PHOTOACOUSTIC DETECTION OF KINETIC PROCESSES BY SINGLE PULSE AND RESONANCE TECHNIQUES

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PHOTOACOUSTIC DETECTION OF KINETIC PROCESSES BY SINGLE PULSE AND RESONANCE

TECHNIQUES

P. Hess, R. Kadibelban, A. Karbach, J. Röper

To cite this version:

P. Hess, R. Kadibelban, A. Karbach, J. Röper. PHOTOACOUSTIC DETECTION OF KINETIC

PROCESSES BY SINGLE PULSE AND RESONANCE TECHNIQUES. Journal de Physique Collo-

ques, 1983, 44 (C6), pp.C6-419-C6-424. �10.1051/jphyscol:1983669�. �jpa-00223228�

JOURNAL

DE

PHYSIQUE

Colloque C6, suppl6rnent a u nO1O, Tome 44, octobre 1983 page C6- 419

PHOTOACOUSTIC DETECTION OF KINETIC PROCESSES BY S I N G L E PULSE AND RESONANCE T E C H N I Q U E S

P. Hess, R . Kadibelban, A . Karbach and J. Roper

Physikaliseh-Chemisches Institut der Universitdt Heidelberg, Im Neuenheimer Feld 253, D-6900 Heidelberg 1, F.R. G.

Rksumi! - Les principes des experiences basBes s u r un seul laser pulse e t l a m6thode de resonance sont dCcrits. La dBtection photoacoustique de mklanges gazeux et de rkactions chimiques en fonction du temps est discutke. De plus, on a BtudiB des processus d'gchanges collisionels dlBnergie.

Abstract - The principles of the single laser pulse technique and of the photoacoustic resonance method are outlined. The detection of kinetic processes such a s mixing of gases, energy transfer processes, and chemical reactions are described.

Introduction

To generate an acoustic signal in a gas, the molecules can be excited with a single short laser pulse or a train of pulses generated, for example, by modulating a cw laser beam. In a single pulse experiment a high amplitude of the acoustic signal is achieved and problems arising from interference and reflection of acoustic waves can be avoided by time resolved analysis of the acoustic signal. For the kinetic study the first undisturbed part of the acoustic signal i s used. The principles of photoacoustic single pulse experiments are outlined in Fig. 1.

signal recording

L_rJ

cell

experimental setup

- ^time

photoacoustic signal

Fig. 1 - Schematic diagram of an experimental setup using a pulsed laser, a non- resonant photoacoustic cell, a detector to monitor fluctuations of the laser output, and electronics for time resolved detection of t h e acoustic signal. The first pulse of the signal i s analyzed by integration or determination of the amplitude.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983669

C6-420 JOURNAL DE PHYSIQUE

For modulated energy input the maximum amplitude achieved for the signal at steady state may be smaller than in the single pulse experiment. The reason for this behavior i s destructive interference of acoustic waves from previous cycles with waves of the following cycle. A considerable amplification of the acoustic signal can be obtained, however, in a resonance experiment. In this case, the acoustic cell i s carefully designed to minimize dissipation of acoustic energy and the cw laser i s modulated with one of the resonance frequencies of the acoustic cavity. Such

a

system works as an acoustic amplifier, where the energy of many cycles is accumu- lated in a standing acoustic wave. The number of cycles needed to reach steady state depends on the losses of the resonator. At steady state, the energy gained by absorption of laser photons is equal to the energy lost by various dissipation processes. The information obtained from such a resonance experiment i s the resonance frequency and the halfwidth of the resonance curve. The resonance curve i s detected by linear variation of the modulation frequency in the frequency region of the selected cavity mode. The principles of photoacoustic resonance experiments are shown in Fig. 2

signal recording

Lir'

modulation

experimental setup

resonance

L

frequency

I

band - width

- ^frequency

photoacoustic signal

Fig. 2 - Schematic diagram of an experimental setup consisting of a cw laser, a modulation device, an acoustic resonator, and a recording system for the modulation frequency and the acoustic signal. On the right side the acoustic signal versus modulation frequency in the region of an acoustic mode is shown.

