The 21st century has brought a lot of new results related to graphene. Apparently, graphene has been characterized from all points of view except surface science and, especially, surface thermodynamics. This report aims to close this gap. Since graphene is the first real two-dimensional solid, a general formulation of the thermodynamics of two-dimensional solid bodies is given. The two-dimensional chemical potential tensor coupled with stress tensor is introduced, and fundamental equations are derived for energy, free energy, grand thermodynamic potential (in the classical and hybrid forms), enthalpy, and Gibbs energy. The fundamentals of linear boundary phenomena are formulated with explaining the concept of a dividing line, the mechanical and thermodynamic line tensions, line energy and other linear properties with necessary thermodynamic equations. The one-dimensional analogs of the Gibbs adsorption equation and Shuttleworth–Herring relation are presented. The general thermodynamic relationships are illustrated with calculations based on molecular theory. To make the reader sensible of the harmony of chemical and van der Waals forces in graphene, the remake of the classical graphite theory is presented with additional variable combinations of graphene sheets. The calculation of the line energy of graphene is exhibited including contributions both from chemical bonds and van der Waals forces (expectedly, the latter are considerably smaller than the former). The problem of graphene holes originating from migrating vacancies is discussed on the basis of the Gibbs–Curie principle. An important aspect of line tension is the planar sheet/nanotube transition where line tension acts as a driving force. Using the bending stiffness of graphene, the possible radius range is estimated for achiral (zigzag and armchair) nanotubes.

21世纪带来了许多与石墨烯有关的新结果。显然，除了表面科学，尤其是表面热力学以外，从所有角度都对石墨烯进行了表征。本报告旨在弥合这一差距。由于石墨烯是第一个真正的二维固体，因此给出了二维固体热力学的一般公式。介绍了与应力张量耦合的二维化学势张量，并推导了能量，自由能，大热力学势（经典和混合形式），焓和吉布斯能的基本方程式。线性边界现象的基本原理是通过解释分界线的概念，机械和热力学线的张力来阐述的，线能量和其他线性特性以及必要的热力学方程式。给出了吉布斯吸附方程和Shuttleworth-Herring关系的一维类似物。通过基于分子理论的计算说明了一般的热力学关系。为了使读者对石墨烯中化学力和范德华力的协调性敏感，对经典石墨理论进行了重述，并提供了石墨烯片的其他可变组合。展示了石墨烯线能的计算，包括化学键和范德华力的贡献（预期，后者远小于前者）。基于吉布斯-居里原理，讨论了由迁移空位引起的石墨烯孔问题。线张力的一个重要方面是平板/纳米管的平面过渡，其中线张力充当驱动力。使用石墨烯的弯曲刚度，可以估算非手性（曲折形和扶手椅形）纳米管的可能半径范围。