The Journal
Optical Pulse Sampling by Frequency Conversion
of Physical Chemistty, Vol. 82, No. 21, 1978 2273
Picosecond Optical Pulse Sampling by Frequency Conversion. Studies of Solvent-Induced Molecular Relaxation Leslle Hallidy and Mlchael Topp' Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19 104 (Received December 16, 1977; Revised Manuscript Received April IO, 1978) Publication costs assisted by the National Science Foundation
Frequency conversion techniques have been adapted for use in picosecond optical gating applications,in particular the measurement of subnanosecond fluorescence profiles. The major advantages over Kerr-cell methods are the higher intrinsic signal-to-backgroundratio and the facility for ultraviolet fluorescencetime resolution. Direct picosecond-time-resolved measurements have been made of the temperature-dependent Stokes shift of the fluorescence spectrum of 2-amino-7-nitrofluorene in different polar solvents over a range of temperatures. Fluorescence decay times measured at different wavelengths in a single solution were found to vary by up to an order of magnitude. These findings are interpreted in terms of two independent relaxation processes: solvent polarization and solvent-assisted fluorescence quenching. 1. Introduction
Fluorescence spectroscopy is among the most useful techniques for studying the environment of molecules in solution, since the relative positions of the fluorescence and absorption maxima of polar molecules in solution depend on interactions between the solute dipole and the dielectric properties of the solvent medium. Also, the bandwidth of optical methods permits rapid time resolution. Yet, the prevalent use of time-integrated spectroscopy leads to the loss of much valuable information about liquid structure and molecular relaxation processes. In fact, a solution consists of molecular entities characterized by dipole moments, symmetry, and the presence of specific interactions and, in order to study directly the molecular properties of liquids, it is necessary to measure the time dependence of parameters sensitive to the configuration of the molecular environment. The timescale of solvent-solute molecular relaxation is, for most common solvents, in the subnanosecond range which immediately poses problems for the experimentalist wishing to make direct measurements. That is, although in many cases competition or time-integrated methods can give information about rate constants, they require assumptions which it is frequently difficult to justify and give little information about the energy distribution of solute molecules during the relaxation process. This paper emphasizes the use of picosecond fluorescence spectroscopy to time resolve fast molecular changes. Fluorescence methods have some significant advantages over absorption methods, one of the most important of which is that it is possible to obtain a fluorescence spectrum and information about excited state lifetimes (via quantum-yield measurements) even when either the lifetimes or spectral bandwidths are not directly resolvable because of experimental 1imitations.l-l' Fluorescence measurements reflect the state of the molecule during the lifetime of the emitting state s) whereas the information obtained by absorption spectroscopy represents a time average over the duration of a probing light pulse (which depends on the sophistication of the technique). Over the last few years, picosecond laser methods have been developed and applied to a large number of problems associated with the general topic of radiationless decay. Much progress has been made in areas where the time resolution of the laser has permitted flash photolytic analysis. However, two principal areas have proved more difficult. First, it has been established that, for many large 0022-3654/78/2082-2273$01 .OO/O
molecules in solution, the relaxation times of states higher than the lowest excited singlet states are less than currently available laser pulse durations and therefore have not been time resolved (although their fluorescence is now well known) Second, even for slower processes, technological deficiencies have prevented a major systematic analysis of luminescent phenomena, although the recent development of high-resolution streak cameras has provided a partial (but expensive), solution to the problem. In this paper, we discuss the development of optical sampling in the form of frequency-conversion gating, a highly versatile and reproducible method satisfying most of the exacting requirements for picosecond fluorescence spectroscopy.12 2. Fluorescence Gating In an optical gating experiment, two of the most important factors are the fraction of signal during a given time element which may be transformed and the selectivity of the discriminator in cutting off the unchanged fluorescence pulse. The operation chiefly falls into one of two categories: depolarization or frequency conversion. Both convert a few percent of the gated time segment but the major difference arises in the discrimination step. In considering the required rejection ratio of the discriminator, we assume that the time width of the gate represents 0.1-1 7'0 of the fluorescence profile duration. The conversion efficiency is typically 1-lo%, and it is also important to plan for a signal-to-noise ratio of about lo2 for adequate quantitative analysis of data. Thus, a rejection ratio of about lo6 is needed. Crossed polarizers typically may have a rejection ratio in the vicinity of 104-105, which is also susceptible to any small depolarization effects in intermediate components. On the other hand, frequency-conversion gating has essentially zero background and the above requirements are easily satisfied. The technique of optical sampling by frequency conversion, which was suggested by Duguay and Hansen in 1968,13has been extensively used for gating infrared laser pulses. It has more recently been used for fluorescence work by Hirsch et al.14 who used a continuous wave pumped mode-locked rhodamine dye laser to up-convert fluorescence a t 780 nm by mixing in a type I phasematched lithium iodate crystal. The essential principle of frequency-conversion gating is to combine two optical pulses in a nonlinear optical element such that sum or 0 1978 American Chemical Society
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The Journal of Physical Chemistry, Vol. 82, No. 21, 1978
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excitation or by appropriate geometrical selection, the effect of stimulated emission on the fluorescence decay profiles can be effectively eliminated. For all measurements reported here, we ascertained that the shapes of the fluorescence profiles were independent of excitation intensity.
