peter fratzl lecture notes

Biological Materials with Hierarchical Structure and Mechanical Function

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Reading Material

Peter Fratzl

Max Planck Institute of Colloids and Interfaces Research Campus Golm

14424 Potsdam, Germany

E-mail: [email protected]

Three documents are included in this file: 1. HIERARCHICAL STRUCTURE AND MECHANICAL ADAPTATION OF BIOLOGICAL

MATERIALS P. Fratzl, Lecture notes NATO-Advanced Study Institute on “Learning from Nature how to design new implantable biomaterials”, editors: R.L. Reis and S. Weiner, Kluwer Academic Publishers, 15 - 34 (2004)

2. SKELETON OF EUPLECTELLA SP.: STRUCTURAL HIERARCHY FROM THE NANOSCALE TO THE MACROSCALE Joanna Aizenberg, James C. Weaver, Monica S. Thanawala, Vikram C. Sundar, Daniel E. Morse, Peter Fratzl, Science 309, 275 - 278 (2005)

3. NANOSCALE MECHANISMS OF BONE DEFORMATION AND FRACTURE Peter Fratzl and Himadri S. Gupta, Handbook of Biomineralization Vol.1, Chapter 25 (E. Bäuerlein, editor), to be published in 2007.

Knowledge Based Materials Summer School, 13-23 August 2006, Älvdalen, SwedenLecture Notes - Peter Fratzl

„Learning from Nature How to Design New Implantable Biomaterials: from Biomineralisation Fundamentals to Biomimetic Materials and Processing Routes“ NATO/ASI Series (Ed. R.L. Reis & S. Weiner)

HIERARCHICAL STRUCTURE AND MECHANICAL ADAPTATION OF BIOLOGICAL MATERIALS

PETER FRATZL Max-Planck-Institute of Colloids and Interfaces Department of Biomaterials Science Park Golm, 14424 Potsdam, Germany E-mail: [email protected]

1 Introduction

Biological tissues such as wood, bone or tooth are hierarchically structured to provide maximum strength with a minimum of material. Many of these materials are cellular solids (e.g., cancellous bone or wood) or gradient materials (e.g., dentin). At the lowest level of hierarchy (that is, in the nanometer range), they are usually fibre composites. Due to this hierarchical structure, there is a variety of different possible designs by changing the arrangement of the components at different size levels. In the case of bone, for example, the variability at the nanometer level is in the shape and size of mineral particles, at the micron level in the arrangement of mineralised collagen fibres into lamellar structures and beyond in the inner architecture, the porosity and the shape of the bone. The mechanical properties of bone are well known to depend strongly on all these parameters [1, 2]. A selection of textbooks on the relation between form, hierarchical structure and mechanical properties is given in the references [2-7]. Moreover, on may refer to a number a recent review articles addressing the problem in general [8-12], and treating wood [13-15] or bone [1, 16-20], in particular.

The hierarchical structure requires special methods of investigation, since the scales at the nano-, micro- and millimetre level all need to be considered, as well as the interplay between the hierarchical levels. Furthermore, it is essential not just to study the structures statically but during deformation. “Seeing” the structures deform (by microscopic or diffraction methods, for instance) is the key to understand deformation mechanisms. Typically, a whole range of techniques are being used and combined in this context, two of them using x-rays (and in particular synchrotron radiation) are described in section 2. Section 3 reviews some results on bone and dentin, while section 4 focuses on wood.

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2 Studying hierarchical biological materials with (synchrotron) x-ray methods

2.1 SCANNING MICRODIFFRACTION AND SMALL-ANGLE SCATTERING

One of the difficulties in studying hierarchical structures is that many orders of magnitude need to be covered in the structural analysis. This generally implies the necessity to combine many techniques. For instance transmission electron microscopy is sensitive to structures in the range of nanometers, scanning electron microscopy reveals micron and sub-micron structures, while light microscopy may cover the larger scales. X-ray or neutron diffraction methods are mostly sensitive to the nanometer scale. A powerful approach to study hierarchical materials at different scales simultaneously is scanning x-ray diffraction [21] or scanning small-angle x-ray scattering [22]. The principle of this technique is shown in Fig. 1.

Figure1. Sketch of a scanning diffraction experiment. Structural information in the nanometer range is

obtained from the evaluation of the diffraction (or scattering) pattern. The micrometer range is covered by scanning the specimen across the narrow x-ray beam.

A thin section of the material is scanned across a narrow x-ray beam. The diameter of the x-ray beam defines the lateral resolution of the scanning procedure. It is in the order of 100 micrometer on a laboratory x-ray source [22] and in the order of 1 micrometer (or even below) at synchrotron sources [21, 23]. Ideally, the thickness of the specimen should be the same as the beam diameter, d. Then the scattering volume for each individual measurement will be about d3. Depending on the type of measurement – x-ray diffraction or small-angle scattering - the evaluation of the scattering patterns yields structural data on the nanocomposite, within each d3-volume separately.

Such local information from x-ray scattering can be advantageously combined with local information from other techniques, e.g. microspectroscopy or nanoindentation on the same specimen. The advantage of such a combination is that information about structure at a certain position of the specimen (determined, e.g., by scanning x-ray diffraction) can be correlated with the mechanical properties (determined, e.g., by nanoindentation) or with the chemical composition (determined, e.g., by light or x-ray spectroscopy) at the very same location inside the material. An

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example for this approach is discussed in sect. 3.2 for the investigation of the dentin-enamel interface [24].

2.2 IN-SITU DEFORMATION STUDIES WITH SYNCHROTRON RADIATION

In order to uncover the mechanisms of deformation of complex materials, such as those created by Nature, it is advantageous to watch structural changes occurring at the different hierarchical levels during the deformation process. This implies that the actual macroscopic deformation has to be monitored when load is applied, but also requires methods to study deformation at the lower levels simultaneously. One approach is certainly to extract important structural elements, such as individual cells [25] from the wood tissue or individual osteons (that is, a blood vessel surrounded by bone material) from compact bone [26], and study them separately. This requires skilful preparation of the specimens since wood cells or osteons are rather small objects. Moreover, the loading pattern applied to these small elements can hardly be the same as the one applied to them while they are still part of the intact tissue.

detector

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ray beamray beam

Figure 2. Sketch of an in-situ diffraction experiment (using a wood foil). Structural information on the deformation of the cell walls is obtained by x-ray diffraction (which enables to measure the cellulose

microfibril angle, see sect. 4). In this way it is possible to measure the deformation of cell walls which are still integrated in an intact wood tissue [27].

For this reason, a very promising strategy is to use in-situ x-ray diffraction (or small-angle scattering) methods which allow – in some cases – to study the deformation of smaller elements inside an intact tissue which is being deformed. The principle is that the tissue specimen is deformed inside the x-ray beam and the deformation in the elements of the tissue is monitored by the diffraction signal (see Fig. 2). This method will work in those cases where the structural elements (such as fibres, for instance) provide a diffraction signal which depends on the elongation of the fibre. Recent examples where the method has been applied successfully to biological materials are studies of the deformation mechanisms in the wood cell wall [27] (see sect. 4.3) or of the elongation of collagen fibrils within a tendon [28].

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3 Hierarchical structure of calcified tissue, such as bone and dentin

3.1 BONE TISSUE

As already mentioned, the mechanical properties of calcified tissues cannot be understood without taking into account all structure levels [17, 18]. Some anatomical features known to be important for the strength of the tissue are given on a dimensional scale in Fig. 3.

Typically, a vertebra contains a spongy interior (spongiosa) which prevents it from collapsing when loaded under compression. The struts of this spongy structure, called trabeculae, have a thickness in the order of about 200 microns. In between the trabeculae there is bone marrow. The material of which these trabeculae are made, is lamellar bone. The lamellar structure consists of parallel fibres in each layer, with some rotation of fibre direction in successive layers [18, 29, 30]. The fibres are collagen fibrils reinforced with calcium-phosphate mineral particles of only a few nanometre thickness [31-34]. The mineral is non-stoichiometric, carbonated hydroxyapatite (dahllite).

Figure 3. Hierarchical structure of the human vertebra, as an example of cancellous bone. The human vertebra is filled with a highly porous structure of spongy appearance. The trabeculae forming this cellular material are

typically 200 micrometer wide and made of a composite of collagen and calcium phosphate mineral. This composite has a lamellar structure, where each lamella consists of layers of parallel mineralised collagen

fibrils. Individual collagen fibrils have a diameter of a few hundred nanometers, while the individual reinforcing mineral particles have a thickness of only a few nanometers.

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1 mmprenataladult1 cm

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Figure 4. Evolution of the trabecular structure (top row) and the orientation of the collagen-mineral composite (bottom row) in human vertebra, from the prenatal (left) to the adult (right) state [35]. The bottom row shows a small fraction of the vertebra, with cancellous bone to the left of the corticalis (labelled Co). The white areas

in the bottom row correspond to bone, while the grey areas indicate the marrow space or the outside of the vertebra. The boxes give the age of the individual (2 months, 11 and 45 years). The direction of the bars indicates the predominant orientation of the elongated (plate-like) mineral nano-particles, measured by

scanning-SAXS (see Fig. 1). The length of the bars indicates the degree of alignment. It is evident from the length of the bars that the mineral particles in the collagen tissue are arranged in a much more organized fashion in adult than in young or prenatal bone. Moreover, the orientation inside the cortical shell also

changes with age [35].

Even though the list of hierarchical levels is certainly not complete, it is obvious that the structures are spread over at least eight orders of magnitude. Clearly, no single technology can cover such a wide range. While all structures down to about a micrometer in size are accessible to light microscopy, higher resolution can be achieved by other probes, such as scanning- or transmission-electron microscopy, x-ray diffraction (XRD) or small-angle x-ray scattering (SAXS) and, finally, by a variety of spectroscopic techniques, e.g., nuclear magnetic resonance or Fourier-transform infrared spectroscopy. One of the consequences of the hierarchical architecture is that structures at one size-level may vary systematically throughout the tissue on a larger scale.

Some examples are given in the following. Fig. 4 (top row) shows the evolution of the architecture of the spongiosa in the interior of human vertebra [36]. In the embryonal vertebra, the trabeculae are typically arranged in a concentric fashion. In the adult vertebra, on the contrary, the orientation of the trabeculae is mostly vertical and horizontal. This most likely reflects some adaptation to the predominant loading of the vertebra in compression. After birth (see picture labelled “young” in Fig. 4) the architecture changes from the prenatal to adult state. Most interestingly, the changes at the level of the trabeculae are accompanied by changes also in the arrangement of the mineral particles as shown in the bottom row of Fig. 4. The mineral particles, which are known to be parallel to the collagen fibril direction [32, 37], typically also follow the

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struts in trabecular bone. What is even more remarkable is the orientation of the mineral particles in the cortical shell of the vertebra (labelled Co): While the particles are oriented parallel to the outer surface of the vertebra in adults, they are turned 90° to this direction in embryonal vertebra (bottom row, left). The orientation of mineral particles was measured by scanning-SAXS, the technique discussed in section 2. The diameter of the x-ray beam was 0.2 mm, which also corresponded to the thickness of the bone section. The predominant orientation of the mineral particles and their degree of alignment (indicated by bars in the bottom row of Fig. 4) therefore correspond to averages within volumes of the size 0.2x0.2x0.2 mm3. Hence, a very short bar (such as in bone of very young individuals) means that – within the volume of investigation – almost all orientations occurred with similar probability.

Given the hierarchical nature of the structure, it is clear that the result of scanning-SAXS measurements depends quite crucially on the scanning resolution chosen for the measurement. Hence, it is extremely important to adapt the spatial resolution to the actual needs for a given structural element. Fig. 5 shows scanning-SAXS data, collected within compact bone, using an x-ray beam diameter of 20µm (that is, with a ten times better scanning resolution than in Fig. 4). The results are superimposed onto an image collected with backscattered electrons [21] and they clearly show the concentric lamellar arrangement around an osteon (that is, a blood vessel surrounded by bone material). With a resolution of 200µm (large dotted circle in Fig. 5), the structure could not have been revealed. Within a circle of this size around the center of the osteon, practically all particle orientations occur, and no specific orientation would remain in the average.

Ø 20µm

Ø 200µm

Ø 20µm

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Figure 5. Orientation of mineral particle around an osteon in human compact bone (from [21]). The black

ellipse in the centre is the trace of a blood vessel and there are concentric layers of bone lamellae around it, forming the osteon. Several osteons are visible on the backscattered electron image (BEI). The bars are results from scanning-SAXS, obtained at the synchrotron and superimposed on the BEI. They indicate the orientation of mineral platelets with the same convention as in Fig. 4. The specimen thickness and the diameter of the x-ray beam were 20 micrometers in this case. For comparison, a circle with the radius of 200 µm is also shown

in the figure (dotted line).

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(b)

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Figure 6. (a) Arrangement of molecules and mineral particles in the collagen fibril, according to [38]. Rotated plywood arrangement of mineralised collagen fibrils in cortical lamellar bone, according to [30]. Orientation

of mineral particles in trabeculae of human cancellous bone, according to [39].

As sketched in Fig. 3, the basic building block of bone materials is the mineralized collagen fibril. Fig. 6a shows a schematic view of the arrangement of mineral particles in fibrils, as measured by transmission electron microscopy [32, 38, 40]. The particles are very thin (in the order of a few nanometers only) and arranged parallel to the collagen molecules. Obviously, this building block is very anisotropic. Lamellar bone, such as found in osteons, for example (see Fig. 5) is a very common feature in compact bone [29, 30, 41-45]. Fig. 6b shows a proposal for the arrangement of mineralized fibrils in lamellar bone [29]. Within each lamella, the fibrils run parallel to each other, and the fibril direction is slightly rotated from one such layer to the next, in the form of a rotated plywood structure. A slightly different arrangement was found in the trabeculae of cancellous bone by position-resolved x-ray pole-figure analysis [39]: The mineral particles follow a predominant direction and the structure is, therefore, closer to a fibre texture than to a lamellar arrangement. The predominant direction of the collagen fibrils is lying within the plane of the trabeculum (see Fig. 6c). Further types of arrangement are possible within parallel fibered or plexiform bone (found, e.g., in some types of bovine bone) [41, 45, 46]. This clearly shows that the elementary building block, the mineralized collagen fibril, is used in many different ways to build higher

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hierarchical structures in bone. This is most likely related to the different mechanical functions of different bones.

