Dentin-Composite Interfaces: Static and Viscoelastic Properties. Measured with Nanoindentation. Timothy Pollard

Transcription

1 Dentin-Composite Interfaces: Static and Viscoelastic Properties Measured with Nanoindentation By Timothy Pollard B.S., University of Illinois at Chicago, Chicago, 2010 THESIS Submitted as partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering in the Graduate College of the University of Illinois at Chicago, 2012 Chicago, Illinois Defense Committee: Carmen Lilley, Chair and Advisor Karen Troy, Kinesiology and Advisor Ana Bedran-Russo, Dentistry and Advisor

2 This thesis is dedicated to my wife, Bethany, and my son, Alexander, without whom it would have never been accomplished ii

3 ACKNOWLEDGEMENTS I would like to thank my thesis committee, Dr. Carmen M. Lilley, Dr. Ana Bedran-Russo, Dr. Karen Troy, for their unwavering support and assistance. They provided guidance in how to develop and achieve my research goals and how to enjoy all aspects of research. I would also like to acknowledge Dr. Pete Monaghan for his help and initial guidance in the field of restorative dentistry. In addition I would like to thank Sachin Karol for his help and instruction on learning about nanoindentation; the staff of the RRC and Jack Gibbons for helping me to understand and become a competent user of scanning electron microscopy. Finally, I would like to thank the Chancellor s Discovery funds, without which none of the research would have been possible. iii

4 TABLE OF CONTENTS CHAPTER 1: INTRODUCTION Teeth Tooth Structure Restoration of Dentin Nanoindentation Viscoelasticity Literature Review Study Aims CHAPTER 2: MATERIALS AND METHODS Hysitron Ubi Nanoindenter Force and Roughness Procedure Elastic Modulus vs. Particle Size Particle Size vs. Surface Roughness Elastic Modulus vs. Indentation Force Viscoelastic Procedure Static Viscoelastic Tests Dynamic Viscoelastic Tests CHAPTER 3: RESULTS AND ANALYSIS Statistical Analysis Force and Roughness Elastic Modulus vs. Particle Size Particle Size vs. Surface Roughness Reduced Elastic Modulus vs. Indentation Force Viscoelasticity CHAPTER 4: DISCUSSION Force and Roughness Viscoelasticity CHAPTER 4: CONCLUSION Force and Roughness Viscoelasticity Future Work APPENDIX REFERENCES VITA iv

5 TABLE OF FIGURES Tooth structure of a molar... 3 Nanoindentation scan of Dentin... 5 Typical Collagen type I structure... 6 Dentin-Composite Interfaces... 9 Experimental versus Clinical Restoration... 9 Experimental restoration of Human third molar Dentin restoration preparations Demineralized dentin showing exposed collagen Dentin after application of adhesive and infiltration of collagen Completed restorations with all layers Force versus Displacement for typical nanoindentation curve Various nanoindenter tip types Nanoindentation curve where is the residual depth of indent, is the elastic displacement associated with recovery, is the total depth of indentation, and is the slope of the upper 20% of the unload curve Tip contact. Where the radius of the indenter tip is, the radius of the circle of contact is a, the total depth of indentation is, the depth of the circle of contact is, and the depth of total contact is Smear Layer (not to scale) Nanoindenter False Engage (not to scale) Machine compliance Kelvin and Voigt viscoelastic models Burgers Model where K is the spring constant, C is the dashpot constant, and ε is the strain of each element Dentin-Composite interface prepared from a restored tooth M versus Simplicity showing the width of the Hybrid/Adhesive layer Polishing and testing protocol Force testing flow chart Representative static viscoelastic test series Static Viscoelasticity for polycarbonate Results of the elastic modulus verses particle size. Error bars represent standard deviation Results of the elastic modulus verses the surface roughness. The error bars represent the standard deviation Results of the elastic modulus verses the force. The error represents one standard deviation Dentin storage modulus (left) and loss modulus (right) Macro-Hybrid layer 3M Adper single bond plus. storage modulus (left) and loss modulus (right) Bisco one-step plus Adhesive storage modulus (left) and loss modulus (right) Composite layer Storage modulus (left) and loss modulus (right) Combined results for the viscoelastic response of the macro-dentin-composite Layer SEM image of the dentin composite interface (4000 X magnification) v

6 TABLE OF FIGURES SEM Dentin-Composite junction at 13,000 X magnification (Left), SEM Composite and adhesive boundary at 25,000 X magnification Tubule with peritubular and intertubular dentin at 25,000 X magnification Static Viscoelastic Hybrid layer for 3M Adper One Step Plus test Static Viscoelastic Hybrid layer for 3M Adper One Step Plus test 3 and Static Viscoelastic Hybrid layer for 3M Adper One Step Plus test Static Viscoelastic Hybrid layer for Bisco Single bond plus test 1 and Static Viscoelastic Hybrid layer for Bisco Single bond plus test 3 and Fraction of slope occurrence total (left) and Fraction of slope occurrence per sample (right) vi

7 LIST OF ABBREVIATIONS AND SYMBOLS HBSS UV Hanks Buffered Salt Solution Ultra Violet light NanoDMA Nano-Scale Dynamic Mechanical Amplitude PMMA EDS SEM ABRZ ANOVA RA Poly(methylmethacrylate) Energy Dispersive X-Ray Spectroscopy Microanalysis Scanning Electron Microscopy Acid-Base Resistant Zone Analysis of Variance Roughness Average Residual Depth of Indent Elastic Displacement Associated with Recovery Total Depth of Indentation Slope of the Upper 20% of the Elastic Unload Curve a P Circle of Contact Radius Indenter Load, Mean Contact Pressure Indenter Radius Complex Elastic Modulus ν E Poisson s Ratio Elastic Modulus Depth of the Circle of Contact vii

8 LIST OF ABBREVIATIONS AND SYMBOLS (continued) Depth of total contact α m Material Constant; Surface Roughness Parameter Material Constant Related to Geometry of the Indenter Tip; Geometry Shape Factor; Mass z B n Profile of the Indenter Constant Constant; Constant Associated with the Indenter Tip; Number of Samples Effective Elastic Modulus ε A H B d D Tip Parameter Contact Area Meyer Hardness Brinell Hardness Chord of the Indent Chord of the Indenter Maximum Asperity Height Roughness Average Time from Beginning of Test to Unload Segment S Contact Stiffness Rate of Unloading Initial Height of Surface Instrument Compliance viii

9 LIST OF ABBREVIATIONS AND SYMBOLS (continued) σ K ε C Stress Spring Constant Strain Damper Constant Time Derivative of the Strain Initial Stress Initial Strain Relaxation Time Initial Load on System t x Time Displacement Time Derivative of the Displacement X ϕ ω Second Time Derivative of the Displacement Constant Associated with Displacement Phase Angle Frequency E Storage Modulus E tan δ η Loss Modulus Storage Modulus Divided by Loss Modulus Material Viscosity Retardation time ix

10 LIST OF ABBREVIATIONS AND SYMBOLS (continued) ξ Integration Variable Arithmetic Mean Individual Sample Standard Deviation N Number of Samples Individual Sample x

11 CHAPTER 1: INTRODUCTION This paper has two primary objectives: the first is to examine what effect the force and roughness has on the dentin-composite interface during nanoindentation. The second objective is to examine the effect viscoelasticity has on the dentin composite interface when boundary conditions are neglected. The research questions to be examined in the force and roughness study are: 1. How does the measured elastic modulus vary with polishing particle size? 2. How does the surface roughness vary with polishing particle size? 3. How does the measured elastic modulus vary with the force of indentation? The research questions to be examined in dynamic viscoelastic study are: 1. How does the storage and loss moduli of the dentin differ from the static elastic modulus? 2. How does the storage and loss moduli of the macro-hybrid layer differ from the static elastic modulus? 3. How does the storage and loss moduli of the adhesive layer differ from the static elastic modulus? 4. How does the storage and loss moduli of the composite resin differ from the static elastic modulus? 1

12 2 1.1 Teeth Tooth Structure The tooth structure is very complex and exhibits anisotropic behavior with regards to material properties. The tooth structure is composed two primary structures: enamel and dentin. The enamel provides a thin hard protective layer for the exposed surface of the tooth [1]. Underneath the enamel is dentin, which provides support and comprises the majority of the tooth (Figure 1). At the bottom or root of the tooth, both the pulp and the cementum support the dentin. The pulp is a nutrient interface between the dentin and rest of the body and it contains the nerve of the tooth. The pulp is the primary interface for the body to transport nutrients into the tooth through the dentin tubules, although there are no bioactive cells within dentin or enamel. The cementum is a collagen matrix structurally similar to bone that attaches the tooth to the jaw [2] and is µm thick. The dentin is further comprised of three different regions: intertubular dentin ( ~50% by volume), tubules (~20% by volume) and peritubular dentin (~30% by volume) [3] near the enamel. Closer to the root the tubules and thus peritubular ratios increase while the intertubular dentin ratio decreases.

13 3 Figure 1 Tooth structure of a molar Enamel As illustrated in Figure 1, the enamel is the protective outer layer of the tooth. It is the hardest material found in the body consisting of 85% mineralized tissue [4]. It consists of rods in parallel that are perpendicular to where the dentin and enamel join. Each rod (4-5 m in diameter) consists of protein-covered carbonated apatite fibers of nm in diameter [4, 5]. Enamel is also very brittle and would fracture under the force of mastication without the support of the dentin [6]. The enamel also supports a biofilm that will form within milliseconds of contact with saliva. This biofilm is known as dental plaque, which contains many native species of bacteria that prevent harmful bacteria from forming. The bacteria forms a pellicle which reduces bacteria formation by reducing the surface free energy and acts as lubricating agent to reduce friction [1].

14 4 Dentin At the microscale there are three different types of composite materials located within dentin. They are tubules, intertubular dentin and peritubular dentin [2, 5, 7, 8] as shown in Figure 2. At the nano-scale, dentin is a complex anisotropic material made up of collagen, water, minerals in the form of carbonated apatite crystals and various other trace proteins and minerals. The tubules are essentially hollow tubes filled with biological fluid. There is a great deal of variance between the peritubular and intertubular dentin, which can be seen in their respective hardness and modulus of elasticity values. For intertubular dentin, its hardness and modulus of elasticity are 0.5 GPa and 20 GPa respectively and consist of 30% collagen, 25% water and 45% carbonated apatite crystals. For peritubular dentin, its hardness and modulus of elasticity are 2.3 GPa and 28.6 GPa respectively and consists of 95% carbonated apatite crystals and 5% water, collagen, and proteins [6]. The dentin also acts as a shock absorber for the tooth structure with the intertubular dentin providing immediate impact reduction and the tubules providing a time dependent or viscoelastic damping response.

15 5 Figure 2 Nanoindentation scan of Dentin Intertubular Dentin The intertubular dentin is composed of a mixture of carbonated apatite crystals and collagen and as a result provides the majority of the support structure for the enamel. The intertubular dentin is composed of, by volume, 30% collagen, 25% water and 45% minerals in the form of carbonated apatite crystals. Because of its role in supporting the enamel and since it comprises the largest portion of dentin, the majority of dental research is devoted to exploring the properties of intertubular dentin. Peritubular Dentin The peritubular dentin is a highly mineralized zone around the tubule forming an annular ring that is 1-3µm in thickness. The peritubular dentin contains very little collagen and is instead made up of carbonated apatite crystals (95%) with small percentages of water and collagen. The peritubular dentin provides the support structure for the tubules to diffuse nutrients into the intertubular dentin [9]. Tubules As seen in figure 2, the tubules are hollow tubes that provide nutrient transport within the tooth. They are typically 1µm in diameter and can extend for several millimeters. They run from the crown or top surface of the tooth to the root of the tooth. Near the root pulp, the tubules converge and their diameters can increase significantly. Towards the sides of the tooth, the tubules can bend to close to perpendicular to the tooth wall [2, 6].

