Photothermal determination of thermal diffusivity and polymerization depth profiles of polymerized dental resins

Abstract

The degree and depth of curing due to photopolymerization in a commercial dental resin have been studied using photothermal radiometry. The sample consisted of a thick layer of resin on which a thin metallic gold layer was deposited, thus guaranteeing full opacity. Purely thermal-wave inverse problem techniques without the interference of optical profiles were used. Thermal depth profiles were obtained by heating the gold coating with a modulated laser beam and by performing a frequency scan. Prior to each frequency scan, photopolymerization was induced using a high power blue light emitted diode ͑LED͒. Due to the highly light dispersive nature of dental resins, the polymerization process depends strongly on optical absorption of the blue light, thereby inducing a depth dependent thermal diffusivity profile in the sample. A robust depth profilometric method for reconstructing the thermal diffusivity depth dependence on degree and depth of polymerization has been developed. The thermal diffusivity depth profile was linked to the polymerization kinetics.

Optical and thermal depth profile reconstructions of inhomogeneous photopolymerization in dental resins using photothermal waves

“…Regarding independent validation of the depth profiles, although mechanical hardness measurements were not performed in the studies reported in this paper, the present thermal diffusivity depth profiles are similar in rate of increase and saturation depth to those obtained earlier on the same samples with a thin opaque coating on the surface and single-parameter reconstruction. 28 These facts point to the robustness of the inversion methodology. The simultaneously reconstructed optical absorption coefficient profiles show good anticorrelation with the thermal diffusivity profiles consisting of a steep decrease in the first 60 m followed by a slower decrease up to a final optical absorption value.…”

“…A similar trend was recently observed in the bulk thermal diffusivity value of the present resin, as measured with an opaque thin metallic coating on the surface leading to purely thermal diffusivity reconstruction without the ͑photothermally saturated͒ optical absorption coefficient. 28 Reasonably assuming that all changes in PTR signal after photopolymerization are due to inhomogeneities of the optical and thermal properties of the sample, arbitrary depth profiles for the optical absorption and thermal diffusivity can be reconstructed by numerically determining the optimal pair of ͑␤ f , g͒ and ͑␣ f , q͒ at each angular frequency, so that the assumed profile locally results in the experimentally observed PT wave signal amplitude and phase data.…”

“…10,13,15 Also, several algorithms to invert the depth profiles have been applied, using an inverse procedure to find the Taylor expansion parameters of the conductivity profile, 9,16 a least-squares one-parameter fit to reconstruct a polygonal approximation to the conductivity profile, 17,18 obtaining local thermal diffusivity at each frequency, 12,14,19 global optimization methods as genetic algorithm and neuronal networks, [20][21][22] and particle swarm optimization. 13 Experimentally, some of these theories have been applied to evaluate liquid crystals, 23,24 ceramics, 25 metallurgical specimens, 17,26,27 aluminum oxide thin films, 22 and dental resin composites, 28 to name a few. All these approaches concern only depth-dependent variations in the thermal parameters of materials while the optical properties remain either constant or the material is optically opaque ͑PT saturation͒.…”

Thermal wave propagation in thin films on substrate: the time‐harmonic thermal transfer function

“…In addition, various thermal‐wave imaging methods have been developed such as scanning photoacoustic microscopy 14, photothermal 15, 16 and thermoreflectance 17–19 microscopy as well as lock‐in thermography (LIT) 20–22. Thermal wave‐based measurement and imaging methods are used in a broad area of applications, ranging from non‐destructive evaluation (NDE) of materials 23, 24, biological and medical investigations 25, 26, testing of electronic devices 27, to materials research (see, e.g. , 28), with a resolution reaching down to the micro‐ and nanoscale 29–31.…”

Simultaneous measurement of thermal diffusivity and optical absorption coefficient using photothermal radiometry. II Multilayered solids

“…Since the seminal work by Mandelis and co-workers, 1 modulated PTR has also been used for thermal conductivity depth profile reconstruction of heterogeneous samples as case (surface) hardened steels, [2][3][4][5][6][7] functionally graded materials, 8 and partially cured dental resins. 9 In the last years, two works dealing with the application of modulated PTR to the simultaneous reconstruction of the in-depth varying absorption coefficient (a) and thermal diffusivity (D) of semitransparent heterogeneous samples have been published. 10,11 The aim of this work is to study the capability of modulated PTR to obtain simultaneously a and D in multilayered materials.…”