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Curing characteristics of a composite – Part 1: Cure depth relationship to conversion, hardness and radiant exposure Robert L. Erickson a , Wayne W. Barkmeier a,∗ , Rolf H. Halvorson b a b

Department of General Dentistry, Creighton University School of Dentistry, Omaha, NE, USA 3M ESPE Dental Products Division, St. Paul, MN, USA

a r t i c l e

i n f o

a b s t r a c t

Article history:

Objective. As the first part of a larger study on curing characteristics of a resin-based com-

Received 30 January 2013

posite (RBC), the major objectives were to create an energy-hardness relationship (EHR) that

Received in revised form

relates Knoop hardness (KHN) with radiant exposure (H), and to do the same for degree of

20 November 2013

conversion (DC) in the form of an energy-conversion relationship (ECR). Both of these are

Accepted 13 February 2014

meant to be universal relationships that satisfy reciprocity between irradiance and time for a given H value. Methods. RBC specimens were made by curing the material in 6 mm diameter, stainless steel


molds for 10–40 s and allowing the material to cure for 24 h. Cure depths were determined


by a scrape-back method. KHN and DC values were determined along the central axis of


the specimens, and these values were related to the internal H values using a measured


transmission relationship, T(d), for the RBC.


Results. Suitable EHR and ECR relationships were developed for the RBC material that can


be used to describe the curing characteristics under various curing conditions. However, predictive accuracy is affected for incident radiant exposures below about 12 J/cm2 to some extent. A relationship between KHN and DC was established. Significance. For the RBC examined, KHN measurements can be used as an alternate method or in conjunction with DC for describing the curing characteristics. © 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.



Understanding the light-curing characteristics of resin-based composite (RBC) materials is of interest in developing guidelines for clinical use of these materials. It is of particular interest to be able to understand the relationship between degree of conversion (DC) with depth and incident radiant

exposure (H0 ), and to be able to predict what it will be for differing H0 values. A relationship for the depth of cure, as defined by the scrape-back depth (DSB ) for RBC, was provided by Cook [1–3], and in simplified form is given as:


1 ␣[Log AI0 t]

∗ Corresponding author at: Creighton University School of Dentistry, 2500 California Plaza, Omaha, NE 68178, USA. Tel.: +1 402 280 5912; fax: +1 402 280 5004. E-mail address: [email protected] (W.W. Barkmeier).

http://dx.doi.org/10.1016/j.dental.2014.02.012 0109-5641/© 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.


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where ˛ is the attenuation coefficient of the curing light through the RBC, A is a constant, I0 is the incident light intensity (irradiance) and t is the light exposure time. The logarithmic dependence is a reflection of the assumption that light attenuation follows Lambert’s law. Two observations are notable from this relationship: first, DSB is linear with Log I0 t, having a slope of 1/˛, and second, reciprocity between I0 and t is implied when the product of the two, the incident radiant exposure (H0 ), remains constant. Reciprocity between I0 and t has been demonstrated, not only for DSB , but also for the DC at each depth within an RBC for a given H0 [4–9]. However, there is some question about the validity of reciprocity for extreme combinations of irradiance and time, particularly high irradiance and short time [10–13]. Reciprocity is more likely to apply for materials with oligomer/monomer mass ratios greater than 6:4 and for higher viscosity of the resin system, as well as a greater number of double bonds [14]. These conditions apply to many of the RCB materials used for restorative purposes, however, for some lower viscosity materials such as flowable composites and adhesive resins these conditions may not apply and reciprocity is questionable [10,12,14]. Using the benefit of reciprocity the concept of an energyconversion relationship (ECR) was developed [5–7], which provides a relationship between H and DC within the RBC material. For a specific H0 the value of H at any depth can be determined from a transmission relationship, T(d), and then using the ECR a DC is determined for that depth. This allows prediction of DC depth profiles for different H0 values, or to determine the H0 needed to achieve a particular DC at a certain depth [6,7]. For a given RBC, the DSB is defined as the depth at which polymerization has reached a degree where mechanical properties are such that material cannot be readily scraped away, hence the term scrape-back depth. There is a specific DC associated with the DSB as well as a specific HSB that is obtained by using the T(d) with H0 . An underlying assumption in the use of the T(d), which is derived from cured RBC, is that any changes in the optical properties affecting transmission of light through the RBC during curing, and those of the fully cured form, are insignificant. This assumption has not posed a problem in studies where it has been used [6,7]. An alternative method of obtaining the values of ˛ and HSB is suggested by the equation shown earlier. In this method, experimental values of DSB are obtained for several different values of H0 , usually done by varying the exposure time for a fixed H0 , determined by the curing lamp being used. By plotting DSB against the Log H a straight line with slope value of 1/˛ should be found, and the intercept with the abscissa provides a value for the incident radiant exposure (H0SB ) associated with DSB [4]. This method makes no assumptions about the value of ˛, but does make the same assumption mentioned above and that Lambert’s law with a single ˛ will apply. The fit of the data to a straight line would probably be an indication as to how well this assumption holds. Ideally these two methods should be in agreement on the value of ˛ and HSB , which would validate the use of the T(d) in the first method. The values of H0SB and HSB should be different by the value of reflectance