3.2 GRADED STRUCTURE OF DENTIN

The structure of dentin (the bone-like body of teeth) has been studied by scanning-SAXS [24, 47] and other methods, such as electron microscopy and nanoindentation [48-50]. A gradient from the enamel towards the root was found both for the structure and for the mechanical properties [24]. Fig. 7 shows the orientation and the thickness of mineral particles in dentin as a function of position. The figure shows that the T-parameter (which is a measure of the thickness of mineral particles) increases systematically from the enamel towards the root. The same section was also investigated by nano-indentation in an atomic force microscope, providing the elastic modulus of the tissue as a function of position. Care was taken to avoid the tubuli (small hollow conducts) in dentin and their immediate surroundings which are known to be slightly overmineralized [24, 48]. The indentation modulus (of intertubular dentin) also exhibited a gradient from the enamel towards the root and was plotted in Fig. 7 against the particle thickness (as measured by the T-parameter) determined at the same position on the specimen. The excellent correlation between these two parameters is also shown in Fig. 7. This provides some insight on how the mechanical properties of mineralised tissue was tuned by the type of reinforcing mineral particles. The probable reason for the grading of properties is a better long-term stability against failure of the tooth. Indeed, cracks originating from the enamel seem to stop at the dentin-enamel junction, where the stiffness is lowest [24].

Figure7. Thickness (right) and orientation (left) of mineral particles in human dentin (from [24]). The T-parameter, which is a measure for the particle thickness, varies from 2.3 to 3.6 nanometers. The degree of alignment ρ (a parameter which is =1, if all the mineral platelets are parallel, and =0, if they are randomly

oriented) is larger further away from the enamel (top). The thickness of mineral particles correlates well with the elastic modulus measured (in position-resolved way) on the same specimen by nanoindentation [24].

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3.3 MECHANICAL BEHAVIOUR OF THE COLLAGEN MINERAL NANOCOMPOSITE IN BONE OR DENTIN

Virtually all stiff biological materials are composites with components mostly in the size-range of nanometers. In some cases (plants or insect cuticles, for example), a polymeric matrix is reinforced by stiff polymer fibres, such as cellulose or keratin. Even stiffer structures are obtained when a (fibrous) polymeric matrix is reinforced by hard particles, such as carbonated hydroxyapatite in the case of bone or dentin. The general mechanical performance of these composites is quite remarkable. In particular, they combine two properties which are usually quite contradictory, but essential for the function of these materials. Bones, for example, need to be stiff to prevent bending and buckling, but they must also be tough since they should not break catastrophically even when the load exceeds the normal range. How well these two conditions are fulfilled, becomes obvious in the (schematic) Ashby-map in Fig. 8. Proteins (collagen in the case of bone and dentin) are tough but not very stiff. Mineral, on the contrary, is stiff but not very tough. It is obvious from Fig. 8 that bone and dentin combine the good properties of both.

stiffness (GPa)0,01 0,1 1 10 100 1000

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Figure 8. Stiffness and toughness of proteins and mineral (hydroxyapatite and calcite), as well as a few natural

protein-mineral composites. The schematic Ashby chart is based on a data compilation by Ashby et al. [9].

It is interesting to notice that the thickness of the mineral particles in bone and dentin is in the order of 2-4 nm only. It is likely that the small size of the components is important for the mechanical performance of these materials. A further important aspect is the very anisometric shape of the mineral particles and their detailed arrangement inside the organic collagen-rich matrix. Indeed, particles are known to be plate-shaped and arranged more or less in parallel with the collagen fibrils [17]. A simple mechanical model based on these structural principles (see Fig. 9) has been studied recently [51, 52]. The main feature of this model is that plate-shaped stiff particles are connected by thin layers of soft matrix which is loaded predominantly under shear. A simple expression can be derived for the elastic modulus of the composite which predicts, first, a nearly quadratic dependence on the mineral content (at least for mineral volume fractions smaller than about 60%) and, secondly, a stiffer composite when particles get

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more anisometric (see Fig. 9). When Young’s modulus E is estimated for this model composite, it turns out that the prediction is just intermediate between the Reuss and the Voigt models [2], which represent extreme situations in composites. The predicted dependence of E on the volume fraction of mineral is qualitatively (though not quantitatively) similar to other models for composites as discussed by Akiva et al. [41], for instance.

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Figure 9. Model for the deformation of a mineralized collagen fibril. The stiff particles are platelets (viewed edge-on in the left of the figure) with an anisometric shape defined by the aspect ratio ρ = L/D. The matrix

between the stiff particles is predominantly shear loaded. An analytical expression for Young’s modulus E can be derived by simple considerations [51, 52] and is given in the figure. The graph below the equation shows

the dependence of E on the volume fraction of mineral φ, for different values of the aspect ratio ρ as indicated. The broken line (denoted R) corresponds to the standard prediction of the Reuss model for composites [2].

The situation where ρ → ∞ corresponds to the Voigt model for composites [2]. In order to plot E as a function of φ, numerical values of Em =114 Gpa, Ep = 1.5 Gpa, Gp = 1 Gpa have been taken for Young’s modulus of

the mineral and for Young`s and shear modulus of collagen, respectively.

The model shown in Fig. 9 depends solely on continuum elasticity and as such does not have a characteristic length scale. The stiffness depends on the anisotropy of the particle shape, that is on the ratio ρ = L/D, but not directly on the particle thickness: whether D is in the order of nanometers or micrometers does not change the equation for the elastic modulus, at any given value of ρ. Given the construction of the model, most of the tensile load is carried by the hard particles (which provides the stiffness of the composite). This also means that failure of the composite will depend crucially on defects present in the hard and brittle particles. This problem has been analyzed recently by a numerical method which combines finite element analysis and molecular dynamics [52]. It was shown that the susceptibility to flaws in the particles decreases markedly when the particle size in the order of nanometers. The reason is that – in agreement with Griffith’s law – the stress concentration at the tip of a small defect depends on the size of this defect. The smaller the defect, the smaller the stress concentration. In fact it could be shown that below some critical size of several nanometers the stress concentration vanishes totally and the the composite becomes defect tolerant [52]. This could explain why nanocomposites such as bone and dentin are quite tough, while they

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would be brittle with much larger particles. Hence, nano-sized particles seem essential to reduce the inherent brittleness of the composite, but this effect alone cannot fully explain the high toughness of bone. Energy dissipating mechanisms at larger scales are also contributing to prevent cracks from propagating catastrophically. The fibrous and lamellar character of the bone tissue, its anisotropy and inhomogeneity are important factors controlling toughness. A model describing fracture toughness as a function of these various contributions from different hierarchical levels is, however, still missing.

4 Hierarchical structure of wood

At the macroscopic level, wood can be considered as a cellular solid, mainly composed of parallel hollow tubes, the wood cells. As an example, the hierarchical structure of spruce wood is shown in Fig. 10. The wood cells are clearly visible in Fig. 10a and they have a thicker cell wall in latewood (LW) than in earlywood (EW), within each annual ring. The cell wall is a fibre composite made cellulose microfibrils embedded into a matrix of hemicelluloses and lignin [53].

Figure 10. Hierarchical structure of spruce wood. (a) is a cross-section through the stem showing earlywood (EW) and latewood (LW) within an annual ring (from [54]). Latewood is denser than earlywood because the cell walls are thicker. The breadth of the annual rings varies widely depending on climatic conditions during each particular year. (b) shows scanning electron microscopic pictures of fracture surfaces of spruce wood with two different microfibril angles (from [55]). One of the wood cells (tracheids) is drawn schematically

showing the definition of the microfibril angle between the spiralling cellulose fibrils and the tracheid axis. (c) is a sketch of the (crystalline part) of a cellulose microfibril in spruce (from [56]).

The cellulose fibrils are wound around the tube-like wood cells with an angle called the microfibril angle (MFA, see Fig. 10). The details of how the fibril direction is distributed in a cell has been investigated by scanning-XRD. Results of these investigations are shown in Fig. 11. An-ray beam of 2 µm diameter was used and diffraction patterns from the cell cross-section were determined in steps of 2 µm over

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several adjacent cells [57]. X-ray patterns turned out to be anisotropic and even asymmetric due to the non-standard diffraction geometry (Fig. 11, left). This asymmetry could be used to determine the direction of the cellulose fibrils quantitatively. An arrow corresponding to the projection of the unit vector following the fibril direction is shown in Fig. 11 (right) at each point where a diffraction pattern was collected. It is clearly visible that cellulose fibrils in each of the adjacent cells run according to a right-handed helix. The spatial resolution of this experiment was such that only the main cell wall layer (called S2) was imaged. This cell wall layer is enclosed by other, much thinner layers with different cellulose orientation [53].

Figure 11. X-ray microdiffraction experiment with a 2 µm thick section of spruce wood embedded in resin

(from [57]). Left: typical XRD-patterns from the crystalline part of the cellulose fibrils. Each pattern has been taken with a 2µm wide x-ray beam (at the European Synchrotron Radiation Source). The diffraction patterns are drawn side by side as they were measured. They reproduce several wood cells in cross-section. Note the

asymmetry of the patterns in the enlargement (far left) which can be used to determine the local orientation of cellulose fibrils in the cell wall (arrows) [57]. The arrows are plotted in the right image with the convention that they represent the projection of a vector parallel to the fibrils onto the plane of the cross-section. The

picture clearly shows that all cells are right-handed helices.

The MFA determines to a large extent the elastic modulus and the fracture strain

of wood: When the MFA varies from 0 to 50°, the elastic modulus decreases by about an order of magnitude and the fracture strain increases by a similar factor [55, 58]. In some ways, the wood cell behaves like an elastic spring because the stiff cellulose fibrils are wound helically. The steeper the winding angle is, the stiffer wood becomes. This property can be used by the tree to vary considerably the local mechanical properties by growing cells with different microfibril angle. Hence, with the possibilities given by the hierarchical structure, a growing tree can built graded properties into the stem or the branch, according to needs which may change during its lifetime.

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4.1 MICROFIBRIL ANGLE DISTRIBUTION IN THE STEM

The first example is the distribution of microfibril angles in the stem. For softwood species (such as spruce or pine) and to some extend also for hardwoods (such as oak), the MFA decreases in older trees from a large value in the pith (about 40°) to very small values closer to the bark [54], see Fig. 12. Since the stem thickens by apposition of annual rings at the exterior, the history of a tree is recorded in the succession of annual rings. Hence, the observation that the microfibril angle decreases from pith to bark indicates that younger trees are optimised for flexibility, while the stem becomes more and more optimised for bending stiffness when the tree gets older (see Fig. 12). A possible explanation for this change in strategy could be a compromise between resistance against buckling (which needs stiffness) and flexibility in bending [54] to resist fracture.

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Figure 12. Variation of microfibril angle in a pine stem [54]. Typically, the angle is large in young trees

which are, therefore, optimised for flexibility (since large microfibril angles correspond to low stiffness and large extensibility [58]). Older trees are optimised for stiffness.

4.2 STRUCTURAL GRADING IN THE BRANCH

A further example of the grading of material properties by the use of different microfibril angles is the branch. Fig. 13 (left) shows light microscopic pictures of the cell shape on the upper and on the lower side of the branch. Clearly, the lower side (called compression wood) has rounded cells which are quite different from the square-like cell shapes on the upper side (opposite wood). In addition, the microfibril angles are also quite different on the upper and on the lower side, as revealed by scanning-SAXS (Fig. 13, right). The streaks observed in the SAXS patterns are perpendicular to the direction of the cellulose fibrils and reveal, therefore, the microfibril angle [59]. The differences in both micro-and nanostructure between the upper and the lower side are most certainly due to their different mechanical function, the upper side being mostly under tension and the lower side mostly under compression.

A more detailed picture of the distribution of microfibril angles in a branch of spruce wood is shown in Fig. 14. Since the history of growth is stored in the succession of annual rings, it is possible to plot the fibril angle distribution for different ages of the

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tree. It is remarkable that the young branch (8 years ago) is composed predominantly of flexible wood (with large microfibril angle). With increasing length of the branch (and presumably also an increasing weight from the leaves), a stiff region develops on the upper side of the branch, while the lower side remains with a large MFA (called compression wood) [60]. This means that the asymmetry in the loading pattern is reflected in an asymmetry of the cell microstructure. What is more, the asymmetry develops as a function of age, apparently as a response to modified loading patterns, as the weight and the length of the branch increase. Moreover, it is quite well-known that compression wood my form even in the stem, if there is an asymmetric loading, e.g. due to strong winds from one side.

Figure 13. SAXS-patterns from a spruce branch (from [59]). Left: light-microscopic images of cross-

sections. Note the round cell shape on the compression side (lower side) of the branch. Centre: X-ray transmission micrograph showing the annual rings. Right: SAXS-patterns showing an MFA of 30° on the

upper side and an MFA of 40° on the lower side of the branch.

0 1 2 3 4 m 5

40° – 50°30° – 40°10° – 30°0° – 10°

now

5 years ago

8 years ago

76 m

m

0 1 2 3 4 m 5

40° – 50°30° – 40°10° – 30°0° – 10°

now

5 years ago

8 years ago

76 m

m

µ

0 1 2 3 4 m 5

40° – 50°30° – 40°10° – 30°0° – 10°

now

5 years ago

8 years ago

76 m

m

0 1 2 3 4 m 5

40° – 50°30° – 40°10° – 30°0° – 10°

now

5 years ago

8 years ago

76 m

m

µ

Figure 14. Distribution of microfibril angles measured in a branch of spruce. The age-evolution was deduced

from the pattern of annual rings [60].

- 14 –


4.3 DEFORMATION MECHANISM OF THE WOOD CELL WALL

The deformation behaviour of plant cells is quite intricate, particularly at large

deformations [61, 62]. A typical feature of the stress-strain curve is that a fairly stiff behaviour at low strains is followed by a much “softer” behaviour at large strains (corresponding to a steep increase followed by a smaller slope of the stress-strain curve, Fig. 15c). The mechanisms underlying this deformation behaviour have been studied recently by the diffraction of synchrotron radiation during deformation [27]. Some results of this investigation are shown in Fig. 15. First, the microfibril angle was found to decrease continuously with the applied strain. This relation between micro-fibril angle and strain turned out to be independent of the stress at any given strain. This is shown by stress relaxation experiments (visible as spikes in Fig. 15c), where both strain and microfibril angle µ stay constant, while the stress varies.

µµµµ CellulosefibrilsPolyoses,

Lignin

µ µ‘< µ

σ (M

Pa)

0

10

20

30

40

50

MFA

(deg

)

35

40

45

εmacroscopic

0.00 0.05 0.10 0.15 0.20

mic

ro-s

train

0.00

0.05

0.10

0.15

0.20(a)

(d)

(b)(c)

(e)

(f)

µµµµ CellulosefibrilsPolyoses,

Lignin

µ µ‘< µ

σ (M

Pa)

0

10

20

30

40

50

MFA

(deg

)

35

40

45

εmacroscopic

0.00 0.05 0.10 0.15 0.20

mic

ro-s

train

0.00

0.05

0.10

0.15

0.20

µµµµµµµµ CellulosefibrilsPolyoses,

Lignin

µµ µ‘< µµ‘< µµ‘< µ

σ (M

Pa)

0

10

20

30

40

50

MFA

(deg

)

35

40

45

εmacroscopic

0.00 0.05 0.10 0.15 0.20

mic

ro-s

train

0.00

0.05

0.10

0.15

0.20(a)

(d)

(b)(c)

(e)

(f)

Figure 15. In-situ x-ray diffraction investigation [27] of the deformation of the wood cell wall inside an intact

wood section (compression wood of spruce), shown schematically in (a). The dominant cell-wall layer (b) contains cellulose micro-fibrils tilted with the micro-fibril angle µ. Between the micro-fibrils, there is a matrix of hemicelluloses and lignin. (c) shows the stress-strain curve during the deformation experiment. The spikes in the graph correspond to stress relaxation experiments, where the elongation was kept constant. (d) shows the change in micro-fibril angle during the elongation of the specimen. A micro-strain (e) is calculated under

the assumption that the cellulose fibrils are rigid and all the deformation is just a tilting of the fibrils and shearing of the matrix in-between (f). The nearly one-to-one correspondence (e) of micro- and macro-strain

shows that this is, indeed, the principal mechanism of elongation and that the cellulose fibrils themselves stretch only very little.

