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Direct measurement of the in-plane thermal diffusivity of semitransparent thin films by lock-in thermography: an extension of the slopes method Alexandra Philipp, Nelson Pech-May, Bernd A.F. Kopera, Anna M. Lechner, Sabine Rosenfeldt, and Markus Retsch Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.9b01583 • Publication Date (Web): 31 May 2019 Downloaded from http://pubs.acs.org on June 2, 2019
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Analytical Chemistry
Direct measurement of the in-plane thermal diffusivity of semitransparent thin films by lock-in thermography: an extension of the slopes method Alexandra Philipp1, Nelson W. Pech-May1**, Bernd A. F. Kopera1, Anna M. Lechner1, Sabine Rosenfeldt1, Markus Retsch1* 1University
of Bayreuth, Department of Chemistry, Universitaetsstr. 30, 95447 Bayreuth, Germany *E-mail:
[email protected] **E-mail:
[email protected] Abstract We present an extension of the well-known slopes method for characterization of the in-plane thermal diffusivity of semitransparent polymer films. We introduce a theoretical model which considers heat losses due to convection and radiation mechanisms, as well as semitransparency of the material to the exciting laser heat source (visible range) and multiple reflections at the film surfaces. Most importantly, a potential semitransparency of the material in the IR detection range is also considered. We prove by numerical simulations and by an asymptotic expansion of the surface temperature that the slopes method is also valid for any semitransparent film in the thermally thin regime. Measurements of the in-plane thermal diffusivity performed on semitransparent polymer films covering a wide range of absorption coefficients (to the exciting wavelength and in the IR detection range of our IR camera) validate our theoretical findings.
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1. Introduction Lock-in thermography is a well-known technique for accurate determination of the in-plane thermal diffusivity of solids.1-4 In recent decades, it has attracted the attention of scientists due to its non-contact and non-invasive attributes. Moreover, lock-in thermography has shown versatility for materials characterization, in non-destructive testing and evaluation as well as in biomedical applications.5-6 In particular, for thermal characterization of isotropic solids, the “slopes method”2, 7 has been widely used. Therefore, a free-standing sample is periodically heated by a focused optical source. The temperature oscillations as a function of the radial coordinate are detected, typically using an infrared (IR) camera. The thermographic signal (amplitude 𝑇 and phase Ψ) is either derived from the front-face2 or the rear-face configuration1, i.e., from the non-illuminated face. The thermographic signals (ln(amplitude) and phase) far from the heating spot vary linearly with radial distance under the precondition of isotropic opaque thin films in the thermally thin regime (film thickness
