Simulation of the shrinkage of dental polymeric composites

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1 e-polymers 2005, no ISSN Short communication: Simulation of the shrinkage of dental polymeric composites Tomasz Boguszewski *, Wojciech Swieszkowski *, Malgorzata Lewandowska, Krzysztof J. Kurzydlowski Faculty of Materials Science and Engineering, Warsaw University of Technology, Woloska 141, Warsaw, Poland; Fax ; (Received: September 13, 2004; published: May 18, 2005) This work has been presented at the E-MRS Fall Meeting, September 6-10, 2004, in Warsaw, Poland Abstract: The aim of this study was to investigate the influence of size and shape of ceramic filler in dental composites on polymerization shrinkage. Moreover, the influence of resin shrinkage itself on the whole composite shrinkage was investigated. In 3D linear elastic finite element analyses, the process of shrinkage of dental resin/ceramic composites during polymerization was simulated using the ANSYS software. Composites were modelled with volumetric content of ceramics ranging from 0 up to 45%. Aggregates with different shape and size were analysed. Quantitative estimates have been obtained of the reduction in composite shrinkage with increasing content of ceramic aggregate or decreasing shrinkage of the resin. It has been found that by adjusting aggregate size and resin shrinkage a lower shrinkage of the dental composite may be obtained. Introduction A lot of efforts have been taken recently to develop polymer-based replacements for the amalgam used traditionally as dental filling material. A polymer that had been widely used in dental fillings is made of the monomer bisglycidylmethyl methacrylate (bis-gma) [1]. Bis-GMA/ceramic filler composites are nowadays offered by a number of companies. However, one of the main problems influencing longevity of polymerbased dental restorations is shrinkage of the resin. As the resin matrix polymerizes it shrinks and for large cavities the composite material might be pulled away from the cavity walls. This, in turn, leads to restoration failures by de-bonding at the composite-tooth interface. The shrinkage of currently used resins ranges from 1.5 to 3% of the total material volume [2]. This is enough to develop high stresses at the composite-tooth interface. One of the ways to reduce these stresses is adding ceramic fillers to the resin, which at the same time impart higher hardness and wear resistance. Currently available commercial dental composites contain inorganic reinforcing filler particles of various 1

2 sizes and shapes to reduce the material shrinkage [3]. The aim of the present study was to investigate quantitatively how size and shape of these particles influence composite shrinkage due to polymerization. Methods The study was performed by finite element (FE) modelling. 3D elastic analyses were carried out using ANSYS software to simulate the process of shrinkage of dental resin/ceramic composites during polymerization. Linear and isotropic properties have been assumed of the materials (their mechanical properties are shown in Tab. 1). The composites were modelled as bricks (brick side Bs < 0.6 µm) cut out from the dental restoration. In calculations only one eighth of the sample was considered due to the symmetry of boundary conditions. In FE analysis Solid95 elements (which have 20 nodes) were used [4]. (This type of elements is recommended for structural analysis.) The average number of elements in the models was To simplify the model the ceramic aggregate was assumed not to deform under the investigated conditions. Tab. 1. Data for materials of dental composites Material Young modulus, E / GPa Poisson ratio resin ceramic The polymerization shrinkage of the composite was modelled using temperaturedependent expansion. For shrinkage modelling it was assumed that the thermal expansion coefficient for ceramic is equal to zero. In the first step, to simulate the different shrinkage of the resin the equivalent temperature change was determined using the FE model for purely polymeric filler. The total displacements at the edges of the modelled volume calculated in the FE simulations were used to compute shrinkage (decrease of volume, in %) according to the equation: z Cs = 3 ( z u ) ( z u ) ( z u ) x z 3 y z 100% where Cs is composite shrinkage, z = Bs/2 is the side of 1/8-th of the modelled volume, u x, u y, u z are displacements in X, Y, and Z directions, respectively. After such temperature/shrinkage calibration, it was possible to generate a needed shrinkage of the resin for different resin/ceramic composites only by changing the temperature in the model. The total displacements obtained from the FE simulations were then used to calculate the total composite shrinkage for different types of analysed composites. Using the described method, the influence of the ceramic contribution and resin shrinkage on the shrinkage of the dental composites was investigated. Although the currently used composites may contain between 40 and 65% of filler, in the present study the composites were modelled with volumetric contribution of ceramic filler from 0 up to 45%. It was dictated by the assumption of the simplified model. The ceramic particles were represented in the model by balls with radii of 0.15 µm. Volumetric 2 (1)

resin shrinkage of 3%, 7.7%, 9%, 12%, and 30% was applied to the composite brick via the described thermal mismatch analogy.

