Report
Stimulated Emission Spectroscopy in the Time Domain
F
our fundamental processes form the foundation for the broad range of resonant optical spectroscopies used today—spontaneous absorption, stimulated absorption, spontaneous emission, and stimulated emission. Spontaneous absorption is commonly known as thermal population and is described by Boltzmann statistics. Stimulated absorption is usually referred to simply as absorption and is one of the most widely used measurement techniques in
The purpose of this Report is to provide an update on stimulated emission spectroscopy, especially in the time domain. This work is fundamentally different from previous applications of stimulated emission and demonstrates an evolving technique that is likely to have significant application to the chemical biological and material sciences Although stimulated emission cannot compete with absorption and fluoresrpnrf1 for routine analyses it IQ «pn£} a i\nA&i\T iiO£*/1 rkrtd
extremely sensitive technique. Stimulated emission, though not as widely used as fluorescence and absorption for making direct chemical measurements, enjoys wide application because ct ia the process by which lasers operate. Stimulated emission was predicted as a , optical effect in 1917 (1),
Time-resolved stimulated emission spectroscopy provides the opportunity to measure vibrational state lifetimes in systems where such measurement have previously not been possible
but it waprot until several decades later _
G. J . Blanchard
curiosity.
Michigan State University
0003-2700/97/0368-351 A/$14.00/0 © 1997 American Chemical Society
rescence, and we can expect stimulated emission measurements to fill an increasingly important niche that has been notonously difficult to access. Specifically, stimulated emission can be used to measure thr lifotimes of selected vibrational resonances in complex organic molecules.
Such lifetime information is valuable because it can be related to kinetic information that helps us understand chemical interactions from a molecu-
Analytical Chemistry News & Features, June 1, 1997 351 A
Report lar perspective. Interactions between dissimilar molecules determine many of the fundamental processes that are central to the chemical sciences. For example, solubility, crystallization, the efficiency of separation and extraction, and chemical reactivity all depend on the extent and nature of interactions between dissimilar molecules. Although the energetics of these interactions can be understood in macroscopic terms, such as chemical potential, an understanding of bulk behavior cannot provide molecular or structural insight into these To understand chemical interactions from a molecular perspective several kinetic spectroscopies in which stimulated emission is the optical property that communicates information including chromophore rotational diffn'intermolecular transfer from the system
Basic considerations
Absorption and stimulated and spontaneous emission can be described in the context of the Einstein coefficients^ and B for a generic two-level system (i)
in which AE21 is the energy diiffeence between states 1 and 2, kB is the Boltzmann constant, and Tis temperature. It is clear from Eq. 2 that the rate constants of stimulated emission and spontaneous emission are related, and it is typically assumed that the chemical information contained in stimulated emission data is equivalent to that available from spontaneous emission. Because of the high sensitivity of spontaneous emission spectroscopy and the relative ease of measuring it, there has been, until recently, only a limited effort aimed at using stimulated emission directly for chemical spectroscopy applications. For most organic chromophores, however, the assumption that stimulated emission and spontaneous emission data are equivalent is incorrect. The spontaneous emission rate for a given (excited) molecule does not depend on the presence of an external light source, whereas the stimulated emission rate does (Eq. 1). Although not a concern for simple twolevel systems, for multilevel molecular systems spontaneous emission is a measure of the depopulation of a single state with no predetermination of the final state for any given photon.
