NpH-MD-Simulations of the Elastic Moduli of Cellulose II at Room Temperatue

We have used molecular dynamics modeling to investigate the stucture and mechanical properties of regenerated cellulose fibres. This work is motivated by continued interest in replacing the environmentally hazardous viscose process by alternative spinning methods. An important input parameter for any realistic model of the elastic properties is the stiffness tensor of the crystalline constituent, cellulose II. Conventional molecular mechanics techniques can be used to estimate the elastic reaction of a material with respect to small external stresses or strains, i.e. the compliance and stiffness tensors, and the elastic moduli derived therefrom, at zero temperature. In order to access non-zero temperatures, it is necessary to use either the quasi-harmonic approximation for the vibrational free energy or molecular dynamics (MD) simulations. In the present work, Parrinello-Rahman constant-stress MD was performed to generate trajectories in constant particle number (N), constant external stress tensor (p or t) and constant enthalpy H (NpH or HtN) ensemble. This was found to be less time consuming than working with isothermal conditions, as done by other authors. The fluctuations in kinetic energy and MD cell vectors were then used to calculate adiabatic elastic constants, thermal expansion coefficients and heat capacity. The isothermal elastic constants were found by applying a standard thermodynamic relation. The Youngs modulus along the chain direction, E_l, was determined to be 155 GPa, whereas the values in the perpendicular directions vary between 51 and 24 GPa. These results are of the same order of magnitude as those obtained by Tashiro and Kobayashi [1] with the static (T = 0K) method, but our value of E_l is 5% lower and, unexpectedly, the lateral values are up to six times higher. A strong anisotropy is found for shear along the chains in planes containing the chain axis, the shear modulus ranging from 5 to 20 GPa. Convergence was achieved in the simulations, to the extend that the elastic constants become stationary, but significant internal stresses remain, pointing to shortcomings in the software used. Further work is necessary to resolve these problems, although the major conclusions should be unaffected.     

Micromechanical understanding of the cell-wall structure

For improving properties of pulp fibres, a better understanding of the relationships between its macroscopic mechanical properties, fibre ultrastructure, and properties of the wood polymers is important. This paper discusses such relations between elastic properties of fibres, their matrix structure and the wood polymer elastic constants. It is argued that an orientation of all of the wood polymers in the direction of the cellulose microfibrils is most likely. The elastic longitudinal modulus of cellulose is well described by the value of 134 GPa dominating the longitudinal fibre properties. In the transverse direction the amorphous polymers play a more important role.     

Mechanical properties of physiological and pathological models of collagen peptides investigated via steered molecular dynamics simulations

In this work we used molecular simulations to investigate the elastic properties of collagen single chain and triple helix with the aim of understanding its features starting from first principles. We analysed ideal collagen peptides, homotrimeric and heterotrimeric collagen type I and pathological models of collagen. Triple helices were found much more rigid than single chains, thus enlightening the important role of interchain stabilizing forces, like hydrophobic interaction and hydrogen bonds. We obtained Young's moduli close to 4.5GPa for the ideal model of collagen and for the physiological heterotrimer, while the physiological homotrimer presented a Young's modulus of 2.51GPa, that can be related to a mild form of Osteogenesis Imperfecta in which only the homotrimeric form of collagen type I is produced. Otherwise, the pathological model (presenting a glycine to alanine substitution) showed an elastic modulus of 4.32GPa, thus only slightly lower than the ideal model. This suggests that this mutation only slightly affects the mechanical properties of the collagen molecule, but possibly acts on an higher scale, such as the packing of collagen fibrils.     

Determination of Young's modulus for nanofibrillated cellulose multilayer thin films using buckling mechanics

The Young's modulus of multilayer films containing nanofibrillated cellulose (NFC) and polyethyleneimine (PEI) was determined using the strain-induced elastic buckling instability for mechanical measurements (SIEBIMM) technique. (1) Multilayer films were built up on polydimethylsiloxane substrates using electrostatic layer-by-layer assembly. At 50% relative humidity, SIEBIMM gave a constant Young's modulus of 1.5 ± 0.2 GPa for 35-75 nm thick films. Conversely, in vacuum, the Young's modulus was 10 times larger, at 17.2 ± 1.2 GPa. A slight decrease in buckling wavelength with increasing strain was observed by scanning electron microscopy with in situ compression, and above 10% strain, extensive cracking parallel to the compressive direction occurred. We conclude that whereas PEI acts as a "glue" to hold multiple layers of NFC together, it prevents full development of hydrogen bonding and specific fibril-fibril interactions, and at high humidity, its hygroscopic nature decreases the elastic modulus when compared with pure NFC films.     

