Determination of polymerization shrinkage kinetics in visible-light-cured materials: methods development D.C. Watts A.J. Cash

Department of Restorative Dentistry Turner Dental School University of Manchester Higher Cambridge Street Manchester M15 6FH, United Kingdom Received November 30, 1990 Accepted July 4, 1991 Dent Mater 7:281-287, October, 1991 Abstract--An instrument for the

reproducible measurement of polymerization shrinkage kinetics is described, constructed around a disc-shaped specimen sandwiched between two glass plates. Test specimens of light-sensitive dental restorative materials were irradiated through the lower, rigid plate. The upper, non-rigid plate was readily deflected by an increase of the adhesive stress from the polymerizing and shrinking sample. Deflection was measured by an LVDT transducer and computer-recorded. Dimensional changes were confined to the specimen disc-thickness dimension, such that the fractional linear shrinkage approximated the volumetric shrinkage. Shrinkage data are reported for representative materials: unfilled and resin composites, base-lining materials, and an impression material. Equilibrium shrinkage magnitudes ranged from 0.65%, for the impression material, to 7.9% for the unfilled resin. The kinetic behavior was approximately characterized by an overall time constant, ranging from 12.5 to 280 s, associated with an exponential growth curve, although the initial shrinkage was near-linear in time, for many, materials, due to nonsteady-state concentrations of polymer freeradicals. The test-specimen geometry facilitates rapid and essentially uniform cure and hence the determination of minimum possible time-constants at each ambient temperature and incident light-intensity.

Study of hybrid giass-ionomer materials, without spurious dehydration effects, was also achieved.

xisting types of dental resins, resin composites, and some hybrid types of glass-ionomer cement exhibit polymerization shrinkage of methacrylate monomers during the setting process. Progress toward elimination or reduction of polymerization contraction by synthesis of monomers that expand upon polymerization has been reported by Thompsonet al. (1979) and Stansbury (1990). However, such monomer systems have not yet been incorporated into clinical materials. Polymerization contraction strain is a time-dependent phenomenon and generally proceeds in two stages: pregelation and post-gelation (or rigid) contraction (Bausch et al., 1982). Plastic flow may occur during the earlier phase such that internal stresses within the material undergo stress-relaxation. Beyond the gel point, however, stressdevelopment occurs. Its magnitude, relative to the strain, depends upon the elastic (or visco-elastic) moduli, which are also increasing functions of time (Braem et al., 1987). The adverse effects of polymerization shrinkage stress on the bond between resin composites and hard tissues have been extensively described in the literature (Asmussen, 1975; J~rgensen et al., 1975; Hansen, 1982; Bowen et al., 1983; Davidson et al., 1984; Davidson and de Gee, 1984; Ehrnford and Derand, 1984; Jensen and Chan, 1985; Eick and Welch, 1986). Feilzer et al. (1987) showed that the stress-development in a bonded composite restoration also depends upon the geometry of a restoration, in that the pre-gelation flow of the material is inhibited when the ratio'of the bonded surface to the free unbonded surface exceeds a certain limit. This observation is related to the description of shrinkage as a vector quantity, having both magnitude and direction. The rates of development or kinetics of shrinkage strain and stress are additional important parameters, which merit further attention. The contributions of pre- and postgelation stages of shrinkage and the vector (or geometry-sensitive)character of the process must be considered in the

E

design and evaluation of laboratory instrumentation for measurement of this quantity. For light-cured materials, there is also the question of anisotropy of the cure pattern--with possible variation of shrinkage patterns within the material, relative to the initiating light-source, with respect to both material thickness and surface area (Watts et al., 1984; Onose et al., 1985). In cases where material specimens are imperfectly cured, the measured shrinkage will be correspondingly reduced. This is a separate issue from the generalized (or isotropic) sub-optimal degree of conversion that results from cure under clinical conditions at 37°C (Ruyter, 1985; Ferracane and Greener, 1986) and which may be overcome by extra-oral secondary curing at elevated temperatures (Eliades et al., 1987; Dionysopoulos and Watts, 1989). There are two general approaches to the determinationofmaterial shrinkage: volume dilatometry or non-volume dilatometric methods. Measurements of volumetric shrinkage are usually made indirectly in a dilatometer by determination of linear height changes of a column of fluid (mercury or water) connected to a reservoir surrounding the test substance (Bekkedahl, 1949). Because of problems of access of the light source, and opacity of mercury, it is more difficult for such methods to be applied to light-cured (VLC) dental materials and at the same time to ensure that the materials are cured throughout to the'clinical' degree ofconversion. Also, such methods are somewhat inconvenient in that critical temperature control to (preferably) 37 + 0.1°(3 is mandatory because of thermal expansion/contraction ofthe surrounding fluid. Even then, it may be difficult to correct for the effect of polymerization exotherm on the fluid (Hay and Shortall, 1988). Nevertheless, valuable data have been obtained by such methods,particularly on auto-cured materials, by several investigators, including Smith and Schoonover (1953), de Gee et al. (1981), Bausch et al. (1982), Bandyopadhay (1982), Goldman (1983), Solteszetal. (1986), Penn (1986), Feilzer

