Hello there, curious researcher friend Md. Jahid Hasan Sagor! Let's delve into the intriguing world of your graphene-vacuum-graphene system. You've certainly embarked on a fascinating journey.

Modeling a graphene-vacuum-graphene structure connected by a Lennard-Jones (L-J) potential through a vacuum gap is a creative approach. The Lennard-Jones potential is often used to describe the van der Waals interactions between atoms and molecules, including carbon atoms in graphene.

However, it's important to consider a few factors in your simulation:

1. **Distance and Forces:** As you've rightly pointed out, at a vacuum gap of 0.2 Angstroms, the repulsive forces between the graphene sheets will be quite high due to the close proximity of the atoms. This might not be a physically realistic scenario, as it could lead to unphysical results or artifacts in your simulation.

2. **Physical Realism:** In most real-world situations, graphene layers are not directly connected through a vacuum gap of such a small distance. Typically, there's some spacing or other material (like a dielectric) between graphene layers. Your model could be used to understand the behavior at very close distances, but it might not correspond to a typical graphene-vacuum-graphene system.

3. **Thermal Vibrations:** The thermal root mean square distance you've obtained (0.17 Angstrom) indicates that the graphene sheets are vibrating due to thermal energy. This implies that even at such close distances, there's thermal motion between the sheets.

In summary, while your simulation is intriguing and can provide insights into the behavior of graphene layers at very close distances, it may not represent a physically realistic scenario for most graphene-vacuum-graphene systems. It's not necessarily invalid, but it's important to interpret the results in the context of your specific simulation setup and understand its limitations.

If you're looking to model a more typical scenario, you might want to consider adding a dielectric or other material between the graphene sheets to better represent real-world conditions. It's always a balance between computational convenience and physical realism in simulations.