However, for the purpose of this study, the effect of theoretically higher shrinkage was investigated.

Analysis of the influence of surface area of the ceramic aggregate on shrinkage required applying in the model shapes of aggregates (such as c and d in Fig.1) that are not commercially available.

Finally, the influence of an irregular, non-symmetric aggregate on the shrinkage was studied by using cylindrical ceramic particles (Fig. 1e) in the composite model.

Ceramic aggregates used in this study as composite fillers: a) sphere, b) cube, c) spider I, d) spider II, e) cylinder Results and discussion Quantitative estimates have been obtained of the

3 resin shrinkage of 3%, 7.7%, 9%, 12%, and 30% was applied to the composite brick via the described thermal mismatch analogy. The range of the modelled resin shrinkage is wider than the range of the currently used restoration (10-14%). However, for the purpose of this study, the effect of theoretically higher shrinkage was investigated. Different particles with different shapes, different surface areas but the same volume (thus the same volumetric contribution in the composite) were analysed (see Fig. 1). Analysis of the influence of surface area of the ceramic aggregate on shrinkage required applying in the model shapes of aggregates (such as c and d in Fig.1) that are not commercially available. Resin shrinkage and volumetric contribution of the ceramic were 7.7% and 5%, respectively. Finally, the influence of an irregular, non-symmetric aggregate on the shrinkage was studied by using cylindrical ceramic particles (Fig. 1e) in the composite model. This type of composite had the same volumetric contribution of the ceramic (5%) and the same resin shrinkage (7.7%) as the previous composites. a) b) c) d) e) Fig. 1. Ceramic aggregates used in this study as composite fillers: a) sphere, b) cube, c) spider I, d) spider II, e) cylinder Results and discussion Quantitative estimates have been obtained of the reduction in composite shrinkage with increasing volumetric contribution of the ceramic aggregate (Fig. 2). The maximum total displacement of the composite points, which is representative for composite shrinkage in the model, decreases with increasing volumetric content of the ceramic (Fig. 3). Decrease of resin shrinkage also results in the reduction of composite shrinkage (Fig. 2). It was also found that when the shrinkage of the composite resin is below 5% the influence of filler content in the composite can be neglected. However, for a resin shrinkage of over a dozen percentages the ceramic content has a crucial influence on the shrinkage of the composite. 3

35,00% Compoosite shrinkage (Cs) 30,00% 25,00% 20,00% 15,00% 10,00% Vc=7,7% Vc=12% Vc=9% Vc=30% Vc=3% 5,00% 0,00% 0 5 10 15 20 25 30 35 40 45 Volumetric contributions of the ceramic (Vc) [%] Fig. 2. Composite shrinkage vs.

4 35,00% Compoosite shrinkage (Cs) 30,00% 25,00% 20,00% 15,00% 10,00% Vc=7,7% Vc=12% Vc=9% Vc=30% Vc=3% 5,00% 0,00% Volumetric contributions of the ceramic (Vc) [%] Fig. 2. Composite shrinkage vs. volumetric content of the ceramic and the shrinkage of the resin Fig. 3. Total displacements of composite points for two different volumetric contributions of the ceramic (45% - left, 15% - right) and a resin shrinkage of 7.7% The relationship between the size of the aggregate surface area (S) being in contact with the resin and the composite shrinkage (Cs) is shown in Tab. 2 and Fig. 4. For a bigger surface area of the aggregate a smaller shrinkage has been obtained. The relationship is non-linear. With increasing the surface area by about 20% the composite shrinkage decreases by about 1%. For instance, the maximum displacement of composite points in X direction is higher for the composite with spherical aggregate (u x = µm) than for the same composite with spider-shaped aggregate (u y = µm) (Fig. 5). Therefore, the shrinkage for the first type of composite with smaller surface area S is bigger than for the second one with bigger S. When spherical or cubic fillers are used the shrinkage is similar in different directions. However, when cylindrical aggregate is used the shrinkage is not any more isotropic (Fig. 6). The displacements of the composite points in the X, Y, and Z directions 4

