Lars Rosgaard Jensen

IUTAM Symposium on Modelling Nanomaterials and Nanosystems

Separation of two particles is characterized by a magnitude of the bond energy that limits the accumulated energy of the particle interaction. In the case of a solid comprised of many particles there exist a magnitude of the average bond energy that limits the energy that can be accumulated in a small material volume. The average bond energy can be calculated if the statistical distribution of the bond density is known for a particular material. Alternatively, the average bond energy can be determined in macroscopic experiments if the energy limiter is introduced in a material constitutive model. Traditional continuum models of materials do not have energy limiters and, consequently, allow for the unlimited accumulation of the strain energy. The latter is unphysical, of course, because no material can sustain large enough strains without failure. The average bond energy limits the strain energy and controls material softening, which indicates failure. Thus, by limiting the strain energy we include a description of material failure in the constitutive model. Generally, elasticity including energy limiters can be called softening hyperelasticity because it can describe material failure via softening. We illustrate the capability of softening hyperelasticity in examples of brittle fracture and arterial failure. First, we analyze the overall strength of arteries under the blood pressure. For this purpose we enhance various arterial models with the energy limiters. The models vary from the phenomenological Fung-type theory to the microstructural theories regarding the arterial wall as a bi-layer fiber-reinforced composite. Based on the simulation results we find, firstly, that residual stresses accumulated during artery growth can significantly delay the onset of arterial rupture like the pre-existing compression in the pre-stressed concrete delays the crack opening. Secondly, we find that the media layer is the main load-bearing layer of the artery. And, thirdly, we find that the strength of the collagen fibers dominates the media strength. Second, we numerically simulate tension of a thin plate with a preexisting central crack within a softening hyperelasticity framework and we find that the critical load essentially depends on the crack sharpness: the sharper is the crack the lower is the K.Y. Volokh Technion – Israel Institute of Technology, Haifa 32000, Israel; e-mail: cvolokh@technion.ac.il R. Pyrz and J.C. Rauhe (eds.), IUTAM Symposium on Modelling Nanomaterials and Nanosystems, 1–12.

Temperature-dependent densification of sodium borosilicate glass

Densified glasses recovered from a high-pressure state are of potential technological interest due to their modified physical and chemical properties. Here we investigate the temperature-dependent densification behavior of a sodium borosilicate glass in a gas pressure chamber at 1 GPa. The temperature is varied for a 30 min treatment between 0.6Tg and 1.15Tg, where Tg is the glass transition temperature, and the treatment duration is varied between 10 and 10 000 min for compression at 0.9Tg. Permanent densification occurs for temperatures above 0.7Tg and the degree of densification increases with increasing compression temperature and time, until attaining an approximately constant value for temperatures above Tg. The same temperature and time dependence is also found for the glass mechanical properties (hardness and brittleness) and the network structure, i.e., fraction of three-fold versus four-fold coordinated boron atoms and ring versus non-ring trigonal boron atoms, and the extent of mixing of Si and B. The results provide insights into the temperature-dependence of the network densification and the relative roles of viscous flow and more localized rearrangements.

Volume and structural relaxation in compressed sodium borate glass

The structure and properties of glass can be modified through compression near the glass transition temperature (Tg), and such modified structure and properties can be maintained at ambient temperature and pressure. However, once the compressed glass undergoes annealing near Tg at ambient pressure, the modified structure and properties will relax. The challenging question is how the property relaxation is correlated with both the local and the medium-range structural relaxation. In this paper, we answer this question by studying the volume (density) and structural relaxation of a sodium borate glass that has first been pressure-quenched from its Tg at 1 GPa, and then annealed at ambient pressure under different temperature-time conditions. Using 11B MAS NMR and Raman spectroscopy, we find that the pressure-induced densification of the glass is accompanied by a conversion of six-membered rings into non-ring trigonal boron (BIII) units, i.e. a structural change in medium-range order, and an increase in the fraction of tetrahedral boron (BIV), i.e. a structural change in short-range order. These pressure-induced structural conversions are reversible during ambient pressure annealing near Tg, but exhibit a dependence on the annealing temperature, e.g. the ring/non-ring BIII ratio stabilizes at different values depending on the applied annealing temperature. We find that conversions between structural units cannot account for the pressure-induced densification, and instead we suggest the packing of structural units as the main densification mechanism.

Foaming of Microcellular PP-MWCNT Nanocomposite in a Sub-Critical CO2 Process

The present work covers the processing route and investigation of PP-MWCNT nanocomposite foams. CO2 is used as a blowing agent in a batch foaming process with a saturation pressure range of 3-7 MPa. Carbon nanotubes act as nucleating agents during the foaming process, which is supported by SEM image analysis and DSC study. Relative density measurements have demonstrated that even though MWCNT promote nucleation of a large amount of cells, the densities of PP-MWCNT nanocomposite foams do not differ significantly from pure PP samples.