In contrast, stimulated emission is a process in which two stationary states are coupled by an external electric field. For spontaneous emission, the important parameters in determining emission intensity are the Franck-Condon factors for the transitions and population of the excited state. Only electronically excited molecules are involved in the process. The intensity of stimulated emission also depends on the Franck-Condon factors for the transition under investigation; howthe populations of both the initial (excited electronic) and final (ground vibrational) states also contribute This latter point is central to the ability of stimulated emission spectrosconv to measure ground-state vibrational lifetimes Stimulating t h e emission
We use a stimulated emission pump-probe technique (Figure 1) to measure vibrational state lifetimes (2). This experimental approach has broad application because it allows the introduction of a perturbation to the chemical system at a well-defined time. How the system responds to the perturbation provides insight into interactions between molecules, including any persistent molecular-scale organization that may exist
dN./dtl^-B^N, dN2/dt\stimem = -B21pvN2 dN2/dt\spontem = -A2lN2
(1)
in which N is the population of the subscripted states (state 1 is the ground state and state 2 is the excited state), pv is the power density of the incident electric field at frequency v, A21 is the rate constant for spontaneous emission, B12 is the rate constant for absorption, and B21 is the rate constant for stimulated emission. Einstein derived the relationships between the rate constants for the processes, B12 = (gi/g2>B22 A21 = (8nhv /c )B21 (2) in which g is the degeneracy of states 1 and 2. None of these processes can be considered in isolation: All are active for Nj > 0 and dv > 0. For spontaneous absorption, the steady-state population N2 is given by Boltzmann statistics "2 = ^rl'^r2)"leXP'""^'21' *B-' > 352 A
W
Figure 1 . Pump-probe spectrometer used for stimulated emission measurements. Time resolution is ~ 10 ps. Although shorter pulse lasers can be used, the loss of spectral selectivity associated with short pulses limits their utility for this application. For these experiments, typical signal size is AT/T— 10~4.
Analytical Chemistry News & Features, June 1, 1997
in the system. For most measurements of this type, a perturbation is applled and the dissipation of the perturbation is measured directly. Photobleaching experiments, for example, monitor the recovery of the ground-state population depleted by the pump laser through the transient reduction in absorption of the probe laser. For vibrational lifetime measurements using stimulated emission, we practice a little-used variant of the pump-probe technique. For our experiments, it is the excited electronic-state population that is established by the pump pulse, and the stimulated response depends on the rate at which the steady-state population of the selected vibrational resonance is established. The evolution of the vibrational population of interest is mediated by spontaneous emission from the excited electronic state and spontaneous population and depopulation of the vibrational state The probe laser pulse acts only as a means to ocauire a "snapshot" of the system at a giventimeafter excitation and does not itself alter the relaxation of the system because thp timp interval hptwppn individual pumn—nrnhp eventQ i«
much longer than the relaxationtimeof the entire molecular system An important consideration in measuring vibrational relaxation is the trade-off between time resolution and frequency resolution, which is ultimately limited by the uncertainty principle. Although femtosecond lasers may seem suitable for measuring vibrational dynamics because of the shortness of their pulses, the bandwidth of these lasers is too large in many cases to achieve the requisite frequency resolution. The best trade-off for vibrational lifetime measurements ii so use picosecondtimeresolution correspondinsf to a transform-limited light bandwidth of several cm"1 a good match with typical room-temperature molecular vibrational resonances Information content of the stimulated signal
For any pump-probe laser experiment, absorption and stimulated emission need to be considered for each transition to achieve a quantitative understanding of the signal. The signal we detect is AT/T, the fractional gain or loss in intensity of the probe pulse caused by the action of the pump pulse on the sample.
To understand the stimulated gain signal in the time domain and extract vibrational relaxation information, the probe molecule is modeled as a strongly coupled three-level system (Figure 2). Absorption and stimulated emission will proceed for any two levels coupled by an external electric field, and both processes for the 1 o 2 (0-0) transition and the 2 > (0-v) transition need to be considered. For fluorescent probe molecules, the cross section for the 1 2 absorption all contribute measurably. For our experiment, the stimulated gain on the probe laser beam resulting from the 2 —> 3 transition is ~ ~100 photons per pulse, and 3 —> 2 absorptive loss is ~ 100 photons per pulse, yielding AT/T ~ 1.5 x 10"4, in good agreement with the data. A unique characteristic of this measurement is that the magnitude of the AT/T signal is independent of the probe laser intensity because it is the balance
Figure 2. Transitions accessed by the pump and probe lasers in a coupled three-level system.
between stimulated emission and absorption that givesriseto the net signal, and both processes depend on the incident electric-field power density pv in the same way (Eq. 1). In fact, this property is used as a check to ensure that stimulated emission and absorption contribute to our experimental signal, in which the probe laser intensity independence of these AT/T decays is seen over a range of 103 variation in probe laser incident The general case for pump-probe measurements on a coupled three-level system is
in which levels 1,2, and 3 and populations Nv N2, and N3 for this kinetic scheme correspond to states 1,2, and 3 in Figure 2. For pump-probe measurements, the excitation of the 1 2 transitioo nan nb considered an instantaneous process to establish the initial condition for a simpler kinetic scheme sensed by the probe laser acting on the 2 o 3 transition.