16 6 Carbonated Apatite Crystals Carbonated Apatite Crystals provide a rigid structure for dentin. This material is a calcium phosphate salt known as dahllite, composed of carbonated hydroxyl-apatite nanocrystals of ~36 X 25 X 10 nm in size [2]. Throughout the tooth, they are in a plate shaped configuration with typically irregular edges [10]. These crystals are typically distributed at two sites, ~75% unattached to collagen fibrils and 25% attached to the fibrils usually by way of the other types of collagen or proteins [8]. Collagen Collagen in dentin is made up of 90% type I collagen by volume and the remaining collagen is of type IV, V, and VI [2]. Type I collagen is typically found in connective tissues like cartilage or tendons and provides the primary structure for bone. Collagen molecules are triple helical amino acid chains with a diameter of 1-3 nm and a length of nm. In dentin, the collagen fibrils typically forms into cylinders of nm in diameter and mm in length [5] (Figure 3). The length of the collagen fibrils is almost impossible to determine due to their 3-dimensional nature. As a direct result, some studies of fibril length failed to find both ends of the fibril [11]. Figure 3 Typical Collagen type I structure

17 7 Tooth Storage Since teeth are a biological material, they break down when removed from the body, particularly if they become dehydrated. Storage in water can chemically bond the collagen fibrils and plasticize them, but this is insignificant for periods of less than a week. If left in water for a month, the tooth dentin loses approximately 40% of its strength, mostly due to surface minerals, like carbonated apatite crystals, leaching into the water. If the tooth is stored in alcohol, this causes a shrinkage of tissue due to the increase in the level of inter-peptide hydrogen bonding which in turn increases the mechanical properties [12]. Anjum et al. showed that human saliva can maintain the properties of dentin but only for a period of less than two weeks [13] making it a poor choice for long term storage. In Guidoni s research, they showed that if the sample was frozen in HBSS for a long time, it weakened the mechanical properties of dentin by 20-28%. If instead the sample was first dehydrated then frozen the sample suffered no damage [12]. They theorized that the expansion of the water within in the sample created irreversible mechanical damage. The samples were dehydrated using ethanol and frozen and thawed. The same study by Guidoni et al. showed that dehydration with ethanol and rehydration with HBSS was not statistically significant from the control group. Finally, if teeth are stored in Hanks Buffered Salt Solution (HBSS), which is a saline solution with calcium and other trace minerals added to prevent the demineralization of the dentin, then the teeth can maintain their properties for several years [4, 12, 13]. For this research, teeth were stored in HBSS resulting in unaltered dentin.

18 8 Swelling If a tooth sample is completely demineralized, it undergoes an 18% reduction in volume [14]. For common restorations, the surface is demineralized and then dried or dehydrated. In this case, the collagen fibrils will collapse 73 ± 45 nm. Upon rehydration, the sample will regain all of its lost height within 30 minutes [15]. This process is reversible and has no impact on the material properties of the sample after full rehydration [14, 15] Restoration of Dentin The restoration of dentin involves several steps: the removal of carious tissue to create a cavity, preparation of the surface, and application of the adhesive and composite materials. The various layers created during restoration include the original dentin, a hybrid layer that is partially dentin and partially adhesive; an adhesive layer; and the composite layer, as shown in Figure 4. In clinical situations, it is preferable to remove the minimum amount of tooth as possible. In experimental situations, the primary goal is to ensure that all measurements are repeatable and thus as much tooth is removed as necessary to create a reliable surface for experimentation (Figure 5, Figure 6).

19 9 Figure 4 Dentin-Composite Interfaces Figure 5 Experimental versus Clinical Restoration

20 10 Figure 6 Experimental restoration of Human third molar Dentin The creation of a cavity or hollowed out section of tooth can be carried out in two ways. In clinical situations, the cavity is formed using a high-speed dental bur; in experimental conditions, the tooth is prepared by removing the crown enamel (Figure 8) with a high-speed saw and wet polishing (600 grit) the surface to remove surface irregularities and any remaining enamel. After the tooth surface is prepared, it is then demineralized to remove the carbonated apatite crystals at the surface of the exposed dentin. This leaves the collagen exposed and removes any smear layer formed during cavity preparation. The exposed collagen forms long structures (~4-5µm high) on the surface much like trees trunks in a forest as seen in Typically, a 32% phosphoric acid gel is left on the surface for seconds (depending on the manufacturer s instructions) and then rinsed off with water. The surface must be kept hydrated since the water provides the primary support to keep the collagen fibrils upright. If the surface dehydrates, the collagen fibrils will collapse from 4µm to ~0.5µm, thus forming a mat that can take several hours to rehydrate; however, during the application of the adhesive, it is

21 11 important to ensure that there is a minimum of water on the surface so that the adhesive does not become too diluted. Figure 7 Dentin restoration preparations Figure 8 Demineralized dentin showing exposed collagen

22 12 Hybrid layer and Adhesive layer When the adhesive is applied, it enters the gaps left from the dissolved carbonated apatite crystals, thus providing a strong bond to the dentin surface (Figure 8) [16]. Adhesive can flow down the tubules and forms structures called resin tags, as seen in all of the tubules in Figure 4. The remaining adhesive on top of the hybrid layer is simply called the adhesive layer. The experiments for this study used three different types of adhesive: Simplicity, 3M ESPE Adper single bond plus adhesive and Bisco one-step plus. Typically, adhesives can work in many different ways. For example, Simplicity is a two-step self-etch adhesive system. This means that using phosphoric acid to etch the surface is unnecessary. The first step is to apply part A and it then etches the surface and provides part A of the resin. The second step is to apply part B of the resin and subsequently Ultra Violet (UV) light cures it to achieve full polymerization. This results in a very small combined adhesive and hybrid layer (~5-10µm). The other systems (3M, Bisco) uses the phosphoric acid etch system described previously. The 3M Adper single bond plus polymer is solvated in ethanol and applied directly to the demineralized surface. The polymer is then dried under compressed air according the manufactures instructions to remove the solvent. Using the manufacturer s instructions, a UV light source cures the adhesive. The Bisco one-step plus has the same steps as the 3M system except the solvent is acetone and the polymers are different. The 3M and Bisco systems create a much larger hybrid layers (~5µm) and adhesive layers (10-25µm) than does the Simplicity system.

23 13 Composite Figure 9 Dentin after application of adhesive and infiltration of collagen The composite layer is typically a ceramic within a polymer matrix that cures in the presence of a UV light source. Most composites are 75-85% ceramic beads, primarily silicates or zirconium based and 15-25% polymer resin. The composite is applied directly to the surface of the adhesive (Figure 10) and then cured using a UV light source to initiate the polymerization reaction [16]. In this study, we used 3M ESPE Filtek Supreme Ultra and Venus Composite (Heraeus Kulzer, Hanau, Germany). According to 3M The resin contains bis-gma, UDMA, TEGDMA, and bis-ema resins... The fillers are a combination of non-agglomerated/nonaggregated 20 nm silica filler, non-agglomerated/non-aggregated 4 to 11 nm zirconia filler, and aggregated zirconia/silica cluster filler (comprised of 20 nm silica and 4 to 11 nm zirconia particles). The Dentin, Enamel and Body (DEB)3 shades have an average cluster particle size of 0.6 to 10 microns. The Translucent (T)4 shades have an average cluster particle size of 0.6 to 20 microns. The inorganic filler loading is about 72.5% by weight (55.6% by volume) for the Translucent shades and 78.5% by weight (63.3% by volume) for all other shades. [17] In

24 14 comparison the Heraeus Kulzer composite contains 62% by weight of a barium glass as inorganic fillers and is based on a Bis-GMA/TEGDMA matrix. [18] Figure 10 Completed restorations with all layers 1.2 Nanoindentation Introduction Nanoindentation has the ability to precisely resolve and determine material properties in relatively small areas (0.5-4 µm diameter which depends on the depth or force of indentation) which lends itself to microscopic material properties determination and to the investigation of biological materials. Typical mineralized biological structures are approximately 10 µm and thus far larger than the area of the indent. When looking at the dentin-composite hybrid layer (Figure 4), typical structures are the intertubular dentin (~10 µm between tubules), the hybrid layer (3-5 µm), the adhesive layer (10 µm), and the composite layer (>> 10 µm). Nanoindentation is a tool similar to Rockwell hardness testing where a material is indented with a probe approximately 100 nm in diameter. The primary goal of this test is to

25 15 measure the elastic properties of the material in question. The probe of the indenter penetrates into the material several hundred nanometers and at the same time exact values of the force are measured. As the probe retracts, an unloading curve is plotted so that a graph of force vs. indentation depth is produced. The first 20% of the unloading curve is used to fit a straight line, whose slope is taken as the measured elastic modulus (Figure 11). Oliver and Pharr determined that during unloading, at a minimum, the first 30% is in pure elastic release with no plastic deformation [19]. Also, since the actual tip is rather small, the force per area of the tip is very large. Thus the level of force needed to produce appropriate force vs. depth plots is on the order of several hundred micronewton s [20]. Figure 11 Force versus Displacement for typical nanoindentation curve Nanoindentation of materials is patterned after macro-scale indentation tests such as Rockwell and Brinell hardness tests. Nanoindentaion uses the same theory of operation and many of the same calculations used in these traditional methods. It is based on the work by Hertz in the 1880 s and later by Timoshenko in the 1950 s [20]. The primary difference is that the Rockwell test measures the indent after the test has been completed and the force during loading. With nanoindentation, the size of indent is calculated by knowing the exact tip geometry

26 16 and the depth of penetration into the material and the force during the unloading segment is used [20]. Nanoindenters can also perform surface profilometery measurements that can be used to determine both the roughness of the surface and to build both 2-D and 3-D pictures of the sample. The images created can also be used to verify the location of the indent. Tip Types There are many different types of tip geometries used for indentation experiments, as seen in Figure 12, each of which has advantages and disadvantages. In general, the most common types are spherical, conical, cube, Berkovich, Vickers and Knoop. The spherical indenters operate exactly like Rockwell hardness probes and are good for materials such as metals [20]. These indenters enable the elastic and plastic properties of the material to be examined, along with their strain hardening characteristics. Figure 12 Various nanoindenter tip types

27 17 The Vickers tip is a four-sided pyramid that induces low strain in the indent surface. The Berkovich tip is a three-sided tip that is essentially identical to the Vickers tip and is designed in such a way that the actual projected area is identical for both tips. The Berkovich tip was designed because the Vickers tip was considered an ideal tip to use for experimentation; however manufacturing difficulties in ensuring that the Vickers tip had 4 faces converging to a point led to the creation of the Berkovich tip is a three sided pyramids with equal faces. They have the advantage of being fairly easy to produce and also produce an 8% strain in the material being indented and are standard for nanoindentation [20]. Because of their construction, they offer good long-term wear, meaning that the tip does not become overly rounded, which in turn decreases the experimental error of the measurements. Knoop indenters are in the shape of a diamond with one diagonal much larger than the other diagonal. The Knoop indenter is very useful for very hard materials because the long diagonal is easier to measure to compute the area of the impression made and most often used for micro-hardness testers or other large-scale (~10 mm indent width) indenters. Finally, the cube indenter is positioned so that one corner of the cube does the indentation. This indenter also provides three faces like the Berkovich but the tip is much sharper and thus produces a 22% strain in the material it is indenting [20]. This means that from the first moment of contact, the indenter produces plastic deformation. The most important factor that is taken into account when selecting a material with significant elastic recovery is the geometry of the tip. The type of tip is generally selected depending on the known properties of the material. For instance a very low elastic modulus material like a chocolate bar or a hydro-gel would use a large diameter (~ µm) spherical tip. If the material in question has a very high elastic modulus, the depth of the indent will be very small and a Knoop indenter is commonly used so that the long axis of the indent can be measured and the properties calculated from this

28 18 value. If the purpose of the study is to look at crack propagation, a cube corner tip is the best choice. The cube corner tip provides a very high stress at the corners of the indent promoting the formation of cracks. If no cracks are desired, a conical indenter might be used; however, conical tips are very difficult to make and thus difficult to obtain. The Vickers tip is the best tip to use for indentation (described in the following sections); however, it is very difficult to manufacture due to the difficulty encountered when trying to machine four distinct surfaces into a point. The best overall choice for general indenting is the Berkovich tip, which generally does not induce crack formation, and is relatively easy to fashion compared to the other tip geometries because it only requires that three faces be machined into a point. In general, the indentation modulus is equal to the elastic modulus of the material if material does not pile up around the indentation since pile up is not taken into account when calculating the elastic modulus. Tip Area The tip area is of particular interest because in reality no tip conforms to the exact geometry specified. For example, a new Berkovich tip has a radius of 90nm, this means that for radii greater than 90nm the tip is assumed to meet the specifications of a Berkovich tip. For values smaller than 90nm, the tip geometry is unknown. Another factor influencing the tip area is wear. Diamond tips wear slowly for softer materials and faster for harder materials. The wear characteristics and tip irregularities are accounted for in the long-term calibrations of the nanoindenter (1-2 months or longer depending on the wear rate of the tip, which is affected by the number of hours spent indenting and the hardness of material being indented). Typically this is done by serially (100 indents) indenting the surface at varying forces ( µN) (which implies different depths) on a reference material, usually fused silica which has an elastic