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Figure 1. Optical arrangement for type I1 phase-matched frequency conversion of picosecond fluorescence signals. A variable optical delay is used to vary the synchronization of the short sampling pulse with the sample fluorescence profile at the KDP frequency converter.
difference-frequency pulses are produced. If a single frequency is incident and the phase matching is type I, then the measured pulse profile, generated by scanning the arrival time of one of the pulses, resembles that obtained from a two-photon fluorescence experiment. That is, a symmetric pulse autocorrelation profile is produced, with substantial background signal. However, if the two pulses have different wavelengths, or if type I1 phase matching is used, then the background is essentially zero. In our system, shown in Figure 1,the fundamental from a mode-locked Nd3+glass laser was used as the pump beam and the mixing was accomplished in a KDP crystal with type I1 phase matching. The fluorescence was detected as either the sum or difference frequency. The sampling time was -10 ps as determined by the 7-ps duration of the 1060-nm pulse and a dispersion of -2.1 ps/cm between 1060 and 530 nm. In contrast with the Kerr cell, we note that the device is not only a time gate, but a frequency gate as well, Le., by changing the angle of the incident 1060-nm and fluorescent pulses with respect to the optic axis in the crystal, the phase-matching conditions may be changed to select a different fluorescence wavelength for conversion. At the same time, the degree of coarse tuning is such that a single angle-tuned crystal is sufficient for gating signals from 250 to >1100 nm, and almost all of this range is covered by a span of 15' in phase-matching angle.12 We are now in a position to obtain valuable new information about certain subnanosecond molecular relaxation processes including (a) time-resolved fluorescence Stokes shifts, the study of solvent-solute relaxation by dipole-induced molecular reorientation; (b) fluorescence depolarization, the study of relaxation by free reorientation of solute molecules or solvent-solute aggregates; and (c) rapid fluorescence quenching, a mechanistic study of radiationless relaxation induced by specific solvent-solute interactions. In addition to the above processes the tendency for fluorescent samples, on laser excitation, to emit amplified fluorescence is quite strong, as has been evidenced by many of the early publications on picosecond luminescence measurements. This effect has been quantitatively analyzed by Robinson and c o - ~ o r k e r susing , ~ ~ streak camera techniques, In general though, for dilute samples, for weak
3. Time-Resolved Fluorescence Spectroscopy of 2-Amino-7-nitrofluorene (ANF) Lippert and others1G19have put forward theories which roughly describe the spectral behavior of molecules in solution, in particular medium-sized molecules in solvents of various polarities. However, the fluorescence frequency shifts so calculated will only be observed in the limit of complete relaxation within the upper state and thus the Lippert equations are not applicable to highly viscous solutions, or to the emission spectra of short-lived excited states. The equations, which do not allow for shape changes of the spectra, also assume a homogeneous dielectric and therefore they cannot account for fluorescence behavior in mixed solvents. Several attempts have been made to time resolve molecular Stokes fluorescence shifts including (a) application of nanosecond techniques to low temperature or otherwise viscous solutions;2k22(b) competitive quenching, for example, by molecular oxygen;23and (c) directly using picosecond laser Direct measurements have the advantage that an accurate and systematic study will permit a quantitative understanding of the various relaxation processes involved, since the population distribution of excited states can be measured and few, if any, assumptions are necessary. 4. 2-Propanol Solutions We have applied frequency-conversiongating to the time resolution of the Stokes fluorescence shift by measuring the temperature and wavelength dependence of the fluorescence profile of ANF in 2-propan01.