The Calorimetric Detection of Excited States

Calorimetric techniques offer the photophysicist and photochemist the opportunity to measure a number of parameters of excited states which may be difficult to obtain by other techniques. The calorimetric strategy seeks to measure the heating of a sample resulting from radiationless decays or chemical reactions of excited states. Heating is best measured through volume and pressure transducers, and four calorimeters based on these are described. With calorimetric instrumentation one can perform measurements on samples in the gas, liquid and solid phases over a wide temperature range. Moreover time dependent processes with time constants ranging from microseconds to seconds are amenable to study. Examples of the application of calorimetric techniques to the determination of quantum yields of fluorescence, triplet formation and photochemistry are given.


Introduction
In underst a ndin g th e na ture of exci ted electroni c sta tes it is well a ppreciated that a wide variety of para mete rs a re accessible to photo metric meas ure· ment. Among the m ar e th e a bsorptio n spectrum of the excited state, th e excitation spectrum , and the lifetime. If the excited sta te decays by e mi ssion of photons, one can also meas ure the s pec tral di stribu · tion of e mi ss ion , the polariz ati on , a nd the quantum yield of e mitted photons . U nfortuna tely, it is not so ge ner all y a ppreciated th a t a number of parame te rs of an excited s ta te are also accessible to calorim etri c measure ment. Th e calorime tri c strategy see ks to meas ure how muc h of the li ght ab sorbed by a sample is converted to heat energy by radiationless processes a nd/or photoc he mistry. Para meters whi c h can be measured includ e : the lifetime of an excited state , the excitation spectrum for a parti c ular process, the e nergy yield of a radiationless process , and the enthalpy of a photoche mical process.
A simple e xample illus tra tes how c alorimetric measure me nts can comple ment photom e tric meas ure me nts. Most air satura ted liquid solutions of luminescent organic molec ules exhibit only Auoresce nce at room te mpera ture. By measurin g th e ra tio of the heating of the Auoresce nt s ubs tance in res ponse to photoexcitation to th a t of a non-Auoresce nt but equally a bsorbin g s ubsta nce, one obtains th e e nergy yield of r adia tion-·Papcr prese nt ed at th e Work s hop Se min ar 'Standa rdizat ion in Spectrop ho tomet ry and Lumin escence Meas ure me nt s' he ld at t he Na tiona l Bu rea u of S ta nda rds. Gai thersburg, Md .. Novemher 19-20. 1975. less processes Y" [1 , 2]. I In th e a bse nce of ph oto· c he mis try, th e Au oresce nce e ne rgy yield is th e co m· pl e ment of y", a nd th e qu a ntum yield of Au oresce nce <pJ is related to it by th e formula (1) wher e Va a nd vJ a re th e a verage fre qu e ncies of a bsorbed a nd e mitted photo ns respecti vely. Calori · metric qu a ntum yield s de termin ed in this mann e r [1 , 2 , 3] are a mong the mos t precise and acc urate re ported in th e literature , and in additi on provide a valuable inde pe nde nt technique for verifying the man y as sumptions that go into th e derivatio n of quantum yields from photometric meas ure me nts [4 , 5]. Des pite th ese advantages , very few quantum yield s have been measured calorimetrically. This unfortunate situation exists because most workers in the fi eld are un· familiar with calorimetric techniques , and moreover, the me as ure ments are time consumin g and tedious to perform. It is the purpose of thi s pa pe r to point out some recent work whi c h shows th a t us in g capacitor microphones and pi ezoelectric cr ys tals as heat Aow trans ducers, calorimetry can be a rapid , simple and se nsitive technique for · use in meas urin g a wide varie ty of para me ters of excited s tates. Also, sa mples in the gas, liquid and solid phases, includin g thin film s and monolayers are a menable to study. I F'il-\ure s in brackets ind ica te t he lit e rat ure refe re nces at the e nd of Ihi s paper.

