Morphologic and structural analysis of material-tissue interfaces relevant to dental reconstruction

J.H. Purk , in Material-Tissue Interfacial Phenomena, 2017

8.3 Structure of dentin and effect on adhesive bonding

Dentin is a biological composite composed of dentin tubules; peritubular dentin, which encircles each tubule; and a collagen matrix of intertubular dentin dispersed between the dentin tubules. In contrast to enamel, the composition of dentin is very heterogeneous. The intertubular collagen matrix is filled with submicrometer- to nanometer-sized, calcium-deficient, carbonate-rich hydroxyapatite crystallites [46–48]. The dentin tubules are parallel micrometer-sized hypermineralized, collagen-poor cylinders lined with inorganic peritubular dentin [47,48]. The peritubular dentin can have a mineral content greater than 90%. In contrast, the intertubular dentin has a mineral content of 70%. Dentin is approximately 55   vol% mineral, 30   vol% organic material (primarily type I collagen), and 15   vol% fluid [46], but dentin composition varies with the age and tooth type. The organic portion of collagen is surrounded by water, and hydrogen bonding exists between the strands of the collagen [48].

Dentin contains continuous tubules that run from the DEJ to the dentin–pulp border. Each tubule is an inverted, elongated cone, with its smallest diameter (c. 0.8   μm) at the DEJ and its largest diameter (c. 3.0   μm) at the pulp. As the tubules converge on the pulp chamber, the surface area of the intertubular dentin decreases and the tubule density increases from about 1.9   ×   106 tubules/cm2 at the DEJ to between 4.5 and 6.5   ×   106 tubules/cm2 at the dentin–pulp border [19].

The surface area occupied by intertubular dentin and dentin tubules varies as a function of the location, ie, close to the pulp or the DEJ. At a location close to the pulp (0.1–0.5   mm from the pulp), the percent of surface area occupied by the intertubular dentin and dentin tubules is about 51% and 12%, respectively. After acid etching, intertubular dentin comprises 70% and the tubules 30%. In comparison, at a location close to the DEJ, the percent of surface area occupied by intertubular dentin and dentin tubules is about 94% and 2%, respectively. After acid etching dentin that is close to the DEJ, 84% of the surface area is intertubular dentin and the tubules make up 16% of the surface area [48,49]. Based on these comparisons, for dentin close to the pulp, intertubular dentin accounts for less surface area, whereas the tubules, which are filled with pulpal fluid, occupy more of the surface area. Close to the pulp and prior to acid etching, dentin tubules account for ∼12% of the surface area, whereas after acid etching the tubules account for 30% of the surface area.

The fluid content of the dentin tubules varies by depth, with superficial dentin containing the lowest fluid content and deeper dentin, ie, dentin closest to the pulp, containing more fluid [50]. The amount of collagen in dentin decreases from superficial to deep dentin [51]. Bonding to dentin is variable, depending on the number, density, and size of the tubules. The more the amount of tubules present, the wetter the dentin surface. There is an inverse correlation between the bond strength of the composite resin and that of the superficial and deep dentin, ie, the deeper the dentin, the lower the adhesive bond strength [52–54].

Depending on the location of the cervical wall, the tubule density on the cervical wall of premolars is different from the tubule density on the axial walls. When the cervical tubule density was counted 1.0   mm above the CEJ, there were 149 tubules for every 100 tubules on the axial wall [55]. Incipient to small cavities usually end 1.0–2.0   mm above the CEJ. At these sites, 49% more tubules means that there is less intertubular dentin for bonding on the cervical wall when compared with the axial wall. The increase in tubule density also translates to increased fluid content on the cervical wall. There is an inverse relationship between dentin tubules and intertubular dentin, ie, as the surface area of dentin tubules increases, the surface area of intertubular dentin decreases.

Dentin tubules are filled with pulpal fluid, and after acid etching, more dentinal tubules comprise the total surface area of the dentin. This is true no matter the depth of dentin that is acid etched. The wetter the dentin, the more difficult it is to bond.

Deep dentin with more tubules has a higher fluid content than does superficial dentin, which has less dentin tubules [56]. Pulpal fluid from the dentin tubules may dilute the organic solvents of some bonding agents. Diluting the organic solvent can cause monomers to leave the soluble phase and form resin globules [57].

When a rotating dental bur comes in contact with the tooth surface, it leaves a smear layer over the surface of the dentin [58] and smear plugs over the openings of the dentinal tubules [19]. The composition of the smear layer includes collagen, mineral, and other debris. Based on morphologic studies, it is theorized that acid etching removes the smear layer and smear plugs [19]. There is no chemical evidence to support the theory that acid etchants remove the dentin smear layer [59]. The collagen of the smear layer is not removed by acid etching, and residual mineral is trapped in the denatured, gelatinized collagen. Ultimately, this gelatinous layer could inhibit the formation of an impervious seal at the dentin/adhesive interface; it could act as a weak link in the coupling of adhesive to dentin [59].

Acid etching opens the dentinal tubules, increases dentin permeability, and decalcifies the intertubular and peritubular dentin [26]. When dentin is acid etched with phosphoric acid, the apatitic mineral is removed, leaving a collagen fibril network. The collagen is supported by water—the water may either be part of the native structure or be water that has been used to rinse the acid-etched dentin surface [48]. After acid conditioning, the dentin surface is represented as a collagen meshwork 2–4   μm thick [48] that can collapse and shrink due to the loss of support from mineral and/or water [70].

When bonded to the cavity surfaces, the polymerizing composite restoration induces the development of stress inside the material, which is transmitted to the tooth structure via bonded interfaces. The magnitude of the polymerization shrinkage stress is influenced by several factors including the volume of material to be polymerized, the filler content and monomer composition, the insertion technique, the flow properties of the composite resin, and the geometry of the cavity [62]. It has been estimated that shear bond strengths of 17–20   MPa are required to resist the contraction forces associated with polymerization shrinkage and to produce gap-free restoration margins [19,63]. If the composite resin cannot bond stronger to the dentin than its polymerization shrinkage stress, then the composite resin can separate from the dentin leaving microgaps [62,64,65]. Leakage of the fluid from the dentin tubules into these microgaps can occur [65,66] (Fig. 8.4). When the patient occludes on the restoration or experiences temperature changes, this fluid movement can cause tooth sensitivity.

