Graphene oxides for homogeneous dispersion of carbon nanotubes

Graphene oxides (GOs) in terms of both structure and property are essentially polyelectrolytes in a two-dimensional sheet configuration. As is well-established in the literature, polyelectrolytes are, in general, good dispersion agents for single-walled carbon nanotubes (SWNTs), which are otherwise in bundles because of strong van der Waals interactions. We report here a study in which GOs were used to disperse SWNTs, both as-purified and separated semiconducting SWNTs, for solution-like homogeneous suspensions. As a demonstration for their potentials, the optically transparent dispersions were used in a more accurate determination of the absorptivities for the band-gap transitions in semiconducting SWNTs. Results on exploration of the use of the GO-dispersed SWNTs in the development of unique carbon nanocomposite materials are also presented and discussed.     

Nonlinear elastic equation of state of solids subjected to uniaxial homogeneous loading

Applying the finite deformation theory to a solid, which possesses either cubic or isotropic symmetry at stress-free natural state and is subsequently loaded homogeneously in uniaxial direction, one obtains a stress (or strain) dependence of the Young's modulus, Poisson's ratio, and a volume (or density) change, together with a nonlinear elastic relation between stress and strain. These are all expressed in terms of the second and third order elastic constants of the solid material. These expressions are illustrated with examples of cubic silicon crystal, isotropic carbon steel, Pyrex glass, and polystyrene at the relaxed state.     

Temperature-dependent dispersion equations for KTiOPO4 and KTiOAsO4

We have measured the thermal expansion and the temperature dependence of z and y components of the refractive index for KTiOPO4 and KTiOAsO4, in the wavelength range 532-1585 nm and temperature range 25-200 degrees C, using an interferometric technique. The measurements were used to derive temperature-dependent Sellmeier equations for the two materials. These equations predict with good agreement the temperature dependence of quasi-phase-matched nonlinear frequency converters.     

Generalized hybrid-combined methods for the singularity problems of homogeneous elliptic equations

Combinations of the Ritz–Galerkin and finite element methods are applied to solving singularity problems of homogeneous, elliptic equations. The Ritz-Galerkin method is used in the subdomains where there exist singular points; and the finite element method is still used in the rest of the solution domains. More general coupling techniques than those of Reference 6 along the common boundary of subdomains are discussed. Numerical experiments using these kinds of coupling techniques are provided for the first time. It is interesting that the calculated results of Motz's problem have shown the simplified hybrid strategy in Reference 6 to be optimal for both error bounds and stability of numerical solutions, among all general coupling techniques.     

Analysis of Reynolds stress equations for stratified rotating homogeneous shear flow

An assessment of the Reynolds stress model of Gibson and Launder (GL model) in the prediction of rotation effects on stably stratified homogeneous shear flows has been conducted. The GL model is found to be capable of predicting the stabilizing and destabilizing effects of rotation. However, the quantitative predictions of the GL model are rather quite poor. In particular, the bifurcation diagrams of (ε/SK) are found not to be consistent with experimental findings. Deficiencies are traced to the pressure-strain model and the modeled dissipation equation.     

Non-local constitutive equations for functionally graded materials

In this paper, composites with a graded distribution of heterogeneities are considered. The heterogeneities vary in statistically non-uniform fashion since in a finite layer (or region) properties such as local volume fraction vary gradually. In order to study this class of composites, a procedure of analysis which leads to the effective constitutive non-local operator of the medium is proposed. For two-phase composites, an approximation of Hashin–Shtrikman type for this operator has been obtained in real space and this has been developed explicitly in the case of laminates.     

Digital algorithm for dispersion correction in optical coherence tomography for homogeneous and stratified media

The resolution of optical coherence tomography (OCT) often suffers from blurring caused by material dispersion. We present a numerical algorithm for computationally correcting the effect of material dispersion on OCT reflectance data for homogeneous and stratified media. This is experimentally demonstrated by correcting the image of a polydimethyl siloxane microfludic structure and of glass slides. The algorithm can be implemented using the fast Fourier transform. With broad spectral bandwidths and highly dispersive media or thick objects, dispersion correction becomes increasingly important.     