- 15 –


In the simplest possible picture, the decrease of the microfibril angle is related to a deformation of each wood cell in a way similar to a spring: The spiral angle of the cellulose microfibrils (that is, the microfibril angle) is reduced from µ to some smaller value µ’ and the matrix in-between the fibrils is sheared (Fig. 15b and 15f). In fact, if it is assumed that the elongation of the cellulose microfibrils is negligible, then the elongation of the cell depends solely on the reduction of the microfibril angle as:

micro-strain = δ(cos µ) / cos µ= -tan µ δµ. This expression is plotted in Fig. 15e as a function of the measured macroscopic elongation (εmacroscopic) of the wood tissue. The graph shows that the wood cells actually extend like an elastic spring, and the fact that the cellulose fibrils are not totally inextensible accounts for the slight deviation between the measured data and the straight line in Fig. 15e.

There is, however, one major difference between the behaviour of the wood cell and an elastic spring: indeed – beyond the change in slope in Fig. 15c – the deformation becomes partially irreversible, but without a serious damage to the material [27, 62]. The model which can be inferred from the synchrotron diffraction data in Fig. 15 is as follows: When the cell elongates, the microfibril angle is decreasing and the matrix between the cellulose fibrils is sheared. This corresponds to the initial stiff behaviour of the wood cells (initial slope in Fig. 15c). Beyond a certain critical strain, the matrix is sheared to an extent, where bonds are broken and the shearing becomes irreversible. Since some of the bonds are broken, the response is now “softer”. After releasing the stress, the unspecific bonds in the matrix reform immediately (a bit like in a velcro connection) and the cell is arrested in the elongated position. In such a model, the matrix is not irreversibly damaged even though the cell is irreversibly elongated [27].

5 Conclusions

Most stiff biological tissues are hierarchically structured, bone and wood being prominent examples. This means that the nanometer structure varies on a micrometer scale. As a consequence, the mechanical properties can be adjusted locally by the organism. Functional gradients and complex structural elements are common in natural tissues. The stiffness of dentin, for example, is graded in such a way that a minimum appears right at the dentin-enamel junction, which is important to prevent catastrophic failure (section 3.2). The flexibility of the material in a branch is also graded to account for the asymmetric loading due to gravitational forces (section 4.2). Mechanical adaptation also leads to age-related changes in the hierarchical structure, both in bone (section 3.1) and wood (sections 4.1 and 4.2). Continued research on natural hierarchical structures is necessary, not only to improve our understanding of biological tissues but also to reveal the strategies and mechanisms used by nature and which may be applied in an engineering context for improving material properties.

The author thanks all collaborators involved during the last few years in the reported studies, including in particular: I. Burgert, J. Färber, H. Gupta, K. Klaushofer, H. Lichtenegger, M. Müller, O. Paris, Ch. Riekel, A. Reiterer, P. Roschger, S. Stanzl-Tschegg, W. Tesch, R. Weinkamer and I. Zizak.

- 16 –


6 References:

1. Currey, J.D. (2003) How well are bones designed to resist fracture?, J Bone

Miner Res 18, 591-598. 2. Currey, J.D. (2002) Bones - Structure and Mechanics. Princeton University

Press, Princeton. 3. Thompson, A.W. (1992) On Growth and Form - the complete revised edition.

(unaltered republication of Cambridge Univ. Press, 1942) ed. Dover Publications.

4. Mattheck, C., Kubler, H. (1995) The internal Optimization of Trees. Springer Verlag, Berlin.

5. Vincent, J.F.V. (1990) Structural Biomaterials. revised edition ed. Princeton University Press, Princeton.

6. Wainwright, S.A., Biggs, W.D., Currey, J.D., Gosline, J.M. (1982) Mechanical Design in Organisms. Princeton University Press.

7. Niklas, K.J. (1992) Plant Biomechanics: an engineering approach to plant form and function. University of Chicago Press, Chicago.

8. Jeronimidis, G., Chapters 1 and 2, in Structural Biological Materials, Design and Structure-Property Relationships, Elices, M., Editor. 2000, Pergamon: Amsterdam. p. 3-29.

9. Ashby, M.F., Gibson, L.J., Wegst, U., and Olive, R. (1995) The Mechanical-Properties of Natural Materials .1. Material Property Charts, Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 450, 123-140.

10. Gibson, L.J., Ashby, M.F., Karam, G.N., Wegst, U., and Shercliff, H.R. (1995) The Mechanical-Properties of Natural Materials .2. Microstructures for Mechanical Efficiency, Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 450, 141-162.

11. Jeronimidis, G., and Atkins, A.G. (1995) Mechanics of Biological-Materials and Structures - Natures Lessons for the Engineer, Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science 209, 221-235.

12. Weiner, S., Addadi, L., and Wagner, H.D. (2000) Materials design in biology, Materials Science & Engineering C-Biomimetic and Supramolecular Systems 11, 1-8.

13. Fratzl, P. (2003) Cellulose and collagen: from fibres to tissues, Curr Opin Coll Interf Sci 8, 32-39.

14. Mattheck, C., and Bethge, K. (1998) The structural optimization of trees, Naturwissenschaften 85, 1-10.

15. Vincent, J.F.V. (1999) From cellulose to cell, Journal of Experimental Biology 202, 3263-3268.

16. Weiner, S., and Traub, W. (1992) Bone-Structure - from Angstroms to Microns, Faseb J 6, 879-885.

17. Weiner, S., and Wagner, H.D. (1998) The material bone: Structure mechanical function relations, Annual Review of Materials Science 28, 271-298.

- 17 –


18. Rho, J.Y., Kuhn-Spearing, L., and Zioupos, P. (1998) Mechanical properties and the hierarchical structure of bone, Medical Engineering & Physics 20, 92-102.

19. Currey, J.D. (1999) The design of mineralised hard tissues for their mechanical functions, Journal of Experimental Biology 202, 3285-3294.

20. Mann, S., and Weiner, S. (1999) Biomineralization: Structural questions at all length scales, J Struct Biol 126, 179-181.

21. Paris, O., Zizak, I., Lichtenegger, H., Roschger, P., Klaushofer, K., and Fratzl, P. (2000) Analysis of the hierarchical structure of biological tissues by scanning X-ray scattering using a micro-beam, Cell Mol Biol 46, 993-1004.

22. Fratzl, P., Jakob, H.F., Rinnerthaler, S., Roschger, P., and Klaushofer, K. (1997) Position-resolved small-angle X-ray scattering of complex biological materials, J Appl Cryst 30, 765-769.

23. Riekel, C., Burghammer, M., and Müller, M. (2000) Microbeam small-angle scattering experiments and their combination with microdiffraction, J Appl Cryst 33, 421-423.

24. Tesch, W., Eidelman, N., Roschger, P., Goldenberg, F., Klaushofer, K., and Fratzl, P. (2001) Graded microstructure and mechanical properties of human crown dentin, Calcif Tissue Int 69, 147-157.

25. Burgert, I., Keckes, J., Fruhmann, K., Fratzl, P., and Tschegg, S.E. (2002) A comparison of two techniques for wood fibre isolation evaluation by tensile tests on single fibres with different microfibril angle, Plant Biol 4, 9-12.

26. Ascenzi, A., Benvenuti, A., Bigi, A., Foresti, E., Koch, M.H.J., Mango, F., Ripamonti, A., and Roveri, N. (1998) X-ray diffraction on cyclically loaded osteons, Calcif Tissue Int 62, 266-273.

27. Keckes, J., Burgert, I., Frühmann, K., Müller, M., Kölln, K., Hamilton, M., Burghammer, M., Roth, S.V., Stanzl-Tschegg, S., and Fratzl, P. (2003) Cell-wall recovery after irreversible deformation, Nature Materials (in press).

28. Puxkandl, R., Zizak, I., Paris, O., Keckes, J., Tesch, W., Bernstorff, S., Purslow, P., and Fratzl, P. (2002) Viscoelastic properties of collagen: synchrotron radiation investigations and structural model, Phil Trans Roy Soc Lond B 357, 191-197.

29. Weiner, S., Arad, T., Sabanay, I., and Traub, W. (1997) Rotated plywood structure of primary lamellar bone in the rat: Orientations of the collagen fibril arrays, Bone 20, 509-514.

30. Weiner, S., Traub, W., and Wagner, H.D. (1999) Lamellar bone: Structure-function relations, J Struct Biol 126, 241-255.

31. Landis, W.J. (1996) Mineral characterization in calcifying tissues: Atomic, molecular and macromolecular perspectives, Conn Tissue Res 35, 1-8.

32. Rubin, M.A., Jasiuk, I., Taylor, J., Rubin, J., Ganey, T., and P., A.R. (2003) TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone, Bone 37, 270-282.

33. Fratzl, P., Fratzlzelman, N., Klaushofer, K., Vogl, G., and Koller, K. (1991) Nucleation and Growth of Mineral Crystals in Bone Studied by Small-Angle X-Ray-Scattering, Calcif Tissue Int 48, 407-413.

- 18 –


34. Fratzl, P., Groschner, M., Vogl, G., Plenk, H., Eschberger, J., Fratzlzelman, N., Koller, K., and Klaushofer, K. (1992) Mineral Crystals in Calcified Tissues - a Comparative-Study by Saxs, J Bone Miner Res 7, 329-334.

35. Roschger, P., Grabner, B.M., Rinnerthaler, S., Tesch, W., Kneissel, M., Berzlanovich, A., Klaushofer, K., and Fratzl, P. (2001) Structural development of the mineralized tissue in the human L4 vertebral body, J Struct Biol 136, 126-136.

36. Roschger, P., Rinnerthaler, S., Yates, J., Rodan, G.A., Fratzl, P., and Klaushofer, K. (2001) Alendronate increases degree and uniformity of mineralization in cancellous bone and decreases the porosity in cortical bone of osteoporotic women, Bone 29, 185-191.

37. Rinnerthaler, S., Roschger, P., Jakob, H.F., Nader, A., Klaushofer, K., and Fratzl, P. (1999) Scanning small angle X-ray scattering analysis of human bone sections, Calcif Tissue Int 64, 422-429.

38. Landis, W.J., Librizzi, J.J., Dunn, M.G., and Silver, F.H. (1995) A Study of the Relationship between Mineral-Content and Mechanical-Properties of Turkey Gastrocnemius Tendon, J Bone Miner Res 10, 859-867.

39. Jaschouz, D., Paris, O., Roschger, P., Hwang, H.S., and Fratzl, P. (2003) Pole figure analysis of mineral nanoparticle orientation in individual trabecula of human vertebral bone, J Appl Cryst 36, 494-498.

40. Landis, W.J., Hodgens, K.J., Arena, J., Song, M.J., and McEwen, B.F. (1996) Structural relations between collagen and mineral in bone as determined by high voltage electron microscopic tomography, Microscopy Research and Technique 33, 192-202.

41. Akiva, U., Wagner, H.D., and Weiner, S. (1998) Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone, J Mater Sci 33, 1497-1509.

42. Hoffler, C.E., Moore, K.E., Kozloff, K., Zysset, P.K., Brown, M.B., and Goldstein, S.A. (2000) Heterogeneity of bone lamellar-level elastic moduli, Bone 26, 603-609.

43. Liu, D.M., Weiner, S., and Wagner, H.D. (1999) Anisotropic mechanical properties of lamellar bone using miniature cantilever bending specimens, J Biomech 32, 647-654.

44. Rho, J.Y., Zioupos, P., Currey, J.D., and Pharr, G.M. (1999) Variations in the individual thick lamellar properties within osteons by nanoindentation, Bone 25, 295-300.

45. Ziv, V., Wagner, H.D., and Weiner, S. (1996) Microstructure-microhardness relations in parallel-fibered and lamellar bone, Bone 18, 417-428.

46. Sasaki, N., Ikawa, T., and Fukuda, A. (1991) Orientation of Mineral in Bovine Bone and the Anisotropic Mechanical-Properties of Plexiform Bone, J Biomech 24, 57-61.

47. Kinney, J.H., Pople, J.A., Marshall, G.W., and Marshall, S.J. (2001) Collagen orientation and crystallite size in human dentin: a small angle X-ray scattering study., Calcified Tissue International 69, 31-37.

48. Beniash, E., Traub, W., Veis, A., and Weiner, S. (2000) A transmission electron microscope study using vitrified ice sections of predentin: Structural

- 19 –


changes in the dentin collagenous matrix prior to mineralization, J Struct Biol 132, 212-225.

49. Habelitz, S., Balooch, M., Marshall, S.J., Balooch, G., and Marshall, G.W. (2002) In situ atomic force microscopy of partially demineralized human dentin collagen fibrils, J Struct Biol 138, 227-236.

50. Nalla, R.K., Kinney, J.H., and Ritchie, R.O. (2003) Effect of orientation on the in vitro fracture toughness of dentin: the role of toughening mechanisms, Biomaterials 24, 3955-3968.

51. Jager, I., and Fratzl, P. (2000) Mineralized collagen fibrils: A mechanical model with a staggered arrangement of mineral particles, Biophys J 79, 1737-1746.

52. Gao, H.J., Ji, B.H., Jager, I.L., Arzt, E., and Fratzl, P. (2003) Materials become insensitive to flaws at nanoscale: Lessons from nature, Proc Natl Acad Sci USA 100, 5597-5600.

53. Fengel, D., Wegener, G. (1989) Wood: chemistry, ultrustructure, reactions. de Gruyter, Berlin.

54. Lichtenegger, H., Reiterer, A., Stanzl-Tschegg, S.E., and Fratzl, P. (1999) Variation of cellulose microfibril angles in softwoods and hardwoods - A possible strategy of mechanical optimization, J Struct Biol 128, 257-269.

55. Reiterer, A., Lichtenegger, H., Fratzl, P., and Stanzl-Tschegg, S.E. (2001) Deformation and energy absorption of wood cell walls with different nanostructure under tensile loading, J Mater Sci 36, 4681-4686.

56. Jakob, H.F., Fengel, D., Tschegg, S.E., and Fratzl, P. (1995) The elementary cellulose fibril in Picea abies: Comparison of transmission electron microscopy, small-angle X-ray scattering, and wide-angle X-ray scattering results, Macromolecules 28, 8782-8787.