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Polymers in Biology and Medicine

W. Wagermaier , P. Fratzl , in Polymer Science: A Comprehensive Reference, 2012

9.03.3.3 A Tissue Made to Last a Life Time: Dentin

Dentin is a bone-like tissue, consisting of collagen fibrils reinforced with carbonated hydroxyapatite particles. It constitutes the body of teeth and is covered by a hard enamel layer. It has long been used by humans as a material in the form of ivory. Given the function of teeth, the design of the dentine structure needs to sustain many years of extreme loads without any repair mechanism similar to bone remodeling. As a consequence, the dentin structure is likely to be very well adapted for its mechanical function. For recent reviews on dentin structure, see Reference 96 . A special feature that differentiates dentin from bone is the existence of tubules that are essentially empty tubes housing cell processes surrounded by strongly mineralized tissue, the peritubular dentin (PTD). Figure 16 shows a picture of tubules in cross-section with the PTD that surrounds them. These tubules are housing cell processes and it has also been speculated that they may have a mechanical function, but the evidence is not entirely clear. 96

Figure 16. Tubules as seen in a backscattered scanning electron microscopy image of a polished slice of dentin. The inset shows a magnified tubule that includes a void (black) and a dense peritubular sheath (white).

Reproduced from Zabler, S.; Riesemeier, H.; Fratzl, P.; Zaslansky, P. Opt. Express 2006, 14, 8584–8597. 97 The black scale bar corresponds to 20   µm.

The collagen fibrils in dentin have been described as being oriented perpendicular to the direction of the tubules. 61 This would imply a strong correlation between the orientation of tubules and the orientation of collagen fibrils and mineral particles. Recent analysis has shown that the orientation of mineral particles mostly follows the direction of typical load ( Figure 17 ) and is less related to the tubule orientation than previously thought. 98 Moreover, the distribution, orientation, and size of mineral particles are found to be graded throughout dentin, in agreement with a grading of the mechanical properties. In particular, the stiffness seems to be minimal close to the dentin–enamel junction which could be a crack-stopping mechanism. It was also found that the mineral particle size (and density) was the best predictor for the local variation of mechanical properties. 99

Figure 17. The degree of mineral co-alignment (ρ) and the typical particle orientation in dentin, shown by color and by the orientation of the bar, respectively. The border corresponds to the dentin–enamel junction (DEJ). The values of ρ range from 0 for no alignment to 1 for perfect alignment. Note zones with a higher degree of orientation on occlusal dentin, diagonally supporting the cusps as well as on lower side crown flanks (near the DEJ border). The direction of the mineral particles corresponds to the typical direction of compressive loads.

Reproduced from Marten, A.; Fratzl, P.; Paris, O.; Zaslansky, P. Biomaterials 2010, 31, 5479–5490. 98 Copyright (2010), with permission from Elsevier.

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Teeth: Structure/Mechanical Design Strategies

S. Weiner , P. Zaslansky , in Encyclopedia of Materials: Science and Technology, 2004

4 Human Teeth

Human teeth, like most teeth of vertebrates, are composed of a hard thin working surface (enamel) that overlies the bulk of the tooth which is composed of a softer more pliant material called dentin (Fig. 4(a)). The mineral phase in both layers is composed of carbonated apatite (also known as dahllite), but the crystal sizes and shapes are very different. In enamel the crystals are highly elongated (spaghetti-shaped). They are arranged in bundles or prisms, and in many species, these bundles are aligned in no less than three different orientations (Fig. 4(b)). The mineral phase comprises ∼99% by weight of the material. The dentin, alternatively, contains exceedingly small crystals, just 2–4   nm. They are amongst the smallest known to be formed biologically. The mineral comprises about ∼65% by weight. A major portion of the dentin crystals are located inside fibrils of collagen, the protein that comprises the bulk of the matrix. They are arranged in layers that traverse across the fibril (reviewed in Lowenstam and Weiner 1989).

Figure 4. Micrographs of human teeth. (a) View of a fractured cross-section of a human premolar. The arrow shows the outer enamel layer. (b) SEM of human enamel showing parts of prisms with elongated crystals oriented in different directions. (c) SEM of dentin in the crown of the tooth, showing the presence of peritubular dentin around the tubules (arrow).

The dentin and, to a certain extent, the enamel are graded materials in that their structural and hence mechanical properties continuously change. This has been demonstrated by microhardness profiles (Craig et al. 1959). One characteristic of dentin is the presence of numerous long and thin tubules (Fig. 4(c)). They usually have an internal diameter of 1 μm and extend from just below the dentin–enamel junction (DEJ) to the pulp cavity. The dentin immediately below the enamel layer in the crown of the tooth contains yet another material type called peritubular dentin. This is a dense collar of mineral that surrounds each of the tubules ( Fig. 4(c)). It contains crystals of the same shape, size, and basic organization as in the bulk of the dentin, but almost no collagen (Weiner et al. 1999). It is much harder than intertubular dentin and presumably much stiffer.

Various materials properties of enamel and dentin have been measured separately. These include both elastic and fracture properties (Kinney et al. 1996). Surprisingly, very little is known about the design strategy of whole teeth. Some human teeth (canines for example) function mainly as cutting tools, whereas others are mainly for grinding. During mastication the forces applied to the tooth are not only exerted in a direction perpendicular to the cutting surface, but can be from oblique directions. Furthermore, the manner in which the stress is applied can vary greatly depending upon the nature of the food being chewed. Thus, the tooth structure presumably has many design strategies for dealing with different mechanical challenges. Here we identify a few.

The position and orientations of the tubules surrounded by peritubular dentin location below the enamel working surface point to a buttressing function for peritubular dentin such that it supports the enamel cap. The tubules with their collar of hard peritubular dentin provide added stiffness to the crown dentin. Strangely, the peritubular dentin does not extend all the way to the dentin–enamel interface or junction (DEJ). Nor do the tubules extend all the way to the DEJ. Both are absent in a transition zone some 100–200   μm below the DEJ. In this same zone, the hardness decreases significantly as compared to the bulk dentin below. All these structural properties point to a unique role for this area of the dentin (Weiner et al. 1999).

Wang and Weiner (1998) reasoned that because of the marked differences in stiffness between the enamel and the dentin, some sort of soft intermediate layer must be present to allow the two materials to "work" together. The microhardness profiles supported this supposition. They used Moiré interferometry to map the strain on the surface of a human tooth slice subjected to compressive forces comparable to those incurred during mastication. They found that indeed the highest strains were measured in the 200   μm zone below the DEJ. Furthermore, the extent of the strain was asymmetric when comparing the labial (external) and the lingual (internal) sides of the tooth. It was postulated that this soft zone is actually the working part of the tooth (Wang and Weiner 1998). It apparently acts as a gasket to allow the very hard and stiff enamel to "work" together with the softer more pliant dentin. Similar experiments were repeated at much higher resolution, but instead of using compressive forces, the tooth slices were subjected to changes of humidity. In one experimental configuration the enamel confined the dentin and prevented it from contracting as a function of dehydration, whereas in another configuration the dentin contracted and expanded freely. Most of the expansion was in the same soft zone below the DEJ (Wood et al. 2000).