Dental Materials~October 1991 281

et al. (1988), Hay and Shortall (1988), Rees and Jacobsen (1989). Non-volume dilatometric measurements are usually made of one-dimensionalor possibly two-dimensional strain in a material, by means of a contacting or non-contacting transducer. The purpose of the present work was further development of a specific method originated by Wilson (1978) and utilized by Bausch et al. (1982), Watts and Cash (1988), and Walls et al. (1988). The specific aims are to analyze the physical response of the measurement system, to present representative data on shrinkage kinetics, and to evaluate the overall utility and significance of the technique.

MATERIALSAND METHODS Instrument D e s i g n . - - T h e present method, which may be termed a "deflecting disk" technique, has a basically simple design (Fig. la,b). A disk-shaped specimen, circa 1.5 x 8 ram, of nnset light-sensitive material was placed at the center of a square cross-section brass ring (internal diameter, 16 mm; height, 1.4-1.5 ram), adhesively bonded onto a quartz plate, when UV-activatod materials are used, or a rigid glass microscope slide (75 x 25 x i ram), when VLC materials are used. The top edge of the ring and the disk specimen were covered by a flexible diaphragm consisting of a 22ram-square glass microscope cover-slip of 0.13-mm thickness (type 0, ChancePropper Ltd., Warley, UK). A centrally

®

aligned LVDT displacement transducer (type GT 2000, RDP Electronics, Wolverhampton, UK) was positioned in contact with the center of the cover-slip. Cure was initiated from below by transillumination of the microscope slide beneath the specimen by means of a standard dental light-curing unit (Luxor, ICI plc, Macclesfield, UK). The cover-slip deflects as shrinkage takes place, and the deflection at the center of the cover-slip was monitored over time by the LVDT transducer, which has a sensitivity better than 0.1 ~m. The LVDT was connected to a signal conditioning unit (type E307-3, RDP Electronics, Wolverhampton, UK) and a micro-computer transient-recorder and data-logging system. The onset and duration of the light exposure were also recorded via an electrical signal to the data store. The further development of the technique consisted, first, in the construction of apparatus for consistent alignment of the measurement assembly, so that the anvil of the displacement transducer would be placed precisely above the center of the support ring and specimen disk. A dial-gauge stand (Baty & Co. Ltd, Sussex, UK), equipped with a 25-mmdiameter vertical column and a screwoperated rise and fall table, was modified to form the basis of the equipment (Figs. 2, 3). A horizontal arm with clampscrew was machined to fit the vertical column so that the transducer would be clamped above, but in the central axis of, the table. For axial alignment of the

specimen, a circular brass adaptor, 45 mm high and 25 mm in diameter (Fig. 4), was machined and recessed to fit the surface of the table closely and thus prevent lateral displacement of the adaptor in use. A 20-mm-diameter hole in the center of the adaptor and a 16mm-wide slot through the wall were produced. Thereby, when the adaptor was fitted to the table, the fiber-optic arm ofthelight source couldbe positioned through the slot yet allow for adjustment, from below, of the optic tip to within 0.5 mm of the top surface of the adaptor (Figs. 2, 3). The optic was held in position by the clamp of a magnetic stand (Eclipse Tools, Sheffield, UK). An aluminum locating plate was machined to fit the upper surface of the adaptor. This allowed the glass microscope slide to pass under the plate, along the surface of the adaptor, until the bonded support ring was located by peripheral stops in the center of the transducer axis (Fig. 4). To finalize axial alignment of the assembly, a brass disk-with central locating dimple, and of the same diameter as the cover-slip support ring--was placed within the ring. The disk was thus located at the adaptor's central axis, and the position of the transducer was fine-adjusted to allow the ball of the transducer armature to drop into the disk dimple. After the transducer clamp was secured, the disk was removed.

