3.1. Influence of photopolymerization parameters
This part involves finding a reliable model for maximizing the factors that influence the efficiency of the polymerization process. The aim is to optimize the conversion degree using an experimental design.
BoxBehnken design
The BoxBehnken design was used to optimize the degree of conversion, which depends on three factors (irradiation time, intensity, distance between sample and light), the design results in a second order model. 15 tests (12 tests plus 3 center points) were performed, for each test, three repetitions were carried out. The matrix of tests and their responses are shown in Table 2.
Table 2
BoxBehnken design matrix
Test

Timea) [s]

Distance [mm]

Intensity
[mW cm− 2]

DCb) [%]

1

10

0

1450

49.3

2

60

0

1450

63.8

3

10

20

1450

48.6

4

60

20

1450

59.3

5

10

10

600

45.8

6

60

10

600

59.4

7

10

10

2300

52.6

8

60

10

2300

63.9

9

35

0

600

59.2

10

35

20

600

54.9

11

35

0

2300

62.2

12

35

20

2300

59.4

13

35

10

1450

59.3

14

35

10

1450

59.4

15

35

10

1450

59.4

a)Photopolymerization time; b)conversion degree calculated by FTIR spectroscopy with ATR 
The experimental matrix consists of a BoxBehnken type design with three factors on three levels each, with a central point (the test where all the factors are adjusted to their mean). The time was varied from 10 to 60 s, while the intensity was set from 600 to 2300 mw cm− 2 and the distance was changed from 0 to 20 mm.
The analysis of the results was done with Minitab, a response model is established by neglecting interactions of order 3. Eq. 2 represents the model of the conversion rate by the BoxBehnken design.
With, t: time of polymerization (s); D: distance between the composite and the light (mm) and I: intensity of the light (mW cm− 2).
The model shows that the interaction between factors can be neglected as the coefficient value is not significant.
This model includes second order terms, proving that certain factors follow a nonlinear trend. Figure 3's main effect diagram shows that the polymerization time follows a secondorder curve, while the other factors exhibit a linear behavior. Time is also the main factor with the highest coefficient, it reaches a plate around 40 s. On the other hand, distance is the least significant factor, being inversely proportional to the degree of conversion, while the intensity of the light source is directly proportional.
Analysis of variance
The analysis of variance (ANOVA) indicates that the model has acceptable correlation coefficients.
The critical Fisher factor was obtained using the Fisher table, with F = 147.2, which is significantly higher than its critical value Fc = 2.8. The R2 and R2 adjusted value were 99.2 and 98.6, respectively, indicating that the model is therefore valid.
Factors optimization
The model allowed the selection of factors to maximize the degree of conversion. According to the literature, the achievable conversion degree for composite resins is around 60%.[2] Values above this rate are considered favorable.
The distance factor is found to be less significant, allowing for a distance value of 5 mm to facilitate polymerization in the mouth for the operator. Figure 4 displays the favorable combinations of polymerization time and light source intensity in white area, while the blue area indicates the conversion rate values below 60%. To optimize energy and heat generation, the optimal point is 40 seconds of polymerization time, 5 mm of distance, and an intensity of 1500 mW cm2, as determined by the preset intensity of the dental lamp. This composition results in a conversion rate of 61.2%.
Figure 5 displays the infrared spectra of the composite at different polymerization time and using the optimum values of intensity and distance obtained by the BoxBenkhen design model, 1500 mw cm2 and 5 mm respectively. The figure shows the decrease in the elongation vibration peaks of methacrylate double bonds at 1636 cm1 as a function of polymerization time.
3.2. Analysis of monomer released in saliva
This part reports the quantification of TEGDMA released by the resin obtained with the optimized parameters. The purpose of this analysis is to measure the amount of the potentially toxic monomer that may be released into the organism while the composite is in the oral environment.
To simulate the aging of resins in an in vitro system, four different media were used. An artificial saliva with three different pH values (acidic pH of 3.5, neutral pH of 7, and basic pH of 10)[18] and an ethanol/water medium with a 75% v/v ratio were used as two of the media.[15] The other two media were saliva with different pH values, which were used to simulate changes in pH when consuming different meals. Meanwhile ethanol was used to accelerate the degradation and aging of the composite resin as it is a good solvent for the monomers.
The experiment involved three factors: (1) the medium (artificial saliva at three different pH values and ethanol at 75%), (2) the incubation temperature (37°C and 50°C), and (3) the incubation time (1 and 7 days).
Preparation of samples
Cylindrical specimens of 5 mm diameter and 2 mm thickness of the “NT Premium Enamel B2” resin composite were prepared using a Teflon mold. The composites were compressed in the mold between two glass plates and polymerized at room temperature for 40 s using an “Eighteeth curing pen” LED dental lamp with an intensity of 1500 mW cm2 at a distance of 5 mm.
The polymerized specimens were removed from the mold, and flushed with ethanol. Then, they were immersed in 1 ml of aging medium in a 2 ml capped vial. The vials were subsequently incubated in an oven at the designated temperature for the appropriate length of time.
The analysis was conducted using highperformance liquid chromatography (HPLC). Table 3 summarizes the samples prepared, their aging conditions and the results obtained for the samples submitted to different conditions.
The study findings suggest that the amount of TEGDMA released is influenced by the type of medium, pH, and incubation temperature. Moreover, the release of TEGDMA is increased with the residence time of the composite in the medium.
Table 3
Resin composite aging conditions and HPLC analysis results
Sample