29 19 modulus of. The depth of indentation and the known elastic modulus are used to develop what the tip area is and thus a tip area function can be created as shown below. For fused silica, this gives a calibration depth range of ~2-180 nm and depths greater than 180 nm are assumed to follow the curve fitted data. In general, the first constant of the curve fitted equation can be exactly correlated to the type of tip used. Figure 13 Nanoindentation curve where is the residual depth of indent, is the elastic displacement associated with recovery, is the total depth of indentation, and is the slope of the upper 20% of the unload curve. The most basic case for evaluating the area of contact is that of a spherical indenter investigated in 1881 and 1882 by Hertz [21]. He found that that the relationship (Figure 14) between the circle of contact a, the indenter load P, the indenter radius, and the elastic properties with the following:

30 20 (1) The value of is the combined or complex modulus of the indenter tip and the material being tested and can be found using the following rule of mixtures for two spring elements in series: ( ) ( ) (2) where the subscript 1 refers to the elastic modulus and Poisson s ratio (ν) of the tip and subscript 2 refers to the modulus and Poisson s ratio of the material in question. Utilizing equation (1) and (2) it can be shown that (3) where R is the radius of the indenter and it is assumed that [20]. This assumption generally holds for most materials since the indenter tip is diamond and most other materials have elastic moduli orders of magnitude smaller than that of the diamond tip. Figure 14 Tip contact. Where the radius of the indenter tip is, the radius of the circle of contact is a, the total depth of indentation is, the depth of the circle of contact is, and the depth of total contact is. To curve fit the unloading curve, Pharr and Bolshakov[22] applied Sneddon s solution with finite element analysis to predict the tip geometry (a non-trivial exercise) and create an

31 21 empirical solution for the indentation data. The analysis of non-flat indentations indicates that for materials with elastic recovery the residual impression does not have straight sides due to elastic recovery of the material. In other words for a tip like the Berkovich, when the tip is fully indented the hole conforms to the tip. As the tip withdraws the hole left in the material partially recovers closing the hole completely at the bottom and recovering along the tip length leaving a shallower residual impression ( ) than the total depth of indentation ( ). Pharr and Bolshakov used these results to determine the unloading force as: ( ) (4) where P is the load, is the total depth of the indent, is the depth of the residual indentation and α and m is related to the material and determined by curve fitting the specific material to the equation. The value for m is determined from the tip geometry, for a punch or flat tip and for a conical tip [22]; however, a parabola of revolution (standard parabola revolved around an axis) would have which approximates the value for a Berkovich tip. When determining the actual value of m from a regression analysis, however it varies from slightly depending on the material being analyzed. The determination of α is highly dependent on the material being tested and α can range from and can be larger or smaller. The profile of the indenter is calculated using Sneddon s solution given below (5) where B and n are constants and is the radius [23]. Using the following equation: ( ) ( ) [ ( ) ( ) ] (6)

32 22 and with Γ as the factorial gamma function, h is the elastic displacement ( ) (Figure 14) and ( ) (simplification of equation (2)). Using these two equations along with equations (5) and (6) gives the following relation (7) thus relating the geometry shape factor m and the measured value n ( a measured constant associated with the tip) [22]. Using Figure 14 the circle of contact can be calculated with the following equation: (8) where can be found by curve fitting a second order polynomial to the unloading curve (Figure 13) and estimating from the top 20-30% of the unload curve (in practice this results in an insignificant error of the calculated value). The value for ε (tip parameter) can be found using: ( ( ) ( ) ) (9) Using the above equations, a value for the tip area function can be found. Hardness (Berkovich) For the Berkovich tip, the contact area, A, is calculated using: (10)

33 23 (equation) where h p is the depth of tip penetration and is a constant associated with the Berkovich geometry[20]. Knowing the mean contact pressure, P, from the nanoindenter, the hardness can be directly calculated using: (11) where the hardness (H) is the Meyer hardness (MHN) which can be directly converted into the Brinell hardness [24] using: (12) where d is the chord of the indent and D is the chord of the indenter. Elastic Modulus (Berkovich) The elastic modulus can be calculated using equation (10) and the following equation: (13) Nanoindentation Error There are many sources of error when performing nanoindentation measurements [20]. In general, the error can be divided into two categories: how the sample is prepared and intrinsic errors of nanoindentation. The sample preparation can affect the nanoindentation process through the smear layer, the surface roughness, and general preparation processes. The intrinsic errors include thermal drift, penetration depth, compliance, indenter shape, vibrations, piling-up or sinking-in, indentation size effect, and residual stresses.

34 24 Smear Layer In the case of sample preparation, the surface polishing of a sample directly affects the depth of the smear layer created [25]. The smear layer is roughly one third to one-half the size of the particle size used for polishing (Figure 15). If the indentation load is not large enough to penetrate the smear layer, the measured elastic modulus could reflect the value of the smear layer, or the underlying substrate or some combination thereof thus giving a false value of the sample in question. Figure 15 Smear Layer (not to scale) Surface roughness The surface roughness creates error because the nanoindenter tip may encounter peaks on the sample surface and prevent the tip from contacting the surface (Figure 16). Generally, this is overcome by decreasing the surface roughness by polishing the surface or by increasing the force of indentation so that the peaks cannot support the load of the indenter to give a false surface engagement. When using the nanoindenter to create a topographic map, however the forces used are very small which implies that unless the sample is highly polished, the image created will be of the smear layer and not of the sample.

35 25 Figure 16 Nanoindenter False Engage (not to scale) In general, the surface roughness parameter can be calculated using the following: (14) where is the surface roughness parameter (unitless), is the maximum asperity height, is the indenter radius and a is the contact radius that would be obtained under the same load P for smooth surfaces [26]. Furthermore, ( ) (15) Where is the roughness average of the sample surface [26]. For the surface roughness plays an important role in estimating the elastic contact. The net result is that the combined modulus is reduced[20]. For sharper indenters such as the Berkovich indenter however, the surface roughness effects are less severe.

36 26 Sample preparation The sample preparation can affect the values of the measured elastic modulus by altering the surface composition. Often with biological materials, chemicals are used to fix the sample or prepare the sample in some way to stabilize it for testing. The chemicals used can then either form a thin coating on the surface or chemically alter the surface properties of the sample. Thermal Drift Thermal drift can accounts for two sources of error, the first is creep within the specimen because of plastic flow and can be seen if the indenter is held at constant load, where the measured displacement increases with time. This effect is minimized by ensuring that the time for the test is less than, as described below (16) where is the time from the beginning of the test until the beginning of the unload segment (Figure 13), S is the contact stiffness, is the rate of unloading and is the maximum contact depth [27]. The second error can result from expansion or contraction of the apparatus. By holding the indenter for a short time period (~40 seconds) just above the material surface, a linear drift will occur (and can be tracked). The resulting measured drift can then be calculated and accounted for during the actual indentation process [20]. Through careful calibration, the error from thermal drift can be eliminated. Penetration Depth Another source of error can come from the estimation of the initial penetration depth. In order for the nanoindenter to measure the zero position of an indentation depth, it first must

37 27 come in contact with the surface. Consequently, the indenter must first pass through its noise threshold, which is ~1 µn. This is experimentally corrected by using: ( ) (17) where P and h are experimentally determined, m has been previous developed (in calculating the tip area function with Equation (7) and is the unknown variable [20]. Compliance Instrument compliance plays a role in the error of all measurements with nanoidentation. The slope for the compliance can be described with dh dp 1 C (18) f S where is calculated from the unload curve (Figure 13), C f the compliance of the instrument (Figure 17) and S is the stiffness of contact [20]. These values are calculated using a standard material such as fused silica and performing indents at varying levels of high forces ( µn) [28] Figure 17 Machine compliance

38 28 Vibrations and Air A typical source of error in the nanoindentation of materials comes from temperature differences of the specimen and the nanoindenter itself, vibration and acoustical noise. Finally, another source of error that can be found is from the resistance of air within the testing chamber. By performing an indention in air, a load curve can be created by polynomial approximation. Because air pressure and humidity varies greatly from day to day, this calibration must be performed at least once per day to ensure accurate results. Stray vibrations from traffic, construction and conversations in the room can affect the accuracy of the indenter. For low vibrations (0-200 Hz), transducers actively dampen the vibration, for higher frequencies a granite base can be used to passively dampen the vibrations. Other means of controlling the temperature and vibrations is to use a sound isolation chamber. This ensures a low possibility of temperature swings and helps to isolate the testing equipment from vibrations [28]. Indentation size effect For shallow indentations, the effect of the surface energy and preparation can have an effect on the measured properties of the specimen. These effects are most apparent in the properties of crystalline materials and polymers [20, 29]. The most common solution is to increase the indentation force past a critical indentation depth. For indentations in the size effect region, the most common result is an increase in the measured material properties (2-3 times the bulk properties) [29].

39 Viscoelasticity Maxwell Model The Maxwell model is where a spring element and a dashpot or damper element are connected in series with each other (Figure 18). The stress strain relationships are: (19) (20) where σ is the stress for the spring element, K is the spring constant, and is the strain for the spring, correspondingly is the stress for the dashpot element, C is the damper constant, and is the derivative with respect to time of the strain. Since the spring and dashpot are connected in series, the total strain is [30]: (21) and (22) Taking equation (21) the time derivative of equations (19) and (20) and inserting them into (22) and eliminating variables produces the following: (23) If the model is assumed to have a constant strain,, at time, and the initial stress is, then the following stress response can be obtained: ( ) (24) The time that it would take for the stress to equal zero is at the time and is called the relaxation time of the material. The downside to this model is that the Maxwell model shows no

40 30 time-dependent recovery and does not show the effects of creep which is a decrease in strain (i.e. strain relaxation) under constant stress. The Kelvin model, however takes into account these time-dependent recovery characteristics. Kelvin Model The Kelvin model is a spring element and a dashpot or damper element connected in parallel (see Figure 18). The corresponding stress strain relationships are: (25) (26) where is the stress for the spring element, K is the spring constant, and ε is the strain, correspondingly is the stress for the dashpot element, C is the damper constant, and is the derivative with respect to time of the strain. Since the elements are in parallel, the total stress is [30]: (27) Combining equations (25), (26), and (27) gives the following relationship:. (28) Assuming that the previous equation is under a constant stress,, applied at gives: ( ) (29) Equation (29) indicates that at + the primary influence on the strain comes from the term, as the equation becomes. This implies that initially the damper element has a large influence; however, under stress the viscous element elongates transferring more and more of the load from the damper element to the spring element. This type of response is called

41 31 delayed elasticity [30]. The downside to the Kelvin model is that it does not exhibit timeindependent strain for loading or unloading a system. Burgers Model Figure 18 Kelvin and Voigt viscoelastic models Neither the Maxwell nor Kelvin model adequately accounts for both time dependent recovery or strain. In an attempt to address the limitations with the Maxwell and Kelvin models, the Burgers model was created which combines the Maxwell and Kelvin models into a single system (Figure 19). By using similar construction of equations in the Maxwell and Kelvin models, the strain is found to be: ( ) ( ) (30) Where is the strain at and the constants can be seen in Figure 19. A close examination between equation (30) and equations (24) and (29) shows that the first two terms represent the Maxwell model and the second term represents the Kelvin model [30]. Very few viscoelastic

42 32 materials, however, behave according to equation (30) because for small time values the experimental viscoelastic system does not follow the theoretical equation. The middle part of the experimental results are in close agreement with the theoretical model while for large time values equation (30) fails again to predict the experimental results. In general, the Burgers model is the basic model that describes the viscoelastic equations for a material. In practice, the Burgers model is modified by adding Kelvin and Maxwell elements until the model approaches the values obtained through experimentation [30]. Figure 19 Burgers Model where K is the spring constant, C is the dashpot constant, and ε is the strain of each element. Dynamic Nanoindentation NanoDMA (Nano-scale Dynamic Mechanical Amplitude) is a test procedure where a dynamic mechanical force is induced in the tip to obtain viscoelastic properties. The nanoindenter has three basic variables: Quasi-static load, dynamic load amplitude and dynamic

