Preparation and characterization of Gd2O3:Eu rods by surfactant assemblies—microwave heating

Gd₂O₃:Eu³⁺ rods were successfully obtained by microwave heating the as-prepared substance, which templated by surfactant assemblies of gadolinium hydroxide and europium hydroxide, formed in a reaction between Gd(NO₃)₃-Eu(NO₃)₃ and urea. Transmission electron microscopy (TEM) characterizations indicated that the synthesized rods with an averaging diameter of 100-150 nm and agglomerates slightly. Powder X-ray diffraction (XRD) results indicated that the resultant rods were cubic Gd₂O₃. The luminescent of Gd₂O₃:Eu³⁺ rods were investigated by photoluminescence (PL). Upon excitation with 257 and 277 nm, respectively, Gd₂O₃:Eu³⁺ rods show a strong red emission line at around 611 nm. Furthermore, this novel method required a very short heating time, thus reducing the energy consumption.     

Cadmium thiosemicarbazide complexes as precursors for the synthesis of nanodimensional crystals of CdS

The single X-ray structures of the thiosemicarbazide complexes [Cd(NH₂CSNHNH₂)Cl₂]_n·H₂O (A) and [Cd(NH₂CSNHNH₂)₂Cl₂]_n (B) are reported. Both compounds have been found to be effective as single source precursors for the preparation of CdS nanomaterials. Thermal decomposition of the precursors in hexadecylamine (HDA) results in the formation of nanorods of different dimensions. The powder X-ray diffraction patterns of the nanodimensional materials reveal differences in the phases of the CdS synthesized from the two complexes. The particles synthesized from both precursors show quantum confinement effects in their absorption spectra, with the evidence of a broad defect emission in their photoluminescence spectra.     

Plectoneme formation in twisted fluctuating rods

The mechanics of DNA supercoiling is a subject of crucial importance to uncover the mechanism and kinetics of several enzymes. It is therefore being investigated using several biochemical and biophysical methods including single molecule experimental techniques. An interesting problem within this realm is that of torsional buckling and plectoneme formation in DNA as it is simultaneously put under tensile and torsional stress. Analytical solutions to this problem are difficult to find since it involves nonlinear kinematics and thermal fluctuations. In this paper we use ideas from the Kirchhoff theory of filaments to find semi-analytical solutions for the average shape of the fluctuating DNA under the assumption that there is no self-contact. The basic step in our method consists of combining a helical solution of the rod with a non-planar localizing solution in such a way that the force, moment, position and slope remain continuous everywhere along the rod. Our solutions allow us to predict the extension vs. linking number behavior of long pieces of DNA for various values of the tension and temperature. An interesting outcome of our calculations is the prediction of a sudden change in extension at buckling which does not seem to have been emphasized in earlier theoretical models or experiments. Our predictions are amenable to falsification by recently developed single molecule techniques which can simultaneously track the force-extension as well as the torque-rotation behavior of DNA.     

Dynamics of strings made of phase-transforming materials

This paper presents a theory to describe the dynamical behavior of a string made of a phase-transforming material like a shape-memory alloy. The study of phase boundaries, the driving force acting on them and the kinetic relation governing their propagation is of central concern. The paper proposes a qualitative experimental test of the notion of a kinetic relation, as well as a simple experimental method for measuring it quantitatively. It presents a numerical method for studying general initial and boundary value problems in strings, and concludes by exploring the use of phase transforming strings to generate motion at very small scales.     

Vibrations of rod-rigid element systems with a local non-linearity

The paper deals with vibrations of systems consisting of non-coaxial rods connected by rigid bodies and of a local non-linearity. The motion of the rods is described by classical wave equation and the solution of the d’Alembert type is applied in the study. This leads to solving ordinary differential equations with a retarded argument. The local non-linearity is described through irrational functions and in a special case it includes the polynomial of the third degree. Detailed considerations are given for a system consisting of three rods and two rigid bodies. In numerical analysis non-linear effects are discussed. The results concerning harmonic vibrations are presented for the local non-linearities having characteristics of a soft type as well as of a hard type.     

Matched asymptotic expansions for twisted elastic knots: A self-contact problem with non-trivial contact topology

We derive solutions of the Kirchhoff equations for a knot tied on an infinitely long elastic rod subjected to combined tension and twist, and held at both endpoints at infinity. We consider the case of simple (trefoil) and double (cinquefoil) knots; other knot topologies can be investigated similarly. The rod model is based on Hookean elasticity but is geometrically nonlinear. The problem is formulated as a nonlinear self-contact problem with unknown contact regions. It is solved by means of matched asymptotic expansions in the limit of a loose knot. We obtain a family of equilibrium solutions depending on a single loading parameter (proportional to applied twisting moment divided by square root of pulling force), which are asymptotically valid in the limit of a loose knot, ε→0. Without any a priori assumption, we derive the topology of the contact set, which consists of an interval of contact flanked by two isolated points of contacts. We study the influence of the applied twist on the equilibrium.     

Large-scale CdX (X=S, Se) microtube arrays on glass substrate: transformation of CdOHCl microrod arrays by a simple template-sacrificing solution method

Large-scale arrayed CdX (X=S, Se) microtubes have been successfully prepared on glass substrate by a simple solution route. In this process, cadmium hydroxyl chloride (CdOHCl) microrod arrays, which could be directly grown on glass surface in solution of CdCl₂ and methenamine, were used not only as a source of cadmium but also as a new reactive template to fabricate these highly ordered cadmium chalcogenide tube arrays, and the orientation of CdOHCl microrods on glass substrate could be easily achieved by pretreating the glass surface with appropriate concentration of NaOH aqueous solution. The transformation from arrayed CdOHCl rods to CdS and CdSe microtube arrays were conducted in thioacetamide and Na₂SeSO₃ solution, respectively. The conversion was convenient, and no CdOHCl crystallites were detected in the final products measured by X-ray powder diffraction. The hexagonal prismatic morphology and orientation of CdOHCl rods were perfectly maintained in the as-prepared cadmium chalcogenide films according to scanning electron microscopy. Transmission electron microscopy was used to further characterize these microtube structures. The effect of NaOH pretreatment on CdOHCl orientation and the formation of tubular structures were also discussed.     

Exact solution of the problem for dynamic field of displacements in rods of variable length

Initial boundary value problems are considered for rods that change length over time. These problems are transformed to problems about rods with mobile ends. A special method which allows one to obtain exact solutions of such problems is developed. This method is a generalization of a method of reflections for rods and strings of constant length. As an application of this class of problems, the hoisting of ropes in mining lifts, including their problems, are considered. Exact expressions for displacements in rods of variable length are obtained. The same results can be applied to cross oscillations of strings of variable length.     

Compact waves on planar elastic rods

Planar Kirchhoff elastic rods with non-linear constitutive relations are shown to admit traveling wave solutions with compact support. The existence of planar compact waves is a general property of all non-linearly elastic intrinsically straight rods, while intrinsically curved rods do not exhibit this type of behavior.