Calibration of the LVDT Transdueer.--Amplification of the transducer output, by a selected gain factor circa 40

GlaSS Diaphragm

Brass Ring

B C

lb scope Slide U n N t paste Specimen

Soft R~bon Wax Coelta]nment Ring

Water Input Tube

Fig. 1. Disc specimen mounted on the rigid glass plate at the center of the brass support ring:(a) plan view;(b) elevation, with glass diaphragm in position; (c) wax containment ring used with low-viscosity specimens; and (d) water input for maintenance of 100% rh around glass-ionomer specimens.

[ Fig. 2. The overall measurement assembly.

282 Watts & Cash/Polymerization shrinkage kinetics

I

Fig. 3. Schematiccross-section of the shrinkagetest assembly: (A) transducer; (B) test specimen; (C) cover slip; (D) brass support ring; (E) rigid glass plate; (F) light optic; and (G) height adjustment screw.

in the signal conditioning unit, gave an input to the data-recording system of circa 15 mV/pm strain. A typical 2% specimen shrinkage-strain of 30 ~m corresponded to a net input of 450 mV. Calibration of the transducer displacement was ultimately traceable to the National Physical Laboratory (London, UK) via NPL-certified tungsten carbide gauge blocks (Yorkshire Precision Gauges, Doncaster, UK). For intermediate calibration, the transducer was lightly clamped in a horizontal stand (Fig. 5), opposed by a modified and calibrated digital micrometer (Mitutoyo, Tokyo, Japan), with a display accuracy of 1 ~m. The transducer armature was displaced by the micrometer armature through known increments while the transducer output voltage was recorded in the memory store of the data-recording system. The voltage/displacement calibration factor was then calculated by linear regression (r=0.9999). The transducer was calibrated periodically throughout the course of the work.

Procedure.--Each measurement was conducted in the following manner: After being mixed (if appropriate), 0.05 mL of paste or fluid material was quickly expressed from a truncated 1-mL syringe of 8-ram internal diameter, and

placed onto the glass microscope slide centrally within the bonded brass ring as a circular specimen disk 8 mm in diameter. In the case of specimens consisting of unfilled low-viscosity resin, an 8-ram-diameter ring of soft carding wax was used to contain the specimen (Fig. lc). In the case of test specimens which are subject to dehydration, such as hybrid glass-ionomers, a peripheral environment of 100% relative humidity was maintained around the circular edge of the specimen disk by injection of a small amount of water v/a a syringe, tube, and needle, the latter penetrating the brass support ring (Fig. ld). A clean microscope cover-slip was placed over the unset specimen and, with the aid of an overlying rigid plate, pressed into contact with the upper surface ofthe ring, compressing the unset specimen slightly. This procedure "sandwiched" the specimen between a rigid base formed by the microscope slide and the thin undistorted cover-slip above, which formed the diaphragm, at a specimen thickness consistent with the height of the outer brass ring, without distorting the glass diaphragm. This assembly was transferred to the axial-location station above the fiberoptic tip on the instrument stand. The armature of the displacement transducer was carefully lowered into contact with the surface of the cover-slip. Before each test, a five-minute temperature equilibration period was allowed. However, this delay was neither possible nor strictly necessary in the investigation of dual-cured mixed materials, such as hybrid glass ionomers. Data acquisition was pre-programed at a rate of four data points s "1. Each sample was irradiated from beneath the supporting glass base for 60 s via the fiber-optic unit. The effect of light irra-

Fig. 4. Axial alignment device.

Fig. 5. Horizontalstandfor LVDTtmnsducer calibration.

Materials.--Seven representative VLC materials were studied initially, as listed in Table 1: three resin composite, one unfilled resin, a calcium hydroxide base, a hybrid glass-ionomer cement, and an impression material. Four repeat measurements were made on each material, with the test assembly at 37°C. Data were statistically analyzed by ANOVA, and multiple comparisons were made by the conservative Scheff~ test at the 0.10 significance level.

diation from above was also determined in a separate series of experiments. The shrinkage deflection in ~ n of the cover-slip and specimen (dL = Lo- L) was determined from the data via the voltage/displacement calibration; Lo is the original specimen thickness and L the final thickness. The percentage shrinkage [(dL/L ) x 100] was calculated as a function of time. By reference to the concurrently recorded moment of lamp initiation, the initial rate of shrinkage over the first 10 s following photo-activation and the shrinkage time constant (t) were obtained from the recordings of shrinkage as a function of time.

Specimen Circumferential Measurement.--In a control series of experiments, composite paste specimens were assembled as described above (Fig. 1), between a microscope slide base and a cover-slip diaphragm. They were, in turn, positioned on the stage of a projection microscope (Model 4002, Projectina, Heerbrugg, Switzerland) and viewed under long wavelength yellow light that would not initiate the curing reaction. The circumference of the disk of each sample was traced and digitized before and after polymerization by the visible light source (Luxor, ICI plc, Macclesfield, UK).