Medium

pH

Temperature
[°C]

Time [days]

Massa [mg]

Areab [mV*mV]

TEGDMA Concentrationc [mg L− 1]

TEGDMA quantity [µg g− 1]

Cp1

ASd

7

37

1

69.6

33983

0.5

0.01

Cp2

AS

3.5

37

1

74.9

1633419

26.7

0.35

Cp3

AS

10

37

1

61.3

41939

0.7

0.01

Cp4

AS

7

50

1

46.4

43653

0.7

0.02

Cp5

EtOH/water

7

37

1

62.4

1975042

32.2

0.51

Cp6

AS

7

37

7

66.3

237474

3.8

0.06

Cp7

AS

3.5

37

7

67.3

2660754

43.4

0.64

Cp8

AS

10

37

7

64.9

698364

11.4

0.17

Cp9

AS

7

50

7

68.9

369540

6

0.09

Cp10

EtOH/water

7

37

7

77.8

3690466

60.3

0.77

Cp11e

EtOH/water

7

37

7

67.5

23141306

378.1

5.60

ainitial mass of the sample before degradation; barea of the TEGDMA peak obtained by HPLC at 8.6 minutes; cconcentration of TEGMA in the sample determined by the calibration curve; dartificial saliva;eunpolymerized sample 
The Table 3 displays the effect of the degree of conversion on monomer release in saliva. The Cp11 sample unpolymerized had the greatest amount of released TEGDMA. This release represents the dissolution and migration of TEGDMA in artificial saliva. As the conversion degree increased after polymerization, the number of unbound monomers decreased, resulting in a small amount of TEGDMA released in all polymerized samples.
The amount of TEGDMA released varies from 0.01 to 0.77 µg g1. This indicates that HPLC is a reliable method for determining and quantifying the monomers. Figure 6 shows the amount of TEGDMA measured for each type of medium, demonstrating that the type of aging medium used has a real effect on the release of TEGDMA.
As expected, ethanol/water at 75% was the medium with the highest release of TEGDMA. This high release is attributed to the ability of ethanol to be a good solvent for monomers, including TEGDMA. The artificial saliva with acid pH of 3.5 also showed a significant amount of released. The low pH values promote the release of monomers as well as the degradation of composite resins.
The neutral medium showed stability during the 7 days of incubation. This stability is less evident during incubation at high temperature. The basic medium, on the other hand, showed stability in the short term, but began to release monomers gradually.
3.3. Modeling of the kinetic release
TGA analysis
Thermogravimetric analysis provides the mass loss as a function of time and temperature. It was carried out on two samples (Cp10 and Cp7) that have undergone different aging conditions and exhibit the highest TEGDMA release. As a reference, an untreated sample (Cp0) was also analyzed by TGA. These three samples were submitted to three heating rates (5, 10 and 20°C min1).
The TGA curves of sample Cp7 for the three heating rates are shown in Fig. 7. This thermogram displays three degradation zones that are almost similar for all samples.[22] For temperatures below 300°C, the degradation was negligible due to the high thermal resistance of the composite. The main degradation was observed in the temperature range between 300°C and 500°C, where a rapid mass loss occurs due to the degradation of the polymer chains. Above 500°C, the residue is due to the inorganic part of the composite.
The heating rate affects the degradation temperature profiles. The higher the heating rate, the more degradation is shifted to high temperatures due to degradation kinetics. For example, at the heating rate of 5°C min1 the sample reaches 5% degradation at a temperature of 352°C, while the sample at the heating rate of 20°C min1 does not reach the 5% degradation until reaching a temperature of 393°C.
Under the influence of the kinetics of degradation, the exploitation of these different curves allowed the determination of kinetic models.
Kinetic model of release
The kinetic equation of degradation is equivalent to that of chemical kinetics, expressed as:
$$\frac{\varvec{d}\varvec{a}}{\varvec{d}\varvec{t}}=\varvec{K}\varvec{f}\left(\varvec{a}\right)$$
3
Where, f(α) is the kinetic model, and k is the rate constant obtained by the Arrhenius law:
k =\(\varvec{A}\varvec{e}\varvec{x}\varvec{p}(\frac{{\varvec{E}}_{\varvec{a}}}{\varvec{R}\varvec{T}})\) (4)
The variable α represents the mass lost during the thermogravimetry experiment:
α = \(\frac{{\varvec{W}}_{\varvec{i}}{\varvec{W}}_{\varvec{f}}}{{\varvec{W}}_{\varvec{f}}}\) (5)
Where Wi is the initial mass, and Wf is the final mass. Finally, the combination of Equations 3 and 4 results in the following formula:
$$\frac{\varvec{d}\varvec{a}}{\varvec{d}\varvec{t}}=\varvec{A}\varvec{e}\varvec{x}\varvec{p}(\frac{{\varvec{E}}_{\varvec{a}}}{\varvec{R}\varvec{T}})\varvec{f}\left(\varvec{a}\right)$$
6
Various methodologies can be applied to determine kinetic triplet values. The most common approach is to select a suitable kinetic model from the existing ones. The majority of these models are derived from the modified version of the empirical equation of SestakBeggren, refer to Eq. 7, by adjusting the constants c, n, and m. This technique is referred to as "model fitting". [20]
f(α) = c(1α) nαm (7)
Combining the Eq. 7 of SestakBeggren model with the kinetic Eq. 6 yields the following relation:
ln (\(\frac{\frac{\varvec{d}\varvec{a}}{\varvec{d}\varvec{t}}}{{\left(1\varvec{\alpha }\right)}^{\mathbf{n}}{\varvec{\alpha }}^{\mathbf{m}}}\)) = lncA \(\frac{{\varvec{E}}_{\varvec{a}}}{\varvec{R}}\frac{1}{\varvec{T}}\) (8)
The Eq. 8 can be expressed as a linear function of the form y = bax, with x = 1/T .
The equation for this model requires the determination of the values of α, t and T, which can be obtained from TGA measurements. However, the values of the constants n and m are still unknown. To determine them, a MATLAB program was used to optimize the correlation coefficient (r) of Eq. 8, with the aim of finding the values of n and m that produce a Pearson correlation coefficient closest to 1. [20, 21]
The straightline regression of the degradation data (Fig. 8) obtained by ATG on the 3 samples and at different speeds was used to determine the values of the constants. These data, given in Table 4, were finally exploited to measure the activation energies for each sample.
Triangles depict the raw TGA data and the line displays the corresponding calculated regression.
Table 4
Calculated values of constants obtained by fitting the model
Sample