Changes in the molecular orientation and tensile properties of uniaxially drawn cellulose films

Cellulose films were prepared by dissolving lyocell fibers in LiCl/N,N-dimethylacetamide solvent and subsequently coagulating and drying them under ambient conditions. To introduce preferred orientation, the films were uniaxially drawn under air-dry and rewetted conditions, respectively. Preferred orientation was determined by birefringence measurements and by wide-angle X-ray scattering. Mechanical properties were characterized by means of tensile tests with films conditioned to standard temperatures and humidity. Drawing resulted in the substantial reorientation of cellulose, whereby the molecular chains in the amorphous regions exhibited clearly stronger reorientation than the crystalline fraction. The average degree of orientation was comparable to orientation achieved in spun cellulose fibers. Wet-drawing resulted in improved tensile strength and modulus of elasticity but reduced elongation at break. The mechanical properties of wet-drawn films are competitive with regard to cellophane and melt-blown cellulose films, particularly considering their high modulus of elasticity of up to 26 GPa, which is also comparable to values obtained for industrially produced cellulose fibers.     

Bacterial cellulose nanocrystals exhibiting high thermal stability and their polymer nanocomposites

Nanocrystals prepared from bacterial cellulose are considered as 'green nanomaterials' depending on their renewable nature and ease of production without the involvement of hazardous chemical treatments. In this investigation, a top down approach was followed for the preparation of bacterial cellulose nanocrystals (BCNC) using a commercially available cellulase enzyme so as to retain native properties of bacterial cellulose even in its nanodimensional form. The morphological and dimensional parameters of BCNC were studied using atomic force microscope (AFM) and transmission electron microscope (TEM). Thermal properties of BCNC produced using the novel enzyme treatment and conventional sulfuric acid hydrolysis were compared. The thermal stability of enzyme processed BCNC was almost two fold higher than sulfuric acid processed ones. Further, the activation energy required for decomposition of enzyme processed BCNC was much higher than the other. Using this enzyme processed BCNC, Polyvinylalcohol (PVA) nanocomposite films were prepared and characterized. Incorporation of these nanocrystals in polymer matrix resulted in a remarkable improvement in the thermal stability as well as mechanical properties of nanocomposite films. These nanocomposites exhibited higher melting temperature (Tm) and enthalpy of melting (ΔHm) than those of pure PVA, suggesting that the addition of nanocrystals modified the thermal properties of PVA. The effective load transfer from polymer chains to the BCNC resulted in an improved tensile strength from 62.5 MPa to 128 MPa, by the addition of just 4 wt% of BCNC. Furthermore, the elastic modulus was found to increase from 2 GPa to 3.4 GPa. The BCNC obtained through cellulose treatment under controlled conditions were associated with several desirable properties and appear to be superior over the conventional methods of nanocrystals production. The enzymatic method followed in this study is expected to contribute the fabrication of high performance polymer nanocomposites in a much greener and innovative manner.     

Effects of age on elastic moduli of human lungs.

The model of the lung as an elastic continuum undergoing small distortions from a uniformly inflated state has been used to describe many lung deformation problems. Lung stress-strain material properties needed for this model are described by two elastic moduli: the bulk modulus, which describes a uniform inflation, and the shear modulus, which describes an isovolume deformation. In this study we measured the bulk modulus and shear modulus of human lungs obtained at autopsy at several fixed transpulmonary pressures (Ptp). The bulk modulus was obtained from small pressure-volume perturbations on different points of the deflation pressure-volume curve. The shear modulus was obtained from indentation tests on the lung surface. The results indicated that, at a constant Ptp, both bulk and shear moduli increased with age, and the increase was greater at higher Ptp values. The micromechanical basis for these changes remains to be elucidated.     

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 microns). While the modulus values for relatively large specimens (h greater than 500 microns) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.     

Mechanical properties of primary plant cell wall analogues

Mechanical effects of turgor pressure on cell walls were simulated by deforming cell wall analogues based on Acetobacter xylinus cellulose under equi-biaxial tension. This experimental set-up, with associated modelling, allowed quantitative information to be obtained on cellulose alone and in composites with pectin and/or xyloglucan. Cellulose was the main load-bearing component, pectin and xyloglucan leading to a decrease in modulus when incorporated. The cellulose-only system could be regarded as an essentially linear elastic material with a modulus ranging from 200 to 500 MPa. Pectin incorporation modified extensibility properties of the system by topology/architecture changes of cellulose fibril assemblies, but the cellulose/pectin composites could still be described as a linear elastic material with a modulus ranging from 120 to 250 MPa. The xyloglucan/cellulose composite could not be modelled as a linear elastic material. Introducing xyloglucan into a cellulose network or a cellulose/pectin composite led to very compliant materials characterised by time-dependent creep behaviour. Modulus values obtained for the composite materials were compared with mechanical data found for plant-derived systems. After comparing bi-axial and uni-axial behaviour of the different composites, structural models were proposed to explain the role of each polysaccharide in determining the mechanical properties of these plant primary cell wall analogues.     