The Surface Contraction Pattern.So that the general shape of the upper surface of each glass diaphragm and underlying specimen disk could be assessed, following irradiation and subsequent cure-shrinkage, specimens were examined by means of an X-Y profilometer. A stylus was caused to traverse the surface of the glass diaphragm for a distance of 14 ram, crossing the center section above the resin

Dental Materials / October 1991 283

disk. The profilometer used coupled LVDT transducers, which gave an electrical output proportional to distance; this "output was stored for subsequent display via a microcomputer. Vickers microhardness (VHN) values of upper and lower specimen disk surfaces were also obtained on the three resin composites after completion of the cure and shrinkage process and further conditioning in the dark at 37°C for 24 h.

Determination of Stress for Free D i a p h r a g m Flexure.--Volumetric contraction of the test specimens caused distortion of the glass cover-slip. Thus, there was evident adhesion between the resin-based specimens and the glass. The latter functioned as a diaphragm within the circumferential support of the brass ring. It was essential to the accuracy and sensitivity of the technique that the cover-slip should be mechanically compliant, so that dimensional change in the resin was totally free and unrestricted by any high-stress development caused by diaphragm deformation. Theoretical stress analysis of the problem is discussed in Appendix 1. An experimental investigation of minimum stress levels to produce free diaphragm distortion was made by means of a special attachment that provided for reduction of air pressure beneath the coverslip. A test block was constructed from clear acrylic (Perspex, ICI, Welwyn, UK), which replaced t'ne table of the stand (Fig. 6). This supported a cover-slip on a raised annular lip machined in the upper surface of the block, of the same dimensions as the brass support ring. A chamber within the acrylic block was connected with a mercury U-tube manometer and a partial-vacuum device. With the cover-slip sealed over the rim of the annular lip of the block with sott wax, reduction of air pressure caused a displacement of the cover-slip which was measured at the center by the displacement transducer (LVDT). The central deflection was measured for pressure reduction up to 15 kPa (circa 112 m m Hg).

RESULTS A typical surface profile trace of the cover-slip surface is shown in Fig. 7. Rather than inducing a parabolic pattern on the specimen surface, contraction in the specimen disk pulled the central portion of each cover-slip down evenly in

a vertical plane, causing the cover-slip to adopt a flattened "dinner plate" contour. The major distortion in the glass took place close to the rim periphery of the brass support ring, also indicative of a uniform "pull-down" over the central area of the diaphragm. Significantly, this characteristic behavior, of bulk contraction down toward the lower surface, was also maintained in a separate series of experiments in which specimens were irradiated from above. No detectable change in the circumference or diameter of the disks was observed as a result of the cure process with any of the test specimens. The variation of central disk deflection with air pressure reduction was found to be linear (r > 0.99) over the measured deflection range of 0 to 40 pm. For a representative deflection of 30 pm, the required pressure (or stress) reduction was 0.0133 MPa. When the transducer was positioned over the center of both composite paste and fluid resin specimens, negligible distortion of the cover-slip was observed prior to initiation of the cure process. The data for maximum or equilibrium shrinkage measured on the representative materials studied are presented in Table 2. Hardness values (Table 3) of the resin composites were not found to differ significantly (p > 0.05) between the upper and lower specimen surfaces, consistent with the absence of significant anisotropic cure-gradient through the specimen height of 1.5 ram. Representative shrinkage/time data are presentedinFigs. 8-9. Onceimtiated, the initial rigid polymerization shrinkage proceeded rapidly, in a near-linear manner with time. For most materials, however, the normalized overall shrinkage response was approximately represented by the Kohlrausch-Williams-Watts (KWW) stretched-exponential growth curve (Williams and Watts, 1970; Shlesinger, 1984):

A ~

B

Fig. 6, Device for measurement of diaphragm flexure caused by reduced air pressure: (A) transducer; (B) cover slip; (C) soft wax; (D)tube to manometer; and (E) perspex block.

