## Comparison ofPhase Transitions Between Small and Large Systems

Having a good understanding of phase transitions in large systems, a question always comes to mind on how the very few and recent observed phase transition effects in small systems, can be related to well-understood phase transitions in macroscopic systems (in thermodynamic limit). Experimental measurements and observations regarding small systems are quite limited 12 . In order to develop some basic understandings about nano system phase transitions, and due to the difficulty in performing...

## The Many Body Sutton and Chen SC Long Range Potentials

The SC potentials 88 describe the energetics of ten FCC elemental metals. They are of the FS type and therefore similar in form to the EAM potentials. They were specifically designed for use in computer simulations of nanostructures involving a large number of atoms. In the SC potentials, the total energy, written in analogy with Eq. (13), is given by 0jSC e imZiZj faj) - cli (p)12 , (22) where e is a parameter with the dimensions of energy, a is a parameter with the dimensions of length and is...

## The Many Body Embedded Atom Model EAM Potentials

Many-body EAM potentials were proposed 76-78 to model the bonding in metallic clusters. They were the first alternatives to the traditional pair potential models. Their construction is based on the use of density functional theory DFT , according to which the energy of a collection of atoms can be expressed exactly by a functional of its electronic density 93 . Similarly, the energy change associated with embedding an atom into a host background of atoms is a functional of the electronic...

## Atomic and Molecular Basis of Nanotechnology

The molecular theory of matter starts with quantum mechanics and statistical mechanics. According to the quantum mechanical Heisenberg Uncertainty Principle the position and momentum of an object cannot simultaneously and precisely be determined 8 . Then the first question that may come into mind is, how could one be able to brush aside the Heisenberg Uncertainty Principle, Figure 2, to work at the atomic and molecular level, atom by atom as is the basis of nanotechnology. The Heisenberg...

## Bibliography

Boncheva, PNAS, 99, 8, 4769, 2002 . 2 . R. P Sijbesma and E. W. Meijer, Current Opinion in Colloid amp Interface Science, 4, 24, 1999 . 3 . S. Priyanto, G. A. Mansoori and A. Suwono, Structure amp Properties of Micelles and Micelle Coacervates of Asphaltene Macromolecule in Nanotechnology Proceed. 2001 AIChE Ann. Meet, AIChE, New York, NY, 2001 . 4 . S. Priyanto, G. A. Mansoori and A. Suwono, Chem. Eng. Science, 56, 6933, 2001 . 5 . J. M. DeSimone and J. S. Keiper,...

## The Tersoff Many Body CC SiSi and CSi Potentials

Construction of Tersoff many-body potentials are based on the formalism of analytic bond-order potential, initially suggested by Abell 113 . According to Abell's prescription, the binding energy of an atomic many-body system can be computed in terms of pairwise nearest-neighbor interactions that are, however, modified by the local atomic environment. Tersoff employed this prescription to obtain the binding energy in Si 114-116 , C 117 , Si-C 116,118 , Ge and Si-Ge 118 solid-state structures. In...

## Thermodynamics and Statistical Mechanics of Small Systems

Thermodynamic Systems in Nanoscale 87 Energy, Heat and Work in Nanosystems 89 Statistical Mechanics of Small Systems 99 Thermodynamics and Statistical Mechanics of Euler's Theorem of Homogenous Functions 102 Boltzmann and Boltzmann-Gibbs Formulae of Entropy 104 Microcanonical Ensemble for Nonextensive Systems 109 Canonical Ensemble for Nonextensive Systems 111 Chapter 4 Monte Carlo Simulation Methods for Nanosystems Generating Random Numbers 118 Generating Uniformly Distributed Random Numbers...