Saswati Pujari

Leah Dougherty

Christophe Mobuchon

Pierre J Carreau

Marie-Claude Heuzey

Wesley R Burghardt
email: w-burghardt@northwestern.edu

Marie-Claude Heuzey

M.-C Heuzey

X-ray scattering measurements of particle orientation in a sheared polymer/clay dispersion

Keywords: Nanocomposite, X-ray scattering, Particle orientation

come

Introduction

The addition of layered silicates to polymers is an important method to produce new and improved materials. Relative to neat polymers, clay nanocomposites have shown enhanced mechanical and flame retardant properties, increased dimensional stability, and reduced permeability [START_REF] Kojima | Gas permeabilities in rubber clay hybrid[END_REF][START_REF] Giannelis | Polymer layered silicate nanocomposites[END_REF][START_REF] Fornes | Nylon 6 nanocomposites: the effect of matrix molecular weight[END_REF][START_REF] Nam | A hierarchical structure and properties of intercalated polypropylene/clay nanocomposites[END_REF]. A variety of polymer matrices, including polyamides, polystyrene, and polypropylene, have been used to produce clay nanocomposites [START_REF] Okada | Synthesis and characterization of a nylon 6-clay hybrid[END_REF][START_REF] Giannelis | Polymersilicate nanocomposites: model systems for confined polymers and polymer brushes[END_REF][START_REF] Alexandre | Polymer-layered silicate nanocomposites: preparation, properties and uses of a new class of materials[END_REF][START_REF] Fornes | Nylon 6 nanocomposites: the effect of matrix molecular weight[END_REF]. In all nanocomposites, achieving the desired property improvements requires understanding and control of the structure of the dispersed clay particles. Nanocomposite properties will depend critically on two aspects of structure: the relative position of the clay particles with respect to each other (especially the degree of exfoliation of individual nanoscale clay sheets) and the orientation distribution of the dispersed clay particles. Thermodynamics is expected to play a central role in determining the equilibrium state of dispersion [START_REF] Balazs | Predicting the morphology of nanostructured composites[END_REF]; however, flow fields during processingeither in nanocomposite preparation, or production of final products-will also significantly influence the nanocomposite structure. Thus, to design nanocomposites with stable dispersed states and desired final properties, it is important to study structural changes taking place during flow.

Rheology is an important tool for interrogating flowinduced structural changes in polymer nanocomposites [START_REF] Vermant | Quantifying dispersion of layered nanocomposites via melt rheology[END_REF]). Many researchers have reported rheological phenomena such as the emergence of a solid-like low frequency shear modulus [START_REF] Galgali | A rheological study on the kinetics of hybrid formation in polypropylene nanocomposites[END_REF][START_REF] Krishnamoorti | Rheology of polymer layered silicate nanocomposites[END_REF][START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF][START_REF] Aubry | Rheological investigation of the melt state elastic and yield properties of a polyamide-12 layered silicate nanocomposite[END_REF][START_REF] Xu | Structure and melt rheology of polystyrene-based layered silicate nanocomposites[END_REF] and nonlinear behavior in transient flow conditions [START_REF] Lim | Phase morphology and rheological behavior of polymer/layered silicate nanocomposites[END_REF][START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF][START_REF] Koo | Mechanical and rheological properties of the maleated polypropylene-layered silicate nanocomposites with different morphology[END_REF][START_REF] Ren | Nonlinear viscoelastic properties of layered-silicate-based intercalated nanocomposites[END_REF][START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF]). Both linear and nonlinear rheology are sensitive to microstructural changes, and each provides a means to study the structural state of clay nanocomposites in the melt state. However, the observed rheological behavior may be influenced by several factors, such as particle orientation induced by the external flow field, interparticle interactions and associated formation of percolated network structures, and possible direct coupling between polymer and particle dynamics. Such complexity places limitations on rheology-by itself-as a structural characterization tool.

Kinetics of structural relaxation in clay nanocomposites have been studied by [START_REF] Ren | Nonlinear viscoelastic properties of layered-silicate-based intercalated nanocomposites[END_REF] using linear viscoelastic measurements. These studies found that the increase in storage modulus was independent of the nanoparticle size, temperature and viscosity of the polymeric matrix, leading to the conclusion that, in the system studied, the underlying structural changes were not a consequence of Brownian randomization. [START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF] observed that stress overshoots following reversal of steady shear flow were dependent on the rest time before reversal. The magnitude of the overshoot increased with increasing rest time, but over time scales much shorter than that expected for Brownian rotation in such systems. [START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF] thus concluded that the reorientation of structure was due to attractive interactions between the clay platelets and not due to Brownian motion. [START_REF] Lele | In situ rheox-ray investigation of flow-induced orientation in layered silicate-syndiotactic polypropylene nanocomposite melt[END_REF] reported relaxation of orientation after steady pre-shearing using both rheology and in situ X-ray diffraction. The time scales for relaxation were found to be shorter than the time scale required for Brownian relaxation. However, since they found that an uncompatibilized clay dispersion showed slower relaxation than a compatibilized system, they ruled out the possibility that attractive interactions promote relaxation. X-ray scattering has been used by several researchers to characterize orientation in sheared or processed clay nanocomposites [START_REF] Varlot | Clay-reinforced polyamide: preferential orientation of the montmorillonite sheets and the polyamide crystalline lamellae[END_REF][START_REF] Bafna | 3D Hierarchical orientation in polymer-clay nanocomposite films[END_REF][START_REF] Galgali | Effect of clay orientation on the tensile modulus of polypropylene-nanoclay composites[END_REF]. However, most studies have involved ex situ measurements on the final orientation in the solid state. While limited in situ data are available [START_REF] Medellin-Rodriguez | Time-resolved shear behavior of endtethered Nylon 6-clay nanocomposites followed by nonisothermal crystallization[END_REF][START_REF] Lele | In situ rheox-ray investigation of flow-induced orientation in layered silicate-syndiotactic polypropylene nanocomposite melt[END_REF][START_REF] Camerel | Combined SAXS-rheological studies of liquidcrystalline colloidal dispersions of mineral particles[END_REF], there is still a paucity of time-resolved orientation data in transient flows. [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF] performed an extensive rheological characterization of a clay dispersion in a Newtonian polybutene matrix, yielding a partially dispersed, intercalated suspension. Since the matrix was rheologically uninteresting, the non-Newtonian rheology of the suspension could be directly attributed to the dispersed clay nanoparticles. Both linear and nonlinear rheological testing were used to probe the effects of flow history on rheology. Linear viscoelastic measurements following cessation of shear flow revealed that (1) the complex modulus observed immediately upon flow cessation depended on the prior shear rate; (2) the complex modulus evolved over an extended period during relaxation; and (3) the final complex modulus also depended on the previous shear rate. The particles used for this study were Brownian, providing a logical explanation for structural relaxation after shear cessation. The existence of shear history-dependent equilibrium states (attributed to the formation of different final structural states of the clay particles) was argued to be due to the large hydrodynamic forces required to overcome the effects of the excluded volume of the clay particles, hence restricting the Brownian mobility of clay particles due to "lack of space." At the same time, transient experiments such as flow reversal and step down suggested that a single unique structural steady state is associated with each shear rate, although thixotropic responses meant that some amount of shearing was required to reach that state.

As illustrated by the above discussion, rheological data on polymer nanocomposites are often interpreted in terms of two distinct structural characteristics: the orientation distribution of the individual clay particles, and particle "network" structures, mediated by interparticle interactions; indeed, attempts have been made to model both types of structure to provide insights into the interpretation of transient rheological phenomena [START_REF] Letwimolnun | Stress overshoots of organoclay nanocomposites in transient shear flow[END_REF]. [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF] have previously coordinated rheological studies with rheooptical investigations using light scattering and dichroism (Mobuchon et al. 2009a), and real-space imaging using confocal microscopy (Mobuchon et al. 2009b) under shear; these techniques intrinsically probe relatively large length scales. In this work, X-ray scattering is used to directly measure the degree of particle orientation in both steady and time dependent shear flows; our goal is to directly interrogate the extent to which bulk rheology is correlated with local particle orientation. Both wide-angle and small-angle X-ray scattering are used to probe orientation. Since it relies on diffraction from the layered internal structure of individual clay tactoids, wide angle X-ray scattering (WAXS) provides a robust and reliable representation of the particle orientation distribution. In principle, anisotropic small-angle X-ray scattering (SAXS), arising from the overall anisotropic disk-like shape of clay particles, should yield equivalent information. However, the propensity for formation of interparticle clusters or networks on larger length scales in clay dispersions [START_REF] Pignon | Yield stress thixotropic clay suspension: investigations of structure by light, neutron and x-ray scattering[END_REF][START_REF] Pignon | Thixotropic behavior of clay dispersions: combinations of scattering and rheometric techniques[END_REF][START_REF] Schaeffer | How nano are nanocomposites?[END_REF] may be manifested in SAXS data; indeed it will be shown that SAXS and WAXS data provide somewhat different perspectives on the flow induced orientation state.

