Letter pubs.acs.org/NanoLett
Compressive Residual Strains in Mineral Nanoparticles as a Possible Origin of Enhanced Crack Resistance in Human Tooth Dentin Jean-Baptiste Forien,† Claudia Fleck,‡ Peter Cloetens,§ Georg Duda,† Peter Fratzl,⊥ Emil Zolotoyabko,¶ and Paul Zaslansky*,† †
Julius Wolff Institute, Charité−Universitätsmedizin, 13353 Berlin, Germany Materials Engineering, Berlin Institute of Technology, 10623 Berlin, Germany § European Synchrotron Radiation Facility, 38043 Grenoble, France ⊥ Department of Biomaterials, Max-Planck-Institute of Colloids and Interfaces, 14424 Potsdam, Germany ¶ Department of Materials Science and Engineering, Technion−Israel Institute of Technology, 32000 Haifa, Israel ‡
S Supporting Information *
ABSTRACT: The tough bulk of dentin in teeth supports enamel, creating cutting and grinding biostructures with superior failure resistance that is not fully understood. Synchrotron-based diffraction methods, utilizing micro- and nanofocused X-ray beams, reveal that the nm-sized mineral particles aligned with collagen are precompressed and that the residual strains vanish upon mild annealing. We show the link between the mineral nanoparticles and known damage propagation trajectories in dentin, suggesting a previously overlooked compression-mediated toughening mechanism.
KEYWORDS: X-ray diffraction, apatite, residual strain, mineralized-collagen-fibers, diffraction nanotomography
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Tooth dentin is thus a compound bionano-composite, and it is fascinating because it is a bone-like tissue that lacks remodeling/regeneration capacity. Consequently, accumulated damage is not removed biologically as is the case in bones, yet dentin structures exhibit remarkable life-long endurance even without healing. Dentin must therefore be exceptionally welldesigned, possessing damage tolerance and ample toughness. A variety of mechanisms jointly contribute to fracture toughness8 and crack-growth resistance9 in dentin. For example, uncracked ligament bridging shows discontinuous segments of cracks, separated by unbroken tissue that reduces stress concentration at the crack tip, slowing down crack propagation. At smaller length scales, microcracks create energy-consuming damage-resisting zones.10 Fracture toughness further increases with fiber pull-out and local deflections of crack paths, for example, at ITD/PTD interfaces. Overall, similar to other bone-like tissues, dentinal toughening mechanisms largely depend on structural inhomogeneity and anisotropy. Fracture toughness is significantly higher along dental-tubule trajectories and orthogonal to the fiber layers, a design that hinders damage from advancing toward the pulp. Cracks thus propagate more easily sideways across tubules because such cracks advance between the layers of mineralized collagen fibrils. In this orientation, a lower fracture toughness KIC ≈ 1.8 MPa m1/2 was reported,11 while in the orthogonal
ermanent human teeth, once fully erupted, serve for entire lifetimes despite repeated exposure to stresses during mastication. Teeth endure largely due to the impressive fracture toughness of dentin, a bone-like material1 that forms the bulk of the crown and roots. Unlike bone, dentin does not remodel nor does it heal as other tissues do. Dentin contains no living cells, only cell extensions that are confined to characteristic channels, so-called dental tubules, (Figure 1) which perforate the entire structure. The tubules radiate outward from the pulp, encasing the cellular outgrowths that extend from the sensitive dentalpulp odontoblast cells. Many tubules in dentin, especially in the crown, are lined by a 1−2 μm thick mineral sheath (peritubular dentin, PTD) devoid of collagen protein.2 The mineral tablets in PTD have no overall preferred orientations,3 although some local order is observed when examined with electron or X-ray beams at the nanometer length-scale.3,4 The matrix surrounding tubules and encasing the pulp is a fibrous mass of intertubular dentin (ITD). A typical fracture surface of ITD (Figure 1a) reveals mineralized collagen fibers5 arranged in layers oriented predominantly orthogonal to the tubules6 (Figure 1b). Like all biological nanocomposites of the bone family of materials,7 dentin comprises ∼48 vol % dahllite mineral, a carbonate-rich hydroxyapatite in the form of tablet-shaped nanoparticles, which in this work we refer to simply as “apatite”. An additional 20 vol % of dentin is occupied by water, whereas the rest are proteins, mainly collagen fibers randomly oriented within incremental growth layers in the ITD. Many of the mineral particles are embedded in these collagen fibers with a preferred orientation of the crystal c-axes along the collagen fiber axis. © XXXX American Chemical Society
Received: January 13, 2015 Revised: April 28, 2015
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DOI: 10.1021/acs.nanolett.5b00143 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Typical human dentin microstructure: (a) scanning electron micrograph taken from a fractured root surface; mineralized collagen fibers (∗) form a matrix in which tubules (black arrow) are located; scale bar = 2 μm; (b) schematic illustration of idealized dentin microstructure, in which tubules (yellow hollow cylinders, marked with rrows), radiating outward from the pulp (not shown), are surrounded by layers of mineralized collagen fibers (brown rods, ∗), oriented mostly orthogonally to the tubule axis. PTD mineral surrounding the tubules has no overall preferred crystallographic orientation,3 whereas the apatite c-axis of mineral crystallites associated with the fibers is aligned with the fiber axis.
