30_700.pdf

Dental Materials Journal 2011; 30(5): 700706

INTRODUCTION

Gypsum is a mineral composed of calcium sulfate dihydrate. Upon calcination of calcium sulfate dihydrate, the partially dehydrated mineral is called calcium sulfate hemihydrate. Gypsum is one of the most extensively used materials in dental prosthesis laboratories because of its low cost and easy modification of its properties by adding other chemical components.

When the powder particles of gypsum are mixed with water, a setting reaction occurs. It is an exothermic chemical reaction according to the following equation1):

(1)

During the setting reaction shown in Eq (1) above, the hemihydrate is converted to dihydrate when mixed with water. A volumetric contraction is associated with this setting process, which varies according to the density difference between the reagents (sulfate hemihydrate and water) and the reaction product (sulfate dihydrate). However, an expansion of the material occurs instead which can be explained by crystallographic theory namely the outward thrusting of the gypsum crystals in their growth during setting2,3). Consequently, because of expansion caused by the growth of calcium sulfate dihydrate crystals during setting, the final material will be porous. Therefore, a good knowledge of the setting expansion of dental gypsum is essential to the accuracy of fit and clinical performance of dental prostheses. By the same token, linear thermal expansion coefficient is an equally important property to dental professionals

and technicians too.Although the manufacturers of all gypsum products

provide information on the water/powder (w/p) ratio to be used for optimal performance, these recommendations are not correctly or faithfully followed by some dental technicians. It is extremely important to examine the clinical implications of such procedural deviations, in particular any adverse impact on the final product properties.

The main goal of this work was the characterization of different w/p ratios, with a view to investigating the influence of water amount on gypsum properties. The material analyzed was dental gypsum type IV, and five w/p ratios were examined in this study for this material. As for the gypsum properties being investigated, they were setting expansion and thermal variation that occurred during setting, and the coefficient of thermal expansion.

For the measurement of setting expansion or shrinkage that typically occurs during the polymerization of dental composites, numerous methods have been employed: micrometer slide cathetometer4), gas pycnometer5), electrical resistance strain gauge6), water dilatometer7), and bonded-disk method8). In the present study, the experiments were performed and the data collected using fiber Bragg grating (FBG) sensors.

Fiber optic sensors offer smaller size and reduced weight characteristics, and a slew of other advantages such as high sensitivity, chemical inertness, and installation and handling ease. Taken together, these attractive advantages allow fiber optic sensors to be embedded in different materials for measurement of

CaSO4. CaSO4.H2O+ 2H2O+ heatH2O1 2 3 2

Characterization of different water/powder ratios of dental gypsum using fiber Bragg grating sensorsNlia ALBERTO1, Ldia CARVALHO2,3, Hugo LIMA1, Paulo ANTUNES1, Rogrio NOGUEIRA2,4 and Joo L. PINTO1

1Department of Physics, I3N, University of Aveiro, Campus Universitrio de Santiago, 3810-193 Aveiro, Portugal2Instituto Politcnico de Sade do Norte, Rua Central de Gandra, 4585-116 Gandra Prd, Portugal3Centro de Tecnologia Mecnica e Automao, Departamento de Engenharia Mecnica, Universidade de Aveiro, Campus Universitrio de Santiago, 3810-193 Aveiro, Portugal4Instituto de Telecomunicaes Plo de Aveiro, Campus Universitrio de Santiago, 3810-193 Aveiro, PortugalCorresponding author, Nlia Jordo ALBERTO; E-mail: [email protected]

The impact of five different water/powder (w/p) ratios in the characterization of high strength dental stone was evaluated, since the recommendations of the gypsum manufacturers are not always correctly followed by the dental prosthesis technicians. Fiber Bragg grating (FBG) sensors were used to measure the setting expansion and temperature variation which occurred during the setting reaction for each w/p ratio, as well as the thermal expansion coefficient. Thick mixtures with low w/p ratios had more crystals impinging upon each other during crystal growth, resulting in more expansion and more heat released. This thermal behavior was only achieved to w/p ratios within the manufacturer-recommended mixing ratio range. The results also revealed the existence of boundary condition; this corresponding to the limit of the mixing ratio recommended by the gypsum manufacturer. Data provided in this study are particularly important for dental technicians with a view to attaining the best results in accuracy of fit for their prosthetic works.