Experimental methods

The layered silicate used to prepare the model suspension was an organically modified montmorillonite, clay (Cloisite 15A, Southern Clay Products). The nonpolar Newtonian dispersing matrix was a blend of polybutenes (Indopol, BP), with a viscosity of 28.5 Pa s at 25 • C. All measurements reported here were conducted on a sample with a 0.02 volume fraction of clay. The sample preparation protocols are identical to those reported by [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF]; however, this sample is lower in volume fraction. Nevertheless, the rheological data reported below are very similar to those reported by [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF]. Using an estimated average particle diameter of 320 nm [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF], the rotational diffusivity D r = 3k B T 4ηd 3 of the clay particles is calculated to be 0.0033 s -1 . TEM imaging of similar samples [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF], and the presence of strong diffraction peaks in WAXS data presented below indicate that complete exfoliation of individual clay sheets is not achieved. Rather, the clay particles consist of layered "tactoids."

Rheological testing was carried out using a strain controlled rheometer (ARES, Rheometric Scientific). All tests were conducted at room temperature using 50 mm cone and plate fixtures with a cone angle of 0.04 rad. To maintain a consistent shear history at the beginning of each measurement, the suspension was subjected to pre-shearing at 25 s -1 for 120 s. This protocol was adopted directly from [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF].

SAXS studies were performed using synchrotron radiation at beam line 5ID-D of the Advanced Photon Source (APS) at the Argonne National Lab. Highly collimated X-rays with energy of 15 keV were se-lected from an undulator beam using a double crystal monochromator. To study particle orientation in the 1-2 (flow-gradient) plane, the sample was sheared using a custom designed annular cone and plate shear cell [START_REF] Caputo | Real-time 1-2 plane SAXS measurements of molecular orientation in sheared liquid crystalline polymers[END_REF]. The high energy used in these experiments reduces absorption due to the sample thickness (∼1 cm) in this shear cell. Twodimensional (2D) scattering patterns were collected using a CCD detector (MarCCD) at rates of up to 0.25 frames/s, with a 9-m sample to detector distance. WAXS studies were conducted using the same shear cell, at APS beam line 5BM-D. Here, a focused bending magnet X-ray beam was passed through a double crystal monochromator to provide energy of 20 keV. The sample to detector distance in WAXS experiments was 73 cm, and scattering patterns were collected using a similar 2D detector at rates of up to 0.4 frames/s. In addition to reducing absorption, the use of high X-ray energy has the beneficial effect of shifting diffraction to smaller angles, allowing the WAXS feature of interest to cleanly exit the shear cell. All scattering patterns are automatically corrected for background electronic noise. In both SAXS and WAXS experiments, vacuum tanks were placed between the shear cell and the detector to minimize background air scattering. Since homogenous polymer melts are expected to scatter negligibly at the low scattering angles used here (save for density fluctuations associated with compressibility), both wide-and small-angle scattering should be dominated by the dispersed particles. Thus, no further baseline subtraction was attempted.

The cone and plate shear cell used for X-ray experiments has a wide cone angle (5 • ), and the sample has a free surface at its outer edge. Experience has shown that high shear rates can cause expulsion of viscoelastic samples from the test fixtures. The prolonged high shear rate pre-shearing protocol was thus avoided in the X-ray experiments. We have nevertheless found that orientation data are quite reproducible, provided the sample is sheared sufficiently long at the desired shear rate (in the end, this precaution appears not to have been necessary, as WAXS experimentsperformed some time after the SAXS experimentswere ultimately extended to shear rates as high as 100 s -1 without sample expulsion).

Anisotropic X-ray scattering from dispersions of layered clays offers two possible avenues for probing the particle orientation state. In reciprocal space, wideangle diffraction from the internal layered structure of each individual clay particle is slaved to that particle's orientation, providing a direct mapping of the particle orientation distribution function to anisotropic azimuthal intensity distributions in WAXS patterns. On the other hand, small-angle scattering probes length scales commensurate with the macroscopic dimensions of clay particles (tens of nanometers in thickness; hundreds of nanometers in diameter). Any flowinduced particle orientation should also be manifested in anisotropic scattering in the SAXS regime, as well. Thus, SAXS and WAXS can provide complimentary probes of particle orientation in sheared suspensions, at different length scales.

A sample with perfectly aligned disk-like particles would exhibit a 2D SAXS pattern with a sharp streak of scattered intensity along the direction normal to the particles' flat surfaces. Similarly, in the WAXS regime, a 2D pattern would show sharp diffraction spots along the particle normals. Decreasing degrees of alignment would lead to azimuthal broadening of each of these features, ultimately yielding, for a randomly oriented sample, an isotropic blob-like feature in 2D SAXS, and an isotropic diffraction ring in 2D WAXS. In 2D small angle scattering (and even in the 'wide angle' measurements reported here, for which the scattering angle of the diffraction feature of interest is just 1.18 • owing to the high energy), a 'slice' of reciprocal space, roughly perpendicular to the incident beam, is sampled. In this geometry, only those particles whose normal vectors lie within this slice will contribute to observable scattering. In this work, therefore, scattering measurements sample the orientation distribution function of those particles whose normals lie within the 1-2 plane. Dilute solution hydrodynamics of thin disk-like particles shows that as particles execute Jeffery orbits (Jeffery 1922), they spend the majority of their time 'lying down flat' in shear flow, with normals tending to accumulate along the velocity gradient direction. Thus, the sampling of reciprocal space employed here is best suited for probing flow-induced orientation, and facilitates measurements of both the degree and direction of particle alignment in the 1-2 plane.

A quantitative measure of the shear-induced anisotropy in each SAXS pattern was obtained by calculating a second moment tensor of the scattering vector q weighted by the scattering intensity I(q), an approach introduced by [START_REF] Salem | Small angle light scattering as a probe of flow-induced particle orientation[END_REF]. In the 1-2 plane of shear flow, the second moment tensor is defined by: qq = q 1 q 1 q 1 q 2 q 1 q 2 q 2 q 2 = qqI q dq 1 dq 2

q 2 I q dq 1 dq 2 , ( 1
)
where 1 and 2 designate the flow and velocity gradient directions, respectively. The normalization by the total scattering intensity in Eq. 1 eliminates effects due to fluctuations in the incident beam intensity. The degree of anisotropy in each scattering pattern may be quantified by an "anisotropy factor" (AF), computed as the difference in the principal values of qq , while the orientation angle relative to the flow direction (χ) is determined from the principal directions of qq :

AF = ( q 1 q 1 -q 2 q 2 ) 2 + 4 q 1 q 2 2 , (2) χ = 1 2 tan -1 2 q 1 q 2 q 1 q 1 -q 2 q 2 . ( 3
)
Defined in this way, AF ranges from 0 to 1 for random and perfect alignment, respectively. Thus, it is functionally similar to the Hermann's order parameter ( P 2 ) frequently used to quantify alignment in oriented polymer materials. Methods for computing P 2 from 2D X-ray scattering images require an assumption that the underlying orientation state is uniaxially symmetric, an assumption that is generally false in shear flow. The second moment tensor approach used here neither requires nor imposes prior assumptions about symmetry of the orientation state, while providing a direct and quantitative representation of the degree and direction of anisotropy present in the scattering pattern. This method of quantifying anisotropy and orientation angle from SAXS patterns has been used for other systems like bicontinuous microemulsions [START_REF] Caputo | Time-resolved small-angle x-ray scattering measurements of a polymer bicontinuous microemulsion structure factor under shear[END_REF] and carbon nanotube suspensions [START_REF] Pujari | Orientation dynamics in multi-wall carbon nanotube dispersions under shear flow[END_REF].

A similar analysis may be applied to WAXS patterns, for which a convenient starting point is an azimuthal intensity distribution, I(θ), extracted from each 2D scattering pattern over a radial range encompassing the layer diffraction peak (Fig. 1f). The azimuthal angle, θ, is measured away from the flow direction towards the gradient direction. Each point on an azimuthal scan is represented by a unit vector u. A second moment tensor of this vector, weighted by the scattered intensity, is then defined as:

uu = u 1 u 1 u 1 u 2 u 1 u 2 u 2 u 2 = uuI (θ ) dθ I (θ ) dθ , ( 4
)
where 1 and 2 designate the flow and velocity gradient directions, respectively. The degree of anisotropy in each scattering pattern is, again, quantified by an anisotropy factor (AF), computed in this case as the difference in the principal values of uu , while the orientation angle relative to the flow direction (χ ) is determined from the principal directions of uu :

AF = ( u 1 u 1 -u 2 u 2 ) 2 + 4 u 1 u 2 2 , (5) χ = 1 2 tan -1 2 u 1 u 2 u 1 u 1 -u 2 u 2 . ( 6
)
The analysis methods represented by Eqs. 1-6 are closely related. In fact, Eqs. 4-6 follow directly from Eqs. 1-3 for the case in which scattered intensity is concentrated in a peak at a single value of q. In either regime, a (hypothetical) case of perfect alignment would lead to concentration of all scattered intensity along the direction of the particle normals, resulting in AF = 1. As a result, it is anticipated that SAXS and WAXS should yield similar measures of anisotropy.

