- Email: [email protected]
Temperature lens and temperature grating in aqueous solution
Chemical Physics ELSEVIER
Chemical Physics 189 ( 1994) 793-804
Temperature lens and temperature grating in aqueous solution Masahide Terazima Department oj’Chemistry, Faculty
of Science Kyoto University, Kyoto 606, Japun
Received 4 February 1994; in final form 14 August 1994
Abstract Time profiles of the thermal lens (TL) and transient grating (TG) signals after photoexcitation of several substances in water are observed at various temperatures. These signals are analyzed in terms of the superposition of the temperature lens (Temp.L) and density lens (Dens.L) in the TL case, and of the temperature grating (Temp.G) and density grating (Dens.G) in the TG case. Pure Temp.G and Temp.L signals are observed at N 4°C. The fast response of the Temp.L and Temp.G signals can be used to investigate the fast dynamics of the excited state or fast electronic-translational energy transfer processes.
1. Introduction
After photoexcitation of molecules to their excited states, various photophysical or photochemical processes take place. The radiationless transition is one of the most common phenomena among these processes no matter how stable the molecule photochemically is. The energy released by the radiationless transition ultimately flows into the translational energy of the medium as heat. Therefore photothermal techniques with laser excitation could be powerful and universal methods for investigating the dynamics of excited states and/or photochemical processes. The thermal lens (TL) [ 1-2 l] and the transient grating (TG) [5,12-181 methods are well known to be sensitive optical detection methods of heat with fairly fast time resolutions. These methods detect the variation of the refractive index in solution, which is induced by heat from the radiationless transition. In this report, we discuss two sources and ‘I’L signals.
of refractive
In the TL method, spatially non-uniform
index variation
in the TG
a sample solution is irradiated by light, then a probe beam expan-
sion due to the spatially
non-uniform
refractive index
0301.0104/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDlO301-0104(94)00289-4
distribution induced by that excitation light is detected as a change of the probe light density. In the TG experiment, two coherent excitation beams are crossed at an angle in the sample. The interference between the two beams produces a sinusoidal pattern and the heat in the bright region produces the refractive index grating. If a probe beam passes through the grating region satisfying the Bragg condition, the light is partly diffracted as the TG signal [ 161. The key point of these two techniques is the refractive index variation due to the released heat from the photoexcited states or species. The variation of the refractive index (An) after depositing heat in solution will be expressed by
(1) In many organic solvents, the first term dominates over the second term significantly [ 19,201. Due to this large difference, the density change which results from the heating effect has been the main cause of the TL or TG signals so far. It is important to note that the density change does not take place immediately after the heat is released. As a consequence, there is always a finite time lag between the heat releasing and the appearance
of the signal. The time constant of the signal rise is determined by the escape time of the acoustic pressure from the i~adiated region. It is given by ra:,,= U/U ( w is the excitation laser spot size, u is the speed of sound in the medium) [ l-1 11, in the TL case, and is around 100 ns under normal experimental conditions. ln the TG case, the effect of the volume expansion of the medium appears as an acoustic oscillation with a period ~,,=J%/u (A is the fringe s~aciog) [ ISIS]. These escape times of the pressure wave have been time limitations of these methods. In order to investigate the fast dynamics by these useful photothermal methods, it is desirable to find another source of the photothermal signal with a faster time response [ 2 1 ] . Recently we have reported the first observation of the TL signal due to the second term of Eq. ( 1) and referred to that signal component as the temperature lens (Temp.L) signal [ 221. Since the time response of this signa does not suffer from the escape time of the pressure wave, it is predicted that the Temp.L signal sbo~ld response i~staut~neous~y after the heat is released. Indeed, our previously observed Temp.L signal rises faster than the normal TL signal [ 221. (In this paper, we explicitly use the term “density lens” (Dens.L) signal for denoting the TL signal due to the first term in Eq. ( 1f ; namely, the Dens.L signal comes from the refractive index variation by the volume expansion. The notation “TL signal” is reserved to indicate the experimentally observed signal, which may containTemp.L and/or Dens.L.) Naturally, it is expected that a similar type of TG signal which originates from the second term, should be observable. These new type of signals could be used for a fast response method in the photothermal techniques. In this paper, first, we report the temperature dependence of the TL signal in water as an extension of our previous work. In e previous paper [ 22 f , the Temp.L signal appeared as a shoulder in a relatively strong Dens.L signal. Since the intensity of the Dens.1, signal should be proportional to the quantity of dp/dT and that of water sensitively depends on the temperature, the contribution of the Temp.L is expected to be observed more clearly by choosing a sui~ble temperature for it. Second, the Temp.G, which is defined as the TG signal due to the second term of Eq. ( 1>, is observed in the TG signal. (Similar to the names Temp.L and DensL, only the TG signal due to the first
term is called “density grating” (Dens.G) signal in this paper.) previously water has been sometimes used as a unique medium in the TL or TG experiments [ 23-263 . Frank0 and Tran have used water to enhance the sensitivity of the TL signal in aqueous solution by increasing the solution temperature [ 231. Also water is an important medium for biological molecules. Miller et al. have measured the TG signals for studying mottoes of proteins and bio olymers 1261. However, to our knowledge, our pre ous [ 221 and present papers are the first reports utilizing the water medium for obtaining a fast response signal in the photothermal techniques.
2, Experimental An excimer laser-pumped dye laser (Lumonics Hyper 400 and Hyper Dye 300) was used for the excitation light at 360 nm in the TL and TG ex~rimen~s” In the TL experiment, this dye laser beam was shaped to have a nearly Gaussian spatial profile by a pinhole and slightly focused (beam radius - 300 pm) to a sample in a quartz cell with a 5 mm optical path length by a concave lens cf= 80 cm). A He-Ne laser was used as the probe beam. The beam was collimated at the sample position and then expanded by a concave lens. The decrease of the probe light density at the center of the excitation beam was monitored through a glass filter and a pinhole (0.3 mm 0). In the TG experiment, the excitation beam was split into two with a beam splitter and crossed inside the sample cell at an angle 0.19” (fringe spacing - 100 pm). The He-Ne laser, probe beam, was brought into the sample at the Bragg condition. The diffracted probe beam was isolated from the excitation beam with the glass filter and pinhole oth TG and signals were monitored by a system. photomultiplier (~~amatsu R928) and averaged by a digital oscilloscope (Tektronix TDS-520) and a microcomputer. In order to investigate the time profiles of the TC and TL signals, heat should be injected in the sample solution impulsively compared with the instrumen~l response time, which was determined by the pulse width ( 15 ns) in this experiment. We tried to use several solutes, such as nitrobenzene, 9,l O-diazaphenanthrene (DAP) and F&I,, for that purpose. The
M. Terazima /Chemical
dynamics of the excited states of DAP has been studied and the excited states are known to be deactivated to the ground state rapidly compared with our laser pulse width [ 271. The fast deactivation ensures that it is not necessary to consider the slow rise of the thermal energy, any excited singlet-singlet (S,-S,) or excited triplet-triplet (T,-T,) transient absorptions, and the contribution of the population lens or the population grating due to metastable states. Moreover, the molecular structure is rigid enough not to allow a change of the molecular volume upon photoexcitation. However, it fluoresces relatively strongly and the emission disturbes the measurement especially at early time scale after the photoexcitation, The photoexcited states of nitrobenzene are also deactivated to the ground state much faster than our laser pulse width without accompanying noticeable luminescence or photochemical reactions [ 281 in our experiment. The negligible contribution of metastable states of nitrobenzene in our observation time range is confirmed by measuring the rise profile of the TG signal with a small fringe spacing ( - 2 rJ,m). The rise profile was determined by the laser pulse width and there is no indication of a slow heating process. This fact means that the concentration of metastable states of nitrobenzene even if it exists is negligibly small. FeCl, in aqueous solution was sometimes used for a standard of calorimetric measurement [2] and we also confirmed that there is no slow decay component in the excited state dynamics within our observation time scale. In the case of DAP and nitrobenzene, SDS was used as a surfactant ( - 0.02 M) to enhance the solubility in water. This concentration was higher than the critical micelle concentration of SDS in water ( 8 X 10 ~’ M) [ 291, but the concentration of the micelle should be lower due to the aggregation of the monomer SDS. Since the micellar size is quite small and it was dilute, we expect that the thermodynamical properties of the micellar solution are similar to those of water. The concentration of FeCl, was also very low ( - 5 X lop3 M), and this ion should not change the thermodynamical properties of water, either. The temperature of the sample solution was controlled by flowing methanol around a metal cell holder. A thermostated bath (Lauda RLS6-D) was used to circulate the methanol. A thermocouple wire was directly dipped into the sample solution and the voltage was monitored by a digital volt meter. The stability of the temperature was fO.l “C. Below zero degree or
79.5
Physics 189 (1994) 793-804
around a low temperature region, SDS could be precipitated or the water could be frozen. However, we could cool the temperature down to - - 4°C without precipitation or freezing. When the measurement was extended to a long time at such low temperatures, precipitation of SDS is observable as the scattering of the probe light. Nitrobenzene and benzene (Wako Chemical Co.) of spectrograde, and FeCl, (Nakarai Chem. Co.) were used as received. DAP purchased from Aldrich Co. was purified by recrystallization. Distilled water was used. Absorbance of the sample was adjusted to 0.2 at the excitation wavelength.