Types of Calorimeters Suitable for Measuring Photochemical and Photophysical Processes
The most obvious approach for detection of heat production is to use a co nventional calorimeter based upon the usual temperature sensors: thermistors and thermopiles . We will not disc uss these instruments he re because they have already been reviewed [3,4,5] and because they have inherent disadvantages in sensiti vi ty, risetime and speed at whic h measurements can be made. Instead, we will concentrate on alternative s trategies for measuring heat flow based on volume a nd pressure c hanges produced in the sample _ In general , addition of an amo unt of heat dQ to the sample gives rise to both a pressure change dP and a volume change dV according to the thermodynamic relationship [6] (2) where CI' and Cr are the heat capacities at constant pressure and constant volum e, V th e volume of the solution, a= V-I (av/a T)p is the coefficient of thermal expansion, and {3=-v -l (av/ap )T is th e compressibility of the sa mple. Three of the calorimeters we will describe use the capacitor mi crophone to detect volume c hanges in the sample. In all of th ese devices the sample is enclosed in a cell with rigid walls_ One of these walls, generally normal to the direction of propagation of exitin g light is replaced by th e compliant diap hragm of a capacitor microphone. Because of the diaphragm, a second relationship between dP and dV must be simultaneously obeyed: We have assumed that the changes are small so that a linear relationship exists, and K, the lin ear constant, is approximately given for a cubic cell by ki t where k is the force constant for displacing th e diaphragm, and t is the linear dimension of the cell. Combining eq (2) and (3) we have (4) Equation (4) shows that: (a) the volume c hange is independent of any gradients in the distribution of energy in the cells; (b) the larges t volume changes are obtained for samples which have the highest values of a and the lowest heat capacities (gases give the largest signals; water gives low signals); (c) the compliance of the diaphragm must be kept low enough so that the product K{3 is as small as poss ible_ The capacitor microphone for measuring the volume changes consists of the diaphragm and a stationary electrode spaced a small distance apart; together they form a capacitor whose capacitance C is given by C=EA/x (5) where E is the dielectric constant, A is the area of the electrodes, and x is the spacing between them, and edge effects were neglected. If the change in spacing of the electrodes is small enough, the capacitance will be related to it linearly_ Several methods have been used successfully for the detection of the capacitance change. In the most common method [7], the microphone is polarized either with an externally supplied dc voltage or by placing an electret [8] in the gap between the electrodes; when the capacitance changes, charge flows to maintain a constant voltage. The charge flow is then converted to a voltage change by a charge sensitive pre-amp [9]. Capacitance changes can also be detected with an ac bridge circuit [10]. Even with simple detection systems, a displacement of the diaphragm of the order of one angstrom is easily measured with a bandwidth of 10 kHz [6]. The frequency response of the microphone is linear over a very wide range; the upper limit is set by the lowest mechanical resonance of the diaphragm (10-20kHz), and the low er limit is determined by the low freque ncy cut-off of the electronics or the thermal in st,abilities of the system_ With th ese fundamental co nsiderations in mind, we may now discuss three types of calorimeters based upon the use of capacitor microphone pressure transducers: th e "acoustic spectrophone" for study of gas phase syste ms , the "o ptoacoustic cell" for study of thin films and thin sections of solid materials, and the "flash calorimeter" for studie s of liquid samples_ The acoustic spectrophone has been widely used as a technique for infrared gas analysis [12] and for measuring vibrational relaxation rates [13]. A typical aco ustic spectrophone [11] consists of a cylindrical cell with tran sparent windows at each end to allow radiation to e nter and leave; the microphone is generally mounted on the cylin drical wall with the diaphragm normal to the direction of propagation of the excitation beam. Ofte n , a regulated leak is provided so that long term press ure drifts can be relieved.
The design of acoustic spectrophones is discussed in detail by Rosengren [14] , Parker and Ritke [11] and Kerr and Atwood [15]. The ultimate limit of signal to noise arises from the Brownian motion of th e gas molecules. Present designs can come within two orders of magnitude of this limit at reasonable gas pressures. The present limitations arise from noise in the detection electronics, temperature instabilities (es pecially at low frequencies) and spurious contributions to the signal arising from gas adsorbed on the windows [14]. Even with these limitations, energy inputs as small as one microwatt may be easily detected_ Parker has shown [11] that the rise time for the volume change is set by the lowest acoustical resonance frequency in the cavity whose frequency is given by c/2/, where c is the speed of so und in the gas, and 1 is the length of the cavity.
