New Laser-Based Methods for the Measurement of Transient

8 New Laser-Based Methods for the Measurement of Transient Chemical Events GARY M. HIEFTJE and J. MICHAEL RAMSEY Department of Chemistry, Indiana University, Bloomington, IN 47401 GILBERT R. HAUGEN

Downloaded by TUFTS UNIV on June 22, 2017 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0085.ch008

Department of Chemistry, Lawrence Livermore Laboratory, Livermore, CA 94550 One of the trends i n modern chemical research is toward the observation and measurement of p r o g r e s s i v e l y b r i e f e r events. Such observations and measurements might be o f t r a n s i e n t chemical spec i e s , of e x c i t e d s t a t e l i f e t i m e s , o f energy t r a n s f e r processes, or of chemical r e a c t i o n r a t e s themselves. Obviously, the ability to c h a r a c t e r i z e ever b r i e f e r chemical phenomena will lead to an improved understanding of many areas o f chemistry; consequently, the methodology o f high-speed observations has almost become an end i n itself. In keeping with these improvements in methodology, our d e f i n i t i o n s o f " b r i e f " and " t r a n s i e n t " have changed over the y e a r s . Whereas before 1950 it was common t o consider m i l l i s e c o n d events b r i e f , measurements on such a time s c a l e became commonplace a f t e r that time and we learned to consider microsecond events r e a d i l y measurable. In the 1960's, nanosecond processes were the subjects of study while the present decade has extended our t h i n k i n g to the picosecond and sub-picosecond time s c a l e . T h i s movement toward f a s t e r and f a s t e r time s c a l e s is not without i t s l i m i t . As f a r as s p e c t r o s c o p i c monitoring i s concerned, there i s l i t t l e reason to attempt examination o f events f a s t e r than one femtosecond ( 1 0 ~ s e c ) , since measurements on such a time s c a l e have a Heisenberg energy u n c e r t a i n t y approximately equal to that of the chemical bond. S i g n i f i c a n t l y , measurements on a femtosecond time s c a l e are already f e a s i b l e (1) and might be expected to become commonplace i n the next decade. In t h i s chapter, a new approach w i l l be presented f o r the measurement o f t r a n s i e n t chemical events. B a s i c a l l y , the new measurement techniques are an outgrowth o f i n f o r m a t i o n theory, p a r t i c u l a r l y that branch o f i n f o r m a t i o n theory d e a l i n g with l i n e a r response theory, c o r r e l a t i o n a n a l y s i s and s p e c t r a l power measurement. Although the methods have p o t e n t i a l l y broad a p p l i c a t i o n to areas as d i v e r s e as chemical k i n e t i c s and n u c l e a r magnetic resonance spectroscopy, t h e i r use i n f l u o r e s c e n c e l i f e t i m e determinat i o n w i l l serve here to i l l u s t r a t e t h e i r u t i l i t y . To begin, i t i s necessary to l a y some b a s i c groundwork so the 1 5

0-8412-0459-4/78/47-085-118$05.00/0 © 1978 American Chemical Society

Hieftje; New Applications of Lasers to Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

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nature and scope of the new approach can be a p p r e c i a t e d . f o l l o w i n g s e c t i o n e s t a b l i s h e s t h i s groundwork.