43 33 frequency. The most common variable to use is to sweep the dynamic frequency to obtain the storage and loss moduli of the material. Hysitron has found that the majority of users find that nanodma gives the most relevant data when testing under 50 Hz [31]. NanoDMA testing is very similar to static nanoindentation and uses a relatively large static load and a smaller dynamic load at a specified frequency. The primary concern is to ensure that the dynamic load corresponds to a dynamic amplitude of 1-2nm to obtain optimal results. For measurement purposes, the equation of the tip motion is: ( ) (31) where the displacement of the tip is ( ) (32) and ω is the frequency of oscillation, t is the time, m is the mass of the system, C is the damper or dashpot coefficient, K is the spring constant, x is the displacement and its time derivatives are and. is the initial load on the system, ω is the frequency, X is a constant associated with the displacement (equation (33)), and ϕ is the phase angle (equation (34)) [31]. ( ) ( ) (33) ( ) (34) The equations can then be rearranged to solve for the spring and damper constants as follows: and (35)

44 34 ( ) ( ) (36) The values for K and C, however, are for the combined spring constant and damping constants for the system (nanoindenter and sample) or (37) and (38) where the subscript i stands for the instrument and the subscript s is the sample value. The spring and damper constants can be found for the system by measuring the tip oscillations in air to obtain K i and C i [31]. The viscoelastic properties can then be directly calculated using: (39) where is the storage modulus, is the contact area function of the tip (defined earlier), is the loss modulus and is Tan represents the mechanical loss due to internal friction. In addition, the relationship between the dynamic values and the static relaxation time ( ) can be developed [30] for the Maxwell model as follows: (40) where η is the viscosity of the material. From equation (40), it is apparent that as ω approaches infinity, the dynamic modulus approaches the spring constant. In a similar manner the retardation time ( ) of the Kelvin model [30] can be found as: (41)

45 35 From equation (41), it is apparent that at low frequencies the complex modulus approaches the spring constant while at high frequencies (>100Hz) the dynamic modulus increases very rapidly. In general, the stress-strain-time relationship for variable strain history is given by: ( ) ( ) ( ) (42) where ξ is a variable of integration. At steady state, ξ is described as [30]. To convert from the oscillating viscoelastic properties to the static viscoelastic properties a one-sided Fourier transform can be used as seen: ( ) ( ) (43) ( ) ( ) (44) As direct result equations (43) and (44) can be used to convert curve fit dynamic experimental data (frequency vs. loss or storage moduli) into values for the static storage and loss moduli. In addition equations (40) and (41) can be used to determine the spring and damper constants respectively. These equations in turn can be used for the creation of finite element models to model the behavior of the filling during mastication. 1.4 Literature Review Static Indentation Literature In a 2009 study by Hosoya et al.[32], they evaluated the dentin-composite interface with both sound and caries-affected dentin. They compared the measured elastic modulus and

46 36 hardness values between each layer and also performed a chemical analysis of the surface. Hosoya found no significant difference between the elastic modulus or hardness of the sound versus carious-dentin. They did find that the calcium content was significantly different. They also stained the interface to determine if there was a difference in the nanoleakage (of fluids along the boundary) for sound and carious dentin. They concluded that there was no effect of carious versus sound dentin on the properties of the interface. For their study, they used a force of 300µN with a hold time of 10 seconds and aspacing between indents of 10µm. They polished the teeth with a final particle size of 0.3µm and then stored them for 2-4 days distilled water. In a 2008 study by Flores-Ramirez et al. [33], they studied the measured elastic modulus and hardness of Poly(methyl methacrylate ) (PMMA) a common dental polymer and chitosan, a biopolymer derived from chitin. The chitosan was chosen because it has shown some regenerative properties and encouraged self healing. The force chosen was µN and the polished resin disks had a final polishing of 0.05µm. They showed that the elastic modulus decreased from 9 to 4.7 GPa with increasing force (or contact depth). They also compared the results obtained through nanoindentation to those obtained through micro-hardness testing. They were unable to correlate the values that they obtained between the two tests. In a 2006 study by Hosoya et al. [34], they examined the dentin-composite interface to determine the measured elastic modulus and the hardness of the interface. They looked at both sound and caries-affected dentin with particular attention paid to the dimensions and values of the hybrid layer. Hosoya restored the caries-affected teeth using the standard dental practice of using a chemical stain to locate the caries and then removed them with a dental bur. After restoration, they determined that there was no significant difference between the elastic moduli of the sound dentin and the carious dentin. They did find that the hybrid layer of the caries-

47 37 affected dentin was larger and had more complicated topographical features; however, both the sound and caries-affected hybrid layer was generally less than 1µm. The adhesive used is a onestep adhesive (One-Up Bond F Plus, Tokuyama Dental Co., Tokuyama, Japan) similar to the Simplicity used in the experiments described in this thesis. The final polishing particle size was 0.3µm with a force of 300µN with 10µm spacing between indentations. In a 2001 study by Akimoto et al. [35], they examined how the dentin-composite interface remineralizes in vivo using 4 year old adult rhesus monkeys tested at 7 days and at 6 months, after extraction, then sacrifice using nanoindentation, energy dispersive x-ray spectroscopy microanalysis (EDS) and scanning electron microscopy (SEM). They used two different adhesives Protect Liner (resin, Kuraray) and Clearfil Photobond (bonding agent, Kuraray) with Protect Liner. After 6 months in vivo, the boundary showed remineralization and increasing levels of hardness and calcium concentration. The final polishing particle size was 0.25µm with a force of 100 mgf (assumed to be 100µN). In a 2005 study by Hosoya [36], they examined the hardness and elasticity of bonded carious and sound primary tooth dentin, where primary tooth dentin are commonly known as baby teeth. The teeth were bonded with Clearfil SE Bond (Kuraray Medical Inc., Kurashiki, Japan) or Single Bond (3M). They determined that there were no significant differences between the two different bonding systems. They did show however, that the values for the elastic modulus and the hardness were lower than that of permanent dentin. The final polishing particle size was 0.5µm stored in distilled water until testing and then tested dry. The force used was 300 mgf (assumed to be 300 µn) with a spacing between indents of 10 µm. In a 2007 study by Hosoya et al. [37], they theorized that there was no difference in the elastic modulus and hardness between sound and caries affected primary dentin bonded with a

48 38 one-step self-etch adhesive. The adhesive used was a single bottle, one-step self-etch adhesive (Clearfil Tri-S Bond, Kuraray Medical Inc., Kurashiki, Japan). They found that the elastic modulus of the dentin near then interface was significantly lower than that of dentin away from the interface. They also noted that the elastic modulus of interfacial dentin was significantly greater in sound versus caries affected dentin. The study also looked at the effect of nanoleakage on the dentin-composite interface. They found that the sound dentin provided an incomplete bond with the adhesive and that caries affected dentin had significantly less nanoleakage compared to the sound interface. The final polishing particle size was 0.3 µm and stored wet in distilled water until testing and then tested dry. The force used was 300mgf (assumed as 300 µn). In the 2006 study by Inoue et al. [38] they examined the dentin-composite interface after the creation of artificial caries. The adhesive used was Clearfil SE Bond (Kuraray Medical, Japan). Initially half the samples were carries-affected and the other half were sound. In each of these groups half of the samples were tested after restoration and the other half were tested after being stored in a demineralizing solution for 90 minutes. There was an acid-base resistant zone (ABRZ) found directly below the hybrid layer as determined by argon laser etching and scanning electron microscopy (SEM). The ABRZ was found to be much larger in caries affected dentin as compared to sound dentin. The final polishing particle size was 0.25 µm followed by argon ion beam etching. The force used was 5 gf (assumed to be 5000 µn). In the 2007 study by Pongprueska et al. [39], they evaluated the difference between the elastic modulus of unfilled adhesive resin (Adper Single Bond, 3M) and filled adhesive resin (Adper Single Bond 2, 3M). They found that the elastic moduli were significantly different between layers except for the filled and unfilled hybrid layers. They also concluded that the

49 39 elastic modulus was significantly higher for the filled adhesive as compared to the unfilled adhesive. The final polishing particle size was 0.25 µm with a nanoindentation force of 5000 mgf (assumed to be 5000 µn) for the dentin, adhesive and composite resin, and nanoindentation force of 1000 mgf (assumed to be 1000mgf) for the hybrid layer. In the 2007 study by Sadr et al. [40], they evaluated the micro-shear bond strength and the nanoindentation hardness of two self-etch adhesive systems. The adhesives used were Clearfil Tri-S bond (Kuraray Medical, Japan) and Clearfil SE bond (Kuraray Medical, Japan). They examined how the length of time spent air drying the adhesive related to the bond strength and hardness of the interface. They determined that the two different adhesives preformed the best when air dried for 10 seconds while a 2 second dry time resulted in a very poor bond that was statistically significant from the 10 second bond. The teeth were stored in deionized water for a minimum of 24 hours before testing. They final polishing particle size was 0.25 µm and a nanoindentation force of 250 mgf (assumed to be 250 µn). In the 2005 study by Schultze et al. [41], they compared the effect of hydration variability on the adhesive and hybrid layer properties for two adhesive systems. The adhesives used were Clearfil SE bond (a self-etch system) and Single bond (first etch, then apply the adhesive system). They looked at how each of these systems performed under different levels of surface hydration. They found that there was no significant difference in the elastic modulus of the selfetch system (Clearfil SE bond, Kuraray, Japan) for varying hydration states, while the etch then apply adhesive system (Single bond, 3M, USA) showed significant differences in the elastic moduli for varying hydration states. The final polishing particle size was 0.25 µm and nanoindentation force was 300 µn.

50 40 In the 2008 literature review by Lewis et al. [42], they reviewed nanoindentation of mineralized hard tissues, which are generally bone and teeth. The authors indicated that there does not exist a standard for nanoindentation testing of mineralized hard tissues. Dynamic Nanoindentation Literature In the 2004 study by Balooch et al. [43] they evaluated a novel technique using a Hysitron Triboscope nanoindenter mounted on a Multimode Atomic Force Microscope to study the Dentin-Enamel interface (or Dentin-Enamel junction). They induced a sinusoidal oscillation (200 Hz) in their topography scan, called modulus mapping, which was the first instance where this technique has been used to investigate teeth. They prepared their samples by polishing them to 0.25µm and then testing the samples dry. They used a cube corner tip with a radius of 150nm with a static scan force of 1-3µN and a dynamic scan force of µN. The dynamic forces for the scan were chosen because they were large enough to maintain good signal-to-noise ratio for all material phases but small enough to prevent intermittent contact. The static forces were chosen to minimize damage to the surface during scanning. The study obtained modulus maps of 20x20µm areas. The primary purpose of their study was to determine the width of the Dentin- Enamel junction. They also reported that the intertubular storage modulus was 21 GPa, the storage modulus for enamel was 63 GPa, which are generally consistent with previous studies. In the 2008 study by Ilie et al. [44], they evaluated the dynamic mechanical properties of the composite resin Filtek Supreme XT (3M, USA) utilizing modulus mapping techniques with a nanoindenter (Hysitron Triboindenter) for various cure times. They investigated the dynamic response for composite resin that was cured for 5, 10, 20, and 40 seconds and then stored for greater than 24 hours in distilled water. They then created 5 x 5 µm modulus maps of the resin.