A device similar to th e acoustic s pectrophone has been developed by Rosen cwaig [17] for the study of radiationless processes and photochemistry in thin films of solids, and semis olid materials such as crystals, evaporated films, powders, gels, thin layer chromatography plates, and e ve n thin layers of ti ss ue. The photoacousti c cell is quite si milar to th e acoustic s pectrophone of Parker, e xce pt it is mu c h s horter in cavity le n gth. Th e thin sample is simply mounted flu s h with the exit window, and th e cell is fill ed with a s uitable gas whic h is tran s pare nt to the exciting radiation.
The origin of th e photoacousti c e ffect is believed to be as follow s [11 , 18]: irradiation of th e sa mple with pulsed or chopped steady state li ght results in a localized heating du e to non-radiative decay processes by the excited states. Some of the heatin g . is tran sferred via diffu sion from th e solid to a thin boundary layer of gas adjacent to th e solid. Adiabati c expansion of the gas th e n gi ves ri se to a press ure wave in th e gas which is de tected by a capacitor mi crophone. A quantitative version of thi s process has bee n proposed [11 , 18]. Like th e acoustic s pectrophone thi s device can e asily de tect mi crowatts of absorbed radiation , and the risetim e is se t by the tran sit tim e for so und in the cavity.
Th e third device based on th e use of th e capacitor microphon e is th e fl as h ca lorim e te r of Callis, Couterman and Danielson [6]. A sche mati c of th e device is given in Figure 1. Th e sampl e cell is co nstruc ted from 25 X 25 mm square Pyrex 2 tubing. Join ed to the sides are two 4-mm Pyrex-Teflon vac uum stopcoc ks. One of these provides co nn ection to a vacuum line, allowing for introd uctio n of degassed samples. The other stopcoc k ope ns into a s mall reli ef rese rvoir. It provides a controlled leak so that liquid can slowly enter or leave th e cell, thus preventing slow pressure chan ges that would occur in a completely closed cell subj ect to te mperature drifts. To allow use of a circular diaphrag m a s hort pi ece of 25 -mm Pyrex tubing is fused to th e top of th e cell. The diaphragm is made from 1 mm aluminum. which is s ufficie ntly thick so that it does not deform perman e ntly und e r vacuum, yet not so thi c k that th e product K{3 excee ds unity. Th e microphon e co nsists of the diaphragm , an e poxy glass circ uit board s pacer, and a stationary electrod e-guard ring asse mbly fabricated from brass and e poxy glass circ uit board mate rial. Th e s pacer rin g is ground down until the gap between diaphragm and stationary electrode is approximately 0.25 mm and th e e ntire assembly is potted with epoxy ce me nt. Th e cell is mounted in a brass bloc k whi c h is te m perature stabilized by means of a the rmoelectri c heat pump. Th e entire asse mbly is mounted in an acoustically s hi elded aluminum box which res ts on a vibration iso lation ta ble.
As with other de vi ces based on th e use of mi c rophones, th e ri se tim e of th e flas h calorim e ter is de te rmin ed by th e tran s it tim e for sound in th e cavity. This limits th e use of the in strum e nt in kine ti c studi es to ph e nom e na with tim e co ns tant s lon ge r than lOOIL S. Th e se nsitivity of th e fl as h calorim e te r is quite re markable; a di s place me nt of th e di a phragm of 10-8 c m is easil y detected with a bandwidth of 10 kHz. For ethanol thi s corres ponds to a t e mperature ri se of -10-6°C or an e ne rgy input of -641LJ. Th e limits of de tection at hi gh fre quencies are largely due to the noi se in the preamplifier stage; we are presently many orders of magnitude above the limit imposed by the thermal noise of the sample.