Heating rate [°C min− 1]

na)

ma)

r b)

Ea
[Kj mol− 1]

Cp0c

20
10
5

0.8
5.5
1.7

1.7
1.2
2.3

0.97
0.95
0.96

113
119
65

Cp7

20
10
5

5.7
20.4
12.2

2
1.9
1.8

0.97
0.96
0.95

106
109
72

Cp10

20
10
5

49.9
29.3
19.2

1.2
1.8
2.0

0.95
0.95
0.95

221
111
85

constants of SestakBeggren determined by MATLAB; b)Pearson correlation coefficient; c)untreated sample
Given the correlation coefficients greater than 0.95 (Table 4), the validity of the kinetic model is confirmed for the n and m values determined. The n and m values have a variability depending on the samples and heating rates, which shows that the kinetic model does not have a constant equation with fixed coefficients. This feature highlights the advantage of using this method to determine variable coefficients, adapted to our conditions, compared with the application of preexisting models.
Concerning the activation energies, it can be seen that for high heating rates (10 and 20°C min1), the activation energy values are close. They are significantly higher than the values obtained at a heating rate of 5°C min1. This result suggests that excessive heating rates do not allow the system to reach a correct equilibrium and affect the Ea measurements. Consequently, we considered the data obtained at 5°C min1 to determine the coefficients n and m and subsequently the activation energy.
The activation energies of the three samples determined at a heating rate of 5°C min1 are quite similar. Sample Cp0, which was not subjected to conditions that could degrade the resin, shows a lower activation energy, proving the presence of residual monomers in the resin and facilitating its degradation. In contrast, sample Cp10, which was exposed to the most favorable conditions for the release of monomer (as shown in Table 3), has the highest activation energy, meaning that it will require more energy to degrade. Sample Cp7, which has a monomer release rate between the two samples (as shown in Table 3's HPLC measurement), exhibits an intermediate activation energy.
Finally, these study on activation energy highlights the importance of achieving an optimum photopolymerization conversion to increase the activation energy of the sample, thereby improving its resistance to usage conditions. In addition to its health implications, the reduced presence of residual monomer in the resin contributes to a longer material lifetime.