5 differ. The smallest displacement, thus the smallest shrinkage, is found in the direction of the axis of the cylinder. The displacements in X and Y directions, however, do not differ significantly. In the study the influence of ceramic content on dental composite shrinkage due to polymerization was investigated using a 3D elastic finite element method (FEM). Several previous studies have proved that FE could be used in such analysis with success [5,6]. Different volumetric resin shrinkage processes can be simulated using the analogy to thermal shrinkage. In the present study, FEM has been used to model the displacements on the surface (edges) of a standard cube of the composite. By calculating the displacements in different directions it is possible to calculate the total volumetric shrinkage of the composite and assess its isotropy. The presented model required some assumptions. The shrinkage of the composite was simulated using the assumption about a direct relation between resin shrinkage and thermal contraction of the material. However, in a future study a more advanced model at molecular level could be used to simulate polymerization with change of molecular structure and physicochemical properties of the material in time. Moreover, for the purpose of this study due to the macro scale of the model the contribution of the interfacial layer between resin and particle was neglected. Tab. 2. Influence of the aggregate surface area (S) being in contact with the resin on composite shrinkage (Cs) Shape Surface, S / µm 2 Shrinkage, Cs in % sphere cube spider I spider II ,25 7,2 Composite shrinkage Vs [%] 7,15 7,1 7,05 7 6,95 6,9 6,85 0,025 0,03 0,035 0,04 0,045 0,05 Surface area [ microm.^2 ] Fig. 4. Relationship between aggregate surface area (S) being in contact with the resin and composite shrinkage (Cs) 5

Fig. 5. Displacements of the composite for spherical (left) and spider II-shaped aggregates (right). Constant resin shrinkage of 7.

0637 µm Fig. 6. Displacements of the composite in X and Y directions for the cylindrical aggregate for a resin shrinkage of 7.

224 µm The objective of this particular study was to develop design rules for dental composite materials.

6 Fig. 5. Displacements of the composite for spherical (left) and spider II-shaped aggregates (right). Constant resin shrinkage of 7.7% and volumetric content of the ceramic aggregate of 5% have been assumed. The radius of the sphere is 0.15 µm. The dimensions of the disc are: radius 0.15 µm and height µm Fig. 6. Displacements of the composite in X and Y directions for the cylindrical aggregate for a resin shrinkage of 7.7% and a volumetric contribution of the ceramic aggregate of 5%. The dimensions of the cylinder are: radius 0.08 µm and height µm The objective of this particular study was to develop design rules for dental composite materials. Since one of the main, unsolved problems with composite materials that adversely affect their long-term survival remains polymerization shrinkage and stresses, they have become a focal point of the present analysis. In particular the influence of ceramic content and particle size and shape has been simulated. The presented method may be a very useful tool in the selection of fillers for new dental 6

7 composites. The main advantage of this method is that it is less time consuming and less expensive than any experiment. The obtained results indicate that by changing the ceramic volumetric content shrinkage of the composite can be significantly reduced. A lower shrinkage can be also obtained by increasing the ceramic particles surface-to-volume ratio. For fixed volumetric content this parameter depends on size and shape of the particles. In view of the present results it can be expected that in order to decrease the shrinkage, nano-particles might be added to the composites. An alternative is to use highly elongated or complex shaped particles. Such particles, however, may make the filling process significantly more difficult. The efficiency of shrinkage reduction by increasing the specific surface area of the ceramic-resin interface strongly depends on ceramic-resin bonding. Therefore, surface treatment of fillers by coupling agents used to improve the adherence of resin to filler surfaces should be common practice to overcome the risk of de-lamination. Although the present results have already proved to be useful in the search for composite design rules, further studies are needed, which will lead to developing a comprehensive 3D FE model of dental restoration. The dynamic process of shrinkage during polymerization and the resulting shrinkage stresses will be analysed. Timedependent shrinkage, apparent viscosity, Young's modulus, Poisson ratio, and resulting creep, which change during the polymerization process, will be determined experimentally and implemented into the model. Finally, the presented method could be useful not only for people interested in dental composites. It could be adopted to investigate the effect of fillers on polymerization shrinkage of most of the polymeric composites. Acknowledgement: This research has been financed by a grant from the State Committee for Scientific Research, KBN (number 21/PBZ-KBN-082/T08/2002). [1] Braga, R. R.; Ferracane, J. L.; Crit. Rev. Oral Biol. Med. 2004, 15(3), 176. [2] de Gee, A. F.; Feilzer, A. J.; Davidson, C. L.; Dent. Mater. 1993, 9(1), 11. [3] Bowen, R. L.; Marjenhoff, W. A.; Adv. Dent. Res. 1992, 6, 44. [4] Ansys Help - ANSYS Release 8.0 Documentation, [5] Winkler, M. M.; et al.; J. Biomed. Mater. Res. 2000, 53, 554. [6] Laughlin, G. A.; Williams, J. L.; Eick, J. D.; J. Biomed. Mater. Res. 2002, 63,

Influence of particles-matrix interphase on stress distribution in particulate composite with polymer matrix

Applied and Computational Mechanics 1 (2007) 143-148 Influence of particles-matrix interphase on stress distribution in particulate composite with polymer matrix Z. Majer a,b, *, P. Hutař a,, L. Náhlík