Keywords: Dental gypsum, Fiber Bragg grating sensors, Water/powder ratio, Setting expansion, Thermal expansion coefficient

Received Jan 11, 2011: Accepted Jun 2, 2011doi:10.4012/dmj.2011-004 JOI JST.JSTAGE/dmj/2011-004

Dent Mater J 2011; 30(5): 700706 701

different kinds of parameters. Researchers have used FBG sensors for the measurement of hygroscopic setting expansion and polymerization shrinkage of dental materials, and favorable promising results were reported9-12). Thus, during the last few years, research work devoted to studying and exploring the potential application of fiber optic technology in biomedicine has increased significantly13-16).

MATERIALS AND METHODS

Gypsum and w/p ratiosHigh-strength dental stone (Ugistone Class IV, UGINdentaire, Seyssins, France) was selected for use as gypsum in this study. According to the manufacturer, the recommended mixing ratio should range between 0.150 and 0.240.

A key aim of this study was to assess the influence of w/p ratio on several physical properties of the final gypsum product. Five different w/p ratios were used in this study: 0.204, 0.216, 0.240, 0.264, and 0.276. The first two ratios corresponded respectively to 15% and 10% decrease in water amount relative to w/p=0.240. The last two ratios corresponded respectively to 10% and 15% increase in water amount relative to w/p=0.240, and they were not within the manufacturer-recommended mixing ratio range. Temperature at which water was mixed with gypsum powder to prepare the mixture was 21C.

Fiber Bragg grating sensorsIn its simplest form, an FBG is a segment of the optical fiber with a periodic modulation of the core refractive index along the fibers longitudinal axis. Periodic modulation of core refractive index is achieved by exposing the core of a photosensitive optical fiber to an intense ultraviolet light interference pattern. This pattern could be created by using a phase mask or by interferometric processes.

When an FBG is illuminated by a broadband light source, only wavelengths that satisfy the Bragg condition are reflected while all the others are transmitted (Fig. 1). The Bragg condition is defined by the following expression:

(2)

where B is the central wavelength of the back-reflected light (Bragg wavelength), neff is the effective refractive index of the fiber core, and is the period of refractive index modulation.

When the grating is subjected to temperature changes and/or mechanical perturbations, the reflected Bragg wavelength changes according to Eq (3) as follows:

(3)

The first term on the right hand side of Eq (3)

represents the strain effect on Bragg wavelength variation, and the second term temperature dependence on the same parameter. Based on this equation, it is possible to use an FBG as a sensing element, monitoring the back-reflected light from the Bragg grating17).

One drawback of FBG sensors is their cross sensitivity to both strain and temperature, which requires special techniques to compensate one of the parameters when measuring the other. Several methods have already been proposed to overcome this drawback, some of which involved the use of a single FBG sensor for the simultaneous measurement of temperature and strain18-20). In this study, two FBG sensors were used to resolve this drawback and setup details are discussed further in the ensuing section.

Experimental setupUsing an automated phase mask-based interferometer system, two FBGs were inscribed into photosensitive, single-mode optical fiber (PS1250/1500, FiberCore Ltd., Southampton, England) by continuous wave (CW) ultraviolet laser irradiation (244 nm). One FBG sensor consisted of an exposed FBG which would be in direct contact with dental gypsum, and hence sensitive to strain and temperature variations. The other FBG sensor was the temperature sensor, and it was placed inside a double needle to overcome the cross sensitivity problem (Fig. 2). The double needle protected the optical

B=2neff

B= 2 l+2 T +neff neff l l( ) +neff neff T T( )

Fig. 1 Schematic diagram of an FBG sensor and the reflected and transmitted signals.

Fig. 2 Temperature sensor: (a) FBG inside a needle; and (b) FBG sensor inside a double needle.

