Exposure reciprocity suggests that, as long as the same radiant exposure is delivered, different combinations of irradiance and exposure time will achieve the same degree of resin polymerization. This study examined the validity of exposure reciprocity using real time degree of conversion results from one commercial flowable dental resin. Additionally a new fitting function to describe the polymerization kinetics is proposed.
A Plasma Arc Light Curing Unit (LCU) was used to deliver 0.75, 1.2, 1.5, 3.7 or 7.5 W/cm 2 to 2 mm thick samples of Tetric EvoFlow (Ivoclar Vivadent). The irradiances and radiant exposures received by the resin were determined using an integrating sphere connected to a fiber-optic spectrometer. The degree of conversion (DC) was recorded at a rate of 8.5 measurements a second at the bottom of the resin using attenuated total reflectance Fourier Transform mid-infrared spectroscopy (FT-MIR). Five specimens were exposed at each irradiance level. The DC reached after 170 s and after 5, 10 and 15 J/cm 2 had been delivered was compared using analysis of variance and Fisher’s PLSD post hoc multiple comparison tests (alpha = 0.05).
The same DC values were not reached after the same radiant exposures of 5, 10 and 15 J/cm 2 had been delivered at an irradiance of 3.7 and 7.5 W/cm 2 . Thus exposure reciprocity was not supported for Tetric EvoFlow ( p < 0.05).
For Tetric EvoFlow, there was no significant difference in the DC when 5, 10 and 15 J/cm 2 were delivered at irradiance levels of 0.75, 1.2 and 1.5 W/cm 2 . The optimum combination of irradiance and exposure time for this commercial dental resin may be close to 1.5 W/cm 2 for 12 s.
Photo-polymerizable resin-based composites (RBCs) have become the material of choice for direct restorations . The radiant exposure (RE), namely the product of irradiance and exposure time, is an important factor that determines the degree of conversion (DC) and mechanical properties of photo-polymerizable RBCs . The RE required to adequately polymerize a 1–2 mm thick increment of RBC is considered to be between 18 and 24 J/cm 2 . This is based on studies using quartz-tungsten-halogen (QTH) light-curing units (LCUs), which found that it was necessary to deliver a minimum irradiance of 300–400 mW/cm 2 for 60 s . To obviate the need to spend 30 to 60 seconds light curing light curing each increment of RBC, high power curing lights have been introduced to reduce light exposure times and thus shorten chairside procedures. Several authors have investigated what they have described as the ‘Exposure Reciprocity Law’ , which proposes that there exists reciprocity between irradiance and exposure time to achieve equivalent polymerization of RBCs. Consequently, some contemporary LCUs now deliver irradiance levels up to 6 W/cm 2 , which, their manufacturers’ claim, can allow for very short exposure times (1–3 s) to be used . This makes these high output LCUs attractive to dentists who wish reduce the time they spend light curing. It is possible many resins appear to follow exposure reciprocity simply because they have been cured to a high DC , but this does not necessarily mean that their physical properties will be the same. Depending on the rate of cure, it has been reported that some RBCs may have different physical properties even when a similar DC is achieved . It has been reported that curing a resin at a higher irradiance with a shorter exposure time can increase the shrinkage stress . It also results in a lower degree of cure, lower flexural strength and lower modulus than curing with a lower irradiance for a longer time .
It has been reported that the greater the viscosity of the RBC, the more likely it is to exhibit exposure reciprocity compared to its flowable counterpart . In the very early phase of polymerization the RBC has yet to develop a polymeric network to effectively trap the radicals . Thus during this phase the principle of exposure reciprocity is likely violated. Near the end of polymerization, the principle should hold because almost all of the radicals are now trapped in the glassy network. For each resin system, there appears to be an optimum rate of initiation that produces the highest quantum yield. If the initiation rate is too high, more of the generated free radicals are prematurely spent via bimolecular termination because the medium has yet to develop a polymeric network to trap these free radicals effectively. Conversely, if the initiation rate is too low, many photons may be wasted if the network has already been well established, as this network will trap and annihilate the primary radicals, preventing them from producing polymers . When the resin receives a high irradiance, the reaction rates between production and destruction of intermediate molecular species may not be in balance, and steady-state assumptions may not hold .
In some cases the irradiance and exposure time can influence the polymer chain length, extent of cross-linking, and mechanical properties of the resin . At high irradiance levels only short polymer chain lengths can be achieved before cross-linking occurs . Hadis et al. examined 10 RBCs and reported that a reciprocal relationship between irradiance and the exposure time was observed for five commercial paste RBCs, but only for three out of the five flowable products. They delivered a RE of 18 J/cm 2 to verify the applicability of the exposure reciprocity concept using irradiance values between 400 and 3000 mW/cm 2 . Using a Fourier Transform near-infrared spectrometer (FT-NIR) in the transmission mode, the time dependent DC and rates of polymerization R p were measured through 1.4 mm thick RBC specimens. Two of the flowable resins exhibited a lower degree of conversion when exposed to 3000 mW/cm 2 for 6 s, compared to 400 mW/cm 2 for 45 s. Using differential scanning calorimetry, Feng et al. reported that for experimental resins with an oligomer/monomer mass ratio equal to or greater than 6:4, the degree of double bond conversion followed a reciprocal arrangement when low irradiance levels between 3.1 mW/cm 2 and 50 mW/cm 2 were delivered to the resins. Since most commercial dental resins are similar binary systems, containing mostly viscous oligomers, they concluded that the ‘exposure reciprocity law’ might also apply to dental RBCs.