Table 1 – Methods for determining attenuation coefficient (˛) and radiant exposure (HSB ) at scrape-back depth. Method one

Method two

Using the measured transmission relationship for cured composite to obtain the attenuation coefficient and the transmission value for DSB ; then T * H0 = HSB . Plot DSB vs. log H0 for each cure condition. The plot intercept with the Log H axis gives Log H0SB and the inverse of the plot slope gives the attenuation coefficient.

which is available from the T(d). Table 1 provides an outline of the two methods. Hardness measurements have also been used to assess the relative degree of cure for RBC materials [15–18], and comparisons to DC have been made with varying success. However, it seems reasonable that a hardness measurement, such as the Knoop hardness number (KHN), should be related to DC, for a given RBC, even if the exact relationship in not readily defined. Furthermore, the dependence of KHN with H might be expected to show reciprocity between irradiance and time of exposure in a way similar to DC. Reciprocity has been found for hardness [19] and other mechanical properties [20,21]. It then might be possible to construct an energy-hardness relationship (EHR) that could function like the ECR described above. This would allow simpler hardness measurements to be used for gathering data in studies and to characterize the cure properties of an RBC, but still allow for converting to DC values if desired. It was found by Cook [1,2] in his studies that KHN values with depth into an RBC extrapolated to a value of zero at the same depth as found for DSB , which is convenient for analysis. The purposes of this work were: (1) to define a T(d) and ECR for the RBC used in this work and to obtain relevant curing parameters for other parts of this study and related studies. (2) To compare the two methods outlined in Table 1 for the purpose of validating assumptions related to the use of the T(d). (3) Construct an EHR that can describe the curing characteristics of the RBC and function as a replacement or adjunct to the ECR. (4) Develop an accurate relationship between KHN and DC that can be used to cross reference values. All of the above work is needed to provide information and tools for analyzing results of related studies.


Materials and methods


Light-curing considerations of the RBC

A single quartz-tungsten-halogen (QTH) lamp, fit with a 7.0 mm diameter light guide, was used for all procedures in this study (3M XL3000 Curing Lamp, 3M-ESPE, St. Paul, MN, USA). The power from the light guide was checked at the beginning of each testing session, using a power meter (Power Max 500D Laser Power Meter, Molectron Detector Inc., Portland, OR, USA). The measured power stabilized after 30 s at 260 mW and all curing was done using this stabilization period prior to exposing the RBC. A clear polyester film was used on top of all test specimens when curing was carried out. Reflection from this film was accounted for by using a 10% reflectance

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correction to the 684 mw/cm2 irradiance from the light guide, leaving 616 mW/cm2 irradiation to the RBC surface. These values remained consistent throughout the course of the study. The RBC material used in this study was Z100 (A3.5), all from a single lot of material (Z100 Restorative, lot 3GY, 3MEspe, St. Paul, MN, USA).

2.2. Energy conversion relationship and transmission relationship 2.2.1.

Transmission relationship

Transmission of light from the QTH lamp through the RBC material was determined using fully polymerized material in 6.0 mm stainless steel molds of various lengths. Each mold was placed on the detector of a power meter (351 Power Meter, UDT Instruments, Baltimore, MD, USA). The light guide was centered over the cylindrical mold in contact with the cured material and after a stabilization period a measurement of transmitted power was obtained. The light guide was similarly placed on the detector, with a 6.0 mm aperture applied, to obtain the incident power to the RBC. Three replications of the measurements were done for each length of mold and mean values were calculated. A relationship between transmission and depth, T(d) was determined by regression analysis.


