Abstract
During the curing process of light curing dental composites the mobility of molecules and molecule segments is reduced leading to a significant increase of the viscosity as well as the ion viscosity. Thus, the kinetics of the curing behavior of 6 different composites was derived from dielectric analysis (DEA) using especially redesigned flat sensors with interdigit comb electrodes allowing for irradiation at the top side and measuring the ion viscosity at the bottom side. As the ion viscosities of dental composites change 1–3 orders of magnitude during the curing process, DEA provides a sensitive approach to evaluate their curing behavior, especially in the phase of undisturbed chain growth. In order to determine quantitative kinetic parameters a kinetic model is presented and examined for the evaluation of the ion viscosity curves. From the obtained results it is seen that DEA might be employed in the investigation of the primary curing process, the quality assurance of ingredients as well as the control of processing stability of the light curing dental composites.
1
Introduction
Light curing dental resin composites are used as an alternative to amalgam fillings now for over 40 years. However, in spite of their long availability in dentistry and a lot of research work in optimizing their performance and endurance, the primary curing within the initial stages of irradiation, in particular the curing kinetics, was out of focus for a long time.
Some first attempts to investigate the primary curing process of dental resin (composites) were made in the 90s. It is known that most of the curing process happens within the first 10–20 s after irradiation. In order to obtain reliable data a method having a time resolution of minimum five readings per second is required. Furthermore, the experimental conditions and boundaries should be chosen very close to application procedures in dentistry. The methods employed for real time monitoring of the curing process include (i) optical differential scanning calorimetry (DSC) , (ii) shrinkage measurements , (iii) FT-IR spectroscopy in the ATR mode show that in the final cured state remain 20–25% unreacted MA groups , and (iv) dielectric analysis (DEA) using frequencies in the kilohertz range.
DEA has been used to monitor curing reactions of epoxy resins and optimizing RIM processing of polyurethanes . A thorough overview of real-time in situ applications of DEA is given by NAHM . The first applications of DEA to dental resins and resin composites were limited because of the necessity to irradiate through parallel arranged capacitor plates set up to measure the dielectric constant frequency and time dependently. Due to this technical obstacle DEA was considered to be hardly applicable to light curing dental resins and composites and mainly applied to auto-curing resins .
The situation changed with the upcoming of small and flat sensors such as
- •
IDEX-sensors having interdigit comb electrodes with distances of 115 μm, 100 μm and 30 μm and allow for to measure the local curing processes within a layer above the sensor surface having the thickness of the electrode distance and
- •
monotrode sensors measuring an overall dielectric constant of samples having a thickness of a few millimeters .
Both sensor types allow for a dentist-like handling of the light curing dental resin composites with respect to procedure and sample mass. In order to gain information of degree of conversion or curing kinetics one requires only the time dependent change of the dielectric constant–more precisely: the change of the conductivity of the sample is the relevant quantity describing the actual curing state. As the sample is irradiated from the top and the DEA measurement is performed at the bottom, it can be investigated how the curing behavior is affected by the initiator content, different monomers and monomer ratios, or the thickness of sample .
The frequency and time dependent dielectric loss consists of a conductivity part due to the motion of ions in the resin and a dipole part due to the orientation of polar groups of the resin molecules.
ε ″ r ( ω , t ) = σ ion ( ω , t ) ε 0 ω + ε ″ dipole ( ω , t )
with dielectric loss the sample <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='ε″r’>ε′′rε″r
ε ″ r
, ion conductivity σ ion , dielectric susceptibility ɛ 0 , frequency ω and dielectric loss of dipoles <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='ε″dipole’>ε′′dipoleε″dipole
ε ″ dipole
. If there are sufficient ions in the resin they dominate the dielectric loss of resins completely. Therefore, the contribution of the dipoles to the dielectric loss is negligible in the phase of primary curing. During curing reactions the dielectric loss changes significantly because the ion conductivity σ ion decreases with the ongoing polymerization and cross-linking. In analogy to the viscosity in rheology one defines the ion viscosity η ion
η ion ( ω , t ) = 1 σ ion ( ω , t ) = 1 ε 0 ω ε ″ r ( ω , t ) 1 − ( ε ″ dipole ( ω , t ) / ε ″ r ( ω , t ) ) ︸ < < 1 in resins ≈ 1 ε 0 ω ε ″ r ( ω , t )
which is the quantity considered to describe the curing reaction. Investigations of Zahouily et al. showed that the ion viscosity is a function of ion mobility μ , ion concentration c ion and ion charge q .
η ion ( ω , t ) = 1 μ ion ( ω , t ) * c ion ( t ) * q ion ( t )
A change of the measured ion viscosity is caused either by a change of the ion mobility due to an increase of the viscosity of the curing resin or by further reactions affecting the ion concentration or ion charge, respectively. This also indicates that ion viscosity measurements become problematic if the ion concentration in the resin is very small, e.g. in the case of very pure resins. The presence of filler particles affects the ion viscosity in two ways:
- 1.
Decrease of the ion viscosity The filler particles increase the ion concentration of the cured resin during the mixing process due to ionic impurities and makes the DEA functioning.