About the dynamic uniaxial tensile strength of concrete-like materials

Experimental methods for determining the tensile strength of concrete-like materials over a wide range of strain-rates from 10⁻⁴ to 10² s⁻¹ are examined in this paper. Experimental data based on these techniques show that the tensile strength increases apparently with strain-rate when the strain-rate is above a critical value of around 10⁰-10¹ s⁻¹. However, it is still not clear that whether the tensile strength enhancement of concrete-like materials with strain-rate is genuine (i.e. it can be attributed to only the strain-rate effect) or it involves “structural” effects such as inertia and stress triaxility effects. To clarify this argumentation, numerical analyses of direct dynamic tensile tests, dynamic splitting tests and spalling tests are performed by employing a hydrostatic-stress-dependent macroscopic model (K&C concrete model) without considering strain-rate effect. It is found that the predicted results from these three types of dynamic tensile tests do not show any strain-rate dependency, which indicates that the strain-rate enhancement of the tensile strength observed in dynamic tensile tests is a genuine material effect. A micro-mechanism model is developed to demonstrate that microcrack inertia is one of the mechanisms responsible for the increase of dynamic tensile strength with strain-rate observed in the dynamic tensile tests on concrete-like materials.     

Pseudodielectric functions of uniaxial materials in certain symmetry directions

The pseudodielectric function is often used to represent ellipsometric data and corresponds to the actual dielectric functions of materials when there is no surface overlayer and the material is isotropic. If a uniaxial material is oriented such that the optic axis is in the plane of incidence or is perpendicular to the plane of incidence, then the cross-polarization terms are zero and appropriate pseudodielectric functions can be determined from the ellipsometry data. We calculate the pseudodielectric functions for uniaxial crystals in three primary symmetry directions: (1) the optic axis is perpendicular to the plane of incidence, (2) the optic axis is in the plane of the sample surface and parallel to the plane of incidence, and (3) the optic axis is in the plane of the sample surface and perpendicular to the plane of incidence. These results are expanded in terms of the difference in the ordinary and extraordinary dielectric functions and compared with the approximation of Aspnes [J. Opt. Soc. Am. 70, 1275 (1980)]. Comparisons are made with experimental results on oriented crystals of rutile (TiO2), and a simple procedure is presented to determine the complex dielectric function from standard ellipsometry techniques.     

Field and Poynting vectors of homogeneous waves in uniaxial and absorbing dielectric media

The propagation of a homogeneous plane wave in uniaxial and absorbing dielectric media is described in detail. Complete expressions for electric displacement field, electric field, magnetic field and Poynting vector are derived using a new formalism that simplifies the interpretation of polarization. These expressions are analysed and verified in some particular situations. Whilst absorption is directly determined by the absorption coeffcient k, the field geometry depends exclusively on the absorption index X for given ordinary and extraordinary refractive indices. When ordinary and extraordinary absorption indices are equal, the field geometry coincides with the field geometry in a transparent medium with the same refractive index as the absorbing medium.     

Well-posedness of domain integral equations for a dielectric object in homogeneous background

An analysis of the mapping properties of three commonly used domain integro–differential operators for electromagnetic scattering by an inhomogeneous dielectric object embedded in a homogeneous background is presented in the Laplace domain. The corresponding three integro–differential equations are shown to be equivalent and well-posed under finite-energy conditions. The analysis allows for non-smooth changes, including edges and corners, in the dielectric properties. The results are obtained via the Riesz–Fredholm theory, in combination with the Helmholtz decomposition and the Sobolev embedding theorem.     

Fabrication of homogeneous titania/MWNT composite materials

MWNT/titania nanocomposites were prepared by an impregnation method and subsequent heat treatment at 400 °C. Precursor compounds such as titanium (IV) propoxide and titanium (IV) ethoxide were used to cover the surface of CNTs under solution conditions. Electron microscopy and X-ray diffraction techniques were carried out to characterize the as-prepared titania layers.     