FTIR measurements of resin conversion

The details of the technique for determining the degree of conversion, with depth for the RBC are contained in a previous article [6] and will be outlined below. Specimens were cured in a cylindrical split mold of stainless steel, 6.0 mm diameter by 16 mm long. Two stainless steel wedges were placed along the junction of the split mold with their edges protruding about 0.5 mm into the cylinder. The mold was placed on a glass slide and RBC was extruded into the mold until filled. A polyester film was placed on top of the mold followed by a glass slide and pressure was applied to condense the RBC and squeeze out the excess on the top. The glass slide was removed from the top and the RBC was cured for 30 s (18,480 mJ/cm2 ) by centering the light guide over the mold in contact with the polyester film, after stabilization of the light output. Then the mold, with the RBC specimen, was stored in the dark for 24 h. Following the storage period, the screws holding the mold together were removed and one of the wedges was gently tapped to split the cylindrical specimen along a central plane. Uncured material was carefully separated from the cured RBC with a scalpel. This work was done under safe lighting to prevent further polymerization taking place. Microscopic specimens were dissected with a scalpel at selected depths along the central part of each half cylinder using a binocular microscope with filtered light. The microscope reticule was used to determine the depth along the cylinder where specimens were dissected. Three cylindrical specimens were treated in the above manner and for each half-cylinder, three specimens were harvested at each depth. All specimens were stored in the dark until measurements were made. Conversion of the resin system of the RBC was done using transmission FTIR microscopy with a Nic-Plan Microscope combined with a Magna-IR 750 spectrometer (Nicolet, Madison, WI, USA), co-adding 90 scans at a resolution of 4 cm−1 . Conversion


was determined using the methacylate double-bond vibration at 1638 cm−1 and, as a reference, the aromatic skeletal absorbance from Bis-GMA at 1582 cm−1 was used.


Energy-conversion relationship

Radiant exposures, H, were determined for each depth where specimens described above were harvested from the cured cylinders of RBC, using the T(d) and the incident radiant exposure. The conversion at those depths was then matched with the respective H values and a plot of degree of conversion, DC, as a function of H was constructed. This relationship is termed the energy-conversion relationship (ECR), and provides a unique description of the DC that is produced by a specific H value within the RBC.


Depth of cure and energy-hardness relationship


Depth of cure

Depth of cure was determined using a scrape-back method. Stainless steel, split-cylindrical molds of 6 mm diameter and 12 mm length were used to prepare RBC specimens for testing. Molds were placed on top of a glass slide that was covered with a polyester film, and RBC was extruded into the top of the mold from the syringe containing the RBC. When filled, most of the excess at the top was removed with a razor blade, and then a polyester film was placed on top followed by a glass slide and the RBC was compressed into the mold while also squeezing out the remaining excess at the top. The glass slide was removed leaving a flat surface covered with the polyester film. Cured RBC specimens were made with the QTH lamp using 10, 20, 30 and 40 s exposures, which equated to 6160, 12,320, 18,480 and 24,640 mJ/cm2 radiant exposures to the RBC surface itself. The lamp was allowed to equilibrate before the RBC was exposed and the light guide was carefully centered on the cylinder with the light guide in contact with the polyester film. Four specimens were made for each curing condition, and after the curing step the molds with the cured RBC were stored in the dark for 24 h. After storage, the molds were separated and the cured RBC carefully removed. This and all following procedures were done in either reduced or filtered lighting conditions to prevent further polymerization of the RBC. Uncured material was removed and the end of the cylinder was then scraped with a stainless steel, composite placement instrument to remove all crumbly material and produce a hard surface. The lengths of the cured cylindrical specimens were measured to the nearest 0.01 mm using a digital caliper. Three measurements were made on each cylinder, rotating about one third revolution for each measurement. These measurements were averaged and provided the scrape-back depth, DSB , for each curing condition.