Much more remains to be understood about the manner in which whole human teeth are designed to fulfill their functions. This information may have far-reaching implications on treatment regimes and on the design of new dental materials.

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Clinical presentation

B.S. Bohaty , F. Sene , in Material-Tissue Interfacial Phenomena, 2017

1.2 Bonding substrates: enamel and dentin

Human enamel is one of the most mineralized tissues in the human body. The composition of enamel is 96   wt% inorganic materials, 4   wt% organic materials, and water. The inorganic material is predominantly composed of calcium phosphate related to the hexagonal hydroxyapatite, whose chemical formula is Ca10(PO4)6·(OH)2 (Gwinett, and Matsui, 1967; Carvalho et al., 2000). Bonding resin materials to this structure has been for the most part successful by using an acid to render the surface microporous (Fig. 1.1). The prepared surface can then be penetrated by low-viscosity resins (Gwinett and Matsui, 1967). Although the technique has been slightly modified and new products developed and introduced over time, the general tenet of using acid in concentrations of 35–40% to etch enamel and provide micromechanical retention for resin composites has endured. Bonding to enamel has been proved to be successful and reliable over decades of clinical use (Kugel and Ferrari, 2000). The composition of human enamel is relatively well understood, and its chemical components demonstrate a fairly consistent response to acid conditioning and resin infiltration.

Figure 1.1. Acid etch process to prepare enamel.

Dentin is a complex, biologic substrate. The structural components of dentin consist of approximately 50   vol% mineral, 30   vol% organic matrix (primarily Type I collagen) and 20   vol% water (Ten Cate, 1994). The composition of this hydrated organic complex is not static, ie, the composition is influenced by the relative position of the dentin within the tooth, the age of the dentin, and the presence or absence of disease (Marshall et al., 1997). One of the most important aspects of the dentinal structure is the presence of tubules. This unique compositional feature results from odontoblastic activity during dentin formation. The tubules traverse from the dentinoenamel junction (DEJ) to the pulp, and the density and location of the tubules differ from location to location within the tooth. An example of dentinal tubule structure is shown in Fig. 1.2.

Figure 1.2. Scanning electron microscope photomicrograph of dentinal tubules.

In permanent teeth, the tubule density decreases from the pulp to DEJ, and inside the tubules are odontoblastic processes and fluid (Marshall et al., 1997). Pashley (1989) reported that the percentage of tubule area including tubule diameters differs from place to place within the permanent tooth. For example, the diameter of the dentinal tubules ranges from 2.5   μm adjacent to the pulp to 0.8   μm near the DEJ. Similarly, the percentage of dentin area occupied by tubules varies from 22% near the pulp to 1% at the DEJ. Dentinal area occupied by intertubular dentin has been reported to be 12% in proximity of the pulp and 96% near the DEJ. The area occupied by peritubular dentin ranges from 3% close to the pulp to 60% at the DEJ. Numerous studies on permanent teeth have reported that the mean numerical density of tubules increases from the DEJ to the pulp ( Garberoglio and Brannstrom, 1976; Fosse et al., 1992).

Tubules are lined with peritubular (intratubular) dentin consisting of a layer of highly mineralized matrix material made primarily of apatite crystals. The intertubular dentin, which lies between the tubules, is a less-calcified matrix that consists of some apatite crystals embedded within a collagen matrix. The influence of peritubular and intertubular dentin on successful dentin bonding has been postulated by numerous investigators (Nör et al., 1997; Sumikawa et al., 1999; Hosoya, 2006). Numerous studies suggest that when traversing from the DEJ to the pulp, in primary and permanent teeth, the dentinal tubule diameters increase and the peritubular thickness decreases (Allred, 1968; Ten Cate, 1994).

A critical factor in the clinical success of composite resins is the adhesive bond formed at the restorative material/tooth surface interface. Although acid etching provides effective mechanical bonding between the composite restoration and treated enamel in permanent teeth, breakdown at the dentin surface continues to challenge the long-term viability of these restorations. Current theories on dentin bonding suggest that two fundamental processes are involved in bonding an adhesive to dentin. First, the mineral phase must be extracted from the dentin substrate without altering the collagen matrix, and second, the voids left by the mineral must be filled with adhesive resin that undergoes complete in situ polymerization, ie, the formation of a resin-reinforced or hybrid layer. The ideal hybrid layer (Fig. 1.3) would be characterized as a three-dimensional polymer/collagen network that provides both a continuous and stable link between the bulk adhesive and dentin substrate (Nakabayashi et al., 1991; Eick et al., 1993). There is substantial evidence to suggest that this ideal objective is not achieved. Instead of serving as a stable connection between the bulk adhesive and subjacent intact dentin, the hybrid layer has been called the weakest link in the dentin/adhesive (d/a) bond (Sano et al., 1999; Spencer and Wang, 2002).

Figure 1.3. Scanning electron micrograph of the hybrid layer.

A poor-quality hybrid layer can leave unreinforced and exposed collagen at the composite margin and/or beneath the restoration (Spencer and Swafford, 1999; Spencer et al., 2000; Wang and Spencer, 2002). This zone of exposed collagen is susceptible to breakdown after only 3   years storage in aqueous media (Burrow et al., 1996). Poor-quality hybrid layers translate to sites of incomplete adhesive penetration, sites where the adhesive is unstable because of inadequate monomer/polymer conversion, or sites where the adhesive fails to form a cross-linked polymer (Wang and Spencer, 2005a,b; Spencer et al., 2006) Because of the profound effect the seal at the d/a interface has on the clinical performance of composite restorations, it is very likely that a weak hybrid layer threatens the serviceability of the composite. This relationship may be particularly relevant at the gingival margin of Class II composite restorations where there is little enamel available for bonding. Clinical studies have reported that as many as half of the failures in class II composite restorations are due to recurrent caries at the gingival margin (Nordbo et al., 1988; Purk et al., 2007).

Clinical failure of Class II composite restorations are demonstrated in Figs. 1.4 and 1.5. These figures show the gingival margins of an in vivo Class II resin restoration in a permanent tooth and the gingival margin of a Class II resin restoration in an extracted primary tooth. Both show marked demineralization and recurrent caries at the gingival margin of the restoration.

Figure 1.4. Class II resin failure in permanent tooth.

Figure 1.5. Class II resin restoration from recovered primary tooth.

An additional component of tooth preparation that influences the potential success or failure of ideal hybridization is the presence or absence of debris left behind during tooth preparation. Whenever dentin is cut to prepare a tooth to receive any type of restoration, the residual organic and inorganic components of the cut dentin leave a "layer" of debris on the surface. This debris is called the smear layer (Eick et al., 1970). The smear layer complicates the bonding process by acting as a physical barrier to bonding agent penetration (Brannstrom, 1984). Although there may be some advantages in keeping the smear layer intact, the majority of the literature supports the idea that the smear layer must be either removed or rendered permeable so that the bonding agent can penetrate the tooth substrate directly (Pashley et al.1988, 1991; Perdigao, 2007; Spencer et al., 2001; Wang and Spencer, 2002).

