Modelling polymer interactions of the ‘molecular Velcro’ type in wood under mechanical stress
Introduction
To withstand the physical stresses imposed by its environment, a tall tree needs to direct a very large investment of fixed carbon into wood. That is why wood is the most abundant organic material on the planet (Gower, 2003). The scale of the investment means that there are strong adaptive advantages in tailoring the structure of wood and the structure of the tree to cope with the physical demands of the environment as economically as possible. There are many kinds of evidence that this adaptive process has been very effective. For example, the hydraulic and structural functions of wood—transmitting water and providing mechanical strength—are met independently but are so effectively combined that their relative importance is quite hard to disentangle (Koch et al., 2004; Niklas, 2007; Rosner et al., 2007). The strength of a typical conifer trunk is sufficient to withstand almost all winds that the tree will meet during its lifetime, but is balanced against the strength of the root anchorage so that neither greatly exceeds the other (Peltola et al., 2000) and a mixture of uprooted and broken trees is commonly found after an exceptional storm (Braun et al., 2003).
Likewise, economy in the use of fixed carbon to build the above-ground section of a tree can be achieved if every part of it approaches breaking point simultaneously, and it is a common observation that the main stems and branches of trees are tapered in such a way that bending stresses remain approximately uniform along their length (Morgan and Cannell, 1994). Dean et al. (2002) expressed a simplified form of this uniform stress hypothesis aswhere Dh is the diameter, Mh is the bending moment at height h, and φ is a fitted coefficient inversely related to the structural bending modulus of the wood, Estruct (Spatz and Bruechert, 2000). Estruct is defined on the assumption that the mechanical properties of the wood are constant throughout the cross-section of the tree stem at any given height. In this version of the hypothesis, it is additionally assumed, for simplicity, that Estruct and therefore φ are constant throughout the tree so that only the dimensions, i.e. diameter and taper, are tailored to meet the mechanical stresses imposed by the environment.
This simple form of the uniform-stress hypothesis involves many further approximations. It was originally derived for wind speeds so low that the tree remains almost vertical and the gravitational contribution to bending can be neglected (Dean et al., 2002). The distribution of bending load varies with wind speed (Morgan and Cannell, 1994) and differs when frozen ground prevents root movement (Peltola et al., 2000) or when deciduous trees are without foliage (McMahon and Kronauer, 1976). Also the response of trees to wind is dynamic (Moore and Maguire, 2004) and wind gradients vary with turbulence and topography (Marshall et al., 2002; Vosper et al., 2002). Snow and ice add vertical loads (Proulx et al., 2001; Nishimura 2005).
The simplifying approximation that Estruct (or φ) remains constant has been critically examined in a number of studies. Where axial variation is found within the main stem, Estruct generally declines with height (Bruchert and Gardiner, 2006; Dean et al., 2002; Spatz and Bruechert, 2000). Branches, especially those high in the tree, have lower Estruct than the main stem in conifers (Spatz and Bruechert, 2000) and broadleaved trees (Niklas and Spatz, 2000). That is, the wood in a tree becomes more flexible towards the periphery of the crown, consistent with the reduced importance of Euler buckling under the weight above (McMahon and Kronauer, 1976) and with the increasing potential for flexible peripheral branches to shed wind or snow loads by bending. Elastic streamlining of the crown can reduce its frontal area by up to 60% in strong winds (Gardiner et al., 2000; Vollsinger et al., 2005).
Nevertheless, the mature main stems of eight of the nine conifer species examined by Dean et al. (2002) tapered in a way that matched their formulation of the uniform stress hypothesis quite closely, consistent with the assumption that Estruct remains approximately constant as observed by Morgan and Cannell (1994).
It might therefore be suggested that the mechanical properties of the wood do not vary much throughout the tree, but that is completely incorrect. The structural bending modulus Estruct is itself a composite parameter. At a given height in the stem the local longitudinal modulus, E varies across each annual ring and increases from pith to bark, with stiffer and denser wood being laid down as the tree matures (Koponen et al., 2005; Thibaut et al., 2001). The range in E across one radius may be as much as a factor of 10 (Cowdrey and Preston, 1966). In the lower trunk of a mature tree, the overall Estruct is dominated by the stiff outer rings furthest from the bending axis, but the variation in E from the pith outwards preserves a chronological record of changing mechanical strategy, progressing from flexibility to let the sapling shed wind load by bending (Rudnicki et al., 2004), to rigidity against buckling at maturity.