~~ We have measured the (time-integrated) fluorescence maximum of ANF in 2-propanol to be near 690 nm, shifted by >10000 cm-' from the absorption maximumO2'Further, the fluorescence is strongly quenched by hydrogen-bonded interactions and therefore it was anticipated that two relaxation processes should be observed. Two general types of fluorescent excited state are involved: FranckCondon states which are thermally cold but which are environmentally unrelaxed, and fully environmentally relaxed states. To resolve the Stokes shift, the fluorescence profile was monitored over a range of temperatures, a t four principal wavelengths, 487,563,628 and 707 nm, by up-conversion to 334, 368,395, and 424 nm, respectively, Typical results are presented in Figure 2. It is possible to describe the temperature dependence of the rate constants in terms of two activation energies. First, it is important in anticipation of future discussion to express the deactivation rate of the high-frequency fluorescent states as a sum of two rate constants. The Franck-Condon states are being deactivated not only by environmental equilibration, k,, but almost as importantly, by a combination of radiative and radiationless processes, kd. Thus, the effective yield of environmentally relaxed states from the Franck-Condon states is
k, a=------k, + kd
- 85-90%
The loss is predominantly nonradiative, since the fluorescence quantum yield of the Franck-Condon states is -0.1% a t room temperature. In the absence of evidence
The Journal of Physical Chemistry, Vol. 82, No. 21, 1978 2275
Optical Pulse Sampling by Frequency Conversion
T I M E (psec)
Flgure 2. Sample measured fluorescence profiles of ANF in 2-PrOH close to 200 K. The rise at 630 nm is the inverse of the fall at 490 nm indicating that initial high-frequency fluorescence due to FranckCondon states is being replaced by a low-frequency spectrum due to
fully relaxed states.
argument in which electronic relaxation is assumed to compete more effectively with that for relaxation of the Franck-Condon states. Several conclusions may therefore be drawn from our preliminary work. (1) The shape, position, and quantum yield of the fluorescence spectrum of ANF in 2-propanol as a function of temperature can be analyzed in terms of two distinct relaxation processes. (2) The time-integrated fluorescence spectrum a t low temperatures is primarily that of the environmentally relaxed species, as determined by the ratio of k,'/kd. It is clear that the spectrum of the fully relaxed state depends on temperature in a manner in direct opposition to predictions based on the magnitude of the bulk dielectric constant. Such spectra need to be measured accurately for a better picture of dipolar solvation to emerge. (3) The rate of the Stokes shift is significantly faster than predicted on the basis of spontaneous solvent dielectric relaxation. For example, we measure a relaxation time a t room temperature to be e10 ps whereas the measured spontaneous dielectric relaxation time is 25 ps. 5. Rotational Depolarization
t o the contrary, we assume that kd also characterizes the decay of the relaxed states, in which case, the two observed rate constants are k,' = k , + k d , observed a t short wavelengths and k d , observed on the long wavelength side of the fluorescence spectrum. From our data, we find activation energies for k , and kd to be 1.5 and 2.6 kcal mol-', respectively. This is consistent with our mechanistic interpretation since k , results from molecular rotation whereas k d involves hydrogen-bonded interactions. However, further work is necessary on similar systems to allow a more quantitative understanding of the mechanistic differences. Thus the total time-integrated spectrum results from a superposition of spectra from many states of different lifetimes, of which the "Franck-Condon" and environmentally relaxed states represent the extremes. It is therefore tempting to rationalize the position and shape changes of the spectra with temperature on the basis of different proportions of these. However, it is clearly not valid to assume that the shapes of the spectra of either the relaxed or unrelaxed forms are temperature independent, since the total spectra are blue-shifted with decreasing temperature, although there is apparently ample time for full Franck-Condon relaxation to occur. In fact, k , decreases more slowly than kd and the total spectrum should have a greater contribution from relaxed levels. (Inspection of the high-frequency edge confirms this by showing a red shift a t lower temperatures.) Also, proportionately increased fluorescence quantum yields are definitely observed with decreasing temperature, showing that no extra competitive deactivation processes come into play. Hence the spectrum of the relaxed state must shift to the blue with decreasing temperature. We note that a simple dielectric constant argument does not hold, since E increases to lower temperatures and a greater red shift would be predicted. Clearly, the spectrum a t low temperatures (which is predominantly dynamically relaxed, since k,'/kd 10) is much sharper and it is probable that the more tightly bound structure of the alcohol at low temperature actually inhibits dipole-induced polarization producing a much more highly ordered solvate. Thus, we should refer to the nature of the final solvation state in considering the temperature-depehdent blue shift. We believe this to be a more satisfactory explanation than the simple dynamic
