Characterizing surface viscoelastic integrity of ultra-fast photo-polymerized composites: Methods development

Highlights

  • The rapidly developing surface integrity of ultra-fast (3 s) photo-cure composites can be probed “immediately” by a new macroscopic indentation-creep methodology.

  • PowerCure system and materials demonstrated an acceptable level of polymerization/property performance, despite the ultra-short irradiation times, as judged by this experimental criterion.

Abstract

Objective

Resin-Composites are now available designed for polymerization using 3 s of intense light irradiation. The aim was to develop an experimental method to probe their surface viscoelastic integrity immediately following such rapid photo-cure via macroscopic surface indentation under constant stress as a function of time.

Methods

Two bulk-fill composites (Ivoclar AG) were studied: Tetric PowerFill (PFill) and PowerFlow (PFlow). Split molds were used to fabricate cylindrical {4 mm (dia) × 4 mm} paste specimens, irradiated at 23 °C at 0 mm from the top surface with a Bluephase PowerCure LED-LCU, with 3 s or 5 s modes, emitting 3 and 2 W/cm 2 , respectively. Post-irradiation specimens were immediately transferred to an apparatus equipped with a flat-ended indentor of 1.5 mm diameter. 14 MPa compressive stress at the indentor tip was applied centrally in < 2 min and maintained constant for 2 h. Indentation (I) magnitudes were recorded in real-time (t), with I(t) data re-expressed as % indentation relative to the 4 mm specimen height. After 2 h, the indentor was unloaded and indentation recovery was monitored for a further 2 h. Parallel sets of measurements were made where indentation was delayed for 24 h. Further measurements were made with more conventional composites: EvoCeram Bulk Fill (ECeram) and Tetric EvoFlow Bulk Fill (EFlow). These were irradiated for 20 s at 1.2 W/cm 2 . Kinetic data were curve-fitted to exponential growth functions and key parameters analyzed by ANOVA and post-hoc tests (α = 0.05).

Results

I(t) plots looked initially similar to bulk creep/recovery: rapid deformation plus viscoelastic response; then, upon unloading: rapid (elastic) recovery followed by partial viscoelastic recovery. However, unlike multiply irradiated and stored bulk-creep specimens, the present specimens were exposed to only 3 or 5 s “occlusal” irradiation; generating “hard” surfaces. Subsequently, during the 2 h indentation, the polymer matrix network continued to harden and consolidate. Upon initial loading, I(t) reached 2–3% indentation, depending upon the formulation. Upon unloading at 2 h, elastic recovery was only ca. 1 %. Delayed loading for 24 h, generated I(t) plots of significantly reduced magnitude. Most importantly, however, the I(t) plots for ECeram and EFlow, after 20 s irradiation, showed I(t) magnitudes quite comparable to the PFill and PFlow rapid-cure composites.

Significance

Macroscopic indentation creep has been shown to be a workable procedure that can be applied to rapid-cure materials to assess their immediate surface integrity and developing viscoelastic characteristics. The applied stress of 14 MPa was relatively severe and the indentation/recovery profiles of PowerFill materials with only 3 or 5 s irradiation demonstrated comparability with their established 20 s cure siblings, evidencing the suitability of the PowerCure system for clinical application.

Introduction

There are several current trends in the incremental development of dental resin-composites by academic researchers and particularly by the R&D departments of dental manufacturing companies [ ]. Many developments are driven by (a) competition between manufacturers and (b) requested innovations by clinical dentists. One of the items on the ‘wish list’ of many restorative dentists is more rapid photo curing (photo polymerization) that maintains the reliability of the cure process, assuming that the clinician follows the manufacturers’ instructions precisely.

Visible Light Curing (VLC) by means of Light Curing Units (LCUs) has changed in many respects since the 1970s when it was first introduced [ , ]. The major changes were: (i) the early transition from UV to visible blue light curing (wavelengths ca. 470 nm) and (ii) the change from filtered multi-wavelength Quartz Tungsten halogen (QTH) LCUs to Light Emitting Diode (LED-LCUs), with either a single LED chip (output at 470 nm) or two types of chip (blue: 470 nm and violet: 410 nm) [ ]. The latter are effectively wide-spectrum LCUs.

