Modeling curing kinetics and degree of conversion of visible light curing resin based composites (VLC RBC) using a time dependent reaction constant
P33
B. MÖGINGER1, T. HAENEL1,2, J. STEINHAUS1,2, B. HAUSNEROVÁ2 and R.B. PRICE3
Objectives: IR measurements show that the degree of double bond conversion of camphor quinone initiated VLC RBC never reach 100%. This is mainly attributed to the increase of i) viscosity during polymerization and ii) glass temperature. In principle, this means that the reaction constant depends on time. The aim of this study was to calculate the time dependent degree of conversion (DC(t) using an appropriate “reaction function” which generates experimentally found final DC in the range of 50 to 90% depending on irradiation conditions. Table 1: Fit parameters for time range of 15 s
Polymerization kinetics of VLC RBC The growth reaction of the polymer chain is given by kucg
Irradiance [mW/cm²]
A ( DMA) n ( DMA) DMA A ( DMA) n1 ( DMA)
dc
dt
(t )
kcg * c
DMA
having the solution [1] c DMA (t ) c0DMA * e
k cg * t
treac Q tgrow DC3min Grandio
(1)
(t )
c0DMA * e
Fig. 1: Effect of growing time constant tgrow
t
t 0reac
Bluephase 16i High
Bluephase 20i High
Celalux I
Bluephase 20i Turbo
661 (1.9)
950 (1.0)
1460 (5.4)
1655 (43)
2196 (9.3)
7.5 (0.6)
6.3 (0.44)
5.4 (0.4)
4.3 (0.3)
0.64 (0.23)
0.49 (0.13)
0.54 (0.09)
2.2 (0.1) 52.3 (1.1)
1.8 (0.06) 53.8 (2.07)
1.8 (0.1) 55.8 (0.9)
4.9 (0.2) 0.50 (0.13) 1.6 (0.1) 55.4 (0.9)
9.7 (1.1)
7.4 (0.2)
6.7 (0.5)
0.62(0.17)
0.58 (0.05)
0.56 (0.13)
2.4(0.1) 50.2(0.9)
2.1 (0.1) 52.1 (0.6)
2.0 (0.1) 53.0 (0.2)
Arabesk
Assuming that the radical concentration becomes constant after a short initiation time because of the high irradiance of the light curing units leads to a simple differential equation. DMA
Bluephase 20i Low
(2)
treac Q tgrow DC3min
6.5 (0.5) 0.54 (0.15) 1.9 (0.1) 53.0 (1.3)
0.28 (0.05) 1.3 (0.1) 57.0 (1.3) 5.3 (0.3) 0.44 (0.07) 1.6 (0.0) 53.9 (0.5)
with concentration of DMA monomers c0DMA, global reaction constant kcg and reaction time constant t0reac. The reaction time constant t0reac shows a square root The monomer concentration for long times tends to dependency on irradiance, Fig. 4. zero meaning a DC of 100% [2,3]. Due to the polymerization reaction the viscosity of the resin-polymermixture increases with time, and after reaching a certain degree of polymerization the resin vitrifies. Both processes decrease the reaction rate. This can be taken into account using a time dependent reaction function consisting of a constant part t0reac’ which describes the reaction at small DC where the viscosity Fig. 2: Effect of pre-exponential factor Q is hardly affected by polymerization and a time dependent part Q which accounts for effects of Results polymerization and vitrification and grows due to tgrow. Equation (5) fits well the data in a time range of 1.5 1 0 0 t to 2 t , Fig. 3, which can be considered as the kcg (t ) reac reac (3) t range of primary curing. The fit parameters are t grow 0 t ' Q * e tabulated in Table 1. The increase of DC in the long term range is not reproduced as equation (5) Fig. 4: Irradiance dependency of reaction time constant t0reac Introduction of (3) in (1) provides the modified solution: approaches its limit. kucg
A ( DMA) n ( DMA) DMA A ( DMA) n1 ( DMA)
reac
c
DMA
(t ) c
DMA 0
*e
t0 reac
t t 0 ' Q * e grow * reac 0 t reac ' Q t
t '
t grow
Conclusions
t 0reac '
• The time depend reaction function yields a correction term restricting the final DC of the primary curing process to t
(4)
Q DC final 1 0 t ' Q t reac
The time dependent DC is given by: t grow
t t 0 Q * e grow * reac 0 (5) t reac ' Q t
t
0 c DMA (t ) t reac ' DC(t ) 1 DMA 1 e c0
t 0reac '
constant 1
which is close to 50% for both VLC RBC. • The further DC increase to 68% (Arabesk) and 64% (Grandio) has to be attributed to post-curing which must have a significant different time dependency. • Now primary and post-curing can be separated. • The reaction rates expressed by t0reac show a square root dependency for both commercial VLC RBC predicted from theoretical considerations [4]. • The DC data exhibits scatter in the order ±7% before irradiation. As the reason of the scatter is unknown baseline data has to be shown if reaction rates are determined using IR spectroscopy based DC data.
c)
correction term K ( t )
The long term limit of (5) yields a final DC less than 100%, Fig 1. and 2.
Materials and light curing units (LCU) VLC RBC: Arabesk TOP OA2 (microhybrid) and Grandio OA2 (nanohybrid) supplied by VOCO, Germany. LCU: Celalux I, monowave, VOCO, Germany Bluephase 16i, monowave, Ivoclar Vivadent, Liechtenstein Bluephase 20i, polywave, Ivoclar Vivadent, Liechtenstein
grow t 0reac '
References:
Fig. 3:Comparison of measured data and fits
Affiliations and Contact: Acknowledgements: This study was supported by the German Ministry of Education and Research. Grant No.: 17081X10. The authors also thank Voco GmbH for supplying dental resins and LCU.
[1] Steinhaus J.et al, Dent Mater, 30 (2014) 372-380 [2] Ferracane J et al, Dent Mater, 1 (1985) 11-14 [3] Rueggeberg F et al, Dent Mater, 6 (1990) 241-249 [4] Andrzejewska E, Progress in Polymer Science,26 (2001) 605–665
e-mail:
[email protected] 1.
Department of Natural Sciences, Bonn-Rhein-Sieg University of Applied Sciences, Rheinbach, Germany
2.
Faculty of Technology, Tomas Bata University in Zlín, Zlín, Czech Republic
3.
Faculty of Dentistry, Dalhousie University, Halifax, Canada