57. Lichtenegger, H., Muller, M., Paris, O., Riekel, C., and Fratzl, P. (1999) Imaging of the helical arrangement of cellulose fibrils in wood by synchrotron X-ray microdiffraction, J Appl Cryst 32, 1127-1133.

58. Reiterer, A., Lichtenegger, H., Tschegg, S., and Fratzl, P. (1999) Experimental evidence for a mechanical function of the cellulose microfibril angle in wood cell walls, Phil Mag A 79, 2173-2184.

59. Reiterer, A., Jakob, H.F., Stanzl-Tschegg, S.E., and Fratzl, P. (1998) Spiral angle of elementary cellulose fibrils in cell walls of Picea abies determined by small-angle X-ray scattering, Wood Sci Tech 32, 335-345.

60. Farber, J., Lichtenegger, H.C., Reiterer, A., Stanzl-Tschegg, S., and Fratzl, P. (2001) Cellulose microfibril angles in a spruce branch and mechanical implications, J Mater Sci 36, 5087-5092.

61. Spatz, H.C., Kohler, L., and Niklas, K.J. (1999) Mechanical behaviour of plant tissues: Composite materials or structures?, Journal of Experimental Biology 202, 3269-3272.

62. Kohler, L., and Spatz, H.C. (2002) Micromechanics of plant tissues beyond the linear-elastic range, Planta 215, 33-40.

- 20 –

14. T. Nishino, M. Miyake, Y. Harada, U. Kawabe, IEEEElectron Device Lett. EDL-6, 297 (1985).

15. H. Takayanagi, T. Kawakami, Phys. Rev. Lett. 54,2449 (1985).

16. A. W. Kleinsasser et al., Appl. Phys. Lett. 55, 1909(1989).

17. C. Nguyen, J. Werking, H. Kroemer, E. L. Hu, Appl.Phys. Lett. 57, 87 (1990).

18. B. D. Josephson, Phys. Lett. 1, 251 (1962).19. A. F. Andreev, Zh. Eksp. Theor. Fiz. 46, 1823 (1964)

[Sov. Phys. JETP 19, 1228 (1964)].20. B. Pannetier, H. Courtois, J. Low Temp. Phys. 118,

599 (2000).21. K. Flensberg, J. B. Hansen, M. Octavio, Phys. Rev. B

38, 8707 (1988).

22. A. Chrestin, U. Merkt, Appl. Phys. Lett. 70, 3149 (1997).23. M. Octavio, M. Tinkham, G. E. Blonder, T. M. Klapwijk,

Phys. Rev. B 27, 6739 (1983).24. E. Scheer et al., Phys. Rev. Lett. 86, 284 (2001).25. M. R. Buitelaar et al., Phys. Rev. Lett. 91, 057005 (2003).26. P. A. Lee, A. D. Stone, Phys. Rev. Lett. 55, 1622 (1985).27. C. W. J. Beenakker, Phys. Rev. Lett. 67, 3836 (1991).28. B. L. Al’tshuler, B. Z. Spivak, Zh. Eksp. Theor. Fiz. 92,

609 (1987) [Sov. Phys. JETP 65, 343 (1987)].29. Y. Makhlin, G. Schon, A. Shnirman, Rev. Mod. Phys.

73, 357 (2001).30. M. J. Storcz, F. K. Wilhelm, Appl. Phys. Lett. 83, 2387

(2003).31. We thank J. Eroms, R. Schouten, C. Harmans, P.

Hadley, Yu. Nazarov, C. Beenakker, T. Klapwijk, B. van

Wees, and F. Giazotto. Financial support wasobtained from the Dutch Fundamenteel Onderzoekder Materie, the Japanese Solution Oriented Re-search for Science and Technology program, and theKorean Science and Engineering Foundation.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/309/5732/272/DC1Materials and MethodsFigs. S1 to S4References

13 April 2005; accepted 25 May 200510.1126/science.1113523

Skeleton of Euplectella sp.:Structural Hierarchy from theNanoscale to the Macroscale

Joanna Aizenberg,1* James C. Weaver,2 Monica S. Thanawala,1

Vikram C. Sundar,1 Daniel E. Morse,2 Peter Fratzl3

Structural materials in nature exhibit remarkable designs with building blocks,often hierarchically arranged from the nanometer to the macroscopic lengthscales. We report on the structural properties of biosilica observed in thehexactinellid sponge Euplectella sp. Consolidated, nanometer-scaled silicaspheres are arranged in well-defined microscopic concentric rings glued to-gether by organic matrix to form laminated spicules. The assembly of thesespicules into bundles, effected by the laminated silica-based cement, resultsin the formation of a macroscopic cylindrical square-lattice cagelike structurereinforced by diagonal ridges. The ensuing design overcomes the brittleness ofits constituent material, glass, and shows outstanding mechanical rigidity andstability. The mechanical benefits of each of seven identified hierarchicallevels and their comparison with common mechanical engineering strategiesare discussed.

Nature fascinates scientists and engineers

with numerous examples of exceptionally

strong building materials. These materials

often show complex hierarchical organiza-

tion from the nanometer to the macroscopic

scale (1–7). Every structural level contrib-

utes to the mechanical stability and tough-

ness of the resulting design. For instance, the

subtle interplay between the lattice structure,

fibril structure, and cellulose is responsible

for the remarkable properties of wood. In par-

ticular, it consists of parallel hollow tubes, the

wood cells, which are reinforced by nanometer-

thick cellulose fibrils wound helically around

the cell to adjust the material as needed (8).

Deformation occurs by shearing of a matrix

rich in hemicelluloses and lignin, Bgluing[neighboring fibrils, and allowing a stick-slip

movement of the fibrils (9). Wood is an ex-

ample that shows the wide range of mechan-

ical performance achievable by constructing

with fibers. Bone is another example of a

hierarchically assembled fibrous material. Its

strength critically depends on the interplay

between different structural levels—from the

molecular/nanoscale interaction between crys-

tallites of calcium phosphate and an organic

framework, through the micrometer-scale as-

sembly of collagen fibrils, to the millimeter-

level organization of lamellar bone (4, 10–12).

Whereas wood is fully organic material, bone

is a composite, with about half organic and

half mineral components tightly intercon-

nected at the nanoscale. However, nature has

also evolved almost pure mineral structures,

which—despite the inherent brittleness of

most minerals—are tough enough to serve as

protection for the organism. In mollusk nacre,

for example, the toughening effect is due to

well-defined nanolayers of organics at the

interfaces between microtablets of calcium

carbonate (5, 6). In such structures, the stiff

components (usually mineral) absorb the bulk

of the externally applied loads. The organic

layers, in turn, provide toughness, prevent the

spread of the cracks into the interior of the

structure, and even confer a remarkable ca-

pacity for recovery after deformation (13).

Glass is widely used as a building mate-

rial in the biological world, despite its fra-

gility (14–20). Organisms have evolved means

to effectively reinforce this inherently brittle

material. It has been shown that spicules in

siliceous sponges exhibit exceptional flexibil-

ity and toughness compared with brittle

synthetic glass rods of similar length scales

(15, 20). The mechanical protection of diatom

cells was suggested to arise from the increased

strength of their silica frustules (16). We have

recently described the structural and optical

properties of individual spicules of the glass

sponge Euplectella sp., a deep-sea, sediment-

dwelling sponge from the Western Pacific

(21, 22). Not only do these spicules have op-

tical properties similar to manufactured optical

fibers, but they are also structurally resistant.

The individual spicules are, however, just one

structural level in a highly sophisticated, nearly

purely mineral skeleton of this siliceous sponge

(23). Here, we discuss the structural hierarchy

of the entire skeleton of Euplectella sp. from

the nanoscale to the macroscale. We show that

the assembly of a macroscopic, mechanically

resistant cylindrical glass cage is possible in a

modular, bottom-up fashion comprising at least

seven hierarchical levels, all contributing to

mechanical performance. These include silica

nanospheres that are arranged into concentric

layers separated from one another by alter-

nating organic layers to yield lamellar fibers.

The fibers are in turn bundled and organized

within a silica matrix to produce flexurally

rigid composite beams at the micron scale. The

macroscopic arrangement of these beams in a

rectangular lattice with ancillary crossbeams is

ideal for resisting tensile and shearing stresses.

Finally, we identify various structural motifs

that provide additional structural benefits to this

unique glass skeletal system.

Figure 1A is a photograph of the entire

skeleton of Euplectella sp., showing the in-

tricate, cylindrical cagelike structure (20 to 25

cm long, 2 to 4 cm in diameter) with lateral

(Boscular[) openings (1 to 3 mm in diameter).

The diameter of the cylinder and the size of the

oscular openings gradually increase from the

bottom to the top of the structure. The basal

segment of Euplectella sp. is anchored into the

soft sediments of the sea floor and is loosely

connected to the rigid cage structure, which is

1Bell Laboratories/Lucent Technologies, Murray Hill,NJ 07974, USA. 2Institute for Collaborative Biotech-nologies and Materials Research Laboratory, Universi-ty of California, Santa Barbara, CA 93106, USA. 3MaxPlanck Institute of Colloids and Interfaces, D-14424Potsdam, Germany.

*To whom correspondence should be addressed.E-mail: [email protected]

R E P O R T S

www.sciencemag.org SCIENCE VOL 309 8 JULY 2005 275

exposed to ocean currents and supports the

living portion of the sponge responsible for

filtering and metabolite trapping (23, 24). The

characteristic sizes and construction mech-

anisms of the Euplectella sp. skeletal sys-

tem are expected to be fine-tuned for these

functions.

At the macroscale, the cylindrical structure

is reinforced by external ridges that extend

perpendicular to the surface of the cylinder

and spiral the cage at an angle of 45- (shown

by arrows in Fig. 1B). The pitch of the ex-

ternal ridges decreases from the basal to the

top portion of the cage. The surface of the

cylinder consists of a regular square lattice

composed of a series of cemented vertical and

horizontal struts (Fig. 1B), each consisting of

bundled spicules aligned parallel to one

another (Fig. 1C), with diagonal elements

positioned in every second square cell (Fig.

1B). Cross-sectional analyses of these beams

at the micron scale reveal that they are

composed of collections of silica spicules (5

to 50 mm in diameter) embedded in a layered

silica matrix (Fig. 1, D to F). The higher

solubility of the cement when treated with

hydrofluoric acid (HF) (25), compared with

the underlying spicules, suggests that the

cement is composed of more hydrated silica

(Fig. 1, D and E). The constituent spicules

have a concentric lamellar structure, with the

layer thickness decreasing from È1.5 mm at

the center of the spicule to È0.2 mm at the

spicule periphery (Fig. 1G). These layers are

arranged in a cylindrical fashion around a

central proteinaceous filament and are sep-

arated from one another by organic inter-

layers (Fig. 1H). Etching of spicule layers

and the surrounding cement showed that at

the nanoscale the fundamental construction

unit consists of consolidated hydrated silica

nanoparticles (50 to 200 nm in diameter)

(Fig. 1I) (17–19, 22). The different levels of

structural complexity are schematically shown

in Fig. 2. In the following discussion, each

hierarchical level is examined from the me-

chanical perspective.

The first level is biologically produced

glass composed of consolidated silica nano-

spheres formed around a protein filament (Fig.

2A). Glass as a building material suffers

primarily from its brittleness. This means that

its strength is limited mostly by surface

defects where the applied stresses concentrate.

A scratch in the surface of glass readily in-

duces fracture. If we consider that surface

defects in the biosilica may be induced by

external point loads, either biologically or

otherwise applied, a scratched plain glass

spicule would lose most of its strength and

would fracture when subsequently loaded in

tension or bending. This can be expressed

quantitatively by the well-known Griffith law,

which relates the strength sf

to the size of the

largest defect, h, for h Q h*, as

sf 0K1Cffiffiffiffiffi

php , sth

f

ffiffiffiffiffih�

h

rðEq: 1Þ

where K1C is the fracture toughness of the

glass, sthf is the theoretical strength of the

defect-free material, and h* is a characteristic

length (for typical ceramic materials, this

length is on the order of 10 to 30 nm) (26).

For defects smaller than h*, there is no stress

concentration at the defect, and the strength of

the material is equal to its defect-free value

(26). Because the mineral particles in bone,

for example, are thinner than this value, these

particles should be insensitive to defects and

therefore flaw tolerant. This argument does

not apply, however, to biologically produced

glass, because individual silica nanospheres

range from 50 nm to 200 nm in diameter and

thus are larger than h*.

The intrinsically low strength of the glass

is balanced at the next structural level. The

spicule as a whole can be regarded as a lam-

inated composite (27) in which the organic

interlayers act as crack stoppers (Fig. 2B). If

a point load is applied to the surface, one

may expect that the damage will be restricted

to the outermost layers (28). A larger number

of individual glass layers should protect the

spicule more effectively from this type of

damage. Thin organic interlayers seem also

to be important to prevent cracks from prop-

agating to inner layers under the influence of

indentation (28). The observed decrease of the

silica layer thickness from the spicule core to

the periphery is likely to provide an additional

reinforcement to the spicules. Thicker inner

layers help enhance mechanical rigidity of the

Fig. 1. Structural analysis of the mineralized skeletal system of Euplectellasp. (A) Photograph of the entire skeleton, showing cylindrical glass cage.Scale bar, 1 cm. (B) Fragment of the cage structure showing the square-gridlattice of vertical and horizontal struts with diagonal elements arranged ina chessboard manner. Orthogonal ridges on the cylinder surface are in-dicated by arrows. Scale bar, 5 mm. (C) Scanning electron micrograph(SEM) showing that each strut (enclosed by a bracket) is composed ofbundled multiple spicules (the arrow indicates the long axis of the skeletallattice). Scale bar, 100 mm. (D) SEM of a fractured and partially HF-etched(25) single beam revealing its ceramic fiber-composite structure. Scale

bar, 20 mm. (E) SEM of the HF-etched (25) junction area showing that thelattice is cemented with laminated silica layers. Scale bar, 25 mm. (F)Contrast-enhanced SEM image of a cross section through one of thespicular struts, revealing that they are composed of a wide range ofdifferent-sized spicules surrounded by a laminated silica matrix. Scale bar,10 mm. (G) SEM of a cross section through a typical spicule in a strut,showing its characteristic laminated architecture. Scale bar, 5 mm. (H) SEMof a fractured spicule, revealing an organic interlayer. Scale bar, 1 mm. (I)Bleaching of biosilica surface revealing its consolidated nanoparticulatenature (25). Scale bar, 500 nm.

R E P O R T S

8 JULY 2005 VOL 309 SCIENCE www.sciencemag.org276

spicule, whereas the thinner outer layers ef-

fectively limit the depth of crack penetration.

The crack deviation by organic interlayers

in laminated spicules can be clearly seen in

Fig. 3.

In a further level of hierarchy, spicules

are joined into parallel bundles (Fig. 2C), a

well-known construction principle in ceram-

ic materials (29). Generally, a bundle of fi-

bers with slightly different strength will have a

much larger defect tolerance (and, therefore,

strength) than each of the individual fibers.

