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Analytical Formulation of Stress Distribution in Cellulose Nanocomposites

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Abstract

Cellulose nanofibers are known to possess aspect ratios larger than 200 and mechanical properties comparable to carbon nanotubes. Combined with other significant properties including low cost, low density, and biocompatibility, cellulose nanofibers are an attractive reinforcement material for nanocomposites. The load transfer between embedded fibers and matrix play a major role in designing nanocomposites with ultimate mechanical properties. In this work, we studied a general case where a simple axial loading exists along the axis of a cellulose fiber embedded in a polymer matrix. Then analytical relation between the applied load, the longitudinal stress along the fiber, and shear stresses along the interface of fiber and matrix was derived. It is shown that the maximum longitudinal stress occurs at the middle of the fiber, while maximum shear stress occurs at the extreme ends. Also, it is shown that the shear stress along the cellulose fibers can be approximated as a linear function of applied load. The derived relationships are useful for design of cellulose-based nanocomposites with enhanced mechanical properties.

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An account is given on natural and man-made cellulose fiber reinforced plastics. Possible applications of this material group are detailed. A survey is also discussed about physical and chemical treatment methods that improve fiber matrix adhesion, as well as their results and effects on the physical properties of composites. The results show that natural fibers can be processed with the already commonly applied methods: glass mat thermoplastic matrix (GMT, sheet moulding compound (SMC) or bulk moulding compound (BMC).
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Hydroxyapatite (HAp) and bacterial cellulose (BC) are both excellent materials for use in biomaterial areas. The former has outstanding osteoconductivity and bioactivity and the latter is a high-strength nano-fibrous and extensively used biomaterial. In this work, the HAp/BC nanocomposites with a 3-dimensional (3-D) network were synthesized via a biological route by soaking both phosphorylated and unphosphorylated BCs in 1.5 simulated body fluid (SBF). Scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier transformed infrared spectroscopy (FTIR), and transmission electron microscopy (TEM) were employed to characterize the HAp/BC nanocomposites. SEM observations demonstrated that HAp crystals were uniformly formed on the phosphorylated BC fibers after soaking in 1.5 SBF whereas little HAp was observed on individual unphosphorylated BC fibers. Our experimental results suggested that the unphosphorylated BC did not induce HAp growth and that phosphorylation effectively triggered HAp formation on BC. Mechanisms were proposed for the explanation of the experimental observations. XRD and FTIR results revealed that the HAp crystals formed on the phosphorylated BC fibers were carbonate-containing with nano-sized crystallites and crystallinities less than 1%. These structural features were close to those of biological apatites.
Article
In previous works, the processing of nanocomposites of cellulose whisker filled thermoplastics was presented as well as their mechanical behaviour in the glassy state, both in the linear and non-linear domains. The purpose of the present work is to evaluate the mechanical properties of these composites in the rubbery state. A simple modelling of the mechanical behaviour, using the classical entropy elasticity theory, is proposed and discussed. Particular attention was paid to damage phenomena, already observed with stretched composite in the glassy state. Damage is mainly explained as a debonding of the matrix at the whisker interface. Small-Angle Neutron Scattering experiments performed on stretched composites provide supplementary information on the matrix microstructure with and without whiskers, and on the evolution of this microstructure with the sample deformation. Results confirm the heterogeneous characteristic of the matrix. Void scattering is identified and interpreted.
Article
The hardness and elastic modulus of the cellulose fiber and polypropylene (PP) matrix in a cellulose fiber-reinforced PP composite were investigated by nanoindentation with a continuous stiffness technique. Nanoindentation with different indentation depths and spacings was conducted to measure hardness and elastic modulus in the interphase region, which was modified by maleic anhydride-grafted PP and γ-amino propyltrimethoxy silane (γ-APS) sizing. A line of indents was produced from the fiber to the matrix. There was a gradient of hardness and modulus across the interphase region. The distinct properties of the transition zone were revealed by 1–4 indents, depending on nanoindentation depth and spacing. Based on the results of nanoindentation, it was assumed that the width of the property transition zone is less than 1 μm. However, three dimensional finite element analysis shows that even a perfect interface without property transition has almost same interphase width as that measured by nanoindentation. Using existing nanoindentation techniques, it will be difficult to calculate exact mechanical properties without the effect of neighboring material property in at least 8 times smaller region than indent size.