Investigation of kinetic processes by resonance experiments

The resonance frequencies of the acoustic normal modes in a spherical or cvlindrical cavity are proportional to the sound velocity (1). Any change in the composition of the gas leading to an alteration of the sound velocity causes a shift in the reso- nance frequencies. Therefore, concentration changes can be monitored via the reso- nance frequency of an acoustic mode. The time resolution of such a kinetic experi- ment i s determined by the time needed to reach steady state in the resonator and to measure the resonance frequency, for example, by recording the resonance curve.

This method can be used to monitor slow reaction processes and mixing processes (2). An example for the photoacoustic detection of mixing processes is shown in

Fig. 3 .

.\ ^{CHI, - N2} -

⁰

\ 0,

O\ 0

- b,o

^"0

' 0

condensation

- 1 :

'!.cw.. - - - - - - - - - -4

^0-00000-

^{- -}

0

I I I

10 2 0 30

time [hl

Fig. 3 - Detection of mixing between CH4 and

N 2

by measuring the frequency shift of the first radial mode in a cylindrical cavity as a function of time: *fast mixing by adding

200

Torr

N 2

to

200

Torr CH4 from a high pressure bottle; 0 slow diffu- sion controlled mixing of CH4 and

N2

originally separated in two containers (one i s the resonator!) of equal volume filled with equal pressure.

The resonance method also allows the investigation of very fast kinetic processes such as vibrational relaxation (31, (4). It i s known from ultrasonics that in the region of vibrational or rotational relaxation a dispersion of the sound velocity i s found as a function of pressure. This effect produces a dispersion of the resonance frequencies. Therefore, the corresponding relaxation time can also be obtained from the inflexion point of the frequency dispersion curve. The advantage of the photo- acoustic method in comparison with the ultrasonic method i s that the resonance frequency can

be

measured in a very large pressure range with high accuracy. To obtain the pure frequency dispersion curve caused by molecular relaxation, not only the real gas corrections as in ultrasonics, but also dissipation processes occuring in the acoustic cavity have to be taken into account. The theory of these loss mechan- isms is well developed. The main contributions come from the viscous and thermal dissipation inside the boundary layers at the internal surfaces and the free space viscous and thermal losses. The influence of both surface losses and volumetric losses increases rapidly with decreasing pressure.

To study the contributions of the different effects on the pressure dependence of

the resonance frequency and halfwidth, resonance experiments have been performed

for CH4 and CH3F. In the case of CH4 the first radial mode in a cylindrical cavity

was excited by the modulated 3,39

Nm

radiation of a He-Ne laser. Resonance

curves were recorded between

3

Torr and

760

Torr. Fig. 4 shows the dependence

of the resonance frequency on pressure found in these experiments.

JOURNAL DE PHYSIQUE

Fig. 4

-

Pressure dependence of the frequency of the first radial mode of CH4 in a cylindrical cavity. The points represent the measured frequencies. The decrease of the resonance frequency caused by surface losses especially at low pressures and by intermolecular forces at high pressures i s indicated. The resulting upper curve shows the pure frequency dispersion effect due to vibrational relaxation.

For CH3F the 3.39

um

line was used for vibrational excitation and measurements were performed in the pressure range 7-500 Torr. In the investigated pressure range, vibrational relaxation occurs in both molecules. The influence of dissipation effects has been calculated for CH4 using literature values for the viscosity and thermal conductivity. For CH3F no data were available and, therefore, the transport coefficients were estimated using a Stockhausen potential derived from measurements of the second virial coefficient. The influence of the surface effect i s much larger than the contribution of the volume effect. In the region of vibration dispersion these corrections are larger for CH4 than for CH3F. This means that possible errors in the estimated transport coefficients have a small influence on the relaxation time determined for CH3F. The real gas correction, however, is much larger for the polar CH3F molecule than for CH4. The corresponding second virial coefficients were taken from the literature. The good agreement of the calculated pressure dependence of the resonance frequency and halfwidth with the experi- mental data points indicates that the contribution of additional losses such a s wave scattering at surface obstructions (gas inlet, microphone, windows etc.) is below a few percent in the whole pressure range studied.