Knoop hardness measurements

Along with determining the DSB values, it was of interest to know the hardness values along the central axis of the cylindrical specimens. Each of the cylindrical specimens was marked with pencil lines placed on opposite sides to indicate a central plane. They were then fixed on top of a cylindrical, brass, polishing fixture with the lines parallel to the top of the fixture. A translucent self curing resin material (Triad


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DuaLine Visible Light Cure, Dual-Cure Reline Material, Dentsply International Inc., York, PA, USA) was syringed around the specimen until slightly above the pencil lines. After this material was hardened, the specimens were polished to the pencil lines, with water cooling, using sequentially finer grit polishing paper to a 4000 grit final polish. The specimens were then rinsed and dried with compressed air, followed by storage to dry completely before doing hardness measurements. Knoop hardness testing was done with a Buehler Micromet II micro-hardness tester (Buehler, Lake Bluff, IL, USA). The brass polishing fixtures with the RBC specimens were placed on the specimen stage of the test apparatus, which had x and y micrometer adjustments. The specimen was viewed through a microscope with a marker for the point of contact for the Knoop indenter. Each cylindrical specimen was oriented with its central axis aligned with the y-axis of the specimen stage and the x-axis of the stage set at the midline of the specimen. Hardness measurements could then be done at accurately determined depths by translating the specimen along the yaxis. Measurements were made using a 100 g load for 12 s dwell time. The same depths were used for all four specimens of each group giving four Knoop hardness numbers (KHN) for each depth, which were averaged. These average values were used to plot KHN depth profiles for each group.


Energy-hardness relationship

The average KHN for varying depth levels in the RBC could be paired with radiant exposure, H, values by using the T(d) and incident radiant exposure values, H0 , for each group. An energy-hardness relationship (EHR) could then be obtained by plotting all KHN values as a function of H.



Table 2 gives a summary of major parameters found from this work. A transmission relationship with depth was found to be T(d) = 0.6201 × 10−0.385d , (R2 = 0.9999). Fig. 1a shows the ECR for the RBC, which relates the DC with the internal radiant exposure, H. Extrapolation of the curve to zero conversion gives an H value of about 26 mJ/cm2 , and maximum conversion (56%) occurs around 30 J/cm2 , which is beyond the scale shown, but the curve is not changing very much at higher H values so for clarity in the region of H values where larger changes occur, the H scale was terminated at 10 J/cm2 as a convenience. Table 3 shows the mean values of DSB for RBC cured in 6 mm cylinders at the four different curing times. Analysis of variance and Tukey–Kramer post hoc comparisons show that all

Table 2 – Summary of results related to the ECR and EHR. T(d) = 0.6201 × 10−0.385d Max DC – 56% Max KHN – 101.5 DC@DSB – 20.2% (36% of Max DC) KHN@DSB – 0 H@DC = 0–22.3 mJ/cm2 HSB – 46 mJ/cm2

Table 3 – Scrape-back depths (DSB ) for four curing times (irradiance = 616 mW/cm2 ). Cure time (s)

DSB (mm)

10 20 30 40

4.97 (0.03)a 5.76 (0.09)b 6.24 (0.05)c 6.51(0.04)d

DSB values with different letters are significantly different, p = 0.01.

the DSB values are significantly different at a 1% level of significance. In Fig. 2b, the variation of KHN with depth for the same specimens is shown. The data points on the abscissa are the DSB values in Table 3, and they provide a good match to extrapolation of the curves to KHN = 0, which is in agreement with the results of Cook [1,2]. Radiant exposure values for the DSB values in Table 3 were calculated using the T(d) with each H0 , and the mean value for HSB is 46.1 (1.1) mJ/cm2 . Fig. 1b shows a plot of all the data points from Knoop hardness testing where the depth data has been converted to H values by using the T(d) and the H0 values for each group. Two separate curves are shown, the lower one being for the 10 s cure group, while the data for the 20–40 s cure groups seem to coalesce to justify a single curve. It was expected that the data from all four groups would merge to form a single curve. The upper curve, fit to the 20–40 s data, represents the more universal EHR. Using the value of HSB = 46 mJ/cm2 , and going to the ECR, this value of H coincides with a DC of about 20.2% or %MaxDC = 36% at the scrape-back depth. Fig. 2a shows depth profiles for %Max DC that were calculated using the ECR in conjunction with the T(d) and H0 of each group. Table 1 provides an outline of the two procedures for obtaining values for the attenuation constant, ˛, and HSB . Fig. 3 shows the recommended plot of DSB values against the Log H0 values and the same plot with the H0 values corrected for reflectance using the value from the T(d) relationship. The results are shown in Table 4 and the agreement is quite good. While the ECR and EHR can be compared for any given H value, it was of interest to construct a curve giving a direct comparison between hardness and conversion as Fig. 4 demonstrates.