Dent Mater J 2011; 30(5): 700706702

fiber from mechanical perturbations, so that the FBG sensor was sensitive to temperature variations only. Temperature and strain sensitivity coefficients of the FBG sensors were calculated to be 8.3 pm/C and 1.15 pm/ respectively.

The exposed FBG was placed inside a metallic container (35 mm diameter and 70 mm height) which contained a hole at the bottom, through which the fiber could be pulled. The fiber was attached to a support and slightly tensioned (about 500 ), allowing the FBG sensor to measure not only the gypsums setting expansion, but also its initial shrinkage. Due to the fibers smooth surface texture, our preliminary analysis suggested that there was some degree of sliding between the gypsum and the fiber. To overcome this, two plastic spheres were glued to the fiber, below and above the sensor (Fig. 3). This thus allowed the sensor to accurately measure the changes that took place during the setting reaction of dental gypsum. Further, the experiments were carried out at a controlled ambient temperature of 21C to preclude the influence of thermal fluctuations on the results.

Sample preparation and measurementFor each w/p ratio, powder was gradually added to distilled water and the mixture hand-spatulated for 45 seconds before it was poured into the cylinder shown in Fig. 3. These precautions were taken to avoid the formation of porous samples.1. Strain and temperature variation measurementTo measure both the setting expansion and temperature variation which occurred during the setting reaction of dental gypsum, the temperature sensor in a double

needle was inserted into the cylinder and close to the exposed FBG sensor (Fig. 3). For both FBG sensors, wavelength measurement was done using an FBG interrogation system (sm125 Optical Sensing Interrogator, Micron Optics Inc, Atlanta, GA, USA) with an interval of 5 seconds between each measurement and for a total duration of more than 3 hours.

Five experiments were performed for each w/p ratio. Result shown for each w/p ratio was the mean curve of these five experiments. Maximum temperature variation and minimum/maximum strain values were obtained from these mean curves. For each w/p ratio, the presented error corresponded to the maximum deviation of the obtained values from the five experiments relative to the average value.2. Linear thermal expansion coefficient measurementTaking advantage of the strain and temperature sensors already embedded in the gypsum sample, the linear thermal expansion coefficient could next be determined using Eq (4) below which defines the relative deformation of a material when its temperature is raised or lowered by 1C:

(4)

where L represents the linear thermal expansion coefficient, li and lf are the initial and final lengths of the material before and after temperature change respectively, and (Tf -Ti) represents the temperature variation that causes this material deformation.

Cured gypsum samples were taken out of the cylinder and placed inside an environmental chamber (CH 340, Angelantoni Industrie, Massa Martina, Italy). Temperature was set from 20C to 80C in 10C step increments. After temperature had stabilized at each new temperature setting, data from both FBG sensors were recorded. Humidity control for all experiments was set at 60%.

Five experiments were performed for each w/p ratio. Result shown for each w/p ratio was the mean curve of these five experiments. For each w/p ratio, the associated error was the standard deviation derived from the slope of the linear fit to the experimental data.

Statistical analysisFor all the strain and temperature data obtained in this study for each w/p ratio, the presence of any statistical significance was determined using one-way ANOVA. Tamhanes and Tukeys post hoc tests were used to determine differences in data among the w/p ratios.

RESULTS

Strain and temperature variationFigures 4 and 5 show the strain evolution and temperature variation curves, as a function of time during the setting reaction, for all the five w/p ratios examined in this study. Strain evolution curve was

(lf li)li (Tf Ti)

=L

Fig. 3 Schematic representation of the experimental setup.

Dent Mater J 2011; 30(5): 700706 703

obtained by subtracting the temperature variation measured using the FBG sensor inside the double needle from the overall signal measured using the exposed sensor.

Results in Figs. 4 and 5 showed that the maximum strain and temperature variation values increased as the w/p ratio decreased. For all w/p ratios, shrinkage reached their maximum values during the first 15 min of the setting reaction. As temperature increased, an accentuated expansion of the gypsum material was observed. Setting expansion continued for all w/p ratios even after material temperature reached its maximum and started to decline to its initial value of 21C. However, for w/p ratio=0.276, 90% of its maximum expansion was already achieved at 45 min after the setting reaction started.

