Photoacoustic Spectroscopy

Photoacoustic Spectroscopy Seminar by Deepak Rajput PHYS 605 Advanced Topics: Laser Spectroscopy July 10, 2007 Center for Laser Applications University of Tennessee Space Institute Tullahoma, TN 37388 Email: [email_address] Web: http://drajput.com

Introduction ,[object Object],[object Object]

PA spectroscopy in gases ,[object Object],[object Object]

Theory ,[object Object],[object Object],[object Object],Where A r is the radiative decay rate of the excited state, A n is the non-radiative decay rate due to collisions of the excited state, and R is the excitation rate due to the light beam of flux Φ photons per cm -2 sec -1 with an absorption cross section σ cm 2 . … 1

Theory cont.. ,[object Object],[object Object],Where the lifetime of the excited state … 2

Theory cont.. ,[object Object],Where E` is the average thermal energy released due to a non-radiative de-excitation collision of the excited state. … 3

[object Object],[object Object],Theory cont..

Theory cont.. ,[object Object],[object Object],[object Object],[object Object],… 4 … 5

Theory cont.. ,[object Object],[object Object],[object Object],[object Object],… 6

Theory cont.. ,[object Object],[object Object],[object Object]

[object Object],[object Object],Theory cont.. … 7 After Morse and Ingard (1968) Where c is the velocity of sound and is the ratio of specific heats of the gas; all dissipative terms have been neglected.

Theory cont.. ,[object Object],[object Object],… 8

Theory cont.. ,[object Object],[object Object],[object Object],[object Object],… 9 … 10

[object Object],[object Object],[object Object],Theory cont.. … 11 … 12

Theory cont.. ,[object Object],[object Object],[object Object],Here we have lumped the space- and time-independent coefficients of Φ 0 (r) together as the coefficient q .

Theory cont.. ,[object Object],[object Object],With an eigenfrequency ω j given by Special case: Beam along the axis of cylinder OA cell in weak absorption limit, and only Normal modes can be excited by the heat source, i.e., we need only the radial normal modes.

Theory cont.. ,[object Object],Where, g 1 = normalization factor for , and L = cell length and we have used

Theory cont.. ,[object Object],… 13 ,[object Object],[object Object],[object Object]

[object Object],Theory cont.. ,[object Object],[object Object]

Theory cont.. Page 8, Chap 1, Photoacoustics: Spectroscopy and Other Applications, Andrew C. Tam, Ultrasensitive Laser Spectroscopy, edited by David S Kliger, Academic Press (1983)

[object Object],[object Object],[object Object],Theory cont..

Theory cont.. ,[object Object],where W is the total number of photons absorbed ,[object Object],Where R is the universal gas constant, M is the molecular weight, and Cv is the specific heat per unit mass at constant volume.

Theory cont.. ,[object Object],where a is the beam radius and D is the thermal diffusivity of the gas The initial rise in p(t) depends on the lifetime of the excited state, while the final slow decrease of p(t) back to zero depends on the thermal decay time constant τ D .

Instrumentation for OA Studies of Gases

[object Object],[object Object],[object Object],[object Object],Instrumentation for OA Studies of Gases

Instrumentation: Light Source ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],Instrumentation: Light Source

Applications ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

PA Spectroscopy in Condensed Matter ,[object Object],[object Object],[object Object]

Gas-Coupling Method ,[object Object],[object Object]

Gas-Coupling Method ,[object Object],[object Object],D s and D g are the thermal diffusivities in the sample and in the gas, respectively and f is the modulation frequency of the light beam

Gas-Coupling Method A light beam of radius r striking a flat opaque surface of radius R.

Gas-Coupling Method ,[object Object],Where θ 0 is the amplitude of the surface temperature modulation and I 0 is the modulated light absorbed θ 0 is coupled to an active gas volume V act near the sample surface, given by: for l g > μ g for l g < μ g

Gas-Coupling Method ,[object Object],(T 0 is the ambient temperature) ,[object Object],Where V is the total PA cell volume given by:

Gas-Coupling Method ,[object Object],where ,[object Object]

Direct-Coupling Method ,[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],Direct-Coupling Method

Substance ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object]

References ,[object Object],[object Object]

Photoacoustic Spectroscopy

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Photoacoustic Spectroscopy