The term k13 is included to account for vibrational resonances that are affected by spontaneous thermal population. For vibrational resonances higher in energy than ~ 750 cm-1, thermal population affects the vibrational lifetime k'z\ negligibly. The time evolution of the populations of all states can be modeled using a set of coupled differential equations that can be solved analytically (4). Eq. A-D are the
Analytical Chemistry News & Features, June 1, 1997 353 A
Report out of phase. The signal S(t) appears as the sum of the populations N2(t) and N3(t) instead of the difference.
Equations for the analytical solutions of the differential rate equations describing Scheme II. Equations A and B are the population evolution of the excited electronic state and ground vibrational state of interest. Equations C and D are the roots of the quadratic that is the solution of the secular equation. Equation E is the expression for the time-resolved stimulated gain signal.
S(t) = (AT/T)(t) =N2(t) -[-N3(ty\ = N2(t) + N3(t)
gV / = LV 32"13-'' ^32"13
23 13
The experimental signal expressed in (A)terms of the rate constants is shown by Eq. E. When the approximations X+ = k1x + k31 and d._ = k23 are included and the thermal rate constant is small (k13 ~ 0), a signal is recovered that is substantially simplified and easy to visualize as (B)
{[X+/(X+ - -_ )]exp(-A.J) + [X_ /(X+-X_ y\exp(-Xj) + 11 + l[(A.+- k23)/iX+ - X_ )]exp(-A,_0 - [(X_[ k23)/(Xi-X_ )]exp(-A.+r)) Thefirstterm in brackets equals km. N3(t) = [(A23^13)/(^32A13 + #23^13 + ^23^3l)M - ^y(^"+ - ^- )] ex P(~^J) +
[X_/(X+-X_)]exp(-XJ) +11 + {[k23/{X+-X_)[exp(-X_t) -exp(-XJ)]} The first term in brackets equals km.
S(t) = eXp(-&230 - ((23/&3l)exP(-^3l0 (5)
A+ = ( { / 2 ) {(fe23 + &32 + k31 + k13) k [(fc23 + &32 + ^31 2 ^13) ~ '*V"'23 31
X_ = (1/Z)\(K23 '*v"'23 3i
23 13
32"13'-!
'
* W
+ kr>2 + «31 + «yx) - L(«23 "*" 32 + 31 "^ 13^ 23 13
32 13^-1
'
W)
S{t) = kN2 + km m [A.+/(^.+ - X- )][kN2 + km + l]exp(-Xj) [X_ /{X+ - X_)][l-km - km]exp(-Xj)
solutions to the rate equations describing Scheme II, but the physical significance of the quantities X+ and X_ is not immediately apparent in this form. It is useful to consider the simplifications that are appropriate under the conditions typical for solution-phase organic chromophores. Specifically, the rate constant used to describe vibrational-state population relaxation k31 is typically much larger than the rate constant k23, which for these measurements is the sum of the spontaneous and stimulated emission rate constants. Under these conditions A = k +k 1nd K._ =
R23.