A primary objective of this work was to establish and validate the tools and database (Table 2) for their use in other related studies, where the curing configuration is different than the stainless steel cylinder used to gather this information. The ECR is one of these tools, and has been explored in previous studies [6,7] with good success in predicting the DC as a function of depth into an RBC for different incident radiant exposures, H0 . Because the ECR provides a unique relationship between DC and internal H values, it holds the possibility to predict DC for a variety of situations. For example it may predict the H0 needed to obtain 80% of MaxDC at a specific depth into an RBC. It is however dependent on another tool, the transmission relationship, T(d), which for a given H0 is used to provide values of radiant exposure at specific depths. While


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Fig. 1 – (a) The ECR for two ranges of radiant exposure, displaying the degree of conversion (%) vs. radiant exposure. The upper curve is a continuation of the lower curve and is represented by the lower set of radiant exposures. (b) The EHR for two ranges of radiant exposure, displaying Knoop hardness numbers (KHN) vs. radiant exposure, is represented by the uppermost curve. The lower curve is indicative of a breakdown in the relationship between T(d) and H (see Section 4). The upper curve for each range defines the EHR.

these tools have been used successfully in the limited case of RBC contained in stainless steel cylinders [6,7], it is likely that they can be applied to other configurations, which is a goal of this work. There are some limitations to the use of the ECR, which should be explained. The ECR is valid only for the particular

RBC material for which it was produced, or for RBC materials of the same family (e.g. different shades), as long as the curing components are the same [6]. The T(d) relationship, however, is unique not only to the specific RBC, but also to the curing configuration; in the present case the stainless steel cylinder surrounding the RBC which influences how light is

Table 4 – Curing parameters obtained by two methods. Method one ˛

(cm−1 )

0.385 a

Corrected for reflectance.

Method two HSB

(mJ/cm2 ) 46.1


(cm−1 ) 0.387

H0SB (mJ/cm2 )

HSB (mJ/cm2 )




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Fig. 2 – (a) Calculated conversion depth profiles for four radiant exposures (6160, 12,320, 18,480 and 24,640 mJ/cm2 ), displayed as % Max DC vs. depth. (b) Measured hardness depth profiles for the same radiant exposures, displayed as Knoop hardness numbers (KHN).

transmitted. Therefore, a new T(d) would need to be generated to use the ECR effectively with other configurations. The ECR itself, although it was generated in the configuration of the stainless steel cylinder, is a unique relationship between DC and H, which should apply to other configurations. However, the ECR is dependent, to some extent, on the curing lamp that was used to generate it, as the efficiency of the lamp relative to absorption by the photoinitiator affects the DC values. Still, the same ECR can be used with other lamps by a correction for the relative efficiencies of the lamps [7]. The ECR produced in this study (Fig. 1) is similar to that found in a previous study [6], with some differences, as might be expected from a different lot of the RBC. An extrapolation of the ECR curve to DC = 0 gives a value for H (Table 2) of about 26 mJ/cm2 , which is a little larger than the 22 mJ/cm2 value found in the previous study. Although the difference is not large it might indicate a difference in the photoinitiator/amine components or an increase in the inhibitor level for this lot. In Fig. 2a depth profiles for DC are shown, that were calculated from the ECR and the T(d) for the four curing times examined.

The transmission relationship, T(d), is crucial to making conversions between internal radiant exposure values and depths within the RBC for a given H0 value. The usual method for obtaining transmission values for RBC materials is to make measurements on fully cured material. However, this method is inherently coupled with the assumption that, for applications where such a T(d) is used, differences in optical properties between uncured and cured material will not have a significant effect on measured results. Since the T(d) is so important a second method (Table 1) was examined to verify the values of the attenuation coefficient, ˛, and the value of HSB that are determined using the T(d) relationship derived from cured RBC material. This second method was described in Section 1, and utilizes measured values of DSB for RBC cured using various values of H0 . To accomplish this, cylindrical specimens were cured for four different lengths of time (10–40 s), and the 24-h DSB values were measured. Table 3 shows the mean values for each group. Using the T(d), values for HSB were determined for each group and the values were in good agreement with a mean value of

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Fig. 3 – Plot of scrape-back depths vs. Log of the incident radiant exposure for composite light-cured with four radiant exposures (6160, 12,320, 18,480 and 24,640 mJ/cm2 ), the curve to the left is corrected for reflectance of incident light.