Article
We used molecular mechanics and molecular dynamics to study the nature of load transfer in a single walled carbon nanotube (SWCNT) bundle consisting of seven (10,10) SWCNTs: one core tube surrounded by six tubes on the perimeter. The surface tension and the inter-tube corrugation are identified as the two factors that contribute to load transfer. The surface tension effectively acts over a “line” (roughly over the circumference of each tube). The inter-tube corrugation scales linearly with respect to the contact surface area, and increases non-linearly as the inter-tube distance decreases. Relaxation in the nanotube cross-section leads to better inter-tube load transfer as a slight “faceting” develops; the tubes appear to be partially polygonized, rather than perfect cylinders. Compared with parallel bundles, twisting can significantly enhance the load transfer between neighboring tubes; this has been computed as a function of twist angle for this nanotube bundle system.
Article
Nanocomposite materials were prepared from copolymers of polyvinyl alcohol and polyvinyl acetate and a colloidal aqueous suspension of cellulose whiskers prepared from cotton linter. The degree of hydrolysis of the matrix was varied in order to vary the hydrophilic character of the polymer matrix and then the degree of interaction between the filler and the matrix. Nanocomposite films were conditioned at various moisture contents, and the dynamic mechanical and thermal properties were characterized using dynamic mechanical analysis and differential scanning calorimetry, respectively. Tensile tests were performed at room temperature to estimate mechanical properties of the films in the non linear range. All the results show that stronger filler/matrix interactions occur for fully hydrolyzed PVA compared to partially hydrolyzed samples. For moist samples, a water accumulation at the interface was evidenced. The reinforcing effect was found to be all the higher as the degree of hydrolysis of the matrix was high.
Article
The mechanical properties of the material surrounding a single carbon fiber in an epoxy matrix have been studied. Properties were determined within 100 nm of the fiber. A pronounced soft interphase was revealed adjacent to the fiber.A single fiber was embedded in a small supported disk of epoxy matrix. The fiber was loaded in tension. Examination of the surface displacements in the resin revealed that the matrix material within 250 nm of the fiber was substantially softer than the matrix far from the fiber. This interphase material was active in creep. Measurement of indentation properties of the matrix around a single fiber showed that the material close to the fiber exhibited an apparent high modulus due to restriction by the fiber. The implications of these findings are discussed.
Article
An analytical model has been developed to study stress transfer in single walled carbon nanotube (SWNT) reinforced polymer matrix composites. This model can be used to predict axial stress (σn) and interfacial shear stress (τi) along the carbon nanotube (CNT) embedded in matrix materials. A simplified 2D representative volume element (RVE) of CNT has been considered in this analysis. An expression for the effective length (Leff) of the carbon nanotube (CNT) has also been established for studying load transfer efficiency in CNT reinforced composites. The effects of CNT aspect ratio, CNT volume fraction and matrix modulus on axial stress (σn) and interfacial shear stress (τi) has also been analyzed in details. Finally, the results of this analytical model are compared with finite element analysis.
Article
There are many examples where animals or plants synthesize extracellular high-performance skeletal biocomposites consisting of a matrix reinforced by fibrous biopolymers. Cellulose is one, which occur as whiskerlike microfibrils that are biosynthesized and deposited in a continuous fashion. Mostly, this mode of biogenesis leads to crystalline microfibrils that are almost defect-free. In this study, attempts to imitate biocomposites are made by blending cellulose whiskers from the mantles of tunicates with synthetic polymer lattices. The films cast from such mixtures have a nanocomposite organization whose structure and mechanical properties are described in this paper.
Article
Nanocomposite materials were prepared from an elastomeric medium-chain-length poly(hydroxyalkanoate) (Mcl-PHA) latex as semicrystalline matrix using a colloidal suspension of hydrolyzed cellulose whiskers as natural and biodegradable filler. After stirring, the preparations were cast and evaporated. High-performance materials were obtained from this system, preserving the natural character of PHA. However, differences were reported by comparison with amorphous PHA filled systems. These differences were ascribed to a transcrystallization phenomenon of semicrystalline PHA on cellulose whiskers, evidenced by dynamic mechanical analysis. Transcrystallization hindered the mechanical percolation of cellulose whiskers and the formation of a rigid network within the polymer matrix during the film formation by evaporation. The whiskers network can reorganize under thermal aging.
Article
This work describes the static and the dynamic properties of fractionated microcrystal cellulose "whiskers" using elastic and quasi-elastic light scattering techniques. These colloidal particles have been obtained by acid hydrolysis from raw materials (tunicate, a marine animal) that lead to stable aqueous suspensions. The presence of charges along these rod-shaped particles induces a structural order in these suspensions, This has been highlighted, using light scattering, by the existence of several scattering peaks in the structure factor S(q) = 1(q)/P(q) as a function of the wavevector q. We have studied the static structure factor as well as the autocorrelation functions as a function of whisker concentration, C (2.6 x 10(-3) to 1.3 x 10(-2) g/cm(3)) and ionic strength (1 x 10(-6) to 1 x 10(-5) mol/L NaCl). In the absence of added salt, "salt-free" suspensions, the observed maxima, that are due to the electrostatic interactions, depend on the whisker concentration C and scale roughly as C-1/2. These maxima disappear progressively as the ionic strength is increased. At high ionic strength, the intensity scattered by these charged colloidal particles increases and reaches neutral system behavior, before the suspension flocculates. All these properties are found also in the dynamic behavior where the measured effective diffusion coefficient Gamma(q)/q(2), at low ionic strength, presents minima and maxima as a function of q and, as expected, is found to be inversely proportional to S(q).