3. Analysis Neglecting any absorption of the probe beam by the solute and any contribution of the metastable state, the TL and TG signals originate from the variation of the refractive index in the solution. The refractive index variation due to the thermal effect in an isotropic liquid is determined by the variation of the density and the temperature through Eq. ( 1). The time profiles of the density and temperature changes are calculated from the linearized hydrodynamic equations. The basic equations [ 30,311 for a liquid with a uniform density pO, temperature T,, unperturbed refractive index II, and speed of sound II, are derived by the continuity and Navier-Stokes equations as 2
(
2
U2PPo V2T
-L+;v2+32
p,+_
at2
=
2
1
Y
1
V21(r, t) ,
and the energy transport equation poC,;& -AV2
=dul(r, t) ,
T, -
C,,(Y-
I> +, t P (3)
where p, and T, are the perturbations in density and temperature, C, and C,, the heat capacities at constant pressure and at constant volume, y= C,,/C,,, 17 is the viscosity, /3 the coefficient of thermal expansion, A the thermal conductivity, c the vacuum velocity of light, (Y the optical absorption coefficient, y“ the electrostric-
796
M. Terazima/ Chemical Physics 189 (1994) 793-804
tion coupling constant, and Z( r, t) the intensity of the excitation laser. The difference between the TL and TG experiments is the condition of the excitation laser. 3. I. TL signal In the case of the TL experiment, a spatial profile of the excitation laser with a Gaussian-type is generally used, exp( -2r2/m2)
Z(r, t) =Z,B(t)
,
(4)
where r is the radical distance from the center of the cylindrical symmetry and w is the beam radius. In this Section, we assume an impulsive photoexcitation. Brueck et al. [30] have solved the above equations under the following assumptions: a multiphoton absorption process is negligible, the lifetimes of the photoexcited states by the radiationless transition are short enough compared to the acoustic transit time, and the terms of the viscosity and thermal conductivity are negligible. Under a further assumption of negligible electrostriction, which is valid under our experimental conditions (relatively large absorbance of the sample), the equation is simplified as A exp( - r2/D)
PI = -
D a
+B
r {exp{ -2[(s-ut)lw]‘)
J
I
-exp{
-2 ,[
where A = H/31&,, D= w2/2,
B=HP/(2n3)
“*ovC,d/dt,
H= m3’Zocd2.
The first term in Eq. (5) represents the diffusive mode of the density variation (p;““) and the second one is the acoustic mode ( py ) . The variation of the temperature (T, ) is calculated from T, = [ -p;“”
+ (y-
l)pF]
/ppo.
(6)
The time profile of the TL signal is evaluated by the numerical differentiation of p, and Ti with respect to r, d2p,lar2 and d2T,13r2.
Fig. I. Calculated time profiles of the Dens.L signal (A) and the Temp.L signal (B) in water at 20°C.
Typical time developments of d2p,ldr2 and a2T, / dr* in water at 20°C are depicted in Fig. 1. The various thermodynamical properties of water are taken from Refs. [ 31-331. The Dens.L signal rises gradually after the heat depositing time (t = 0)) reaches a maximum and decays down to a plateau. This time profile is similar to that in a typical organic solvent, such as benzene, as reported in the previous paper [ 221 except for the weak signal intensity. The Temp.L signal rises instantaneously and has a slight disturbance on the top of the signal, which is caused by the acoustic effect; it decays down to a minimum and takes a plateau. Compared with the signal in benzene, the disturbance at t 2 0 is weak, because y of water is close to unity and, as a result, ( 1 - y)py -0 in Eq. (6). Therefore the time profile of the Temp.L is almost a step function. The time profile of the total TL signal is given by
+ (dn/c3T),(d2T,/dr2)
(7)
Hereafter, d*p,lar* or d2T,ldr2 is written as just p1 or T, for simplicity, because the magnitude of d*p,/dr’ and a ‘T, ldr* are, respectively, proportional to pi and T, as long as the spatial profile of the excitation beam
M. Terazima/Chemical
797
Physics 1R9 (1994) 793-804
is fixed. Note that this notation is used only for the TL case. 3.2. TG signal In the TG experiment, the interference pattern of the two excitation laser light beams is used for the photoexcitation and is described by a one-dimensional equation, Z(r, t) =&6(t)
[l +cos(2rrxlA)]
(8)
Here we assume a plane wave for the light and an equal light intensity for the two beams. The fringe spacing, A, is given by the wavelength of the excitation light A,, and the crossing angle 9 as A = A,,/2 sin( %/2) .
(9)
Since only the first order diffracted signal is monitored here, we are interested in the time profiles of the Fourier component at 9 = 2rr/A of pi and T,. On the basis of the same assumptions as in the TL case, Eqs. (2) and (3) can be solved, and the q components are given by
#h(q)=C[1-cos(qt)l
3
0
1
2
‘
3 tI
Zac
Fig. 2. Calculated time profiles of the Dens.C signal (A) and the Temp.G signal (B) in water at 20°C.
(10) The time profile of the total TG signal (&(t)) calculated from
%7) =ff’hpoC,. + [Cl- lly)~‘lp,C,,l
J
I
cos(uqt) I
is
(11)
where C= - @H’/C, and H’ = c&. (Hereafter, the q components of ~5, and F, are represented just as p, and T, in the TG case.) Similar to the TL case, pi in Eq. ( 10) can be equivalently treated as the sum of two density waves; the diffusive (isobaric) and acoustic (adiabatic) waves as p;iiff = C and py = - C cos( uqt). (Note that these are the Fourier components of p,.) Then T, can be given by Eq. (6). The spatial and temporal behaviors of these two waves are schematically shown in Ref. [20]. The typical time development of the ITo in water at 20°C is depicted in Fig. 2. The Dens.G rises from a zero signal intensity at t > 0, and oscillates by the acoustic effect with a period of rA, = A/u. On the other hand, the Temp.G signal rises immediately after the heating, and takes almost a flat signal after the rise, though a minor acoustic oscillation is observable on it. Similar to the TL case, the minor contribution of the oscillation is due to y- 1 in water. If the Temp.G signal in benzene is calculated, the acoustic oscillation even in the Temp.G signal should be stronger.
(12)
4. Results and discussion 4. I. Temperature and densi@ lenses Fig. 3 shows the time profile of the TL signal after the photoexcitation of nitrobenzene in water at 7.8”C. For the purpose of comparison, the TL signal in benzene under the same experimental conditions except the excitation laser power is shown in Fig. 3. Since the photothermal signal intensity in water is much weaker than that in ordinary organic solvents, as will be mentioned in a later section, the excitation laser power in the aqueous solution case ( - 70 p,J/pulse) is increased to obtain a reasonably strong intensity. Even at this laser power, the signal intensity shows a linear dependence on the excitation laser power. This fact ensures that there is no saturation effect in the TL signal and
798
M. Terazima / Chemical Physics 189 (1994) 793GW4
Fig. 3. Observed time resolved TL signals of nitrobenzene in water (solid line) and in benzene (dotted line). The leading edge of the excitation laser pulse is set to be t = 0. Both signals are normalized at the peak intensity.
that a multiphoton absorption process of nitrobenzene can be neglected. Upward of this figure indicates the decrease of the probe beam intensity by the beam expansion; namely, the TL is a diverging lens. The signal in benzene gradually appears after the photoexcitation and after it reaches maximum at 100 ns, decays down to a plateau. The time at the peak is mainly determined by the radius of the excitation beam and the speed of sound. This time dependence can be fitted well only by the pr term (Dens.L) in Eq. (5). The time dependence is similar to that observed by Bailey et al. for the gas phase TL experiment with fast vibrational-translational energy transfer [ 1 I]. Compared with this signal in benzene, the signal in water rises earlier and the signal intensity at the plateau region is slightly stronger. Apparently, this time profile cannot be explained only by the Dens.L signal. Previously, these differences had been explained by the nonnegligible contribution of the T, term (Temp.L). The contribution of this component is more apparent at lower temperatures. Fig. 4A shows the observed TL signals at various temperatures. The fast rising component becomes stronger with decreasing the temperature. At 4.O”C, the signal rises with an instrumental response time and becomes almost flat after the initial rise part. Further decreasing temperature, the signal shows a dip in the flat region and ultimately it becomes negative (negative signal indicates the increase of the probe beam intensity (converging lens) ) .
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0.8
L 0.8 t I ClS
Fig. 4. (A) Time profiles of the TL signals in water at various temperatures (a) 7.9”C, (b) 4.O”C, (c) 1.7”C. (d) -3.5”C. (B) Best fitted calculated signals with a superposition of the Temp.L and Dens.L contributions at the same temperatures as in (A).