Photo curing requires the active material to incorporate a photo-initiator (PI) with an absorption spectrum that corresponds to the output spectrum of the LCU. Sufficient light irradiance ( I λ ) is also necessary (corresponding to the LED emission rate: photons/s). Each photon carries a certain energy given by where h = Planck’s constant and ν is the frequency of the light. The further major variable is the time period of irradiation ( t ).

The first photo-cured dental resin-composites were considered to require irradiation for t = 60 s.

Subsequent developments have enabled irradiation times to be reduced from 60 > 40 > 20 > 10 s.

Commercial composites exist for which the required time is claimed to be as low as 5 s. And there is now a product – or product system – available for which t = 3 s (Ivoclar-Vivadent AG) [ ].

These developments have been facilitated by (i) refinements of the photo-initiator system and (ii) boosting the irradiance (or Radiant Emittance; mW/cm 2 ) of the LCUs. The Ivoclar PowerCure system comprises an advanced Bluephase PowerCure LED-LCU able to deliver 3 W/cm 2 for 3 s irradiation and two specially formulated composites: PowerFill and PowerFlow .

Photo-polymerization of resin-composites rapidly transforms fluid or ‘plastic’ paste formulations into hard solids within the irradiation period. However, further post-curing is known to occur that increases both surface and bulk mechanical properties over timescales ranging up to a month post-irradiation [ , ]. The 3 s PowerCure irradiation mode should therefore be capable of producing sufficient material properties within 3 seconds that are demonstrably comparable to properties attained by generally equivalent composites after the more conventional 20 s irradiation.

The experimental challenge is to devise a method to probe mechanical material properties immediately following 3 s PowerCure irradiation. This requirement rules out time-consuming specimen preparation to fabricate flexural bar specimens, for example. It also rules out bulk compressive creep measurements that typically require 6 x 4 mm solid cylindrical specimen that have been well irradiated from multiple directions [ ]. Nano-indentation might at first sight appear to be a possibility [ ]. However, this requires polished specimen surfaces and only probes a shallow surface layer and a very small indentation area. Hence, with composite materials, anomalies are possible by nano-indentation of particle phases, rather than the organic matrix [ ].

In this investigation, we propose a method that is novel in the context of photo-polymerized resin-composites. This involves immediate time-dependent indentation-creep measurements, with a rigid loaded axisymmetric cylindrical flat-ended punch, into a plane photo-polymerized composite surface. Indentation-recovery measurements are also to be made subsequently on the unloaded specimens.

The null hypotheses to be tested are that:

No significant differences exist between indentation/time profiles, during the loading and recovery periods, for 3 & 5 s PowerCure composites and conventionally photo-cured comparator composites.

Theoretical background

Two distinct levels of theoretical analysis are relevant to this topic: (i) continuum mechanics of indentation into materials exhibiting plastic, elastic and/or viscoelastic behavior; (ii) molecular theory of photo-polymerization.

Continuum mechanics of surface indentation

The problem of a rod or pillar loading a “foundation” material is an ancient one, dating back to the temples built in classical Greece, especially when the supporting material was non-rigid soil, with important implications for the safety of foundations. Within the terms of the classical theory of elasticity, the distribution of stress in a solid when deformed by a rigid punch was first considered in 1885 by Boussinesq [ ]. Subsequently several alternative solutions were derived, as summarized by Galin [ ], particularly by Harding and Sneddon [ ] and Sneddon [ , ].

A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies’ surfaces (the normal direction) and frictional stresses acting tangentially between the surfaces.

For a cylindrical flat-ended punch indentation the contact geometry is relatively simple because there is no pile-up at the contact edge. The radius of the contact remains fixed and equal to the radius, R , of the punch ( Fig. 1 ). When it is pressed into the free surface of an elastic solid, the relationship between the indentation depth ( d ) and the normal compressive force ( F ) is given by the linear relationship, [ ] (p.117):

F = 2R.E*.d

where the reduced (or combined) modulus, E* is given by

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='1E*=1−v12E1+1−v22E2′>1𝐸=1𝑣21𝐸1+1𝑣22𝐸21E*=1−v12E1+1−v22E2
1E*=1−v12E1+1−v22E2

Fig. 1
Indentation of a plane surface by a flat-ended cylindrical punch of diameter 2R to a depth d under an applied axial load, F .