We now describe an instrument which is particularly well suited for measurement of radiationless processes in bulk solids. This device, the piezoelectric calorimeter, uses a piezoelectric crystal to measure pressure changes in the sample. In certain crystals and polycrystalline materials with assymetric charge distribution, an applied pressure results in displacement of the positive and negative charges relative to each other. The displacement of the charges can be measured by applying electrodes to the surfaces and measuring the potential difference between them caused by charge migration. Piezoelectric crystals are available which are rugged, inexpensive, and linear and which will perform at temperatures from 4 K to 700 K.
A simple piezoelectric calorimeter is shown in figure 2. The piezoelectric crystal may be conveniently thought of as measuring the pressure generated by heating at constant volume. Equation (4) then becomes The open circuit voltage response to a pressure change is given by: E=gtdP where g is the open circuit voltage constant in units of m 2 /C, t is the thickness of the crystal in m, and E is the voltage produced [7]. The simplest method for operating these devices is to use a charge sensitive preamplifier, as with the capacitor microphone. The upper end of the frequency response will then be limited by the lowest acoustic resonance, while the lower end will be limited by the low frequency response of the preamplifier. The response of the piezoelectric calorimeter to an infrared heating flash shows characteristics similar to that of the flash calorimeter. The ring period is shorter due to the higher speed of sound in the cavity, but is not damped as effectively. With the present apparatus we can easily detect a step rise of E ~ 1O-3 V which corresponds to a pressure change of 0.073 dyn/cm 2 for a lucite rod of 1 cm thickness, which in turn corresponds to a temperature change of 6.7 X 10-7 °C. For our samples we find that dQ -4.7 M-cal is easily detected.
In addition to the calorimeter, the measurement of calorimetric parameters also requires a light source, a means for selecting a bandwidth of the radiation, and suitable signal processing electronics. The ideal light source for calorimetry must be of high intensity, stable with time, and of high spectral purity. Clearly the laser approaches most closely this ideal, and a number of authors have employed both cw and pulsed lasers. For excitation spectrum studies a Xenon arc lamp-monochromator combination possesses the one advantage of infinite wavelength tunability and the capability of ultraviolet irradiation. Since the calorimeters are ac coupled, the light source must be intensity modulated. For a cw light source , a simple and common method to achieve intensity modulation is with a mechanical chopper. In this case, the most attractive form of signal processing is to use a phase sensitive amplifier, operated in synchrony with the c hopper. If all of the heating from the sample appears with a rate constant greater than the chopping rate, then all of the signal will be in phase with the chopper. However, if some of the heating arises from processes which have rate constants comparable to or less than the chopping rate, then some of the heating will be out of phase. Quantitation of these effects leads to methods for measuring rates of relaxation of excited states and the yield of heating of a particular process. The disadvantages of modulation of a cw source and phase sensitive detection is that the signal decreases linearly with the frequency, and that a series of measurements must be made at a number of different frequencies if the order of the kinetics is to be specified.
For the measurement of the time dependence of the heating, the use of a pulsed light source is advantageous. Large amounts of energy can be output in very short times , thus providing a good signal to noise ratio for fast time dependent processes, as well as giving the heating curve directly. This technique re-quires s om e me thod for transie nt recordin g and signal a veragin g is often d esirable. A pote ntial proble m with pulsed excitati on is that it s tro ngly excites th e lowest cavity resonan ce of the chambe r. Th e res ultant oscillation is s uperimposed on th e signal and often ob· sc ures the heating c urve at s ho rt tim es.