Similar signals and similar temperature dependence are observed after the photoexcitation of DAP and FeCl, in aqueous solution. Without these solutes, there is no detectable signal under the same experimental conditions. Therefore, we believe that the observed non-Dens.L component should not come from a refrac-
799
M. Terazima / Chemical Physics 189 (1994) 793-804
tive index variation due to photochemical products or unknown me&stable states, because it is very unlikely that the three solutes with very different chemical properties give a very similar non-thermal signal by photochemical reactions or photophysical processes. Rather is it reasonable to consider that the non-Dens.L signal is due to a (non-density) thermal effect, i.e. temperature lens component. Another evidence against the assignment of this signal to the population lens of a photochemical species due to a photochemical reaction or due to a metastable state comes from the decay rate of the signal. The signal decays to the baseline with the time constant of the thermal diffusion in water. If the signal comes from the refractive index lens by a chemical species, the signal should decay with the time constant of the mass diffusion, which is much smaller than that of the thermal diffusion. Since the signals from these three compounds are the same within the experimental error, we will discuss the signals obtained by using nitrobenzene hereafter. These temperature dependence can be well reproduced by the superposition of Temp.L and Dens.L as shown in Fig. 4B. In this calculation, the calculated p, and T, from Eqs. (5) and (6) with the reported thermodynamical properties of water [32-341 are convoluted with the instrumental response function and added together with an appropriate weighting factor. Only the adjustable parameters for the fitting are a normalization factor of the signal intensity, the excitation beam radius and the ratio of Dens.L to Temp.L (p,/T, ). The best fitted ratio at the various temperatures are shown in Fig. 5. One of the error sources in the determination of pi/T, comes from the noise in the TL signal, because of the weak signal intensity in water. The range of error of this type can be estimated from the fitting procedure ( f 0.2). A systematic error may come from the factors which are neglected in the theoretical equations. For example, acoustic dumping of py has been neglected. The determined p, /T, decreases with decreasing temperature and becomes zero at 3.8”C. In order to obtain more quantitative information, the signal intensity is measured at each temperature. Since the acoustic wave, which is sensitive to the various factors such as speed of sound and acoustic damping, contributes to the peak intensity, the maximum intensity is not a good indicator for the signal intensity. Hence the signal intensity is defined by the intensity at
12/
Fig. 5. Temperature dependence of p, /T, determined from the TL signal (circles) and from the TG signal (squares) of nitrobenzene
aqueoussolution. the plateau region here. In this region, the signal due to the acoustic mode (py ) can be neglected in the TL signal and the intensity is given by ptf and T,. The values are plotted in Fig. 6. The most accessible quantity in a literature is (dnldT), and it is related to the quantities we are interested in here by (13) Experimentally the temperature dependence found to be expressed as [ 34,351
n*- 1 n*+l
= A’pt’ exp( -CT)
,
of n is
(14)
where A’, B’, and C’ are constants which are given in Ref. [ 341. We calculate n at various temperatures from this expression and obtain (dn/dT), by differentiating n with respect to T. The calculated (dn/dT), is plotted in Fig. 6 with an appropriate normalization factor. The agreement between the determined value in this work and the literature values is quite good. The plot intercepts the Z,, = 0 line at - 0.2”C. It is known that the refractive index of pure water goes through the maximum value at - 0.01 “C [ 231, and at this temperature dn/dT should vanish. The slight difference between the literature and observed values may be due to the solute effect ‘on the thermodynamical properties of water and/or a temperature gradient between the temperature-monitored region and the
. j
’
*-
10
*
J 20
T/K
Fig. fi Tem~e~~tn~ dependences af the total TL signal intensity (circles) and the ~~teosit~esofthe D6ns.L {squares) and the Temp.L (triangles) signals after the phot~xcit~tion of nitrobenzene in water. Reported (dn/dT), and (+‘U),/C, [32-341 are also shown by the solid line and the broken line, respectively. They are, respectively, jollied to the total TL signd j~tensity and the Dens.L signal intensity at 11“C, Thesequ~t~t~es below 0°C are extm@ated by
rtsing a 6X&e~~~~U~~~ tit ffom0°C to 20°C. laser-irradiated region. This signal-vanishing temperature is the one that Song and Endicott have used for neglecting the thermal effect in the TL signal [ 241, and Miller in the TC ex~~rn~~ts [26] *Ttney have measured the TL or 733 sign& at this temperature and tried to observe the probe beam absorbance or molecular volume change effect in the signal. Note however, that, the TL signal vanishes because the effects of TI and of pt” are ~an~elled at this temFe.ra~re. When the signal is observed with a fast time response detector, the Temp.L and the signal due to p:” are still apparent even at this temperature as shown in Fig. 4. From the signal intensity and the determined quantity of pI / Tt, the tem~rat~e d~~e~den~e of the Dens.L and Ternary ~~rn~~~e~~~are ~~~~~ated and they are ptotted in Fig. 6. After passing over the pressure wave from the detection region, the temperature and density change in the region are given by
pt = (apA3T),HI
C, .
Therefore the t~m~ratur~ d~p~ndenc~s of the Dens.L (moreexactly, pdi” component in Dens.L) and Temp.L
components correspond to those of (&/ap),( ap/ ~~~~~C~ and (~~~~~~~~C~, res~t~v~ly. The intercept e fact ns,t ~~teusity reflects at 3,8”@ to the zero that the density of water takes a maxima value at 4°C. In Fig. 6, (&z~B’),/ C, is plotted with an appropriate notarization factor, As is seen from this figure, the tern~~atu~e dependence of Dens.L s&al intensity fits very well with that of (~~~~~~~C~. Since C, is rather insensitive to the temperate, the variation of Dens.L is controlled by the factor (&z/U), Eq_ ( 13) suggest that we might be able to calcculate (~~~~~~, which is usuatiy difficult to be measured, from this equation with the more easily accessible q~~t~t~es (d~/d~~ and (~~~~~~ if (~~~~~~= is known. Sorn~t~rnes~ this quantity ~~~~~ is discussed on the basis of the Lor~n~z-Lorenz relation [ 35 ] , an
(n”$_2)(n2-
ap’
6prz
1) *
(15)
However, the tern~~at~re d~~~d~~~e of ~~~~~ allot be ~r~~~~d fram this relation, because this equation is based on the assumption that the molecular polarizability is a constant and this assumption is not valid for water [ 20,35,36], Therefore, as pointed out: in the previous paper [ 22]+ me~sur~rnen~ uf the time resolved TL (TG) signal wiff give a good way to determine the (&E/X), value. Fig. 6 shows that the quantity (an/ an, gradually increases with decreasing temperature,
The time deve~~prn~n~ of the TG signal after the phatoexcitatian of nitrobenzene in water is depicted in Fig. 7 and compared with that in benzene. Again, the excitation laser power is stronger in the case of water. Under this ex~rirn~n~~ ~ondi~o~ fa small glossing angle) J the excitation laser pulse width is shorter than the acoustic transit time between the fringe, so that acoustic oscillation is observed in bath signals. Since the fringe spacing can be much smaller than the beam radius in the TL experiments the signal takes its maxiat an earlier time thrtn the TL signal. This is the main reason why the TG myths has been known to have a fast time resolution among the photothermal t~~~~ques [ 12-181. comparing the signals in benzene and water, one finds that the signal in water rises slightly faster, the
M. Terazimu / Chemical Physics 189 (1994) 793-804
period of oscillation is shorter, and the amplitude of the oscillation is smaller. The short oscillation period in water reflects the faster speed of sound compared with that in benzene. The faster rise and smaller amplitude become more obvious at lower temperature (Fig. 8A). At 4.O”C, the acoustic oscillation almost disappears and the signal consists only of a step function with a rise time determined by the time response of our instrument. Below this temperature, acoustic grating appears again as a dip on the step function signal. Further below that temperature, the acoustic oscillation appears again. The same temperature dependence is observed by using a DAP or FeC& aqueous sample. Following the same idea as in the Temp.L case, the non-density grating component is attributed to the temperature grating. We tried to reproduce the observed temperature dependence of the TG signals by the superposition of the Temp.G and Dens.G signals. The basic equations for that calculation are Eqs. ( lo)-( 12). However, we find that the acoustic damping, which is neglected in the equation, cannot be neglected in this time range for the fitting. This damping effect is explicitly taken into consideration phenomenologically and Eq. ( 10) is modified to p, =C[ 1 -cos(uqt)
exp( -k,,t)]
,
801
(b)
./-
(16)
1
where kac is the rate constant of the damping. The fitting parameters, u and k,,, at various temperatures will give us important information on the solution structure [ 37, 381. However, we will not discuss the acoustic para-
t I ns Fig. 8. (A) Time profile of the observed TG signals of nitrobenzene in water at various temperatures (a) 5.2”C, (b) 4.O”C, (c) 3.O”C, (d) - 2.1 “C with a crossing angle 0.19” of the excitation beams. (B) Best fitted calculated signals with a superposition of the Temp.G and Dens.G contributions.
Fig. 7. Observed time resolved TG signals of nitrobenzene in water (solid line) and in benzene (dotted line) with a crossing angle 0.27” of the excitation beams.
meters further in this paper to focus our attention on the Temp.G signal. The best fitted time profiles of the TG signals are shown in Fig. 8B. The agreement of the observed and calculated ones is quite satisfactory. The determined p1 / TI at various temperatures are plotted in Fig. 5. The ratio agrees fairly with those determined from the TL
802
M. Terazima / Chemical Physics 189 (1994) 793404
experiment. The difference at the low temperature region might be due to the acoustic dumping, which is neglected in the TL case. Similar types of discussions as those in the previous section can be made in this TG case as well. Since the TG method is the background-free detection, the noise in the signal is much smaller than that in the TL signal and it is expected that the pllT, value could be more precise than that determined from the TL signals. However, the time resolution of this method is sufficiently high compared with the laser pulse width even under this small crossing angle, the fast development of the Temp.G signal is hidden in the strong Dens.G signal at higher temperatures, where the relative contribution of Temp.G is smaller. Therefore the pl/Tl value determined from the TG signal has a larger uncertainty than that from the TL signal especially at high temperatures (not shown in Fig. 5). If one uses a shorter excitation laser pulse, the accuracy of the pr and T, will be much improved and the discussion on the thermodynamical properties of water can be more precise. 4.3 Fast response of the Temp.L and Temp.G Even though the photothermal methods are powerful and widely applicable tools as mentioned in the Introduction, some limitations have prohibited applications to study ultrafast phenomena. One of the limitations of the photothermal techniques has been the relatively slow time resolution. This limitation comes from the fact that the effect of the density change to the refractive index variation is so large that the rise time of the signal is determined by the acoustic transit time. For example, the acoustic oscillation in the TG signal masks the fast time response. These acoustic effects will mask not only the fast heating effect but also any signals such as the transient absorption, population lens, or population grating. However, by applying the Temp.L and Temp.G signals observed clearly in this work, the photothermal signals can be made free from the acoustic perturbation and the time response is solely determined by the instrumental response function and the heat release processes. Here we just shortly mention an observation of fast response in the Temp.L by taking quinoxaline as an example. More detailed investigations of the excited state dynamics will be published elsewhere.