Figure 2. X-ray diffraction nanotomography reveals the spatial separation of apatite orientations with respect to the axis of dental tubules: (a) schematic illustration of a sample with longitudinally oriented tubules mounted on edge, parallel to the azimuthal rotation axis, ω. The tubules, marked by the green arrows and depicted in yellow/white, run along the sample longitudinal axis. Diffraction patterns of the mineral (002) reflection were collected by scanning lines across the rotated sample on the gray marked plane. (b, c) Reconstructed nanotomography slices showing the spatial distribution of diffraction intensities “in plane” and “out of plane” (see plane in panel a). The in-plane integrated diffraction signal shown in panel b arises from apatite crystals predominantly oriented with their c-axes aligned with the collagen fibrils layers. A rather homogeneous distribution of diffraction intensities corresponds to the overall felt-like pattern of ITD. The spatial distribution of the integrated diffraction signal of apatite crystals, with the c-axes oriented out of the plane of the collagen fibrils layers (c), exhibits high brightness spots (green arrows). The size and spacing of these spots suggest that they correspond to PTD surrounding tubules that are observed in cross-section. Scale bar = 50 μm.
orientation parallel to the tubules, values as high as KIC ≈ 3.4 MPa m1/2 were found.12,13 A similar relationship to structure is known for the fatigue behavior of dentin14 where the endurance strength is only 24 MPa in orientations across the tubules, as compared with 44 MPa reported for orientations along the tubules. Though it is difficult to associate specific dentin microstructures to the toughness contributions that they entail,8 collagen fiber-orientations appear to be particularly important for the overall tissue strength and damage resistance. To shed additional light on the link between the microarchitecture of dentin and its remarkable longevity and resistance to damage propagation, we studied the material properties of the embedded mineral nanoparticles. We measured the c-lattice parameters of apatite in differently treated human-tooth dentin samples by using focused X-ray beams at synchrotron beamlines (BESSY II, Helmholtz-
Zentrum-Berlin, Germany, and ESRF, Grenoble, France). We found apatite crystallites to be compressed along the c-axis; the compression was significantly larger in crystallites aligned with collagen, as compared to those having the c-axis in other orientations. Mineral compression impedes crack propagation across the fibers, and stops cracks from running between the tubules, because excessive tensile stress is needed to allow such crack opening/propagation. We thus propose that a previously unidentified toughness mechanism exists in dentin, directly arising from the nanocomposite ultrastructure of ITD, a mechanism that probably exists in other collagen-based members of the bone family of materials.7 By means of X-ray diffraction nanotomography15,16 (see Supporting Information), we studied the spatial arrangement and orientation of apatite crystallites in human root dentin (Figure 2a, Figure S2) where collagen fibrils in the ITD17 have B
DOI: 10.1021/acs.nanolett.5b00143 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters well-known orientations, predominantly orthogonal to the tubules. We observe a clear spatial separation between crystal orientations in the ITD and in the PTD, known to have no preferred orientation of the mineral.3 Complementary crosssectional diffraction-tomography (Figure 2a) reconstructed slices reveal dissimilar spatial distributions of the diffraction intensities when integrating counts either across (Figure 2b) or along (Figure 2c) tubule trajectories. For comparison, Figure S3 shows the same tubules as visualized by phase contrastenhanced nanotomography. The reconstructed (002) diffraction intensities across the tubules (Figure 2b) are relatively homogeneous, mainly revealing intensity contributions from mineral in the uniform in-plane fibers of the ITD matrix surrounding the tubules. In contrast, diffracted intensities from apatite crystallites with the c-axes oriented parallel to the tubules, that is, orthogonal to the ITD collagen layers, reveal dispersed white spots, manifesting higher local intensities. The periodic appearance of these spots in the cross-section suggests that their source is the PTD (Figure 2c), where the average random apatite orientation differs from those in the collagen fiber layers.3 Thus, the different groups of crystallites in ITD and PTD are distinguishable, and it is therefore possible to differentiate between them when mapping (002) diffraction intensities. We determined the c-lattice parameters