How filler properties, filler fraction, sample thickness and light source affect light attenuation in particulate filled resin composites
Introduction
Visible light-cured dental composites (VLCDC) are widely used as direct filling materials because of their ‘snap-on-command’ curing mechanism [1]. VLCDC are partly translucent and scatter light. Light penetration decreases with increased material thickness [2]. This is due to the absorption and scattering of light by fillers and other additives [3]. Unfortunately, light scattering leads to limited depth of cure [4], [5]. Limited depth of cure has been pointed out by several researchers [6], [7] as a major clinical drawback with VLCDC, because unpolymerized or partially polymerized material can lead to poor mechanical properties, poor dentin bonding and eventually initiate pulp reactions [8].
By measuring of light transmission through experimental and commercial VLCD composites some investigators have developed mathematical relationships between different factors affecting light transmission [2], [5], [9], [10], [11], [12]. Further studies have shown that light transmission affects depth of cure of the composite [2], [4], [5], [13], [14], [15]. In 1980, Cook claimed that the depth of cure is mainly depended on the composition of the composite, the irradiance light characteristics and the exposure time [9]. Later, O'Keefe et al. [16] showed that there was a wavelength dependency of light transmission through light cured composites.
Because of the above aspects, light transmission of the composite and irradiance of the light source are important factors to consider when one wants to improve depth of cure. In practice different commercial VLCDC containing different matrices and filler particles are used and different light sources are available to cure these composites. Due to these variations, it is important to understand how different material components as well as different light sources affect light penetration through VLCDC.
One approach to enhance our understanding of light penetration in dental composites is to use Beer–Lambert's law. According to this law, if a beam of monochromatic radiation passes through a medium its power attenuates based on the following equationwhere P0 is the initial optical power, RF is the total Fresnel reflectance coefficient, α is the attenuation coefficient and d is the thickness of the sample [17]. Forming the quotient P/P0 and taking the natural logarithm result in the expressiondescribing the loss in optical power due to reflections, absorption and scattering upon transmission through the medium, in our case the VLCDC. As a consequence of Beer–Lambert's law, Eq. (2) becomes a linear function where the constant factor results in the efficient Fresnel reflectance coefficient and the inclination give by the attenuation coefficient. The attenuation coefficient, α, should further be divided into an absorption coefficient, αa, and scattering coefficient, αs, which express bywhere the dependence of resin volume fraction, Vr, the filler volume fraction, Vf, relative refractive index, Δn, particle radius, r, and surface treatment, S, are variables affecting the scattering coefficient.
The photo-initiator, e.g. camphoroquinon (CQ), has an absorption peak at about 467.5 nm which is shown in Fig. 1. No other absorption bands are present in either the resin or the filler particles within the spectrum of interest wherefore the absorption coefficient αa is assumed to depend only on the matrix volume fraction. This dependency will be predominantly linear wherefore the absorption coefficient is modeled by the first two terms in its Taylor expansion that gives,where is a higher order term and other higher order terms are assumed negligible. Eq. (4) can be written in the form of Eq. (4′) since the relation between Vr and Vf represents as: Vr=1−Vf,The scattering coefficient, αs, of the filler will vary even more due to all the variables indicated in Eq. (1). In the following, however, we will treat each type of filler particle separately and only consider the variation due to filler volume fraction and sample thickness for each specific material combination. By further approximation, it is assumed that the scattering coefficient is relatively consistent among the volume fractions being tested. The scattering coefficient may therefore be approximated by its Taylor expansion around the point Vf=0, giving the expressionwhere αs and are two new constants. The higher order terms of the Taylor expansion are assumed negligible. Accordingly, Eq. (2) can be rewritten aswhich is rewritten as
Eq. (6) can be simplified aswhere Z=ln(P/P0), A=ln(1−Rf) or reflection term, or absorption plus scattering factor and or a factor showing the difference between higher-order absorption and scattering terms. The term CdVf depends on filler volume.
Based on the above relationship, we hypothesize that by standardizing variables such as light sources, filler types and filler surface treatment, it should be possible to employ Eqs. (6), (7) for predicting light absorption in VLCD composites. Accordingly, the objective with this study is to test whether the light absorption in VLCDC can be mathematically modeled by using Eqs. (6), (7) or not.
Section snippets
Composition of the experimental materials
The resin system used in this study consisted of a mixture of 50 wt% bisGMA (2,2-bis[4-(2-hydroxy-3-methacrylyloxy-propoxy)-phenyl] propane) and 50 wt% TEGDMA (triethyleneglycol dimethacrylate) to which a photo-initiator (0.35 wt% champhorquinone) and a co-initiator (0.7 wt% of dimethylaminoethylmethacrylate [DMAEMA]) had been added. Different filler types at different volume fractions were added to that mixture. Two of the filler particle types (SBB and HBB) consisted of spherical Ba–Al–B–Si glass
Refractive index determinations of matrix and filler systems
The obtained results from refractive index measurements for both the resins and the filler particles were: bisGMA/TEGDMA=1.5020 (0.0002), γ-methacryloxypropyl-trimethoxysilane=1.4297 (0.0002), SBB=1.5509 (0.0002), HBB=1.5481 (0.0001), and KU=1.5454 (0.0002). It can be confirmed from above results that all filler particles had significantly higher refractive indices than the matrix. Of the filler particles, however SBB shows biggest difference with respect to the matrix. While KU presents the
Discussion
Based on our approach with respect to Lambert–Beer's law to develop a model and the outcomes of our regression analysis of the experimental results, it seems reasonable to conclude that theoretical predictions and experimental findings coincide. That finding, by itself, is not surprising because Beer-Lambert's law is well established for solutions absorbing radiation, where absorption depends on concentration and path-length of light [5], [18]. Watts and Cash [5] also emphasized that surface
Acknowledgements
The curing unit was generously donated by Dentsply (Spectrum™ 800, Dentsply, De-Trey, Germany). Dr Göran Manneberg, Department for Physics, Royal Institute of Technology, Stockholm, Sweden is highly acknowledged for his help with refractive index measurements for glass particles. This investigation was supported by the Swedish Engineering Research Council.
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