51 41 They also evaluated the real-time degree of cure using ATR-FTIR after photo-initiation of polymerization. They showed that by increasing the cure time they were able to maximize the polymerization. The resulting modulus maps created showed four distinct regions: filler-cluster, filler-defects, filler-interphase and resin matrix. For the testing they used a 100 nm radius Berkovich tip oscillated at 110 Hz with a dynamic force of 5µN. In the 2011 study by Ryou et al. [45] they looked at the effect of remineralization on the dynamic nanomechanical properties of the dentin-composite interface. They created 25 x 25 µm area scans of the interface and then evaluated the properties. By running a Lanczos pixel interpolation algorithm they were able identify individual collagen fibrils using a 100 nm radius Berkovich tip. Their study looked at the effect of biomimetic remineralization after in vitro aging. They concluded that there was a difference in the dynamic mechanical properties of those with biomimetric agents and those that did not. For testing, they used a 100 nm radius Berkovich tip with a static set-point force of 4 µn, a dynamic force of 2 µn, oscillated at 100 Hz with a scan rate of 0.2 Hz. They also suggested that for dynamic analysis that the tip area calibration should be performed on a material with a similar elastic modulus instead of the standard fused silica. They also varied the frequency from Hz and the set-point force from 1-4µN on a macro hybrid layer (5mm x 2mm x 0.3mm) to determine the ideal conditions for their test. During their initial testing, the dynamic load was set to 50% of the set-point force. They found that there was no major difference in the moduli for the various set-point forces but that the higher the force the clearer the image and the least amount of noise produced. During initial testing, they ran into issues where the water used for hydration was evaporating and causing a force on the tip. This force after minutes was high enough that the z-axis piezo reached a travel limit resulting in an incomplete scan. Their solution was to apply a thin film of

52 42 100% ethylene glycol (chosen for its low vapor pressure of 0.13mm Hg) over the surface of a fully hydrated specimen. The high molar ethylene glycol effectively lowers the vapor pressure of water to near zero eliminating evaporation losses on the surface of the sample. 1.5 Study Aims The hybrid layer of a dental restoration is of particular interest since approximately 60% of direct dental restorative treatments replace failed restorations, caused primarily by debonding between the tooth-resin composite interfaces. It is important to understand the mechanical properties of each dentin-resin composite interface component to model the failure mechanism. Nanoindentation is an invaluable tool to evaluate the material properties of the dentincomposite hybrid layer. It has been used with great effect to determine the material properties across the hybrid layer with many different types of adhesives [32-41, 46, 47]. Typical ranges for the force values are from µN and particle polishing sizes of µm with most forces in the range of µn and most particle sizes of 0.25 µm. The studies looked at the effect of caries, remineralization, baby teeth, effect of hydration and filler particles. Generally they were focused on the hardness of the adhesives used to bond the composite layer. As discussed in detail above, surface roughness, penetration depth and smear layer can be sources of error that result in inconsistent measurements of elastic modulus of a dentincomposite system. These sources of error can be almost entirely eliminated by determining the depth of penetration necessary to overcome these effects. The effect of force and roughness has not be sufficiently examined to determine what effect if any on the measured elastic modulus and hardness of the dentin-composite interface. The guiding motivation for the effect of force and roughness is to develop a means of evaluating what force and polishing levels to use when

53 43 nanoindenting across the hybrid layer. Currently there exists no standardization of nanoindentation for mineralized tissue specimens [42]. To date no studies could be found that looked at the effect of viscoelasticity on the tooth let alone the dentin-composite interface. The literature available looked at the modulus maps across the interface. Although these studies looked at the dynamic values at the interface, they were generally performed at very low force values, namely 2-4µN. The values found are generally in line with the static body of data on the interface. The modulus map can be misleading since the dynamic properties for each of the four regions (dentin, hybrid, adhesive and composite) varies widely. As a result each region has different properties which leads to innacuracies in measurement because the indenter is adjusted for the harder regions (dentin and composite) or the softer regions (hybrid and adhesive). As part of this thesis research, initial viscoelastic studies performed looked at using static indentation force to determine the relaxation time for the systems; however, issues were raised with the effectiveness of indenting the surface for long periods of time. These issues were primarily concerned with the effectiveness of the thermal drift calculated for the system. Another issue was the effect of boundary conditions on the test data. Since the hybrid layer is 4-5µm wide and the diameter of the indent was at least 2-3µm in diameter (larger values could be possible since the indent could not be seen after indentation for the majority of indents), the effect of boundary conditions was deemed to be significant. It is estimated, that for a test to assume that boundary conditions do not apply, the boundary must be greater than 4 times the radius of the indent. With the reliability issues raised with the thermal drift and the boundary conditions the test was changed. To deal with possible boundary layer issues, each layer was created in a macro setting. To deal with the thermal drift problem testing was changed from long

54 44 static tests (>5 minutes) to NanoDMA testing which utilizes dynamic mechanical techniques to find the storage modulus and loss modulus of the material being tested. The most common test is to use a dynamic frequency analysis where a static force and a dynamic force are held constant while the frequency is swept from low to high (1-250Hz). Using the previous logic this paper has two primary objectives. The first is to examine what effect the force and roughness has on the dentin-composite interface during nanoindentation. The second objective is to examine the effect viscoelasticity has on the dentin composite interface when boundary conditions are neglected as a result it can be hypothesized: 1. Test the hypothesis that surface preparation will influence the measurement of the elastic properties of a composite tooth structure 2. Test the hypothesis that the indentation loads will also influence the measurements of elastic properties of a composite tooth structure. 3. Test the hypothesis that the effect of viscoelasticity has minimal effect on the properties of the dentin-composite interface.

55 CHAPTER 2: MATERIALS AND METHODS All samples were tested in accordance with the University of Illinois at Chicago s Office for the Protection of Research Subjects. The teeth used in this study were exempt because the molars used did not have any identifying information or marks on them. Samples were tested in distilled water due to practical concerns, primarily when samples are tested in HBSS the minerals tend to collect on the tip as the solution evaporates. This causes the tip to become dirty and invalidates the tip area function used to calculate material properties thus giving erroneous measured elastic modulus values. Figure 20 Dentin-Composite interface prepared from a restored tooth 45

56 Hysitron Ubi Nanoindenter The nanoindenter that was used for all testing is a customized Hysitron Ubi Nanoindenter. The manufacturer has specified a load noise floor of 100 nn with a load resolution of 1 nn. The maximum load is 10 mn. The displacement resolution is 0.04 nm with a noise floor of 0.2 nm in the z direction and a displacement resolution is 4 nm with a noise floor of 10 nm in the x-y direction [28]. In addition to electromechanical motors that control x, y, z displacements, the nanoindenter also uses both transducer and piezoelectric systems to achieve high spatial resolution. The piezoelectric tube system consists of two sub-systems: one for movement in the x-y plane consisting of 4 piezoceramic drivers divided into quadrants and the second system is attached to the bottom of the first system and controls motion in the z direction. A transducer system is attached to the bottom of the piezo-tube on one side and the indenter tip is attached to the other side. The transducer uses a three plate capacitive design that provides a high sensitivity with a low spring mass (~200 mg), enables dampening of exterior vibrations, and also allows for applied loads of less than 25 N to be applied [28]. The Hysitron nanoindenter also allows for fully automated testing. The nanoindenter uses both active and passive systems that are designed to dampen vibrations and it is also enclosed in a sound and vibration isolation chamber. Prior to starting a research project, the compliance and tip area function were calibrated on fused silica. Prior to the start of each day s research, a calibration was performed to determine the electrostatic force constant for the transducers. If the day s research involved the use of NanoDMA, a dynamic force calibration was performed to determine the mass, spring and damper constants for the system.

57 Force and Roughness Procedure The specimens used in this study were randomly selected non-carious human molars extracted during routine treatment and used in accordance with the University of Illinois at Chicago s Office for the Protection of Research Subjects. The materials investigated in this study were primary molars with composite fillings. There were two different bonding systems used, Adper Single Bond Plus (3M ESPE St. Paul, Minnesota) and Simplicity (Apex Lake Zurich, Illinois). The 3M system used a 3M - ESPE Adper Scotchbond etchant and a 3M ESPE Adper single bond plus adhesive. The Simplicity system is a no rinse, two part bonding system. The composite used was the Venus Composite (Heraeus Kulzer, Hanau, Germany) for both bonding systems. The two systems were used to minimize the influence of the adhesive on the results (see Figure 21 for comparison of each system in SEM). Four teeth were prepared by first removing the enamel using diamond blade and water irrigation with slow speed saw sectioning perpendicular to the long axis of the tooth. Once the majority of the enamel crown was removed, the superficial dentin was flattened and exposed using wet sanding with 600 grit paper (Carbimet 2 Buehler, Lake Bluff, Illinois, USA) to remove any remaining enamel from the center of the tooth. Next Simplicity and the 3M bonding systems were according to the manufacturer s instructions on the exposed dentin surface. The adhesive systems were light cured according to manufacturer instructions using a halogen light unit (Optilux sds Kerr, Orange, CA, USA). A ~2mm thick layer of Venus resin composite was then applied to the adhesive and due to the large size of the restoration, the composite was light cured for a total of 80 seconds with ~20 seconds used in each quadrant. Finally, resin-dentin samples were then prepared by cutting the specimen parallel to the long axis

58 48 of the tooth into three 1.5mm thick sections (Figure 20). The tooth surface was leveled for testing by removing any protrusions with wet sanding at 600 grit. Figure 21 3M versus Simplicity showing the width of the Hybrid/Adhesive layer Elastic Modulus vs. Particle Size Teeth samples were polished so that that the samples were level and uniform in thickness (1-1.5mm) as verified with a digital caliper. The sample was ground using wet sanding with grit sizes of 600 and 1200 (Carbimet 2, Buehler) for 3 minutes per grit size. Then, the sample was further polished using 9µm polycrystalline diamond suspension followed by a second rinse in deionized water and 3 minutes in an ultrasonic water bath. The sample was then serially polished in a 6, 3, 1 and 0.05 µm diamond suspension followed by an ultrasonic bath (a flow chart of this procedure is show in Figure 22) between steps. Between pastes and after cleaning, specimens were tested using the nanoindenter. Each sample was tested in a deionized water bath to maintain the material properties. Every sample was tested using a Hysitron customized Ubi nanoindenter with a constant force of 800µN. The indenter was set up to automatically indent using three series of five indents each (Figure 20 with the top and bottom most indents not shown) with a spacing of 15 µm between indents. The middle or third of each 5 indent series

59 49 was set up with the center indent on the hybrid layer as determined with a 5x light microscope attached to the nanoindenter. For each sample there were a total of 15 indents per tooth per polishing particle size which gives 60 indents per sample. Since there were 4 samples with 2 samples per adhesive the total number of indents were 480 indents or 120 indents per polishing particle size. In order to minimize the influence of peritubular dentin, the indents were kept towards the center of the tooth with a spacing of ~1mm between series. Figure 22 Polishing and testing protocol

60 Particle Size vs. Surface Roughness The surface roughness was calculated from the topographical images produced by each layer in the particle size tests. Topographical maps were created from Scanning Probe Microscopy (SPM), which uses a raster pattern to obtain a series of data points in x, y, and z coordinates giving a topographical map. Each image was obtained as a 10µm by 10µm square scan area at a scan rate of 1.5 Hz. The roughness average (z-axis values) was measured with a ~ 4 µm² scan area of the x-y plane near the indent and away from any surface defects or tubules. These values were then compared to the roughness given by the polishing particle size Elastic Modulus vs. Indentation Force Four teeth specimens were polished so that that the samples were uniform in thickness as verified with a digital micrometer as described previously. The sample was ground using wet sanding with grit sizes of 600, and 1200 for 3 minutes per grit size. Then the sample was further polished using 9 µm polycrystalline diamond suspension followed by a second rinse in deionized water and 3 minutes in an ultrasonic water bath. Each tooth was then polished at 6, 3, and 1µm with polishing times of 3 minutes, a second rinse, and 3 minutes in an ultrasonic bath. The tooth was then polished at 0.05 µm for 3 minutes followed by a second rinse and a 6 minute 20 second ultrasonic bath followed by nanoindentation testing. The force level was then varied from N to determine if the measured elastic modulus for the dentin, hybrid layer and composite was dependent on the nanoindentation force. The force level was varied by using the following values for the force: 100, 200, 300, 600, 1200, 1800, 2400 and 3000 µn (Figure 23). Each test series was set up identically to the test series in the roughness test.

61 51 Figure 23 Force testing flow chart 2.2 Viscoelastic Procedure Static Viscoelastic Tests Dentin-Composite Hybrid Layer The static viscoelastic tests were performed using similar testing to that of the force and roughness. The total number of tests was nine, five using 3M adper single bond plus and four using Bisco one-step plus. The samples were held at 3000µN for either 500 seconds or 1000 seconds. For the loading and unloading curves the force was increased at 300 µn/s for 10 seconds and was unloaded at the same rate and time. Each sample generally showed the same characteristics, namely that each sample settled to a constant slope at about seconds that was positive, negative or neutral and generally all three for each sample, see Figure 24 and Appendix 2. The positive slope is consistent with materials like rubber or other polymers that deform at a constant rate under a constant load. The neutral slope is consistent with the majority

62 52 of viscoelastic materials which exhibit behavior that is a combination of liquid and solid interaction. What happens is that during the time it takes for the material to reach equilibrium the material experiences viscoelastic behavior, after it reaches equilibrium (the fluid movement is reaches a minimum) the material behaves like a solid and no longer deforms. The negative slope is not consistent with any material that could be found in literature. The behavior is such that there could be several factors involved. One theory could be that first, the force of indentation could be the dominant behavior until seconds into the test. Second, some type of polymer, collagen interaction happens where it requires a high enough energy input to overcome some energy well at which point the interaction restores energy to the material pushing the tip out of the surface. Another possible sources of error could come from the thermal drift inaccuracies of the nanoindenter for long periods of time. It is possible to estimate the maximum time that the indent is accurate by using the estimates developed by Feng et. al. [27]. Another source of suspected error is boundary condition effects. The width of a well-defined hybrid layer is 4-5µm and the width of the tip at 600µN in the hybrid layer is about 2-3µm. As a result the boundaries of the hybrid layer (dentin and adhesive layer) play a role in evaluating the properties. In an effort to eliminate the thermal drift problem, it was decided to switch from static to dynamic testing. To eliminate the boundary condition effects, the various layers were split into macro-layers creating continuous infinite plains for testing. Where an infinite plane is defined as a plane greater than five times the diameter of the indent.