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Laser surface modification of biological hard tissues

L.T. Cangueiro , ... R. Vilar , in Laser Surface Modification of Biomaterials, 2016

8.4.2.2 Dentin

When dentin is removed or polished with mechanical burs, a smear layer weakly bonded to the underlying material forms. This layer entirely covers the dentinal structure and consists of an aggregate of HAp and denatured collagen debris (Eick et al., 1970). When dentin is ablated with 500   fs duration laser pulses with 1030   nm radiation wavelength at a pulse repetition rate of 1   kHz and fluences between 1 and 1.8   J/cm2, the smear is entirely removed and the dentinal tubules are exposed (Alves et al., 2012). The surface morphology of dentin surfaces treated in these conditions is depicted in Fig. 8.5.

Figure 8.5. SEM micrographs of a large area dentin surface after a laser treatment with an average fluence of (a, b and c) 1   J/cm2; and (d) 1.8   J/cm2.

Alves, S., Oliveira, V., Vilar, R., 2012. Femtosecond laser ablation of dentin. J. Phys. D: Appl. Phys. 45 (24), 245401.

The ablation surface is relatively smooth and the dentinal structure is entirely preserved. No melting or cracking is observed. The peritubular dentin sheets are clearly visible, revealed as flat cross-sectional surfaces as if they underwent brittle fracture perpendicularly to the tubules axis. The areas corresponding to intertubular dentin present a scaly and relative porous surface. At low fluences, a few particles with an angular irregular shape are observed, typical of thermomechanical solid spallation. These angular particles coexist with spherical resolidified particles, which indicate that liquid spallation also took place. The proportion of these particles increases with fluence (Fig. 8.6(b)). A cross-sectional view of a surface treated with 3   J/cm2 (Fig. 8.6(c)) shows that no cracking occurred below the surface, in contrast with the observations carried out for Er,Cr:YSGG lasers (Cardoso et al., 2008a,b).

Figure 8.6. (a, b) SEM images of a large area dentin surface after laser treatment with 3   J/cm2. The white arrow in (b) shows a spherical particle. (c) SEM micrograph of the transverse cross-section across a laser-treated dentin surface.

Alves, S., Oliveira, V., Vilar, R., 2012. Femtosecond laser ablation of dentin. J. Phys. D: Appl. Phys. 45 (24), 245401.

The relevant regions of XPS spectra for untreated and treated dentin are presented in Fig. 8.7 (curves 1 and 2, respectively). The C 1s carbon peak observed in both spectra (Fig. 8.7(a)) was deconvoluted into two peaks, one at a binding energy of 285   eV, corresponding to surface contamination by hydrocarbons, and the second one, located at about 287.5   eV, due to carbon atoms in the organic compounds present in dentin, in particular type I collagen (Lin et al., 1992). The same observation is valid for the N 1s peak at 400   eV (Fig. 8.7(b)), which is associated with the amide groups in type I collagen molecules. The peaks in the Ca 2p and P 2p regions (Fig. 8.7(c) and (d)) correspond to HAp. The relative amplitudes of these peaks do not change significantly due to the laser treatment (Alves et al., 2012).

Figure 8.7. Relevant regions of the XPS spectra of untreated (curve 1) and laser-treated (curve 2) dentin sample: (a) C 1s; (b) N 1s; (c) Ca 2p and (d) P 2p.

Alves, S., Oliveira, V., Vilar, R., 2012. Femtosecond laser ablation of dentin. J. Phys. D: Appl. Phys. 45 (24), 245401.

The FTIR spectra of untreated dentin and dentin treated with an average fluence of 1   J/cm2 (Fig. 8.8) reveal more clearly the effect of laser irradiation. The phosphate and carbonate absorption bands in these spectra are associated with the mineral phase of dentin, a calcium-deficient carbonated apatite. The most intense peaks associated with P O 4 3 appear at about 1045 and 964   cm−1 and correspond to the ν3 antisymmetric PO stretching mode and the ν1 symmetric stretching mode, respectively (Bachmann et al., 2009; Engel and Bachinger, 2005). The absorption bands at 1437 and 1456   cm−1 can be attributed to the ν3 mode of C O 3 2 substituted in B-type P O 4 3 sites and A-type OH anionic sites, respectively (Zhao et al., 2012). The band at 872   cm−1 is due to ν 2 mode C O 3 2 (Leone et al., 2014). The bands between 1650 and 1200   cm−1 can be ascribed to the amide group of collagen, the main organic component of dentin. The bands at 1647, 1541 and 1227   cm−1 are also due to the amide I (C–O bond), amide II (C–N stretching and N–H deformation modes) and amide III groups of the collagen molecule, respectively. The broad absorption band centred at 3320   cm−1 can be attributed to the amide A (N–H stretching mode) of collagen. The peaks at 2920 and 2850   cm−1 correspond to C–H bonds of organic compounds in general, including surface contaminants (Strickland and Mourou, 1985; Keller, 2003; Leone et al., 2014). The laser treatment causes changes in the structure of the band corresponding to C–H bonds in the organic compounds, indicating partial denaturation of collagen in the ablation surface (Alves et al., 2012).

Figure 8.8. Infrared spectra of untreated (a) and laser-treated (b) dentin samples.

Alves, S., Oliveira, V., Vilar, R., 2012. Femtosecond laser ablation of dentin. J. Phys. D: Appl. Phys. 45 (24), 245401.

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Fracture and aging of dentine

D. AROLA , in Dental Biomaterials, 2008

12.3 Elastic behavior and strength

According to the higher mineral content, sclerotic dentine would be expected to exhibit differences in mechanical behavior when compared with normal (young) dentine. Balooch et al. (2001) were the first to examine properties of sclerotic dentine in detail and used an atomic force microscope (AFM) to achieve independent evaluations of the intertubular, peritubular and intratubular (filling the tubules) components. They found that there was no significant difference in either the hardness or elastic modulus between the intertubular and peritubular components of normal and sclerotic root dentine. Properties of the material filling the tubules within sclerotic dentine were between those reported for the intertubular and peritubular dentine. According to the consistency in chemistry of the peritubular and intratubular dentine (Kinney et al., 2005), it would appear that the crystals formed within the lumens are less densely packed than in the peritubular wall. An evaluation of the elastic constants for root dentine using resonant ultrasound spectroscopy (RUS) also found no significant differences in either the Young's modulus or shear modulus between normal and sclerotic tissue. However, in a comparison of tissue from young (22 ± 3 years) and old (61 ± 6 years) patients, Senawongse et al. (2006) recently reported that there are regional differences in the hardness and elastic modulus of dentine with age. While properties of transparent and normal tissue were not significantly different, they identified that the old dentine just beneath the DEJ (within 5 µm from the DEJ in the mantle dentine) exhibited larger hardness and elastic modulus. The increase in hardness was found to be concentrated in areas of enamel wear.