These results show that precise relaxation times can be obtained by the photo- acoustic resonance technique. The resonator must be carefully optimized to minimize all dissipation processes which cannot be taken into account theoretically. The unique feature of the photoacoustic method i s additional information on transport coefficients in the low pressure region. Such low pressure measurements can be

performed if a laser is available for efficient excitation of cavity modes. For many molecules data on relaxation processes can be found in the literature; however, transport coefficients are often not available. In these cases transport and virial coefficients may be determined from the deviations at low and high pressures.

Single pulse analysis of kinetic processes

In single pulse experiments only the first interference free part of the acoustic signal detected by the microphone after pulsed laser excitation is considered. If the signal strength of this first acoustic pulse is proportional to the concentration of the absorbing species, concentration changes can be monitored. With a suitable laser, isotope specific excitation and detection of components in the gas mixture is possible as a function of time.

In the case of a chemical reaction, the fall of reactant concentration and the rise of product concentration can be monitored. The time resolution which can be achieved with the single pulse method is determined by the time constant of the signal detection system or the repetition rate of the laser.

As an example, results obtained for H-D exchange in the system H2S-D2S are dis- cussed. Details of the experimental setup are reported elsewhere (5). The reactant D2S and the product HDS can be excited separately with a line-tunable TEA C02 laser. In a stainless steel cell equilibrium i s reached after about 40 minutes. Thus, several thousand measurements can be performed during the reaction time. In Fig.

5 examples are presented for the photoacoustic detection of the fall of D?S con-

-

centration and the rise of HDS concentration.

10 20 3 0 10 20 30 4 0

t i m e [minl time [minl

H-D EXCHANGE REACTION

:

H2S

+

D2S = ^{2 HDS}

Fig. 5

-

Variation of the photoacoustic signal versus time after fast mixing of H2S and D2S and excitation of D2S at 10,74

u m

(left side) and excitation of HDS at 9,695

u m

(right side) with a pulsed C02 laser. The repetition rate was one pulse every two seconds.

0zS HDS

I

C6-424 JOURNAL DE PHYSIQUE

The order of the H-D exchange reaction was determined from the reaction rate at the beginning of the reaction process. From log-log plots of the rate of HDS pro- duction versus the partial pressure varied in the experiment, a reaction order of about one half i s found for each reactant, H2S as well as D2S. Within experimental e r r o r , the first order rate coefficient extracted from the first part of the D3S fall

-

curve agrees with that obtained from the first part of the HDS-rise curve. At a later stage of the reaction the influence of the backward reaction increases and causes deviations from the first order rate law. A variation of the cell material shows that H-D exchange occurs on the cell walls and that a glass surface is about a factor of 20 more effective than a stainless steel surface. The strong temperature dependence of the reaction rate indicates that not diffusion, but the heterogeneous reaction process on the surface i s the rate determining step. Thus, a heterogeneous reaction i s monitored via photoacoustic analysis of gas phase concentration.

The single pulse photoacoustic technique allows an accurate and fast detection of concentration changes in the gas phase. Isotope selective vibrational excitation allows the independent observation of reactant and product concentration without disturbing the reaction process itself. An influence of the laser excitation on the surface reaction could only be expected for vibrational excitation of molecules very near the surface. For a larger distance between laser beam and surface, the method provides a selective, continuous, and non-disturbing detection of heterogeneous kinetic phenomena such a s catalysis. In catalysis several processes are taking place continuously: reactant molecules are absorbed on the surface, rearrange by breaking old and forming new bonds, and desorb from the surface.

( I ) P. Hess, Topics in Current Chemistry, Vol. 111 (1983) 1-32 (2) J. Roper, P. Hess, Appl. Phys. Lett. 39 (1981) 946

(3)

K.

Frank, P. Hess, Chem. Phys. ~ e t t . 6 8 (1979) 540

(4) K . Frank, P. Hess, Ber. Bunsenges. ~ h y s . Chem.

84

(1980) 724 (5) R. Kadibelban, P. Hess, Appl. Optics - 2 1 (1982) 61