Elastic modulus and stress-transfer properties of tunicate cellulose whiskers

Experimental deformation micromechanics of natural cellulose fibers using Raman spectroscopy and X-ray diffraction have been widely reported. However, little has been published on the direct measurements of the mechanical properties, and in particular the elastic modulus, of the highly crystalline material in the native state. Here we report on measurements of the elastic modulus of tunicate cellulose using a Raman spectroscopic technique. A dispersed sample of the material is deformed using a four-point bending test, and a shift in a characteristic Raman band (located at 1095 cm(-1)) is used as an indication of the stress in the material. Relatively little intensity change of the Raman band located at 1095 cm(-1) is shown to occur for samples oriented parallel and perpendicular to the polarization direction of the laser, as compared to a highly oriented flax sample. This indicates that the tunicate sample is a two-dimensional in-plane random network of fibers. By use of this result, the Raman shift, and calibrations with strain from other materials, it is shown that the modulus of the material is very high, at about 143 GPa, and a lack of Raman band broadening is thought to be due to the fact that there is pure crystalline deformation occurring without the effect of crystalline/amorphous fractions. A strain sensitivity of the shift in the 1095-cm(-1) Raman peak for this specimen is shown to be -2.4 +/- 0.2 cm(-1)/%. A molecular mechanics approach, using computer simulation and an empirical force field, was used to predict the modulus of a highly oriented chain of the material, and this is found to be 145 GPa, which is in agreement with the experimental data. However, by use of a normal-mode analysis, it is found that a number of modes have positions close to the central positions of the experimental Raman band. One in particular is found to shift at a rate of 2.5 cm(-1)/%, but due to the complex nature of the structure, it is not entirely conclusive that this band is representative of the experimental findings.     

Anharmonic compression of the glitter lattice

A previous report has described the crystal structure of glitter, which is a dense 3-,4-connected net composed of ethylenic columns that run parallel to the c-axis of the unit cell. Such a structure invites speculation as to its relative stiffness along that axis. A semiempirical expression due to Cohen was used in a previous communication to estimate its zero-pressure bulk modulus. This estimate exceeds that of any known material at 440 GPa. Further, by treating the ethylenic units as harmonic springs, a correction was computed for the elastic deformation of the carbon-carbon double bonds along the c-axis. This correction is on the order of 300 GPa for deformations of the double bonds of approximately 0.1 angstroms. The present communication treats the ethylenic units along the c-axis of glitter as anharmonic springs obeying a Morse potential and a Morse's law force. Within the anharmonic approximation, at modest bond length deformations, x', the bulk modulus at pressure of the glitter lattice exceeds 1 TPa.     

Ab initio predictions of structural and elastic properties of struvite: contribution to urinary stone research

In the present work, we carried out density functional calculations of struvite--the main component of the so-called infectious urinary stones--to study its structural and elastic properties. Using a local density approximation and a generalised gradient approximation, we calculated the equilibrium structural parameters and elastic constants C(ijkl). At present, there is no experimental data for these elastic constants C (ijkl) for comparison. Besides the elastic constants, we also present the calculated macroscopic mechanical parameters, namely the bulk modulus (K), the shear modulus (G) and Young's modulus (E). The values of these moduli are found to be in good agreement with available experimental data. Our results imply that the mechanical stability of struvite is limited by the shear modulus, G. The study also explores the energy-band structure to understand the obtained values of the elastic constants.     