Results and discussion

Both SAXS and WAXS patterns reveal that clay particles become progressively aligned with increasing shear rate (Fig. 1). SAXS shows a nearly isotropic "blob" of scattering at low shear rates (Fig. 1a), indicative of nearly random orientation. As shear rate increases, the SAXS feature becomes increasingly anisotropic (Fig. 1b,c). Recalling that scattering from disk-like particles is concentrated normal to their long axis, the higher intensity observed along the gradient axis in these images corresponds to a preferred orientation of the clay particles' long axes towards the flow direction. It can also be readily observed that the direction of the most intense scattering in these patterns is not simply aligned along the gradient direction but is rotated somewhat counter clockwise. Correspondingly, this means that the average particle orientation direction is rotated away from the flow direction. As shear rate increases, the direction of the most intense scattering rotates closer to the gradient direction, indicating particle orientation closer to the flow direction. Similar features are also seen in WAXS patterns (Fig. 1d-f), where a nearly isotropic ring of scattered intensity at low rates gives way to peaks that both increase in magnitude and rotate progressively towards the gradient direction as shear rate increases. Again, since wide-angle diffraction from the layered disk-like clay particles is confined along the particle normals, these patterns indicate increasing degrees of particle alignment towards the flow direction with increasing shear rate. The WAXS patterns also reveal anisotropic scattering at smaller q values; this is simply the wideangle limit of the SAXS feature in Fig. 1a-c. All SAXSderived calculations of anisotropy reported here are derived from the dedicated SAXS experiments. However, calculations of anisotropy and orientation angle from the limited SAXS data in the small q regime of the WAXS images yield similar results.

The first order diffraction feature observed in WAXS patterns is unambiguously associated with the internal layering of clay tactoids. To better define the structural length scales being probed in the SAXS data, Fig. 2 compares azimuthally integrated I(q) data to representative theoretical calculations of the singleparticle form factor, P(q), for randomly oriented disks of radius R and thickness t [START_REF] Guinier | The motion of ellipsoidal particles immersed in a viscous fluid[END_REF]:

P (q) = 4 1 0 ⎛ ⎝ J 1 qR √ 1 -x 2 qR √ 1 -x 2 ⎞ ⎠ 2 sin qtx 2 qtx 2 2 dx.
(7)

In the limit t → 0, P(q) is given by the simpler expression [START_REF] Guinier | The motion of ellipsoidal particles immersed in a viscous fluid[END_REF]:

P (q) = 2 q 2 R 2 1 - J 1 (2qR) qR . ( 8
)
Intraparticle interference begins to suppress scattered intensity in thin disks when qR ∼ O(1), the Guinier regime. For qR >> 1, Eq. 8 predicts the characteristic q -2 power law associated with random thin disks.

Accounting for finite disk thickness, Eq. 7 predicts a pseudo q -2 power law for 1/R < q < 1/t (here we assume R > t). For q > 1/t, scattered intensity drops off more rapidly and, for monodisperse thickness, exhibits Fig. 2 Azimuthally averaged small-angle X-ray scattering data, I(q), collected during shear at a rate of 0.02 s -1 (symbols), compared with form factor, P(q), computed for randomly oriented disks using representative values of radius R = 160 nm, and thickness t = 40 nm (solid line, Eq. 7) and in limit of zero thickness (dashed line, Eq. 8)

well-defined diffraction "fringes." In the presence of a distribution of thicknesses, these fringes would be smeared out, and the q ∼ 1/t region would instead be characterized by a transition from a q -2 power law to a q -4 power law (the Porod regime). Since Eqs. 7 and 8 assume a random orientation distribution, the data selected for Fig. 2 were obtained at a low shear rate; results presented below (Fig. 4) show the sample to be nearly isotropic under these conditions, at least within the 1-2 plane. Spanning a q-range of 0.02 to 0.25 nm -1 , our SAXS experiments probe structure on roughly 4 to 50 nm length scales, commensurate with the range of tactoid thicknesses observed by TEM of similar organoclay/polybutene dispersions by [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF]. Thus, while SAXS inherently probes larger length scales than WAXS, under the conditions used here, SAXS data still reflect anisotropy in structure at the single-particle length scale, reinforcing the expectation that SAXS and WAXS may provide similar insights into flow-induced particle orientation. In particular, note that even the average particle radius of 160 nm is too large to be resolved in these SAXS experiments. The observed I(q) is rather featureless over the accessible q-range, exhibiting roughly a powerlaw with slope = -2.7, which can be interpreted as the predicted crossover between slopes of -2 (disk) and -4 (Porod), broadened by polydispersity in tactoid thickness.

Steady shear rheology of this 2 vol.% dispersion shows behavior very similar to that observed by [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF] in the analogous 4 vol.% dispersion, approaching a yield stress behavior at low rates Fig. 3 Steady shear viscosity (f illed circles) and shear stress (unf illed circles) measured as a function of shear rate for the 2 vol.% clay dispersion and a viscosity plateau at high rates (Fig. 3). The yield stress at low rates is attributed to the solid-like properties of a particulate network. When the suspension is sheared at high rates, this network structure is broken down and the measured viscosity measured drops close to the matrix viscosity (28.5 Pa s in this sample).

Direct insights into the shear-rate dependent structural state are obtained from corresponding steady state X-ray scattering measurements (Fig. 4). In both SAXS and WAXS experiments, time resolved measurements of orientation were performed in series of experiments including inception, reversal and step changes at various shear rates. The steady state anisotropy and orientation angle were calculated by averaging values after prolonged shearing (at least 30 strain units). Error bars indicate the variability in anisotropy measured during repeated trials of shearing at particular rates. Most of the error bars are small, demonstrating that a unique orientation state may be reproducibly achieved at each shear rate. As expected from the scattering patterns (Fig. 1), anisotropy increases with increasing shear rate. At low shear rates, in the yielding regime, the clay particles exhibit nearly random orientation, and high degree of misalignment away from the flow direction (χ = 30 • ). As shear rate increases the particles become increasingly oriented towards the flow direction (χ drops below 10 • ) while anisotropy factor increases substantially. Based on the estimate of rotational diffusivity given above, the Peclet number Pe = γ D r varies from 3 to 3 × 10 4 over the shear rate range covered in Fig. 4; it is hence not surprising to see these types of changes in the degree and direction of particle orientation. Under conditions of low Pe/low orientation, one normally would expect the orientation angle to approach a limiting value of 45 • in shear flow. However, the presence of a particle network structure associated with yield stress behavior at low rates may affect particle dynamics to prevent this. There is excellent qualitative agreement between Fig. 4 and linear dichroism measurements of steady orientation in the 1-2 plane reported recently by Mobuchon et al. (2009a, b)-including the failure to reach 45 • in the low shear rate orientation angle. Such agreement is remarkable given the wide disparity in length scales probed by X-ray and light scattering. Indeed, in light of differences found between X-ray and dichroism measurements of structural anisotropy upon flow cessation (see below), this agreement may well be somewhat fortuitous.

It is interesting to note the difference between our observation of significant alignment of individual clay particles, and the observations of [START_REF] Pignon | Thixotropic behavior of clay dispersions: combinations of scattering and rheometric techniques[END_REF] on aqueous clay dispersions. While Pignon et al. observed significant shear-induced alignment of largerscale fractal network structures using light scattering under shear, SANS data collected at smaller length scales showed no evidence of flow-induced anisotropy at the single-particle level. However, their clay particles were much smaller, and dispersed in a much lower viscosity matrix, so that the single particle rotational diffusivity would be over seven orders of magnitude larger than in the present work; indeed, Pignon et al. concluded that shear was insufficient to overcome the dominance of Brownian motion in their experiments.

SAXS and WAXS measurements of anisotropy are broadly consistent with one another. However, there are certain quantitative differences. Anisotropy at lower shear rates is very similar for both SAXS and WAXS data. However, at higher shear rates (>1 s -1 ), the anisotropy measured via SAXS is systematically lower than that measured via WAXS. Also, orientation angle data show small but systematic differences across all shear rates. There are a few possible reasons for these differences. First, the layered clay nanoparticles are polydisperse in size and shape. Within a polydisperse sample, different populations of particles will respond to flow differently. The polydispersity also means that some particles will have more silicate layers than others. The WAXS peak reflects Bragg diffraction from the layered structure of each clay particle. In particles consisting of relatively few layers, the Bragg diffraction will be more diffuse; as a result, larger particles with a greater number of layers would be expected to have greater contribution to the WAXS scattering feature, and associated measurements of particle orientation. A second important difference in SAXS and WAXS is the length scale probed by the two techniques. Specifically, due to the larger length scale probed by SAXS, particle clustering due to interparticle interactions may affect the presumed relationship between the particle orientation distribution and anisotropic scattering in the SAXS regime. For very dilute suspensions with widely separated particles, SAXS should also report individual particle orientation. But in a more concentrated suspension, like the one studied here, anisotropic scattering from a cluster of several particles may lead to a SAXS pattern that differs from a simple superposition of anisotropic patterns from the constituent clay particles. Mobuchon et al. (2009a, b) have, in fact, observed shear rate-dependent states of aggregation in similar nonpolar dispersions via microscopic imaging. Conversely, the WAXS feature intrinsically probes the orientation at an individual particle level, and its fidelity in representing the particle orientation distribution should not be affected by the presence or absence of particle clusters. Such factors may contribute to the subtle differences seen in SAXS and WAXS results of Fig. 4. Their influence appears to be relatively minor in the case of steady shear flow; however, greater differences between SAXS and WAXS measurements of anisotropy are found in transient data described below.