The available evidence for exposure reciprocity at any irradiance level is contradictory, most likely because different research groups have used different resins, ranges of irradiance and radiant exposures to investigate this phenomenon . One study used very low irradiance levels (3–24 mW/cm 2 ) to investigate the relationship between the radiant exposure and the DC . Using a kinetic model, the authors reported that the polymerization kinetics should not be expected to follow the reciprocity law behavior. At these low levels, as the irradiance increased, the overall radiant exposure required to achieve full conversion also increased. The ultimate conversion did not only depend on the radiant exposure, but also on the irradiation intensity and corresponding polymerization rate . Another study using irradiance levels between 50 and 1000 mW/cm 2 described a parabolic relationship between irradiance and both flexural strength and flexural modulus for Tetric Ceram (Ivoclar-Vivadent, Schaan, Liechtenstein). For this RBC, the maximum flexural strength and flexural modulus occurred at an intermediate irradiance level. This relationship may be applicable to other resins . Other reports examining the concept of exposure reciprocity have based their conclusions on properties such as the elastic modulus , the micro-hardness , or the depth of cure of the resin measured at a fixed time point after light exposure that ranged from 180 s to 1 week.
Fourier Transform mid-infrared spectroscopy (FT-MIR) is often used to measure the DC of dental resins by assessing the change in ratio of characteristic absorbance peaks of the cured and uncured resin. Commonly the methacrylate aliphatic C C double bond peak height or area at 1638 cm −1 is compared to the aromatic C C double bond peak height or area at 1608 cm −1 . Additionally, although not commonly carried out, it is recommended that the equipment response be determined using different mixtures of known molar ratios of aliphatic to aromatic groups . Depending on the irradiance level, most of the polymerization reaction occurs within the first 5 s of light exposure . Previous studies have reported DC results based on conclusions drawn from curve fitting all the data using a single fitting function , or more recently a five parameter bi-exponential fitting function . However, these fitting functions often do not fit the DC data gathered in the first few seconds very well and this is the time period of greatest interest. Also, as these studies collected relatively few data points during the first 5 s, they were unable to accurately follow the early changes in the DC.
Currently there is no research available to support the existence of exposure reciprocity for high output lights delivering more than 3 W/cm 2 , even though there are LCUs on the market that deliver 6 W/cm 2 . Therefore, the use of such high output lights may introduce the risk of under-curing photo-polymerizable RBCs. Given that more than 261 million RBC restorations and sealants are placed annually , this could have great health and financial implications. There is good indirect evidence that under-curing a RBC restoration may result in more bulk fracture, greater wear of the restoration, or more secondary caries . Class II restorations are especially at risk of undercuring at the gingival portion of the proximal box . This is the region that is the most difficult to reach with the curing light and interestingly it is the region where most failures occur . Under-cured dental RBCs are also more likely to leach unwanted chemicals into the mouth . Arbitrarily increasing light exposure times in an effort to prevent under-curing is not the answer as this may cause unacceptable thermal trauma to the pulp and surrounding tissues . Thus, both dentists and manufacturers of dental light curing units (LCU) need to know if it is appropriate to use high irradiance values of 6 W/cm 2 and above to photo-cure dental resins in a short time.
This study exposed one commercial RBC to different levels of irradiance from 0.75 to 7.5 W/cm 2 and adjusted the time to deliver similar radiant exposures. The DC was measured in real time at a rate of approximately 8.5 DC measurements a second. A new curve fitting function was developed to better address the early polymerization kinetics (primary curing) as well as the long term curing in the glassy state (post-curing). The hypothesis is that the same DC will be reached when the same radiant exposures of 5, 10 and 15 J/cm 2 has been received at irradiance levels from 0.75 to 7.5 W/cm 2 .
Materials and methods
A flowable resin, Tetric EvoFlow (Ivoclar Vivadent, Amherst, NY, USA) shade T, from the same lot was used to make all the specimens. According to the manufacturer, Tetric EvoFlow has a resin content of 38 wt% and a total filler content of 62 wt%. The resin contains 0.25 wt% camphorquinone (CQ) and 0.4 wt% 2,4,6-trimethylbenzoyl-diphenylphosphine oxide (TPO) photo-initiators. To ensure adequate spectral overlap, the spectral emission from the LCU ( Fig. 1 ) was compared to the relative absorbance spectrum for these two photo-initiators (obtained from Aldrich Chemical Co., Milwaukee, WI, USA) using a UV–visible spectrophotometer (Helios Alpha, Thermo Spectronic, Rochester, NY, USA).