0
0.2
0.4
0.6
ti p Fig. 9. Rise profile of the Temp.L slgnal after the photoexcitation quinoxaline in water at 4.O”C.
of
After the photoexcitation of quinoxaline, one of the prototypes of nitrogen heteroaromatic compounds, to the excited singlet state, the T, state is created efficiently with a quantum yield of nearly unity [ 3,391. In SDS micelles, the hydrogen abstraction reaction takes place from the T, state and that state is expected to be short lived [40]. Fig. 9 shows the time profile of the Temp.L after the photoexcitation of quinoxaline in a SDS aqueous solution at 4.O”C. The signal shows a fast rise limited by the instrumental response time followed by a fast decay with a time constant - 50 ns. In the longer time scale, the signal decays to the baseline by the thermal diffusion, which is not shown here. If the signal originates only from the thermal effect due to the deactivation of the excited state, we expect a relatively slow rise instead of the fast decay. Therefore the signal should be explained by the Temp.L and the fast decay component, which is probably the transient absorption or the population lens signal by the TI state. This observation of the fast time development in the Temp.L signal will open a possibility to study fast dynamics by the TL method. Of course, tens of nanosecond time resolution can be achieved by using the TG method with a larger crossing angle. However, if one wants to investigate a faster dynamics, a shorter excitation laser pulse should be used and then the acoustic oscillation will appear to mask such dynamics as long as the Dens.G is used [ 17,18,25]. This limitation can be removed by using water as a medium and observing the Temp.G or Temp.L signals. The limitation in utilizing these signals, except the inherent limitation in the choice of solvent, is the low
sensitivity. It is known that the (dnlc2p) ,-value of water is about an order of magnitude smaller than those of other organic solvents [ 191 and this is the reason why water has been considered to be the worst medium for the photothermal techniques. On the other hand, the obtained (Wa7’), value of water is not much smaller than those of other solvents [ 19 1. Therefore the relativeIy large contribution of the temperature effect in the observed “TL signal” is due to the small farz/ 3~)~; in other words, the c~~tribut~o~ of TempL or Temp.G is manifest in water because of the small Dens.L or Dens.G signal intensity. This disadvantage should be overcome by increasing the excitation laser power. However, then we should be careful about the ~on~ibutio~s of multi~h~to~ abso~tio~ processes or the higher order interaction between the transient states, such as the excited state-excited state annihilation. Nevertheless, a method utilizing these signals will provide powerful tools for studying the fast dynamics of the energy transfer processes, especially heat releasing or vibrational rel~atio~ processes.
5. Summary Con~i~ut~~~s of the tern~~~t~re lens (~emp.L~ and temperature grating (Temp-G) signals in aqueous solution are reported. Depending on whether the measurements are performed at temperatures lower or higher than 3.8”C, the Dens.L or Dens.G signals have either ative ~on~ib~t~o~s on the Tern~.~ or At 3.8”C, pure Temp.L and Temp.G ese relative con~ibutions are mainly controlled by the small and temperature dependent dpldT of water. Since the rise times of these signals are governed only by the instrumental response time and the rate of the heat released from the excited state, these signals permit precise investigations of the fast dynamics of the photoexcited states in solution or electronic (vibrational)-translational energy transfer processes.
References i 11H.L. Fong and R.L. Swofford* in: Ultra sensitive
laser s~c~os~opy, ed. D.S. Kliger (Academic Press, New York, 1983). 121 SE. Braslavsky and GE. Heibel, Chem. Rev. 92 ( 1992) 1381. [3] M. Terazima and T. Azumi, Chem. Phys. Letters 141 (1987) 237; 145 (1988) 286; 153 (1988) 27. j4] M. Terazima and N. Nirota, J. Phys. Chem. 95 ( 1991) 9080. IS] M. Terazima, T. Azumi and N. Hirota. J. Photocfiem* pbotobio~. A 65 [ 1992) 21. {6] AJ. Twarowski and D.S. Kliger, Chem. Phys. 20 (1977) 253. [ 71 G. Rossbroich, N.A. Garciaand S.E. Braslavsky, I. Photochem. 31 (1985) 37. J8 1 R.W.Redmond and SE. Braslavsky, Chem. Phys. Letters 148 Il988) 523. [9] B.M. Toselli, T.L, Waling and JR Barker, J. Cbem. Phys. 92 (1990) 4793. [ 101S.J.Jacobs, Chem. Phys. 132 (1989) 71. [ 111R.T.Bailey, F.R. Cruickshank, R. Guthrie, D. Rugh and I.J.M. Weir, Mol. Phys. 48 (1983) 81. [ 121MB. Zimmt, Chem. Phys. Letters 160 ( 1989) 564; J. Morais, J. Ma and MB, Bmmt, J. Phys. Chem. 95 ( 1991) 2885. [I31 X,~.ZhuandJ.M. Harris,Chem. Phys. 157 (1991) 409;Chem. Phys.Letters 186 (1991) 183. [ 141 M. Terazima and N. Hirota, J. Chem. Phys, 95 ( 1991) 6490; Chem. Phys. Letters 189 (1992) 560; J. Appl. Phys. 73 ( 1993) 7672. I:151L. Gove-Jah~, J. Kasinski and R.J.D. Miller, Chem, Phys. Letters 125 (1986) 500. 1161 H.J. Eichler, D. Gunter and D.W. Fohl, in: Laser induced dynamic gratings (Springer, New York, 1983). 1171 K.A. Nelson and M.D. Fayer, J. Chem. Phys. 72 ( 1980) 5202. [ 181AR. Duggal and K.A. Nelson, J. Chem. Phys. 94 ( 1991) 7677. [ 191 R.C. Desai, M.D. Levenson and J.A. Barker, Phys. Rev. 27A (1983) 1968. j20J f. Scarlet, Phys. Rev. 6 11972) 2281. [Zi] ‘I’. Kawasaki, A. &rata and T. Sawada, Anal. Sci. 7 Suppl. (1991) 653. [ 221 M. Terazima and N. Hirota, J. Chem. Phys. 100 ( 1994) 2481, [ 231 M. Frank0 and CD. Trm, Anal. Chem. 61 ( 1989) 1660. [ 241 X. Song and J.F. Endicott, Chem. Phys. Letters 204 ( 2993) 400. 1251 L. Genberg, Q. Baa, S. Cracewski and R.J.D. Miller, Chem. Phys. 131 (1989) 81. [26] R.J.D. Miller, L. Genberg, L. Richard and S,M. Gracewski, in: Photoacoustic and photothermal phenomena 11, eds. J.C. Murphy, J.W.M. Spicer, L.C. Aamodt and B.S.H. Royce (Springer, Berlin, 1990); R.J,D. Miller, Annu. Rev. Phys. Chem. 42 ( 1991) 581; L, Genberg, L. Richard, G. MeLendon and R.J.D. Miller, Science 251 (1991) 1051.
[ 271 M. Terazima, S. Yamauchi and N. Hirota, J. Phys. Chem. 89 The author is indebted to Professor N. Wirota for valuable discussions and encouragement.
(1985) 1220; M. Terazima, Chem. Phys. Letters 140 ( 1987) 6.
804
M. Terazima / Chemical Physics 189 (1994) 793-804
1281 C.J. Seliskar, O.S. Khahl and S.P. McGlynn, in: Excited state, ed. E.C. Lim (Academic Press, New York, 1974). [29] K. Kalyanasundaram, in: Photochemistry in microheterogeneous systems (Academic Press, London, 1987). [30] S.R.J. Brueck, H. Kildal and L.J. Belanger, Opt. Commun. 34 (1980) 199. [31] J.-M. Heritier, Opt. Commun. 44 (1983) 267. [32] G.S. Kell, in: Water, Vol. 1, ed. F. Franks (Plenum Press, New York, 1972). [33] C.M. Davis Jr. and J. Jarzynski, in: Water, Vol. 1, ed. F. Franks (Plenum Press, New York, 1972).
1341D. Eisenberg
and W. Kauzmann, in: The structure properties of water (Oxford Univ. Press, Oxford, 1969).
and
[351 H.J. Eisenberg, J. Chem. Phys. 43 (1965) 3887. 1361I.Thormahlen, J. Straub and U. Grigull, J. Phys. Chem. Ref. Data 14 (1933) 933. [371 A.B. Bhatia, Ultrasonicabsorption
(Dover, New York, 1967).
[381 L. Hall, Phys. Rev. 73 (1948) 775. [Xl 1 D.W. Boldridge, G.W. Scott and T.A. Spiglanin, J. Phys. Chem. 86 (1988)
1976.