- 2.
Increase of the ion viscosity The filler particles represent inert material and therefore they dilute the resin due to the volume content.
The rheological viscosity of particle filled liquids shows a significant increase with the filler content. It is obvious that the mobility of ions is only affected by the viscosity of the pure liquid in which the ions move driven by an alternating electric field as long as there are no side reactions, e.g. adsorption of initiator and accelerator molecules on the filler surface.
Up to now there has been no attempt to link the ion viscosity measured by DEA to the curing reaction in a quantitative manner. Therefore, this paper focuses on the question if the time dependent ion viscosity is able to provide information of the curing process and how it is linked to the degree of conversion.
2
Theoretical considerations of the reaction kinetics
The samples are irradiated from the top with a very high intensity. This leads to a very fast activation of almost all camphor quinone molecules (CQ) and subsequently amine co-initiator molecules after a certain initiation time. As the molecules of the initiator system are homogeneously distributed in the resin, there is a mean distance between them determined by their concentrations. From an amine ion radical or an amine radical the polymerization reaction starts and the macromolecule is growing in a random walk. This means that two neighboring polymer chains have to grow to a certain length before cross-linking can take place. Therefore, one has to distinguish clearly between the polymerization process at the beginning and the later occurring cross-linking process. The polymerization at the beginning is an “undisturbed chain growth” during the first steps. It is obvious that the phase of ucg comes to an end if the glass transition temperature of polymer chain exceeds the temperature of sample. There are two processes increasing the glass transition temperature ( T g ):
- 1.
gradual increase of the glass transition temperature T g : the polymerization continuously increases the molecular weight of the macromolecule and, as a consequence, the glass transition temperature.
- 2.
sudden increase of glass transition temperature T g . Cross-linking typically doubles the molecular weight of the macromolecule and generates sudden increases of T g .
If the glass temperature T g of the resin surmounts the sample temperature T sample , the chains can only grow in a diffusion controlled manner. Then the polymerization rate as well as the cross-linking processes slow down significantly.
The rheological viscosity of polymers depends linearly on molecular mass as long as the chain lengths are too short to form entanglements indicated by the critical molecular weight M crit . The ion viscosity η ion can be considered as a measure of the mobility of a charged probe on the molecular level in a viscous surrounding. Therefore, it has to be proportional to the rheological viscosity η rheo after the initiation phase and to the molecular mass M of the growing chains as long as the resin is above T g and the molecular weight does not exceed the critical molecular M crit .
η ion ( t ) ∼ η rheo ( t ) ∼ M ( t )
with η ion ; ion viscosity, η rheo ; viscosity of melt or monomer liquid, M ; molecular mass.
The initiator molecule is partly brought to an excited long living triplet state which allows for a reaction to radicalize the non-light sensitive co-agent molecule:
I + A → electron transfer k init I 0 , h ν I − • + A + • ︸ ion radicals → proton transfer I • + A • ︸ radicals
The kinetics of all possible initiation reactions is described in detail by . For our purpose it is sufficient to assume an instantaneous generation of radicals for the first approximation which only depends on the depth due to the intensity reduction caused by absorption and scatter of light. Then the relevant initiation time is very short and can be considered as a reaction delay.
The undisturbed chain growth reaction is started either by an amine ion radical <SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='A+•’>A+∙A+•
A + •
or an amine radical <SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='A•’>A∙A•
A •
, which reacts with neighboring dimetharcylate monomers (DMA):
Start reaction : A • + D M A → k start A − ( D M A ) • Growth reaction : A − ( D M A ) n − ( D M A • ) + D M A → k ucg A − ( D M A ) n + 1 − ( D M A • )
with k start ; reaction constant of amine radicals, k ucg ; reaction constant of undisturbed chain growth.
The concentration of radicalized initiator molecules <SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='c0initiator’>cinitiator0c0initiator
c 0 initiator
is small compared to the DMA monomers concentration. For high light intensities it is depth dependent but not time independent. Then the undisturbed chain growth reaction is almost completely determined by the reaction constant k ucg . Under this condition the reaction rate is given by a linear differential equation in terms of c DMA :
d c D M A ( t ) d t = − k ucg * c 0 initiator ( x ) * c D M A ( t )
with c DMA , concentration of DMA monomers; <SPAN role=presentation tabIndex=0 id=MathJax-Element-13-Frame class=MathJax style="POSITION: relative" data-mathml='c0initiator’>cinitiator0c0initiator
c 0 initiator
, concentration of radicalized initiator molecules.
Solving (2.2) yields the time dependent decrease of the DMA monomer concentration:
c D M A ( t ) = c 0 D M A * e − k ucg * c 0 initiator ( x ) * t
Then the time dependent degree of conversion DC( t ) is given by:
D C ( t ) = c 0 D M A − c D M A ( t ) c 0 D M A = 1 − c D M A ( t ) c 0 D M A = 1 − e − k ucg * c 0 initiator ( x ) * t
This corresponds to a linear relationship in a semi-logarithmic representation:
log ( 1 − D C ( t ) ) = − k ucg * c 0 initiator ( x ) * t
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