贝壳珍珠层不同取向弹性模量的研究

研究天然生物材料的组织结构特征与其性能之间的关系对于材料的仿生有重要意义．在自制的激光测试设备上用三点弯曲法对贝壳珍珠层不同取向的弹性模量进行了研究,报道了不同取向和加载方式条件下弹性模量的变化规律。结果表明,在平行和倾斜于生长纹路方向上弹性模量的平均值分别为60．3GPa和56．7GPa,而垂直于纹路方向的为48GPa,呈现出各向异性。弹性模量的各向异性主要来自于珍珠层微观组织结构和贝壳生长纹结构的特点．     

Use of a Digital Image Correlation Technique for Measuring the Material Properties of Beetle Wing

Beetle wings are very specialized flight organs consisting of the veins and membranes.Therefore it is necessary from abionic view to investigate the material properties of a beetle wing experimentally.In the present study,we have used a DigitalImage Correlation (DIC) technique to measure the elastic modulus of a beetle wing membrane.Specimens were prepared bycarefully cutting a beetle hind wing into 3.0 mm by 7.0 mm segments (the gage length was 5 mm).We used a scanning electronmicroscope for a precise measurement of the thickness of the beetle wing membrane.The specimen was attached to a designedfixture to induce a uniform displacement by means of a micromanipulator.We used an ARAMISTM system based on the digitalimage correlation technique to measure the corresponding displacement of a specimen.The thickness of the beetle wing variedat different points of the membrane.The elastic modulus differed in relation to the membrane arrangement showing a structuralanisotropy;the elastic modulus in the chordwise direction is approximately 2.65 GPa,which is three times larger than the elasticmodulus in the spanwise direction of 0.84 GPa.As a result,the digital image correlation-based ARAMIS system was suc-cessfully used to measure the elastic modulus of a beetle wing.In addition to membrane’s elastic modulus,we considered thePoisson’s ratio of the membrane and measured the elastic modulus of a vein using an Instron universal tensile machine.Theresult reveals the Poisson’s ratio is nearly zero and the elastic modulus of a vein is about 11 GPa.     

Elastic energy storage in human articular cartilage: estimation of the elastic modulus for type II collagen and changes associated with osteoarthritis.

The viscoelastic mechanical properties of normal and osteoarthritic articular were analyzed based on data reported by Kempson [in: Adult Articular Cartilage (1973)] and Silver et al. (Connect. Tissue Res., 2001b). Results of the analysis of tensile elastic stress-strain curves suggest that the elastic modulus of cartilage from the superficial zone is approximately 7.0 GPa parallel and 2.21 GPa perpendicular to the cleavage line pattern. Collagen fibril lengths in the superficial zone were found to be approximately 1265 microm parallel and 668 microm perpendicular to the cleavage line direction. The values for the elastic modulus and fibril lengths decreased with increased extent of osteoarthritis. The elastic modulus of type II collagen parallel to the cleavage line pattern in the superficial zone approaches that of type I collagen in tendon, suggesting that elastic energy storage occurs in the superficial zone due to the tensile pre-tension that exists in this region. Decreases in the elastic modulus associated with osteoarthritis reflect decreased ability of cartilage to store elastic energy, which leads to cartilage fibrillation and fissure formation. We hypothesize that under normal physiological conditions, collagen fibrils in cartilage function to store elastic energy associated with weight bearing and locomotion. Enzymatic cleavage of cartilage proteoglycans and collagen observed in osteoarthritis may lead to fibrillation and fissure formation as a result of impaired energy storage capability of cartilage.     

Effect of long-term anemia and retransfusion on central circulation during exercise

The bulk modulus and the shear modulus describe the capacity of material to resist a change in volume and a change of shape, respectively. The values of these elastic coefficients for air-filled lung parenchyma suggest that there is a qualitative difference between the mechanisms by which the parenchyma resists expansion and shear deformation; the bulk modulus changes roughly exponentially with the transpulmonary pressure, whereas the shear modulus is nearly a constant fraction of the transpulmonary pressure for a wide range of volumes. The bulk modulus is approximately 6.5 times as large as the shear modulus. In recent microstructural modeling of lung parenchyma, these mechanisms have been pictured as being similar to the mechanisms by which an open cell liquid foam resists deformations. In this paper, we report values for the bulk moduli and the shear moduli of normal air-filled rabbit lungs and of air-filled lungs in which alveolar surface tension is maintained constant at 16 dyn/cm. Elevating surface tension above normal physiological values causes the bulk modulus to decrease and the shear modulus to increase. Furthermore, the bulk modulus is found to be sensitive to a dependence of surface tension on surface area, but the shear modulus is not. These results agree qualitatively with the predictions of the model, but there are quantitative differences between the data and the model.     

Elastic modulus of trabecular bone material

An ultrasonic technique was used to measure both the elastic modulus (Young's modulus) of trabecular bone material and the elastic modulus of the cancellous structure. The average trabecular modulus, measured on specimens obtained from three human and one bovine distal femora, was 13.0 GPa (S.D. 1.47) and 10.9 GPa (S.D. 1.57), respectively. On human specimens the structural elastic modulus was found to be related to the structural (apparent) density raised to the 1.88 power. The elastic modulus from the bovine specimens showed a more linear relationship with the density of the cancellous structure (density raised to the 1.57 power).     