The time evolution of gain will, in general, differ from that of loss, because the initial population conditions of the states responsible for gain and loss are different. Near time zero, where the signal is virtually all gain because N3(0) ~ 0, intuitioo nuggests that a larger signal will be detected compared with later times when gain and loss both contribute. This form of the signal could be observed if we measured the absolute number of photons resulting from the interaction of the probe laser pulse with the 354 A
(4)
23 31^-1
(E)
sample. However, the modulations applied experimentally to extract the signal from the background affect its form. The sign and phase of the modulations applied to populations N2 and N3 by the pump and probe lasers must be considered. Although we use three modulations to encode the experimental signal (5-7), the resultant modulation is equivalent to a single amplitude modulation applied to the excited electronic-state population N2 (8,9). The action of spontaneous emission populates state 3 on a time scale significantly faster than the modulation period thus the modulated populations of states 2 3.nd 3 are effectively in ph3.se with another The sign of the gain modulation is positive with respect to the ambient condition, and the sign of the loss modulation is negative compared with the absorptionfree background. Because the gain- and loss-inducing populations are in phase but their associated signals possess opposite signs with respect to their background conditions, the gain and loss modulations are seen by the detection electronics to be
Analytics! Chemistry News & Features, June 1, 1997
The difference between two exponential functions is the form of the experimental signal. The pre-factor k23/k31 of the second term in Eq. 5 is typically a few percent of the total signal intensity. The signature of vibrational population relaxation in pumpprobe experimental data is subtle, and for noisy data it is possible that vibrational lifetime information will be obscured. The above treatment applies to population dynamics and measurements in solution need to be made with the pump and probe laser polarizations offset by 54.7°. A case study
The measurement of vibrational population relaxation in the liquid phase has received limited attention, in part because it is commonly assumed that, for roomtemperature liquids, all of the vibrational energy in a given molecule is thermalized "instantaneously" and dispersed to the bath modes in a purely statistical manner. This expectation is based on the high density of states available in such systems and the assumption that coupling between a given solute vibrational resonance and all bath modes is relatively strong. Although it is reasonable to expect pathwayselective vibrational relaxation in lowtemperature solids (10-14) and possibly in gases the case for pathway-selective relaxation in room-temperature liquids is develnnino" only now
Recent data on perylene in alkane solvents have demonstrated that vibrational population relaxation into specific solvent bath modes can be seen. The relaxation of the perylene 1375 cm-1 ring breathing
mode proceeds with a time constant of 30 ps in «-C8H18 and 300 ps in «-C8D18 (15), counter to the expectations of a simple density-of-states argument and consistent with resonant coupling—primarily to a specific bath mode. Considerable chemical information is available from vibrational lifetime measurements, and a simple "thermal" argument does not provide an adequate explanation for our data. Beyond the ability to measure relaxation time(s) of a given solute molecule vibrational mode, it is important to be able to discern and interpret the chemical information available from these data. For rotational diffusion, the relaxation time constant (s) for a given solvent-solute system can be related to chemically useful information, such as the solute rotational diffusion constant and the angle between ground-state and excited-state transition moments, according to a well-developed theoretical foundation. Likewise a theoretical framework exists for the interpretation of certain fluorescence lifetime data Unfortunately, there is no comparable model to apply to the interpretation of vibrational lifetime data. Part of the problem is die variety of possible relaxation mechanisms. Although intuition may suggest that inelastic collisions are the dominant relaxation mechanism for intermolecular vibrational relaxation, mis is not the case (16)) Long-range polar-energy transfer, such as that described by Forster for dipole-dipole coupling (17), dominates in llquids. Understanding polar coupling—electronic or vibrational requires considering the spectral overlap of the donor and acceptor and the distance between the two species and their relative orientations Although donor-acceptor vibrational spectral overlap is measurable the latter two nnantities cannot hp ; and it it difficult to relate information from such experiments to that available from other dynamic measurements that are sensitive to the dielectric properties of the local environment, such as rotational diffusion. In contrast to other measurements the absence of symmetry can actually be advantageous in interpreting vibrational lifetime data