Indeed, if one fiber fails (e.g., under tension),

neighboring ones still hold, and the crack in

the first fiber will be deflected at the interface

to its neighbors (or at the interface between

the fiber and cement). A weak lateral bonding

between fibers (or between fiber and matrix)

is essential for this toughening mechanism to

work (30).

The bundled spicules are arranged hor-

izontally and vertically into a square-grid

cylindrical cage reinforced by ancillary diag-

onal fibers running in both directions (Fig.

2D). Theoretical analyses of strut structures

have shown that when the number of struts

per node, Z, exceeds a certain value, the struc-

ture is stable even if the nodes can rotate

freely. Deshpande et al. (31) have given the

stability limit as

Z Q 6 ðD j 1Þ ðEq: 2Þ

for grids in D 0 2 or in D 0 3 dimensions. A

simple square grid made of fibers (with D 02 and Z 0 4) is clearly unstable with respect

to shear when the nodes can rotate freely. In

cases where a free rotation of the nodes is

not possible, the shear stability of the simple

square grid is limited by the bending mo-

ments, which the nodes and struts can with-

stand. However, cellular structures are usually

much stronger when the struts are loaded in

tension rather than in bending (32). Hence,

structures fulfilling inequality (Eq. 2), where

any type of loading will result in tension and

compression of the fibers only, are likely to

be stronger. In the Euplectella skeletal

system, three main spicular struts (horizontal,

vertical, and one of the two possible diago-

nals) are joined in every node of the square

grid, which means that Z 0 6. This is just

sufficient to fulfill Eq. 2 for a two-dimensional

grid. Most remarkably, every second square in

the skeletal lattice is left without a diagonal

fiber. By adding the crossbeams in these

empty squares, the number Z would jump to

8, which would be an overdesign in terms of

Eq. 2, with no apparent structural advantages

for the prevention of shear stresses.

Hierarchical levels shown in Fig. 2, A to

D, describe the structure of the Euplectella

skeletal system at its early stages of devel-

opment Ethe Bflexible phase[ (24)^. During

maturation, the flexible cage is rigidified into

a Bstiff sponge[ (24) as a result of the use of

two additional levels of structural hierarchy.

All the fibers become joined at the nodes of

the square grid with silica cement that

effectively coats the entire skeletal lattice

(Fig. 2E) and thus forms the matrix of a

ceramic fiber composite. The only exception

is the region where basalia (anchor spicules)

emerge from the base of the composite

structure. It is also noteworthy that the

cement itself exhibits a laminated architec-

ture (Fig. 1, D to F) that hinders crack

propagation through this silica matrix.

The resultant rigid structure ensures that

the sheet forming the cylinder is very stable

in two dimensions with a number of mea-

sures to reduce the intrinsic brittleness of

glass. Finally, the cylindrical cage must also

be stable in three dimensions, and the main

limitation is the ovalization of the cylinder,

which reduces the bending stability of the

tubelike cage. In this sense, it is very likely

that the helical ridges around the skeleton of

Euplectella sp. (Fig. 2F), in conjunction with

the consolidating silica matrix discussed

above, serve primarily a mechanical function

in preventing ovalization of the sponge

skeleton. This argument is further supported

by the fact that the ridges are absent in the

narrow bottom portion of the tube and ap-

Fig. 3. Fracture surfaces in the spicules fromEuplectella sp. (A) SEM of a fractured laminatedspicule. (B) Examination of a polished crosssection of the spicule from a related speciesclearly reveals crack deviation by the organiclayers. Scale bars for both micrographs, 10 mm.

F i g . 2 . Proposedscheme summarizingthe seven levels of struc-turalhierarchy intheskel-etal system of Euplectellasp. (A) Consolidated sil-ica nanoparticles depos-ited around a preformedorganic axial filament(shown on the right).(B) Lamellar structureof spicule made of al-ternating organic andsilica layers. Inset depictsthe organically glued in-terlayer region. (C)Bundling of spicules.(D) (Right) Vertical andhorizontal ordering ofbundled spicules forminga square-lattice cylindri-cal cage with every sec-ond cell reinforced bydiagonal elements (seeEq. 2). (Left) The nodestructure. (E) Cementation of nodes and spicules in the skeletal lattice with layered silica matrix. (Inset) Fiber-reinforced composite of an individual beam in thestrut. (F) Surface ridges protect against ovalization of the skeleton tube. (G) Flexural anchoring of the rigid cage into the soft sediments of the sea floor.

R E P O R T S

www.sciencemag.org SCIENCE VOL 309 8 JULY 2005 277

pear in the middle region where the sponge

diameter increases beyond a specific point.

To ensure the stability of the tube with the

vertically growing diameter, there is a distinct

increase of the surface density and thickness

of the external ridges in the upper regions of

the skeletal system (Fig. 1A) (23, 24).

Exposed to currents, the elevated rigid

sponge cage attached to the ocean floor will

experience bending stresses that are concen-

trated at the anchor point. Two mechanical

strategies may counteract the stress concen-

tration: to stiffen the anchor point, which

will withstand bending forces up to a certain

limit and then break, or to make the anchor

very flexible. The sponge uses the latter

strategy by loosely incorporating the basalia

(anchor) spicules into the vertical struts of the

rigid cage (Fig. 2G). The advantage of this

strategy is that there is no limiting stress from

currents, and the cage swings freely in the

ocean because of the inherent flexibility of the

individual spicules that form the connection.

The structural complexity of the glass

skeleton in the sponge Euplectella sp. is an

example of nature_s ability to improve in-

herently poor building materials. The excep-

tional mechanical stability of the skeleton

arises from the successive hierarchical assem-

bly of the constituent glass from the nano-

meter to the macroscopic scale. The resultant

structure might be regarded as a textbook

example in mechanical engineering, because

the seven hierarchical levels in the sponge skel-

eton represent major fundamental construction

strategies such as laminated structures, fiber-

reinforced composites, bundled beams, and

diagonally reinforced square-grid cells, to

name a few (33). We conclude that the

Euplectella sp. skeletal system is designed to

provide structural stability at minimum cost, a

common theme in biological systems where

critical resources are often limited. We believe

that the study of the structural complexity of

unique biological materials and the underlying

mechanisms of their synthesis will help us

understand how organisms evolved their so-

phisticated structures for survival and adapta-

tion and ultimately will offer new materials

concepts and design solutions.

References and Notes1. S. A. Wainwright, W. D. Biggs, J. D. Currey, J. M.

Gosline, Mechanical Design in Organisms (Wiley,New York, 1976).

2. J. D. Currey, J. Exp. Biol. 202, 3285 (1999).3. H. A. Lowenstam, S. Weiner, On Biomineralization

(Oxford Univ. Press, Oxford, 1989).4. S. Weiner, H. D. Wagner, Annu. Rev. Mater. Sci. 28,

271 (1998).5. S. Kamat, X. Su, R. Ballarini, A. H. Heuer, Nature 405,

1036 (2000).6. A. G. Evans et al., J. Mater. Res. 16, 2475 (2001).7. G. Mayer, M. Sarikaya, Exp. Mech. 42, 395 (2002).8. H. Lichtenegger, A. Reiterer, S. E. Stanzl-Tschegg,

P. Fratzl, J. Struct. Biol. 128, 257 (1999).9. J. Keckes et al., Nat. Mater. 2, 810 (2003).

10. P. Fratzl, H. S. Gupta, E. P. Paschalis, P. Roschger,J. Mater. Chem. 14, 2115 (2004).

11. A. E. Porter, L. W. Hobbs, V. B. Rosen, M. Spector,Biomaterials 23, 725 (2002).

12. T. Hassenkam et al., Bone 35, 4 (2004).13. B. L. Smith et al., Nature 399, 761 (1999).14. C. C. Perry, T. Keeling-Tucker, J. Biol. Inorg. Chem. 5,

537 (2000).15. C. Levi, J. L. Barton, C. Guillemet, E. Le Bras, P. Lehuede,

J. Mater. Sci. Lett. 8, 337 (1989).16. C. E. Hamm et al., Nature 421, 841 (2003).

17. J. N. Cha et al., Proc. Natl. Acad. Sci. U.S.A. 96, 361(1999).

18. N. Kroger, S. Lorenz, E. Brunner, M. Sumper, Science298, 584 (2002).

19. J. C. Weaver et al., J. Struct. Biol. 144, 271 (2003).20. M. Sarikaya et al., J. Mater. Res. 16, 1420 (2001).21. V. C. Sundar, A. D. Yablon, J. L. Grazul, M. Ilan, J.

Aizenberg, Nature 424, 899 (2003).22. J. Aizenberg, V. C. Sundar, A. D. Yablon, J. C. Weaver, G.

Chen, Proc. Natl. Acad. Sci. U.S.A. 101, 3358 (2004).23. F. E. Schulze, Report on the Hexactinellida Collected

by H. M. S. Challenger During the Years 1873-1876,vol. XXI (Berlin, 1887).

24. T. Saito, I. Uchida, M. Takeda, J. Zool. 258, 521 (2002).25. HF treatment and bleaching experiments: Small sec-

tions (2 cm by 2 cm) of the Euplectella sp. skeletallattice were soaked for 10 min in 5 M NH4F:2.5 M HFor 2.5% NaOCl solution, respectively. The remainingskeletal material was removed, rinsed with water and95% ethanol, dried, and prepared for examination byscanning electron microscope.

26. H. J. Gao, B. H. Ji, I. L. Jager, E. Arzt, P. Fratzl, Proc.Natl. Acad. Sci. U.S.A. 100, 5597 (2003).

27. M. Seshadri, S. J. Bennison, A. Jagota, S. Saigal, ActaMater. 50, 4477 (2002).

28. H. Chai, B. R. Lawn, Acta Materialia 50, 2613 (2002).29. W. J. Clegg, K. Kendall, N. M. Alford, T. W. Button,

J. D. Birchall, Nature 347, 455 (1990).30. K. T. Faber, Annu. Rev. Mater. Sci. 27, 499 (1997).31. V. S. Deshpande, M. F. Ashby, N. A. Fleck, Acta

Materialia 49, 1035 (2001).32. L. J. Gibson, M. F. Ashby, Cellular Solids: Structure

and Properties (Cambridge University Press, ed. 2,1999).

33. G. Mayer, Ceram. Bull. 83, 9305 (2004).34. We thank M. Ilan, G. E. Fantner, D. Kisailus, and M. J.

Porter for their help. J.C.W. and D.E.M. were supportedby grants from NASA (NAG1-01-003 and NCC-1-02037), the Institute for Collaborative Biotechnologiesthrough grant DAAD19-03D-0004 from the ArmyResearch Office, and the NOAA National Sea GrantCollege Program, U.S. Department of Commerce(NA36RG0537, Project R/MP-92) through the Califor-nia Sea Grant College System.

14 March 2005; accepted 4 May 200510.1126/science.1112255

Isolation of Two Seven-MemberedRing C58 Fullerene Derivatives:

C58F17CF3 and C58F18

Pavel A. Troshin,1 Anthony G. Avent,2 Adam D. Darwish,2

Natalia Martsinovich,2 Ala’a K. Abdul-Sada,2 Joan M. Street,3

Roger Taylor2*

Fluorination of C60 at 550-C leads to milligram quantities of two stablefullerene derivatives with 58-carbon cage structures: C58F18 and C58F17CF3. Thecompounds were characterized by mass spectrometry and fluorine nuclearmagnetic resonance spectroscopy, and the data support a heptagonal ring inthe framework. The resulting strain, which has hindered past attempts to pre-pare these smaller quasi-fullerenes, is mitigated here by hybridization change ofsome of the carbons in the pentagons from sp2 to sp3 because of fluorineaddition. The loss of carbon from C60 is believed to occur via sequential fluorineaddition to a C–C single bond and an adjacent C0C bond, followed by loss of a:CF2 carbene.

Numerous papers describe the structure and

properties of fullerenes larger than C60

and

C70

and their derivatives (1). The stability of

these compounds has been explained by the

low strain inherent in a framework of pen-

tagonal carbon rings surrounded by hexagons.

By contrast, smaller fullerenes violate this non-

adjacent pentagon rule and accordingly have

been hard to prepare. Examples comprise the

recent isolation of C50

Cl10

(2) and a contro-

versial report of C36

(3, 4).

The possibility of fullerenes having seven-

as well as five- and six-membered rings (quasi-

fullerenes) was first proposed in 1992 (5). The

structure of C58

requires a seven-membered

ring produced by removal from C60

of a 6:5

bond, that is, one shared by a pentagon and a

hexagon (6, 7). The resultant C58

structure

violates the strain-based nonadjacent pentagon

rule (8), but a C58

derivative will be less

strained because of the presence of sp3

carbons and isolation ought to be feasible

(6). Both phenylated and methylated C58

fragment ions have been observed in electron

impact (EI) mass spectrometry of correspond-

ing C60

precursors, together with C58

/C60

ion

intensity ratios of up to 76% (9–13). A C58

1Institute of Problems of Chemical Physics of RussianAcademy of Sciences, Chernogolovka 142432, Russia.2Chemistry Department, Sussex University, BrightonBN1 9QJ, UK. 3School of Chemistry, University ofSouthampton, Southampton SO17 1BJ, UK.

*To whom correspondence should be addressed.E-mail: [email protected]

R E P O R T S

8 JULY 2005 VOL 309 SCIENCE www.sciencemag.org278

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 1

25 Nanoscale Mechanisms of Bone Deformation and Fracture

Peter Fratzl and Himadri S. Gupta

Max Planck Institute of Colloids and Interfaces, Department of Biomaterials,

14424 Potsdam, Germany,

E-mail: [email protected]

Bone is a biomineralized tissue with remarkable mechanical performance, specifically a

combination of large stiffness with high work to fracture. While its structure is extremely

complex and variable, extending over seven or more levels of hierarchy, its basic building

block, the mineralized collagen fibril, is rather universal. It consists of staggered arrays of

collagen molecules reinforced by nanometer sized mineral platelets. The mineral is

carbonated hydroxyapatite (dahlite) and its amount is usually thought to determine the

stiffness of the material. However, the properties of the organic matrix and the geometrical

arrangement of the organic and the mineral components at all levels of hierarchy

determine the way in which the material deforms and fractures. The hierarchical structure

is known to adapt to the biological function of the bone, and plays a critical role in

controlling its susceptibility to fracture. This chapter reviews the structural features of bone

material in the sub-micrometer range, as well as recent results on deformation and fracture

mechanisms, some of them obtained with new experimental methods based on the

diffraction of synchrotron radiation. A better knowledge of these mechanisms is crucial for

the understanding and the prevention of osteoporotic fractures, and it may serve as

inspiration for the development of new bio-inspired composite materials.

Keywords: bone, collagen, hydroxyapatite, fracture, deformation, synchrotron radiation,

diffraction, nanomechanical testing, nanocomposite, toughness


25.1 Hierarchical structure of bone The hierarchical structure of bone is thought to be optimised to achieve a

remarkable mechanical performance [1-5]. The basic building block is the mineralized

collagen fibril. Clearly, the mineral and the collagen matrix have extremely different

mechanical properties (Fig. 1). While mineral is extremely stiff and brittle, the protein

collagen is tough but much less stiff than mineral. Bone and similar mineralized tissues,

such as dentin for example, combine high toughness with reasonable stiffness (Fig. 1).

