*Graphene Exfoliation from HOPG Using the Difference in Binding Energy between Graphite… DOI: http://dx.doi.org/10.5772/intechopen.107142*

dispersion forces, London forces, induced-dipoles forces, etc. but they are all referred as Van der Walls forces (VDW). As we know, these forces are present between graphite layers. In fact, the carbon layers are dipole-induced dipole that created forces between layers. These VDW forces created between two layers form a potential energy which is known as the bonding energy of graphite (binding energy). In order to exfoliate a graphene layer then, the cohesive energy has to be overcome. Exfoliation of graphite is a top-down method which consists in finding ways to surpass these interlayers forces, to breakdown or overcome that cohesive energy, hence the name of cleavage energy. We distinguish two types of exfoliation techniques for graphene: mechanical and chemical exfoliation.

In mechanical exfoliation a longitudinal or transversal stress is generated on the surface of the layered material by a scotch, AFM tip or a substrate [10]. The goal here is to overcome the energy between the layers. The difficulty in mechanical exfoliation is that the energy between layers is too small and by consequent easy to overcome resulting in many layers which is not graphene. Mechanical exfoliation is a simple and easy method for small lab experiments and cannot be used for industrial purpose. It is irreproducible, it has no control in layers, defects and size. Our goal is to change that, to make mechanical exfoliation reproducible and predictable by using intermolecular forces to exfoliate (**Figure 1**).

On the other hand, chemical exfoliation mostly known as liquid phase exfoliation (LPE) is almost the same as mechanical exfoliation. In LPE, transversal and longitudinal stress are provided by sonication, high shear mixing or micro fluidization [12] and it is happening in a liquid. LPE is a cheap, easy and scalable method to produce nano-flakes of graphite, but it has its challenges. Depending on the type of solvent used, we can face problems like aggregation, pollution, conservation and washing problems to some degrees. It also has a low yield (**Figure 2**).

#### **2.2 Cohesive energy and implications**

The first challenge for exfoliation technique is the requirement of an energy close to the cohesive energy of graphite, and we need to know its value first. In 1956, L. Girifalco and Lad [14], calculated the binding energy (cohesive energy) of graphite using the summation lattice with the LJ potential. They found the binding energy was approximately 0.33 *<sup>J</sup>=m*<sup>2</sup> (53.96 *meV=atom*). They confirmed this result by comparing it to values got from Heat wetting experiment. Since the expansion of

#### **Figure 1.**

*Mechanical exfoliation principle. (reprinted from reference Yi and Shen [11] with permission of CCC Inc.).*

**Figure 2.**

*LPE using sonication (reprinted from reference [13]).*

graphene, the cohesive energy of graphite has attracted a lot of attention to understand better its properties for better exfoliation experiments design.

Xiaobin and colleagues calculated the interlayer potential by combining the Mobius inversion method with ab initio calculation [15]. They found the binding energy to be between 55 and 60 *meV=atom*. According to them, the binding/cohesive energy is between 50 and 60 *meV=atom*. They also found the interlayer space to be 3.1 Å. In the same way, using Quantum mechanics orbital occupancy approach and second order perturbation theory, Y.J Dappe and colleagues obtain a binding energy of 60–72 *meV=atom* and interlayer space distance of 3.1–3.2 Å [16]. Throughout our literature review, we can say that the binding energy of graphite *Eg* lies between 50 and 72 *meV=atom* and the interlayer distance is 3.34 Å as confirmed by XRD studies of graphite. So the goal of all exfoliation technique is to provide an energy *Ex* (by many means) which is: *Eg* <*Ex*<2 ∗ *Eg* to exfoliate a single graphene layer. When *Ex* exceeds, we can have bilayers and more.