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The b a s i s f o r the new family o f techniques f o r studying t r a n s i e n t phenomena can be found i n l i n e a r response theory. Accordi n g l y , l e t us adopt a linear-response-theory view of chemical measurements to understand the techniques. From such a view, any chemical measurement can be thought of as an attempt to a s c e r t a i n the response f u n c t i o n o f a chemical substance, instrument, energy l e v e l , or whatever. Conveniently, the time response f u n c t i o n i s one o f the most f r e q u e n t l y and e a s i l y determined kinds of r e s ponse f u n c t i o n s , and w e l l - e s t a b l i s h e d l i n e a r - r e s p o n s e - t h e o r y approaches f o r i t s determination have been e s t a b l i s h e d . Perhaps the most e a s i l y understood and conveniently a p p l i e d such t e c h n i que i n v o l v e s the determination o f an impulse-response f u n c t i o n . Measurement o f an impulse-response f u n c t i o n i s s t r a i g h t f o r ward. As shown i n F i g u r e 1, any system (substance, energy l e v e l , etc.) can be considered to have one or more inputs and one or more outputs, each o f which can be used to l e a r n something about the system. For convenience, l e t us assume that the system to be measured has only one input and one output. As w i l l be obvious l a t e r , t h i s simple two-terminal model can be used to represent many systems of chemical i n t e r e s t . The impulse response o f the system i s then j u s t the observed output which r e s u l t s from a p p l i c a t i o n o f a s u i t a b l e impulse to the input. In t h i s treatment, i t i s assumed that the t e s t e d system responds l i n e a r l y to the a p p l i e d stimulus. For example, i f the system to be measured were a simple r e s i s t o r - c a p a c i t o r (RC) e l e c t r o n i c network, i t s time response would be e x p o n e n t i a l . A p p l i c a t i o n o f an impulse (or pulse) to the input o f the RC network would then produce the expected s t r e t c h e d pulse at the output o f the network. From t h i s simple example, i t can be a p p r e c i a t e d that the time response f u n c t i o n i s merely a c o n v o l u t i o n (2, _3) o f the input impulse and the syst e m ^ impulse response f u n c t i o n and, indeed, i f we do apply a perf e c t impulse ( d e l t a f u n c t i o n ) , the observed output w i l l be the impulse response f u n c t i o n i t s e l f . S i g n i f i c a n t l y , the impulse response f u n c t i o n i s merely one of a f a m i l y of response f u n c t i o n s , each o f which r e s u l t s from a p p l i c a t i o n o f a d i f f e r e n t kind of input to the system under i n v e s t i g a t i o n . In general, i t can be shown that each p a r t i c u l a r response f u n c t i o n i s approximated by the c o n v o l u t i o n of a s p e c i f i e d input with the t r a n s f e r f u n c t i o n o f the t e s t e d system. More e x a c t l y , the t r a n s f e r f u n c t i o n o f the system (which i s the i n f o r m a t i o n a c t u a l l y being sought) i s the r a t i o o f the Laplace transform of the observed output to that o f the p e r t u r b i n g input. From a more q u a l i t a t i v e standpoint, the impulse response f u n c t i o n can be viewed as a time-domain r e p r e s e n t a t i o n o f the


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frequency response o f the system being t e s t e d . Because an i d e a l impulse ( e f f e c t i v e l y a d e l t a function) contains a l l frequencies, a p p l i c a t i o n o f the impulse t o a t e s t e d system involves sending a l l frequencies simultaneously i n t o the t e s t e d network. The r e s u l t i n g output then r e f l e c t s the frequency response o f the network, but r e v e a l s the network s phase response as w e l l . The importance o f the impulse-response f u n c t i o n to chemistry can be r e a d i l y i l l u s t r a t e d . For i n s t a n c e , temperature-jump and pressure-jump methods o f r e a c t i o n - r a t e measurement are e s s e n t i a l l y impulse-response approaches. In a d d i t i o n , the measurement o f luminescence decay times i s o r d i n a r i l y accomplished by a p p l i c a t i o n of an impulse o f o p t i c a l r a d i a t i o n and measurement o f the r e s u l t i n g response; o b v i o u s l y , t h i s procedure c o n s t i t u t e s another impulse-response measurement. From these simple examples, i t should be appreciated that the input impulse need not be an e l e c t r i c a l f u n c t i o n but could be any impulse-shaped p e r t u r b a t i o n which produces a meaningful response from the system under t e s t . An a l t e r n a t i v e approach can be used to o b t a i n impulseresponse f u n c t i o n s . In t h i s second approach, a random or pseudorandom input p e r t u r b a t i o n i s employed and the r e s u l t i n g output observed. The output i s then e i t h e r a u t o c o r r e l a t e d or c r o s s c o r r e l a t e d with the s t o c h a s t i c p e r t u r b i n g f u n c t i o n to y i e l d , r e s p e c t i v e l y , the a u t o c o r r e l a t i o n o f the impulse response or the impulse response f u n c t i o n d i r e c t l y (2,3). Although less i n t u i t i v e l y obvious than the d i r e c t determination o f an impulse r e s ponse f u n c t i o n d e s c r i b e d above, t h i s l a t t e r technique has s e v e r a l advantages. Most importantly, the p e r t u r b i n g f u n c t i o n need not be a "spike", c o n t a i n i n g a great deal o f power at one moment i n time, but r a t h e r can d i s t r i b u t e the p e r t u r b i n g energy over a much greater time, thereby p l a c i n g less s t r e s s on the system under test. Q u a l i t a t i v e l y , t h i s l a t t e r s t o c h a s t i c method can be e a s i l y understood i f one remembers that a u t o c o r r e l a t i o n o f a waveform or c r o s s - c o r r e l a t i o n o f two waveforms r e s u l t s i n a p h a s e - r e g i s t r a t i o n of a l l frequency components present i n the o r i g i n a l waves. For a completely s t o c h a s t i c (random) f u n c t i o n , a u t o c o r r e l a t i o n y i e l d s a d e l t a f u n c t i o n or impulse (2,3). Consequently, c r o s s - c o r r e l a t i o n of a random f u n c t i o n with the response i t e l i c i t s produces the impulse-response f u n c t i o n . T h i s s t o c h a s t i c - e x c i t a t i o n approach has already found a p p l i c a t i o n i n chemistry. In NMR spectroscopy, Ernst (4) has found that a p p l i c a t i o n o f a s t o c h a s t i c radio-frequency p e r t u r b i n g funct i o n to sought-for n u c l e i , followed by c r o s s - c o r r e l a t i o n o f the response o f the n u c l e i to the o r i g i n a l p e r t u r b i n g f u n c t i o n , r e s u l t s i n a waveform i d e n t i c a l t o that obtainable by conventional pulse-Fourier-transform NMR techniques. However, Ernst noted that the s t o c h a s t i c e x c i t i n g f u n c t i o n could be a p p l i e d at much higher average power than could a conventional pulse without producing s a t u r a t i o n o f the n u c l e i under observation. In the microscopic world, the s t o c h a s t i c - e x c i t a t i o n approach