This could not be achieved by a random mixture of the two components and means that

structural design at many levels of hierarchy is required to obtain these good overall

properties.

Figure 1: Typical values of stiffness (Young’s modulus) and toughness (fracture energy) for

tissues mineralized with hydroxyapatite. The dotted lines represent the extreme cases of linear

and inverse rules of mixture for both parameters.

A great variety of structures results from the assembly of mineralised collagen fibrils, thus

allowing for the adaptation of different bones to their respective mechanical functions. In

bones such as the femoral head (Fig. 2), a dense external shell (cortical bone) is partially

filled with spongy material having pores in the sub-millimetre range (cancellous bone).

Only about 20% of the volume is filled with bone material and the rest with bone marrow.

The pores visible in cortical bone (Fig. 2b) are due to blood vessels. Cortical bone has

usually a lamellar structure (Fig. 2d) consisting of mineralised collagen fibrils assembled in

a rotated plywood-like fashion [4, 6], though other arrangements of collagen fibrils (woven

or parallel fibered) also exist. The rotated plywood structure consists of successive layers

with parallel collagen fibrils, whereby the orientation of the fibrils turns in successive

layers. In particular, each blood vessel in cortical bone is surrounded by concentric bone

lamellae. The structural unit consisting of the central channel for the blood vessel and the

surrounding lamellar material is called osteon (“O” in fig. 2b. Details of the osteon structure

are discussed in Section 25.3.

Figure 2: (a) Section through a femoral head showing the shell of cortical bone (C) and the

cancellous bone (S) inside. (b) Enlargement of the cortical bone region visualized by

backscattered electron imaging (BEI), revealing several osteons (O) corresponding to blood

vessels surrounded by concentric layers of bone material. (c) single trabecula from the


cancellous bone region. The arrows in both (b) and (c) indicate osteocyte lacunae where bone

cells have previously been living. (d) Further enlargement showing the lamellar and fibrillar

material texture around an osteocyte lacuna (OC). All pictures were taken with the scanning

electron microscope [7].

At the nanoscale, bone material consists of collagen fibrils reinforced with mineral particles

consisting essentially of carbonated hydroxyapatite. The bone forming cells (osteoblasts)

deposit the organic collageneous matrix in units called bone packets, where the mineral

particles subsequently precipitate. As a consequence both the mineral content as well as

the size of the mineral particles increases as a function of the age of a given bone packet.

Due to the permanent remodelling of existing bone tissue, whereby bone is first resorbed

by osteoclasts and later replaced by new bone formed by osteoblasts, bone packets of

different ages coexist at the same time in any bone. Typically, bone packets tend to be on

average younger when there is a fast turnover by the cells. A third type of cells deriving

from osteoblasts is trapped in bone material and my serve as strain sensors in bone.

These osteocytes (arrows in Fig. 2b and 2c and “OC” in Fig. 2d) are connected between

each other and with the outside of the tissue by a network of fine capillaries (white arrow in

Fig. 2d).

25.2 Structural design of bone at the nanoscale

At the nanoscale, bone is a composite material, consisting of an organic matrix (collagen)

in which mineral crystals are embedded. While bone mineral is stiff and brittle, the protein

is much softer and tougher [8]. Both the individual characteristics of mineral crystals and

collagen as well as the interaction between them are crucial for the mechanical

performance of bone.

The organic matrix of bone consists of collagen and a series of non-collageneous

proteins and lipids. Some 85%-90% of the total bone protein consists of collagen fibrils [9].

Type I collagen, the principal component of the organic matrix of bone, as well as other

connective tissues, is a large fibrous protein with a highly repetitive amino acid sequence

based on -Gly-X-Y- (where Gly is glycine and X, Y are often proline and hydroxyproline) [10-

12]. This repetitive sequence allows three polypeptide chains (called α chains; type I collagen

is composed of two α1 and one α2 chains) to fold into a triple-helical structure. The structure

of collagen has been studied in great detail [13-17] and the main results concern the details

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 4 of the packing of collagen molecules in the fibril [14]. The mineralized collagen fibril of

about 100 nm in diameter is the basic building block of the bone material. The 300 nm long

and 1.5 nm thick collagen molecules are deposited by the osteoblasts (bone forming cells)

into the extracellular space and then self-assemble into fibrils. Adjacent molecules are

staggered along the axial direction by D ≈ 67 nm, generating a characteristic pattern of

gap zones with 35 nm length and overlap zones with 32 nm length within the fibril [18] (Fig.

3). This banded structure of the fibril was demonstrated by TEM methods [19] and by

neutron scattering [20].

Figure 3: The mineral crystals are arranged parallel to each other and parallel to the collagen

fibrils in the bone composite, in a regularly repeating, staggered arrangement [19, 21]

Neutron scattering experiments [22] also showed that the equatorial spacing d in

non mineralized wet fibrils is about 1.6 nm, whereas in dried conditions the spacing of the

molecules is reduced to 1.1 nm. In mineralized wet bone, an intermediate d value of 1.25

nm was found. Comparison of computer modeling and SAXS experiments confirmed the

process of closer packing of the collageneous molecules when clusters of mineral crystals

replace the water within the fibril [23]. Figure 4 shows this scenario: When the packing

density of molecules increases due to water loss from drying, the typical lateral spacing

between molecules in the fibrils decreases from about 1.6 to 1.1 nm (Fig. 4 a to c). If the

water in Fig. 4a is replaced by mineral, the results may be a situation such as shown

schematically in Fig. 4d. The growing mineral particles compress the molecule packets

between them, effectively reducing the molecular spacing to the value in dry tendon. The

peak at 1.1 nm is, however, much lower and broader in the fully mineralized fibril (Fig. 4d)

than in a dry fibril (Fig. 4c), because the size of the islands with dense packing of collagen

molecules is much smaller. Hence, the mineralized fibril has an average density of

collagen molecules similar to the wet fibrils, but a typical molecular spacing similar to the

dry fibril.

Figure 4: Equatorial diffuse x-ray scattering peak showing the spacing of collagen molecules as

a function of water content (decreasing from fully wet in (a) to fully dry in (b)). The black circles

symbolize collagen molecules in the cross-section of a fibril. ρ is the number of collagen

molecules per unit surface in the fibril cross-section. Fig. 4d shows schematically a mineralized

collagen fibril. The mineral particles are elongated in the direction perpendicular to the book

page (which corresponds to the horizontal axis in Fig. 3) and are needle or plate shaped. Note


that the number of molecules in (d) is about the same as in the fully wet case (a). The average

spacing d between molecules as determined from the peak of the x-ray scattering data is about

the same in mineralized and in dry fibrils [23].

The mineral crystals are mainly flat plates [19] and are mostly arranged parallel to

each other and to the long axis of the collagen fibrils. Crystals occur at regular intervals

along the fibrils, with an approximate repeat distance of 67 nm [24], which corresponds to

the distance by which adjacent collagen molecules are staggered (Figure 3). In addition to

crystals embedded in fibrils, there is also extrafibrillar mineral [25], which probably coats

the 50-200 nm thick collagen fibrils [26]. The intrafibrillar mineral is thought to nucleate

within the gap region (groves or channels) of the collagen fibril structure [27]. These gap

regions are due to the staggered arrangement of collagen fibrils [28-30], whereby

neighbouring molecules are shifted axially by the D-period of D ≈ 67nm, while the length of

the molecules is just about 300nm. Hence, molecules extend over a little less than 5 D

periods (5 × 67 nm = 335 nm), leaving a gap of about 35 nm to the next molecule in axial

direction (Figure 3). Within the gap zones, crystal formation is triggered by collagen or –

more likely – by other non-collageneous proteins acting as nucleation centres [31]. After

nucleation, the crystals are elongated , typically plate-like [19, 32, 33], but extremely thin

and they grow in thickness later [27, 34]. In bone tissue from several different mammalian

and nonmammalian species, bone mineral crystals have a thickness of typically 1.5 to 4.5

nm [7, 25, 27, 35-38]. The basic hydroxyapatite mineral of bone — Ca5(PO4)3OH — often

contains other elements that replace either the calcium ions or the phosphate or hydroxyl

groups, one of the most common occurrences being the replacement of the phosphate

group by a carbonate group [5, 7].

The volume fraction as well as the size, shape and arrangement of the reinforcing

particles play a pivotal role in defining the mechanical properties of any composite, and

bone is no exception. In bone, the average mineral content of bone tissue is species

dependent and lies within the range of 30 to 55 volume % or 50 to 74 weight %

respectively, as measured by the ash weight/dry weight ratios, or scanning electron

microscopic methods [39-43]. However, the bone matrix, which is forming the structural

motifs of bone tissue, such as trabeculae in cancellous bone (Fig. 1c) and osteons in

compact bone (Fig. 1b), is not uniformly mineralized, but shows a pronounced local

variation at the length scale of 10 – 100 micrometers. Considering human bone matrix, its

degree of mineralization can vary between 0 to 43 vol % mineral content. Two coupled

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 6 processes are responsible for this: First, old bone matrix is continuously resorbed and

replaced by new bone (remodeling) by the activities of bone cells [44], which lay down

bone packets of width typically 5 – 10 microns at a time (lamellar width). Second, the

progressive mineralization (or maturation) of the newly formed bone matrix follows a

characteristic time course. After a lag time of 13 days the collageneous matrix starts to

mineralize rapidly up to 70% of full mineralization capacity within a few days, a

phenomenon known as primary mineralization [45]. The residual 30% of increase in

mineral content lasts for several years [46] (secondary mineralization). As a consequence,

the bone material is composed of bone packets of about 5 – 10 microns in size, each

having its own mineral content corresponding to its tissue age, which today can be best

visualized and quantified by backscattered electron imaging methods [39, 47]. These

spatial discontinuities in the bone matrix mineralization might have an important influence

on the crack initiation and propagation behavior in the material and thus are essential for

its high toughness [2, 46]. The in-vivo mineralization process is not yet fully elucidated.

The size and shape of mineral particles in bone tissue were mainly analyzed by

transmission electron microscopy [19, 21, 48] and small angle x-ray scattering [23, 27, 38,

49-51]. The majority of the studies [19, 32, 33, 52] describe the mineral particles as plate-

like in shape. A rather wide range of geometrical dimensions is reported. The thickness of

the platelets ranges from 2 to 7 nm, the length from 15 to 200 nm and the width from 10 to

80 nm45. A point of controversy in the literature of the late 1980s and early to mid 1990s

concerned the shape of the mineral particle shapes – needles [53-55] or platelets [19, 32,

52, 56-59]. One reason for the confusion was that the side-on view of the particles has the

strongest absorption contrast in the TEM, which gave the predominant needle like

impression. After more refined image analysis, platelets viewed face - on were observed

as well [60]. However, the existence of more needle-like mineral particles in bone tissues

of certain species or developmental ages can not be excluded [7, 38].

It was shown that the high stiffness and high work to fracture of the mineralized

collagen matrix of bone could be explained by a mechanical model where the stresses

were transferred via tensile strains in the mineral platelets and shear strains in the ductile

organic (collagen) matrix [61]. Such a scheme for deformation makes good use of the high

contact area between the mineral platelets and the collagen matrix, as well as the optimal

use of the high stiffness of mineral particles and high ductility of the collagen matrix.

Refined in later work [62], the model was used to explain the variation of the local

mechanical stiffness in the zone of mineralized cartilage in the human knee patella. The

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 7 nanosize thickness of mineral particles is thought responsible for the high toughness of the

collagen mineral composite [63], because very small particles are less sensitive to flaws.

25.3 Lamellar organisation of bone

Mineralized fibrils self assemble into fibril arrays (sometimes called fibres) on the scale of

1 – 10 µm. While a diversity of structural motifs exist between tissues [5], the most

common in bone is the lamellar unit [4, 6]. A lamella refers to a planar layer of bone tissue,

around 5 µm thick, which is found in a repetitive stacked arrangement in both trabecular

(spongy) and osteonal (compact) bone. In what follows, we consider lamellae belonging to

the cylindrical secondary osteon. The secondary osteon is the basic building block of

compact bone, and is essentially a hollow cylindrical laminate composite (~ 200 µm in

diameter) surrounding a blood vessel traversing the outer shaft of long bones. It is

expected to be a mechanical support as well as protective covering for the sensitive inner

vascular channel.

While the existence of the lamellar unit in bone has been known for over a century [64],

the internal structure of this basic building block and its correlation to mechanical function

have remained unclear for a long time. Light microscopic imaging led Ascenzi and co-

workers [65-67] to classify lamellae as either (a) orthogonal plywood with alternate layers

showing a fibril orientation parallel and perpendicular to the cylindrical axis of the osteon,

or (b) unidirectional plywood, with the fibril orientation predominantly parallel or

perpendicular to the osteon axis. Electron microscopic analysis by Marie Giraud-Guille and

co-workers suggested the existence of a “twisted plywood” structure [6], with fibril

orientation ranging continuously over a period of 90° across the width of the lamella.

Weiner and co-workers refined this to a “rotated plywood” configuration [4], where the

fibrils not only rotate with respect to the osteon axis, but also around their own axis across

the width of the lamella. An alternate model suggests that alternately denser and looser

packed fibrils give the impression of lamellar units in bone tissue [68]. Nonetheless, a

detailed quantitative understanding of the structure of the osteonal lamellae and its

variation across the entire osteon was, until recently, not available.

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 8 Detailed quantitative information on the osteon structure was obtained with a novel method

combining synchrotron X – ray texture measurements with a 1 µm wide beam and

rastering of a thin (3 – 5 µm thick) section of an secondary osteon in steps of 1 µm [69,

70]. The results are summarized in Figure 5, which shows the variation of the fibril

orientation across and within bone lamellae, with 1 µm spatial resolution. The fibre axis

orientation varies periodically with a period of 5 µm corresponding approximately to the

width of a single lamella. This implies that each lamella consists of a series of fibril layers

oriented at different angles to the osteon axis. What is more surprising is that the angles

are always positive, implying that on average each lamellae has a nonzero spiral fibril

angle with respect to the long axis of the osteon, with a right – handed helicity.

Figure 5: A model of the fiber orientation inside the lamellae of an osteon (a). The fibers are

arranged at different angles inside single lamellae (b). On average they have a positive spiral

angle µ, implying that on average, the fibers form a right – handed spiral around the osteon

axis, like a spring. In addition, there is a periodic variation of the spiral angle µ across the

osteon diameter (c), with a period close to the lamellar width (~ 5 µm).The spiral angle is

always positive, except when after the cross-over into the interstitial bone surrounding the

osteon (at radii larger than 40 microns).