Thus the wood within a single tree does indeed vary in its mechanical properties, and how this variation comes about is a significant element in the developmental biomechanics of trees. Because wood is a major engineering material there is no lack of theory relating its mechanical performance to its structure (Barnett and Bonham, 2004; Navi et al., 1995; Salmén, 2004; Yamamoto and Kojima, 2002). However, current constitutive models are not directly applicable to wood in living trees, for two reasons: these models are formulated for dry wood and they are restricted to small deformations. For example: strictly E and Estruct describe the initial, linear portion of the load–deformation curve but the measurements of Spatz and Bruechert (2000) on small spruce branches showed that their load–deformation behaviour at large deformations became strongly non-linear, with large increases in bending from small increases in load. Such behaviour is consistent with shedding loads, rather than resisting them as in most engineering structures. But a sapling cannot tolerate damage as part of the cost of this flexibility, because then both its ability to withstand future storms and its capacity for water transport would be compromised.
The ‘molecular Velcro’ model of Keckes et al. (2003) differs from other models of wood deformation in being supported by experiments on single, hydrated wood cells, which are capable of large deformations in tension without subsequent loss of mechanical performance; that is, without apparent damage. In principle, therefore, this model is applicable to wood in living trees. Because its starting point is at the scale of polymer molecules its prospects for linking mechanics to genomic data are perhaps better than for ‘top-down’ constitutive models.
In this paper, we explore the structural basis of the ‘molecular Velcro’ model, identifying some inconsistencies with current understanding of wood nanostructure. With the aim of providing insights into the structural basis of developmental variation in wood stiffness, we propose a new model based on a different principle at the molecular level. The new model remains relevant to the high water contents and large deformations found in living trees. It will first be necessary to review the current understanding of the structure of wood at the nanometre scale, before the deformation of the structure can be examined.
Section snippets
Polymer composition of coniferous wood
Wood is a biocomposite based on cellulose fibres or microfibrils that are at least several micrometres in length, oriented at the microfibril angle to the cell axis (Harrington et al., 1998). The cell axis corresponds to the local grain of the wood and, approximately, to the developmental axis of the tree. In the longitudinal direction, the tensile properties of wood depend strongly on the microfibril angle. When allowance is made for density the increasing rigidity from pith to bark, and from
Geometry of hemicellulose bridges
Fratzl et al. (2004a) did not recognise the presence of macrofibrils and assumed that each microfibril was displaced with respect to the next when the material deforms under tension, but this assumption is not in fact essential to the model that they present. Most features of their model can be retained if shear occurs between macrofibrils rather than microfibrils. We therefore examine the rather complex evidence concerning polymer structures between macrofibrils.
The experiments of Navi and
Discussion
Both models (Figs. 7A and B) capture the distinctive features of the experimental data on which the original ‘molecular Velcro’ model was based (Fratzl et al., 2004a; Keckes et al., 2003) and which are supported by more recent experimental data (Burgert et al., 2004, Burgert et al., 2005; Kamiyama et al., 2005; Kölln et al., 2005; Sedighi-Gilani and Navi, 2007). Despite the fundamental differences in the underlying mechanisms, load–deformation experiments of high precision would be required to
Acknowledgments
We thank the Scottish Higher Education Funding Council for financial support through the Scottish Integrated Research in Timber (SIRT) project. We also thank Dr. Ingo Burgert for helpful comments on a draft of the manuscript.
References (91)
- et al.
Interactions between wood polymers studied by dynamic FT-IR spectroscopy
Polymer
(2001) - et al.
Experimental evidence for a semi-flexible conformation for arabinoxylans
Carbohyd. Res.
(2001) - et al.
Comparison of two models for predicting the critical wind speeds required to damage coniferous trees
Ecol. Model.
(2000) - et al.
NMR structural determination of dissolved O-acetylated galactoglucomannan isolated from spruce thermomechanical pulp
Carbohyd. Res.
(2004) - et al.
Size and arrangement of elementary cellulose fibrils in wood cells—a small-angle X-ray-scattering study of Picea abies
J. Struct. Biol.
(1994) - et al.
Structural differences of xylans affect their interaction with cellulose
Carbohydrate Polym.
(2007) - et al.
