MATHEMATICAL MODELING FOR THE NEXT GENERATIONOF TRACE GAS SENSORS

Susan E. MinkoffThanks to: Noemi Petra, John Zweck, Michael Reid (UMBC),

Anatoliy Kosterev, Frank Tittel, James. H. Doty III, and David Thomazy (Rice University)

MIRTHE Goals: To develop trace gas sensors usingtwo new technologies:

• Quantum Cascade Lasers (QCL’s) – see ex-hibit by Claire Gmachl (Princeton)

• Quartz-Enhanced PhotoAcoustic Spec-troscopy (QEPAS) developed by Kosterevand Tittel at Rice University.

NSF ENGINEERING RESEARCHCENTER: MID–INFRARED TECH-

NOLOGIES FOR HEALTH ANDTHE ENVIRONMENT (MIRTHE)

• Non-invasive disease diagnosis (e.g., liverdisease and lung cancer) using breath bio-markers.

• Environmental and industrial monitoring us-ing networks of sensors (e.g., monitoring ofatmospheric carbon dioxide levels).

• Homeland security (e.g., chemical weapondetection at airports, train stations, etc).

APPLICATIONS

• In 1888 Alexander Graham Bell discoveredthe photoacoustic effect:

∗ Specifically that periodic absorption oflight by matter produces sound.

∗ He used this phenomenon to develop awireless communication device.

• Since light is only absorbed by the gas at par-ticular wavelengths the photoacoustic effectcan detect trace gases.

• In the 1970’s PAS was used to detect nitricoxide in the stratosphere which was proof ofozone depletion by man-made chemicals.

PHOTOACOUSTIC SPECTROSCOPY (PAS)

QEPAS Sensors detect the sound produced in PAS us-ing a quartz tuning fork (like the one in your watch)to amplify and detect the sound wave.

QEPAS

• Greater sensitivity due to the strong absorp-tion by simple molecules in the infrared spec-trum and the power of QCL’s.

• Rugged and small in size → portable

• Cost Effective → can be deployed in sensornetworks.

Left: Actual QEPAS sensor device. Right: Schematic diagram ofQEPAS device for simulation.

ADVANTAGES OF QEPAS WITHQCL’S OVER PREVIOUS TECHNIQUES

Goals:

• Increase physical understanding of QEPAS,

• Optimize design of sensors.

Outline of Model

• The interaction of the laser and the trace gasgenerates a sound wave which we model us-ing a forced acoustic wave equation.

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Simulated acoustic pressure wave as a function of radial distancefrom laser beam.

• The sound wave excites a vibration of the quartz tuning fork.

Left: The displacement of the 32.8 kHz tuning fork. The red andblue colors show the maximum and minimum displacement, re-spectively. Right: The first principal stress. The stress is largest(red) where the tines of the tuning fork meet the base.

• The photoelectric effect in quartz converts this vibration to anelectric current whose strength is proportional to the concen-tration of the trace gas.

A MATHEMATICAL MODELFOR QEPAS SENSORS

Left: Mathematical Modeling Group (John Zweck, Noemi Petra,Susan Minkoff). Right: Experimental Group (Lei Dong, AnatoliyKosterev, Jim Doty, Christian Zaugg; Not shown: Frank Tittel andDavid Thomazy).

PROJECT PARTICIPANTS

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Normalized amplitude of the piezoelectric current as a function ofthe vertical position of the laser beam for a QEPAS sensor with a32.8 kHz tuning fork.

• We used experiments and computer simulation to find the po-sition that produces the largest current.

• These results validate the model and confirm the optimalplacement of the laser beam.

SENSOR OPTIMIZATION

• The heat generated by absorption of light canbe directly detected using a tuning fork.

• ROTADE and QEPAS are complementarytechniques operating in different pressureregimes.

• Experiments and simulations show that thelaser must be positioned close to the walls ofthe tuning fork and near the base of the tines.

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Left: The normalized experimental signal strength vs the positionof the laser beam. Right: the numerically computed signal strengthvs laser position.

Experimental Results. Left: tuning fork image depicting transmit-ted power and signal as a function of beam position for 300 torr ofpure CO2 . Observed signal primarily due to photoacoustic effect.Right: tuning fork (in black) shows the signal due to ROTADE asa function of beam position at a reduced pressure of 20 torr of pureCO2 .

• We plan to use the models to improve performance of bothmethods by optimizing the geometry of the tuning fork.

RESONANT OPTOTHERMOA-COUSTIC DETECTION (ROTADE)

This research was funded by the National Science Foundation un-der Grant No. EEC-0540832.

ACKNOWLEDGEMENT