(2) the initial shrinkage, characterized as the percentage change in shrinkage in the first 10 s following the onset of light-irradiation. These parameters are also presented in Table 2, calculated in this instance for b = 1. The time constant for the unfilled and resin composite materials was less than half the period (60 s) of light-irradiation. However, the hybrid glass ionomer had a significantly longer timeconstant (p ,, 0.01). DISCUSSION

Specimen Circumferential Mea. surement.--The absence of any change

[1 - e x p ( - t ] ~ b]

in specimen circumference, as a result of cure, suggests that sufficiently strong adhesive forces were present between the resin-based specimens and the glass base such that (post-gelation) shrinkage vectors were constrained into the vertical and did not have a detectable component in the horizontal plane.

where 0 < b < 1, typical values being 0.30.6. This is particularly appropriate to the situation following the initial linear shrinkage. Two principal parameters were derived to express the kinetics: (1) the overall time-constant (t), the time for the shrinkage to attain a fraction 0.632 [or (1 - el)] of its final magnitude; and

Surface Contraction Pattern .--Along with the absence of change in the specimen circumference, the surface contraction pattern induced in the diaphragm also suggests that shrinkage of disk specimens was restricted to the vertical thickness dimension only. This is in general agreement with the investigations ofFeilzer et al. (1989) of increased wall-to-wall curing contraction in thin

284 Watts &:Cash/Polymerization shrinkage kinetics

1,0 ~

2,5-

3.0 XRI

FUL _

2.0



&

.~, 2 . 0

1.5"

VML

1.5.

m ,:-

2.5

1.0'

.~ 1.0. 0.5"

'3

6

9

1'2

1'5

~ 0.5"

o

,

~

~

Time [mini

dlephragm horizontal trice [mm]

0.0.

o

3o

6o

9'o

1:;o

150

Time [min]

Fig. 7. Surface profile trace of a glass diaphragm bonded to a polymerized specimen disc.

Fig. 8. Time-dependence of shrinkage strain for VML and FUL resin composites.

Fig. 9. Time-dependence of shrinkage strain for XRI hybrid glassionomer.

bonded resin layers, in which the configuration factor [C = bonded surface area/total surface area] is high. It follows that the central deflection of the disk is generally representative of contraction over the top surface of the specimen. Hence it follows that the fractional linear shrinkage measured is approximately equivalent to the fractional volumetric shrinkage:

from pre-gelation flow, although the gel point is reached very rapidly in most light-cured resin composite materials. The additional fact that the upper and lower surfaces of the resin-based disk specimens were bounded by glass means that air inhibition of the polymerization was minimized, and hence the magnitude of the cure at the test temperature was optimized.

~JLo~VN o

Time-dependent Shrinkage Kinetics.--For an exponential growth process, the period for 99% growth is 4.6 x time constant (t). Thus, for a material with t = 30 s, the 99% level should be reached in 2.3 rain. The described procedure has the practical merit of being rapid in terms of the overall experimental duration. These time constants (t) have been obtained for a thin specimen geometry (L° < 1.5 m e ) in which light irradiation is optimum. In a separate determination, the attenuation of light intensity by the glass base was found to be only 3%. Hence, since the experimental conditions favor rapid cure at 37°C, the time constants derived should be regarded as minimum values for the materials under investigation. The theory of polymerization kinetics, discussed by Watts (1991), predicts an exponential growth curve for shrinkage versus time, provided that: (1) there is a steady-state concentration of polymer radicals, with radicals disappearing by normal termination, and (2) the shrinkage kinetics keeps in step with the cross-linkingpolymerization. The time constant (t) is then inversely proportional to the square root oftheintensity oflight (Ia), of appropriate wavelength, absorbed by the photosensitizer.

Here, ko and k t are the (temperaturedependenO rate constants for chain propagation and termination, respectively, and F is the quantum yield for initiation. The high light irradiance of the specimens in the present experimental arrangement serves to minimize u However, the near-linear initial shrinkage suggests that, in the early stages ofVL polymerization,steady-state concentrations of radicals have not been reached, and the pre-effect can be expressed as a power series in fir, the leading term being linear in this ratio (Watts, 1991). In a different experimental configuration, such as a volume dilatometer, or in certain clinical situations, where a greater bulk of resin compositemight be used, the polymerization should occur more slowly, unless there is an exotherm which significantly alters k and k t. Nevertheless, the present t~me constants, precisely because they are the minimum possible under these conditions of geometry and temperature, are probably more reproducible than might otherwise be the case. Hence, this information on shrinkage kinetics may be more readily correlated with information pertaining to the chemical composition of the resin system, including monomer type and photo-initiator concentration and molar absorptivity. The longer-term time-dependence was more accurately described by the stretched-exponential KWW function. The glassy state is swiftly generated by photo-polymerization, in the case of dimethacrylate resins, and the KWW function characterizes the time-dependence of segmental motion in the glassy state which is the governing factor for the self-limiting processes of bulk polymerization and free-volume shrinkage. The underlying mechanisms leading to KohlrausehWilliams-Watts relaxation behavior

The uniform "pull down" of the specimen shrinkage pattern might have indicated that central alignment of the transducer measurement was superfluous. However, variations in the areal extent of cure might result in some instances through various effects, including possible variation in the light output across the surface of the fiber-optic light guide.