The dispersion of birefringence in photoelastic materials

A spectral analyser was used to determine the variation with wavelength known as the dispersion of birefringence of the fringe constant f and the stress optic coefficient C for photoelastic materials. A disc was loaded diametrically and was subjected to the stress freezing thermal cycle. The intensity was measured along the diameter perpendicular to the load for wavelengths between 450 and 850 nm at 5 nm intervals. Using the theoretical solution to the stresses it was possible to calculate the stress optic coefficient for all wavelengths employed. A similar technique was used for an identical disc that was loaded at room temperature. It was found that the fringe constant was extremely linear with wavelength for both types of loading and for the materials CT200, CT1200 and MY750. The stress optic coefficient did not change much between sheets of the same material but was markedly different between materials. The dispersion of birefringence was found to be approximately constant but showed evidence of anomalous dispersion.     

Volumetric strain measurement of polymeric materials subjected to uniaxial tension

A novel method for measuring and calculating volumetric strain in circular cylindrical uniaxial tension samples made from polymeric materials is proposed. It is shown that special considerations must be taken when calculating volumetric strain when a sample is in a postnecking state. Solely based on surface data, the key feature of the proposed correction is that it allows for an inhomogeneous distribution of longitudinal strain through the diameter of the sample, where a more traditional approach would be to assume a homogeneous distribution. These two approaches are evaluated by applying them to data from a close‐to‐incompressible steel sample. Whereas the proposed method indicates only a small positive increase in volume, the assumption of a homogeneous distribution results in substantial negative volumetric strains. Applying the two methods to tension samples made from HDPE and PVC, where plastic dilatation is nonlinear, again shows an initial negative volumetric strain for HDPE with the assumption of a homogeneous longitudinal strain. The proposed method predicts close‐to‐zero early‐stage volumetric strain for the same test. The differences are more subtle for samples of PVC. Micrographs obtained with scanning electron microscope show that the dilatation of PVC is related to voiding of the material around filler particles, while the underlying mechanism for HDPE is less clear. The results indicate that earlier reports of negative volumetric strain in polymers subjected to uniaxial tension might be artefacts of the implicit assumption made when calculating the volumetric strain.     

Classification of all travelling-wave solutions for some nonlinear dispersive equations

We present a method for the classification of all weak travelling-wave solutions for some dispersive nonlinear wave equations. When applied to the Camassa-Holm or the Degasperis-Procesi equation, the approach shows the existence of not only smooth, peaked and cusped travelling-wave solutions, but also more exotic solutions with fractal-like wave profiles.     

Simple process for building large homogeneous adaptable retarders made from polymeric materials

A process for building large, homogeneous, adaptable retarders easily and at low cost is proposed and analyzed. This method is based on the properties of high polymers to present variable birefringence as a function of applied stresses and on the possibility of freezing these stresses inside the material by a thermal process. Various geometries for the applied forces make obtaining a large range of birefringence profiles possible. In the process that we describe composed bending leads to a linear birefringence profile. The superimposition of two pieces with identical profiles with opposite directions gives homogeneous constant retardation. This retardation can be adjusted by a relative displacement between the pieces. A precision of better than 1% over large areas (more than 3 cm in diameter) for a quarter-wave value has been obtained. The correct choice of material makes many applications possible with a large range of wavelengths.     

Stress intensity formulas for three-dimensional cracks in homogeneous and bonded dissimilar materials

This paper is concerned with maximum stress intensity factors of arbitrary shaped defects or cracks under mixed mode loading and also cracks terminating at an interface. A convenient formula is proposed in terms of parameter, where “area” is the projected area of the defects or cracks. First, a rectangular crack under mixed mode loading is considered with varying the aspect ratio and compared with the results of elliptical cracks. Then, parameter is found to be useful under mixed mode loading. Second, a rectangular crack, which is perpendicular to and terminating at a bimaterial interface, is investigated with varying the combinations of materials constants. At the crack front the maximum stress intensity factors are expressed as a function of the elastic ratio of the materials. On the other hand, the generalized stress intensity factors at the interface are expressed as a function of Dundurs parameters α and β. Proposed formulas are usefully evaluating defects with any aspect ratio under any combinations of the materials.