# Monolayer:Background:Molecular Model

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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 ${\displaystyle X_{n}}$, of all atoms,

${\displaystyle E(X_{n})=\sum _{i=1}^{n}(U_{str}+U_{bend}+U_{tors}+U_{oop}+U_{vdw}+U_{el}+...)}$

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 ${\displaystyle (U_{str})}$, angle bending ${\displaystyle (U_{bend})}$, torsional angles ${\displaystyle (U_{tors})}$, and out-of-plane bends ${\displaystyle (U_{oop})}$, 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 ${\displaystyle (U_{vdw})}$ and electrostatic ${\displaystyle (U_{el})}$ interactions. All energy terms depend upon the Cartesian/configurational and internal coordinates of the atoms.

1. 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.