On the overall, all w/p ratios exhibited the same strain evolution and temperature variation behaviors as a function of time, although the maximum temperature variation and minimum/maximum strain values reached were different among the w/p ratios. These values, as derived from Figs. 4 and 5, are presented in Table 1 for each w/p ratio. The corresponding setting expansion values, expressed in percentage, are also given in Table

1.1. Statistical analysis of strain valuesAccording to one-way ANOVA for the strain values, statistically significant differences were detected for each w/p ratio (p

Dent Mater J 2011; 30(5): 700706704

df=4). Test of homogeneity of variances revealed the following statistics: df1=4, df2=20, and p=0.521. This meant that the variances between w/p ratios were equal, and thus Tukeys post hoc test was carried out.

For w/p ratios 0.204 and 0.216, their mean temperature variation values were significantly different from the other w/p ratios. On the other hand, temperature variation values between the following w/p ratios were considered statistically equal: w/p ratios 0.264 and 0.276 (p=0.590); 0.240 and 0.264 (p=0.787); 0.240 and 0.276 (p=0.997).

Applying Tukeys post hoc test to identify statistically homogeneous subsets (=0.05), three groups based on the means of temperature were revealed. Group 1 consisted of w/p ratio 0.204; Group 2 consisted of w/p ratio 0.216; and Group 3 consisted of w/p ratios 0.240, 0.264, and 0.276.

Linear thermal expansion coefficientFigure 6 shows the strain of gypsum as a function of temperature. Likewise, each strain value was obtained by subtracting the temperature variation measured using the FBG sensor inside the double needle from the overall signal measured using the exposed sensor.

For w/p ratios within the manufacturer-recommended range (i.e., 0.204, 0.216, 0.240), a linear thermal expansion behavior was observed from 20C to 50C. However, this tendency changed after the temperature reached 50C and the gypsum material began to shrink. For w/p ratios 0.264 and 0.276, a small amount of shrinkage was observed between 20C and 30C. After which, the gypsum material started to expand until 60C. As temperature continued to increase above 60C, the material started to shrink again. On the overall, maximum shrinkage values were recorded for w/p ratios 0.204, 0.216, 0.240; interestingly, these ratios were within the mixing ratio range recommended by the

gypsum manufacturer.For w/p ratios 0.264 and 0.276, no linear thermal

behaviors were observed for them and thus they were not considered for linear thermal expansion coefficient determination. For the remaining three w/p ratios, the coefficient was calculated using the slope of the line fitted to the experimental data. Table 2 displays their results and the respective standard deviations. The greatest linear thermal expansion coefficient, L=14.2106C1, was obtained for w/p ratio 0.204. Interestingly, this w/p ratio could be deemed as the mean value of the mixing ratio range recommended by the gypsum manufacturer, but the linear thermal expansion coefficient obtained was approximately twice that of other ratios.

DISCUSSION

FBG sensors were used in the characterization of five different w/p ratios of a high-strength dental stone. Setting expansion and temperature variation were measured during the setting reaction for all w/p ratios, and thermal expansion coefficients were also determined.

At 120 min after the setting reaction had started, the linear setting expansion for all w/p ratios was lower than 0.15%, which was in compliance with the requirement specified in ISO 6873:1998(E) standard. This international standard gives a classification of, and specifies requirements for, gypsum products used for dental purposes. It also specifies the test methods to be employed to determine compliance with these requirements. In this study, linear setting expansion was measured using an extensometer.

Table 1 revealed that the maximum strain exhibited during the setting reaction decreased linearly with increase in w/p ratio, as further illustrated in Fig. 7. Higher setting expansion for lower w/p ratios was attributed to an increase in crystal impingement between the large amounts of crystals formed. In other words, the greater the amount of water used, the fewer the nuclei per unit volume, and hence less expansion2,3).

