An effective medium model for the elastic moduli of fiber networks and nanocomposites

Chatterjee, Avik P.; Prokhorova, Darya A.

doi:10.1063/1.2732437

Cited by 13 publications

(18 citation statements)

References 39 publications

(33 reference statements)

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“…In recent years, this has triggered considerable investigation in characterizing the mechanical properties of continuous nanofibers ͑e.g., Young's modulus [9][10][11][12][13][14][15] ͒ and relevant mechanics modeling of fibers, fiber networks, and nanofiber composites. [16][17][18][19][20][21] To mention a few, atomic force microscopy ͑AFM͒-based uniaxial tension and three-point bending tests [9][10][11][12][13][14] have been conducted recently to characterize the Young's modulus and ultimate tensile strength of electrospun polymer nanofibers with diameters ranging from 1 m down to hundreds of nanometers. In a typical uniaxial tension test, one end of the nanofiber is fastened on the surface of a silicon wafer by adhesive and the other is tethered to the AFM tip.…”

Section: Introductionmentioning

confidence: 99%

Size effect in polymer nanofibers under tension

Dzenis

2007

Journal of Applied Physics

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This article studies the size effect on the elastic behavior of solid and hollow polymer nanofibers ͑e.g., electrospun nanofibers͒ subjected to uniaxial tension. A one-dimensional nonlinear elastic tension model is proposed that takes into account the coupling effect of fiber elastic deformation and surface tension. The fiber axial force-displacement and stress-strain relations are obtained in explicit forms. It is shown that, at nanoscale, fiber radius has appreciable effect on the elastic response of polymer nanofibers. With consideration of the fiber radial effect, it is shown that the actual contribution of surface energy of the solid polymer fibers to the axial tensile force is r 0 ␥ rather than 2r 0 ␥ ͑where r 0 is the fiber radius after deformation and ␥ is the surface tension͒, as commonly used in literature. Compared to solid polymer fibers, the tensile behavior of hollow polymer nanofibers appears more complex with greater axial stiffening effect depending upon the combination effect of the fiber exterior and interior radii and the material properties. The results presented in this study can be utilized for data reduction of the nanoscale tension tests of polymer nanofibers and the analysis and design of nanofiber devices.

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Section: Introductionmentioning

confidence: 99%

Size effect in polymer nanofibers under tension

Dzenis

2007

Journal of Applied Physics

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“…From Figure 2, it can be observed that for a given fiber radius, the area of the contact zone decreases rapidly with an increase of the angle φ between fibers since the adhesive force decreases very fast with an increase in the angle φ. In the case of fibers in orthogonal contact, the area of the contact zone reaches its minimum value: (22) In this case, the fiber pair has the minimum adhesive force based on relation (18), and therefore the fibers have the minimum deformation and elastic strain energy. Relation (21) also indicates the scaling properties of the area of the contact zone with respect to the fiber radius and the intrinsic length, i.e.…”

Section: Numerical Evaluation and Discussionmentioning

confidence: 99%

“…Neither fiber-fiber bonds nor transverse fiber deflections were taken into account. Moreover, by refining the fiber contact and deflection assumptions, quite a few fiber network models have been proposed afterwards that were validated by experiments and numerical simulations [12][13][14][15][16][17][18][19][20][21][22]. Among these, Carnaby and Pan [12,13] considered the effect of fiber friction and sliding on the mechanical response of fiber assemblies subjected to compression.…”

Section: Introductionmentioning

confidence: 99%

Adhesive contact in filaments

Wu¹,

Dzenis²

2007

J. Phys. D: Appl. Phys.

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This paper studies the elastic contact in filaments induced by surface adhesion, which plays an important role in the mechanical response of fibrous materials (e.g. fibre friction, sliding, compression hysteresis, etc). During the process, a simple 3D elastic contact model was proposed. The filaments were assumed to be uniform, smooth elastic cylinders and the adhesive force between filaments in contact was estimated according to Bradley's approach (Bradley 1932 Phil. Mag. 13 853) that relies on the filament configurations before deformation. Under the action of fibre surface adhesion, the elastic deformation and the size of the contact zone were determined in closed-form based on the DMT theory (Derjaguin et al 1975 J. Colloid Interface Sci. 53 314). Effects of filament radius and orientation, surface energies and elasticity on the elastic deformation and the size of the contact zone were explored numerically. The model developed in this work can be used for the study of the mechanisms of filament contacts, friction, sliding and compression hysteresis in fibrous materials subjected to external loading.

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“…The common approach to account for the adhesive potential is to simply treat contacts between fibers as rigid junctions, [19][20][21][22] which is only appropriate when fiber interactions are very strong. For viscoelastic fiber networks, Chatterjee 23 applied an energy penalty to the breaking of each fiberfiber contact and related it to the stored elastic energy of deformation. 23 However, a reliable model for any particular system requires accurate knowledge of the adhesive potential between fibers at network junctions, which is only obtained through experiments.…”

Section: Introductionmentioning

confidence: 99%

“…For viscoelastic fiber networks, Chatterjee 23 applied an energy penalty to the breaking of each fiberfiber contact and related it to the stored elastic energy of deformation. 23 However, a reliable model for any particular system requires accurate knowledge of the adhesive potential between fibers at network junctions, which is only obtained through experiments.…”

Section: Introductionmentioning

confidence: 99%

Dip-and-Drag Lateral Force Spectroscopy for Measuring Adhesive Forces between Nanofibers

Dolan¹,

Yakubov²,

Greene

et al. 2016

Langmuir

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Adhesive interactions between nano-fibers strongly influence the mechanical behavior of soft materials comprised of fibrous networks. We use atomic force microscopy (AFM) in lateral force mode to drag a cantilever tip through fibrous networks, and use the measured lateral force response to determine the adhesive forces between fibers of the order of 100 nm diameter. The peaks in lateral force curves are directly related to the detachment energy between two fibers; the data is analyzed using the Jarzynski equality to yield the average adhesion energy of the weakest links. The method is successfully used to measure adhesion forces arising from van der Waals interactions between electrospun polymer fibers in networks of varying density. This approach overcomes the need to isolate and handle individual fibers, and can be readily employed in the design and evaluation of advanced materials and biomaterials which, through inspiration from nature, are increasingly incorporating nano-fibers. The data obtained with this technique may also be of critical importance in the development of network models capable of predicting the mechanics of fibrous materials.

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An effective medium model for the elastic moduli of fiber networks and nanocomposites

Cited by 13 publications

References 39 publications

Size effect in polymer nanofibers under tension

Size effect in polymer nanofibers under tension

Adhesive contact in filaments

Dip-and-Drag Lateral Force Spectroscopy for Measuring Adhesive Forces between Nanofibers

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