The RBC specimens were exposed to light from a Sapphire Plus Plasma Arc LCU (DenMat, Lompoc, CA, USA) with a 4-mm diameter turbo light guide. This turbo light guide delivered a maximum irradiance of 7.5 W/cm 2 to the RBC. To provide five different irradiance values to the RBC, the distance between the RBC and the end of the light guide was adjusted by predetermined amounts using an adjustable stage with a 0.1-millimeter vernier scale (#55024, Edmund Optics, Barrington, NJ). Five distances were used: 0 mm, 4.5 mm, 9.0 mm, 10.5 mm, and 13.5 mm. The irradiance, radiant exposure and spectral emission from the LCU at each distance were measured using an integrating sphere (Labsphere, North Sutton, NH, USA) connected to a fiber-optic spectrometer (USB 4000, Ocean Optics, Dunedin, FL, USA). There was a 4 mm aperture into the integrating sphere, which matched the diameter of the specimens and the diameter of the light guide. Thus, the sphere measured the total spectral radiant power that would be received by the specimens at each distance. This fiber-optic system was calibrated before the experiment using the internal reference lamp contained within the sphere. Spectrasuite v2.0.162 software (Ocean Optics) was used to collect and analyze the data.
Fig. 2 illustrates how the DC at the bottom of the specimens was measured before, during and after light exposure using Fourier Transform mid-infrared (FT-MIR) spectroscopy. The spectrometer (Tensor 27, Bruker, Billerica, MA, USA) was equipped with a temperature controlled attenuated total reflectance (ATR) unit (Golden Gate, Specac, Orpington, Kent, UK) containing a single reflection monolithic 2.0 mm × 2.0 mm diameter diamond prism with a 0.8 mm diameter active sampling area. Prior to the start of the experiment, mixtures with known molar ratios of aliphatic to aromatic groups were prepared using a technique previously described to calibrate the equipment . These mixtures were made from TEGDMA (Sigma Aldrich, St. Louis, MO, USA), BisGMA (Sigma Aldrich), bisphenol-A-diglycidylether (Sigma Aldrich) and hydrogenated BisGMA (provided by Dr. J. Stansbury). These mixtures were measured using the FT-MIR equipment used in this study. A second order polynomial relationship with an excellent degree of correlation ( R 2 ) of 0.999 between the molar ratio and the absorption ratio was achieved using Eq. (1) .
Equation 1: Degree of conversion
DC exp = 100 % × 1 − 0.141 Abs Aliphatic Abs Aromatic Polymer 2 + 1.1424 Abs Aliphatic Abs Aromatic Polymer 0.141 Abs Aliphatic Abs Aromatic Monomer 2 + 1.1424 Abs Aliphatic Abs Aromatic Monomer
where Abs Aliphatic and Abs Aromatic are the absorbances of the aliphatic and aromatic double bonds of polymer and monomer, respectively.
The specimens of Tetric EvoFlow were prepared in 2 mm thick aluminum rings with an inner diameter of 4 mm, which matched the diameter of the light guide and the aperture into the integrating sphere. A 50 μm thick Mylar Strip (Patterson, Montreal, Quebec, Canada) covered the top surface of the uncured composite. The uncured RBC was allowed to stabilize by resting on the temperature controlled ATR for 2 min in the dark before light curing. Based on a pilot study, this was sufficient time to achieve a stable temperature of 30 °C. Five specimens ( n = 5) were irradiated at each irradiance level for 3 s, 6 s, 12 s, 15 s, and 23 s according to the digital timer of the LCU.
The DC was determined as follows:
Mid-IR data collection was started at a rate of approximately 8.5 measurements per second to determine the baseline of the uncured RBC.
After 10 s, the LCU was switched on for the predetermined time.
Data were collected for 170 s after the start of light exposure to determine the DC both during and after light exposure .
The spectrometer acquired all spectra at a resolution of 8-wavenumbers. For each data point, the forward and backward scans of six interferograms were resolved and averaged. This procedure achieved a final acquisition rate of 8.5 DC points per second. The last 20 data points of each FT-MIR run, corresponding to a time range of approximately 2.4 s, were averaged to determine the static DC exp at 170 s for each light exposure protocol.
Using Eq. (1) , the DC values at any given time were calculated using the aliphatic carbon–carbon double bond peak at 1638 cm −1 (Abs Aliphatic ) and the aromatic carbon–carbon double bond peak at 1608 cm −1 (Abs Aromatic ). The area of each peak was calculated using a straight baseline between the minima on either side of the peak. The Bruker Opus software v.6.5 used a proprietary concave rubber band baseline correction with five iterations.
From the calculated DC results, a new fitting function given by Eq. (2) was developed. This equation consists of two factors describing the two curing processes. The first factor takes into account the primary curing phase from the liquid resin up to the glass transition, or vitrified state, and is an exponential function. The second factor takes into account the slow post-curing processes that occur in the glassy state and is a logarithmic function.
Equation 2: Fitting function
DC ( t ) = 1 − exp − t − t LCU τ r e a c 0 ∗ A ︸ p r i m a r y c u r i n g ∗ 1 + B ∗ ln t t LCU ︸ p o s t – c u r i n g