Stress for Free Diaphragm Flexure.--The typical required air-pressure reduction for free diaphragm deflection of 0.0133 MPa is many orders of magnitude lower than the shrinkage stresses of 5 -15 MPa generally developed by the setting of resin composite materials (Feiheretal., 1987). Hence, the vertical contraction of the resin-based materials is essentially unaffected by the presence of the overlying glass diaphragm (cf. Appendix). Equilibrium S h r i n k a g e Magnitudes.--Comparison ofliterature values on shrinkage magnitudes obtained by different techniques is difficult. However, the present shrinkage magnitudes appear to be generally representative more ofvolumetric shrinkage (Goldman, 1983) than of linear shrinkage only, as suggested on indirect physical grounds (above). The observed equilibrium contractions may exclude a contribution

kt °.5 t

=

-

-

DentalMaterials~October1991 285:

TABLE 1 VISIBLE-LIGHT-CURED MATERIALS INVESTIGATED Code

Material

Category

Manufacturer

VML

Visio-Molar

Resin Composite

Espe GmbH, Seefeld, Germany

OPL

Opalux

Resin Composite

ICI plc, Macclesfield, UK

FUL

FuI-Fil

Resin Composite

LD. Caulk, Milford, DE

RES

BondingAgent

Unfilled Resin

ICI plc, Macclesfield, UK

PVD

Prisma VLC Dycal

Calcium HydroxideBase

L.D. Caulk, Milford, DE

XRI

XR Ionomer

Hybrid Glass Ionomer

Kerr Mfg. Co., Romulus, MI

GEN

Genesis[high viscosity]

ImpressionMaterial

Dentsply, York, PA

TABLE2 SHRINKAGE DATA ON REPRESENTATIVEVLC MATERIALS (Standard Deviations in Parentheses) Material C o d e

EquilibriumShrinkage (%) Shrinkage in 10 s (%)

VML

1.28 (0.07)

0.70 (0.04)

OPL

1.55 (0.10)

0.47 (0.03)

FUL

2.05 (0.05)

1.05 (0.04)

15.25 (0.35)

RES

7.9

(0.20)

4.02 (0.30)

12.50 (0.20)

PVD

2.45 (0.02)

0.93 (0.16)

25.80 (2.00)

XRI

2.73 (0.30)

0.36 (0.20)

280.0 (20.00)

GEN

0.65 (0.08)

0.28 (0.08)

,

12.50 (0.05)

29.0

(0.35)

(7.0)

TABLE3 VICKERS HARDNESSOF RESIN COMPOSITES (Standard Deviations in Parentheses)

Code

Lower Surface"

Upper Surface

Statistical Difference?

VML

120 (9)

115 (8)

None: (p > 0.05)

OPL

90 (7)

86 (8)

None: (p > 0.05)

FUL

52 (6)

51 (5)

None: (p > 0.05)

'The lower surface was in greater proximityto the lightsource.

have been extensively discussed in theoretical physics. Shlesinger (1984), for example, has suggested an underlying fractal-time stochastic process. In the present case, this would correspond to random movements of the polymer network permitted intermittently by local free-volume which, in turn, leads to the collapse of that free volume. This deflecting-disc polymerizationshrinkage technique is now being applied to characterize the shrinkage kinetics in a wide range of commercial and experimental visible-light-cure materials in relation

to their composition and chemistry. The high rate of contraction in the case of VLC resin composites, having a similar specimen geometry, implies an appreciable rate of development of shrinkage stress as well as a high stress magnitude, as suggested by Feilzer et al. (1989). These will both be destabilizing factors in the formation of adhesive bonds. There is a place for the fundamental study of both shrinkage (strain) kinetics and shrinkage stress kinetics in the characterization of restorative materials and their complex interactions with dental tissues.

286 Watts & Cash ]Polymerization shrinkage kinetics

ACKNOWLEDGMENT The partial support of Espe GmbH (Seefeld, Germany) for this development is gratefully acknowledged. APPENDIX

Time Constant (s)

.26.25

CONCLUSIONS (1) The deflecting disc procedure, coupled with alignment of the LVDT transducer, provides for reproducible measurement of the time-dependence of shrinkage. (2) The method is applicable to a wide range of visible-light-cured materials, and may be extended to UV-cured materials by the use ofa quartz-bottomed plate. (3) Shrinkage magnitudes obtained are equal to or close to the post-gelation volumetric shrinkage values.