Article
The cellulose nanofibrils that are found in wood and other natural materials are similar to carbon nanotubes in many ways and could be used to strengthen composites for manufacturing.
Article
Sulfuric acid hydrolysis of native cellulose fibers produces stable suspensions of cellulose nanocrystals. Above a critical concentration, the suspensions spontaneously form an anisotropic chiral nematic liquid crystal phase. We have examined the effect of reaction time and acid-to-pulp ratio on nanocrystal and suspension properties for hydrolyzed black spruce acid sulfite pulp. Longer hydrolysis times produced shorter, less polydisperse black spruce cellulose nanocrystals and slightly increased the critical concentration for anisotropic phase formation. Increased acid-to-pulp ratio reduced the dimensions of the nanocrystals thus produced; the critical concentration was increased and the biphasic range became narrower. A suspension made from a bleached kraft eucalyptus pulp gave very similar properties to the softwood nanocrystal suspension when prepared under similar hydrolysis conditions.
Article
The ability of the atomic force microscope to measure forces with subnanonewton sensitivity at nanometer-scale lateral resolutions has led to its use in the mechanical characterization of nanomaterials. Recent studies have shown that the atomic force microscope can be used to measure the elastic moduli of suspended fibers by performing a nanoscale three-point bending test, in which the center of the fiber is deflected by a known force. We extend this technique by modeling the deflection measured at several points along a suspended fiber, allowing us to obtain more accurate data, as well as to justify the mechanical model used. As a demonstration, we have measured a value of 78 +/- 17 GPa for Young's modulus of bacterial cellulose fibers with diameters ranging from 35 to 90 nm. This value is considerably higher than previous estimates, obtained by less direct means, of the mechanical strength of individual cellulose fibers.
Article
Polymer nanocomposites are one of the important application areas for nanotechnology. Naturally derived organic nanophase materials are of special interest in the case of polymer nanocomposites. Carboxymethyl cellulose is a polyelectrolyte derived from natural materials. It has been extensively studied as a hydrogel polymer. Methods to modify the mechanical properties of gels and films made from CMC are of interest in our lab and in the commercial marketplace. The effect of nano-sized fillers on the properties of CMC-based composites is of interest in the development of novel or improved applications for hydrogel polymers in general and CMC in particular. This project investigated cellulose nanocrystals (CNXLs) as a filler in CMC and compared the effects to microcrystalline cellulose (MCC). The composite material was composed of CMC, MCC or CNXL, with glycerin as a plasticizer. CNXL and MCC concentrations ranged from 5% to 30%. Glycerin concentrations were kept constant at 10%. CNXLs improved the strength and stiffness of the resulting composite compared to MCC. In addition, a simple heat treatment was found to render the nanocomposite water resistant.
Article
New nanocomposite films were prepared from a suspension of cellulose nanocrystals as the filler and a polycaprolactone-based waterborne polyurethane (WPU) as the matrix. The cellulose nanocrystals, prepared by acid hydrolysis of flax fiber, consisted of slender rods with an average length of 327 +/- 108 nm and diameter of 21 +/- 7 nm, respectively. After the two aqueous suspensions were mixed homogeneously, the nanocomposite films were obtained by casting and evaporating. The morphology, thermal behavior, and mechanical properties of the films were investigated by means of attenuated total reflection Fourier transform infrared spectroscopy, wide-angle X-ray diffraction, differential scanning calorimetry, scanning electron microscopy, and tensile testing. The results indicated that the cellulose nanocrystals could disperse in the WPU uniformly and resulted in an improvement of microphase separation between the soft and hard segments of the WPU matrix. The films showed a significant increase in Young's modulus and tensile strength from 0.51 to 344 MPa and 4.27 to 14.86 MPa, respectively, with increasing filler content from 0 to 30 wt %. Of note is that the Young's modulus increased exponentially with the filler up to a content of 10 wt %. The synergistic interaction between fillers and between the filler and WPU matrix played an important role in reinforcing the nanocomposites. The superior properties of the new nanocomposite materials could have great potential applications.
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