive distance could be ruled out as the cause of the different T1 times. For the solvents benzene and toluene, perylene and 1-methylperylene yield similar T1 times. The solvent dependence of T1 in the alkanes for both solutes excludes the possibility of intramolecular relaxation dominating the relaxation of these donor modes. We attribute these effects to coupling of the solute donor resonances to several solvent acceptor resonances as well as at least some alignment of the donor and acceptor vibrational mode coordinates. Perylene, in principle, allows for better alignment of the solvent molecules with the donor coordinate because of its planar structure, where the twisted conformation of 1-methylperylene79 inhibits an analogous degree of alignment. There is one somewhat longer T1 time in these data, that for 1-methylperylene in benzene. It is not possible to determine the origin of the longer T1 time for this system absent another, complementary means of examining solvent organization about the solute. Rotational diffusion measurements can provide this additional information, and we consider reorientation data on these systems below. Rotational Diffusion Dynamics. The T1 data for the systems studied indicate that the efficiency of vibrational energy transfer is substantially the same for perylene and 1-methylperylene in toluene, but the interactions between perylene and benzene are measurably different than they are for 1-methylperylene and benzene. Rotational diffusion measurements have proven useful in the past in helping to elucidate local organization about
14596 J. Phys. Chem., Vol. 100, No. 35, 1996
McCarthy and Blanchard
Figure 5. (a) I|(t) and I⊥(t) and (b) R(t) for 1-methylperylene in toluene.
perylene and 1-methylperylene,24,56 and there is a growing understanding of the role of polar intermolecular interactions in determining orientational relaxation behavior.80 Previous data on 1-methylperylene in n-alkanes indicate that the probe molecule reorients as a prolate rotor in short n-alkanes and as an oblate rotor in n-alkanes longer than n-octane.56 In contrast, perylene was seen to reorient as a prolate rotor in all of the same n-alkanes.24 Comparison of these two bodies of data indicates that the nonplanar conformation of 1-methylperylene affects its interaction with surrounding solvents significantly. The rotational diffusion data we present here for perylene in benzene and toluene both yield single-exponential decays of the induced orientational anisotropy, R(t), indicating that perylene behaves as a prolate rotor in both of these solvents.24,56 The achievement of a single-exponential anisotropy decay for these systems is not limited by the achievable signal-to-noise ratio. The reorientation behavior of 1-methylperylene is different in the two solvents. In toluene, 1-methylperylene exhibits a single-exponential anisotropy decay (Figure 5), indicating that it reorients as a prolate rotor.56 In benzene, a double-exponential anisotropy decay is measured, indicating reorientation as an oblate rotor (Figure 6). The equations for R(t) for oblate and prolate rotors are useful in interpreting the τOR data. For these equations, the long chromophore π-plane axis is taken as the x axis and the z axis is perpendicular to the chromophore π plane. A prolate rotor is given by the condition Dx > Dy ) Dz and an oblate rotor by Dz > Dx ) Dy.
prolate:
R(t) ) (4/10) exp(-6Dzt)
(6)
oblate: R(t) ) (3/10) exp(-(2Dx + 4Dz)t) + (1/10) exp(-6Dxt) (7) The single-exponential decays we recover for perylene in both solvents and for 1-methylperylene in toluene yield τOR ) 6Dz-1 ) 15 ps, or Dz ) 9.26 GHz. Despite the fact that Dx is not determined in these measurements, Dx > Dz, yielding Dz/Dx < 1. For the double-exponential decay seen for 1-methylperylene in benzene, the times τOR correspond to Dz ) 16.4 GHz and Dx
Figure 6. (a) I|(t) and I⊥(t) and (b) R(t) for 1-methylperylene in benzene.
) 0.60 GHz. Thus Dz/Dx = 27, implying a very significant change in the effective rotor shape of 1-methylperylene for the two solvents. Perhaps even more striking is that the limiting value for 1-methylperylene in the n-alkanes was found to be Dz/Dx ) 8.5.56 Correlation of the reorientation behavior with the T1 relaxation behavior indicates that the organization of benzene about 1-methylperylene is such that the alignment of the donor and acceptor modes yields a value of 〈κ2〉 < 2/3. While the fundamental reason for the apparently anomalous reorientation behavior of 1-methylperylene in benzene remains unclear and requires further examination, a clear implication of these data is that the efficiency of T1 relaxation for both probe molecules is mediated primarily by intermolecular alignment effects, in agreement with the relaxation behavior measured for 1-methylperylene in the branched alkanes.57 While it is fair to question what changes in intermolecular alignment could account for these data, we do not have sufficient information to draw definitive conclusions regarding solvent local organization about the solute(s). Conclusions We have measured the vibrational population relaxation and rotational diffusion dynamics of perylene and 1-methylperylene in benzene and toluene using pump-probe stimulated emission spectroscopy. We find that the vibrational relaxation dynamics do not correlate simply with the order of polar D-A coupling. The reorientation dynamics of 1-methylperylene in benzene are fundamentally different than for this same probe molecule in toluene or for perylene in benzene. The fundamental reason for this unexpected confinement of the 1-methylperylene motion in benzene is unclear as yet, but is strongly indicative of local organization of the solvent about the solute. The fact that the T1 time for 1-methylperylene in benzene is measurably slower than for the other systems we report indicates that the solute confinement is effected in such a way that the donor and acceptor vibrational coordinates (in-plane ring distortions) are poorly aligned. It is apparent that the organization of the solvent about the solute can play a dominant role in determining reorientation as well as vibrational population relaxation. It is
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