The author and his colleagues have been examining the importance of aging on the mechanical behavior of dentine under both static and fatigue loads (Arola and Reprogel, 2005, 2006). These investigations have been conducted using the coronal dentine of third molars obtained from patients ranging in age from 17 to 77 years old. Briefly, rectangular beams are obtained using conventional diamond slicing equipment and then subjected to four-point flexure within a hydration bath of Hanks' balanced salt solution (HBSS) at 22 °C. In the quasi-static evaluations, the load and load-line displacement are used with the beam geometry and flexural arrangement to generate stress–strain diagrams for the response.

Representative results from flexure tests are shown in Fig. 12.4a for specimens prepared with the dentine tubules aligned perpendicularly to the length and parallel to the plane of maximum normal stress. As evident in this figure, the dentine of younger patients exhibited linear elastic behavior, followed by a region of non-linear inelastic deformation to failure. In contrast, specimens obtained from older patients exhibited linear-elastic behavior only, and a lower strength and strain to failure in comparison with responses of the young tissue. The flexure strength distribution over the entire patient age range examined is shown in Fig. 12.4b. The energy to fracture can be obtained from the area under the flexural stress-strain curves and the distribution in this property with patient age is shown in Fig. 12.4c. There is a 50% reduction in strength and nearly a 90% reduction in the energy to fracture over the 60 year age span presented. Both the strength and energy to fracture undergo a decrease in magnitude throughout the period of aging, but the largest rate of reduction takes place shortly following eruption. Beyond age 50, the reduction in strength and energy to fracture were not significant. Interestingly, none of the beams examined were completely sclerotic. Therefore, in the coronal dentine there are significant changes in the mechanical behavior that take place before sclerosis. The property distributions in Fig. 12.4b and 12.4c suggest that the coronal dentine undergoes a transition in mechanical behavior and approaches a threshold near age ≥50 years. Earlier examinations of the structure and chemistry appeared to suggest that the tissue remained young for age ≤30 years. Using these definitions for characterizing the 'young' (age ≤30 years) and old (age ≥50 years) responses, the strength and energy to fracture of the old dentine are significantly lower (p < 0.0001) than those of the young dentine. However, there was no significant difference (p > 0.05) between the flexure modulus of the young (mean age, 24 ± 5 years) and old (mean age, 65 ± 13 years) tissue; the average flexure modulus of the dentine was 14.8 ± 2.6 GPa. These results are consistent with earlier evaluations in which there was no significant difference between the elastic modulus of normal and sclerotic dentine (Kinney et al., 2005; Senawongse et al., 2006).

12.4. Mechanical properties of dentine in terms of the patient age: a typical flexural responses for dentine obtained from young (age = 17 years) and old (age = 77 years) patients; b flexure strength as a function of patient age; c energy to fracture.

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Teeth

Haifeng Chen , Yihong Liu , in Advanced Ceramics for Dentistry, 2014

2.2.2 Dentin

Dentin constitutes the bulk of the tooth, which is covered by enamel on the crown surface, cementum on the root, and pulp in the center. 3,4 The formation of dentin (dentinogenesis) is initiated by odontoblasts, which develop from dental papilla contact with the enamel organ. Unlike enamel, dentin continues to form throughout life and can be initiated in response to stimuli, such as tooth decay or abrasion.

With progressive deposition of dentin matrix, the odontoblastic process lengthens and becomes embedded in mineralized tissue. The space occupied by the odontoblastic process is known as the dentinal tubule. The dentinal tubule extends from the DEJ or cementum at the root to the predentin at the junction to the pulp chamber, where the odontoblastic cell bodies lie in nearly a close-packed array. Figure 2.7 shows the typical SEM image of dentin. Most of the collagen fibers arrange vertically to the dentinal tubules and interweave into a mesh. In the interstitial dentin, due to different degrees of mineralization, they can be divided into the following areas: peritubular dentin, intertubular dentin, incremental line, Tomes' granular layer, and predentin.

Figure 2.7. SEM image of human dentin.

The overall composition of dentin is about 70% mineral by weight, about 20% organic matter, and 10% water. 4 The mineral of dentin is also comprised of crystals of a substituted carbonated hydroxyapatite with an organic matrix. However, unlike the long crystals in enamel, the crystals in dentin are much smaller and irregular. Figure 2.8 shows the atomic force microscopic (AFM) images of isolated dentin crystals.

Figure 2.8. AFM images of dentin crystals isolated from human tooth crown. (a) Topography image; and (b) Lateral force image.

It is widely accepted that these nanometer-sized crystals are needle or plate-like in morphology, based on studies using TEM and AFM. Figure 2.4b shows the XRD pattern of human dentin, which has a different crystallinity as compared to enamel crystals. Dentin crystals are only partially crystalline, while the enamel crystals are completely crystalline. The dentin mineralization process involves the formation and growth of hydroxyapatite crystals in an extracellular matrix. 15,16 Type I collagen accounts for 90% of the extracellular matrix of dentin. The collagen fibers provide the framework for HA deposition and the subsequent crystal growth to form a mineralized matrix. This biomineralization process is highly regulated by a set of matrix proteins that are secreted by odontoblasts. The function of these dentin matrix proteins in dentin mineralization has been widely discussed. Of these dentin matrix proteins, phosphophoryn (PP) is the most abundant noncollagenous protein.

More than 80% of this protein's amino acid composition is aspartic acid and serine, and 85–90% of the serine residues are phosphorylated. 15 These unique characteristics make PP a very acidic protein. Early studies have suggested that PP is a mineral nucleator and may have the ability to regulate HA formation. 16 Later studies have shown that PP affects in vitro mineralization in various ways. It was reported that mineral formation could be induced at low supersaturation by covalently binding rat PP to agarose beads and, conversely, that mineral formation could be inhibited when PP was free in the solution. 15,16

Another important acidic extracellular matrix protein, dentin matrix protein 1 (DMP-1), was shown to be expressed in the early stages of dentin mineralization. Expression decreased after the appearance of mineral formation. Thus, it is postulated that DMP-1 has a regulatory role in dentin mineralization. The amino acid composition of DMP-1 is 28% glutamic acid and aspartic acid, which suggests that DMP-1 should have a great capacity for binding divalent cations such as calcium. 15 In an in vitro Ca-binding assay and nucleating test, recombinant DMP-1 showed not only strong Ca-binding ability, but also the capability to assemble calcium and phosphate ions to facilitate HA crystal formation. An in vitro study of apatite growth in a gelatin gel system showed that the length and degree of phosphorylation of DMP-1 affected the initiation and regulation of mineral formation. DMP-1 initiates mineralization when it is dephosphorylated or cleaved, but inhibits mineralization when it is in its native form. Phosphorylation of acidic dentin matrix proteins such as DMP-1 and PP has been reported to affect crystal nucleation and subsequent mineral formation. More direct evidence using AFM revealed that PP had a stronger capacity for binding to enamel crystals than dephosphorylated PP. 16

