Buckling Behavior of Carbon Nanotubes Functionalized with Carbene under Physical Adsorption of Polymer Chains: a Molecular Dynamics Study

The buckling analysis of functionalized carbon nanotubes (CNTs) is of great importance for the better understanding of mechanical behavior of nanocomposites. The buckling behavior of carbene-functionalized CNTs (cfCNTs) under physical adsorption of polymer chains (cfCNTs/polymers) is studied in this paper by the classical molecular dynamics (MD) simulations. In this regard, to investigate the interactions between non-covalent polymer chains and cfCNTs, two different non-covalent functional groups, i.e. polycarbonate (PC) and polypropylene (PP), are selected. The findings are compared with those of pure CNTs under the physical adsorption of polymer chains (pCNTs/polymers). The obtained results show that at a given weight percentage of non-covalent functional groups, the gyration radius of cfCNTs/polymers is higher than that of pCNTs/polymers. Furthermore, an increase in the critical buckling force of cfCNTs/polymers is dependent on the type of non-covalent polymer chains. For cfCNTs/PC and cfCNTs/PP, the critical buckling force is respectively lower and higher than that of pCNTs/polymers for the similar weight percentage of non-covalent functional groups. In addition, it is found that the critical buckling strain of cfCNTs/polymers is smaller than that of pCNTs/polymers for the same weight percentage of non-covalent polymer chains.     

Buckling instability in liquid crystalline physical gels

In a nematic gel we observe a low-energy buckling deformation arising from soft and semisoft elastic modes. We prepare the self-assembled gel by dissolving a coil-side-group liquid-crystalline polymer-coil copolymer in a nematic liquid crystal. The gel has long network strands and a precisely tailored structure, making it ideal for studying nematic rubber elasticity. Under polarized optical microscopy we observe a striped texture that forms when gels uniformly aligned at 35 degrees C are cooled to room temperature. We model the instability using the molecular theory of nematic rubber elasticity, and the theory correctly captures the change in pitch length with sample thickness and polymer concentration. This buckling instability is a clear example of a low-energy deformation that arises in materials where polymer network strains are coupled to the director orientation.     

Buckling of hybrid nanocomposites with embedded graphene and carbon nanotubes

With the aid of atomistic multiscale modelling and analytical approaches, buckling strength has been determined for carbon nanofibres/epoxy composite systems. Various nanofibres configurations considered are single walled carbon nano tube (SWCNT) and single layer graphene sheet (SLGS) and SLGS/SWCNT hybrid systems. Computationally, both eigen-value and non-linear large deformation-based methods have been employed to calculate the buckling strength. The non-linear computational model generated here takes into account of complex features such as debonding between polymer and filler (delamination under compression), nonlinearity in the polymer, strain-based damage criteria for the matrix, contact between fillers and interlocking of distorted filler surfaces with polymer. The effect of bridging nanofibres with an interlinking compound on the buckling strength of nano-composites has also been presented here. Computed enhancement in buckling strength of the polymer system due to nano reinforcement is found to be in the range of experimental and molecular dynamics based results available in open literature. The findings of this work indicate that carbon based nanofillers enhance the buckling strength of host polymers through various local failure mechanisms.     

Buckling of carbon nanotubes wrapped by polyethylene molecules

The discovery of a buckling instability of a single-walled carbon nanotube wrapped by a polyethylene molecule subjected to compression is reported through molecular mechanics simulations. A decrease up to 44% in the buckling strain of the nano-structure owing to the van der Waals interaction between the two molecules is uncovered. A continuum model is developed to calculate both the interaction between the tube and the polymer and the decreased buckling strain of the structure by fitting the molecular mechanics results.     

Polymerization of Langmuir–Blodgett films of diacetylenes

Monolayer and multilayer assemblies of Langmuir–Blodgett films of 10–12 pentacosadyinoic acid (12–8 diacetylene) were deposited on flat gold substrates. Micrometre-size features were patterned by polymerization of the films by using standard electron beam lithography. Polymerized areas on a monolayer and bilayer, as well as multilayer films, were examined by scanning electron microscopy, atomic force microscopy and resonant Raman spectroscopy. It was established that polymerized areas on a monolayer and bilayer LB film adhere onto the gold substrate after development. The exposure curve, sensitivity, contrast and resolution of the polymer have been determined by using atomic force microscopy and correlated with the deposition conditions and molecular parameters. Stresses induced in the organic film during polymerization lead to an in-plane buckling of the micrometre-size polymer structure. A simple self-consistent theory was developed to predict critical strain and critical length of buckling. The observed effect of buckling of polymers might open an avenue for a wide range of important practical applications in the area of nanomechanical engineering.     

