Modelling polymer interactions of the ‘molecular Velcro’ type in wood under mechanical stress

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Abstract

Trees withstand wind and snow loads by synthesising wood that varies greatly in mechanical properties: flexible in twigs and in the stem of the sapling, and rigid in the outer part of the mature stem. The ‘molecular Velcro’ model of Keckes et al. [2003. Cell-wall recovery after irreversible deformation of wood. Nat. Mater. 2, 810–814] permits the simulation of the tensile properties of water-saturated wood as found in living trees. A basic feature of this model is the presence of non-covalent interactions between hemicellulose chains attached to adjacent cellulose microfibrils, which are disrupted above a threshold level of interfibrillar shear. However, other evidence does not confirm the importance of hemicellulose–hemicellulose association in the cohesion of the interfibrillar matrix. Here, we present an alternative model in which hemicellulose chains bridging continuously from one microfibril aggregate (macrofibril) to the next provide most of the cohesion. We show that such hemicellulose bridges exist and that the stripping of the bridging chains from the cellulose surfaces under the tensile stress component normal to the macrofibrils can provide an alternative triggering mechanism for shear deformation between one macrofibril and the next. When one macrofibril then slides past another, a domain of the wood cell wall can extend but simultaneously it twists until the spacing between macrofibrils is reduced again and contact through hemicelluloses bridges is restored. Overall deformation therefore takes place through a series of local stick–slip events involving temporary twisting of small domains within the wood cell wall. Modelled load–deformation curves for this modified ‘molecular Velcro’ model are similar, although not identical, to those for the original model. However, the mechanism is different and more consistent with current views of the structure of wood cell walls, providing a framework within which the developmental control of rigidity in wood synthesised in different parts of a tree may be considered.

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 asDh=φMh1/3where 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.

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