Dentin sialoprotein (DSP) is another extracellular matrix protein that has been widely investigated. DSP and PP are the cleavage products from a large transcript encoded by the gene dentin sialophosphoprotein (DSPP), but the amount of DSP found in dentin is much less than in DPP. The DSP transcript is expressed in odontoblasts and transiently expressed in preameloblasts. Immunohistochemical studies of DSP have shown that it is present in dentin and predentin. These results indicate a role for DSP in dentin mineralization, but as yet this role has not been defined. 15

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Recent Progress in the Solid-State NMR Studies of Biomineralization

Tim W.T. Tsai , Jerry C.C. Chan , in Annual Reports on NMR Spectroscopy, 2011

5.5 Dentin

There are three distinct biological minerals in an individual tooth, viz. enamel, dentin, and cementum. The chemical composition of dentin is quite similar to that of bone, containing 70   wt% of inorganic phase, 20   wt% of organic matrix and 10   wt% of water. 83 The inorganic phase of tooth dentin was identified as calcium phosphate with an apatite structure. 132 Dentin is a hierarchical composite material comprising type-I collagen fibrils and nanocrystalline apatite. 212 The structure of dentin has as a feature the presence of dental tubules. Therefore, dentin can be categorized further into peritubular dentin (highly mineralized) and intertubular dentin (less mineralized). A recent TEM study shows that the intertubular mineral of age-induced transparent dentin contains apatite crystallites embedded in amorphous matrix. 213 Dentin samples of the incisor taken from Wistar rats of different ages were chosen for recent solid-state NMR studies. 16,33 Rat incisor is "rootless" in which the root canal is open and the tooth continues to grow indefinitely. The dentin sample was prepared by grinding the rat incisors into powder form after removing the enamel layer. To quantify the various 31P species in dentin, a commercial HAp sample was used as the spin-counting standard. The contribution of the 31P signal from the organic component is expected to be negligible. 2 To probe the 31P species which are remote from any protons, the spin-echo technique incorporated with 1H rotary resonance was employed. The 31P signal intensities extrapolated at vanishing spin-echo delay reveals the data free from transverse relaxation effect. The acquired 31P spectra invariably contain a single sharp peak at 3.2   ppm, with FWHM equal to 288   Hz (2.4   ppm). The relatively narrow FWHM indicates that the phosphorus species are of crystalline nature, which was subsequently assigned to HDAp, that is, OH-deficient apatite. The overall phosphate content decreases from the 3-week to the 24-month sample by 12%, which is mainly due to the decrease of the phosphorus content in the amorphous phase. The relative amounts of the HAp and ACP components were determined by measurement of a series of 31P{1H} HETCOR with different contact times. 16 The 31P NMR data show that the phosphorus species in the amorphous phase account for more than 50% of the total phosphorus amount in rat dentin. After explicitly taking HO–H⋯O–PO3 3− and HPO4 2− into account, it has been shown that 19% of the apatite crystallites in our dentin samples contain hydroxyl groups, which is quite similar to the result reported for bone minerals. 28 Furthermore, the total amount of HO–H⋯O–PO3 3– and HPO4 2− decreases as rat dentins mature with age, consistent with the earlier FT-IR results of bone. 214 Because of their disorder nature, it is very difficult to separately quantify the amounts of HO–H⋯O–PO3 3− and HPO4 2− in the amorphous phase. Nevertheless, the τ CP data have led to the conclusion that in the 24-month sample the amount of HO–H⋯O–PO3 3− is significantly less than that of HPO4 2−. 16

Using the pulse sequences shown in Figure 4, the spin diffusion rate between two inorganic phases such as HAp/HDAp can be estimated. The results show that the 31P spin diffusion rates of HAp/HDAP and ACP/HDAp are approximately the same, whereas the rate of HAp/ACP is considerably smaller. In other words, ACP and HDAp are in close proximity, and so are HAp and HDAp. Because the phases of HAp and ACP are spatially more remote, the "average" structure of Wistar rat dentin is constructed as shown in Figure 17. Note that the phase of HDAp has a wide range of levels of hydroxyl deficiency. One may attempt to deduce the dimension of the apatite crystallites from the spin diffusion data. However, it is not easy to take into account the effect of 1H−31P dipole−dipole interaction, which is relatively strong in ACP, on the spin diffusion rate. In any case, the faster spin diffusion rate for ACP/HDAp indicates that such effect would not affect our major conclusion, that is, HAp constitutes the core of an apatite crystallite. The most intriguing aspect of our model is that the core of each apatite crystallite consists of HAp. During the dentinogenesis, the highly phosphorylated protein, dentin phosphoprotein, would induce the precipitation of calcium phosphate in the organic matrix to trigger the mineralization of dentin at the mineralization front. 215 The mechanism of the initiation of biological mineralization has been under debate for many years. 216 The major dispute is whether a non-apatitic phase such as ACP is the nucleating phase for in vivo biological apatite, or the biomineralization process proceeds via poorly crystalline apatitic mineral. Although the NMR data cannot directly address the issue concerning the role of ACP in the incipient formation of the apatitic phase, the results are indeed consistent with the scenario that ACP provides the nucleation sites for the formation of non-stoichiometric apatite crystallites (HDAp), which may then slowly transform to HAp as driven by thermodynamics.

Figure 17. Structural model of rat dentin based on the 31P solid-state NMR measurements. (Reprinted with permission from Ref. 33. © 2009 American Chemical Society.)