"Stimulated emission has yet to be fully explored for chemical measurements." We chose 1-methylperylene as a probe molecule because it has sufficiently low symmetry for all of its normal modes to be IR- and Raman-active, and dipolar donoracceptor interactions dominate its vibrational relaxation behavior. In addition, its fluorescence quantum yield is near unity, precluding the need to consider competing nonradiative relaxation channels from the Sj state. We focused on alkane solvents because of their outward chemical simplicity and because their terminal methyl rocking modes have frequency of ~ 1378 cm -1 essentially degenerate with the chromophore 1370-cm-1 ring breathing mode Although almost coupling 1-methylperylene breathing mode to several solvent vibrations our experimental data can be explained hv relaxation nreriominantlv to the sol ent terminal kino-morie
1-Methylperylene in n-alkanes. The motional and vibrational energy relaxatton dynamics in thera-alkanesare highly correlated. The blue-shifted and broadened absorption and emission spectra of 1-methylperylene in M-decane compared with those for perylene can be understood in terms of the 13-23° of strain imposed on the perylene ring structure by the addition of the methyl group at the 1-posiiion (18)) The lifetimes of the 1-methylperylene 1370-cm"1 mode in the w-alkanes are shown as a function of solvent chain length in Figure 3. For solvents «-pentane through «-octane, the vibrational lifetime is fast and independent of the solvent aliphatic chain length. For solvents »-decane through w-hexadecane, the vibrational lifetime is significantly slower and solvent dependent. The solvent dependence of the vibrational lifetime data indicates the dominance of polar coupling over collisional relaxation processes. If collisional energy transfer dominated the time constant k"1 would smoothly increase with solvent alkane chain length because of the direct relationship between solvent-solute collision rate and Sfilvent viDy = Dz)z In this context, D„ Dy, and Dz are the Cartesian components of the rotational diffusion constant D. The functionality of R(t) depends on the effective rotor shape (21), prolate R(t) = 0Aexp((6Df)
shorter «-alkanes, we expect a longer vibrational lifetime, consistent with our expenmentalfindings.The change in the reorientation and vibrational lifetime data i
,
,
1
1
•
i.
,
between «-octane and «-decane indicates that the effective length of the 1-methylperylene 1370-cm" vibrational i i • • i mode coordinate is in the same range as the average length of the ensemble mf these solvent moleculel. In room-tempera-
(6)
e o e xi s, o coy se, tne aDove explanation is oDviousiy qualitative but consistent with our data. R(f) = 0,lexp(SDJ) ) 1-Methylperylene in branched 0.3exp[-(2Z)J. + 4Dz)t] (7) alkanes. The data for 1-methylperylene in M-alkanes do not resolve whether vibrational population relaxation can be exThe reorientation data for 1-methylperylene in the alkanes are shown in Fig- plained simply in stoichiometric terms for cases in which the solvent is precluded ure 3. In »-pentane through «-octane, a from forming well-organized local environsingle exponential is seen; in «-nonane ments. To resolve this issue, we studied through »-hexadecane, a double expothe 1-methylperylene 1370-cm"1 mode nential decay is measured. As the sollifetime in selected C7 alkanes, in which vent chain length increases, the rotor shape of the probe changes from prolate the density of CH3 groups and structural to oblate. For short-chain solvents, we ob- irregularity of the solvent can be controlled systematically. The vibrational lifetain only Dx from the data, yielding little times are all relatively short consistent explicit rotor shape information save for with the data for 1-methylperylene in DJDX < 1. For rhe llnger rlkane solventss short »-alkanes (24) As before the llfeboth Dx and Dz can be extracted from the times depend on the identity of the solexperimental data. We can determine vent in a way that is inconsistent with a from Dz /Dx ~ 8 that, for longer chain solor oblate
Analytical Chemistry News & Features, June 1, 1997
random solvent environment in the vicinity of the solute. The measured solventdependence of the vibrational lifetime correlates directly with solvent boiling point (25), indicating that intermolecular orientation effects dominate over simple acceptor density in determining the efficiency of resonant vibrational energy transfer in liquids. The 1-methylperylene 1370-cm"1 mode lifetime should decrease with increasing CH3 (acceptor) group concentration if the orientational distribution of solvent CH3 groups is truly random with respect to the excited donor vibrational coordinate. Our experimental data show the opposite trend (26). The most-branched alkanes give rise to the longest 1-methylperylene vibrational lifetimes, indicating local organization of the solvent molecules around the solute. The vibrational lifetimes are many times longer than the solvent Debye relaxation times meaning vibrational deDooulation is averaged over many rotations of individual solvent molecules Despite the significant onnortunity for orientational avpnginff the data reveal nprsistent solvent organization dilute The solvent moWule*;
"
i nliernment" n m r r s a
lt
of the numerous solvent conformers present in solution. The distribution of solvent CH 3 group orientations about the 1-methylperylene molecule is not sumciently random to yield a simple CrL density-dependent T•, response. These i
i
i
.
