**1. Introduction**

Graphene, the world's thinnest material, was first introduced theoretically in 1947 by PR Wallace [1] to understand the properties of graphite. From this theoretical study, many scientific tried to isolate a single layer of graphite without success. It always resulted in few layers of graphene [2]. Graphene (single layer of graphite) becomes a reality in 2004 [3] when Andre Geim and Konstantin Novoselov isolated for the first time graphene using an adhesive scotch tape to exfoliate graphene and test its properties. The outstanding properties of graphene attracted a lot of interest in the scientific community and in the industry, opening a large range of opportunities and applications in electronics, medicine, etc. From 2004, the goal became then to find a

reliable method to produce graphene layers. Today, we have many synthetics methods [4] that can be reliable in many aspects such as: Chemical Vapor Deposition (CVD), Liquid Phase Exfoliation (LPE) and reduction of graphene oxide. These methods allowed the transition from laboratory to industrial production.

In 2014, the global graphene market was projected to reach 190 million by 2022 [5], but recent studies by Report Link [6] shows that the graphene market will grow from 600 million USD (2020) to 1479 million in 2025. This huge grow in such a small time is really high, but compared to the carbon global market [7] (272 billion in 2020), it is almost insignificant. This is mostly because graphene is in its incubation phase and there is not yet a precise control on synthesis method. What could then be responsible for such growth? According to Li Lin and co-workers [8], the use of graphene in specific or targeted applications where it has a huge and clear advantage over other materials like in composites and electronics is the reason of graphene fast growth. More than that, the notable success of graphene in applications where chemical processes are required is because of its irregularities or defects [9]. This is to say that even though perfect flat graphene is hard to get, the small defective graphene plays a huge role in its growth.

Graphene has a large range of applications, but because of challenges related to quality, cost, reproducibility, processability and safety, we cannot really exploit it. So how, how to overcome these limits? Should we focus on enhancing the existing methods? Should we find new targeted applications? Should we focus more on standardization? Etc. The graphene industry still has a lot of work to accomplish, and anyone can work on something particular.

The aim of this project is to propose a new model of graphene exfoliation from Highly Oriented Pyrolytic Graphite (HOPG). Here, we gave a new look at the mechanical exfoliation by Andre Geim and Konstantin Novoselov [3]. Basically, using a scotch tape, they applied a force on top of graphite surface, graphite (many layers) sticks to the scotch, and by peeling it off using another scotch, they were able to get graphene. Why they did not get graphene the first time they put the scotch on graphite? Simply because the applied force was too superior to the interlayer force (cohesive or cleavage energy of graphite) that hold graphite layers together. Considering *F* as the interlayer force of graphite, if the applied force *Fa* was superior to *F* and inferior to 2*F*, then they would have got a single layer, but it is really difficult to achieve such small forces. Just like intermolecular forces like VDW forces are holding graphite layers together, putting a substrate to a certain distance from the graphite surface will create such forces. Using a substrate on top of graphite, our first goal is to show that we can exfoliate a single layer by controlling the resulting force (binding energy) between *F* and 2*F*. Thanks to the standard Lennard-Jones (LJ) potential we will calculate the binding energies of graphite surface/substrate and compare it to the interlayer binding energy of graphite (cleavage energy) to show that we can exfoliate. This work is divided into 3 parts. The first part is a review of exfoliation principles. The second part discusses our model and the calculations equations and finally the third part is about results and discussions.
