A study of polymerization shrinkage kinetics using digital image correlation

Highlights

  • A technique for measuring real-time shrinkage strain in composite resin is proposed.

  • An inversely synchronized external shutter allows for measurement during irradiation.

  • Polymerization shrinkage kinetics parameters are calculated for Filtek LS and Z100.

  • Full-field strain contour plots and shrinkage strain time series are presented.

Abstract

Objective

To investigate the polymerization shrinkage kinetics of dental resin composites by measuring in real time the full-field shrinkage strain using a novel technique based on digital image correlation (DIC).

Methods

Polymerization shrinkage in resin composite specimens (Filtek LS and Z100) was measured as a function of time and position. The main experimental setup included a CCD camera and an external shutter inversely synchronized to that of the camera. The specimens (2 mm × 4 mm × 5 mm) were irradiated for 40 s at 1200 mW/cm 2 , while alternating image acquisition and obstruction of the curing light occurred at 15 fps. The acquired images were processed using proprietary software to obtain the full-field strain maps as a function of time.

Results

Z100 showed a higher final shrinkage value and rate of development than LS. The final volumetric shrinkage for Z100 and LS were 1.99% and 1.19%, respectively. The shrinkage behavior followed an established shrinkage strain kinetics model. The corresponding characteristic time and reaction order exponent for LS and Z100 were calculated to be approximately 23 s and 0.84, and 14 s and 0.7, respectively, at a distance of 1.0 mm from the irradiated surface, the position where maximum shrinkage strain occurred. Thermal expansion from the exothermic reaction could have affected the accuracy of these parameters.

Significance

The new DIC method using an inversely synchronized shutter provided realtime, full-field results that could aid in assessing the shrinkage strain kinetics of dental resin composites as a function of specimen depth. It could also help determine the optimal curing modes for dental resin composites.

Introduction

The use of light-cured resin composites has become commonplace in restorative dentistry. These dental biomaterials have a high aesthetic value, good mechanical and physical properties, and are easy to use. A drawback of using resin composites to restore teeth, however, is the polymerization shrinkage that occurs during the curing of these materials. Therefore, resin composites need to be chemically and/or micro-mechanically adhered to the tooth substrate to ensure that no gaps are formed between the tooth substrate and the restorative material after curing . Otherwise, the restored tooth will be structurally compromised and bacteria may invade through the interfacial gaps and cause secondary caries .

However, bonding the restoration to the tooth can create problems in itself. As the resin composite shrinks, the tooth cavity walls will oppose this shrinkage, leading to the creation of shrinkage stress. Polymerization shrinkage stress poses three main problems: (1) fracture of the tooth tissues, (2) failure of the composite restoration, and (3) debonding at the tooth-restoration interface . Therefore, many studies have been performed to try to measure, understand, and minimize polymerization shrinkage.

There are several methods for measuring polymerization shrinkage. Notable examples include dilatometry , the bonded disc method , and the use of strain gauges . These methods use either a liquid medium or mechanical devices to measure the displacement or volume change of the composite material due to polymerization shrinkage. The mechanical devices require the buildup of a certain level of stiffness in the specimen to deform them, and the liquid medium may exert gravitational or adherent forces on the specimen . In other words, the specimen could be prevented from undergoing free shrinkage when these methods are used for its measurement. Indeed, the strain gage method only measures the so-called post-gel shrinkage of resin composites.

An alternative to measuring shrinkage strain mechanically is the use of optical sensors. These have the ability to perform noncontact shrinkage measurement without the aforementioned problems. One such method is the use of digital image correlation (DIC). DIC works by comparing a series of sequential images of the deforming object under observation. Through the tracking and analysis of distinctive features on the object, its displacements and strains can be determined . Li et al. pioneered the use of DIC for measuring the polymerization shrinkage strain and depth of cure in dental resin composites. In their work, resin composite bar specimens were prepared with irregular speckle patterns created on their surfaces with spray paints. The specimens were then cured from one side using a curing light, followed by 30 min of continuous imaging of the speckled surface using a CCD camera. Through the analysis of the correlated images, the final shrinkage strains caused by polymerization could be determined over the entire surface of observation. Hence, shrinkage strain could be determined as a function of distance from the curing light, from which the depth of cure could be estimated. The limitation of this approach was the interference of the curing light with the imaging during its operation, which prevented measurement of the specimen’s shrinkage during curing. Note that the majority of shrinkage in resin composites occurs during the first few seconds of the polymerization process. Therefore, the kinetics of polymerization shrinkage during curing, which is probably the most important part of the polymerization process, could not be studied with the regular DIC method.

The purpose of this study is to introduce a novel technique for measuring, in real time, the entire process of shrinkage strain development using an enhanced DIC method. The method utilizes an external shutter that is inversely synchronized with the CCD camera’s internal shutter to temporarily block off the curing light when an image is being taken. This allows the shrinkage behavior of resin composites to be assessed in more detail by studying shrinkage kinetics as a function of depth within the specimen. It could also help to determine the optimal curing modes for dental resin composites.

Theory

Based on Watts’ work , the development of polymerization shrinkage strain can be modeled using the following equation:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='εi=εmax1−e−(t−τo)/τcγ’>εi=εmax(1e((tτo)/τc)γ)εi=εmax1−e−(t−τo)/τcγ
ε i = ε max 1 − e − ( t − τ o ) / τ c γ

where ɛ i is the instantaneous strain at any given position x and time t , and ɛ max is the maximum strain exhibited by the resin composite material at that position. The characteristic time τ c controls the rate at which the strain approaches ɛ max : the larger its value, the slower the rate. γ is the reaction order exponent which also controls the rate of shrinkage strain development, as well as the overall shape of the shrinkage strain vs. time curve. A large value would produce a curve with a step change in shrinkage around τ c . The initiation and propagation of polymerization in a resin composite is a diffusive process. Therefore, there is a time delay between turning on the curing light and the onset of conversion, especially for material in a sizable specimen that is some distance away from the light source: the further away a point is from the curing light, the longer the time delay. An additional parameter τ o has thus been added to the model in to take into consideration this time delay. In general, ɛ max , τ o , and τ c all depend on the distance x from the light source.

As seen in Eq. (2) below, by taking double logs on both sides of Eq. (1) , the shrinkage strain kinetics equation can be manipulated to obtain the above parameters from experimental data using linear regression. By plotting the left hand side of Eq. (2) against ln( t τ o ), the reaction order exponent γ can be determined from the slope of the straight line fitted to the experimental data. Once γ is determined, the characteristic time τ c can be found from the y -intercept.

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='ln−ln1−εiεmax=γlnt−τo−γlnτc’>ln(ln(1εiεmax))=γln(tτo)γln(τc)ln−ln1−εiεmax=γlnt−τo−γlnτc
ln − ln 1 − ε i ε max = γ ln t − τ o − γ ln τ c
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Nov 23, 2017 | Posted by in Dental Materials | Comments Off on A study of polymerization shrinkage kinetics using digital image correlation
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