E 1 and E 2 are the elastic moduli of the test material and rod, and ν 1 and ν 2 are their Poisson’s ratios.

If these 4 parameters remain constant, together with force F , then indentation depth ( d ) will also be constant and time invariant. However, if the modulus ( E 1 ) of an elastic test material were to increase (e.g) due to progressive curing, then indentations into successive specimens would exhibit a progressive reduction in elastic indentation depth, under constant load.

The present investigation is concerned with a specific strain history, wherein the creep (progressive deformation) is measured in response to an applied step function of stress, (or loading force). That is, the materials are subjected to an approximately instantaneous loading – and subsequent unloading. The applied stress σ at time t = 0 is:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='σ0=F/A=F/π.R2′>𝜎0=𝐹/𝐴=𝐹/𝜋.𝑅2σ0=F/A=F/π.R2
σ0=F/A=F/π.R2

The strain ε(t) in a viscoelastic material will increase with time. The creep compliance, J (t), is defined as the ratio:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='Jt=εt/σ0′>𝐽(𝑡)=𝜀(𝑡)/𝜎0Jt=εt/σ0
Jt=εt/σ0

The relaxation magnitude, in the compliance formulation, from “start” (0) to “finish” (∞) over the experimental time range is (J – J 0 ).

In linear viscoelastic materials, the creep compliance is independent of stress level. Under those circumstances, constitutive equations may be developed using the Boltzmann superposition principle , which is a statement of linearity : that the effect of a compound cause is the sum of the effects of individual causes. However, particularly in the case of indentation creep, the assumption of linearity may not hold making the scope for exact analysis severely circumscribed, [ , ].

Nevertheless, a range of models have been devised to account for viscoelastic behavior. These commonly incorporate various serial or parallel combinations of elastic and viscous ‘elements’, rather like the spring and damper systems of a motorcar. The springs are assumed to be perfectly elastic. The dashpot element may be envisaged as a piston-cylinder assembly in which motion of the piston causes a viscous fluid to move through an aperture. However, real materials are not generally describable by models containing a small number of springs and dashpots.

The simplest pair of models, due to Voigt and Maxwell respectively, consist of a spring and dashpot – arranged either in parallel or in series. Somewhat more realistic behavior can be modeled by the standard linear solid , which contains three elements ( Fig. 2 ):

Fig. 2
Mechanical model systems consisting of series and/or parallel combinations of elastic and viscous elements.

For the Voigt (or Kelvin) model ( Fig. 2 ), both the spring and the dashpot experience the same deformation, or strain, and the total stress is the sum of the stresses in each element. From this, it can be shown [ ] (p. 55f) that the creep response is:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='Jt=1E1−e−t/τc’>𝐽(𝑡)=1𝐸(1𝑒𝑡/𝜏𝑐)Jt=1E1−e−t/τc
Jt=1E1−e−t/τc

In which <SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='τc=η/E’>𝜏𝑐=𝜂/𝐸τc=η/E
τ c = η / E
is referred to as the retardation time.

A single exponential relaxation or retardation function undergoes most of its change over about one decade (a factor of 10) in time scale. However, real materials creep or relax over many decades of time.

There is a more general and rather ubiquitous expression for a normalized relaxation processes: the stretched exponential or KWW (after Kohlrausch, Williams, Watts) form [ , ] with a fractional exponent: 0 < β ≤ 1.

<SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='ϕt=e−t/τβ’>𝜙(𝑡)=𝑒(𝑡/𝜏)𝛽ϕt=e−t/τβ
ϕt=e−t/τβ

τ is the relaxation (or characteristic) time.

A corresponding normalized stretched-exponential growth process is represented by:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='1−ϕt=1−e−t/τβ’>1𝜙(𝑡)=(1𝑒(𝑡/𝜏)𝛽)1−ϕt=1−e−t/τβ
1−ϕt=1−e−t/τβ
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Jan 10, 2021 | Posted by in Dental Materials | Comments Off on Characterizing surface viscoelastic integrity of ultra-fast photo-polymerized composites: Methods development
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