Measurements of storage modulus following flow cessation provide evidence of structural evolution during relaxation similar to that reported by [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF] (Fig. 5a). Throughout the relaxation process, the storage modulus is strongly dependent on the prior shear rate. For a low pre-shear rate the initial modulus is high, and changes relatively little during relaxation (studied here over an interval of 5,400 s). Conversely, when the pre-shear rate is high, the initial modulus is quite low, and increases substantially over the course of relaxation. However, even after extended relaxation, the final modulus after shearing at a high rate continues to be much lower than that found after shearing at a low rate. This strong dependence of structure on prior shear rate was investigated in detail by [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF].

A common rheological motif in particulate suspensions is the emergence of a solid-like plateau modulus at low frequencies in oscillatory rheological testing [START_REF] Raghavan | Shear-induced microstructural changes in flocculated suspensions of fumed silica[END_REF][START_REF] Du | Nanotube networks in polymer nanocomposites: rheology and electrical conductivity[END_REF], frequently attributed to the presence of a mechanically percolated particulate network [START_REF] Krishnamoorti | Structure and dynamics of polymer-layered silicate nanocomposites[END_REF]. Viscoelastic measurements on pre-sheared, then 'relaxed' samples again reveal the strong influence of pre-shear rate on the structural state of this clay suspension (Fig. 5b). If pre-sheared at a low rate, the sample exhibits a large low frequency modulus, indicating a well developed network microstructure of clay particles. Conversely, even after 5,400 s of relaxation, high pre-shear conditions result in a substantially softer structural state with lower modulus. These observations again closely resemble the behavior documented by [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF] in a more highly concentrated dispersion. For higher pre-shear rates the modulus appears to increase with decreasing frequency. This aphysical result is an experimental artifact, reflecting the fact that the structure, and hence dynamic modulus, continues to evolve at long times (Fig. 5a), even after 5,400 s of relaxation. The frequency sweeps in Fig. 5b were performed from high to low frequency; on the longer time scales required to collect low frequency data, the continued growth in G leads to the apparently anomalous behavior.

The suspending matrix used here is Newtonian and, hence, does not contribute to the storage modulus. All changes in the elastic modulus observed in Fig. 5 are thus directly linked to evolution of the clay microstructure upon flow cessation. The pre-shear rate dependence of the initial G indicates the degree of break down of the clay network like structure: shearing at higher rates disrupts the network more severely than shearing at low rates, within the 'yielding' regime. During rest, a particulate network can slowly reform, manifested by the gradual growth of G ; however, strong pre-shear rate dependence in network structure apparently exists even after prolonged relaxation. Given that the clay particles in the suspension studied here are Brownian, one expects rotational diffusion to play a role in this structural evolution.

Direct measurements of the clay orientation state confirm a strong influence of shear history on the suspension microstructure following flow cessation (Fig. 6; orientation angle data, not presented here, shows negligible change over the course of relaxation). As anticipated by the steady shear data, the initial anisotropy increases with increasing pre-shear rate. A loss of anisotropy during the relaxation period provides direct evidence of Brownian rotation of the clay particles in this suspension; indeed, the time scale of this relaxation is consistent with estimates of rotational diffusivity given above. In every respect, there are close parallels between the orientation data of Fig. 6 and the mechanical data of Fig. 5a. The high anisotropy factor observed at short time and high rates correlates to the suppressed elastic modulus. Relaxation of the induced anisotropy parallels the corresponding growth in G ; in particular, large changes in both modulus and anisotropy are observed for high pre-shear rates, while only small changes are observed in both orientation and modulus during relaxation from low pre-shear rates. Finally, as found in the mechanical response, the structural state is observed to be pre-shear rate dependent even after prolonged relaxation: when sheared at high rates, only a partial decay in anisotropy is observed.

In the nanocomposite literature, changes in dynamic modulus following flow cessation are often in- terpreted in terms of two different microstructural features: either as a direct manifestation of changes in the orientation distribution of the dispersed particles [START_REF] Krishnamoorti | Structure and dynamics of polymer-layered silicate nanocomposites[END_REF][START_REF] Krishnamoorti | Rheology of polymer layered silicate nanocomposites[END_REF][START_REF] Letwimolnun | Stress overshoots of organoclay nanocomposites in transient shear flow[END_REF], or in the context of reformation of a percolated nanoparticle network. In the present case, we hypothesize that these different structural features are strongly coupled. Shearing at high rates both induces particle orientation and disrupts the particle network, leading to suppressed dynamic modulus. During relaxation, Brownian motion both facilitates network reformation and leads to loss of particle orientation. At the same time, the redevelopment of a particle network "freezes" the dispersion in a nonequilibrium state, in which particles are unable to continue to relax towards isotropy. It is well known that percolation in networks of anisotropic particles is highly dependent on the degree of particle orientation, and that lower degrees of percolation result from higher levels of orientation [START_REF] Du | Nanotube networks in polymer nanocomposites: rheology and electrical conductivity[END_REF][START_REF] Du | Effect of nanotube alignment on percolation conductivity in carbon nanotube/polymer composites[END_REF]. During relaxation from a high pre-shear rate, orientation relaxation is halted in a condition of high particle orientation, which limits the extent of possible network reformation. It is important to note that this picture need not be universal. In more highly concentrated clay dispersions (formulated differently than the sample studied here), we have found that evolution of dynamic modulus may be highly decoupled from particle orientation [START_REF] Dykes | Shear-induced orientation in polymer/clay dispersions via in situ X-ray scattering[END_REF]. As mentioned earlier, [START_REF] Letwimolnun | Stress overshoots of organoclay nanocomposites in transient shear flow[END_REF] have attempted to model network structure and orientation dynamics in polymer/clay nanocomposites, but the two structural features were treated independently. Possible coupling between evolution and network structure and orientation suggested in Figs. 5 and 6 may require a more general modeling approach in which evolution of these structural characteristics is interdependent.

It is interesting to note that linear dichroism measurements of structural anisotropy in similar dispersions showed no relaxation upon flow cessation (Mobuchon et al. 2009a, b). To explain this difference, we suggest that it is likely that dichroism-whose origin is anisotropic light scattering-is more sensitive to the larger length-scale anisotropic cluster structures that have been observed following shear via direct realspace imaging using optical microscopy (Mobuchon et al. 2009b), rather than directly measuring orientation at the level of individual clay particles. The lack of any significant structural relaxation at such larger length scales is to be expected.

During relaxation, SAXS (Fig. 6a) and WAXS (Fig. 6b) data reveal qualitatively similar phenomena. Both sets of data show more relaxation of induced anisotropy following high pre-shear rates, and little relaxation of anisotropy following low pre-shear rates. However, there are some noteworthy differences between SAXS and WAXS data. First, the WAXS data do not show as much relaxation as the SAXS data; the final orientation state measured by WAXS is systematically higher. As noted earlier, we expect larger particles (i.e. those with a greater number of silicate layers) to contribute disproportionately to the WAXS scattering. However, such larger particles would relax more slowly than the average, and perhaps be locked into a redeveloping network structure more rapidly, limiting their ultimate degree of relaxation. Another interesting distinction is found at very short times, where the WAXS measurements of orientation show a more rapid initial drop in anisotropy than the SAXS data. The origin of this effect is not clear.

Flow reversal experiments are an effective way to study orientation dynamics under conditions in which the shear rate magnitude-hence, the degree of any persistent network like structure-is held constant. The mechanical response to flow reversal is straightforward (Fig. 7). The steady state stress, which increases monotonically with increasing shear rate, changes sign when the direction of flow is reversed, and returns to its steady state value within ∼5 strain units. While reversals with intermediate periods of relaxation can show significant stress overshoots [START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF][START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF][START_REF] Letwimolnun | Stress overshoots of organoclay nanocomposites in transient shear flow[END_REF], no overshoots are seen in Fig. 7. In the absence of rest time, there is no opportunity for the network reformation believed to be responsible for stress overshoots [START_REF] Solomon | Rheology of polypropylene/clay hybrid materials[END_REF][START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF][START_REF] Letwimolnun | Stress overshoots of organoclay nanocomposites in transient shear flow[END_REF]. Using either SAXS or WAXS, the anisotropy factor shows a transient dip in anisotropy when flow is reversed (Figs. 8a and9a). The drop in anisotropy can be attributed to a more isotropic intermediate clay orientation state, as particles reorient towards the new flow direction. The steady state anisotropy is reestablished in less than 10 strain units. The reorientation of particles is directly manifested in orientation angle data, which show a rapid change in sign following flow reversal (Figs. 8b and9b). After steady state is achieved (again within ∼10 strain units), the magnitude of the orientation angle in the reversed direction is the same as prior to reversal, showing that Fig. 7 Shear stress measured as a function of strain following flow reversal at shear rates of 0.07 (unf illed squares), 0.4 (unf illed triangles), 0.7 (unf illed circles), and 1.0 s -1 (asterisk) Fig. 8 a Anisotropy factor and b orientation angle measured using SAXS as a function of shear strain following flow reversal at shear rates of 0.07 (unf illed squares), 0.4 (unf illed triangles), 0.7 (unf illed circles), and 1.0 s -1 (asterisk) the same structural state is achieved upon reversal, but in the opposite direction.

