GAS ANALYZERS FOR INDUSTRY AND MEDICINE

Photo Acoustic Spectroscopy

a) Basic principles of photoacoustics

In the photoacoustic effect light hitting a molecule is converted into a soundwave carrying information about the kind and concentration of molecules in the sample.

The light source here is a diode laser. Depending on the sample under investigation a corresponding wavelength (colour) is selected which for the majority of applications lies in the infrared region. The laser light will then be directed into the cell filled with the sample which can be a gas or a liquid. The molecules when irradiated by light of this particular wavelength will then emit heat which in turn will lead to local pressure changes. These pressure differences will under normal conditions immediately disappear again.

If, however, the laser light is not applied with constant intensity but as a wave of changing intensity, then the result will be a pressure wave, in other words an acoustic signal which can be detected with a microphone.

A simple set-up for a photoacoustic measurement is shown in figure 1. The sample in the cell is irradiated with modulated infrared laser light. The resulting acoustical wave is detected bv a microphone, passed through a phase sensitive amplifier yielding a constant background-free signal.

b) Advantages of photoacoustic spectroscopy

With this set-up PAS has some advantages over conventional spectroscopic techniques (like e.g. mass spectrometers or NDIR-spectrometers):

• No residual signals
• Small sample cells
• Increased sensitivity
• PAS runs under normal atmospheric pressure
• No cryogenic cooling of detectors required
• Cost efficient since microphones are less expensive than IR detectors

Hence PAS is the choice for a number of applications:

• Sensitive and selective detection of gases, vapours or particles
• Analytic examinations of liquids, solutions or suspensions
• Solid state- or powder analysis (e.g. photoacoustic microscopy).

c) Underlying Physcs

The total energy E_tot of a molecule in thermal equilibrium is basically divided into its rotational energy E_Rot , its vibrational energy E_Vib , its electronic energy E_El as well as its kinetic energy E_kin,

Etot = ERot + EVib + EEl + Ekin

(1)

where the sum of the first three terms is usually referred to as the internal energy of the molecule.

In response to resonant electromagnetic irradiation some molecules of the sample will change from the energetic ground state E₁ to an excited state E₂ by absorbing photons of the energy

h • v = E1 - E2

(2)

( h : Planck's constant). The photoacousic effect PAS often exploits the vibration or rotation transitions of the sample molecules. Fig. 2 shows the energy-term scheme of a single absorbing gas component, which energetically represnts a simple two-level system. The intensity I_abs absorbed by the sample is found by using the Lambert-Beer law

Iabs = I0 • (1 - e-α • L)

(3)

where I₀ is the irradiated intensity and L the sample length. (the above holds in the case of linear absorption, i.e. when neglecting saturation effects or multi photon absorption). The absorption coefficient of the transition E₁ to E₂ is determied by

α = σ • (N1 - N2)

(4)

N₁ and N₂ are the occupation densities of the ground states E₁ and the excited states E₂ repsectively, and &sigma is the absorption cross section of the transition. In case the upper state E₂ is thermically unoccupied, then (N₁ - N₂) represents the total particle density N.

There are two ways for the molecules to transit back from the excited state E2 into the ground state E₁ : radiating or non-radiating. The radiating relaxation will result for the absorbed quantum to be re-emitted after some time, which is the basic principle of fluorescence spectroscopy.

The photoacoustic effect, however, exploits that part of the enrgy which by inelastic collisions is converted into kinetic energy of the collision partners. Here, the collision of an excited molecules with some other will convert the energy difference bewteen the excited and the ground state E₂ - E₁ = h • v into translational energy of the collision partners whereby the velocity of the colliding molecules will increase. In other words, internal (rotational or vibration)energy is converted into kinetic energy.

On the other hand, an increase in teh velocity of the molecules is equivalent to increasing the temperature of the gas. Provided the sample can approximately consideres as an ideal gas, then

p • V = n • k • T

(5)

where p is the pressure and n number of particles of the gas and k the Boltzmann constant. An increase in temperature will therfore result in a thermoelastic expasnsion of the sample the therefore - at constant volume (density) - lead to an increase in pressure.

When the irradiation is stopped diffusion of the molecules will immediately lead to a heat dissipation over the cell volume and therefore reduce the pressure to its initial value. A modulated irradiation, however, will effect periodoc pressure changes (typical 10^-2 to 10^-1 Pa) with der modulation frequency of the radiating source - which is the so called photoacoustic signal (PAS). Detecting this sound wave with a microphone (see Fig. 1) will eliminate the background (atmospheric pressure), since only changes in pressure will be detected. The ensuing phase sensitive measurement of the microphone signal will yield a constant offset-free signal. .

Fig. 3 demonstrates schematically the evolution of pressure, microphone voltage and lock-in signals over time resulting from a hamrmonic modulated irradiation.

The specific advantages of PAS compared to other spectroscopic techniques are:

• It is an offset-free measurement technique. Smallest signals will be detected without background disturbance.
• No long absorption lengths are required which enables the use of small sample cells.
• Exploiting the acoustic resonance frequency of the sample cell will lead to a great signal increase and hence to a marked increase in sensitivity.
• The photoacoustic signal is lenear over many orders of magnitide. No electronic linearisation of the measurement range is required.
• A reduction of absorption line widths by reducing the pressure is not required. Spectroscopic measurements can be performed under atmospheric pressure.
• In spite of using middle or far infrared radiation, no low-temperature cooling of the detector is required which which permits a particularly simple set-up.
• PAS is a cost efficient measurement technique, since simple microphones are much less expensive than infrared detectors.

Hence PAS is the choice for a number of applications:

• Sensitive and selective detection of gases, vapours or particles under normla atmospheric pressure.
• Analytic examinations of liquids, solutions or suspensions
• Solid state- or powder analysis (e.g. photoacoustic microscopy).
• Photoacoustic examinations of collision processes in gases is also a common application (measuring the inelastic cross-section or absorption line shift or broadening).