Multi-scale bending,buckling and vibration analyses of carbon fiber/carbon nanotube-reinforced polymer nanocomposite plates with various shapes

Using a finite element-based multi-scale modeling approach, the bending, buckling and free vibration of hybrid polymer matrix composites reinforced by carbon fibers and carbon nanotubes (CF/CNT-RP) are analyzed herein. Thick composite plates with rectangular, circular, annular and elliptical shapes are considered. First, the equivalent material properties of CF/CNT-RP are calculated for different volume fractions of CF and CNT. To accomplish this aim, a two-step procedure is presented through which the coupled effects of nano- and micro-scale are taken into account. In the first step, modeling of dispersion of CNTs into the polymer matrix is done with considering interphase formed by their chemical interaction with the matrix, and the equivalent properties of resulting composite material are determined accordingly. CFs are then dispersed into CNT-RP which is considered a homogenous material in this step. Both distributions of CNTs and CFs are assumed to be random. After computing the equivalent properties of CF/CNT-RP for different volume fractions of its constituents, the bending, buckling and free vibration analyses of plates with different shapes are performed. It is shown that the reinforcement of the polymer matrix with both CF and CNT significantly affects the bending, buckling and free vibration characteristics of plates.     

Viscoelastic suppression of gravity-driven counterflow instability

Attempts to achieve "top kill" of flowing oil wells by pumping dense drilling "muds," i.e., slurries of dense minerals, from above will fail if the Kelvin-Helmholtz instability in the gravity-driven counterflow produces turbulence that breaks up the denser fluid into small droplets. Here we estimate the droplet size to be submillimeter for fast flows and suggest the addition of a shear-thickening or viscoelastic polymer to suppress turbulence. We find in laboratory experiments a variety of new physical effects for a viscoelastic shear-thickening liquid in a gravity-driven counterstreaming flow. There is a progression from droplet formation to complete turbulence suppression at the relevant high velocities. Thick descending columns show a viscoelastic analogue of the viscous buckling instability. Thinner streams form structures resembling globules on a looping filament.     

Motor-driven bacterial flagella and buckling instabilities

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff’s elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and motor torque. We present a elaborate analytical model for the buckling transition based on a helical rod which quantitatively reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella along the driving torque is not stable and comment on the biological relevance for marine bacteria.     

Structural instability in fluid-structure systems under hydrodynamic shock conditions

The effects of non-linear fluid-structure interaction on the dynamic buckling of structures are investigated. In particular the structural buckling characteristics are studied for the case of a strong shock wave propagating through a fluid medium striking a structure. Non-linear terms are retained for both fluid and structural systems. A one-dimensional example consisting of a perfect gas-spring-mass system is solved for shock wave loading. Solutions are obtained by using the finite element method. The numerical methods utilized appear to be applicable to complex multi-dimensional systems. It is shown that in a non-linear fluid-structure interaction problem the incident pressure may be amplified significantly during reflection from a structure. Thus, an acoustic fluid model may be non-conservative for strong shock problems. Structures in a fluid will buckle at an incident pressure level which is much less than that which causes buckling in a vacuum.     