Both SAXS and (especially) WAXS reversal data show clear evidence of oscillations in the transient response of both anisotropy and orientation angle. The orientation dynamics of isolated anisotropic particles dispersed in Newtonian fluids follow periodic trajectories solved by Jeffery (1922) that provide a natural explanation for oscillations transient flows. Even in the concentrated dispersion studied here, it is reasonable to expect that the fundamental hydrodynamics of disk-like particles may be manifested in these structural oscillations. Note that the oscillations in Fig. 9 scale with shear strain, as would be expected for Jeffery orbit dynamics. The fact that the oscillatory character of the transient response is more clearly manifested in WAXS data may, again, reflect the fact that WAXS measurements may be biased in favor of larger/thicker particles, and hence be dominated by a subset of particles that exhibit more homogeneous orientation dynamics.

Unlike the case of shear reversal, experiments involving a step down in shear rate should involve both time-dependent changes in the particle orientation as well the extent of a particle network. [START_REF] Mobuchon | Effects of flow history on the structure of a non-polar polymer/clay nanocomposite model system[END_REF] observed striking stress undershoots following step down in shear rate, which are also found in the current sample (Fig. 10a). The magnitude of the stress undershoot is strongly dependent on the magnitude of step shear applied. Step down to a final shear rate of 0.02 s -1 from an initial shear rate of 7 s -1 causes a much larger undershoot than from an initial shear rate of 0.1 s -1 (note the log scale on stress in Fig. 10a). Following step down, the shear stress approaches a reproducible steady state value within ∼20 strain units. Relative to transients observed in reversal, SAXS data show a much more gradual evolution of anisotropy and orientation angle toward their new steady state values, particularly for the larger step from 7 to 0.02 s -1 (Fig. 10b). For this larger step, pronounced oscillations in both anisotropy and orientation angle are superimposed on the transition between the steady state values representative of the initial and final shear rates. For the smaller step, in which the degree of orientation is already low to start, the transient orientation dynamics are more subdued. WAXS data (Fig. 10c) reveal similar phenomena as the SAXS data, notably pronounced oscillations in anisotropy and orientation angle following the larger step down. There is, however, a notable discrepancy between SAXS and WAXS data for the orientation angle dynamics for this particular protocol. Since this step down experiment may involve changes in both the orientation state and the degree of clustering of the constituent clay particles, it is difficult to propose possible origins for this difference.

Unlike the case of flow cessation, there appears to be little direct correlation between the transient mechanical and orientation response in this step down experiment. For the larger step down, the mechanical response exhibits a stress undershoot of about 1.5 orders of magnitude. While interesting structural dynamics are observed, neither SAXS nor WAXS measurements show changes dramatic enough to explain this observation. Rather, it is likely that the transient undershoot reflects changes in the particle network structure; such structural changes might be more clearly manifested in light scattering or dichroism experiments which probe larger length scales (Mobuchon et al. 2009a, b). Steady-state viscosity measurements (Fig. 3) suggest that any particle network would be largely disrupted at shear rate of 7 s -1 , where the viscosity is not that much larger than that of the viscous polymer matrix. Immediately upon step down, the sample initially retains this low viscosity, and the stress drops dramatically. Continued shearing, however, leads to reformation of a particle network, and, accordingly, the dramatic increase in viscosity expected from Fig. 3. Conversely, in this same experiment, SAXS and WAXS both show dramatic structural oscillations that have no obvious manifestations in the mechanical response. As in the case of flow reversal, such oscillations are likely due to Jeffery like tumbling motion of the clay particles. The comparative strength of the oscillatory response relative to that found in reversal may reflect the fact that pre-shearing at a high initial rate substantially breaks up particle network/cluster structures, allowing particles-initially-greater latitude to rotate in the shear flow. The comparatively slow approach to steady state in anisotropy factor and orientation angle may be due to hindrance from the developing particle network. All of these characteristics are considerably muted in the smaller step down experiment (0.1 to 0.02 s -1 ), since a much more robust particle network is likely already present during the pre-shearing at this lower rate.

Conclusions

Direct X-ray scattering measurements of particle orientation during steady and transient shear flows in this model polymer/clay nanocomposite provide useful insights into the microscopic origins of the observed rheological behavior. In the low rate, yield-stress regime, there is negligible orientation of clay particles within the 1-2 plane. Increasing shear rate (and hence Peclet number) leads to increased particle alignment, and rotation of the average orientation direction towards the flow direction. Upon flow cessation, partial relaxation of orientation is observed, that correlates extremely closely to evolution of dynamic moduli. Even after prolonged relaxation, the structural state of the sample depends on the prior shear conditions. The orientation state responds quite rapidly to shear flow reversal, and although the structural data show hints of oscillatory Jeffery orbit dynamics, the bulk mechanical response is rather featureless. Conversely, the shear stress shows remarkable undershoots upon step-down in shear rate of large magnitude. There is no obvious explanation for this phenomenon in the observed orientation dynamics at nano scale; rather, this thixotropic behavior is attributed to the reformation of a particle network structure that had been disrupted by the prior shearing at high rates. Orientation measurements derived from small-and wide-angle X-ray scattering generally provide consistent pictures of the steady and transient orientation state, although there are quantitative differences due to the different length scales probed by the two methods.

Fig. 4

 4 Fig. 4 Steady-state anisotropy factor (open symbols) and orientation angle (closed symbols) measured in the 1-2 plane as a function of shear rate for the 2 vol.% clay dispersion using SAXS (unf illed squares, f illed squares) and WAXS (unf illed circles, f illed circles)

Fig. 5 a

 5 Fig. 5 a Storage modulus (measured at an angular frequency of 10 rad/s) measured as a function of time following cessation of steady shear flow. b Frequency sweep measured after steady shear flow and a rest time of 5,400 s. Symbols indicate the pre-shear rates: 0.02 (unf illed squares), 0.1 (unf illed circles), 1.0 (unf illed triangles), and 4.0 s -1 (unf illed diamonds)

Fig. 6

 6 Fig. 6 Anisotropy factor measured using a SAXS and b WAXS, following cessation of steady shear flow at rates of 0.02 (unf illed squares), 0.1 (unf illed circles), 1.0 (unf illed triangles), and 4.0 s -1 (unf illed diamonds)

Fig. 9 a

 9 Fig.9a Anisotropy factor and b orientation angle measured using WAXS as a function of strain following flow reversal at shear rates of 0.07 (unf illed squares), 0.4 (unf illed triangles), 0.7 (unf illed circles), and 1.0 s -1 (asterisk)

Fig. 10

 10 Fig. 10 Mechanical and structural response to step down experiments. a Shear stress measured as a function of strain following step down to a final shear rate 0.02 s -1 . b SAXS and c WAXS measurements of anisotropy factor (open symbols) and orientation angle (closed symbols) as a function of strain following step down to a final shear rate of 0.02 s -1 .Symbols designate initial shear rates: 0.1 (unf illed squares) and 7.0 s -1 (unf illed circles)

Acknowledgements

Funding for this work was provided through the NSF-MRSEC program (Grant DMR-0520513) at the Materials Research Center of Northwestern University. We thank beam line staff at DND-CAT for assistance with Xray scattering experiments. DND-CAT is supported by the E.I. DuPont de Nemours & Co., the Dow Chemical Company, and the National Science Foundation through Grant DMR-9304725 and the State of Illinois through the Department of Commerce and the Board of Higher Education Grant IBHE HECA NWU 96. Use of the Advanced Photon Source was supported by the US Department of Energy, Basic Energy Sciences, Office of Energy Research, under Contract No. W-31-102-Eng-38.


Aisling Ni Annaidh
email: aisling.niannaidh@ucd.ie

Karine Bruyère

Michel Destrade

Michael D Gilchrist

Mélanie Otténio

Aisling Ní Annaidh

Characterization of the anisotropic mechanical properties of excised human skin

Keywords:

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Skin is a complex multi-layered material which can be broadly divided into three main layers, the epidermis, the dermis, and the hypodermis. The epidermis consists of cells and cellular debris, the dermis consists of mostly networks of the fibrous proteins collagen, reticulin and elastin [START_REF] Wilkes | The biomechanical properties of skin[END_REF], and the hypodermis is primarily made up of connective tissue and fat lobules. Collagen fibres account for 75% of the dry weight of dermal tissue [START_REF] Wilkes | The biomechanical properties of skin[END_REF] and it is these fibres which are responsible for the strength of the skin.

Skin is a highly non-linear, anisotropic, viscoelastic and nearly incompressible material. A typical stress-stretch graph for skin exhibits non-linear behaviour and its response is usually described as three-phase [START_REF] Brown | A scanning electron microscope study of the effects of uniaxial tension on human skin[END_REF]. In the initial loading phase, skin is very compliant and large deformation occurs at a relatively low applied load. At this stage, the fibres are largely unaligned. In the second phase, the stiffness of the skin gradually increases as the fibres align themselves in the direction of the load applied. The third phase is an almost linear phase whereby the stiffness increases rapidly as the collagen fibres are mostly aligned and the overall mechanical response becomes dependent on the mechanical properties of the collagen fibres, which are stiffer than elastin by three grades of magnitude.