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to measurement takes on new meaning. On a microscopic s c a l e , a l l energies are quantized, and (above absolute zero) a l l species are i n constant, random motion. Consequently, most microscopic events are continuously and u n i n t e n t i o n a l l y perturbed i n a s t o c h a s t i c or semi-stochastic way, so that e x t e r n a l p e r t u r b a t i o n i s unnecessary. In such cases, temporal or k i n e t i c information can be obtained merely by a u t o c o r r e l a t i n g the s t o c h a s t i c a l l y induced f l u c t u a t i o n s . For example, Brownian motion leads to constant movement of a l l species i n any f l u i d medium. S c a t t e r i n g of l a s e r l i g h t from the r e s u l t i n g inhomogeneities i n r e f r a c t i v e index then enables measurement of the l o c a l i z e d f l u c t u a t i o n s . In t u r n , the measured f l u c t u a t i o n s can be a u t o c o r r e l a t e d to y i e l d such information as d i f f u s i o n r a t e s and net v e l o c i t i e s of species w i t h i n the medium (5_,6_>]_- See a l s o the chapter by B. R. Ware i n t h i s book). These measurements are the b a s i s o f techniques which are now e s t a b l i s h e d and have become known e i t h e r as l a s e r doppler velocimetry or l a s e r doppler anemometry (6,8). The elegant experiments by Ware and Flygare (9) i l l u s t r a t e how u s e f u l such methods can be to chemistry. In other microscopic experiments, the f l u c t u a t i o n s of one component i n a r e a c t i n g mixture have been measured f l u o r i m e t r i c a l l y A u t o c o r r e l a t i o n of the measured fluorescence f l u c t u a t i o n s then enables the r a t e s of formation and l o s s o f that component to be measured, even though the r e a c t i o n mixture was at macroscopic equil i b r i u m . T h i s l a t t e r measurement i s the b a s i s of the new and e x c i t i n g f i e l d of fluorescence c o r r e l a t i o n spectroscopy (10,11,12). In many cases, i t i s more convenient to measure the power spectrum of measured f l u c t u a t i o n s than to determine the autocorrel a t i o n or c r o s s - c o r r e l a t i o n functions themselves (13,14). Whichever approach i s employed, the r e s u l t s are e s s e n t i a l l y the same, s i n c e the power spectrum and a u t o c o r r e l a t i o n f u n c t i o n of a waveform c o n s t i t u t e a F o u r i e r p a i r . That i s , one f u n c t i o n can be r e a d i l y obtained from the other merely by a p p l i c a t i o n of a F o u r i e r transformation. S i m i l a r l y , the c r o s s - c o r r e l a t i o n f u n c t i o n i s merely the F o u r i e r transform o f the cross-power spectrum of two waveforms. The novel approach to fluorescence l i f e t i m e measurement which i s o u t l i n e d below i s s i m i l a r i n concept to the procedures c i t e d above. Because i t , l i k e the others, i n v o l v e s the a n a l y s i s of f l u c t u a t i o n s induced i n a species of chemical i n t e r e s t , and because the f l u c t u a t i o n s are measured s p e c t r o s c o p i c a l l y , we have coined the acronym FAST ( F l u c t u a t i o n A n a l y s i s Spectroscopic Techniques) to c a t e g o r i z e them. F.A.S.T. Luminescence L i f e t i m e Measurement As implied e a r l i e r , luminescence l i f e t i m e s are o r d i n a r i l y determined by methods which, i n essence, are impulse-response f u n c t i o n determinations. A c c o r d i n g l y , i t would seem to be s t r a i g h t f o r w a r d to implement such techniques with a c o r r e l a t i o n approach. An instrument f o r such measurements i s i l l u s t r a t e d i n



