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

Abstract

Photopolymerization is a process that depends, among other factors, on the optical properties of polymerized materials. In turn, this process affects longitudinal light transport in these materials, thereby altering their optical absorption coefficient which is thus expected to exhibit depth dependence. Furthermore, polymerization affects the thermal properties of these materials. A robust theoretical approach to the study of the depth-dependent optical absorption coefficient, ␤͑x͒, and thermal diffusivity, ␣͑x͒, in materials exhibiting depth profiles of these parameters has been developed through the photothermal inverse problem based on the concept of the thermal-harmonic oscillator. Using this concept in the frequency-domain nonhomogeneous photothermal-wave boundary-value problem, the simultaneous reconstruction of arbitrary simultaneous optical and thermal depth profiles was achieved using a multiparameter fitting method to the experimental amplitude and phase. As a first application of the theory to partially polymerized Alert Composite ͑shade A3͒ dental resin, with curing induced by a blue light-emitting diode, the ␤͑x͒ and ␣͑x͒ depth profiles were reconstructed from photothermal radiometric frequency-scanned data. A strong anticorrelation of these two depth profiles was observed and was interpreted in terms of photochemical processes occurring during the optical ͑photocuring͒ creation of long polymeric chains in the resin. The photothermally reconstructed depth profiles may have implications for the optimization of blue light curing methods using such resins in dental clinical practice. Downloaded 24 Dec 2010 to 128.100.48.213. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 054902-2 Martínez-Torres, Mandelis, and Alvarado-Gil J. Appl. Phys. 108, 054902 ͑2010͒ Downloaded 24 Dec 2010 to 128.100.48.213. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 054902-3 Martínez-Torres, Mandelis, and Alvarado-Gil J. Appl. Phys. 108, 054902 ͑2010͒ Downloaded 24 Dec 2010 to 128.100.48.213. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 054902-7 Martínez-Torres, Mandelis, and Alvarado-Gil J. Appl. Phys. 108, 054902 ͑2010͒ Downloaded 24 Dec 2010 to 128.100.48.213. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

The heat transfer problem for inhomogeneous materials in photoacoustic applications and spectral parameter power series

“…One can verify by substitution that (21) satisfies the required boundary conditions (3). In plots of Figures 5 and 6, we present the temperature distribution inside the cell containing a graphite sample of thickness 2 and 5 mm, respectively.…”

“…The mathematical description of the heat flow generated by external heating within inhomogeneous materials is of interest in several branches of applied fields. In photoacoustic applications, the sample located in the cell is illuminated by the intensity modulated light, the temperature distribution within the cell depends on the thermal, optical, and geometric properties of the sample and support materials (see ). There are different methods and techniques that allow one to describe these properties using the knowledge of the temperature distribution within the sample or on its surfaces, for example, the phase‐lag method , self‐normalized techniques .…”

“…Meanwhile, the case of materials with continuously varying optical and thermal properties was studied in . As an alternative to the multilayer approximation, the Wentzel–Kramers–Brillouin (WKB) method was explored in . Both the piecewise constant approximation and the WKB methods are basic mathematical techniques with well‐known considerable limitations.…”

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

“…8 show typical a and D in-depth profiles for partially cured dental resins. 11 Due to photopolymerization, the thermal diffusivity of the resin increases, while the optical absorption coefficient decreases, i.e., the material becomes a better thermal conductor and more transparent. In this process, the heat capacity is assumed to remain constant: qc ¼ 2.5 Â 10 6 Jm À3 K À1 .…”

“…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. First, we apply the thermal quadrupole method to calculate the surface temperature of layered semitransparent materials.…”