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.     

3 种不同弹性模量钛合金股骨假体在羊股骨置换模型中应力分布的三维 有限元分析

目的:通过三维有限元分析方法来观察并比较3种不同弹性模量钛合金股骨假体在羊股骨置换模型中von-Mises应力分布的情况。方法:采用64排螺旋CT对一健康成年羊的下肢股骨进行全长的CT扫描,扫描层厚为0.5 mm,扫描所得的数据存储为DICOM文件。将得到的DICOM文件导入到CT图像分析软件Mimics 10.0,然后利用Mimics 10.0软件来生成股骨的骨质点云数据,再将生成的骨质点云数据导入到Simpleware分析软件,通过机械加工反求中的复杂曲面造型技术建立起精确的三维实体模型。对三维实体模型进行网格划分,确定了髓腔的形状,并根据羊下肢股骨髓腔的形状设计了作者实验用的羊股骨假体模型,然后在ANSYS 12.1软件中进行网格划分。给予加载缓慢行走载荷以及扭转载荷,分析并比较羊股骨以及3种不同弹性模量钛合金股骨假体在股骨置换模型中von-Mises应力分布的情况。结果:在缓慢行走载荷以及扭转载荷条件下,3种不同弹性模量钛合金股骨假体von-Mises应力分布变化趋势一致,假体的柄颈结合部以及假体柄上1/3为应力集中区域。3种不同弹性模量的最大应力集中点均位于柄颈结合部,60 GPa弹性模量的股骨假体植入后假体的最大应力最小(37.8 MPa、29.1 MPa),股骨的最大应力最大(12.6 MPa、24.5 MPa);80 GPa的次之,假体的最大应力(38.4 MPa、33.4 MPa),股骨的最大应力(12.5 MPa、24.5 MPa);110 GPa的股骨假体植入后假体的最大应力最大(38.9 MPa、38.1 MPa),股骨的最大应力最小(12.3 MPa、24.5 MPa)。60 GPa弹性模量的股骨假体植入后的假体最大位移和相对位移均最小(缓慢行走载荷下假体最大位移为0.551 mm、相对位移为0.008 mm,扭转载荷下假体最大位移为0.730 mm、相对位移为0.011 mm)。结论:较低弹性模量的钛合金股骨假体(60 GPa)由于其弹性模量更接近于骨组织的弹性模量,股骨假体与股骨间的"应力遮挡"效应较小,更有利于应力在股骨假体及股骨间的传递,增加了股骨假体的早期稳定性,延长了其临床寿命。     

Viscoelastic properties of f-actin, microtubules, f-actin/alpha-actinin, and f-actin/hexokinase determined in microliter volumes with a novel nondestructive method

A nondestructive method to determine viscoelastic properties of gels and fluids involves an oscillating glass fiber serving as a sensor for the viscosity of the surrounding fluid. Extremely small displacements (typically 1-100 nm) are caused by the glass rod oscillating at its resonance frequency. These displacements are analyzed using a phase-sensitive acoustic microscope. Alterations of the elastic modulus of a fluid or gel change the propagation speed of a longitudinal acoustic wave. The system allows to study quantities as small as 10 microliters with temporal resolution >1 Hz. For 2-100 microM f-actin gels a final viscosity of 1.3-9.4 mPa s and a final elastic modulus of 2.229-2.254 GPa (corresponding to 1493-1501 m/s sound velocity) have been determined. For 10- to 100-microM microtubule gels (native, without stabilization by taxol), a final viscosity of 1.5-124 mPa s and a final elastic modulus of 2.288-2. 547 GPa (approximately 1513-1596 m/s) have been determined. During polymerization the sound velocity in low-concentration actin solutions increased up to +1.3 m/s (approximately 1.69 kPa) and decreased up to -7 m/s (approximately 49 kPa) at high actin concentrations. On polymerization of tubulin a concentration-dependent decrease of sound velocity was observed, too (+48 to -12 m/s approximately 2.3-0.1 MPa, for 10- to 100-microM tubulin). This decrease was interpreted by a nematic phase transition of the actin filaments and microtubules with increasing concentration. 2 mM ATP (when compared to 0.2 mM ATP) increased polymerization rate, final viscosity and elastic modulus of f-actin (17 microM). The actin-binding glycolytic enzyme hexokinase also accelerated the polymerization rate and final viscosity but elastic modulus (2.26 GPa) was less than for f-actin polymerized in presence of 0.2 mM ATP (2.28 GPa).