Effects of structural defects on the compressive buckling of boron nitride nanotubes

In this paper, we examined the buckling of perfect and defective armchair boron nitride nanotubes with three types of vacancy defects, i.e. B- and N- single vacancy defects and B–N- double vacancy defect, using molecular dynamics simulations. To this end, all systems were modeled with a Tersoff-type potential, which is able to accurately describe covalent bonding of BN systems. We applied external uniaxial compressive forces to the nanotubes in vacuum and derived the critical buckling loads and strains, at room temperature in an NVT-ensemble. Our results showed significant differences between the critical buckling strengths of pristine and defective nanotubes. The resistance to axial buckling decreased with the introduction of one vacancy defect, and the B–N- double vacancy was the most seriously damaged structure, followed by B-vacancy and N-vacancy defects. Furthermore, the B-vacancy was shown to have the most significant effect on the decrease of the critical buckling strain. This can be attributed to the excessive asymmetries and perturbations induced in the structure of the nanotube and the local deformations around the defective site around the B-vacancy, even before loading. Moreover, results show that reduction in the buckling strength of the nanotube due to the presence of more than one B-vacancy defect depends on their distribution. If the two or three defects are close to each other, they act as a single point of weakness and the critical buckling load is only slightly reduced (similar to the existence of only one vacancy defect). However, if the defects are at more distant points, the critical buckling load may experience a higher decrease. Results show that vacancy defects play a critical role in the compressive buckling performance of boron nitride nanotubes and special attention must be paid to the presence of structural defects when designing members against buckling, especially for micro- and nano-electro-mechanical systems. On the other hand, defect engineering is a great means for tailoring the buckling strength of boron nitride nanotubes, in cases where the nanotube is expected to absorb energy through compressive buckling deformation and is not designed against, but for buckling.     

Bifurcations in the optimal elastic foundation for a buckling column

We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.     

Pulsed laser deposition of polymer-metal nanocomposites

Different polymer-metal nanocomposites, metal clusters on a polymer surface and for the first time also polymer/metal multilayers, were pulsed laser deposited at a wavelength of 248 nm. Poly(methyl methacrylate) (PMMA) and Bisphenol A dimeth-acrylate (BisDMA), which strongly differ in their hardness of 3 and 180 N/mm², respectively, were taken as polymer components. Metals Ag and Cu were chosen because of their different reactivity to polymers. When depositing Ag on PMMA, spherical clusters are formed due to high diffusion and total coalescence. For Cu, much smaller grains with partially elongated shapes occur because of lower diffusivity and incomplete coalescence. Compared to the results on the soft PMMA, the clusters formed on the harder BisDMA are much larger due to higher diffusivity on this underlayer. In PMMA/Cu multilayers, wavy layered structures and buckling is observed due to relaxation of compressive stress in the Cu layers. Smooth Cu layers with higher thicknesses can only be obtained, when the hardness of the polymer is sufficiently high, as in the case of BisDMA/Cu multilayers.     

Surface modification of poly[2-methoxy,5-(2′-ethyl-hexyloxy)-1,4-phenylene-vinylene] in the optical near field

We have studied the optical properties and the surface morphology of the conjugated polymer poly[2-methoxy,5-(2′-ethyl-hexyloxy)-1,4-phenylene-vinylene] (MEH-PPV), under laser irradiation at 488 nm emanating from the Al coated fiber probe of a near field scanning optical microscope. Laser irradiation of the polymer in the near field induces a degradation of the material demonstrated by a dynamic change in its optical transmission. The surface of the material is modified primarily by heat conduction from the fiber probe, which under our experimental conditions is the dominant heating mechanism in the near field.     

Structural relaxation and dynamic heterogeneity in a polymer melt at attractive surfaces

Molecular dynamics simulations of polymer melts at flat and structured surfaces reveal that, for the former, slow dynamics and increased dynamic heterogeneity for an adsorbed polymer is due to densification of the polymer in a surface layer, while, for the latter, the energy topography of the surface plays the dominant role in determining dynamics of interfacial polymer. The dramatic increase in structural relaxation time for polymer melts at the attractive structured surface is largely the result of dynamic heterogeneity induced by the surface and does not resemble dynamics of a bulk melt approaching T(g).     

考虑介质膨胀速率的锂离子电池管状电极中扩散诱导应力及轴向支反力分析

硅作为锂离子电池阴极材料相对于传统负极材料具有高比容量,价格低廉等优势.本文针对充电过程中锂离子电池中电极建立力学模型和扩散模型,并在扩散模型引入考虑介质膨胀速率的影响.以硅空心柱形电极为例,分析了恒流充电下介质膨胀速率对电极中扩散诱导应力分布的影响,并研究了不同内外半径比、充电速率、材料参数以及锂化诱导软化系数(lithiation induced softening factor,LISF)对轴向的支反力达到临界欧拉屈曲力所需时间的影响.结果表明,随着电极中锂浓度上升,介质膨胀速率对应力分布的影响增大,对轴向的支反力影响较小.弹性模量和应力成正比,但其与轴向的支反力达到临界欧拉屈曲力所需时间无关;扩散系数与所需时间成反比;偏摩尔体积增大时,达到临界屈曲力所需时间减少;随着LISF绝对值增大,完全锂化时轴向力降低.     