Heat released during the exothermic setting reaction of gypsum, as shown in Eq (1), resulted in temperature changes. For the three lower w/p ratios which were within the manufacturer-recommended mixing ratio range, Fig. 8 shows that there was a linear correlation

Table 2 Linear thermal expansion coefficients and their standard deviations calculated for three w/p ratios

w/pratio

Linear thermal expansion coefficient(106 C1)

0.204 14.2 (0.7)

0.216 7.4 (0.8)

0.240 8.4 (0.9)

Fig. 6 Thermal strain of gypsum as a function of temperature for the different w/p ratios.

Dent Mater J 2011; 30(5): 700706 705

between heat release and w/p ratio: the higher the w/p ratio, the lower the amount of heat released. Results for the other two higher w/p ratios suggested that the reaction had reached a saturation level; it should be pointed out than the temperature change for these two ratios could be due to apparatus measurement error.

During thermal expansion coefficient measurement, initial shrinkage was noted for the two higher w/p ratios. This could be due to evaporation of excess water, since initial shrinkage was observed only for the two high w/p ratios which contained a greater amount of water. From 50C for the three lower ratios analyzed, and 60C for the remaining two ratios, the change in strain behavior could be the result of a new crystal phase formation. Information about this behavior is scarce in the published literature, which meant that this issue must be further investigated in future studies. At 80C, maximum

shrinkage values were observed for the three lower w/p ratios. This could be due to water loss by evaporation from the micropores. When compared with thin mixtures (high w/p ratios), thick mixtures (low w/p ratios) led to more micropores being formed in the wake of more crystals impinging upon each other during the setting reaction21).

Results obtained in this study with FBG sensors confirmed the existence of boundary conditions, notably at w/p ratio=0.240. For w/p ratios above this value, a different behavior was observed for the temperature change which occurred during the setting reaction and hence the linear thermal expansion coefficient. Herein lay the importance of dental technicians following the manufacturers recommendations when mixing gypsum for prosthetic works otherwise, exceeding the uppermost limit or boundary of the mixing ratio recommended by the gypsum manufacturer would lead to unpredictable results.

CONCLUSIONS

In this work, FBG sensors were used to investigate the physical properties of dental gypsum type IV rendered by different w/p ratios. Within the limitations of the present study, the following conclusions were drawn:

1. Setting expansion was inversely proportional to w/p ratio.

2. Heat released during the setting reaction was also inversely proportional to w/p ratio for the three w/p ratios within the manufacturer-recommended mixing ratio range.

3. Behavior of strain as a function of temperature, obtained through linear thermal expansion coefficient measurement, suggested the formation of a new crystal phase from 50C for the three lower ratios analyzed, and 60C for the remaining two ratios, and loss of water by evaporation from the micropores for the three lower w/p ratios.

4. Existing boundary conditions corresponded to the uppermost limit of the mixing ratio recommended by the gypsum manufacturer. Change in water amount affected the setting expansion of the gypsum product, which would compromise the proper manipulation and quality of the set mass, and ultimately the accuracy of fit of the fabricated prosthetic work.

5. Further research is recommended to investigate the effect of crystal type (- and -hemihydrates) on transition temperature and the reaction kinetics of the hemihydrate hydration process.

ACKNOWLEDGMENTS

Nlia Alberto, Hugo Lima, and Paulo Antunes acknowledge the financial support from Fundao para a Cincia e a Tecnologia (Portugal) through their respective doctoral grants, (SFRH/BD/30551/2006), (SFRH/BD/30295/2006), and (SFRH/BD/41077/2007). The authors also acknowledge the support received through

Fig. 8 Dependence of temperature variation on w/p ratio.

Fig. 7 Dependence of maximum strain on w/p ratio.

Dent Mater J 2011; 30(5): 700706706

the projects, PTDC/CTM/101538/2008 and PTDC/SAU-BEB/100650/2008.

REFERENCES1) Phillips RW. Skinners science of dental materials. 9th ed.

Philadelphia, WB Saunders Co.: 1991.2) Craig RG, Powers JM. Restorative Dental Materials. 11th ed.

Mosby Year Book, St. Louis, 2002.3) Winkler MM, Monaghan P, Gilbert JL, Lautenschlager EP.