These results thus show that osteonal lamellae are built as three – dimensional helicoids

around the central blood vessel. Such helicoidal structures have been found in other

connective tissues, for example in the secondary wood cell wall [71, 72] and in the insect

cuticle [72]. Remarkably, the sense of the helicity (right – handed) is the same for both the

bone osteon and the wood cell wall. As two structures fulfilling a similar biomechanical

support and protection function – the osteon for the inner blood vessels, and the wood cell

wall for the water/nutrient transport within the cambium – we believe they represent an

example of an optimal mechanical design used in two different phyla. Indeed, the

helicoidal principle of fiber composite design in biomaterials has been proposed as a major

unifying concept across different species [72]. Such a helicoidal structure has

biomechanical advantages as well. From a biophysical standpoint, the nonzero average

spiral angle means that the osteon is extensible (and compressible) like a spring along its

long axis. The elastic extensibility thus imparted would be useful in absorbing energy

during in – vivo mechanical loading, and may help in protecting the sensitive inner blood

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 9 vessels from being disrupted structurally by microcracks [73] propagating from the highly

calcified interstitial tissue through the osteon to the central Haversian canal.

Complementary nanomechanical investigations of the local stiffness and hardness of the

osteon revealed a modulation of micromechanical properties at the lamellar level [74, 75].

Specifically, the compressive modulus of the sublamellae within a single lamella, as

measured by nanoindentation, varied from about 17 to 23 GPa, with thin layers of lower

stiffness alternating with wider layers of higher stiffness (Figure 9). Quantitative

backscattered electron imaging was used to determine the local mineral content at the

same positions as those measured by nanoindentation. The lower axial stiffness is partly

due to the lower stiffness of a fiber normal to its long axis relative to the stiffness along its

long axis. However, the results show that the regions of lower stiffness also had a lower

mineral content, implying that the mechanical difference is not merely an anisotropy effect

but is also due to variation in composition. Hence the differently oriented sublamellae have

also a different mineral content, with the fibers at a large spiral angle being less calcified.

Mechanically, such a modulated structure could serve as a natural example of a crack

stopping mechanism. It is known that microcracks are more frequent in the surrounding

interstitial bone than in the osteon itself [76]. We speculate, therefore, that the modulated

structure at the lamellar level acts to trap microcracks from propagating from the interstitial

bone to the inner blood vessel. Modulations in yield strength and stiffness have been

shown to be effective crack stopping mechanisms in artificial multilayered composites [77-

79].

Figure 6: Two dimensional scanning nanoindentation measurements of local stiffness inside

bone osteons reveal that the lamellar structure results in a periodic mechanical modulation. (a)

Scanning force microscopy (topography) image of a sector of osteon from a polished cross-

section through a human femur, with the two – dimensional grid of indents clearly visible (inside

the white square). (b) The two dimensional plot of indentation modulus E (stiffness) at the

measured locations [75].

The lamellar organisation also leads to a dramatic orientation dependence of the fracture

properties of compact lamellar bone. Cracks propagating parallel to the lamellae need an

energy of less than 400 J/m2 while cracks cutting the lamellae need almost two orders of

magnitude more (about 10 kJ/m2) [80]. The reason is obvious in Fig. 7: While cracks are

able to split the lamellae with comparatively low amounts of energy, they are strongly

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 10 deviated at each interface between successive lamellae, because the lamellae are much

stronger then the interface between them. As a consequence, a huge amount of energy is

dissipated by the zigzagging of cracks propagating in the direction perpendicular to the

lamellae (Fig. 7).

Figure 7: crack extension energy as a function of the angle between the crack propagation

direction and the lamellae (collagen direction) and scanning electron images of corresponding

crack shapes [80].

The lamellar organisation in cancellous bone (Fig. 1c) has not been studied to the same

level of detail. However, Jaschouz et al used texture measurements to obtain the mineral

orientation in single trabeculae of human bone [81]. They found that the mineral particles

show fiber texture along the trabecular axis. It is also known that the degree of mineral

particle orientation is not constant, but increases from the embryonal stage to the mature

adult as seen in Figure 5 [34].

Figure 8: X – ray absorption micrographs of sections through human L4 vertebrae, where

lighter regions indicate bone (and darker regions are marrow) Solid lines give the direction of

mineral particles and their length is proportional to the degree of orientation. An increase in

degree of orientation and approximately 90° rotation in average orientation of mineral particles

is visible as the mineralized matrix changes from growth cartilage (GC) in (a) to cortical bone in

(b) – (c). (a) 2 months (b) 11 years and (c) 45 years.

25.4 Bone deformation at the nanoscale

Bone is a strong and, most importantly, a tough material. Toughness is associated with

large energy dissipation during crack growth, thus reducing the driving force for crack

propagation. Different toughening mechanisms were previously identified at various levels

of the hierarchical structure. For example, the formation of microcracks was visualised in

the vicinity of the main crack due to stress concentrations ahead of the crack tip [82-84].

While microcracks do not contribute to the progression of the main crack, their formation

dissipates mechanical energy. Crack deflection and crack blunting [85] at weak interfaces,

toughening mechanisms well known from composites, were attributed to the interlamellar

boundaries and the cement lines (e.g., at the secondary osteon boundaries). Recently,

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 11 crack bridging was proposed to play a dominant role in reducing the crack tip driving force

[86-88]. A major energy dissipation mechanism is crack deviation at the interfaces

between lamellae (see Figure 7, right picture).

While these mechanisms operate at the micrometer scale, irreversible deformation

mechanisms at the nanometer scale were recently discovered to also play an essential

role in increasing the bone material’s toughness. Deformation energy has been shown to

be dissipated by shearing of a thin “glue” layer between mineral-reinforced collagen fibrils

[89, 90]. The dissipation of energy was attributed to “sacrificial bonds” in collagen needing

time to re-form after pulling [26, 91] and being correlated to the time needed for bone to

recover its toughness, as measured by atomic force microscope indentation. Several other

hypotheses have been proposed on the processes occurring at the supramolecular and

molecular level, based either indirectly from (macroscopic) mechanical tests [92] or from

ex – situ observations of deformed or fracture bone using high – resolution electron

microscopy techniques [93]. These included pressure – induced phase transformations of

the apatite phase and collagen crosslink disruption as suggested by Raman spectroscopic

imaging of zones of high deformation around indents [94], creep in the hydroxyapatite

particles [92], bridging of cracks by unbroken collagen fibrils to enhance toughness [88],

plastic deformation in the collagen phase [95] and decohesion between the mineral

particles and the collagen molecules within the fibrils [96]. Recently, our group has used

time – resolved X – ray diffraction with in – situ mechanical testing to deliver quantitative

information on the deformation processes at the fibrillar level.

Figure 9: Scaled fibril strain (EF/ET)εF, where ET is the tissue modulus, and EF = 13.3 GPa is a

constant [90], as a function of tissue strain, binned in steps of tissue strain for a range. Error

bars are standard errors of mean.

Specifically, the regularity of the collagen fibril structure at the nanoscale gives rise to

coherent X – ray diffraction peaks in the small angle regime [30]. These peaks arise due to

the Hodge – Petruska packing scheme [28], in which regions of high and low electron

density alternate along the fibril axis. A quantitative measure of the fibrillar strain comes

from tracking shifts in the positions of these peaks [97]. Our results show [89, 90] that the

fibril strain is always less than the total strain. On average the fibril/tissue strain ratio is

about ½, although it can increase as the elastic modulus increases [89, 90]. To understand

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 12 the fibrillar level processes corresponding to macroscopic yielding and plasticity in bone,

we show in Figure 11 the rescaled fibril strain (E0/ET)εF, as a function of tissue strain for a

range of samples, and averaged over all samples. In the elastic regime, force balance at

the fibrillar level means that

EF εF = ET εT = macroscopic stress on the tissue.

Hence, if the stiffness of the nanometer sized mineralized fibril unit is taken as constant

between samples, then a plot of (E0/ET)εF should yield a slope of 1, as is indeed seen from

the solid guide – line in Figure 9. Beyond the yield, point, as shown by the dashed guide –

line, (E0/ET)εF approaches a constant value. While there is individual variation between

samples (resulting in large error bars) it is clear that the rescaled fibril strain saturates at a

value of about 0.5 %, and does not strain further. Since the fibrils do not relax back to zero

deformation, we infer that beyond the yield point, they are undamaged, elastic, and under

a constant nonzero stress. Interestingly, we find a similar maximal strain in partially

mineralized turkey leg tendon. This system consists of parallel fibers of mineralized and

unmineralized collagen running parallel to each other. The maximum strain attained by the

mineralized fibers in this tissue is also 0.5 %, leading us to speculate that this is the

maximum or fracture strain of fully mineralized collagen fibrils (with mineral weight

percentages of 60 – 65 % [2] ).

Figure 10: Schematic view of the interface between two mineralized collagen fibrils with a “glue

layer” providing shear deformation, according to [89, 90]. The movement of the fibrils is

indicated by white arrows. According to [24], mineralized fibrils are coated with flat mineral

particles. The white arrows symbolize the movement of the mineralized fibrils (diameter in the

order of several hundred nm), leading to shear deformation in the glue layer.

Based on these two pieces of information, a microscopic model for bone deformation at

the nanoscale was developed (Figure 10). The long (> 5 – 10 µm [26, 93, 98]) and thin

(100 – 200 nm diameter) mineralized fibrils lie parallel to each other and separated by a

thin layer (1 – 2 nm thick) of extrafibrillar matrix (shown in highly exaggerated dimension in

the Figure). When external tensile load is applied to the tissue, it is resolved into a tensile

deformation of the mineralized fibrils and a shearing deformation in the extrafibrillar matrix.

While we do not have precise data on its mechanical behaviour or its composition, it is

likely that it is comprised of noncollagenous proteins like osteopontin and proteoglycans

like decorin. Single molecule spectroscopy of fractured bone surfaces carried at by the

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 13 group of Paul Hansma showed that the extrafibrillar matrix has properties similar to a

glue–layer between the fibrils – specifically, it is relatively weak but ductile and deforms by

the successive breaking of a series of “sacrificial bonds” [26, 91]. The matrix may also be

partially calcified [99], which would increase its shear stiffness and reduce its deformability.

These results point towards a deformation mechanism where the matrix – fibril interface is

disrupted beyond the yield point, and the matrix moves past the fibrils, forming and

reforming the bonds with the fibrils as it does so. Such a situation is analogous to a

viscous flow of a liquid past a solid substrate, and likewise, for a constant velocity of flow

(constant strain rate) a constant shear stress is transmitted to the substrate (mineralized

fibril) which thus holds its strain at a nonzero value. Analogies may also be drawn to the

disaggregation and disruption of fiber bundles under strain [100]. The interface between

the stiff mineralized fibril and the weak extrafibrillar matrix is likely to be weaker than that

between the stiff mineral particles inside the fibril and the adjacent collagen molecules.

Evidence for this comes from the relative stiffness of mineral/collagen (100 GPa / 2 GPa)

[2, 8] versus mineralized fibril/extrafibrillar matrix (20 GPa / 0.1 GPa) [8, 101]

Deformation in the mineralized matrix does not only occur at the hierarchical level of the

mineralized fibril / extrafibrillar matrix alone, but can also occur at the next higher level of

the fibril arrays. We considered the case of partially mineralized collagen from mineralized

turkey leg tendons [102]. At this level, the fibrils aggregate into 1 – 4 µm diameter fiber

bundles. Backscattered electron imaging of the local mineral content at the level of the

individual bundles shows that the fibrils are inhomogeneously mineralized – a mixture of

mineralized fibrils coexists with unmineralized fiber bundles [103]. When stretched to

failure, we observe a novel two – step fracture process at the micron length scale. For low

strains below 1 – 2 %, the all the fibrils stretch homogeneously. For larger strains, the stiff

mineralized fibers break or detach from the neighbouring ductile unmineralized fibers, but

the tissue as a whole remains intact. The macroscopic cohesion comes about because the

unmineralized fibers bear the remaining load, stretching by as much as 8 – 10 %. The

breakage of the stiff component is correlated with the reduction of the slope of the stress –

strain curve (reduction in effective stiffness). By this mechanism, we believe the tendon

achieves both a high stiffness in the normal physiological regime of low working strains (<

0. 2% [104]) as well as a structural protection against sudden, traumatic loads.

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 14 While all hierarchical levels contribute to the outstanding mechanical properties of bone,

the discussion above shows that an essential contribution is due to the structure at the

nanoscale, and the way in which mineral particles are shaped and arranged in the organic

matrix. Most importantly, a thin glue layer between mineralized collagen fibrils seems to

contribute most of the plastic deformability of bone material. Surprisingly, not much is

known about the composition and structure of this layer and further research is needed to

fully elucidate its properties.

REFERENCES

[1] J. D. Currey, Journal of Bone and Mineral Research 2003, 18, 591. [2] J. D. Currey, Bones - Structure and Mechanics, Princeton University Press, Princeton, 2002. [3] J. Y. Rho, L. Kuhn-Spearing, P. Zioupos, Medical Engineering & Physics 1998, 20, 92. [4] S. Weiner, W. Traub, H. D. Wagner, Journal of Structural Biology 1999, 126, 241. [5] S. Weiner, H. D. Wagner, Annual Review of Materials Science 1998, 28, 271. [6] M. M. Giraudguille, Calcified Tissue International 1988, 42, 167. [7] P. Fratzl, H. S. Gupta, E. P. Paschalis, P. Roschger, Journal of Materials Chemistry 2004,

14, 2115. [8] S. A. Wainwright, W. D. Biggs, J. D. Currey, J. M. Gosline, Mechanical design in

organisms, Princeton University Press, Princeton, New Jersey, 1982. [9] J. D. Termine, P. G. Robey, in Primer on the Metabolic Bone Diseases and Disorders of

Mineral Metabolism, 3rd Edition, An Official Publication of the American Society for Bone and Mineral Research (Ed.: M. J. Favus), Lippincott-Raven Publishers, 1996.

[10] D. J. Prockop, K. I. Kivirikko, N Engl J Med 1984, 311, 376. [11] D. J. Prockop, K. I. Kivirikko, Annual Review of Biochemistry 1995, 64, 403. [12] M. Yamauchi, in Calcium and Phosphorus in Health and Disease (Eds.: J. J. B. Anderson,

S. C. Garner), CRC Press, New York, 1996, pp. 127. [13] A. Bigi, A. Ripamonti, G. Cojazzi, G. Pizzuto, N. Roveri, M. H. J. Koch, International

Journal of Biological Macromolecules 1991, 13, 110. [14] P. Fratzl, Current Opinion in Colloid & Interface Science 2003, 8, 32. [15] T. Gutsmann, G. E. Fantner, M. Venturoni, A. Ekani-Nkodo, J. B. Thompson, J. H. Kindt,

D. E. Morse, D. K. Fygenson, P. K. Hansma, Biophysical Journal 2003, 84, 2593. [16] D. J. S. Hulmes, T. J. Wess, D. J. Prockop, P. Fratzl, Biophysical Journal 1995, 68, 1661. [17] K. Misof, G. Rapp, P. Fratzl, Biophysical Journal 1997, 72, 1376. [18] A. J. Hodge, J. A. Petruska, in Aspects of protein structure (Ed.: G. N. Ramachandran),

Academic, New York, 1963, pp. 289. [19] W. J. Landis, K. J. Hodgens, J. Arena, M. J. Song, B. F. McEwen, Microscopy Research

and Technique 1996, 33, 192. [20] S. W. White, D. J. S. Hulmes, A. Miller, P. A. Timmins, Nature 1977, 266, 421. [21] W. J. Landis, Connective Tissue Research 1996, 35, 1. [22] S. Lees, H. A. Mook, Calcified Tissue International 1986, 39, 291. [23] P. Fratzl, N. Fratzlzelman, K. Klaushofer, Biophysical Journal 1993, 64, 260. [24] T. Hassenkam, G. E. Fantner, J. A. Cutroni, J. C. Weaver, D. E. Morse, P. K. Hansma, Bone

2004, 35, 4.