of apatite in human tooth dentin when analyzing diffraction patterns taken from specimens with well visible tubules (Figure 3a,b) and consequently for which the collagen fiber orientation was known.17 Furthermore, we measured the azimuthal variations of the (002) Debye-ring radii (Figure 3c). Six samples were mapped in both hydrated and air-dried states. For comparison, additional samples, annealed at 220 °C for ∼1 h (Figure S2 shows typical temperature ramping), were also measured. We compared the c-lattice parameter in crystallites residing on the collagen−fibril axis with those in other orientations. The crystals attached to collagen in dentin have the c-axis along the collagen fibers,5 and we term them “on-axis” (highlighted in orange, Figures 2b and 3c). Crystallites having the c-axis in other orientations are termed “off-axis” (highlighted in green, Figures 2c and 3c). In hydrated (subscript h) samples, we find a substantial negative difference, Δch = con − coff = −0.0054 ± 0.0016 Å (mean ± standard deviation), between the “on-axis” (con) and “off-axis” (coff) lattice parameters extracted from the very same diffraction patterns. In the same samples, air-dried (subscript d), this difference is smaller, Δcd = −0.0028 ± 0.0018 Å, and the difference tends to zero, Δc = 0.0002 ± 0.0008 Å, in samples annealed at 220 °C. Transforming these data into a relative lattice parameter difference, δ, con − coff δ= (con + coff )/2 (1) we find that in the untreated hydrated samples, “on-axis” mineral crystallites are compressed along their c-axis by δh ≈ −0.08%, as compared with “off-axis” crystallites. After airdrying, which reduces the water content of dentin (by exposure to ambient 33−35 RH%), this relative lattice parameter difference drops to δd ≈ −0.04%. Upon annealing at 220 °C, which destroys the organic molecules, the difference δ vanishes (Figure 4a). By using published estimates for the elastic modulus of apatite E = 114 GPa,18 we convert the native relative difference, δh, into compressive stress of σh = E δh ≈ 90 MPa. Interestingly, this value is well above typical mastication stresses, which do
Figure 3. Schematic illustration of X-ray diffraction measurements and their analysis: (a) spatially resolved nonoverlapping diffraction patterns were collected when scanning across and along dentin samples in the x- and z-directions using slender X-ray beams. (b) The tubule silhouettes, visible by optical microscopy, run in parallel (the approximate orientation indicated by the green arrow) and serve to identify the predominant orientation of the collagen fibers (orange C
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not affected by variations in the absolute values of the apatite lattice parameters, known to have a considerable spread in teeth22 due to local variations in chemical composition.23,24 The in situ measurements reveal relative changes of the c-lattice parameter in the same areas of each sample before and after annealing. Typically, heating carbonated hydroxyapatite results in a decrease of the c-lattice parameter due to the discharge of gaseous products.23 However, this occurs only at temperatures that are much higher than those that we used, and it causes an opposite effect on the c-lattice parameter compared to what we observe in dentin, namely further lattice shrinkage. Interestingly, from the difference between the strain values in air-dried samples in both experiments (Figure 4a,b), we deduce that the “off-axis” mineral in air-dried dentin is also compressed by about 0.1% compared to the annealed state. Our experimental findings allow us to draw two important conclusions: (1) “on-axis” mineral crystals, associated with collagen, are under compressive stress as a result of strong mineral/collagen interactions; (2) “off-axis” mineral crystals, not directly associated with collagen, experience far less stress. We suggest that compressive stresses arise at early stages of biomineral formation, when mineral particles take the place of water.25 When water is expelled from the system (for example following drying), collagen fibrils experience contraction,26 which is transferred to the tightly attached apatite particles. Correspondingly, we expect that collagen in dentin experiences tensile residual strain/stress, as indirectly predicted by other studies.27 We are not able to directly verify this claim since collagen does not sustain heating at 250 °C, and it significantly changes its dimensions due to dehydration and denaturation. However, we found corroborative evidence supporting the notion that tensile stresses exist in dentin collagen fibrils, even under unloaded conditions.27 We compared collagen diffraction patterns taken at room temperature and at 125 °C (Figure S4), considering that collagen fibrils still remain essentially undamaged at this temperature.21 Examination of the Debye rings showed that the lateral spacing between collagen fibrils in the collagen fiber bundles decreases from 11.43 ± 0.06 Å at room temperature down to 10.38 ± 0.19 Å at 125 °C. A similar lateral shrinkage was previously reported in dentin21 and for other sources of collagen.25 It is known that shrinkage in the lateral direction is accompanied by the respective contraction of the collagen molecules along the fibrils, though an order of