-401 M. Terazima and N. Hirota, to be published.
Chemical Physics 189 ( 1994) 793-804
Temperature lens and temperature grating in aqueous solution Masahide Terazima Department oj’Chemistry, Faculty
of Science Kyoto University, Kyoto 606, Japun
Received 4 February 1994; in final form 14 August 1994
Abstract Time profiles of the thermal lens (TL) and transient grating (TG) signals after photoexcitation of several substances in water are observed at various temperatures. These signals are analyzed in terms of the superposition of the temperature lens (Temp.L) and density lens (Dens.L) in the TL case, and of the temperature grating (Temp.G) and density grating (Dens.G) in the TG case. Pure Temp.G and Temp.L signals are observed at N 4°C. The fast response of the Temp.L and Temp.G signals can be used to investigate the fast dynamics of the excited state or fast electronic-translational energy transfer processes.
1. Introduction
After photoexcitation of molecules to their excited states, various photophysical or photochemical processes take place. The radiationless transition is one of the most common phenomena among these processes no matter how stable the molecule photochemically is. The energy released by the radiationless transition ultimately flows into the translational energy of the medium as heat. Therefore photothermal techniques with laser excitation could be powerful and universal methods for investigating the dynamics of excited states and/or photochemical processes. The thermal lens (TL) [ 1-2 l] and the transient grating (TG) [5,12-181 methods are well known to be sensitive optical detection methods of heat with fairly fast time resolutions. These methods detect the variation of the refractive index in solution, which is induced by heat from the radiationless transition. In this report, we discuss two sources and ‘I’L signals.
of refractive
In the TL method, spatially non-uniform
index variation
in the TG
a sample solution is irradiated by light, then a probe beam expan-
sion due to the spatially
non-uniform
refractive index
0301.0104/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDlO301-0104(94)00289-4
distribution induced by that excitation light is detected as a change of the probe light density. In the TG experiment, two coherent excitation beams are crossed at an angle in the sample. The interference between the two beams produces a sinusoidal pattern and the heat in the bright region produces the refractive index grating. If a probe beam passes through the grating region satisfying the Bragg condition, the light is partly diffracted as the TG signal [ 161. The key point of these two techniques is the refractive index variation due to the released heat from the photoexcited states or species. The variation of the refractive index (An) after depositing heat in solution will be expressed by
(1) In many organic solvents, the first term dominates over the second term significantly [ 19,201. Due to this large difference, the density change which results from the heating effect has been the main cause of the TL or TG signals so far. It is important to note that the density change does not take place immediately after the heat is released. As a consequence, there is always a finite time lag between the heat releasing and the appearance
of the signal. The time constant of the signal rise is determined by the escape time of the acoustic pressure from the i~adiated region. It is given by ra:,,= U/U ( w is the excitation laser spot size, u is the speed of sound in the medium) [ l-1 11, in the TL case, and is around 100 ns under normal experimental conditions. ln the TG case, the effect of the volume expansion of the medium appears as an acoustic oscillation with a period ~,,=J%/u (A is the fringe s~aciog) [ ISIS]. These escape times of the pressure wave have been time limitations of these methods. In order to investigate the fast dynamics by these useful photothermal methods, it is desirable to find another source of the photothermal signal with a faster time response [ 2 1 ] . Recently we have reported the first observation of the TL signal due to the second term of Eq. ( 1) and referred to that signal component as the temperature lens (Temp.L) signal [ 221. Since the time response of this signa does not suffer from the escape time of the pressure wave, it is predicted that the Temp.L signal sbo~ld response i~staut~neous~y after the heat is released. Indeed, our previously observed Temp.L signal rises faster than the normal TL signal [ 221. (In this paper, we explicitly use the term “density lens” (Dens.L) signal for denoting the TL signal due to the first term in Eq. ( 1f ; namely, the Dens.L signal comes from the refractive index variation by the volume expansion. The notation “TL signal” is reserved to indicate the experimentally observed signal, which may containTemp.L and/or Dens.L.) Naturally, it is expected that a similar type of TG signal which originates from the second term, should be observable. These new type of signals could be used for a fast response method in the photothermal techniques. In this paper, first, we report the temperature dependence of the TL signal in water as an extension of our previous work. In e previous paper [ 22 f , the Temp.L signal appeared as a shoulder in a relatively strong Dens.L signal. Since the intensity of the Dens.1, signal should be proportional to the quantity of dp/dT and that of water sensitively depends on the temperature, the contribution of the Temp.L is expected to be observed more clearly by choosing a sui~ble temperature for it. Second, the Temp.G, which is defined as the TG signal due to the second term of Eq. ( 1>, is observed in the TG signal. (Similar to the names Temp.L and DensL, only the TG signal due to the first
term is called “density grating” (Dens.G) signal in this paper.) previously water has been sometimes used as a unique medium in the TL or TG experiments [ 23-263 . Frank0 and Tran have used water to enhance the sensitivity of the TL signal in aqueous solution by increasing the solution temperature [ 231. Also water is an important medium for biological molecules. Miller et al. have measured the TG signals for studying mottoes of proteins and bio olymers 1261. However, to our knowledge, our pre ous [ 221 and present papers are the first reports utilizing the water medium for obtaining a fast response signal in the photothermal techniques.
2, Experimental An excimer laser-pumped dye laser (Lumonics Hyper 400 and Hyper Dye 300) was used for the excitation light at 360 nm in the TL and TG ex~rimen~s” In the TL experiment, this dye laser beam was shaped to have a nearly Gaussian spatial profile by a pinhole and slightly focused (beam radius - 300 pm) to a sample in a quartz cell with a 5 mm optical path length by a concave lens cf= 80 cm). A He-Ne laser was used as the probe beam. The beam was collimated at the sample position and then expanded by a concave lens. The decrease of the probe light density at the center of the excitation beam was monitored through a glass filter and a pinhole (0.3 mm 0). In the TG experiment, the excitation beam was split into two with a beam splitter and crossed inside the sample cell at an angle 0.19” (fringe spacing - 100 pm). The He-Ne laser, probe beam, was brought into the sample at the Bragg condition. The diffracted probe beam was isolated from the excitation beam with the glass filter and pinhole oth TG and signals were monitored by a system. photomultiplier (~~amatsu R928) and averaged by a digital oscilloscope (Tektronix TDS-520) and a microcomputer. In order to investigate the time profiles of the TC and TL signals, heat should be injected in the sample solution impulsively compared with the instrumen~l response time, which was determined by the pulse width ( 15 ns) in this experiment. We tried to use several solutes, such as nitrobenzene, 9,l O-diazaphenanthrene (DAP) and F&I,, for that purpose. The
M. Terazima /Chemical
dynamics of the excited states of DAP has been studied and the excited states are known to be deactivated to the ground state rapidly compared with our laser pulse width [ 271. The fast deactivation ensures that it is not necessary to consider the slow rise of the thermal energy, any excited singlet-singlet (S,-S,) or excited triplet-triplet (T,-T,) transient absorptions, and the contribution of the population lens or the population grating due to metastable states. Moreover, the molecular structure is rigid enough not to allow a change of the molecular volume upon photoexcitation. However, it fluoresces relatively strongly and the emission disturbes the measurement especially at early time scale after the photoexcitation, The photoexcited states of nitrobenzene are also deactivated to the ground state much faster than our laser pulse width without accompanying noticeable luminescence or photochemical reactions [ 281 in our experiment. The negligible contribution of metastable states of nitrobenzene in our observation time range is confirmed by measuring the rise profile of the TG signal with a small fringe spacing ( - 2 rJ,m). The rise profile was determined by the laser pulse width and there is no indication of a slow heating process. This fact means that the concentration of metastable states of nitrobenzene even if it exists is negligibly small. FeCl, in aqueous solution was sometimes used for a standard of calorimetric measurement [2] and we also confirmed that there is no slow decay component in the excited state dynamics within our observation time scale. In the case of DAP and nitrobenzene, SDS was used as a surfactant ( - 0.02 M) to enhance the solubility in water. This concentration was higher than the critical micelle concentration of SDS in water ( 8 X 10 ~’ M) [ 291, but the concentration of the micelle should be lower due to the aggregation of the monomer SDS. Since the micellar size is quite small and it was dilute, we expect that the thermodynamical properties of the micellar solution are similar to those of water. The concentration of FeCl, was also very low ( - 5 X lop3 M), and this ion should not change the thermodynamical properties of water, either. The temperature of the sample solution was controlled by flowing methanol around a metal cell holder. A thermostated bath (Lauda RLS6-D) was used to circulate the methanol. A thermocouple wire was directly dipped into the sample solution and the voltage was monitored by a digital volt meter. The stability of the temperature was fO.l “C. Below zero degree or
79.5
Physics 189 (1994) 793-804
around a low temperature region, SDS could be precipitated or the water could be frozen. However, we could cool the temperature down to - - 4°C without precipitation or freezing. When the measurement was extended to a long time at such low temperatures, precipitation of SDS is observable as the scattering of the probe light. Nitrobenzene and benzene (Wako Chemical Co.) of spectrograde, and FeCl, (Nakarai Chem. Co.) were used as received. DAP purchased from Aldrich Co. was purified by recrystallization. Distilled water was used. Absorbance of the sample was adjusted to 0.2 at the excitation wavelength.