That skin is anisotropic was recognized as far back as the 19th century by [START_REF] Langer | On the anatomy and physiology of the skin. The Imperial Academy of Science[END_REF], who mapped the natural lines of tension which occur within the skin. These lines are identified by puncturing the skin with a circular device. The wounds then assume an elliptical shape and by joining the major axes of the ellipses, a system of lines can be drawn as shown in Fig. 1(a). These lines are known as the Langer lines. While the Langer lines are the best known skin tension lines, many variations on the original lines proposed by Langer have been made. These include the Cox lines [START_REF] Cox | The cleavage lines of the skin[END_REF], Kraissl lines [START_REF] Kraissl | The selection of appropriate lines for elective surgical incisions[END_REF] and (RSTL) relaxed skin tension lines [START_REF] Borges | Relaxed skin tension lines (RSTL) versus other skin lines[END_REF].

Early tensile tests suggested that the deformation characteristics of skin are dependent upon specimen orientation with respect to the Langer lines [START_REF] Ridge | The directional effects of skin. A bioengineering study of skin with particular reference to Langer's lines[END_REF]. More recent work conducted using optical coherence elastography in-vivo, indicates a large difference between the Young moduli of skin along directions parallel and orthogonal to the Langer lines [START_REF] Liang | Biomechanical properties of in vivo human skin from dynamic optical coherence elastography[END_REF].

In this study, we provide new experimental data of invitro human skin focusing, in particular, on the anisotropic properties of the skin. We also quantify the degree of anisotropy of the mechanical properties with respect to their Langer line orientation. Finally, we perform a quantitative histological analysis on the dermis of the test samples to examine a possible correlation between the orientation of the Langer lines and the preferred direction of collagen fibres.

While many recent publications on skin report in-vivo experiments [START_REF] Delalleau | Characterization of the mechanical properties of skin by inverse analysis combined with an extensometry test[END_REF][START_REF] Flynn | Mechanical characterisation of in vivo human skin using a 3D force-sensitive microrobot and finite element analysis[END_REF][START_REF] Moerman | Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo[END_REF], here we have limited our experiments to in-vitro uniaxial tensile tests. As discussed by Holzapfel, there are a number of issues involved with tensile tests [START_REF] Holzapfel | Determination of material models for arterial walls from uniaxial extension tests and histological structure[END_REF]: The structural integrity of the samples may be disturbed at the lateral edges and due to the soft nature of the test material, it is difficult to insert samples without subjecting them to an axial load. Despite these shortcomings, it was decided to perform in-vitro tensile tests over in-vivo testing for a number of reasons. First, in-vitro tests provide simple stress-strain relationships that can be modelled and quantified easily, since their boundary conditions are well defined. Second, for the application of this work in a further study into the dynamic rupture of skin, we are also interested in failure and rupture of skin, and in-vitro testing makes it possible to test until failure.

Most in-vitro investigations use human skin substitutes such as pigskin, silicone or polyurethane [START_REF] Mccarthy | On the sharpness of straight edge blades in cutting soft solids: part Iindentation experiments[END_REF][START_REF] Gilchrist | Measuring knife stab penetration into skin simulant using a novel biaxial tension device[END_REF][START_REF] Jor | Modelling collagen fibre orientation in porcine skin based upon confocal laser scanning microscopy[END_REF][START_REF] Mccarthy | On the sharpness of straight edge blades in cutting soft solids: part II-analysis of blade geometry[END_REF] and in-vitro tests on human skin are particularly rare. Those classical publications which do use human skin often rely on outdated equipment and their results can be difficult to interpret [START_REF] Cox | The cleavage lines of the skin[END_REF]Jansen and Rottier, 1958b). However, the development of accurate constitutive models depends heavily upon their material definitions. This study aims to provide new material data for human skin which can be applied to constitutive models in a number of technical areas such as razor blade manufacture, cosmetics, surgical simulation, forensic pathology and impact biomechanics. Uniaxial tensile tests alone are not sufficient to determine multi-dimensional material models for soft tissues and using a simple non-linear regression analysis to determine constitutive parameters may result in non-unique solutions, ill-conditioned equations and slow convergence rates. Ideally, testing of skin would involve planar biaxial tests with an in-plane shear, and separate through-thickness shear tests. While advanced testing protocols like these are not yet available, simple tension tests remain important because they serve to evaluate the level of anisotropy and to provide data which can later be used as validation for models constructed using more complicated testing methods [START_REF] Holzapfel | On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework[END_REF]. Moreover, model parameters can be provided directly from a histological study of the collagen fibre alignment in the dermis which allows for reasonable determination of material responses [START_REF] Holzapfel | Determination of material models for arterial walls from uniaxial extension tests and histological structure[END_REF].

Materials and method

Specimen preparation

Tensile tests and preparation were carried out in IFSTTAR (Institut français des sciences et technologies des transports, de l'aménagement et des réseaux), France. French law allows human corpses that have been donated to science to be used for research purposes. The ethics committee within IFSTTAR approved the use of human biological material. Skin was excised from seven subjects: three males and four females.

The average age of the subjects was 89 ± 6 years and none had any related skin diseases. Table 1 provides details on the gender and age of each subject at the time of death along with the number of days that elapsed prior to testing.

Only the skin from the back of the subject was available for use. This was excised from the body with a scalpel. Each sample of skin was cut into a dogbone shape specimen, according to the ASTM D412 standard tensile test method for vulcanized rubber, using a custom made dye (see Fig. 1). Each specimen then had the epidermis and any underlying adipose tissue carefully removed with a scalpel. The thickness of the skin after removal of adipose tissue was measured using a Vernier Callipers and the mean thickness was 2.56 ± 0.39 mm. It was observed that skin removed from the lumbar area of the back contained more adipose tissue than skin from other areas of the back. The dimensions of the test specimens were measured before and after excision. Specimens were obtained in various orientations, shown in Fig. 1, to correlate the specimens with the direction of the Langer lines. Each sample was grouped into one of three categories: parallel, perpendicular, or at 45 • to the Langer lines. The skin was stored in moistened paper and refrigerated at 4 • C until it was ready to be tested. A total of 56 samples were tested successfully. Although it is widely accepted that preconditioning is necessary at small and intermediate strains, at higher strains the stress-strain response is not significantly affected by preconditioning [START_REF] Eshel | Effects of strain level and proteoglycan depletion on preconditioning and viscoelastic responses of rat dorsal skin[END_REF]. The samples were therefore not pre-conditioned prior to testing.

Tensile tests

Tensile tests were performed using a universal tensile test machine. Samples were clamped using specially designed anti-slip clamps, to counteract the tendency of samples to slip in ordinary grips. The velocity of the crosshead was 50 mm/min. The tensile load was measured with a 1 kN piezoelectric load cell. Each tensile test was videoed with two Dalsa Falcon 1.4M100 digital video cameras at 20 frames/second. This was to record any abnormal behaviour during the experiments and also for the subsequent use of digital image correlation. The gauge length and width were both measured optically. For these tests, the strain rate was 0.012 s -1 , nominally the same strain rate as in tests carried out by Jansen and Rottier (1958a).

The main focus of this study is an investigation into the hyperelastic properties of skin and how these vary according to orientation and location. We thus considered the tensile tests to be taking place at quasi-static speed, and ignored viscoelastic effects for the purpose of constitutive hyperelastic modelling (for examples of studies where this route is chosen, see [START_REF] Jor | Modelling collagen fibre orientation in porcine skin based upon confocal laser scanning microscopy[END_REF][START_REF] Pailler-Mattei | In vivo measurements of the elastic mechanical properties of human skin by indentation tests[END_REF], Evans and Holt, 2009[START_REF] Cavicchi | Computational modeling of reconstructive surgery: the effects of the natural tension on skin wrinkling[END_REF]. Further creep and stress relaxation tests, requiring additional skin samples, would need to be carried out to characterize the viscoelasticity of skin.

Digital Image Correlation

The stretch ratio was calculated via the displacement cell attached to the cross-head of the tensile machine. As validation, the stretch ratio was also calculated via Digital Image Correlation (DIC). DIC is a full-field optical strain measurement technique which uses image registration to measure the 2D or 3D deformation of a material. The technique works by tracking unique features on the surface of the material as it deforms. The correlations were based on images taken with the two Dalsa Falcon video cameras and processed using Vic2D software (Version 2009-Correlated Solution, Inc.). Black spray paint was applied to the surface of the skin to create the desired random speckled pattern necessary for the correlation.

Histology

Three biopsies were procured from the test specimens prior to testing. These biopsies were placed in a formaldehyde solution for fixation for a period exceeding 48 h. Biopsies were then embedded in paraffin prior to slicing. Each biopsy was sectioned at 5 µm intervals, creating a number of thin slices which were transferred onto glass slides. Biopsies were sliced in three orthogonal planes as shown in Fig. 2. The samples were then stained using a Van Gieson stain, which differentiates collagen fibres by making them appear pink/red. Images were taken from each slide using a Nikon E80i transmission microscope and CCD camera. The orientation of collagen fibres were then calculated in a fully-automated customized MATLAB routine using the Image Processing Toolbox. The algorithm is described further in Ní Annaidh et al. (submitted for publication).

Statistical analysis

A statistical analysis of the experimental results was carried out using the general linear model procedure implemented in SAS 9.1 (SAS Institute Inc., USA). A multivariate analysis of variance was utilized, followed by the Tukey-Kramer post-hoc test, to determine the influence of orientation and location of the various test samples. Significance levels for these tests were set to P < 0.05. When performing this test a normal distribution was assumed. To ensure our data set followed a normal distribution, a Lilliefors test was performed using the lillietest function in MATLAB R2007b.