Figure 3. continued arrow), most of which are arranged in layers orthogonal to the tubule axes. Red dots depict approximate beam size and position on the sample. Scale bar = 100 μm. (c) In typical diffraction patterns, the apatite (002) peak intensities and positions vary due to preferred orientations of the crystals, many of which are orientated “on-axis”, along the collagen long axis (orange outlines). A difference in the c-axis lattice parameters can be seen, as compared with the “off-axis” crystals that are not aligned with collagen (green outlines). Variation of the peak positions (2θ) as a function of the azimuthal angle (plotted beneath the diffraction pattern) reveals a different strain state of apatite crystals aligned with the collagen fibrils (orange) as compared with other orientations, for example, along the tubules (green).
not normally exceed 40 MPa.19 Thus, normal “working conditions” of teeth do not usually exceed the in-built residual stress of mineral in dentin suggesting that teeth have an in-built “safety margin” of stress. For damage to propagate through dentin, tensile loads exceeding this value are needed. This suggests that generally this tissue is not overloaded during food processing and therefore should not break under “normal” conditions of use. To verify the overall compressive state of the “on-axis” dentin crystallites, we performed in situ annealing-diffraction experiments with air-dried samples. Diffraction patterns were collected from several root−dentin samples initially at room temperature, then in situ heated to 125 and 250 °C, followed by postannealing room-temperature measurements. We used a thin gold coating as a calibration standard to correct for subtle but significant variations in the sample−detector distance incurred due to thermal expansion (Supporting Information). The “on-axis” c-lattice parameters calculated from the (002) Debye-ring radii were corrected by accounting for apatite thermal expansion20 (α) at each measured temperature (αapatite = 10.6 × 10−6/°C). Mean relative differences in the “on-axis” clattice parameters Δc/c of three investigated samples, measured in the original and in situ heated states and compared to their postannealing room temperature values, are plotted in Figure 4, panel b. We find that prior to annealing, the “on-axis” (collagen-associated) mineral is under compressive strain, ϵ1 = Δc/c = −0.15%, and it endures mild annealing at 125 °C. Indeed, collagen in dentin is known to remain stable at these temperatures.21 The “on-axis” strain drops to zero (ϵ3 = 0) upon annealing at 250 °C, as soon as the collagen molecules are destroyed. We note that strains determined in this manner are
Figure 4. Relative differences (δ) and “on-axis” strain in c-lattice parameters obtained in two types of experiments: (a) comparing diffraction signals within the same Debye ring in each diffraction pattern, collected from “on-axis” and “off-axis” apatite crystallites with respect to the collagen fibrils; relative difference (δ) for hydrated and dried samples were obtained by averaging over six specimens, while data for annealed samples were found by averaging over four specimens; (b) comparing only “on-axis” c-lattice parameters in the same samples measured in situ at different temperatures with the postannealed state; experimental points are obtained by averaging over three specimens; error bars represent standard deviations. D
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mineralized collagen fibers in dentin presumably exist also in bone (see, for example, ref 31) and must serve to enhance strength and fracture toughness at the most fundamental structural length-scale. We propose that this route is used in nature in addition to well-known toughening recipes such as hierarchical architectural designs on different length-scales37 or periodic arrangements of stiff and compliant layers.38