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 15 [25] M. A. Rubin, J. Rubin, W. Jasiuk, Bone 2004, 35, 11. [26] G. Fantner, T. Hassenkam, J. H. Kindt, J. C. Weaver, H. Birkedal, L. Pechenik, J. A.

Cutroni, G. A. G. Cidade, G. D. Stucky, D. E. Morse, P. K. Hansma, Nature Materials 2005, 4, 612.

[27] P. Fratzl, N. Fratzl-Zelman, K. Klaushofer, G. Vogl, K. Koller, Calcified Tissue International 1991, 48, 407.

[28] A. J. Hodge, J. A. Petruska, (Ed.: G. N. Ramachandran), Academic Press, New York, 1963, pp. 289.

[29] A. Veis, Current Opinion in Solid State & Materials Science 1997, 2, 370. [30] T. J. Wess, in Fibrous Proteins: Coiled-Coils, Collagen and Elastomers, Vol. 70 (Eds.: D.

Parry, J. Squire), Elsevier Inc., Burlington, 2005, pp. 341. [31] J. Sodek, B. Ganss, M. D. McKee, Critical Reviews in Oral Biology & Medicine 2000, 11,

279. [32] W. J. Landis, K. J. Hodgens, M. J. Song, J. Arena, S. Kiyonaga, M. Marko, C. Owen, B. F.

McEwen, J. Struct. Biol. 1996, 117, 24. [33] W. Traub, T. Arad, S. Weiner, Matrix 1992, 12, 251. [34] P. Roschger, B. M. Grabner, S. Rinnerthaler, W. Tesch, M. Kneissel, A. Berzlanovich, K.

Klaushofer, P. Fratzl, Journal of Structural Biology 2001, 136, 126. [35] M. J. Glimcher, Phil. Trans. R. Soc. Lond. B 1984, 304, 479. [36] M. Grynpas, L. C. Bonar, M. J. Glimcher, J. Material. Sci. 1985, 19. [37] A. S. Posner, Clin. Orthop. 1985, 200, 87. [38] P. Fratzl, M. Groschner, G. Vogl, H. Plenk, J. Eschberger, N. Fratzlzelman, K. Koller, K.

Klaushofer, Journal of Bone and Mineral Research 1992, 7, 329. [39] R. D. Bloebaum, J. G. Skedros, E. G. Vajda, K. N. Bachus, B. R. Constantz, Bone 1997, 20,

485. [40] P. Roschger, H. P. jr, K. Klaushofer, J. Eschberger, Scanning. Microsc. 1995, 9, 75. [41] K. Akesson, M. D. Grynpas, R. G. V. Hancock, R. Odselius, K. J. Obrant, Calcif. Tissue Int.

1994, 55, 236. [42] P. Roschger, P. Fratzl, J. Eschberger, K. Klaushofer, Bone 1998, 23, 319. [43] P. Roschger, H. S. Gupta, A. Berzanovich, G. Ittner, D. W. Dempster, P. Fratzl, F. Cosman,

M. Parisien, R. Lindsay, J. W. Nieves, K. Klaushofer, Bone 2003, 32, 316. [44] E. F. Eriksen, D. W. Axelrod, F. Melsen, in Bone Histomorphometry, Raven Press, New

York., 1994. [45] B. M. Misof, P. Roschger, F. Cosman, E. S. Kurland, W. Tesch, P. Messmer, D. W.

Dempster, J. Nieves, E. Shane, P. Fratzl, K.Klaushofer, J. Bilezikian, R. Lindsay, J. Clin. Endocrinol, Metab. 2003, 88, 150.

[46] O. Akkus, A. Polyakova-Akkus, F. Adar, M. B. Schaffler, J. Bone Miner. Res. 2003, 18, 1012.

[47] A. Boyde, R. Travers, F.H., Glorieux, S. J. Jones, Calcif. Tissue Int. 1999, 185. [48] S. Weiner, W. Traub, Faseb Journal 1992, 6, 879. [49] P. Fratzl, J. Appl. Cryst. 2003, 36, 397. [50] O. Paris, I. Zizak, H. Lichtenegger, P. Roschger, K. Klaushofer, P. Fratzl, Cellular and

Molecular Biology 2000, 46, 993. [51] S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, P. Fratzl, Calcified

Tissue International 1999, 64, 422. [52] W. J. Landis, M. J. Song, A. Leith, L. Mcewen, B. F. Mcewen, Journal of Structural

Biology 1993, 110, 39. [53] U. Plate, S. Arnold, L. Reimer, H. J. Hohling, A. Boyde, Cell and Tissue Research 1994,

278, 543.

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 16 [54] H. J. Hohling, S. Arnold, R. H. Barckhaus, U. Plate, H. P. Wiesmann, Connective Tissue

Research 1995, 32, 493. [55] S. Arnold, U. Plate, H. P. Wiesmann, U. Stratmann, H. Kohl, H. J. Hohling, Journal of

Microscopy-Oxford 1999, 195, 58. [56] A. L. Arsenault, Bone and Mineral 1989, 6, 165. [57] A. L. Arsenault, Bone and Mineral 1992, 17, 253. [58] S. Weiner, W. Traub, Connective Tissue Research 1989, 21, 589. [59] W. Traub, T. Arad, S. Weiner, Journal of Cellular Biochemistry 1993, 145. [60] M. A. I. Jasiuk, J. Taylor, J. Rubin, T. Ganey, R. P. Apkarian, Bone 2003, 33, 270. [61] I. Jager, P. Fratzl, Biophysical Journal 2000, 79, 1737. [62] H. S. Gupta, S. Schratter, W. Tesch, P. Roschger, A. Berzlanovich, T. Schoeberl, K.

Klaushofer, P. Fratzl, Journal of Structural Biology 2005, 149, 138. [63] H. J. Gao, B. H. Ji, I. L. Jager, E. Arzt, P. Fratzl, Proceedings of the National Academy of

Sciences of the United States of America 2003, 100, 5597. [64] W. Gebhardt, Arch. Entwickl. Mech. Org. 1906, 20, 187. [65] A. Boyde, P. Bianco, M. P. Barbos, A. Ascenzi, Metabolic Bone Disease & Related

Research 1984, 5, 299. [66] M. P. Barbos, P. Bianco, A. Ascenzi, A. Boyde, Metabolic Bone Disease & Related

Research 1984, 5, 309. [67] A. Ascenzi, E. Bonucci, Bocciare.Ds, Journal of Ultrastructure Research 1965, 12, 287. [68] G. Marotti, M. A. Muglia, C. Palumbo, Clinical Rheumatology 1994, 13, 63. [69] W. Wagermaier, H. S. Gupta, A. Gourrier, M. Burghammer, P. Roschger, P. Fratzl,

Biointerphases 2006, 1, 1. [70] W. Wagermaier, H. S. Gupta, A. Gourrier, O. Paris, P. Roschger, M. Burghammer, C.

Riekel, P. Fratzl, Journal of Applied Crystallography 2006, submitted. [71] H. Lichtenegger, A. Reiterer, S. E. Stanzl-Tschegg, P. Fratzl, Journal of Structural Biology

1999, 128, 257. [72] A. C. Neville, Biology of fibrous composites: Development beyond the cell membrane,

Cambridge University Press, New York, NY, 1993. [73] P. Zioupos, Journal of Biomechanics 1999, 32, 209. [74] U. Stachewicz, Max Planck Institute of Colloids and Interfaces (Potsdam), 2004. [75] H. S. Gupta, U. Stachewicz, W. Wagermaier, P. Roschger, H. D. Wagner, P. Fratzl,

Journal of Materials Research 2006, in press. [76] S. J. Qiu, D. S. Rao, D. P. Fyhrie, S. Palnitkar, A. M. Parfitt, Bone 2005, 37, 10. [77] S. Suresh, Y. Sugimura, T. Ogawa, Scripta Metallurgica Et Materialia 1993, 29, 237. [78] N. K. Simha, F. D. Fischer, O. Kolednik, C. R. Chen, Journal of the Mechanics and Physics

of Solids 2003, 51, 209. [79] O. Kolednik, International Journal of Solids and Structures 2000, 37, 781. [80] H. Peterlik, P. Roschger, K. Klaushofer, P. Fratzl, Nature Materials 2006, 5, 52. [81] D. Jaschouz, O. Paris, P. Roschger, H. S. Hwang, P. Fratzl, Journal of Applied

Crystallography 2003, 36, 494. [82] P. Zioupos, J. D. Currey, A. J. Sedman, Med. Engng. & Phys. 1994, 16, 203. [83] P. Zioupos, X. T. Wang, J. D. Currey, Journal of Biomechanics 1996, 29, 989. [84] D. Vashishth, K. E. Tanner, W. Bonfield, Journal of Biomechanics 2003, 36, 121. [85] D. M. Liu, S. Weiner, H. D. Wagner, Journal of Biomechanics 1999, 32, 647. [86] R. K. Nalla, J. H. Kinney, R. O. Ritchie, Nature Materials 2003, 2, 164. [87] R. K. Nalla, J. J. Kruzic, J. H. Kinney, R. O. Ritchie, Biomaterials 2005, 26, 217. [88] R. K. Nalla, J. J. Kruzic, R. O. Ritchie, Bone 2004, 34, 790. [89] H. S. Gupta, W. Wagermaier, G. A. Zickler, D. R. B. Aroush, S. S. Funari, P. Roschger, H.

D. Wagner, P. Fratzl, Nano Letters 2005, 5, 2108.

P. Fratzl & H. S. Gupta Handbook of Biomineralization Vol.1, Chapter 25 17 [90] H. S. Gupta, W. Wagermaier, G. A. Zickler, J. Hartmann, S. S. Funari, P. Roschger, H. D.

Wagner, P. Fratzl, International Journal of Fracture 2006, in press. [91] J. B. Thompson, J. H. Kindt, B. Drake, H. G. Hansma, D. E. Morse, P. K. Hansma, Nature

2001, 414, 773. [92] M. Fondrk, E. Bahniuk, D. T. Davy, C. Michaels, Journal of Biomechanics 1988, 21, 623. [93] P. Braidotti, E. Bemporad, T. D'Alessio, S. A. Sciuto, L. Stagni, Journal of Biomechanics

2000, 33, 1153. [94] A. Carden, R. M. Rajachar, M. D. Morris, D. H. Kohn, Calcified Tissue International 2003,

72, 166. [95] D. T. Reilly, A. H. Burstein, Journal of Biomechanics 1975, 8, 393. [96] C. Mercer, M. Y. He, R. Wang, A. G. Evans, Acta Biomaterialia 2006, 2, 59. [97] P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, S. Bernstorff, Journal of Structural

Biology 1998, 122, 119. [98] A. S. Craig, M. J. Birtles, J. F. Conway, D. A. D. Parry, Connective Tissue Research 1989,

19, 51. [99] L. C. Bonar, S. Lees, H. A. Mook, Journal of Molecular Biology 1985, 181, 265. [100] D. Hull, T. W. Clyne, An introduction to composite materials, 2nd edition ed., Cambridge

University Press, Cambridge, UK, 1996. [101] G. E. Fantner, E. Oroudjev, G. Schitter, L. S. Golde, P. Thurner, M. M. Finch, P. Turner, T.

Gutsmann, D. E. Morse, H. Hansma, P. K. Hansma, Biophysical Journal 2006, 90, 1411. [102] H. S. Gupta, P. Messmer, P. Roschger, S. Bernstorff, K. Klaushofer, P. Fratzl, Physical

Review Letters 2004, 93, 158101. [103] H. S. Gupta, P. Roschger, I. Zizak, N. Fratzl-Zelman, A. Nader, K. Klaushofer, P. Fratzl,

Calcified Tissue International 2003, 72, 567. [104] D. B. Burr, C. Milgrom, D. Fyhrie, M. Forwood, M. Nyska, A. Finestone, S. Hoshaw, E.

Saiag, A. Simkin, Bone 1996, 18, 405.

1

Figure 1

toug

hnes

s[k

J/m

2 ]

stiffness [GPa]1 10 100

100

1

0.1

0.01

0.001

antler

bone

enamel

hydroxyapatite

dentin

collagen10

toug

hnes

s[k

J/m

2 ]

stiffness [GPa]1 10 100

100

1

0.1

0.01

0.001

antler

bone

enamel

hydroxyapatite

dentin

collagen10

Figure 2

100 µm

OC

5 µm

20 mm

(a)

(b) (c)

(d)

O

CS

100 µm 100 µm 100 µm 100 µm

OC

5 µm5 µm

20 mm20 mm

(a)

(b) (c)

(d)

O

CS

2

Figure 3

(a)

(b) (c)

Figure 4

0 5 Q (nm-1)0 50 50 5

1.6 1.4 1.11.1 d (nm)

0.27 0.50 0.63 0.27 ρ (nm-2)

(a) (b) (c) (d)

0 5 Q (nm-1)0 5 Q (nm-1)0 5 Q (nm-1)0 50 50 50 50 50 50 50 50 5

1.6 1.4 1.11.1 d (nm)

0.27 0.50 0.63 0.27 ρ (nm-2)

(a) (b) (c) (d)

3

Figure 5

(a)

(c) (b)

Figure 6

µm0 5 10 15 20

µm

0

5

10

15

20

20 22 24 26 28

E (GPa)

(a) (b)

4

Figure 7

0

2000

4000

6000

8000

10000

12000

14000a

b

375 J m-2

9920 J m-2

orientation ofcollagen fibrils

loading direction

crack pathα

γ

crac

k ex

tens

ion

ener

gy [

J m

-2]

0

2000

4000

6000

8000

10000

12000

14000a

b

375 J m-2

9920 J m-2

orientation ofcollagen fibrils

loading direction

crack pathα

γ orientation ofcollagen fibrils

loading direction

crack pathα

γ

crac

k ex

tens

ion

ener

gy [

J m

-2]

0 20 40 60 800 20 40 60 80

angle to collagen direction (°)

10 µm

Figure 8

5

Figure 9

Figure 10

Mineralized fibrils

mineral particleson fibril surface

molecular „glue“ layer

Collagen fibril bundle

peter fratzl lecture notes

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