Connecting the discrete and continuum theories for carbon nanotubes – a simple example.
University of Akron
A multiwalled carbon nanotube can be visualized as a set of one or more concentric cylindrical graphene sheets. Each graphene sheet is one-atom thick and contains carbon atoms arranged in a hexagonal lattice. Neighboring atoms within a sheet interact via strong covalent bonds, making graphene essentially inextensible, but amenable to large elastic bending deformation. The interaction between the shells is of a weak Van-der-Waals-type and allows for an easy relative sliding between the shells. At the microscopic level, the energy of a multiwalled carbon nanotube consists of the energies of the weak and strong interactions. When upscaled to the macroscopic level, the nanotube can typically be represented by an elastic shell and the strong interactions energy reduces to an elastic energy. The macroscopic analog of weak interactions can be thought of as a pressure-type term that depends only on the local distance between the tubes.
In my talk, I will demonstrate that this reduction is not always correct as the weak interactions also depend on relative arrangements of atoms of the neighboring shells. I will discuss how one can borrow from the idea of a Gamma-development from calculus of variations to obtain a macroscopic Ginzburg-Landau-type model of a multiwalled nanotube. I will also connect the predictions of the model to experimental observations.
Capillary-driven topography and microstructure evolution in metals: matching experiment with theory
Department of Materials Science and Engineering, Technion
Development of atomic force microscopy (AFM) allowed measurements of surface topography of solids with unprecedented accuracy. We will show that fine features of the grain boundary grooves observed in AFM cannot be described in the framework of classical Mullins model with isotropic surfaces and immobile grain boundaries. We introduce the model of strong surface anisotropy and demonstrate how facets (i.e. atomically flat surface regions of particularly low energy) nucleate and grow in the grain boundary groove regions . Furthermore, we demonstrate how quantitative analysis of surface features in the wake of migrating grain boundaries allows determining the dynamics of grain boundary movement in the post-mortem studies .
Further examples will demonstrate the applications of AFM to the study of thermal stability of thin films. We show how surface anisotropy affects the morphologies obtained in the course of solid state dewetting of thin films [3-5]. Slow diffusivity along the singular surfaces of textured films changes the dewetting mechanism from the surface- to grain- or interphase boundary diffusion controlled one. The models allowing extracting the relevant diffusion parameters from experimentally measured surface topographies will be introduced [4-6].
1 . L. Klinger, E. Rabkin
Effects of surface anisotropy on grain boundary grooving
Interface Sci. 9 (2001) 55-63
2. E. Rabkin, Y. Amouyal, L. Klinger
Scanning probe microscopy study of grain boundary migration in NiAl
Acta mater. 52 (2004) 4953-4959
3. O. Malyi, L. Klinger, D.J. Srolovitz, E. Rabkin
Size and shape evolution of faceted bicrystal nanoparticles of gold on sapphire
Acta mater. 59 (2011) 2872-2881
4. O. Malyi, E. Rabkin
The effect of evaporation on size and shape evolution of faceted gold nanoparticles on sapphire
Acta mater. 60 (2012) 261-268
5. D. Amram, L. Klinger, E. Rabkin
Anisotropic hole growth during solid-state dewetting of single crystal Au-Fe thin films on sapphire
Acta mater. 60 (2012) 3047-3056
6. O. Kovalenko, J.R. Greer, E. Rabkin
Solid state dewetting of thin iron films on sapphire substrates controlled by grain boundary diffusion
Acta mater. 61 (2013) 3148-3156
Identifying Global Minimizers to a Nonlocal Isoperimetric Problem
Abstract: The nonlocal isoperimetric problem is a variational problem related the the so-called Ohta-Kawasaki energy modeling micro-phase separation in diblock copolymers. The O-K energy is itself a nonlocal perturbation of the classical Cahn-Hilliard energy. In this problem, there are two competing mechanisms–the local one favors low surface area while the nonlocal one favors high surface area. This makes for a rich and complicated energy landscape. After introducing the problem and its main features, I will discuss some work I’ve done with Ihsan Topaloglu on identifying the global minimizer of this problem in a few settings.
Cryo-TEM and Cryo-SEM of Nanostructured Liquid Systems
Yeshayahu (Ishi) Talmon
Department of Chemical Engineering and
The Russell Berrie Nanotechnology Institute (RBNI)
For complete nanostrucutral characterization of nanostructured liquids (“complex liquids”), i.e., liquid systems with aggregates or building blocks on the nanometric scale, one needs reliable direct-imaging methods. Cryogenic-temperature transmission electron microscopy (cryo-TEM) is now accepted as an essential tool in the study of complex liquids, Methodologies have been developed to capture the nanostructure of liquid systems, while preserving their original state at a given concentration and temperature. Cryo-TEM is now widely used to study synthetic, biological, and medical systems. Originally developed for aqueous systems, it has been also applied successfully in the study of non-aqueous systems. However, this methodology cannot be used to study highly viscous systems, or those containing objects larger than several hundreds of nanometers. For those we need scanning electron microscopy (SEM)
Liquid nanostructured systems can now be studied by cryo-SEM, using much-improved cryogenic specimen holders and transfer systems. That and recent developments in high-resolution scanning electron microscopy (HR-SEM) have made it an ideal tool for the study of nanoparticles and colloids in viscous systems, or in systems containing large objects, hundreds of nanometers and larger, in which small (nanometric) features are to be imaged. Improved field-emission electron guns, electron optics and detectors have made it possible to image features down to a few nanometers. In recent years we have developed a novel cryo-SEM methodology that preserves the original nanostructure of labile complex liquids at specified composition and temperature, quite similarly to what had been done in cryo-TEM. It can be used to directly image aqueous and nonaqueous systems alike.
In my talk I will describe briefly the continuously evolving state-of-the-technology of cryo-TEM and cryo-SEM, and demonstrate the application of these complementary methodologies in the study of nanostructured liquids, showing examples how it has helped support theoretical models. I will present recent data on polyelectrolyte complexes, including lipoplexes of DNA and cationic lipids, and high-resolution direct imaging of microemulsions and of carbon nanotubes in solution and in a nematic phase in chlorosulfonic acid.
Statics and dynamics of phase transitions in electric fields
Ben Gurion University of the Negev
Abstract: Phase transitions can be provoked by a change of the temperature, concentration, pressure, etc. Electric fields are interesting because they are switchable and become more effective as the system size decreases. We will review the recent fundamentals understanding gained in phase transitions in field gradients. This demixing has consequences in microfluidic flows, in electrolubrication, in chemical reactions, and in colloidal stabilization. If time permits we will describe a mathematical model for the demixing dynamics and a new type of interfacial instability.