63 53 Figure 24 Representative static viscoelastic test series Polycarbonate One explanation for the large displacement and differing slopes could come from inaccuracies due to the thermal drift of the system. A series of 24 tests were performed on a sample of polycarbonate (used for nanoindentation calibration) (Figure 25) in differing locations with a force of 3000µN identical to the tests on the hybrid layer. The result was that all 24 tests had essentially zero slope and a maximum displacement of 12-15nm over the course of the 500 second test. The polycarbonate has similar properties to the hybrid layer, it has a measured elastic modulus of 5.36+/-0.11 and has similar displacement depths to that of the hybrid layer. The polycarbonate had an initial displacement of 705nm which is similar to that of the hybrid layer which has an initial displacement of nm. The hybrid samples had varying slopes and a maximum displacement of nm over the course of the 500 second test. The polycarbonate had a measured thermal drift of nm/s, which would account for almost

64 54 the entire displacement of tip seen in the initial study this eliminates the effect of thermal drift on early experimental results. Figure 25 Static Viscoelasticity for polycarbonate Static Macro-Hybrid layer The static macro-hybrid layer was created similar to the dynamic macro-hybrid layer but with a few differences. The resin used to create the macro-hybrid layer was 3M ESPE Adper single bond plus adhesive. The samples were first demineralized in 10% phosphoric acid for 6 hours followed by dehydration and resin infiltration. The demineralized dentin was then dehydrated in individual 0.6 ml eppendorf tubes by starting with 25%, 50%, 75%, and 100% reagent alcohol for 20 minutes for each gradient, followed by 100% ethanol that was exchanged

65 55 three times with new 100% ethanol every 20 minutes. During each dehydration step, the samples were placed on a shaker table to maximize infiltration and minimize incomplete exposure to one side of the beam (i.e. the beam is in contact with the side of the eppendorf tube). The samples were then infiltrated with resin using previously published techniques [48], where the dehydrated dentin was first infiltrated with a 50/50 mix of reagent alcohol for 30 minutes followed by three changes of 100% resin of 30 minutes each. During each resin infiltration, the tilt table (Basic BlotRocker, Denville Scientific, South Plainfield, New Jersey, USA) or vortex mixer (Fisher Scientific, Hanover Park, Illinois, USA) was covered by a box to minimize the contact with light that would prematurely polymerize the macro-hybrid layer. Each sample was then placed between two glass slides and polymerized for 60 seconds per side using a UV light source. The samples were then placed in a mold and covered by a two-part epoxy (Buehler Epoxicure (hardener) and Buehler Epo-thin (epoxy), Lake Bluff, Illinois, USA) in preparation for testing. The samples were then allowed to cure overnight and then polished to expose the macro-hybrid layer. Each sample was then tested by nanoindentation using a force of 3000 µn for 500 seconds. Unfortunately, no results were obtained due to an inability to achieve proper resin infiltration using small variations of the above techniques Dynamic Viscoelastic Tests Each sample was tested in a distilled water bath to maintain the material properties. Every sample was tested using the Hysitron Ubi nanoindenter in nanodma mode with a static force of 700 µn and a dynamic force of 5-55 µn depending on the material tested. Frequency sweeps were performed from Hz with a step size of 10 Hz. The 1 Hz value has particular

66 56 importance due to its clinical relevance of chewing which is commonly in the range of Hz [49, 50]. These static and dynamic force values were determined from preliminary testing results by varying the force from 100µN-1200µN in 100µN steps and sweeping the dynamic force from 10-60µN to optimize the dynamic amplitude to between nm as recommended by Hysitron. In general, the dynamic amplitude was higher at low frequencies and lower at high frequencies. A static force of 700 µn was found to be the minimum force that did not have a significant change from one force to the next i.e. the storage modulus decreased until 600 µn at which point the storage modulus reached a steady value. Dentin The teeth were prepared by first sectioning the tooth into four sections by an Isomet slow speed saw. The outer two sections were discarded, while the inner two sections were tested (similar to the sample sectioning for static testing shown in Figure 20). Every sample was tested using a dynamic force of µn where the dynamic force was varied to ensure that the dynamic amplitude was in the range of nm. The indenter was set up to automatically indent using three series of five indents each with a minimum spacing of 5 µm between indents and with each indent optimized to minimize interference from peritubular dentin or other local artifacts. Each series had a minimum spacing of 300 µm from each other. Macro-hybrid layer The hybrid layer was created using techniques similar to TEM sample preparation, outlined by Chiraputt et al. [48] and modified as necessary. The teeth were cut into sections with dimensions of 0.4 x 1.5 x 10 mm using a slow speed saw so that the 1.5 x 10 mm surface was parallel to the crown enamel (Figure 20). The samples were then demineralized in 1.5 ml of

67 57 10% Phosphoric acid for 6 hrs. After which they were stored in distilled water until they were dehydrated in 90.5% Ethanol, 4.5% Methanol, and 5% Isopropyl Alcohol otherwise known as Reagent Grade Alcohol, for two rinses of 30 minutes each. Then a solvated primer of 50/50 alcohol and resin (the resin was 3M Adper single bond plus) for 30 minutes (0.5ml of both alcohol and resin) followed by two changes of pure resin (1ml). The sample and resin was then air dried for one minute and blown dry for one minute with pressurized air followed by two minutes of UV light curing. The samples were then placed in a mold, encased in a two part epoxy (Buehler Epoxicure (hardener) and Buehler Epo-thin (epoxy), Lake Bluff, Illinois, USA) and then stored dry. The samples were then polished just prior to use and then testing under a distilled water bath. The dynamic force used was 10µN and tested in a similar way to the dentin. Adhesive The resin macro layer was created using a previously established protocol by Carrilho, et al. [51] and adapted for this research. Each sample was created by placing a washer with petroleum jelly on a glass slide to create a watertight seal. Resin was then poured into the mold under low light conditions to minimize polymerization. The sample was then air dried for 60 seconds followed by low flow compressed air for 60 seconds to help evaporate the solvent. A celluloid strip was then placed on top of the resin in the washer and cured with 120 seconds of UV light. The surface used for testing was the surface with the celluloid strip and free from petroleum jelly. The samples were then removed and tested without polishing with a static force of 700µN and a dynamic force of 15µN. The samples were also spaced a minimum of 15µm

68 58 apart since their indent width is ~5µm. The samples were all tested in distilled water to simulate normal testing conditions. Composite The composite sections were created by creating four discs on a glass slide and then placing another glass slide on top to create a uniform thickness. The composite discs were then cured using a UV light source shined through the glass slide for 80 seconds. This enabled the surface to be cured and for the discs to be easily removed due to the shrinkage of the composite. The discs were then polished. The samples were tested with a dynamic force of µn.

69 CHAPTER 3: RESULTS AND ANALYSIS 3.1 Statistical Analysis Two types of statistical analyses were used for this study. The first was calculating the average and standard deviation of the variables in question for the set of experiments and the second was an ANalysis Of VAriance (ANOVA). The first analysis was used to gain insight on how well the data fit expected outcomes and was not used for the testing of significance. The average or mean of the population was determined using: (45) where n is the number of samples and is an individual sample. The standard deviation was calculated using: ( ) (46) where N is the number of samples, is the individual sample and is calculated from (45) [52]. Since biological materials present with a great deal of variation within a sample population there exists a need for advanced statistical analysis. The primary analysis done with biological materials is an ANOVA. ANOVA is a technique of partitioning the variance in a set of data into several components in such a way that the contribution of each of these components to the overall data set may be assessed [52]. The primary type of ANOVA that is used for the types of testing used in this project is the ANOVA randomized complete blocks design. The goal of the complete blocks design is to test the variance between groups, where we can be 59

70 60 reasonably certain that each sample has the same characteristics and undergoes different tests or groups. The premise is that each sample can vary widely but the variation between each test the sample undergoes is only due to the change in experimental variables. The basis of this type of ANOVA test is a generalized form of the t-test. To determine the effect of grit size on elastic modulus using repeated measurements for ANOVA where the four layers were separated using image analysis. They were then compared with the measured elastic modulus versus the polishing particle size. The other test series used similar methods to determine each layer. The software used to evaluate the data was SPSS v12.0 (SPSS, Chicago, IL) with an alpha-criterion of 0.05 being considered significant. The viscoelastic values were similarly compared to ensure that the samples were in agreement with each other. 3.2 Force and Roughness One-way ANOVA was used to test the effect of grit size on surface roughness (RA) and modulus of the dentin. Individual comparisons were made using post hoc t-tests with Bonferroni adjustments. ANOVA is a statistical method where different groups of similar data can be compared to each other that eliminate variability between samples in a group. There was a significant difference between each adhesive systems used (p<0.001) Elastic Modulus vs. Particle Size Grit size did not systematically affect the elastic modulus (p<0.001) in any of the four surfaces: dentin, hybrid layer, adhesive, or composite. The values for dentin varied significantly for each polishing size from GPa, which is in close agreement with previous values found in the literature. The hybrid layer was found to vary from GPa and the adhesive

71 61 layer varied from GPa. The composite layer was the most consistent with values that varied between GPa. Figure 26 Results of the elastic modulus verses particle size. Error bars represent standard deviation Particle Size vs. Surface Roughness Grit size significantly affected RA (p<0.001) for all surfaces, with the 0.05 µm grit producing the smoothest surface RA=8.4±4.0 nm for the dentin surface, RA=9.5±2.6nm for the hybrid surface, RA=2.0±1.4 nm for the adhesive surface, and RA=10.7±4.4 nm for the composite surface. The elastic modulus could not, however, be correlated to the average surface roughness. As expected, the surface decreased in roughness as the particle size of the polishing compound decreased.

72 62 Figure 27 Results of the elastic modulus verses the surface roughness. The error bars represent the standard deviation Reduced Elastic Modulus vs. Indentation Force Here, it was found that indentation force had a significant effect on the elastic modulus (p<0.001). There were no significant differences, however, between moduli measured with indentation forces of 600, 1200, 1800 or 2400 µn where the values remained approximately constant.

73 63 Figure 28 Results of the elastic modulus verses the force. The error represents one standard deviation. 3.3 Viscoelasticity Dentin The storage modulus of dentin had greater moduli than that of the elastic modulus of static dentin. The storage modulus also tended to increase with increasing frequency. The greatest increase occurred between 1 and 10 Hz (Figure 29). The loss modulus of dentin was highest at 1 Hz and decreased significantly for higher frequencies. In each test series, the dentin was additionally tested under static conditions to verify that the dentin was consistent with values in earlier sections as well as in the literature.

74 64 Figure 29 Dentin storage modulus (left) and loss modulus (right) Macro-Hybrid layer (3M ESPE Adper single bond plus) A macro-hybrid 3M ESPE Adper single bond sample was studied for viscoelastic measurements. The hybrid layer storage modulus increased with increasing frequency particularly between 1 and 10 Hz (Figure 30). Similarly, the loss modulus increased significantly between 1 and 10 Hz. Both the storage and loss moduli showed gradual increases between each frequency up to 250 Hz. The Bisco one-step plus macro-hybrid layer could not be successfully created. After nine samples were created, only two gave results dissimilar to the epoxy disks they were embedded in. After discussions with the CEO of Bisco [53], it was suggested that the solvent used to suspend the polymer was interfering with the ability for the adhesive to infiltrate the demineralized dentin and was willing to supply alternative formulations. The Bisco adhesive also needed to be shaken prior to application and it was thought that the polymer was polymerizing on the surface during infiltration and thus preventing further infiltration. The 3M system, however, did not suffer from these problems.