Fluorescence Quantum Yields
In the introduction , we noted th e advantages of the calorimetric strategy for de te rmin a tion of quan tum yields. Thus far, all of th ese meas ure me nts have been done on dilute liquid solutio ns whi c h are easily done photometrically. In co ntrast de termination of quantum yields from thin layers of powd ered samples is a very difficult pro cedure to pe rform photome tri cally [19,20]. Some pion ee rin g work by Rose nc waig [17 , 21] illus· trates how th e o ptoaco us ti c spectrom eter can be us ed to advantage on th ese sys te ms. A number of trivalent rare earth ion s s how narrow absorption bands in th e vi sible and ultravi o let which ari se fro m inner s hell f-f" trans itions. Som e of th ese le vels exhibit fluores· cence, and the fluorescence qu a ntum yield of a particular le vel e xhibits a mark ed de pendence upon which level is excited [22]. Rosencwaig st udi ed th e photoaco us ti c excitation s pectrum of sa mples of powdered holmium oxid e. Th e first sa mple co ntain ed co balt and flu orin e impurities in s uffi cie nt quantity to qu ench a ll of th e Luminescence. He found that th e photoacoustic s pectrum , wh e n corrected for the wave· le ngth depe nd e nce of the relative output of th e excitation beam, corres pond ed well with th e observed absorptio n spectrum. In co ntras t, th e photoacoustic spectrum of pure H 02 0 3 ex hibited a spectrum in whi c h so me of the lin es were greatly dimini shed in inte nsity; th e latter of co urse involve excite d s tates whic h decay by radiative processes. Th e information contain ed in these two scans, togethe r with lifetim es and lumines· ce nce spectra tak e n by excitin g at eac h major absorbance would provid e, for the first time, a co mple te pi cture of the dynami c interrelations hips of these excited states.

Quantum Yields of Triplet Formation
A knowledge of quantum yields of triple t formation is important in unders tanding the intersys te m crossing process, and also in understandin g th e many photo· chemical reactions and energy transfer process which take place through the intermediacy of a triplet state. A number of inge nious methods exist for determination of triplet yields [23] but all are based on the use of various assumptions whi c h are diffic ult to verify experime ntally. The calorimetri c strategy offers an attractive alternative to the oth e r techniqu es, and also provides an ind e pe?de nt chec k on the ass umption s use d in th e other me thods.
states. Thus, we expect that a delta function excitation pul se will produ ce fast heating due to relaxation of the sin gle t states, and slow heating due to relaxation of the tri ple t states. The heatin g may then be partitioned into Qtot = Q rast + Q Siow· (8) It has bee n s hown (6) that <1>, can be obtained from the relation: where <l>f and <1>, are the quantum yields for fluorescence and triplet yields, wh ere k~ is th e triple t decay tim e, and RC is th e decay ~im e of th e ac co upled electronics. For co mpari so n, Th e calorim e tri c meth od is based on the fac t that th e life tim e of th e L owes t triplet state of an organic molec ule is lon g co mpared to that of its excited singlet F I GU RE 3.
Calorimetric response oj degassed acridine orange in glycerol at room temperature. authors ascribe this phenomenon to the efficient formation of a high e nergy unstable intermediate, a dioxetene. Studies with a pulsed light source shows that the intermediate decays to stable low energy products with a time constant of 2 ms. At wave· lengths shorter than 290 nm the heating is again rapid; this is ascribed to the rapid decomposition of vibration ally hot dioxetene to low energy products. Another interesting study using the acoustic spectrophone has been reported by Kaya, Harshbarger and Robin f251. These investigators observed the gas phase optoacoustic excitation spectrum of biacetyl under a -wide variety of conditions. They were able to demonstrate that the lowest excited triplet could be populated only by excitation at wavelengths longer than 443 nm; irradiation at shorter wavelengths reo sulted in intersystem crossing to the second excited triplet which then decayed rapidly and directly to the ground state. In mixtures of benzene and biacetyl, 100 the authors were able to show that energy transfer from benzene to the biacetyl triplet manifold takes place only when exciting into the lowest vibronic bands of the lowest excited singlet of the donor. In pyridinebiacetyl mixtures, the lowest n -7T* state of pyridine was found to transfer to the triplet manifold of biacetyl, but the lowest 7T -7T* state does not. same type of heatin g response as predicted by eq (10).
The value <P t = 0.72 for anthracene in plastic compares well with that determined in mineral oil by other methods [23].