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Fluorescence polarization has been widely studied by immobilizing molecules for periods of time comparable to or greater than their natural fluorescence decay times. In the picosecond region, we have seen from the work of Fleming et a1.l1 the effect of simultaneous depolarization on the fluorescence profiles of rapidly relaxing excited states in low viscosity media. We have presented measurements of the Stokes relaxation of ANF in 2-propanol solutions, involving time-resolved measurements of the subnanosecond profiles a t different temperatures and wavelengths. Now, it is important to observe that phase-matched frequency conversion automatically detects polarized light, since the selection of one or other of the propagating rays in a KDP crystal acts as a polarization operation. Two points are therefore raised: (a) To what extent does depolarization affect our observed profiles? (b) Is it possible using this effect to measure the dynamics of fluorescence depolarization? First, in order to observe the maximum fluorescence polarization, it is necessary that absorption saturation be avoided, since this would affect the isotropic distribution of ground state molecules and a cos2 8 distribution of excited states would not result. Further the effects of directionally amplified fluorescence must be eliminated. Because of the low sensitivity of early picosecond fluorescence detection techniques, much of the early literature is complicated by such anomalies. As we show here, it is possible to avoid these problems and still obtain high signal-to-noise fluorescence time profiles using frequency-conversion gating. For 2-propanol, it was supposed that the depolarization rate due to rotational diffusion was a t least an order of magnitude longer than the relaxation rates being measured, by analogy with recent examples in the l i t e r a t ~ r e . ~ ' , ~ ~ , ~ ~ However, where aggregative solvation is not important, free molecular rotational diffusion would cause the depolarization rate to drop into the range of 10-lo-lO-ll s in low viscosity solvents. This could then interfere with measurements of Stokes relaxation, presumed to be in the same region. Therefore, it was an integral part of this work to determine the fluorescence profile due to depolarization alone, in solutions where fluorescence quenching was unimportant. An excellent example is found in the case of ANF in
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The Journal of Physical Chemistry, Vol. 82, No. 21, 1978
L. Hallidy and M. Topp
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Figure 3. Fluorescence profiles of ANF in odichlorobenzene observed immediately following picosecond-pulsed excitation. Excitation at 354 nm, sampling at 560 nm. Three polarization configurations are indicated in the diagram. The left-hand arrow indicates the sampling polarization, constantly vertical. The right-hand arrow indicates the excitation polarization. The differences in shape are accountable in terms of the theory discussed in ref 11.
o-dichlorobenzene, where the fluorescence decay time is of the order of 2 ns, while in this low viscosity solvent the fluorescence depolarization by rotational diffusion should occur in 10-20 ps. Thus, a profile should be observable in which depolarization is the sole intensity-controlling factor, provided that adequate time resolution is available. The results shown in Figure 3 illustrate this point. The effects of fluorescence depolarization have been summarized mathematically recently by Fleming et al.ll Using the equations presented in that work it is possible to calculate the ratio of intensities of the signals at different times. Thus, the function (Pz[e(0).e(t)])= 1 and 0 at times t = 0 and t = m, respectively. This leads to the conclusion that, for excitation and analyzer polarizations parallel, the detected fluorescence intensity should decrease by a factor of 915 during the depolarization process while for the perpendicular configuration, an increase of a factor of 513 should be observed. This is consistent with the findings reported in Figure 3. It can also be shown that the change in detected polarized fluorescence intensity following polarized excitation can be eliminated by arranging the angle between excitation and analyzer polarization to be tan-' 4 2 = 54.7".
