Frictional contact problem for elastic-viscoplastic materials with thermal effect

A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca’s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.     

Chemisorption of O and O2 on Ag(110): An LCGTO-LSD cluster study

As part of a study aimed at better understanding of molecular and dissociative chemisorption of oxygen on Ag(110), linear combinations of Gaussian type orbitals-local spin density (LCGTO -LSD ) calculations have been performed for O, O^?, O₂, O^?₂, O^2?₂ and a variety of silver clusters interacting with O or O₂. For atomic O adsorption a very small cluster, Ag₄, chosen to model the long-bridge site already affords very good agreement with both recent EXAFS experiments and recent ab initio calculations. We calculate O to be 0.25 Å above the surface (exp. 0.2 Å). The Ag₄? O vibrational frequency is estimated to be 400 cm^?1, in reasonable accord with the experimental EELS value of 325 cm^?1. Determination of the geometry for O₂ (ads.) and, ultimately, of the dissociation path are far more difficult tasks. An extensive search for local minima in the vicinity of the LB site is being carried out. Results to date for small, Ag₂ and Ag₄, clusters have furnished insight into the factors influencing the structure. Overlap between the π* orbital of the O₂ moiety and Ag s functions is a key factor; that is, there is an important covalent component of the binding. For geometries with O₂ parallel to the surface, this is achieved by twisting the O₂ fragment with respect to the [11¯0] grooves (geometries either parallel or perpendicular to the grooves yield zero π‖*?s overlap by symmetry). The structure with O₂ perpendicular to the surface also achieves reasonable overlap and lies close in energy to the most stable ‘parallel’ geometry.     

A frictional contact problem with normal damped response for elastic-visco-plastic materials

We study an evolution problem which describes the dynamic contact of an elastic-visco-plastic body with a foundation. We model the contact with normal damped response and a local friction law. A damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We derive variational formulation for the model which is in the form of a system involving the displacement field, the stress field and the damage field. We prove the existence and uniqueness result of the weak solution. The proof is based on arguments of evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities and fixed point.     

Chemisorption of O2 ON Ag(110): A molecular orbital cluster study

Self-Consistent-Field-Xα-Scattered-Wave molecular orbital calculations have been performed for cluster models of the Ag(110) surface interacting with an oxygen molecule. Twelve possible adsorption geometries have been considered. Comparison of the calculated positions of O₂-derived energy levels with ultraviolet and X-ray photoemission data has allowed most of these to be eliminated. The best candidates for the adsorption geometry both involve the long-bridge site, and have the O₂ moiety parallel to the surface and either parallel to the 11?0 grooves (LB(∥s, ∥ g)) or perpendicular to the gooves (LB(∥ s, ⊥ g)). Some evidence in favor of the latter is outlined, although a definitive structure determination must await further experimental and theoretical work. For both of these geometries significant covalent interactions have been identified involving mixing between O₂ orbitals and Ag sp and d functions. It is suggested that the π_u-d and pσ_g-d interactions are responsible for the observed reduction of the O-O stretching frequency relative to the usual values for peroxides.     

Orientation Control of Molecularly Functionalized Surfaces Applied to the Simultaneous Alignment and Sorting of Carbon Nanotubes

Self‐assembly has been relied upon for molecular alignment in many advanced technological applications. However, although effective, it is inherently limited in its capability for optimization. Despite the potential benefits, the seemingly fundamental strategy of external orientation control has yet to be realized. Herein we demonstrate an approach that allows control of the orientation of small molecules covalently bound to a surface. The method exploits an alignment relay technique, passing alignment information through a liquid‐crystal medium to small molecules to control surface functionalization events. The method is technically simple and can be carried out on a bench top without the need for specialized equipment. Moreover, we demonstrate the utility of the resulting surfaces to address two long‐standing problems in nanoscience: the sorting and alignment of single‐walled carbon nanotubes. This new method enabled significant alignment of the nanotubes as well as length and diameter sorting.     

π-Concave Hosts for Curved Carbon Nanomaterials

Carbon nanomaterials have been at the forefront of nanotechnology since its inception. At the heart of this research are the curved carbon nanomaterial families: fullerenes and carbon nanotubes. While both have incredible properties that have been capitalized upon in a wide variety of applications, there is an aspect that is not commonly exploited by nanoscientists and organic chemists alike: the interaction of curved carbon nanomaterials with curved organic small molecules. By taking advantage of these interactions, new avenues are opened for the use of fullerenes and carbon nanotubes.     

A Dynamic Frictionless Elastic-Viscoplastic Problem with Normal Damped Response and Damage

We consider a mathematical model for the process of a frictionless contact between an elastic-viscoplastic body and a reactive foundation. The material is elastic-viscoplastic with internal state variable which may describe the damage of the system caused by plastic deformations. We establish a variational formulation for the model and prove the existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear equations with monotone operators, on parabolic type inequalities and fixed point.     

Analysis of a Class of Frictional Contact Problems for the Bingham Fluid

We consider a mathematical model which describes the stationary flow of a Bingham fluid with friction. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive a weak formulation of the model which consists in a variational inequality for the velocity field. We establish the existence and uniqueness of the weak solution as well as its continuous dependence with respect to the contact condition. Finally, we describe a number of concrete friction conditions which may be set in this general framework and for which our results apply.