75 65 Figure 30 Macro-Hybrid layer 3M Adper single bond plus. storage modulus (left) and loss modulus (right) Macro-Adhesive Layer The Bisco one-step plus adhesive system showed an increase in both the storage and loss moduli particularly between 1 and 10 Hz. As can be seen in the storage modulus graph (Figure 31) there is a wide variety of values obtained for the modulus. These values represent the four out of 8 successful tests of the macro adhesive layer. The values excluded were those that either were implausible i.e GPa or unreasonable i.e. values that were essentially zero but the tip indicated firm contact. The data series measured from the 3M Adper single bond plus were excluded because after eight tests only two series gave reasonable values. In early pilot testing both the Bisco and 3M samples showed very high levels of stress fractures. This was reduced by blowing compressed air into the samples to help evaporate the solvent (Acetone or Ethanol depending on manufacturer). This reduced the stress cracks from 30 or more per 7mm diameter disk to 0-3 cracks per disk. The samples still showed significant shrinkage, however, over the course of a 24hr period (estimated at 20-30%).

76 66 Figure 31 Bisco one-step plus Adhesive storage modulus (left) and loss modulus (right) Composite Layer The composite layer showed an increase in both the storage and loss moduli particularly between 1 and 10 Hz (Figure 32). The variation seen between each sample possibly comes from indenting in either resin or the composite beads, although each series represents 18 distinct data points sampled with automated testing. General Figure 32 Composite layer Storage modulus (left) and loss modulus (right) In general, the storage modulus increased the greatest between 1 and 10 Hz for all four layers (Figure 33); however, the loss modulus of dentin at 1 Hz was 3.14 ± 1.39 GPa and at 10 Hz

77 67 dropped to 1.06 ± 1.45 GPa and then remained relatively constant at higher frequencies. For the hybrid layer, the loss modulus at 1 Hz was 0.12 ± 0.08 GPa and at 10 Hz was 0.27 ± 0.16 GPa. For the adhesive layer, the loss modulus at 1 Hz was 0.29 ± 0.30 GPa and at 10 Hz was 0.64 ± 0.44 GPa. For the composite layer, the loss modulus at 1 Hz was 3.64 ± 3.15 GPa and at 10 Hz was 7.58 ± 3.81 GPa. From this, it is clear that from 1 to 10 Hz, the loss modulus for dentin dropped approximately by one third while it doubled for the macro-hybrid layer, macro-adhesive layer and composite layer. For values larger than 10 Hz, the loss modulus values generally increased at small rate. From the loss modulus results, it appears that the methods behind the viscoelastic responses of the artificial layers differ from that of the dentin. Figure 33 Combined results for the viscoelastic response of the macro-dentin-composite Layer

78 3.3.1 Measured Storage Modulus Equations Each layer (dentin, macro-hybrid, adhesive and composite) was analyzed using various techniques including: exponential, linear, logarithmic, polynomial (6 th order) and x raised to a non-whole number power using the data compiled in Figure 33. For all the series, the best fit or highest value was found using a logarithmic trend line fit. Where E is in units of GPa and ω has units of Hz. In general, each equation had the poorest fit during the beginning of each experimental series (1-10 Hz) indicating that there is some behavior that is not properly modeled by the following equations. The dentin was found to be ( ) (47) the composite layer was found to be ( ) with, (48) the macro-hybrid layer was found to be ( ) with, (49) and the adhesive layer was found to be ( ) with. (50) Using these with equation (43) developed previously it is possible to determine the static storage and loss moduli if desired and will be discussed in chapter Measured Loss Modulus Equations The various layers of the measured loss modulus did not conform to linear models as the storage moduli did. In order to achieve agreement with the experimental data (Figure 33), it was necessary to fit a 6 th order polynomial to the curves obtained. These equations were severely 68

79 69 affected by the initial 1-10 Hz behavior after which the equations approached linear values. The results were found to be that the dentin was ( ) (51) the composite was ( ) (52) the macro-hybrid layer was ( ) (53) and the adhesive layer was ( ) (54) In a similar fashion to the storage modulus, equation (44) can be used to convert these dynamic loss moduli to static moduli and will be discussed in section 4.

80 CHAPTER 4: DISCUSSION 4.1 Force and Roughness The surface roughness did not affect the value of the elastic modulus. The samples were detached after each step (3000 grit, 9µm, 6µm, 3µm, 1µm and 0.05µm) and also included a larger range of polishing steps then the ones presented earlier. Three samples were run and then analyzed before it became clear that as the samples decreased in roughness, they also decreased in their measured elastic modulus. The samples elastic moduli decreased from ~21 GPa with the 3000 grit (consistent with mineralized dentin) to ~0.5 GPa with the µm polishing particle size (consistent with demineralized dentin). The two main variables that could induce the demineralization were the storage conditions or superglue contamination. The storage condition was ruled out early on since it was stored in HBSS which has been well established to prevent property changes in teeth [12, 13]. Several months after the conclusion of the early study, however, it was found by another researcher that the HBSS we were using had some type of contamination that changed the ph of the solution. As a result, his samples experienced demineralization effects. The other variable, superglue, was suspected of causing the samples to demineralize. The superglue is used to mount the samples on a metal disk used for holding the sample in place during nanoindentation. Typically, after each test the sample is detached from the disk. Other researchers did not typically clean the superglue off their samples and this did not affect their results since they were only tested one time in the nanoindenter. The samples in the roughness testing were detached and reattached after each polishing step and the superglue residue on the tooth and metal stub were left as is. It was also noted that after several detach re- 70

81 71 attach cycles the water used to hydrate the samples would sometimes develop a skin that appeared to be wet superglue. For this reason, it was suspected that the superglue was dissolving into the distilled water creating an acidic solution and thus demineralizing the sample over the course of the several day testing cycle required for each sample. As a result, the protocol was changed to fewer roughness values and the gross majority of the super glue was removed by polishing immediately after it was detached from the metal stub. The samples were also typically tested from start to finish in the minimum time possible for each sample. The surface roughness was calculated using a small area (~ ) as this was judged to be the largest size that could be obtained without encountering surface defects like tubules, material boundaries, composite beads, etc. Larger areas could have been calculated but they resulted in a much larger values for the roughness (~ nm) which were typically attributed to the surface defects. For the force variation tests, there was a statistically significant effect for values less than 600 µn. One of the possible explanations for this effect could have to do with the surface energy of the sample [20, 29]. This effect is most prevalent in shallow indentations, which in turn is directly correlated to the force of the indent. This hypothesis would explain why there is a minimum force needed to obtain an accurate measurement of the elastic modulus. The electronic noise limit of the nanoindenter is 1 nn and thus not a factor in this calculation [28]. 4.2 Viscoelasticity For the purposes of the following discussion, energies will be used to compare the various effects observed. The storage modulus can be interchanged with stored energy, while the loss modulus is lost or unrecoverable energy. In addition, polymers achieve a minimum energy

82 72 state when they form spheres similar in construction to a disorganized ball of yarn (the disorganization is due to the attraction and repulsion of the mers [building block of a polymer]). The polymers store energy similar to a spring, when the polymers are pulled from the ball of yarn this stored energy is similar to stretching a spring. When they are compressed the energy is stored by decreasing the distance between mers which increases the chemical energy much like compressing a spring. The dentin showed that there was a significant drop in the measured loss modulus between 1 and 10 Hz. I hypothesize that this drop comes from the microstructure of the tooth primarily due to an interaction of the tubules and the water within them. At low frequencies, the friction of the water moving in the tubules creates a high loss modulus but as the frequency increases the distance that the water can travel in the tubules decreases. This is because the shock waves or water hammer have time to dissipate the energy but as the frequency increase the waves overlap reducing the ability of the water to effectively transfer energy. This in turn reduces the friction loss and thus there is a reduction in the loss modulus. In the macro-hybrid layer, the primary viscoelastic response is from the polymer chains and the collagen. Both of these materials have similar microstructure features, namely, they both have very large aspect ratios where the diameter of collagen can range from nm in diameter and mm in length [4]; and polymers have diameters of 1-25 nm (depending on: chemical formation, branching etc.) and can be ~1µm in length (depending on: mers, process of polymerization, etc.) [54]. In their natural state, however, polymers tend to form spherical balls to achieve their minimum energy state. Both collagen and polymers also tend to deform significantly (>50%) under relatively small loads. This leads to the hypothesis that both collagen and the adhesive polymers behave similarly. This hypothesis is in good agreement with the responses observed

83 73 for both the macro-hybrid layer and the adhesive layer, where, at low frequencies, the collagen and adhesive were able to come under compression and then relax and come back to a minimum energy state. At higher frequencies, the polymers and collagen can no longer maintain their minimum energy state and thus energy is lost to maintaining the higher energy state that the frequency is imparting. The composite layer is comprised of ~15% polymer and 85% ceramic filler particles (~1µm in diameter). The composite layer behaved differently from the other layers for several reasons. First, it is not composed of a viscoelastic material like the adhesive or collagen and second, it does not have structural geometric components (e.g. tubules) that provide an alternate means of viscoelastic response. The results indicate that at low frequencies (~1Hz) the dentin and composite layers have similar loss moduli (~3.5 GPa). As the frequencies increase (>10Hz), however, the loss modulus dramatically increases (~8 GPa). This indicates that there is a third cause for the viscoelastic response not seen in the other layers. To understand the apparent viscoelastic behavior the following three assumptions are made about the structural behavior of the composite layer. The first assumption is that the composite beads (~85% by volume) undergo no deformation. The second assumption is that the adhesive (~15%) deforms elastically. The third assumption is that the primary mechanism of the response observed occurs at the composite-silane-adhesive boundary (silane is a polymer coating on composite that allows for the adhesive to bond with the composite beads). Using these assumptions, it is hypothesized that at low frequencies the silane boundary has little or no effect on the viscoelastic response and the primary response comes from the adhesive. As the adhesive makes up a small volume of the composite layer the polymers have less room to achieve minimum energy states and are restricted in the volume in which they can deform. The adhesive, however, can manage to

84 74 distribute the energy imparted in a semi effective manner but requiring that the polymers maintain a higher energy state this result in the lower loss modulus observed (~3.5GPa). This is because the energy that would be stored as the elastic modulus is instead lost to maintaining the higher energy state of the polymer. As the frequency increases (>10 Hz), the adhesive can no longer effectively distribute the energy from the oscillations, and, as a consequence, the bonds of the polymers start to break at the silane boundary, which results in the high loss modulus observed (~8GPa). An alternative to this hypothesis is that the silane bonds are broken at a lower energy (<10 Hz), which results in the composite resin beads free floating in the polymer matrix, i.e. not constrained chemically but only physically. Thus, the beads can be thought of as similar to a spinal column where the vertebrae are represented by the composite and the disc represents the resin. This suggests that the energy is absorbed in a similar fashion to how shocks are absorbed by the body. Moreover, when the discs detach from the vertebrae the force tends to become dissipated into the body resulting in pain. Instead of storing or transmitting the energy the energy is instead lost in the form of impacts and friction losses. In a similar fashion to the spinal column, the vertebrae can be thought of as the composite beads and the discs are represented by the resin matrix. The results obtained for the macro-hybrid layer and the adhesive layer were consistent for the four samples tested; however, experimental variables excluded many specimens. The adhesive layer was initially difficult to create due to the high stresses involved in the curing process (the samples were spider webbed with cracks and thus not tested). This was due to the solvent (~30% by volume of the uncured adhesive) exfiltration of the mers chains prior to, during and after the cure process. When the adhesive is prepared clinically, the thickness of the adhesive layer allows for rapid exfiltration of the solvent with minimal final deformation (<3%).