Applications to Photochemistry and Photobiology
In addition to heating from radiationless transitions, one may also detect heating from photochemical processes. Suppose that the sample is excited by Nex photons of energy E ill, and either decays radiationlessly to the ground state, or by photochemistry with a probability <P p to a stable product state of energy E p above the ground state. The total heating dQ will then be given by dQ=Nex (Ein -<ppEp). (11) Equation (11) shows that energy levels of photo· chemical products can be obtained if the yields are known, or the yields can be determined if the energy levels are known. Also, the rates of formation of the photochemical products can be measured or deduced and finally, as Rose ncwaig has pointed out [17], the excitation spectrum of the photochemical process can be obtained, and compared with the conventional absorption spectrum.
The work of deGroot et al. [24] illustrates the use of the acoustic spectrophone to study photochemical processes of acetaldehyde. These authors find that at pressures below a few torr the optoacoustic spectrum in the region 23(}-360 nm resembles the normal absorption spectrum of the compound. When the pressure is increased, however, a minimum appears in the spectrum at 290 nm which indicates that at least some of the absorbed light energy is no longer con· verted to heat on the time scale of chopping. The A final study by Callis, Parson and Gouterman [26] illustrates the potential application of calorimetric techniques to the study of photobiological systems. A very useful model system for the study of the bioenergetics of photosynthesis is the chromatophore of photosynthetic bacteria. The chromatophores are vesicular fragments of the bacterial membrane, which contain the photosensitive pigments and most ef the enzymes necessary for light induced electron transport and coupled phosphorylation. In the chromatophore light induces a cyclic electron flow which is coupled in some unknown manner to the formation of high energy phosphate bonds , in which the free energy available from the photons are stored. In the study of photochemical reactions in the liquid and solid phases using a volume transducer we must include the possibility of a volume difference LlV,. between reactants and products, as well as a contribution from heating. For a system which either returns radiationlessly to the ground state or converts to a product state E p with efficiency <P}J , the total volume change LlV will be If Ep and LlV,. are temperature independent, the measurement of LlV at two different temperatures allows one to obtain E p and LlVr . Figure 5 shows the volume response of Chromatium chromatophores to weak flashes at temperatures of 23°C and 4°C. The traces labeled "light" were obtained in the presence of a strong cw light which saturated all photochemical processes, and resulted in the conversion of all of the input energy to heat. The light response at 4°C is much smaller due to the redu ce d magnitude of a/pCp at thi s te mpe rature. In th e dark at 23°C, a wea k fl as h ca uses a n in stantan eo us volume decrease which is then followed by a fast recovery alm os t to the base line. In th e dark at 4°C we observe an instantaneous volume decrease which recovers about half way with a tim e co nstant of 250 /-LS. From a quantitative e valuation of these data, we have concluded that: (a) th e initial high energy state of th e photosyntheti c ap paratus does not possess a s ignificant enthalpy chan ge from th e ground state, and thu s th e fre e energy c han ge available from the photon is stored in an excited s tate c haracterize d by negative entropy; (b) the high e nergy state also has a decreased volume from the gro und state. Further studi es have shown that the volum e c han ges are altered by the presence of ion trans portin g antibiotics, and un co uplers of phosphorylation. Th e flash calorimeter thus appears to be a valuable tool for th e study of energy conservation in photosyntheti c sys te ms.

Conclusions
Calorime tri c techniques can be used to measure a number of parame ters of excited states s uch as life times, excitation s pectra, e nergy yields of radiationless and photochemical processes, and e nthalpies of photoc he mi cal reaction s. Simple calorimeters capable of 'measurin g th ese parame ters h ave been de ve loped for th e study of molecules in the gas, solid and liquid phases. A wide vari ety of measurements now exist which s how th e usefuln ess of calorimetric techniques for studi es of abso lute fluoresce nce quantum efficiencies, quantum yield s of triple t formation, photoc hemi cal processes in th e gas phase, and for studies of e ne rgy s torage in photosynth esis. As more investi gators realize how simple and co nv e ni e nt these meas ure me nts are, we can expect an in cre ase in th e use of calorim etri c techniqu es in photophys ical and photochemical st udi es.