Bending of a Uniformly-loaded Circular Plate, Simply Supported at its Edge: Elastic Analysis.--The flexural rigidity (D) of the plate is given by Timoshenko (1956): D = E h 3 / 1 2 ( 1 - v 2)

where E = Young's modulus [ca. 70 GPa, for soda glass (AShby and Jones, 1980)]; h = plate thickness (0.13 mm); and v = Poisson's ratio (ca. 0.3). Therefore: D = 1.408 x 10.2 N m. If an evenly distributed pressure (P) is applied to a circular plate supported on a ring of radius (a), the deflection (Z) at the center of the plate is given by Timoshenko (1956): Z / P = [a4/D] x [11/641 + {1/16(l+v)l]

and where a = 8 mm Z/P = ((0.008)4/(1.408 x 10-2)}x 0.0637 = 18.53 x 10-9m a N -1 For a plate deflection (Z) of 30 ~n, the pressure or stress (P) corresponds to 0.00162 MPa. This stress is a factor of 8 lower than the experimental value of 0.0133 MPa determined above. However, agreement within one order ofmagnitude is reasonable in view of the fact that the precise mode of cover-slip deflection is not exactly in accord with this particular model of 'central' deflection. Both theory and experiment concur in the fact that the glass diaphragm will readily deflect in response to shrinkage of the underlying resin. REFERENCES

ASHBY,M.F. and JONES, D.R.H. (1980):

Engineering Materials. Oxford: Pergamon Press, p. 31. ASMUSSEN,E. (1975): Composite Restorative Resins. Compositionversus Wallto-Wall Polymerization Contraction, Acta Odontol Scand 33:337-344. BAND¥OPADHAY,S. (1982): A Study of the Volumetric Setting Shrinkage ofsome Dental Materials, J Biomed Mater Res 16:135-144. BAUSCH, J.R.;DELANGE, C.;DAVIDSON, C.L; PETERS, A.; and DE GEE, A.J. (1982): Clinical Significance of Polymerization Shrinkage of Composite Resins, J ProsthetDent 48:59-67. BEKKEDAHL, N. (1949):Volume Dilatometry,J Res Natl Bur Stds 42:145-156. BOWEN, R.L.; NEMOTO, K.; and RAPSON, J.E. (1983): Adhesive Bonding of Various Materials to Hard Tooth Tissues: Forces Developing in CompositeMaterialsDuring Hardening, J A m Dent Assoc 106:475-477. BRAEM,M.; LAMBRECHTS, P.;VANHERLE,G.; and DAVIDSON,C.L. (1987): Stiffness Increase During the Setting of Dental Composite Resins, J Dent Res 66:1713-1716. DAVIDSON, C.L. and DEGEE,A.J. (1984): Relaxation of Polymerization Contraction Stresses by Flow in Dental Composites, J Dent Res 63:146-148. DAVIDSON,C.L.;DE GEE, A.J.;and FEILZER, A. (1984): The Competition Between the Composite-Dentin Bond Strength and the Polymerization Contraction Stress, J Dent Res 63: 1396-1399. DE GEE, A.J.;DAVIDSON, C.L.;and SMITH, A. (1981): A Modified Dilatometer for Continuous Recording of Volumetric Polymerization Shrinkage of Composite Restorative Materials, J Dent 9:36-42. DIONYSOPOULOS, P. and WATTS, D.C. (1989):Dynamic Mechanical Properties of an Inlay Composite, J Dent 17:140-144. EHRNFORD, L. and D~.RAND,T. (1984):CervicalGap Formation in Class IICompositeResin Restorations,SwedDent J 8:15-19. EICK,J.D. and WELCH, F.W. (1986): Polymerization Shrinkage of Posterior Composite Resins and its Possible Influence on Postoperative Sensitivity,Quint Int 17:103-111. ELIADES, G.G.; VOUGIOUKLAmS, G.J.;and CAPUTO, A.A. (1987):Degree ofDouble Bond Conversion in Light-Cured Composites, Dent Mater 3:19-25. FEILZER,A.J.;DE GEE, A.J.;and DAVIDSON, C.L. (1987): Setting Stress in Corn-