Results

For each tensile test performed, a force-displacement curve was obtained. The nominal stress was then calculated by dividing the force by the undeformed cross sectional area of the specimen. The stretch ratio was calculated by dividing the current length of the specimen by the initial length. In this way, nominal stress vs. stretch ratio graphs were plotted for each specimen. A number of characteristics from these curves were identified as descriptive parameters. They are illustrated in Fig. 3.

Intra-subject and inter-subject variations

A difficulty often encountered with the testing of biological tissue is the large variation in experimental results across samples. Fig. 4(a) indicates the intra-subject and inter-subject variations in the UTS between samples. There is a large intrasubject variation for each subject which is primarily due to anisotropy. Fig. 4(b) shows the stress-stretch graphs of ten different samples taken from five subjects. Note that the left and right samples were adjacent to one another but also in the same orientation with respect to the Langer lines.

The similarity of these responses between the left and right samples from the same subjects indicates good repeatability of our experiments.

Deformation of specimens after excision

It is known that both shrinkage and expansion of specimens can occur upon excision from the body [START_REF] Cox | The cleavage lines of the skin[END_REF]Jansen and Rottier, 1958a;[START_REF] Ridge | The directional effects of skin. A bioengineering study of skin with particular reference to Langer's lines[END_REF][START_REF] Lanir | Two-dimensional mechanical properties of rabbit skin-II. Experimental results[END_REF]. This is due to the release of residual stresses within the skin. What remains unclear is the level of residual stress present within the skin and how this may vary with the orientation of specimens. It has been suggested that the shrinkage of excised specimens is greatest in the direction of the Langer lines [START_REF] Ridge | The directional effects of skin. A bioengineering study of skin with particular reference to Langer's lines[END_REF]; however our results did not corroborate this. Our results showed that 73% of all samples expanded upon excision, while only 27% of all samples shrunk. Of the samples that expanded, there was a mean expansion of 5.1 ± 3.4%. Amongst the samples that shrunk, a mean shrinkage of 3 ± 2.9% was recorded. This is far below the reported maximum figure of 20% shrinkage for human skin (Jansen and Rottier, 1958a) and 40% shrinkage provided for pig skin [START_REF] Jor | Modelling collagen fibre orientation in porcine skin based upon confocal laser scanning microscopy[END_REF].

Histology

The collagen fibres were assumed to form an interweaving lattice structure, as first postulated by [START_REF] Ridge | The directional effects of skin. A bioengineering study of skin with particular reference to Langer's lines[END_REF]. Here, the preferred orientation is defined as the mean of the orientations of two families of interweaving fibres. It was assumed that the collagen fibres are distributed according to a transversely isotropic and π-periodic von Mises distribution. The von Mises distribution is commonly assumed for directional data. The standard π-periodic von Mises distribution is normalized and the resulting distribution is given as follows.

ρ(Θ) = 4  b 2π exp[b(cos(2Θ) + 1)] erfi √ 2b ( 1
)
where Θ is the mean orientation of fibres and b is the concentration parameter associated with the von Mises distribution. The parameter b was evaluated by the approximation given by Fisher (1993) using the CircStat package available on the MATLAB file exchange [START_REF] Berens | Circstat: a MATLAB toolbox for circular statistics[END_REF].

Table 2 shows the calculated concentration parameter b, the mean orientation of collagen fibres and the orientation with respect to the Langer lines. A Pearson correlation test was carried out to test for a correlation between the preferred orientation obtained through histology and the perceived orientation of the Langer lines. The correlation was deemed to be significant (P < 0.001) with a Pearson R value of 0.9487 and an R 2 value of 0.9000.

Influence of orientation

Specimens were analysed by considering their orientation with respect to the Langer lines (parallel, perpendicular or at 45 • to the Langer lines, see Fig. 1). A multiway analysis of variance found the orientation of the Langer lines to have a significant effect on the UTS (P < 0.0001), the strain energy (P = 0.0101), the elastic modulus (P = 0.0002), the initial slope (P = 0.0375), and the failure stretch (P = 0.046). The interaction between orientation and location was also tested i.e., whether the effect of orientation was dependent upon location. This interaction between orientation and location was found to be significant only for the failure stretch (P = 0.0118). The presence of this interaction is probably due to small differences in the perceived orientation of the Langer lines over the body. Fig. 5 and Table 3 display the variations in the mechanical properties between samples of different orientations. The variations are substantial, except for the failure stretch, where the effect of the orientation is complicated by the existence of the interaction between orientation and location.

Influence of location

When results were grouped into three locations (upper back, middle back and lower back, see Fig. 1), a multiway analysis of variance also found the location of specimens to have a significant effect on the UTS (P = 0.0002), the strain energy (P = 0.0052) and the elastic modulus (P = 0.001), but neither on the failure stretch nor the initial slope. Fig. 6 displays variations in the mechanical properties between different locations on the back for the three properties which showed a significant effect i.e., the elastic modulus, UTS and strain energy. Note that there was no significant effect noted for either the initial slope or the failure stretch.

Digital image correlation

An important feature of DIC is its ability to calculate local strains throughout the plane of the test specimens. from the displacement sensor (DS), throughout the duration of a test. It can be seen that there is good agreement for most of the duration of the test. However, upon closer inspection, it was found that a local magnification of the stretch ratio occurred just before rupture, close to the rupture site (for magnitudes, see Table 4). Fig. 7(b) shows the distribution of strains throughout the sample for a frame just before rupture. For some samples this magnification was very localized while for others it was distributed over a larger area. A similar result was reported by [START_REF] Jacquemoud | Methodology to determine failure characteristics of planar soft tissues using a dynamic tensile test[END_REF] who found that at the rupture site, the local strain values can be up to twice as large as what is measured using overall specimen strains calculated over the entire length of a specimen.

Discussion

When comparing our own data to that in the literature, it can be seen that there is much variation between authors. This is to be expected for biological tissues. First, because of the biological variability between subjects; second, because of the anisotropic nature of skin itself; and third, because of the sensitivity of biological tissues to test conditions. In the absence of extensive published literature on the properties of in vitro human skin from the back, Table 5 compares results obtained from the literature from a range of locations and test methods to our own results. The mean ultimate tensile strength was 21.6 ± 8.4 MPa, the mean failure strain 54 ± 17%, the mean initial slope 1.18 ± 0.88 MPa, the mean elastic modulus 83.3 ± 34.9 MPa and the mean strain energy was 3.6 ± 1.6 MJ/m 3 . It can be seen that our experimental results fall within the ranges found in the literature for invitro tests. However there is a large variation with the various types of in-vivo tests. The reasons for this difference has been widely discussed and the primary causes are due to the properties of skin changing once removed from the body; the different testing methods employed; and an inability to establish boundary conditions and to isolate the skin's behaviour from its surrounding tissue in vivo. Furthermore, the modulus defined in-vivo is in the low-strain range, whereas the modulus calculated here is in the high-strain range. The in-vivo modulus should then be compared with the initial slope, rather than with the elastic modulus. It has been well documented over the years that the deformation characteristics of skin are dependent upon specimen orientation, but few authors describe the level of anisotropy involved in much detail. In this study, we have provided statistical information on the effect of the Langer line orientation on the UTS, strain energy, failure strain, initial slope, and elastic modulus. We have been unable to establish a link between the level of shrinkage of skin upon excision and the orientation of the Langer lines. Instead, we found that the majority of samples actually expanded upon excision.

The reason for this discrepancy may be two-fold; first, the skin has been excised from the back, not the abdomen, which may be more extensible to accommodate the shrinkage and expansion of the stomach. Second, the skin samples were excised from elderly subjects which naturally exhibit less extensibility. This has been previously noted by Jansen and Rottier (1958a,b) who stated that skin excised from elderly subjects was more likely to expand rather than retract, when compared to younger subjects. Finally, the authors noted that while shrinkage of the skin may have occurred directly after excision from the body, after subcutaneous fat was removed, the samples often expanded. This poses the question on the effect the subcutaneous fat has on the level of shrinkage/ expansion of the skin, usually thought to be solely due to the release of residual stresses in the skin.

Previous studies show that the properties of skin are dependent upon specimen location [START_REF] Haut | The effects of orientation and location on the strength of dorsal rat skin in high and low speed tensile failure experiments[END_REF][START_REF] Sugihara | The extensibility in human skin: variation according to age and site[END_REF]. Our results also indicate that the UTS, strain energy and elastic modulus vary depending on the location. However, as only skin from the back was available for testing, the location of specimens could only be categorized into upper back, middle back and lower back regions. It was nonetheless advantageous to gain information on skin from the back because it is seldom as readily available as that from the abdominal area. All subjects were between the ages of 81 and 97. This meant that no comparisons based on the age of subjects could be performed. Numerous other studies have investigated the influence of age on the structure and mechanical behaviour of skin [START_REF] Vogel | Age dependence of mechanical and biochemical properties of human skin[END_REF][START_REF] Haut | The effects of orientation and location on the strength of dorsal rat skin in high and low speed tensile failure experiments[END_REF][START_REF] Sugihara | The extensibility in human skin: variation according to age and site[END_REF]. It has been established that progressive straightening of elastin fibres occurs over time [START_REF] Lavker | Aged skin: a study by light, transmission electron, and scanning electron microscopy[END_REF]. This may cause the shortened phase I region of the stress-strain curve leading to an overall reduction in extensibility. The slope of the phase III portion of the curve, however remains relatively constant [START_REF] Wilkes | The biomechanical properties of skin[END_REF]. Nonetheless, it must be highlighted that the results of this study may not reflect the behaviour of younger skin and consideration must be taken to allow for age-related effects when interpreting these results.