6. T h e Stokes Shift in o-Dichlorobenzene Solution Lippert and c o - w ~ r k e rhave s ~ ~ studied the fluorescence Stokes shift in o-dichlorobenzene solution by an indirect method. The principle behind their approach was to shorten the fluorescence decay time by stimulated emission dumping such that the fluorescence a t higher intensities would proceed from progressively less relaxed states thereby blue-shifting the emission. These authors were able to relate their observations qualitatively to a solvent-solute interaction possibly associated with solvent reorientation. We have followed these experiments, by making direct measurements of the wavelength-dependent fluorescence
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Flgure 4. Fluorescence profiles observed at 490 nm for ANF in o-dichlorobenzene. The peaks, proceeding from the most intense to the least, were recorded at 259, 295, and 319 K, respectively. Subsequent fluorescence was effectively unchanged, but the increase in peak height reflects increasing quantum yield and therefore lifetime of Franck-Condon states relaxing within our apparatus resolution.
profiles, as for the 2-propanol solutions. Control experiments between 560 and 630 nm established that, following a rapid, almost pulse-limited rise time, fluorescence persisted into the nanosecond region even a t room temperature, verifying the relatively high quantum yield in this solvent (see Figure 3, middle trace). Subsequently, the high-frequency edge of the spectrum (487 nm) was probed to resolve Franck-Condon state fluorescence such as we have reported in 2-propanol solutions. Sample experimental traces are presented in Figure 4. At the temperatures used, the profiles were seen to have two components, the intensity ratio of which was temperature dependent. Polarization effects here were effectively eliminated by 45" polarization of the exciting beam with respect to the analyzer and, as can be seen, the short-lived component of the fluorescence profile was not resolvable from the apparatus resolution, even close to the freezing point of the solvent. The sharp feature a t early times corresponded to a pulse-limited fluorescence profile, which we attributed to temporally unresolved Franck-Condon states. This profile was observed to be independent of temperature at our time resolution (- 15 ps) and within our experimental error. (We estimated that the normal time resolution of 10 ps was extended to -15 ps by dispersion between the irradiation and fluorescence pulses in 10 mm of o-dichlorobenzene solvent.) The trailing edge of the fluorescence profile appeared constant on this time scale, and was identified with the nanosecond fluorescence decay previously measured a t longer wavelengths. If we make the reasonable assumption that, in this nonassociated solvent, both the fluorescence spectra and radiative lifetimes of the Franck-Condon and relaxed states are temperature independent over our small range, we can estimate the relaxation times of the FranckCondon states, which are observed to relax within the experimental time resolution. (Measurements a t lower temperatures were limited by the freezing point of the solvent (256 K).) We assume that, if the states have much shorter lifetimes than the pulse duration, the integrated fluorescence intensity (Le., as detected by our technique)
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The Journal of Physical Chemistry, Vol. 82,No. 27, 7978 2277
4-Methylumbelliferone Fluorescence
TABLE I: Measured I n t e n s i t y Ratios of Fluorescence at -490 nm for A N F / o - D i c h l o r o b e n z e n e a t t h e Pulse M a x i m u m and after Franck-Condon Relaxation temp,
K
331 319 295 259
intensity ratio 2.6 i. 0 . 3 5.0 f 0 . 3 6.7 i. 0 . 3 22 f. 4
will be proportional to the lifetime. On the other hand, the recorded intensity of the long-lived tail will be constant. Thus, the ratio of the two intensities will allow an estimate of the relative decay times of the Franck-Condon states a t different temperatures. (See Table I.) Since the relaxation time of the fluorescence profiles is not distinct from the pulse (Le., the full widths a t halfmaximum intensity are virtually identical at -20 ps), we may assume an upper limit for the relaxation time of < l o ps a t 259 K. Thus, the computed decay time a t 295 K would be