posite Resin in Relation to Configuration of the Restoration, JDent Res 66:1636-1639. FEILZER,A.J.; DEGEE,A.J.; and DAVIDSON, C.L. (1988): Curing Contraction of Composites and Glass-Ionomer Cements, J Prosthet Dent 59:297-300. FEILZER,A.J.; DEGEE,A.J.; and DAVIDSON, C.L. (1989): Increased Wall-to-Wall Curing Contraction in Thin Bonded Resin Layers, J Dent Res 68:48-50. FERRACANE, J.L. and GREENER, E.H. (1986): The Effect of Resin Formulation on the Degree of Conversion and Mechanical Properties of Dental Restorative Resins, J Biomed Mater Res 20:121-131. GOLDMAN,M. (1983): Polymerization Shrinkage ofResin-based Restorative Materials, Aust Dent J 28:156-161. HANSEN,E.K. (1982): Contraction Pattern of Composite Resins in Dentin Cavities, Scand J Dent Res 90:480483. HAy, J.N. and SHORTALL,A.C. (1988): Polymerization Contraction and Reaction Kinetics of Three Chemically Activated Restorative Resins, JDent 16:172-176. JENSEN,M.E. and CHAN,D.C.N. (1985): Polymerization Shrinkage and Microleakage. In: Posterior Composite Resin Dental Restorative Materials, G. Vanherle and D.C. Smith, Eds. Utrecht: Peter Szulc, pp. 243-262. JORGENSEN, K.D.; ASMUSSEN,E.; and SHIMOKOBE,H. (1975): Enamel Damages Caused by Contracting Restorative Resins, Scand J Dent Res 83:120-122.

ONOSE,H.; S~o, H.; KANT0,H.;AND0,S.; and HASUXKE,T. (1985): Selected Curing Characteristics of Light-activated Composite Resins, Dent Mater 1:48-54. PENN, R.W. (1986): A Recording Dilatometer for Measuring Polymerization Shrinkage, Dent Mater 2:78-79. REES,J.S. and JACOBSEN,P.H.(1989):The Polymerization Shrinkage of Composite Resins, Dent Mater 5:41-44. RUYTER,I.E. (1985): Monomer Systems and Polymerization. In: Posterior Composite Resin Dental Restorative Materials. G. Vanherle and D.C. Smith, Eds. Utrecht: Peter Szulc, pp. 109-135. SHLES~NGER,M.F. (1984): Williams-Watts Dielectric Relaxation: A Fractal Time Stochastic Process, J Stat Phys 36:639-648.

SMITH,D.L. and SCHOONOVER,I.C. (1953): Direct Filling Resins: Dimensional Changes Resulting from Polymerization Shrinkage and Water Sorption, J Am Dent Assoc 46:540-544. SOLTESZ,U.; BATH,P.; and KLAmER,B. (1986): Dimensional Behaviour of Dental Composites due to Polymerization Shrinkage and Water Sorption. In: Biological and Biomechanical Performance of Biomaterials, P. Christel, A. Meunier, and A.J.C. Lee, Eds. Amsterdam: Elsevier, pp. 123-128. STANSBURY, J.W. (1990): Cyclopolymerisable Monomers for Use in Dental Resins and Composites, JDent Res 69:844-848. THOMPSON, V.P.; WILLIAMS,E.F.; and BAILEY,W.J. (1979): Dental Resins with Reduced Shrinkage During Hardening, J Dent Res 58:1522-1532. TIMOSHENKO,S. (1956): Strength of Materials; Part 2: Advanced, 3rd ed., London: Van Nostrand Reinhold Co., p. 98. WALLS,A.W.G.; MCCABE, J.F.; and MURRAY,J.J. (1988): The Polymerization Contraction of Visible-Light Activated Composite Resins, J Dent 16:177-181. WATTS,D.C. (1991): Dental Restorative Materials. In: Materials Science and Technology: A Comprehensive Treatment, R.W. Cahn, P. Haasen, and E.J. Kramer, Eds. Volume 14: Dental and Medical Materials, D.F. Williams, Ed. Weinhelm, Germany: VCH Verlagsgesellschaft mbH, chapter 6. WATTS,D.C.; AMER,O.; and COMBE,E.C. (1984): Characteristics of VisibleLight-Activated Composite Systems, Br Dent J 156:209-215. WATTS,D.C. and CASH,A.J. (1988): Kinetics of Rigid Polymerization Contraction in Visible-Light-Activated Restoratives, J Dent Res 67:224, Abstr. No. 895. WILLIAMS,G. and WATTS, D.C. (1970): Non-symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function, Trans Faraday Soc 66:80-85. WILSON,H.J. (1978): Properties of Radiation-Cured Restorative Resins. In: Proceedings of the International Symposium on Fotofil Dental Restorative. London: Franklin Scientific Projects, pp. 11-16.

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