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Figure 2. As i l l u s t r a t e d i n Figure 2, the elements of a c o r r e l a t i o n l i f e t i m e f l u o r i m e t e r would be a randomly modulated e x c i t a t i o n source, e x c i t a t i o n and luminescence monochromators, a f a s t detect o r , and e i t h e r a c o r r e l a t i o n computer or spectrum analyzer. The s p e c i f i c a t i o n s f o r each one of these u n i t s w i l l be governed by the necessary e x c i t a t i o n and luminescence wavelengths and by the time range of the luminescence l i f e t i m e . In the simplest kind of instrument, the e x c i t a t i o n source would be a free-running flashlamp, the detector could be a f a s t p h o t o m u l t i p l i e r tube, and c o r r e l a t i o n could be c a r r i e d out using any one of a number of commercial hardware c o r r e l a t o r s . Such an approach was t e s t e d i n our laboratory f o r slowly decaying luminescence s i g n a l s and has revealed the p r a c t i c a l i t y of the t e c h n i que. In these i n i t i a l s t u d i e s , i t was found that i t i s important f o r the e x c i t a t i o n source to f l a s h randomly or f o r the duration between f l a s h e s to be considerably longer than the luminescence process being observed. I f these c r i t e r i a are not met, overlap of luminescence decay s i g n a l s with each other makes a l i f e t i m e determination r a t h e r d i f f i c u l t . C l e a r l y , t h i s p r e l i m i n a r y kind of device cannot be employed f o r the measurement of short luminescence l i f e t i m e s . Hardware c o r r e l a t o r s simply are not capable of s u f f i c i e n t l y r a p i d response to enable c a l c u l a t i o n of c o r r e l a t i o n functions on a nanosecond time s c a l e . To achieve nanosecond time r e s o l u t i o n with t h i s approach, somewhat d i f f e r e n t instrumentation i s r e q u i r e d . Nanosecond time r e s o l u t i o n requires that the e x c i t a t i o n source f l u c t u a t e or be modulated on a sub-nanosecond time s c a l e and at a f a i r l y large amplitude. In a d d i t i o n , f o r maximum s i g n a l to-noise r a t i o , the f l u c t u a t i o n s should occur continuously and should not be separated i n time as would the pulses from a f l a s h lamp. In p r e l i m i n a r y i n v e s t i g a t i o n s , s e v e r a l p o t e n t i a l sources were t e s t e d f o r t h i s a p p l i c a t i o n and a continuous-wave l a s e r was found to be most s u i t a b l e . In a d d i t i o n , because nanosecond-scale c o r r e l a t i o n was required, we found i t more expedient to employ spectrum a n a l y s i s than software or hardware c o r r e l a t i o n . The r e s u l t i n g instrument and i t s performance have been described i n a recent p u b l i c a t i o n (13), and w i l l only be b r i e f l y and q u a l i t a t i v e l y o u t l i n e d here. In the new instrument, l a s e r mode noise i s used as a pseudorandom fluorescence e x c i t a t i o n f u n c t i o n . Mode n o i s e i s j u s t the r a p i d f l u c t u a t i o n i n l a s e r output amplitude which r e s u l t s from "beating" (mixing) of the l a s e r o s c i l l a t i o n modes with each other. Because l a s e r modes occur at d i s c r e t e frequencies (wavelengths) (15), they produce v a r i a t i o n s i n the l a s e r ' s output which are a l s o at d i s c r e t e frequencies, as revealed by the comb-like f l u c t u a t i o n power spectrum of the l a s e r ' s output (16,17,18) . These d i s c r e t e frequency f l u c t u a t i o n s occur i n i n t e r v a l s of c/2£ (c = speed of l i g h t ; I = l a s e r c a v i t y length) up to frequencies as high as 4 GHz f o r an argon-ion l a s e r , [ i . e . , up to the Doppler width of the emission p r o f i l e of the a c t i v e medium (Ar i o n s ) ] . For a t y p i c a l