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Mechanical stability of resin–dentine bonds

D. PASHLEY , F. TAY , in Dental Biomaterials, 2008

5.2.4 Source of water for water trees

Three types of fluid movement may occur through the dentine: evaporative, osmotic and convective water fluxes. Convective water fluxes are considerably reduced when smear layers and smear plugs remain intact (such as during the application of mild self-etch adhesives), when vital acid-etched dentine is treated with glutaraldehyde-containing desensitizers to coagulate the plasma proteins in dentinal fluid (Schüpbach et al., 1997), or when acid-etched dentine is treated with potassium oxalate salts to block the subsurface dentinal tubular orifices with calcium oxalate crystals (Pashley et al., 2001; Pereira et al., 2005). However, evaporative water flux may be induced by air blasts (Goodis et al., 1990), such as those that occur during air-drying of a dentine adhesive. The presence of the smear layer and smear plugs offers little resistance to evaporative water loss. Dehydrating dentine with an air blast or with absorbent paper will generate capillary forces that induce rapid outward fluid movement from dentinal tubules (Matthews et al., 1993). Similarly, the application of a porous water-based restorative material such as glass-ionomer cement does not completely eliminate evaporative water flux (Sidhu et al., 2004). Because non-vital dentine also contains water, evaporative water flux may occur irrespective of the tooth's vitality status, even when smear plugs are retained within the dentinal tubules. Although it is mandatory to remove adhesive solvents and water (Yiu et al., 2005) from solvated adhesives before light-curing, the same air-drying process induces outward evaporative water flux from the smear-layer-covered dentine (Hashimoto et al., 2004a). The high concentrations of water-soluble ionic monomers in the presence of water may also induce osmotic water flux from deep dentine if the osmolatities of these comonomers exceed the osmolality of dentinal fluid (Pashley et al., 1992, 1996). The high solute concentrations in dentine adhesives as compared with the solute concentrations in dentinal fluid mean that the water concentration of dental adhesives is much lower than the water concentration in dentinal fluid, thus causing osmotic fluid movement from dentinal fluid into these concentrated comonomer films. When the monomers are converted to polymers the osmotically induced water flux should cease.

Both evaporative and osmotic fluxes may result in the permeation of water along regions within the adhesive where interchain segmental mobility is increased by hydrogen bonding of retained bound water with functional groups in polymers capable of hydrogen bonding. This provides a logical explanation for the predilection of water trees to be oriented perpendicular to the surface of the dentine. In particular, such a theory also accounts for the observation that in the presence of smear plugs or mildly sclerotic dentine (Fig. 5.12(a)), silver-containing tracks are observed around the peritubular dentine (i.e. the channels with the least resistance) that are continuous with silver-containing interfibrillar spaces in hybrid layers formed by mild self-etching primers. These nanoleakage tracks, in turn, are continuous with the vertically oriented water trees along the surface of the hybrid layers.

5.12. a Transmission electron micrograph of water-filled channels (now filled with silver); pointer followed by open arrowhead between a sclerotic dentine tubule (arrow) and peritubular dentine, that are continuous with silver-containing interfibrillar spaces in hybrid layers and with water trees (open arrow) extending into the adhesive layer in primary dentine; b Nanoleakage and water trees were absent from resin bonds made to caries-affected dentine (CD) because the tubules were heavily occluded with fine mineral crystals (open arrow). Note the extensive uptake of silver (pointer) into the caries-affected dentine beneath the hybrid layer (H). This is due to the high water content of caries-affected dentine, which has lost about half of its mineral phase and this phase has been replaced by water. (A, adhesive; C, composite.)

The support for the 'water flux' theory of nanoleakage and water-tree formation in simplified self-etch adhesives is based on work using these adhesives for bonding to caries-affected dentine. When resin bonding is performed on sound dentine with open dentinal tubules, it is difficult to determine whether the entrapped water that causes the formation of nanoleakage and water trees originates from water-containing self-etch adhesives (the 'remnant water theory'; Tay et al., 2004b) or from the hydrated dentine. In order to differentiate residual water from permeating water, we selected impermeable dentine as a bonding substrate. Caries-affected dentine is heavily occluded with intratubular mineral deposits (Ogawa et al., 1983; Silva et al., 2006). Tubular occlusion accounts for the relative water impermeability of this type of bonding substrate (Tagami et al., 1992). When convective and evaporative water fluxes are eliminated by bonding to transparent carious dentine (Lee et al., 2003), any water entrapment within the adhesive should be attributed to the retention of water derived from one-step self-etch adhesives. Surprisingly, despite the presence of heavy silver deposits in the subsurface porous caries-affected dentine, both nanoleakage and water trees that were seen in bonded sound primary dentine (Fig. 5.12a) were completely absent in primary caries-affected dentine (Fig. 5.12b). This demonstrates that the source of the water in water trees is water from dentinal tubules, not residual water from the self-etching adhesive.

The absence of interfacial nanoleakage following the use of self-etch adhesives in transparent carious dentine provides reassurance of the validity of the concept of simultaneous etching and priming in self-etch adhesives. Although tubular occlusion by mineral crystals prevents water-treeing and nanoleakage in one-step self-etch adhesives, it is unrealistic clinically to assume that one can bond only to transparent carious dentine without involving surrounding sound dentine. Unlike the use of etch-and-rinse adhesives in which the dentinal tubules can first be occluded with mineral deposits such as calcium oxalate before bonding (Pashley et al., 2001; Yiu et al., 2006a), such a protocol is not applicable to the application of one-step self-etch adhesives. At least from an in vitro aspect, improvements in bond strength and reductions in nanoleakage and water-tree formation may be achieved when multiple coats of one-step self-etch adhesives are used on sound dentine, instead of the limited number of coats that are recommended by manufacturers (Ito et al., 2005a). Such a technique, however, cannot reduce subsequent water sorption by these adhesives, as they are by nature highly hydrophilic. Alternatively, one-step self-etch adhesives can be rendered less permeable by treating the one-step self-etch adhesive as a primer and covering it with a less hydrophilic resin coating such as those that are employed in conventional etch-and-rinse adhesives. This extra step converts one-step into two-step self-etch adhesives (Brackett et al., 2005; King et al., 2005; Van Landuyt et al., 2006) and renders them less permeable to water movement.

The susceptibility of highly hydrophilic adhesives to water sorption, and the existence of potential water channels that expedited water sorption when simplified versions of these adhesives are bonded to dentine, were demonstrated when Class II resin composite restorations were challenged under functional stresses (Frankenberger et al., 2005). Although high percentages of gap-free margins were initially identified in enamel for all the four classes of adhesives before in vitro thermomechanical loading, etch-and-rinse adhesives exhibited significantly higher percentages of gap-free margins (approximately 90%) when compared with two-step self-etch adhesives (approximately 75%) and one-step self-etch adhesives (approximately 55%), after thermomechanical cycling. For dentine, 89–100% gap-free margins were initially observed for all adhesives. After thermomechanical cycling, there were no statistical differences among etch-and-rinse (62–70%) and two-step self-etch (62–63%) adhesives. However, the one-step self-etch adhesives exhibited significantly fewer gap-free margins (15–40%).

