Shumin Zhao

Buckling and competition of energy and entropy lead conformation of single-walled carbon nanocones

Using a continuum model, expressions for the elastic energy, defect energy, structure entropy, and mixing entropy of carbon nanocones are proposed analytically. The optimal conformation of carbon nanocones is studied by imposing minimization of free energy and analyzing the effects that the buckling of a nanocone’s walls have during formation. The model explains the experimentally observed preference of 19.2° for the cone angle of carbon nanocone. Furthermore, it predicts the optimal conformation of carbon nanocones to result in a cone angle of 19.2°, radius of 0.35nm, and critical length of 24nm, all of which agree very well with experimental observations.

Phase diagram of a tubular vesicle adhering between two parallel rigid planes.

In this study, we propose a two-dimensional (2D) theoretical model to explore the adhesion behavior of a tubular vesicle adhering between two rigid planes, which are constrained by a couple of forces. Based upon the free-energy functional of the system, the equations for the equilibrium shape are derived. The general solution for the system with zero pressure is obtained analytically and the stability of the corresponding equilibrium shapes is tested by numerical simulation. With the volume constraint, three kinds of typical stable shapes are obtained through scanning the parameter space numerically. The phase diagram is obtained and it is occupied mostly by nonsymmetrical shapes. The force-displacement curves obtained for our model are in agreement with experimental results. The catastrophe of force is found at a critical state, which reveals a huge expanding force will act on the two planes by the vesicle. It also implies that vesicles can spontaneously squeeze into a slit only due to adhesion.

THE OPTIMAL CONFIGURATION OF GEL SHEET GOVERNED BY ITS CONCENTRATION

We investigate the configuration of gel sheets with centrosymmetric distribution of monomer concentration in this paper. The configuration energy of these gel sheets consists of the in-plane stretching energy and bending energy. The equilibrium shape equations are derived by variation principle. This provides a way to control the shape of gel sheets by the initial concentration and thickness. From the equilibrium shape equations, we know that the Gaussian curvature on boundary (K|C) of equilibrium shape is determined by the Poisson ratio

THE TRANSPORT PROPERTIES OF NANOTUBES AND ITS CURVATURE EFFECTS

\hat{\nu}

Specific heat of single-walled carbon nanotubes

. K|C is negative when

Ring formation of single-walled carbon nanotubes: Competition between conformation energy and entropy

\hat{\nu}>0

General equilibrium shape equations of polymer chains.

but positive when

Equilibrium conformation of polymer chains with noncircular cross section.

\hat{\nu} 0). Furthermore, we deduce that the initial gel distribution of cylinder sheets is proportional to 1/r and find that N-isopropylacrylamide cylinder ...

Helicity energy of a straight single-wall carbon nanotube

The transport properties across contacts between quantum tubes and metals are studied. The curvature effects on the transmission are also considered. We find that the transmission probability of an electron transporting from the tube into the metal through the contact can be close to 100%. The curvature has a larger effect on the transmission for smaller radii and the effects decrease as the radii increase.