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Figure 1. Conceptual view of a system whose time response is to he measured. The system might he an electronic network, a reacting chemical system, or a fluorescing molecule. The desired corresponding time response might then he, respectively, the RC time con stant, the chemical reaction rate, or the fluorescent lifetime.

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Figure 2. Diagram of an instrument to measure luminescence lifetime using a randomly varying light source



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rare-gas i o n l a s e r , with a 1 meter c a v i t y , c / 2 £ = 150 MHz. Essent i a l l y , the l a s e r output f l u c t u a t e s i n power at a l l these d i s c r e t e frequencies (150 MHz, 300 MHz, 450 MHz, etc.) simultaneously, thus causing f l u c t u a t i o n s i n e x c i t a t i o n o f the i l l u m i n a t e d sample at the same f r e q u e n c i e s . However, because the e x c i t e d s t a t e of a fluorophore e x h i b i t s a f i n i t e l i f e t i m e , f l u c t u a t i o n s i n the induced luminescence cannot occur at the highest frequencies present i n the v a r y i n g l a s e r output. Therefore, the power spectrum o f luminescence f l u c t u a t i o n s i s attenuated at h i g h e r f r e q u e n c i e s . From t h i s a t t e n u a t i o n , the luminescence l i f e t i m e can be c a l c u l a t e d . For example, luminescence from a fluorophore having an upper s t a t e l i f e t i m e o f 1 ns ( i . e . , a frequency response o f 1 GHz) would be able to f o l l o w the lower frequency l a s e r f l u c t u a t i o n s ( i . e . , at 150, 300, 450 MHz, etc.) but would not be able to f a i t h f u l l y follow the highest frequency f l u c t u a t i o n s ( i . e . , above 1 GHz). Consequently, these h i g h e r frequencies would be attenuated i n the power spectrum of luminescence v a r i a t i o n s . Mathematically, the luminescence l i f e t i m e can be found from the envelope o f the d i s c r e t e - f r e q u e n c y peaks i n the luminescence f l u c t u a t i o n power spectrum. A f t e r deconvolution, t h i s envelope i s L o r e n t z i a n , r e v e a l i n g the exponential time-domain p r o f i l e o f luminescence decay. Deconvolution i t s e l f i s s i m p l i f i e d i n t h i s approach, and merely i n v o l v e s a d i v i s i o n , s i n c e data are already i n the frequency (Fourier) domain Q2,3) . The advantages o f t h i s new approach are numerous. For one, the technique i s capable o f measuring luminescence l i f e t i m e s as short as those a c c e s s i b l e with a mode-locked l a s e r . In f a c t , the power spectrum measurement i n v o l v e d i n t h i s technique i m p l i c i t e l y c o r r e l a t e s the l a s e r f l u c t u a t i o n s and thereby emulates the l a s e r s performance when mode locked (19) . However, mode l o c k i n g i t s e l f i s not necessary, so that l a s e r o p e r a t i o n i s rendered both simpler and more r e l i a b l e . A l s o , t h i s method r e q u i r e s no large amplitude output p u l s e from the photodetector, thereby reducing the l i k e l i h o o d of s a t u r a t i o n . T h i s new method has drawbacks as w e l l . Most important o f these i s the need to perform a spectrum a n a l y s i s of the induced f l u o r e s c e n c e f l u c t u a t i o n s . This a n a l y s i s must be performed with the a i d o f a high frequency spectrum analyzer, whose cost i s subs t a n t i a l . From a p r a c t i c a l standpoint, i t would be f a r more a t t r a c t i v e to use less expensive instrumentation. One p o s s i b i l i t y would be to s t a t i o n fixed-frequency bandpass detectors (such as UHF t e l e v i s i o n tuners) at each o f the d i s c r e t e f l u c t u a t i o n f r e quencies. Of course, the exact l o c a t i o n of each o f these f r e quencies i s dependent on the p a r t i c u l a r l a s e r used, and the bandpass frequencies would have to be adjusted i f l a s e r sources were exchanged. Another l i m i t a t i o n i n the system as now c o n f i g u r e d i s the a c c e s s i b l e wavelength and time r e s o l u t i o n range. Although a r a r e gas i o n l a s e r emits only at a number of d i s c r e t e wavelengths, i t would be d e s i r a b l e to have a v a i l a b l e u l t r a v i o l e t 1