magnitude smaller, as observed in tendon samples under controlled drying.26 Thus, collagen fibers in hydrated dentin are elongated as compared with fibers subjected to annealing at 125 °C, and a significant part of this elongation is due to the presence of water. Other studies report lower dentin strength following heat-treatments exceeding 150 °C21 presumably due to a decoupling between the organic phase and mineral and are related to the removal of the tightly bound water layer.28 The strong collagen/mineral interactions in native tooth dentin and forces acting across the collagen/mineral interfaces require that collagen fibrils experience tensile stress to balance the mineral compressive state. Collagen fibrils in dentin thus act as tensed strings resisting buckling during mastication, while the apatite mineral particles serve as compressed fillers that stiffen the fibers. Tensed mineralized fibrils entail stiffness to dentin, supporting the tubular microstructure against collapse under externally applied bending or compressive loads (Figure S5). At the same time, the mineral phase, which is typically brittle in tension, is protected against tensile loads due to its compressive residual-stress state. This structural nanocomposite design thus hinders crack propagation, preferentially in directions orthogonal to the mineralized collagen fibril layers, and results in a tougher tooth structure, specifically along tubules, that is, in the general direction of the pulp, which has great evolutionary advantages for the survival of teeth. Various man-made engineered structures, exhibiting improved strength and endurance, benefit from incorporating residual compressive strains/stresses; tempered glass, reinforced concrete, and gear wheels are well-known examples. Typically, compression stresses are intentionally induced beneath outer surfaces aimed at preventing crack formation and propagation into the component interior.29 In dentin, we find mineral compression widely distributed as a damageprevention mechanism within the collagen-fiber nanostructures, which offers protection against crack initiation due to mastication loads. The notion that compressive forces imposed on the mineral cause tensile forces in collagen implies that the magnitude of the compressive residual stress in the mineral will strongly depend on the mineral/collagen ratio. Thus, regions in teeth with lower mineral content (e.g., the root) will exhibit different residual stress and strain than regions with higher mineral content (e.g., the crown). Incorporating compressive strains into apatite-based biocomposites is yet another remarkable achievement of evolution. We note that there are several reports documenting residual strains/stresses in the apatite mineral in various bone-like tissues (see, for example, refs 27, 30, and 31) although no link to the microstructure was ever shown. The use of residual strains in apatite nanocrystals may thus be an additional structural adaptation that maximizes damage-resistant performance while balancing material overdesign considerations with the strength, stiffness, and toughness needed for teeth to function mechanically for many years. Anisotropic lattice distortions in biogenic crystals produced by organisms are common in nature, aragonitic and calcitic mollusk shells being the best known examples.32,33 These lattice distortions arise due to the strong interaction between intercrystalline organics and the carbonate minerals;34 they are completely removed after annealing at 200−250 °C, which destroys the organic matrix. However, in the case of calcium carbonate, strains are tensile, most likely as side effects of calcium carbonate crystallization35 via amorphous precursor phases.36 The compressive strains/stresses that we identify in apatite within
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information section contains detailed descriptions of the materials and methods used. These include sample preparation steps, diffraction nanotomography, diffraction mapping and in situ annealing procedures and phasecontrast enhanced nanotomography imaging of tubules in dentin. Additionally, details of the data analysis procedures are presented, together with results of collagen small angle scattering. A schematic representation of typical bending forces and stresses acting on teeth is also shown. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b00143.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +49 30 450 55 95 89. Fax: +49 30 450 55 99 69. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge Stefan Siegel, Chenghao Li, and Rémi Tucoulou for their technical support at the beamlines. The Helmholtz-Zentrum Berlin (Bessy II) and the ESRF are gratefully acknowledged for beamtime allocation. P.Z., C.F., and J-B.F. acknowledge funding by the DFG through SPP1420. E.Z. thanks Shore Research Fund in Advanced Composites (Technion) for partial financial support.
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REFERENCES
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