Synthesis and characterization of montmorillonite-carbon nanotubes hybrid fillers for nanocomposites

Montmorillonite-carbon nanotubes hybrids were prepared by growth of carbon nanotubes (CNT) on five different types of iron-montmorillonite clays using the chemical vapour deposition (CVD) method. Microscopy studies revealed the presence of carbon nanotubes protruding from clay surfaces and linking the clay layers in a network structure. X-ray diffraction results showed changes in the clay interlayer spacing induced by growth of carbon nanotubes within the layers of iron-montmorillonites. The quality of the resulting carbon nanotubes was evaluated by Raman spectroscopy and thermogravimetric analyzes were used to evaluate the amount of carbon nanotubes and its thermal stability. The method used for the preparation of the iron-montmorillonites appeared to be critical for the quality and quantity of carbon nanotubes obtained in each hybrid. In a preliminary study the hybrids were used to reinforce polyurethane nanocomposite foams.

Fabrication of microcellular PP-MMT nanocomposite foams in a subcritical CO2 process

The present paper is dedicated to fabrication of microcellular PP-MMT nanocomposite foams blown by CO2 at 3-7 MPa pressure range. XRD and TEM studies showed that MMT particles were well exfoliated upon PP-MMT nanocomposite processing, however presence of the nanoclay particles did not facilitate the foaming process, resulting in non-uniform cell structure and low expansion ratios. SEM images demonstrate that clay nanoparticles have not improved the foam morphology; and no nucleation effect of the clay was observed in the produced foams. These data were supported by DSC studies.

Molecular dynamics modeling of carbon nanotubes and their composites

The tensile modulus of individual nanotubes and nanotube‐polypropylene composites has been determined using molecular dynamics simulations. Simulations of individual single‐walled carbon nanotubes showed that their tensile modulus was dependent on the tube structure and the diameter if the diameter was below 1,6 nm. The tensile modulus was determined for an infinite single‐walled carbon nanotube embedded in an amorphous polypropylene matrix and for a finite and capped single‐walled carbon nanotube embedded in a polypropylene matrix. For the infinite nanotube‐polypropylene system the modulus was found to correspond to the one given by the Voigt approximation. For the finite nanotube‐polypropylene system the reinforcing effect of the nanotube was not very pronounced. A pull out simulation showed that the length of the nanotube in the simulation was much smaller than the critical length and hence no load transfer between the nanotube and the matrix existed.

Mutual-stabilization in chemically bonded graphene oxide–TiO2 heterostructures synthesized by a sol–gel approach

We study the structure of the photocatalytic graphene oxide–titanium dioxide (GO–TiO2) nanocomposites prepared by in situ sol–gel nucleation and growth of TiO2 on GO sheets. Fourier transform-infrared (FTIR) and X-ray photoelectron (XPS) spectra of these composites indicate that the GO sheets and the TiO2 nanoparticles interact through Ti–O–C bonds. This chemical interaction is strong enough to ensure mutual stabilization during thermal annealing, and thereby GO inhibits TiO2 crystallization. In addition, thermal reduction of GO nanoribbons anchored to TiO2 nanoparticles occurs at a higher temperature and with a lower released energy than in the pure GO powder. Understanding of the mutual-stabilization mechanisms is critical for the rational design of GO–TiO2 photocatalysts.

A molecular dynamics study on the interaction between epoxy and functionalized graphene sheets

The interaction between graphene and epoxy resin was studied using molecular dynamics simulations. The interfacial shear strength and pull out force were calculated for functionalised graphene layers (carboxyl, carbonyl, and hydroxyl) and epoxy composites interfaces. The influence of functional groups, as well as their distribution and coverage density on the graphene sheets were also analysed through the determination of the Youngs modulus. Functionalisation proved to be detrimental to the mechanical properties, nonetheless according to interfacial studies the interaction between graphene and epoxy resin increases.

Molecular Dynamics Study of Carbon Nanotubes in Bundles

Molecular mechanics and dynamics have applied to study the behavior of single wall carbon nanotube bundles. A geometrical transformation of the nanotube cross section was observed when the tube diameter exceeded 1,4 nm where the cross section changed from circular to hexagonal. The elastic properties of the bundles were examined and shown to depend on the tube diameter but not on the geometrical transition. The interfacial shear strength between the adjacent tubes was estimated and shown to depend both on the diameter and on the geometrical transition.Copyright