Buckling behaviors of open-tip carbon nanocones at elevated temperatures

This paper used molecular dynamics simulations to investigate buckling behaviors of open-tip carbon nanocones (CNCs) at elevated temperatures ranging from 300 to 700 K. Influences of cone height and apex angle on the buckling behaviors were examined. Some interesting findings, especially on the change in buckling mode shapes of the CNCs, were observed in the study. For the CNCs having an apex angle of 19.2°, the one with a lower cone height exhibited a shrinking/swelling buckling mode shape even at the higher temperature 700 K. However, as the cone height increased, the CNC displayed a deflective buckling mode shape at 300 K, but changed to a shrinking/swelling buckling mode shape when the temperature grew to 500 K. Regarding the influences of apex angle, the CNCs presented a deflective buckling mode shape even at 700 K as the apex angle expanded. This is opposite to the shrinking/swelling buckling mode shape of the CNC having the smallest apex angle of 19.2°.     

Instabilities of monolayered epithelia: shape and structure of villi and crypts

We study theoretically the shapes of a dividing epithelial monolayer of cells lying on top of an elastic stroma. The negative tension created by cell division provokes a buckling instability at a finite wave vector leading to the formation of periodic arrays of villi and crypts. The instability is similar to the buckling of a metallic plate under compression. We use the results to rationalize the various structures of the intestinal lining observed in vivo. Taking into account the coupling between cell division and local curvature, we obtain different patterns of villi and crypts, which could explain the different morphologies of the small intestine and the colon.     

Studying the buckling and vibration characteristics of single-walled zinc oxide nanotubes using a nanoscale finite element model

The free vibration and axial buckling of achiral zinc oxide nanotubes (ZnONTs) are studied in this paper based on a three-dimensional finite-element model in which bonds are modeled using beam elements and mass elements are placed at the joints of beams instead of atoms. To determine the mechanical properties of the nanotubes, a linkage is established between molecular mechanics and density functional theory. The fundamental frequency and critical buckling load of ZnONTs with different geometries, chiralities and boundary conditions are calculated. It is shown that zigzag nanotubes are more stable than armchair ones. Investigating the effect of aspect ratio on the critical force shows that longer nanotubes are less stable. Also, it is indicated that increasing the length of the nanotubes will result in decreasing the frequency. Moreover, as the aspect ratio increases, the effect of end conditions diminishes.     

Robust dithiocarbamate-anchored amine functionalization of Au nanoparticles

We introduce an effective and facile technique that achieves robust amine functionalization of Au nanoparticles by binding the polyamine poly(allylamine hydrochloride) (PAH) to the surface using a dithiocarbamate (DTC) modification of the side group amines. The DTC anchor confers superior short- and long-term colloidal stability compared to a physisorbed layer of the same polymer. We also demonstrate that the surface amines are available for further functionalization and that at least four alternately charged polyelectrolyte layers can be assembled onto the particles. The latter modification could not be performed on a physisorbed functional layer, so this demonstrates the effectiveness of the DTC groups in robustly anchoring the polymer to the particle surface. At the same time, the DTC-anchored polymer layer is less than 2 nm thick in the dry state. This is one-third of the thickness of a physisorbed polyamine layer deposited under the same conditions, and sufficiently thin that the plasmonic field enhancement on the metal particle remains accessible to the outside environment. We attribute the difference in thickness to multiple DTC bonds on each polymer chain forcing it into much closer conformity to the particle surface than in the physisorbed case.     

Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry through folding along portions of meridians. For the thinnest shells, a direct transition from the spherical conformation to the folded one can be observed. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of Poisson's ratio. In the folded conformation, the number of folds and inner pressure are investigated, allowing us to infer shell features from mere observation and/or knowledge of external constraints.