•
i
i
i
i
data implicate intermolecular alegnment rs the dominant factor over simple acceptor density in determining vibrauonal-energy transfer efficiency. In conclusion, stimulated emission has yet to be fully explored for chemical measurements. Recent work on understanding stimulated emission in the time domain has provided information on how solute molecules dissipate excess vibrational energy to their immediate surroundings, and it is now becoming clear that even in nonpolar liquids short-range organization dominates the elementary steps of energy relaxation. The ability to measure vibrational lifetimes of complex organic molecules in solution adds to the arsenal of spectroscopic tools that can be used to attack complex and important
chemical systems such as monolayer and multilayer interfacial assemblies, biological membranes, and proteins. Support for this work by Grant CHE 95-08763 from the Nattonal Science Foundatton is gratefully acknowledged.
References (1) Einstein, A. Phys. Z. 1917,18,1212 (2) Jiang, Y.; Hambir, S. A; Blanchard, G. /. Opt. Commun. 1993, 99,216. (3) Hambir, S. A.; Jiang, Y.; Blanchard, G. J. /. Phys. Chem. 1993, 98, 6075. (4) Szabo, Z. G. In Comprehensive Chemical Kinetics; Bamfordd C.H.; Tipper, C.F.F.H Eds.; Elsevier: Amsterdam, The Netherlands, 1969; Vol. 2, pp. .4-266 (5) Bado, P.; Wilson, S. B.. Wilson. K. R Rev. Sci. Instrum. .982,53, 706. (6) Andor, L; Siemion, J.; Smith, D. D.. Rice. S. A Rev. Sci. Instrum. 1984,55, 64. (7) Blanchard, G. J.; Wirth, M. .. Anal. Chem. 1986,58,532. (8) Levine, B. F.; Bethea, C. G. IEEE J. Quantum Electron. 1980, QE-16,85. (9) Levine, B. F.; Shank, C. V.; Heritage, J. P. IEEE J. Quantum Electron. 19197 QE-15, 1418. (10) Chang, T. C; Dlott, D. D. Chem. Phys. Lett. 1988,147,18. (11) Hill, J. R; Dlott, D. D.J. Chem. Phys. 1988,89,830. (12) Hill, J. R; Dlott, D. D.J. Chem. Phys. 1988,89,842. (13) Chang,T. C; Dlott, D. D.J. Chem. Phys. 1989,90,3590. (14) Kim, H.; Dlott, D. D.J. Chem. Phys. 19919 94,8203. (15) Jiang, Y.; Blanchard, G. J./. Phys. Chem. 1994,98,9411. (16) Yardley, J. T. Introduction to Molecular Energy Transfer, Academic: NeN York, 1980. (17) Fbrster, T.Ann. Phys. (Liepzig) 1948,2, 55. (18) Grimme, S.; Lohmannsroben, H-G. / Phys. Chem. 1992, 96,7005. (19) Edward, J. T.J. Chem. Educ. 1970,47, 261. (20) Debye, P. Polar Molecules; Chemical Catalog: New York, 1929. (21) Chuang, T. J.; Eisenthal, K. B./. Chem. Phys. .972,57, ,094. (22) Perrin, F.J. Phys. Radium 1916, 6,1. (23) Hu, C. M.; Zwanzig, R / Chem. Phys. 1974, 60,4354. (24) Jiang, Y.; Blanchard, G. J.J. Phys. Chem. 1995,99,7904. (25) CRC Handbook of Chemistry and Physics, 71st ed.; Lide, D. R, Ed.; CRC Press: Boca Raton, FL, 1991. (26) McCarthy, P. K.; Blanchard, G. J.J. Phys. Chem. 1996,100, ,182. Gary J. Blanchard is associate professor of chemistry at Michigan State University. Address correspondence about this article et Blanchard at Michigan State University, Dept. of Chemistry, East Lansing, Michigan 48824-1322 (blanchard@photon. .em. msu.edu).
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