3. Analysis Neglecting any absorption of the probe beam by the solute and any contribution of the metastable state, the TL and TG signals originate from the variation of the refractive index in the solution. The refractive index variation due to the thermal effect in an isotropic liquid is determined by the variation of the density and the temperature through Eq. ( 1). The time profiles of the density and temperature changes are calculated from the linearized hydrodynamic equations. The basic equations [ 30,311 for a liquid with a uniform density pO, temperature T,, unperturbed refractive index II, and speed of sound II, are derived by the continuity and Navier-Stokes equations as 2
(
2
U2PPo V2T
-L+;v2+32
p,+_
at2
=
2
1
Y
1
V21(r, t) ,
and the energy transport equation poC,;& -AV2
=dul(r, t) ,
T, -
C,,(Y-
I> +, t P (3)
where p, and T, are the perturbations in density and temperature, C, and C,, the heat capacities at constant pressure and at constant volume, y= C,,/C,,, 17 is the viscosity, /3 the coefficient of thermal expansion, A the thermal conductivity, c the vacuum velocity of light, (Y the optical absorption coefficient, y“ the electrostric-
796
M. Terazima/ Chemical Physics 189 (1994) 793-804
tion coupling constant, and Z( r, t) the intensity of the excitation laser. The difference between the TL and TG experiments is the condition of the excitation laser. 3. I. TL signal In the case of the TL experiment, a spatial profile of the excitation laser with a Gaussian-type is generally used, exp( -2r2/m2)
Z(r, t) =Z,B(t)
,
(4)
where r is the radical distance from the center of the cylindrical symmetry and w is the beam radius. In this Section, we assume an impulsive photoexcitation. Brueck et al. [30] have solved the above equations under the following assumptions: a multiphoton absorption process is negligible, the lifetimes of the photoexcited states by the radiationless transition are short enough compared to the acoustic transit time, and the terms of the viscosity and thermal conductivity are negligible. Under a further assumption of negligible electrostriction, which is valid under our experimental conditions (relatively large absorbance of the sample), the equation is simplified as A exp( - r2/D)
PI = -
D a
+B
r {exp{ -2[(s-ut)lw]‘)
J
I
-exp{
-2 ,[
where A = H/31&,, D= w2/2,
B=HP/(2n3)
“*ovC,d/dt,
H= m3’Zocd2.
The first term in Eq. (5) represents the diffusive mode of the density variation (p;““) and the second one is the acoustic mode ( py ) . The variation of the temperature (T, ) is calculated from T, = [ -p;“”
+ (y-
l)pF]
/ppo.
(6)
The time profile of the TL signal is evaluated by the numerical differentiation of p, and Ti with respect to r, d2p,lar2 and d2T,13r2.
Fig. I. Calculated time profiles of the Dens.L signal (A) and the Temp.L signal (B) in water at 20°C.
Typical time developments of d2p,ldr2 and a2T, / dr* in water at 20°C are depicted in Fig. 1. The various thermodynamical properties of water are taken from Refs. [ 31-331. The Dens.L signal rises gradually after the heat depositing time (t = 0)) reaches a maximum and decays down to a plateau. This time profile is similar to that in a typical organic solvent, such as benzene, as reported in the previous paper [ 221 except for the weak signal intensity. The Temp.L signal rises instantaneously and has a slight disturbance on the top of the signal, which is caused by the acoustic effect; it decays down to a minimum and takes a plateau. Compared with the signal in benzene, the disturbance at t 2 0 is weak, because y of water is close to unity and, as a result, ( 1 - y)py -0 in Eq. (6). Therefore the time profile of the Temp.L is almost a step function. The time profile of the total TL signal is given by
+ (dn/c3T),(d2T,/dr2)
(7)
Hereafter, d*p,lar* or d2T,ldr2 is written as just p1 or T, for simplicity, because the magnitude of d*p,/dr’ and a ‘T, ldr* are, respectively, proportional to pi and T, as long as the spatial profile of the excitation beam
M. Terazima/Chemical
797
Physics 1R9 (1994) 793-804
is fixed. Note that this notation is used only for the TL case. 3.2. TG signal In the TG experiment, the interference pattern of the two excitation laser light beams is used for the photoexcitation and is described by a one-dimensional equation, Z(r, t) =&6(t)
[l +cos(2rrxlA)]
(8)
Here we assume a plane wave for the light and an equal light intensity for the two beams. The fringe spacing, A, is given by the wavelength of the excitation light A,, and the crossing angle 9 as A = A,,/2 sin( %/2) .
(9)
Since only the first order diffracted signal is monitored here, we are interested in the time profiles of the Fourier component at 9 = 2rr/A of pi and T,. On the basis of the same assumptions as in the TL case, Eqs. (2) and (3) can be solved, and the q components are given by
#h(q)=C[1-cos(qt)l
3
0
1
2
‘
3 tI
Zac
Fig. 2. Calculated time profiles of the Dens.C signal (A) and the Temp.G signal (B) in water at 20°C.
(10) The time profile of the total TG signal (&(t)) calculated from
%7) =ff’hpoC,. + [Cl- lly)~‘lp,C,,l
J
I
cos(uqt) I
is
(11)
where C= - @H’/C, and H’ = c&. (Hereafter, the q components of ~5, and F, are represented just as p, and T, in the TG case.) Similar to the TL case, pi in Eq. ( 10) can be equivalently treated as the sum of two density waves; the diffusive (isobaric) and acoustic (adiabatic) waves as p;iiff = C and py = - C cos( uqt). (Note that these are the Fourier components of p,.) Then T, can be given by Eq. (6). The spatial and temporal behaviors of these two waves are schematically shown in Ref. [20]. The typical time development of the ITo in water at 20°C is depicted in Fig. 2. The Dens.G rises from a zero signal intensity at t > 0, and oscillates by the acoustic effect with a period of rA, = A/u. On the other hand, the Temp.G signal rises immediately after the heating, and takes almost a flat signal after the rise, though a minor acoustic oscillation is observable on it. Similar to the TL case, the minor contribution of the oscillation is due to y- 1 in water. If the Temp.G signal in benzene is calculated, the acoustic oscillation even in the Temp.G signal should be stronger.
(12)
4. Results and discussion 4. I. Temperature and densi@ lenses Fig. 3 shows the time profile of the TL signal after the photoexcitation of nitrobenzene in water at 7.8”C. For the purpose of comparison, the TL signal in benzene under the same experimental conditions except the excitation laser power is shown in Fig. 3. Since the photothermal signal intensity in water is much weaker than that in ordinary organic solvents, as will be mentioned in a later section, the excitation laser power in the aqueous solution case ( - 70 p,J/pulse) is increased to obtain a reasonably strong intensity. Even at this laser power, the signal intensity shows a linear dependence on the excitation laser power. This fact ensures that there is no saturation effect in the TL signal and
798
M. Terazima / Chemical Physics 189 (1994) 793GW4
Fig. 3. Observed time resolved TL signals of nitrobenzene in water (solid line) and in benzene (dotted line). The leading edge of the excitation laser pulse is set to be t = 0. Both signals are normalized at the peak intensity.
that a multiphoton absorption process of nitrobenzene can be neglected. Upward of this figure indicates the decrease of the probe beam intensity by the beam expansion; namely, the TL is a diverging lens. The signal in benzene gradually appears after the photoexcitation and after it reaches maximum at 100 ns, decays down to a plateau. The time at the peak is mainly determined by the radius of the excitation beam and the speed of sound. This time dependence can be fitted well only by the pr term (Dens.L) in Eq. (5). The time dependence is similar to that observed by Bailey et al. for the gas phase TL experiment with fast vibrational-translational energy transfer [ 1 I]. Compared with this signal in benzene, the signal in water rises earlier and the signal intensity at the plateau region is slightly stronger. Apparently, this time profile cannot be explained only by the Dens.L signal. Previously, these differences had been explained by the nonnegligible contribution of the T, term (Temp.L). The contribution of this component is more apparent at lower temperatures. Fig. 4A shows the observed TL signals at various temperatures. The fast rising component becomes stronger with decreasing the temperature. At 4.O”C, the signal rises with an instrumental response time and becomes almost flat after the initial rise part. Further decreasing temperature, the signal shows a dip in the flat region and ultimately it becomes negative (negative signal indicates the increase of the probe beam intensity (converging lens) ) .
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0.8
L 0.8 t I ClS
Fig. 4. (A) Time profiles of the TL signals in water at various temperatures (a) 7.9”C, (b) 4.O”C, (c) 1.7”C. (d) -3.5”C. (B) Best fitted calculated signals with a superposition of the Temp.L and Dens.L contributions at the same temperatures as in (A).