Freeze-drying and scanning electron microscopy of setting dental gypsum. Dent Mater 1995; 11: 226-230.

4) Mahler DB, Ady AB. An explanation for the hygroscopic setting expansion of dental gypsum products. J Dent Res 1960; 39: 578-589.

5) Cook WD, Forrest M, Goodwin AA. A simple method for the measurement of polymerization shrinkage in dental composites. Dent Mater 1999; 15: 447-449.

6) Sakaguchi RL, Sasik CT, Bunczak MA, Douglas WH. Strain gage method for measuring polymerization contraction of composite restoratives. J Dent 1991; 19: 312-316.

7) Rees JS, Jacobsen PH. The polymerization shrinkage of composite resins. Dent Mater 1989; 5: 41-44.

8) Watts DC, Cash AJ. Determination of polymerization shrinkage kinetics in visible-light-cured materials: methods development. Dent Mater 1991; 7: 281-287.

9) Milczewski MS, Silva JC, Abe I, Carvalho L, Nogueira R, Paterno AS, Kalinowski HJ, Pinto JL. Determination of setting expansion of dental materials using fibre optical sensing. Meas Sci Technol 2006; 17: 1152-1156.

10) Milczewski MS, Silva JC, Paterno AS, Kuller F, Kalinowski HJ. Measurement of composite shrinkage using a fibre optic Bragg grating sensor. J Biomater Sci Polymer Edn 2007; 18: 383-392.

11) Anttila E, Krintil O, Laurila T, Lassila LVJ, Vallittu PK, Hernberg R. Evaluation of polymerization shrinkage and hydroscopic expansion of fiber-reinforced biocomposites using optical fiber Bragg grating sensors. Dent Mater 2008; 24:

1720-1727.12) Alberto N, Carvalho L, Nogueira R, Pinto J. Characterization

of polymerization reaction of self-curing dental cements using fibre optic sensors. Proceedings of the I International Conference on Biodental Engineering; 2009 June 2627; Porto, Portugal; 161-163.

13) George R, Walsh LJ. Performance assessment of novel side firing flexible optical fibers for dental applications. Lasers Surg Med 2009; 41: 214-221.

14) Jang HS, Park KN, Kim JP, Sim SJ, Kwon OJ, Han YG, Lee KS. Sensitive DNA biosensor based on a long-period grating formed on the side-polished fiber surface. Opt Express 2009; 17: 3855-3860.

15) Mishra V, Singh N, Rai DV, Tiwari U, Poddar GC, Jain SC, Mondal SK, Kapur P. Fiber Bragg grating sensor for monitoring bone decalcification. Orthop Traumatol Surg Res 2010; 96: 646-651.

16) Kanellos G, Papaioannou G, Tsiokos D, Mitrogiannis C, Nianios G, Pleros N. Two dimensional polymer-embedded quasi-distributed FBG pressure sensor for biomedical applications. Opt Express 2010; 18:179-186.

17) Kersey A, Davis M, Patrick H, LeBlanc M, Koo K, Askins C, Putnam M, Friebele E. Fiber grating sensors. J Lightwave Technol 1997; 15: 1442-1463.

18) Lu P, Men L, Chen Q. Resolving cross sensitivity of fiber Bragg gratings with different polymeric coatings. Appl Phys Lett 2008; 92: 171112 (3 pages).

19) Mondal SK, Mishra V, Tiwari U, Poddar GC, Singh N, Jain SC, Sarkar SN, Kapur P. Embedded dual fiber Bragg grating sensor for simultaneous measurement of temperature and load (strain) with enhanced sensitivity. Microwave Opt Technol Lett 2009; 51: 1621-1624.

20) Park SO, Jang BW, Lee YG, Kim CG, Park CY. Simultaneous measurement of strain and temperature using a reverse index fiber Bragg grating sensor. Meas Sci Technol 2010; 21: 035703 (8 pages).

21) Lautenschlager EP, Corbin F. Investigation on the expansion of dental stone. J Dent Res 1969; 48: 206-210.