85 75 The large samples created (~7mm diameter by 2mm) experienced a significant deformation (~30% 24 hours after curing). The procedure was changed so that it included a minute of airdrying and a minute of compressed air drying. This resulted in the samples having few (0-4) cracks in the surface although there was still shrinkage (estimated at 10-30%). The Bisco onestep adhesive performed well with 50% (4 of 8 samples) of the samples tested giving reasonable results. The Adper single bond plus gave poor results with only 12.5% (1 of 8) of the samples giving reasonable results and was thus excluded from analysis. For each sample a static indent was performed to determine the measured elastic modulus and then compared with the results obtained in the force and roughness study. For this experiment, reasonable is defined as having a static indent modulus of less than 10 GPa but greater than 0.5 GPa in other words consistent with the polymers found in the literature. The indent also had to perform in a standard manner, i.e. few or no false surface engages, standard indent loading (10 second load ramp time (0-700µN), 10 second load (700 µn) hold time and 10 decrease load (700-0 µn) time) and a discernible imaging (defined as a topological image obtained with minimal effort and corrections). The samples that were excluded from analysis often had several of these criteria invalidated. For example, a sample could not be imaged and the dynamic load curve was identical to that of air. Another common situation was an unusually high storage modulus ( GPa) that occurred in four of the samples. The macro-hybrid layer had similar problems with poor sample creation. Reasonable for the macro-hybrid layer is defined as a surface that can be imaged and a measured elastic modulus (static) of greater than 1 GPa. The sample was redefined as demineralized dentin if the measured elastic modulus was less than 1 GPa. Unlike the adhesive layer formation, the Adper single bond plus performed well with 100% of the four samples created giving reasonable results. The Bisco

86 76 one-step performed poorly with 11% (1 of 9) giving reasonable results (two separate infiltrations the first with 4 samples and the second with 5). Later the Adper single bond plus was unable to be recreated (0 of 14, 3 slightly different protocols). The hypothesis for the failed samples comes from a failure of the resin to properly infiltrate the demineralized dentin. One theory is that the adhesive is polymerizing on the surface of demineralized dentin upon first contact blocking the remaining adhesive from penetrating the demineralized dentin. Another theory is that the demineralized dentin is partially collapsed at the surface and does not allow the resin to infiltrate. From the analysis of various layers, the storage modulus was relatively easy to model with each layer able to be modeled with a simple natural log function and a y-intercept; however, the storage modulus was difficult to model requiring a 6 th order polynomial function. It is hypothesized that the storage modulus is measured along a continuous curve, while the loss modulus has a discontinuity between 1 and 10 Hz. My hypothesis is that the loss modulus follows one equation for frequencies less than 10 Hz and a different equation for frequencies greater than 10 Hz. The equations developed in section 1.3 can then be used to directly convert the experimental measurements obtained for the dynamic storage and loss moduli into values for the static storage and loss moduli. The results obtained are internally consistent but there are no other relevant studies for comparison.

87 CHAPTER 5: CONCLUSION 5.1 Force and Roughness For the preliminary testing on the roughness series, an analysis of the data indicated that the more tests performed on each sample the lower the measured elastic modulus. After examining other test results from other users, however, it was concluded that the nanoindenter was performing correctly. This suggested that super glue contaminated and demineralized the dentin if the sample was detached and reattached many times (>3-4) even if stored in Hanks buffered salt solution. It was theorized that the superglue used to adhere the tooth sample to the sample stub was reacting with the deionized water during testing and forming an acidic solution, thus demineralizing the tooth. As a result, an effort was made to minimize detaching and reattaching the sample as well as limiting the time to less than 24 hours between the first and last test for each tooth sample. This study characterized the effect of surface polishing and nanoindentation force on the measurement of the elastic modulus of the dentin-hybrid layer-adhesive-composite layers and the error in the measured properties. To date there has been no previous study to standardize what effect if any the force and roughness have upon the measured elastic modulus. For the two different bonding systems the images indicated that Simplicity had a much smaller hybrid/adhesive zone (~5-10µm) compared to that of the 3M system (~15-25µm). In general, each layer followed similar trends for both particle size and the indentation force. There was no significant difference between the two systems and their data was then pooled to give a greater number of data points for the adhesive and hybrid layers. The results obtained indicate that the 77

88 78 final polishing particle size has no significant effect on the measured elastic modulus in each of the four cases studied (dentin, hybrid, adhesive, and composite). The indentation force, however, significantly affected the measured elastic modulus for each of the four dentincomposite layers for values less than 600µN. The results obtained in this study suggest that the force values used in the literature could lead to higher values of the measured elastic modulus than what might actually be the case. The polishing particle size did not affect the measured elastic modulus. As expected, however, it did affect the surface roughness and hence the quality of the scanned image. Smaller polishing particle size resulted in greater clarity for the scanned nanoindenter image. As a result, it is recommended that the particle size should be 0.05µm and the force used be greater than 600µN. 5.2 Viscoelasticity In general, the values obtained for the storage modulus for each of the layers (dentin, macro-hybrid layer, macro-adhesive layer and composite layer) were higher than that of the static case. The loss modulus for dentin, however, decreased approximately one third while the other layers increased approximately twice in value from 1 to 10 Hz. This result suggests that the dentin has different viscoelastic properties compared to macro-hybrid layer (collagen and adhesive), adhesive layer and composite layer. The procedure to create the composite layer was very straightforward and produced reliable results; however, the artificial macro-hybrid layer and the macro-adhesive layers produced inconsistent results. This was primarily due to solvent interactions with the curing or in the case of the macro-hybrid layer the ability of the adhesive to infiltrate. The macro-hybrid layer, although modified from Chiaraputt et al. [48], followed the resin infiltration protocol

89 79 exactly. Thus, it was surprising that it only gave consistent results for the 3M adhesive but not the Bisco. As discussed earlier the solvents for the 3M system and the Bisco system were different and probably led to the inconsistent results for the Bisco adhesive. The adhesive layer, although not created exactly as reported in the literature, was still created in a similar manner. It was also surprising that the adhesive layer was observed to shrink significantly since it is specified that minimal (<3%) shrinkage should occur during the curing process. The shrinkage observed immediately after curing was consistent with minimal shrinkage. The large shrinkage that was observed could be due to many factors including dehydration since the samples were stored dry for 24hrs or over polymerization because the samples were cured for two minutes. The equations developed in and can be further processed using the equations developed in section 1.3. For example, equations (43) and (44) can be used to convert curve fit dynamic experimental data (frequency vs. loss or storage moduli) into values for the static storage and loss moduli. In addition, equations (40) and (41) can be used to determine the spring and damper constants respectively. These equations in turn can be used for the creation of finite element models to model the behavior of the filling during mastication. 5.3 Future Work Future work could include further studies to correlate the results from the force study to the study by Zhang et. al. [29]. Exploration of additional sources of affixing samples to specimens without negatively impacting the material properties of the sample [20, 28] has suggested superglue or wax to affix the samples to the nanoindentation mounting stub. Research could be done to determine what is an acceptable length of time to use the machine without

90 80 effects from thermal drift (equation 15, thermal drift section) so that static viscoelastic measurements could be reliably performed. Further research could be done on comparing the results of the separated viscoelastic layers and that of an actual restored tooth. The data from the dynamic viscoelastic research could be theoretically processed into Voigt and Maxwell models so that finite element analysis could be performed on the tooth using the equations developed in section 1. Another experiment that could be run is to determine if the NanoDMA air calibration for mass and spring constants need to be performed in water and thus accounting for an experimental variable. Other research could be focused on testing the viscoelastic properties could look at clinical restorations to determine how well the testing on the macro layers correlate with the research performed. Furthermore, techniques could be developed that would allow for the use of the modulus mapping techniques on the hybrid layer [45, 55]. In the course of this research, a carious tooth was accidentally investigated using nanodma techniques. The carious region was avoided and carious free dentin was tested. The dynamic testing, however, gave very low values for the storage modulus (5-10 GPa) while in the same location the static values were consistent with good dentin (~20 GPa). This results indicate that carious teeth should be studied to determine if this effect holds true for all samples or if the tooth tested was an outlier. One of the difficulties inherent in this project would be an exact determination of the carious region of the tooth as teeth in-situ react differently than in the lab when stained with caries detector dye. Another way to reduce the effect that water has on the viscoelastic properties of the dentin-composite interface would be to do a comparison study using water and oil. This would greatly reduce the effect that water has on the properties of the sample.

91 APPENDIX Appendix 1: Scanning Electron Microscopy Introduction Scanning Electron Microscope (SEM) although not relevant to the research actually performed, could be relevant to future work on teeth. The procedures used to prepare teeth for testing under SEM are straightforward but more complicated than non-biological samples. This appendix discusses the basics of SEM and the elements needed to create high quality SEM images of the dentin-composite interface. The SEM employs electromagnetic lenses, vacuum systems, apertures and electron guns to produce an image of the surface. The SEM works by accelerating and collimates electrons into a narrow beam that is then impinged on the specimen surface in a vacuum. The electron beam dislodges electrons from the atoms on the surface, which in turn strikes the secondary electron collector. The image that is produced comes from a large number of data points, where each point represents the current of the secondary electrons for that particular location. As a result, the image is built point by point by scanning the electrons on the surface, hence the name scanning electron microscope [56]. There are a number of factors that influence the quality of the image that is produced including the type of filament, focal distance, spot size, accelerating voltage and tilt angle. Decreasing the area where the electron beam impacts the surface magnifies the image. By decreasing the physical focal distance, the field of view is decreased while increasing the overall resolution. Decreasing the spot size is similar to the focal distance because it decreases the size 81

92 82 of the electron beam. The accelerating voltage is used to control the number of electrons in the electron beam; increasing the voltage therefore increases the resolution of the image. Most biological materials, however, cannot efficiently transfer these electrons thus leading to a charge building up on the surface, which in most cases will burn the surface at that point. For this reason most biological and non-conductive materials are sputter coated with a highly conductive material to help discharge these electrons. The x direction, y direction, z direction (focal length) and tilt angle are controlled by mechanical gears and can be used while the SEM is in operation. By adjusting the tilt angle, the surface is tilted out of perpendicular to the electron beam. This is very useful at high magnifications where large portions of the electrons are simply reflected back along the beam path. Tilting the specimen helps to direct the electrons towards the secondary electron detector and thus increase the resolution of the image. An alternative to coating the biological specimen is to introduce air pressure into the specimen chamber. The introduction of air into the vacuum chamber acts as a conductor which allows for greater resolution of the biological material. The major drawback to this type of imaging is that although the pressure of the air is low (<1000 Pa) the atmosphere causes interference throughout the chamber which creates difficulties in focusing and resolution. This imaging can provide an image of a biological sample that would otherwise have important details that could be damaged or obscured by the coating. Procedures Since teeth are biological materials and contain ~30% water, they must first be dehydrated before testing. If they are not, then they are subjected to extensive cracking when the water violently ex-gasses from the tooth. Two different procedures for dehydrating the tooth

93 83 sample were used. In the first method, the SEM sample was first fixed in a 10% formalin solution for greater than 24 hours and then desiccated under vacuum for greater than 24 hours. The samples were then attached to a sample stub with carbon tape and sputter coated with a 5.2nm thick layer of platinum-palladium. The other procedure used for preparation was the critical point drying method. The sample was wiped clean and then submerged in increasing gradients of ethanol. The tooth was dehydrated by starting with 25%, 50%, 75%, and 95% ethanol for 15 minutes for each gradient, followed by 100% ethanol that was exchanged three times with new 100% ethanol every 15 minutes. A critical point dryer chamber was cooled down to ~4 and submerged in ethanol. The sample was placed in a cage being careful not to expose it to air. The sample and cage were then transferred from the beaker of ethanol into the critical point dryer. The sample chamber was sealed and carbon dioxide was then pumped in at 50 bar. The chamber was purged 6 times without allowing the sample to be exposed to air. This process completely removed the ethanol from the tooth and replaced it with liquid carbon dioxide. Next, the chamber was heated to ~40 which is past the critical point of ~31 for carbon dioxide. This allows for the carbon dioxide to transition from liquid to vapor and thus ex-gas from the tooth. Then the chamber was allowed to slowly vent the carbon dioxide leaving the tooth completely dehydrated. The sample was then removed from the critical point dryer affixed to a sample stub and sputter coated with platinum/palladium (~10nm). After the sample was removed from the sputter coater, it was placed inside the SEM for imaging. The SEM was then used to investigate the marks left from nanoindentation by scanning the surface at 3,000 X magnification.

94 84 Analysis The pictures generated using SEM generate clear images of what the dentin-composite layer looks like (Figure 34, Figure 35, and Figure 36). In Figure 34 the composite and dentin layers are clearly shown however the adhesive and hybrid layers are unable to be clearly established. Further magnification (Figure 35) shows that there is no clear boundary between the adhesive and hybrid layers. The composite clearly, however, shows the ceramic beads in their resin matrix, giving a reference point for comparing images from SEM and nanoindentation. Further magnification of the dentin (Figure 36) clearly shows the different types of dentin. Figure 34 SEM image of the dentin composite interface (4000 X magnification)

95 85 Figure 35 SEM Dentin-Composite junction at 13,000 X magnification (Left), SEM Composite and adhesive boundary at 25,000 X magnification Figure 36 Tubule with peritubular and intertubular dentin at 25,000 X magnification Discussion The SEM is a very useful tool for examining the surface of the dentin-composite junction. It provides a large amount of detail of the surface and even gives clues to the structure of the junction. By changing the focal length to 8mm, the spot size to 35 and the tilt angle to 8 degrees, the images generated were increased in maximum resolution from 10,000 to 25,000 X. Nanoindentation marks were not seen, although an exhaustive effort was done to find them including placing marks on the surface of the sample to positively identify the small region (~25