Similar signals and similar temperature dependence are observed after the photoexcitation of DAP and FeCl, in aqueous solution. Without these solutes, there is no detectable signal under the same experimental conditions. Therefore, we believe that the observed non-Dens.L component should not come from a refrac-
799
M. Terazima / Chemical Physics 189 (1994) 793-804
tive index variation due to photochemical products or unknown me&stable states, because it is very unlikely that the three solutes with very different chemical properties give a very similar non-thermal signal by photochemical reactions or photophysical processes. Rather is it reasonable to consider that the non-Dens.L signal is due to a (non-density) thermal effect, i.e. temperature lens component. Another evidence against the assignment of this signal to the population lens of a photochemical species due to a photochemical reaction or due to a metastable state comes from the decay rate of the signal. The signal decays to the baseline with the time constant of the thermal diffusion in water. If the signal comes from the refractive index lens by a chemical species, the signal should decay with the time constant of the mass diffusion, which is much smaller than that of the thermal diffusion. Since the signals from these three compounds are the same within the experimental error, we will discuss the signals obtained by using nitrobenzene hereafter. These temperature dependence can be well reproduced by the superposition of Temp.L and Dens.L as shown in Fig. 4B. In this calculation, the calculated p, and T, from Eqs. (5) and (6) with the reported thermodynamical properties of water [32-341 are convoluted with the instrumental response function and added together with an appropriate weighting factor. Only the adjustable parameters for the fitting are a normalization factor of the signal intensity, the excitation beam radius and the ratio of Dens.L to Temp.L (p,/T, ). The best fitted ratio at the various temperatures are shown in Fig. 5. One of the error sources in the determination of pi/T, comes from the noise in the TL signal, because of the weak signal intensity in water. The range of error of this type can be estimated from the fitting procedure ( f 0.2). A systematic error may come from the factors which are neglected in the theoretical equations. For example, acoustic dumping of py has been neglected. The determined p, /T, decreases with decreasing temperature and becomes zero at 3.8”C. In order to obtain more quantitative information, the signal intensity is measured at each temperature. Since the acoustic wave, which is sensitive to the various factors such as speed of sound and acoustic damping, contributes to the peak intensity, the maximum intensity is not a good indicator for the signal intensity. Hence the signal intensity is defined by the intensity at
12/
Fig. 5. Temperature dependence of p, /T, determined from the TL signal (circles) and from the TG signal (squares) of nitrobenzene
aqueoussolution. the plateau region here. In this region, the signal due to the acoustic mode (py ) can be neglected in the TL signal and the intensity is given by ptf and T,. The values are plotted in Fig. 6. The most accessible quantity in a literature is (dnldT), and it is related to the quantities we are interested in here by (13) Experimentally the temperature dependence found to be expressed as [ 34,351
n*- 1 n*+l
= A’pt’ exp( -CT)
,
of n is
(14)
where A’, B’, and C’ are constants which are given in Ref. [ 341. We calculate n at various temperatures from this expression and obtain (dn/dT), by differentiating n with respect to T. The calculated (dn/dT), is plotted in Fig. 6 with an appropriate normalization factor. The agreement between the determined value in this work and the literature values is quite good. The plot intercepts the Z,, = 0 line at - 0.2”C. It is known that the refractive index of pure water goes through the maximum value at - 0.01 “C [ 231, and at this temperature dn/dT should vanish. The slight difference between the literature and observed values may be due to the solute effect ‘on the thermodynamical properties of water and/or a temperature gradient between the temperature-monitored region and the
. j
’
*-
10
*
J 20
T/K
Fig. fi Tem~e~~tn~ dependences af the total TL signal intensity (circles) and the ~~teosit~esofthe D6ns.L {squares) and the Temp.L (triangles) signals after the phot~xcit~tion of nitrobenzene in water. Reported (dn/dT), and (+‘U),/C, [32-341 are also shown by the solid line and the broken line, respectively. They are, respectively, jollied to the total TL signd j~tensity and the Dens.L signal intensity at 11“C, Thesequ~t~t~es below 0°C are extm@ated by
rtsing a 6X&e~~~~U~~~ tit ffom0°C to 20°C. laser-irradiated region. This signal-vanishing temperature is the one that Song and Endicott have used for neglecting the thermal effect in the TL signal [ 241, and Miller in the TC ex~~rn~~ts [26] *Ttney have measured the TL or 733 sign& at this temperature and tried to observe the probe beam absorbance or molecular volume change effect in the signal. Note however, that, the TL signal vanishes because the effects of TI and of pt” are ~an~elled at this temFe.ra~re. When the signal is observed with a fast time response detector, the Temp.L and the signal due to p:” are still apparent even at this temperature as shown in Fig. 4. From the signal intensity and the determined quantity of pI / Tt, the tem~rat~e d~~e~den~e of the Dens.L and Ternary ~~rn~~~e~~~are ~~~~~ated and they are ptotted in Fig. 6. After passing over the pressure wave from the detection region, the temperature and density change in the region are given by
pt = (apA3T),HI
C, .
Therefore the t~m~ratur~ d~p~ndenc~s of the Dens.L (moreexactly, pdi” component in Dens.L) and Temp.L
components correspond to those of (&/ap),( ap/ ~~~~~C~ and (~~~~~~~~C~, res~t~v~ly. The intercept e fact ns,t ~~teusity reflects at 3,8”@ to the zero that the density of water takes a maxima value at 4°C. In Fig. 6, (&z~B’),/ C, is plotted with an appropriate notarization factor, As is seen from this figure, the tern~~atu~e dependence of Dens.L s&al intensity fits very well with that of (~~~~~~~C~. Since C, is rather insensitive to the temperate, the variation of Dens.L is controlled by the factor (&z/U), Eq_ ( 13) suggest that we might be able to calcculate (~~~~~~, which is usuatiy difficult to be measured, from this equation with the more easily accessible q~~t~t~es (d~/d~~ and (~~~~~~ if (~~~~~~= is known. Sorn~t~rnes~ this quantity ~~~~~ is discussed on the basis of the Lor~n~z-Lorenz relation [ 35 ] , an
(n”$_2)(n2-
ap’
6prz
1) *
(15)
However, the tern~~at~re d~~~d~~~e of ~~~~~ allot be ~r~~~~d fram this relation, because this equation is based on the assumption that the molecular polarizability is a constant and this assumption is not valid for water [ 20,35,36], Therefore, as pointed out: in the previous paper [ 22]+ me~sur~rnen~ uf the time resolved TL (TG) signal wiff give a good way to determine the (&E/X), value. Fig. 6 shows that the quantity (an/ an, gradually increases with decreasing temperature,
The time deve~~prn~n~ of the TG signal after the phatoexcitatian of nitrobenzene in water is depicted in Fig. 7 and compared with that in benzene. Again, the excitation laser power is stronger in the case of water. Under this ex~rirn~n~~ ~ondi~o~ fa small glossing angle) J the excitation laser pulse width is shorter than the acoustic transit time between the fringe, so that acoustic oscillation is observed in bath signals. Since the fringe spacing can be much smaller than the beam radius in the TL experiments the signal takes its maxiat an earlier time thrtn the TL signal. This is the main reason why the TG myths has been known to have a fast time resolution among the photothermal t~~~~ques [ 12-181. comparing the signals in benzene and water, one finds that the signal in water rises slightly faster, the
M. Terazimu / Chemical Physics 189 (1994) 793-804
period of oscillation is shorter, and the amplitude of the oscillation is smaller. The short oscillation period in water reflects the faster speed of sound compared with that in benzene. The faster rise and smaller amplitude become more obvious at lower temperature (Fig. 8A). At 4.O”C, the acoustic oscillation almost disappears and the signal consists only of a step function with a rise time determined by the time response of our instrument. Below this temperature, acoustic grating appears again as a dip on the step function signal. Further below that temperature, the acoustic oscillation appears again. The same temperature dependence is observed by using a DAP or FeC& aqueous sample. Following the same idea as in the Temp.L case, the non-density grating component is attributed to the temperature grating. We tried to reproduce the observed temperature dependence of the TG signals by the superposition of the Temp.G and Dens.G signals. The basic equations for that calculation are Eqs. ( lo)-( 12). However, we find that the acoustic damping, which is neglected in the equation, cannot be neglected in this time range for the fitting. This damping effect is explicitly taken into consideration phenomenologically and Eq. ( 10) is modified to p, =C[ 1 -cos(uqt)
exp( -k,,t)]
,
801
(b)
./-
(16)
1
where kac is the rate constant of the damping. The fitting parameters, u and k,,, at various temperatures will give us important information on the solution structure [ 37, 381. However, we will not discuss the acoustic para-
t I ns Fig. 8. (A) Time profile of the observed TG signals of nitrobenzene in water at various temperatures (a) 5.2”C, (b) 4.O”C, (c) 3.O”C, (d) - 2.1 “C with a crossing angle 0.19” of the excitation beams. (B) Best fitted calculated signals with a superposition of the Temp.G and Dens.G contributions.
Fig. 7. Observed time resolved TG signals of nitrobenzene in water (solid line) and in benzene (dotted line) with a crossing angle 0.27” of the excitation beams.
meters further in this paper to focus our attention on the Temp.G signal. The best fitted time profiles of the TG signals are shown in Fig. 8B. The agreement of the observed and calculated ones is quite satisfactory. The determined p1 / TI at various temperatures are plotted in Fig. 5. The ratio agrees fairly with those determined from the TL
802
M. Terazima / Chemical Physics 189 (1994) 793404
experiment. The difference at the low temperature region might be due to the acoustic dumping, which is neglected in the TL case. Similar types of discussions as those in the previous section can be made in this TG case as well. Since the TG method is the background-free detection, the noise in the signal is much smaller than that in the TL signal and it is expected that the pllT, value could be more precise than that determined from the TL signals. However, the time resolution of this method is sufficiently high compared with the laser pulse width even under this small crossing angle, the fast development of the Temp.G signal is hidden in the strong Dens.G signal at higher temperatures, where the relative contribution of Temp.G is smaller. Therefore the pl/Tl value determined from the TG signal has a larger uncertainty than that from the TL signal especially at high temperatures (not shown in Fig. 5). If one uses a shorter excitation laser pulse, the accuracy of the pr and T, will be much improved and the discussion on the thermodynamical properties of water can be more precise. 4.3 Fast response of the Temp.L and Temp.G Even though the photothermal methods are powerful and widely applicable tools as mentioned in the Introduction, some limitations have prohibited applications to study ultrafast phenomena. One of the limitations of the photothermal techniques has been the relatively slow time resolution. This limitation comes from the fact that the effect of the density change to the refractive index variation is so large that the rise time of the signal is determined by the acoustic transit time. For example, the acoustic oscillation in the TG signal masks the fast time response. These acoustic effects will mask not only the fast heating effect but also any signals such as the transient absorption, population lens, or population grating. However, by applying the Temp.L and Temp.G signals observed clearly in this work, the photothermal signals can be made free from the acoustic perturbation and the time response is solely determined by the instrumental response function and the heat release processes. Here we just shortly mention an observation of fast response in the Temp.L by taking quinoxaline as an example. More detailed investigations of the excited state dynamics will be published elsewhere.