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Nanomechanical Characterization of Mineralized Tissues in the Oral Cavity

Y.L. Chan , ... N.M. King , in Emerging Nanotechnologies in Dentistry, 2012

16.3.5 Microstructural Influence

Biological tissues are a challenging class of materials for mechanical characterization since they have hierarchical structures with important features down to the nanometer or micrometer scale. To fulfill the load bearing function of mineralized tissues, their mechanical properties often vary gradually across the entire tissue, as in the dentin–enamel junction, such that the resulting stress distribution is less likely to cause failure than in a situation with a sharp interface. Such localized variations in mechanical properties of mineralized tissues were attributed to the tissues' microstructural variation such as mineral density, collagen arrangement, and protein content [35–38] . There are also some small structures distributed throughout the volume of the tissues to modify the function of the material and they may create marked differences in the mechanical properties within the matrix tissue, as in the case of the highly mineralized peritubular dentin located within the intertubular dentin. The measurements made with nanoindentation often have a large scatter in the values as a result of the microstructure.

To elucidate the nanoscale differences across the microstructures, extremely precise control over the location of indentation is required, and this can be done in certain commercial nanoindenters which allow nanoindentation to be performed on the same platform as atomic force microscopy (AFM). Typically, this involves operating the nanoindenter tip as a (very blunt) AFM tip when in the microscopy mode. Such a combination was used to identify the thin prism sheaths sandwiched amidst the prisms, and the measured elastic modulus and hardness values demonstrated a transition across these two neighboring regions in enamel [38].

Despite the fact that most nanoindentation can be conducted at penetration depths of 100   nm, the horizontal dimensions are actually much larger at approximately 1   μm due to the large face angle of the Berkovich tip. In cases where the sizes of the microstructures are smaller than such a resolution limit of the nanoindenter, a commercial AFM can be operated as a nanoindenter to produce much smaller indents. The process for AFM indentation is shown schematically in Figure 16.6.

Figure 16.6. Illustration of the photodiode signal–cantilever deflection curve obtained from an AFM indentation.

To calculate the elastic modulus from the AFM data, the tip–sample interaction and the deflection of the cantilever of the AFM tip are treated as two elastic springs in series in the early stage of the indentation, during which the contact between the tip and surface is treated as purely elastic [39]. The ratio K between the specimen height and the diode-electric signal, which measures the AFM cantilever's deflection, can be obtained, and the reduced modulus E r can be calculated as

(16.14) E r = α K / A - 1

Prior to indentation on the material of interest, the same cantilever tip has to indent on two reference samples each with a known elastic modulus, in order to solve for the cantilever sensitivity, A, and the cantilever-tip constant, α [39]. If the sample's deformation is viscoelastic instead of purely elastic, Eq. (16.14) would not be applicable, but it was shown that in this case, E r can be measured by a load schedule involving a rate jump, such as the connection between loading and unloading in Figure 16.6 [40]. E r would still be given by an equation of the same form as Eq. (16.14), albeit that K is now the ratio between the change in the sample's velocity across the jump, and the change in the rate of the photodiode signal across the jump. It is noteworthy that a critical requirement for AFM indentation is that the deformation at the tip–sample contact is significant compared with the deflection of the AFM cantilever. The ratio α/E r in Eq. (16.14) in fact measures the tip–sample deformation compared to the cantilever's deflection, and this provides a useful guideline for the choice of the cantilever-tip property, α [39]. In addition, a further requirement is that E sampleE tip so that an appreciable amount of the deformation at the tip–sample contact is due to the material of interest, rather than due to the tip. For commercially available silicon tips, their elastic modulus is ~169   GPa [41] which may not satisfy the above requirement if they are to indent enamel which may have E as high as 115   GPa [42]. In this case, other available options include tips made of Si3N4 which has an elastic modulus >200   GPa [43].

Enamel, dentin, cementum, and bone are anisotropic materials. The loading direction with respect to the microstructures in the tissues, therefore, has an effect on the measured properties. For most cases, the orientation of the microstructure with respect to the indentation surface is already determined during the initial sectioning process. Full understanding of the deformation behavior of the oral tissues requires independent characterization of the elastic properties along the different axes. However, as the stress field under a Berkovich tip is multiaxial, the deformation response elicited would represent some kind of unknown average over different directions. A two-step technique could be used for characterizing the mechanical properties of anisotropic materials using nanoindenters. The elastic constants, c ijkl , of the biological tissue in question are first characterized by ultrasonic means. An effective indentation modulus can then be calculated from the nanoindentation-derived data using the c ijkl [44]. A relatively easier, and more direct, method for investigating anisotropic effects in mineralized tissues involves making and testing specimen volumes of small (e.g., micron) dimensions and of known orientations. One method for producing such samples is focused ion beam (FIB) milling. Using this technique, micron-sized cantilevers which can be orientated in any desired direction can be produced as shown schematically in Figure 16.7 [23].

Figure 16.7. Milling scheme for the micro-cantilevers: (A) A 3   μm×7   μm trench is first milled, (B) sample is tilted to 45° with respect to the gallium ion beam and a 3   μm×12   μm trench is milled, and (C) a 180° rotation with respect to the specimen normal is made and a 3   μm×12   μm trench is milled. (D) The final product is a cantilever with a triangular cross section.

The free ends of these micro-cantilevers are loaded by the tip of a nanoindenter until the cantilevers fail. From the load–displacement data, E can be calculated as

(16.15) E = S L 3 3 I

where L is the length between the loading point and the fixed end of the cantilever, I=wd 3/36 is the second moment of area of the cantilever's triangular cross section, w is the width of the cantilever, d is the height of the cantilever's triangular cross section, and S is the slope of load–deflection curve. This technique also enables the localized flexural strength, σ cant, to be evaluated as

(16.16) σ cant = P L d 3 I

where P is the load at fracture.

Due to their microstructure, the mechanical properties of both enamel and bone exhibit depth dependency when they are indented.

Figure 16.8 shows the typical nanoindentation results obtained from human enamel. Both the hardness and elastic modulus decrease as the indentation depth increases, and their values begin to plateau only after the indent size exceeds that of the prism underneath the indenter tip. This phenomenon is attributed to the continuously changing microstructure as probed by the indenter tip as it penetrates deeper into the enamel. Upon its initial contact with the specimen surface, the indenter tip only interacts with the prism immediately under it. However, as the penetration goes deeper, the indenter begins to interact with the adjacent prism sheaths and prisms, and the measured mechanical properties then reflect the total contribution of both the prisms and prism sheaths [45]. Despite the fact that both bone and dentin are similar in composition, their deformation behaviors differ slightly at the nanoscale. Theoretically, in these multicomponent materials, there should be a certain length scale under which the constituents of the biological tissue no longer function together as a composite, but instead, would behave as individual elements. Under this length scale, the scatter of the recorded data obtained from repeated measurements on random sites would begin to increase drastically due to the large difference in mechanical properties among the constituents. In bone, this value has been estimated to be approximately 600   nm while, in dentin, this value was found to be in the region of 100   nm [46]. The arrangement of the constituent materials is therefore decisive to the mechanical properties of the oral mineralized tissues.

Figure 16.8. Human enamel elastic modulus E and hardness H data plotted as a function of the maximum indentation depth h max.

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