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r a d i a t i o n or r a d i a t i o n tunable over a broad wavelength range. In a d d i t i o n , mode noise from such a system extends only t o approxi mately 4 GHz, l i m i t i n g time r e s o l u t i o n t o approximately 0.1 ns. Presumably, both these l a t t e r objections could be overcome through use o f a continuous-wave dye l a s e r . With frequency doubling, such a l a s e r would be usable over most o f the wavelength range commonly employed f o r luminescence e x c i t a t i o n . Moreover, the l a s e r should e x h i b i t mode n o i s e t o frequencies as high as 100 GHz, making de t e c t o r speed the l i m i t i n g device i n the measurement o f u l t r a - s h o r t lifetimes.


Literature Cited 1. Ippen, E. P., and Shank, L. V., Opt. Commun. (1976) 18, 27. 2. Bendat, J . S., and P i e r s o l , A. G., "Random Data: A n a l y s i s and Measurement Procedures", W i l e y - I n t e r s c i e n c e , New York, NY, 1971. 3. Bracewell, R., "The F o u r i e r Transform and I t s A p p l i c a t i o n " , McGraw-Hill, New York, NY, 1965. 4. E r n s t , R. R., J. Mag. Resonance (1970) 3, 10. 5. Gabler, R., Westhead, E. W., and Ford, N. C., Biophys. J. (1974) 14, 528. 6. She, C. Y., and Wall, L. S., J. Opt. Soc. Amer. (1975) 65, 69. 7. Brown, J. C., and Pusey, P. N., J. Phys. D. (1974) 7, L31. 8. LeBlond, J., and El Badawy, E. S., Appl. Opt. (1975) 14, 902. 9. Ware, B. R., and Flygare, W. Η., Chem. Phys. L e t t . (1971) 12, 81. 10. Magde, D., E l s o n , E., Webb, W. W., Phys. Rev. L e t t . (1972) 29, 705. 11. E l s o n , E. L., Magde, D., Biopolymers (1974) 13, 1. 12. Magde, D., Elson, E. L., Webb, W. W., Biopolymers (1974) 13, 29. 13. H i e f t j e , G. M., Haugen, G. R., and Ramsey, J. Μ., Appl. Phys. L e t t . (1977) 30, 463 14. Chu, Β., "Laser Light S c a t t e r i n g " , Academic Press, New York, NY, 1974. 15. Lengyel, Β. Α., " I n t r o d u c t i o n t o Laser Physics", John Wiley and Sons, New York, NY, 1966. 16. Casperson, L. W., Opt. Commun. (1975) 13, 213. 17. Bridges, T. J., and Rigrod, W. W., IEEE J. Quantum E l e c t r o n . (1965) QE-1, 303. 18. Sedel'nikov, V. Α., S i n i c h k i n , Y. P., and Tuchkin, V. V., Opt. Spectrosc. (1971) 31, 408. 19. Weber, H. P., and Danielmeyer, H. G., Phys. Rev. A (1970) 2, 2074. RECEIVED August 7, 1978.


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