46.1 (1.1) mJ/cm2 being calculated. The DSB values and their respective H0 values were used for the plots shown in Fig. 3, where the curve to the left used H0 values that were corrected for reflectance (38%) found with the T(d) relationship. Table 4 shows the comparisons between the two methods, and the agreement is quite good. This provides some assurance that the T(d) relationship, as measured, is valid for the purposes intended. A major objective was to develop an energy-hardness relationship, EHR, which could be used instead of, or in conjunction with, the ECR to characterize curing conditions of the RBC. This would be useful because it is easier to gather data with hardness measurements. To accomplish this, the same cylindrical specimens described above were utilized to obtain KHN values along the central axis of these cylindrical specimens. The mean values obtained for each depth provided the data for the KHN depth profiles shown in Fig. 2b, where the data points on the abscissa are the measured DSB values. The good agreement between these DSB values and the extrapolation of the curves shows that KHN = 0 at the DSB , in agreement with the findings of Cook [1,2]. It should be pointed out that the scrape-back surfaces were convex in shape and in this study only the central axis was considered. However, it seems reasonable to assume that the radiant exposure and resulting conversion and hardness would be the same for the entire scrape-back surface. This non-uniformity of radiant exposure over a cross-section of the cylindrical specimen suggests that the HSB value determined using the transmission relationship, T(d), might be overestimated. Non-uniformity in curing will be examined in a following article. The same data linking KHN to depth was transformed into KHN/H data sets and these were used to plot the presumptive


EHR relationship shown in Fig. 1b. It was expected that all the data would be consistent with a single curve, but it is clear that the data from the 10 s group forms a separate curve from the other three groups, the latter forming the basis for a single curve that defines the more universal EHR. There could be arguments made that this is a breakdown in reciprocity, based on polymerization kinetics, but a different explanation that may be considered involves a breakdown in the assumption that T(d) is valid for this particular value of H0 . This explanation proposes that, during the cure time of 10 s, the optical properties governing light transmission were not completely the same as for cured material. Because the uncured material has lower transmission, then use of the T(d) could result in some overestimation of the H values assigned to various depths within the RBC. Studies have shown that the transmission of fully cured RBC may be greater than for uncured RBC [18,22], with the amount of change dependant on the particular RBC [22]. However, during the curing process the RBC is between these two states for some or all of the time, depending upon the depth into the RBC. This is particularly pertinent for the 10 s cure time where the DSB is about 5 mm deep, which is 76% of the depth for a 40 s cure time. Spatiotemporal changes in light transmission may occur by consumption of the photo-initiator molecule [23,24], or by changes in refractive index of the resin system [25,26]. When light is initially incident on the RBC (t = 0) the transmission of light is controlled by the optical properties of uncured material, but polymerization starts quickly afterwards, and most effectively near the top where the light intensity is greatest. As time progresses, the optical properties will shift toward those of cured material in some proportion of the DC, which will vary with depth. However, as the upper parts become more transparent, light energy will be transmitted deeper more efficiently. This dynamic process continues until the light is turned off at 10 s, and an initial state of cure is established that varies with depth. At what point in the increasing DC the properties change to provide transmission similar to cured material is not known; there may be parts of the composite near the top where that is the case, but deeper in the material it is less likely. Over the next 24 h a significant amount of post-irradiation curing may take place [19,27–32], which will increase the DC and the KHN to the values that were measured. However, the H values at a given depth were determined by a variably reduced transmission during the 10 s exposure time. As an example of the post-irradiation curing, the DSB measured immediately after the curing step for the RBC is about 0.5 mm shorter than after 24 h. Since the DC at the scrape-back depth is about 20% and KHN is zero, that means for the 10 s group these values would be valid at around 4.5 mm immediately after curing, but after 24 h they are DC = 34% and KHN = 20. When a 20 s cure is used, the first 10 s are a repeat of the above, but there is another 10 s where the depth only advances by 0.8 mm, so that much of the extra curing time is devoted to better curing of the entire 5.8 mm of the RBC. This is perhaps why when cure times of 20 s or more are used the T(d) relationship works for determining H values. Assuming that the above interpretation is correct and that the KHN values should be associated with specific H values,


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Table 5 – Change in DSB and HSB with age of the composite material (20 s cure, H0 = 12,320 mJ/cm2 ). Age (months)

DSB (mm)

HSB (mJ/cm2 )

0 3 12 17 22

5.82 (0.03)a 5.78 (0.11)ab 5.60 (0.06)b 5.40 (0.04)c 5.30 (0.06)c

43.88 45.46 53.33 63.68 69.58

DSB with different letters are significantly different, p = 0.05.