0
0.2
0.4
0.6
ti p Fig. 9. Rise profile of the Temp.L slgnal after the photoexcitation quinoxaline in water at 4.O”C.
of
After the photoexcitation of quinoxaline, one of the prototypes of nitrogen heteroaromatic compounds, to the excited singlet state, the T, state is created efficiently with a quantum yield of nearly unity [ 3,391. In SDS micelles, the hydrogen abstraction reaction takes place from the T, state and that state is expected to be short lived [40]. Fig. 9 shows the time profile of the Temp.L after the photoexcitation of quinoxaline in a SDS aqueous solution at 4.O”C. The signal shows a fast rise limited by the instrumental response time followed by a fast decay with a time constant - 50 ns. In the longer time scale, the signal decays to the baseline by the thermal diffusion, which is not shown here. If the signal originates only from the thermal effect due to the deactivation of the excited state, we expect a relatively slow rise instead of the fast decay. Therefore the signal should be explained by the Temp.L and the fast decay component, which is probably the transient absorption or the population lens signal by the TI state. This observation of the fast time development in the Temp.L signal will open a possibility to study fast dynamics by the TL method. Of course, tens of nanosecond time resolution can be achieved by using the TG method with a larger crossing angle. However, if one wants to investigate a faster dynamics, a shorter excitation laser pulse should be used and then the acoustic oscillation will appear to mask such dynamics as long as the Dens.G is used [ 17,18,25]. This limitation can be removed by using water as a medium and observing the Temp.G or Temp.L signals. The limitation in utilizing these signals, except the inherent limitation in the choice of solvent, is the low
sensitivity. It is known that the (dnlc2p) ,-value of water is about an order of magnitude smaller than those of other organic solvents [ 191 and this is the reason why water has been considered to be the worst medium for the photothermal techniques. On the other hand, the obtained (Wa7’), value of water is not much smaller than those of other solvents [ 19 1. Therefore the relativeIy large contribution of the temperature effect in the observed “TL signal” is due to the small farz/ 3~)~; in other words, the c~~tribut~o~ of TempL or Temp.G is manifest in water because of the small Dens.L or Dens.G signal intensity. This disadvantage should be overcome by increasing the excitation laser power. However, then we should be careful about the ~on~ibutio~s of multi~h~to~ abso~tio~ processes or the higher order interaction between the transient states, such as the excited state-excited state annihilation. Nevertheless, a method utilizing these signals will provide powerful tools for studying the fast dynamics of the energy transfer processes, especially heat releasing or vibrational rel~atio~ processes.
5. Summary Con~i~ut~~~s of the tern~~~t~re lens (~emp.L~ and temperature grating (Temp-G) signals in aqueous solution are reported. Depending on whether the measurements are performed at temperatures lower or higher than 3.8”C, the Dens.L or Dens.G signals have either ative ~on~ib~t~o~s on the Tern~.~ or At 3.8”C, pure Temp.L and Temp.G ese relative con~ibutions are mainly controlled by the small and temperature dependent dpldT of water. Since the rise times of these signals are governed only by the instrumental response time and the rate of the heat released from the excited state, these signals permit precise investigations of the fast dynamics of the photoexcited states in solution or electronic (vibrational)-translational energy transfer processes.
References i 11H.L. Fong and R.L. Swofford* in: Ultra sensitive
laser s~c~os~opy, ed. D.S. Kliger (Academic Press, New York, 1983). 121 SE. Braslavsky and GE. Heibel, Chem. Rev. 92 ( 1992) 1381. [3] M. Terazima and T. Azumi, Chem. Phys. Letters 141 (1987) 237; 145 (1988) 286; 153 (1988) 27. j4] M. Terazima and N. Nirota, J. Phys. Chem. 95 ( 1991) 9080. IS] M. Terazima, T. Azumi and N. Hirota. J. Photocfiem* pbotobio~. A 65 [ 1992) 21. {6] AJ. Twarowski and D.S. Kliger, Chem. Phys. 20 (1977) 253. [ 71 G. Rossbroich, N.A. Garciaand S.E. Braslavsky, I. Photochem. 31 (1985) 37. J8 1 R.W.Redmond and SE. Braslavsky, Chem. Phys. Letters 148 Il988) 523. [9] B.M. Toselli, T.L, Waling and JR Barker, J. Cbem. Phys. 92 (1990) 4793. [ 101S.J.Jacobs, Chem. Phys. 132 (1989) 71. [ 111R.T.Bailey, F.R. Cruickshank, R. Guthrie, D. Rugh and I.J.M. Weir, Mol. Phys. 48 (1983) 81. [ 121MB. Zimmt, Chem. Phys. Letters 160 ( 1989) 564; J. Morais, J. Ma and MB, Bmmt, J. Phys. Chem. 95 ( 1991) 2885. [I31 X,~.ZhuandJ.M. Harris,Chem. Phys. 157 (1991) 409;Chem. Phys.Letters 186 (1991) 183. [ 141 M. Terazima and N. Hirota, J. Chem. Phys, 95 ( 1991) 6490; Chem. Phys. Letters 189 (1992) 560; J. Appl. Phys. 73 ( 1993) 7672. I:151L. Gove-Jah~, J. Kasinski and R.J.D. Miller, Chem, Phys. Letters 125 (1986) 500. 1161 H.J. Eichler, D. Gunter and D.W. Fohl, in: Laser induced dynamic gratings (Springer, New York, 1983). 1171 K.A. Nelson and M.D. Fayer, J. Chem. Phys. 72 ( 1980) 5202. [ 181AR. Duggal and K.A. Nelson, J. Chem. Phys. 94 ( 1991) 7677. [ 191 R.C. Desai, M.D. Levenson and J.A. Barker, Phys. Rev. 27A (1983) 1968. j20J f. Scarlet, Phys. Rev. 6 11972) 2281. [Zi] ‘I’. Kawasaki, A. &rata and T. Sawada, Anal. Sci. 7 Suppl. (1991) 653. [ 221 M. Terazima and N. Hirota, J. Chem. Phys. 100 ( 1994) 2481, [ 231 M. Frank0 and CD. Trm, Anal. Chem. 61 ( 1989) 1660. [ 241 X. Song and J.F. Endicott, Chem. Phys. Letters 204 ( 2993) 400. 1251 L. Genberg, Q. Baa, S. Cracewski and R.J.D. Miller, Chem. Phys. 131 (1989) 81. [26] R.J.D. Miller, L. Genberg, L. Richard and S,M. Gracewski, in: Photoacoustic and photothermal phenomena 11, eds. J.C. Murphy, J.W.M. Spicer, L.C. Aamodt and B.S.H. Royce (Springer, Berlin, 1990); R.J,D. Miller, Annu. Rev. Phys. Chem. 42 ( 1991) 581; L, Genberg, L. Richard, G. MeLendon and R.J.D. Miller, Science 251 (1991) 1051.
[ 271 M. Terazima, S. Yamauchi and N. Hirota, J. Phys. Chem. 89 The author is indebted to Professor N. Wirota for valuable discussions and encouragement.
(1985) 1220; M. Terazima, Chem. Phys. Letters 140 ( 1987) 6.
804
M. Terazima / Chemical Physics 189 (1994) 793-804
1281 C.J. Seliskar, O.S. Khahl and S.P. McGlynn, in: Excited state, ed. E.C. Lim (Academic Press, New York, 1974). [29] K. Kalyanasundaram, in: Photochemistry in microheterogeneous systems (Academic Press, London, 1987). [30] S.R.J. Brueck, H. Kildal and L.J. Belanger, Opt. Commun. 34 (1980) 199. [31] J.-M. Heritier, Opt. Commun. 44 (1983) 267. [32] G.S. Kell, in: Water, Vol. 1, ed. F. Franks (Plenum Press, New York, 1972). [33] C.M. Davis Jr. and J. Jarzynski, in: Water, Vol. 1, ed. F. Franks (Plenum Press, New York, 1972).
1341D. Eisenberg
and W. Kauzmann, in: The structure properties of water (Oxford Univ. Press, Oxford, 1969).
and
[351 H.J. Eisenberg, J. Chem. Phys. 43 (1965) 3887. 1361I.Thormahlen, J. Straub and U. Grigull, J. Phys. Chem. Ref. Data 14 (1933) 933. [371 A.B. Bhatia, Ultrasonicabsorption
(Dover, New York, 1967).
[381 L. Hall, Phys. Rev. 73 (1948) 775. [Xl 1 D.W. Boldridge, G.W. Scott and T.A. Spiglanin, J. Phys. Chem. 86 (1988)
1976.
-401 M. Terazima and N. Hirota, to be published.