A number of days had elapsed between the time of death and testing (see Table 1), but it has been previously demonstrated that skin samples can be refrigerated for up to 48 h under the right conditions with no discernible effects on the mechanical properties [START_REF] Daly | Biomechanical properties of dermis[END_REF] and for up to 21 days for thoracic aortas under certain conditions [START_REF] R E F E R E N C E S Adham | Mechanical characteristics of fresh and frozen human descending thoracic aorta[END_REF].

DIC is a common strain measurement technique in biomechanics, however until now it has been used mostly for in-vivo experiments or at low strains [START_REF] Moerman | Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo[END_REF]. The results yielded from the present use of DIC may be useful in the future as validation for a finite element approach. Also the local maximum strain values reported are of interest to those who wish to model the failure of biological tissues.

In this paper, our data has been examined with respect to the perceived orientation of the Langer lines. However, the Langer lines are known to vary with location, age and gender and no universal pattern of maximum tensions exist [START_REF] Brown | A scanning electron microscope study of the effects of uniaxial tension on human skin[END_REF]. The orientation of the Langer lines cannot be identified with certainty unless the skin of a whole cadaver is punctured, an option which was not feasible for this study. Given the importance of the Langer lines on the mechanical properties of the skin, there is a need for patientspecific maps to be established in-vivo and in real time. These could be produced by relying on sophisticated imaging techniques such as those produced by ultrasonic surface wave propagation or optical coherence tomography and may eventually have applications in cosmetic surgery. [START_REF] Cox | The cleavage lines of the skin[END_REF] and [START_REF] Stark | Directional variations in the extensibility of human skin[END_REF] both illustrated that the orientations of the Langer lines remain even after the skin is removed from the body and the skin tension released, and concluded that the lines have an anatomical basis. However it remains unclear in the literature whether the Langer lines have a structural basis, and to the authors' knowledge there is no quantitative data published on this point. By identifying the orientation of collagen fibres in the dermis, we have shown that there is a correlation between their orientation and that of the Langer lines. However, it is only when a quantitative study is performed that this becomes apparent.

Knowledge of the collagen fibre orientation along with the stress-strain data presented will also facilitate the determination of material parameters for structurally based constitutive models for skin. While the test method described here is not sufficient to fully describe the full 3D response of the material, [START_REF] Holzapfel | Determination of material models for arterial walls from uniaxial extension tests and histological structure[END_REF] has shown how a combination of tensile tests and histological data can be used to reasonably determine the material parameters of a 3D hyperelastic model. In a companion paper (Ní Annaidh et al., submitted for publication), we use a similar approach in order to determine the material and structural parameters of a suitable anisotropic model, the so-called Gasser-Ogden-Holzapfel model [START_REF] Gasser | Hyperelastic modelling of arterial layers with distributed collagen fibre orientations[END_REF], readily implemented into the commercial finite element code, ABAQUS.

Fig. 1 -

 1 Fig. 1 -(a) Orientation of samples from the back. Specimens are superimposed onto a map of the Langer lines to indicate their orientation with respect to the lines (Langer, 1861). (b) Dimensions of custom made dye (mm).

Fig. 2 -Fig. 3 -

 23 Fig. 2 -Biopsies of skin samples for the purpose of histological staining. Note that the biopsies have been sliced in three orthogonal planes.

  Fig. 4 -(a) Box and whisker plot of the intra-subject and inter-subject variations in UTS (N = 56) for subjects A-G. The whiskers indicate the max and min. The boxes represent the lower and the upper quartile and the line is the median. (b) Stress-stretch response of adjacent samples from the upper back (see Fig. 1) with the same orientation (N = 10). Colours indicate different subjects while solid and dashed lines indicate samples to the right and left of the spinal line respectively.This illustrates the inter-subject and intra-subject variations between adjacent samples with the same orientation.

Fig. 7 Fig. 5 -Fig. 6 -

 756 Fig. 5 -Influence of orientation on the initial slope, elastic modulus, failure stretch, strain energy and UTS. Values given include mean and standard deviations.

Fig

  Fig. 7 -(a) Comparison of stretch measurement from DIC and DS over the length of the specimen throughout the duration of a given tensile test. (b) Distribution of local Lagrangian strains just before rupture. Note the area of localized magnification in red. This is the location where rupture subsequently occurred.

Table 1 -

 1 Information on each test subject.

	Gender	Age (years)	Time elapsed a	Label
	Male	97	9	A
	Male	91	3	B
	Female	97	2	C
	Female	81	3	D
	Male	89	3	E
	Female	85	4	F
	Female	86	4	G
	a Number of days elapsed after death prior to testing.

Table 2 -

 2

	Orientation with	Preferred	Level of
	respect to Langer	orientation, Θ	dispersion,
	lines		b
	0 •	40 •	0.5222
	0 •	16 •	1.1605
	0 •	16 •	1.1471
	0 •	168 •	0.6004
	45 •	40 •	0.8388
	45 •	61 •	0.7926
	45 •	46 •	0.7453
	45 •	53 •	0.4209
	45 •	57 •	0.8326
	45 •	83 •	0.9330
	90 •	73 •	0.9007
	90 •	120 •	0.6197

Mean orientation of collagen fibres and their Langer Line orientations. (Note that the data given is axial data i.e. it represents undirected lines and does not distinguish between θ and π + θ

[START_REF] Jones | Matlab functions to analyze directional (azimuthal) data-I: single-sample inference[END_REF]

e.g. the orientation of 0 • and 180 • are equivalent.)

Table 3 -

 3 Mean ± standard deviation for each orientation/location group.

	Langer line	Location	N	UTS (MPa)	Strain energy	Failure	Elastic modulus	Initial
	orientation				(MJ/m 3 )	stretch	(MPa)	slope (MPa)
	Parallel	Middle	9	28.64 ± 9.03	4.28 ± 1.49	1.46 ± 0.07	112.47 ± 36.49	1.21 ± 0.97
	Parallel	Bottom	7	17.60 ± 4.77	2.54 ± 0.76	1.74 ± 0.32	73.81 ± 19.41	1.95 ± 1.34
	45 •	Top	12	22.7 ± 3.61	3.80 ± 0.92	1.52 ± 0.10	82.62 ± 17.36	0.99 ± 0.51
	45 •	Middle	9	28.85 ± 7.87	5.38 ± 2.59	1.52 ± 0.15	103.49 ± 41.20	1.33 ± 0.96
	45 •	Bottom	5	20.23 ± 4.18	3.31 ± 0.67	1.43 ± 0.04	82.81 ± 18.43	1.30 ± 0.60
	Perpendicular	Middle	9	16.53 ± 5.71	2.98 ± 0.89	1.52 ± 0.08	63.75 ± 24.59	0.91 ± 0.68
	Perpendicular	Bottom	5	10.56 ± 8.41	2.44 ± 1.04	1.61 ± 0.14	37.66 ± 36.41	0.54 ± 0.33

Table 4 -

 4 Local and overall maximum stretch ratios for five different samples. Local magnification of the stretch ratio occurs just before rupture.

	Sample	Local max	Overall specimen
		stretch ratio	stretch ratio
	1	1.47	1.38
	2	1.45	1.40
	3	1.65	1.45
	4	1.70	1.48
	5	1.70	1.50

Table 5 -

 5 Comparison of results obtained to results in the literature. All experiments were carried out in-vitro on excised human skin. Results are displayed as means (± standard deviation) and ranges.

	Author	Test type	UTS	Failure	Elastic	Initial	Site a Age
			(MPa)	strain (%)	modulus (MPa)	slope (MPa)
	Jansen and Rottier (1958b)	In vitro tension	1-24	17-207	2.9-54.0	0.69-3.7	Ab	0-99
	Dunn (1983)	In vitro tension	2-15		18.8	0.1	AB	47-86
							& T
	Vogel (1987)	In vitro tension	5-32	30-115	15-150		V	0-90
	Jacquemoud et al. (2007)	In vitro tension	5.7-12.6	27-59	19.5-87.1		F &	62-98
							A
	Agache et al. (1980)	In vivo torsion			0.42-0.85		Back	3-89
	Diridollou et al. (1998)	In vivo suction			0.12-0.25		A &	20-30
							F
	Khatyr et al. (2004)	In vivo tension			0.13-0.66		Tibia	22-68
	Pailler-Mattei et al. (2008)	In vivo indentation			0.0045-0.008		A	30
	Zahouani et al. (2009)	In vivo indentation			0.0062-0.0021		A	55-70
		and static friction
	Our results	In vitro tensile	21.6 ± 8.4 54 ± 17	83.3 ± 34.9	1.18 ± 0.88	Back	81-97

a Ab = abdomen, T = thorax, V = various, F = forehead, A = arm.

Acknowledgements

This research was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme, awarded to MD. It was also supported by IRCSET (Irish Research Council for Science, Engineering and Technology) through the Ulysses Award, and IRCSET and the Office of the State Pathologist (Irish Department of Justice