Fig. 4 – Plot of % Maximum hardness (KHN) vs. % Max degree of conversion.

then the discrepancy in the H values is determined by the separation of the two curves. If the data points for the 10 s curve are translated laterally to join the main curve, then the corrected H values, when used with the T(d) relationship to determine depth values, allows calculation of a KHN depth profile that is identical to the one that was measured. This may be taken as confirmation that the KHN values are related to specific H values and reinforces the conclusion that for the 10 s cure (6160 mJ/cm2 ) the T(d) relationship is unreliable for assigning H values correctly. Therefore, somewhere below 12 J/cm2 the EHR starts to lose accuracy in predicting the values of KHN for specific depths when using T(d) to determine the radiant exposure, and this may also be true for the ECR. In Fig. 2a the dashed curve for the 10 s profile shows an estimated correction based on new H values determined for the KHN measurements. The fact that two methods of determining the attenuation coefficient and HSB were in good agreement, seemed to validate the use of the T(d) even for a 10 s cure. However, the second method is based solely on the value of the scrape-back depths. The value of HSB is fixed as 46 mJ/cm2 , and does not change, as it represents a physical state of the material that defines DSB , and as can be seen in Fig. 1b the curve representing the 10 s KHN data goes to zero at that value as does the other curve representing the 20–40 s data. Therefore the plot for method 2 gives values for ˛ and HSB that agree with those determined by T(d), but it does not provide validity for the accuracy of the KHN values at other depths in the RBC when a 10 s cure time is used. A comparison of the ECR and EHR (Fig. 1a and b) shows that where the EHR curve goes to zero at 46 mJ/cm2 , the DC is 20.2% (36% MaxDC). If you compare the depth profiles in Fig. 2a and b, the DSB values match with 36% MaxDC for each group. This is a partial verification of the accuracy of the calculated conversion profiles.

While the ECR and EHR can be compared directly to cross reference values, a direct relationship between conversion and hardness would be convenient. Fig. 4 shows the relationship between %max KHN and %Max DC. This curve reflects the fact that the rates of change of the two parameters are different, leading to a relationship that would be difficult to fit accurately with a simple regression curve. Linear fits to data have been tried with modest success [15–18], but in looking at the data points for those studies, you can, perhaps, visualize the shape of this curve. A last item that does not impact the results presented here, but does affect related work is worth discussing. The results of this work were part of a larger set of studies that were to be connected, with this work forming the basis for comparisons to other curing configurations. The DSB value is representative of the cure for a particular H0 , and this was one key marker for judging other results. However, all this work took place over a 22 month period, in which there were some breaks in the ongoing work. After each break it was found that the DSB value was shorter, which led to examinations of equipment, techniques, etc. to determine the cause, but in the end it was determined that the material had to be changing. Table 5 shows the values of DSB at several time periods, with the results of statistical analysis indicated, using analysis of variance and Tukey–Kramer comparisons. It seems unlikely that the T(d) relation was affected so the HSB values were calculated and are shown in the same table. The cause of the change is unknown, but these changes have meant that much of the related work needed to be redone to be consistent with the same time frame for measurement of DSB for the stainless steel cylinder. The ECR and EHR are affected as well, but it is assumed that the basic relationship between the two would remain and that the radiant exposure scale for each would have to be shifted to conform to the new value of HSB at each time frame when data was collected. This seems to be working so far, but it is a lesson that materials can change, so that long programs may be problematic. It must be said that these changes, as difficult as it has made the completion of these studies, does not imply that the material was not suitable for clinical use.



The objectives of creating tools and information to be used for examining the curing characteristics of an RBC were accomplished. In particular the development of an EHR will facilitate data acquisition. The limitations on the use of the ECR and EHR were determined, namely that radiant exposures below

d e n t a l m a t e r i a l s 3 0 ( 2 0 1 4 ) e125–e133

12 J/cm2 are to be avoided if accuracy is to be achieved. This limitation seems to be attributable to a failure of the assumption that a transmission relationship, derived from cured composite material, is suitable for all radiant exposures. In particular, low radiant exposures may be problematic.


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Curing characteristics of a composite - part 1: cure depth relationship to conversion, hardness and radiant exposure.

As the first part of a larger study on curing characteristics of a resin-based composite (RBC), the major objectives were to create an energy-hardness...
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