Studies of the structural change during deformation in Cryptomeria japonica by time-resolved synchrotron small-angle X-ray scattering
J. Struct. Biol.
(2005) - et al.
Isolation and characterization of galactoglucomannan from spruce (Picea abies)
Carbohyd. Polym.
(2002) - et al.
Computer simulation studies of microcrystalline cellulose I beta
Carbohyd. Res.
(2006) - et al.
Tree structures—deducing principle of mechanical design
J. Theor. Biol.
(1976)
Tree characteristics related to stem breakage of Picea glehnii and Abies sachalinensis
For. Ecol. Manage.
Mechanical stability of Scots pine, Norway spruce and birch: an analysis of tree-pulling experiments in Finland
For. Ecol. Manage.
Conformation of galactomannan: experimental and modelling approaches
Food Hydrocolloid.
On the chain flexibility of arabinoxylans and other beta-(l -> 4) polysaccharides
Carbohyd. Res.
Micromechanical understanding of the cell-wall structure
C. R. Biol.
Basic biomechanics of self-supporting plants: wind loads and gravitational loads on a Norway spruce tree
For. Ecol. Manage.
Formation of macromolecular lignin in ginkgo xylem cell walls as observed by field emission scanning electron microscopy
C. R. Biol.
Mechanics of wood and trees: some new highlights for an old story
C. R. De L Academie Des Sciences Serie Ii Fascicule B—Mecanique
Wood Hemicelluloses. 1
Adv. Carbohyd. Chem.
Wood hemicelluloses. 2
Adv. Carbohyd. Chem.
Assignment of non-crystalline forms in cellulose I by CP/MAS C-13 NMR spectroscopy
Carbohyd. Res.
Characterisation of thermally modified hard- and softwoods by C-13 CPMAS NMR
Carbohyd. Polym.
Characterisation of water-soluble galactoglucomannans from Norway spruce wood and thermomechanical pulp
Carbohyd. Polym.
Softening of wood polymers induced by moisture studied by dynamic FTIR spectroscopy
J. Appl. Polym. Sci.
Spatial relationships between polymers in Sitka spruce: proton spin-diffusion studies
Holzforschung
Studies of crystallinity of Scots pine and Norway spruce cellulose
Trees—Struct. Funct.
Xylan deposition on secondary wall of Fagus crenata fiber
Protoplasma
Cellulose microfibril angle in the cell wall of wood fibres
Biol. Rev.
Comment on the structure of amorphous starch as derived from precursors of crystallization: the role of the entanglement network
J. Macromol. Sci.—Phys. B
Forest damages by the storm ‘Lothar’ in permanent observation plots in Switzerland: the significance of soil acidification and nitrogen deposition
Water Air Soil Poll.
The effect of wind exposure on the tree aerial architecture and biomechanics of Sitka Spruce (Picea sitchensis, Pinaceae)
Am. J. Bot.
Adaptive growth of gymnosperm branches—ultrastructural and micromechanical examinations
J. Plant Growth Regul.
Structure–function relationships of four compression wood types: micromechanical properties at the tissue and fibre level
Trees—Struct. Funct.
Properties of chemically and mechanically isolated fibres of spruce (Picea abies L. Karst.). Part 2: Twisting phenomena
Holzforschung
Elasticity and microfibrillar angle in wood of Sitka Spruce
Proc. R. Soc. Ser. B—Biol. Sci.
Modeling of arabinofuranose and arabinan. 2. Nmr and conformational-analysis of Arabinobiose and Arabinan
Biopolymers
An evaluation of the uniform stress hypothesis based on stem geometry in selected North American conifers
Trees—Struct. Funct.
A three-dimensional computer model of the tracheid cell wall as a tool for interpretation of wood cell wall ultrastructure
Iawa J.
Bridge-like structures between cellulose microfibrils in radiata pine (Pinus radiata D. Don) Kraft pulp and holocellulose
Holzforschung
The influence of hemicellulose on fibril aggregation of kraft pulp fibres as revealed by FE-SEM and CP/MAS C-13-NMR
Cellulose
Pore and matrix distribution in the fiber wall revealed by atomic force microscopy and image analysis
Biomacromolecules
Cellulose microfibril angles in a spruce branch and mechanical implications
J. Mater. Sci.
Mechanical model for the deformation of the wood cell wall
Z. Metallkund.
On the role of interface polymers for the mechanics of natural polymeric composites
Phys. Chem. Chem. Phys.
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