# Molecular Model

In order to generate the stress-strain relationship and eventually calculate the values of the mechanical properties of a material, the total force, F, must be estimated beforehand. This is done through the computation of the total energy, E, of the system as F is defined as the gradient of E according to classical mechanics [1]. The potential energy, E, of the molecular system in question, namely, a SAM, depends upon the positions in space, denoted here as $X_n$, of all atoms,

$E(X_n)=\sum_{i=1}^n(U_{str} + U_{bend} + U_{tors} + U_{oop} + U_{vdw} + U_{el} + ...)$

where n is the total number of atoms. The mathematical form (equation above) of the potential energy function consists of two terms, namely, bonded and non-bonded. The bonded terms describe contributions from atoms which are covalently bound, and are energy functions for bond stretching $(U_{str})$, angle bending $(U_{bend})$, torsional angles $(U_{tors})$, and out-of-plane bends $(U_{oop})$, respectively. The non-bonded terms represent contributions to potential energy coming from interactions between atoms that are not covalently bound, and include van der Waals $(U_{vdw})$ and electrostatic $(U_{el})$ interactions. All energy terms depend upon the Cartesian/configurational and internal coordinates of the atoms.

- R. Henda (2004). Mechanical Properties of Self-assembled Organic Monolayers: Experimental Techniques and Modelling Approaches, Chapter 10, in Applied Scanning Probe Methods (NanoScience & Technol. series), Bhushan, B. (USA), Fuchs, H. (Germany), and Hosaka, S. (Japan) (Eds.), Springer-Verlag, New York/Heidelberg, pp. 303-326, ISBN 3-540-00527-7.