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Submitted on 1 Jan 1983
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THEORETICAL ASPECTS OF PHOTOACOUSTIC SIGNAL DETECTION WITH A DIRECT COUPLING
CELL FOR LIQUID
T. Kitamori, M. Fujii, T. Sawada, Y. Gohshi
To cite this version:
T. Kitamori, M. Fujii, T. Sawada, Y. Gohshi. THEORETICAL ASPECTS OF PHOTOACOUSTIC
SIGNAL DETECTION WITH A DIRECT COUPLING CELL FOR LIQUID. Journal de Physique
Colloques, 1983, 44 (C6), pp.C6-209-C6-214. �10.1051/jphyscol:1983632�. �jpa-00223191�
JOURNAL DE PHYSIQUE
Colloque C6, supplement au nOIO, Tome 44, octobre 1983 page C6- 209
THEORETICAL ASPECTS OF PHOTOACOUSTIC SIGNAL DETECTION WITH A DIRECT COUPLING CELL FOR LIQUID
T. Kitamori, M. Fujii, T. ~ a w a d a * and Y. ~ o h s h i *
Energy Research Laboratory, H i t a c h i L t d . , 1168 Moriym-cho, Hitcrchi, fiaraki 316, Japan
'Depmtment of I n d u s t r i a l Chemistry, University of Tokyo, Hongoh, Bunkyo-ku, Tokyo 123, Japan
R6sum6 - On 6tudie la dgpendance en frcquence et en fonction des dimensions g6om6triques de la cellule des signaux photoacoustiques. Le mod6le thgorique diffPre de celui de la theorie de Rosencwaig et Gersho mais est en bon accord avec les expgriences.
Abstract - Dependence of photoacoustic signals on light chopping frequency and on cell geometry was analyzed. The results differed from those for RG theory, but agreed well with experiments.
I. INTRODUCTION
Recently, the direct coupling method has been developed for liquid PA detection, in which cylindrical piezoelectric transducers (PZT) are used as shown in Fig.1. In particular, this method has been shown to be very effective in liquid absorbance detectors, for example the detection limit absorbance reaches 1c5 - 1 F 6 /1/.
However, an analytical method describing properties of the PA signals generated in the direct couplig cell is not readily available.
This report analyzes the properties of PA signals generated in the direct coupling cell, and clarifies differences between this theory and the RG theory for gas-microphone detection /2/.
Experiments are carried out to verify the analytical solution of this model. Finally, a highly sensitive cell for direct coupling is proposed based on this analysis.
11. THEORETICAL
In the direct coupling cell shown in Fig.1, the liquid occupies
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983632
JOURNAL DE PHYSIQUE
the region r g a , while the PZT cylindr occupies a<r<b. The laser beam passing through the region 0 < r < ro has a Gaussian
distribution, where r,, is the e2 point of the peak intensity of the laser beam, and is modulated in a series of pulses.
In tis model, the thermal
diffusion length in liquid Laser beam ( radius : r,) (lo0- 10 rm) is assumed to 1
be negligibly shorter than the radius of the laser beam ( 1 1 0 ~ ) . Under this assumption, the heat generated by the incident laser beam does not accompany thermal diffu-
/ Liquid sample
\
PZT detector sion, and the thermal
energy is instantaneously
converted into mechanical Fig.1 PA cell based on the direct energy of the thermoelestic coupling method.
wave. . Theref ore the
acoustic source is the
thermoelastic vibration in the region where the laser beam passes.
Hence the thermoelastic wave P(r,t) is expressed by the following equation / 3 / ,
where V is the sound velocity in the liquid; / 3 , the coefficient of isothermal expansion; Cp, the specific h e a t ; 8 , the peak intensity of the laser beam; Y , a coefficient of thermal lens effect; and [XI, a Gaussian notation which represents a maximum integer smaller than
X.
Equation (1) was solved with a Fourier transformation and Green's function. The piezoelectric signal is proportional to the cell radius and the intensity of the pressure wave < P >. Therefore
the PA signal S is expressed as follows,
e t i 1
= 681 a R(a, r,)-Am(a, r,, f )
m = I f
where, IO is the modified Bessel function of 0th order and KO the modified Hankel function of 0th order.
The physical meanings of each term in Eq. (2) are given as :
E is the energy convertion ratio from incident light energy to electrical energy of PA signal from PZT; (l/f )Am(a, ro , f) is the frequency characteristics of the PA signal; and aR(a,ro ) is the attenuation of the PA signal when the acoustic wave is being propagated in the cell.
111. EXPERIMENTAL
T o verify the analytical solution of Eq.(2), frequency characteristics (l/f)Am(a, ro , f) and the dependence of the PA signal intensity on cell radius which corresponds to the aR(a,ro) term was measured. The parameters used are listed in Table 1.
The measured frequency characteristics are shown in Fig.2, along with the calculated values of (l/f)Am(a,ro ,f) . The other hand, the measured dependence of PA signal intensity on cell radius is shown in Fig.3, along with the corresponding calculated value of aR(a,ro).
IV. DISCUSSION
In both Figs.2 and 3, the theoretical values agreed with the
experimental results. Peaks PI to P5 which appeared in Fig.2 were
electrical and structual resonances of the PZT and the entire cell
body. These were proved by the impedance measurements of PZT and
calculation of natural frequency of the cell body. The peak P
closely corresponded to the location of the theoretical peak and was
C6-212 JOURNAL DE PHYSIQUE
the resonance of the PA signal in the cell.
In Figure 3, the experimental value at a=3.5 mm was smaller than the theoretical curve. At this radius, the piezoelectric signal was not proportional to the radius, since the thickness of the PZT detector (1.0 mm) could not be ignored with respect to the cell radius /4/.
Table 1. Parameters for the calculated solutions and experiments.
Parameters Value
Cell radius Laser beam radius
Sound wave velocity in water at 25 C
(For calculation)
Coefficient of thermal lens effect
(For experiments)
Incident laser beam power Wave length of incident
laser beam Liquid sample
Concentration of the sample Cell length
PZT length
50 mW 488 nm
(Ar-Laser) Sunset vellow
lfor the measurement of radius dependence
Generally wave generation, propagation and attenuation in a closed cell strongly depend on the profile of the wave source.
Therefore, when analysing PA signals, it is necessary to describe the acoustic source profile correctly. In RG theory for a gas- microphone cell, thermal diffusion from the light illuminated solid surface causes tmperature variation within a thin layer of the gas at the gas-solid boundary, and the acoustic source term results from the piston-like behavior of this layer. However, in the direct coupling cell, heat is generated in the region through which the laser beam passes and thermal diffusion length is negligibly shorter than the radius of the laser beam. Therefore, the acoustic source term is limited to the region where the laser beam passes.
Finally, a maximum sensitive point appeared in the calculated
curve in Fig.3. The direct coupling cell can be designed to have a
high sensitivity by selecting the cell radius corresponding to this
point. This design condition can be easily obtained from Eq. ( 3 ) , as f 0llows;
and the thickness of the PZT should be sufficiently smaller than the cell radius, i.e. less than 1/4 of the radius.
V. CONCLUSION
PA signals generated in the direct coupling cell for liquid were analyzed.
The theoretical results were verified through measurements Of PA signal dependence on the cell radius and its frequency characteristics. The mechanism of PA signal generation in direct coup1 ing cell was clarified, showing that, the main contributing acoustic source term was the light passing and absorbed region. On the other hand, this was the thermal diffusion region in the RG theory for the gas- microphone cell.
A design method for the direct coupling cell for liquid was presented, based on the theory.
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