Abstract
Bending rigidity plays an important role in graphene from mechanical behavior to magnetic and electrical properties. However, it is still in a theoretical debate whether the bending rigidity of graphene increase or decrease with increasing temperature. The liquid membranes renormalization theory is always used to calculate the bending modulus of 2D membrane (graphene) at different temperatures. Although this theory has been successfully used to describe the mechanical behavior of liquid membranes like cell membrane, we point out some possible unsuitable places when it is used to evaluate the temperature effect on the bending rigidity of graphene. The energy difference between the notional planar and pure bending graphene is related to the definition of the bending rigidity directly. Based on this energy variation analysis, we demonstrate that the bending rigidity of graphene increases with increasing temperature. Moreover, we reveal the mechanism is that the configurational entropy plays a crucial role in the variation of the free energy of graphene with increasing temperature. Our approach also paves a way to investigate the temperature effect on the bending rigidity of other 2D materials.
Highlights
The liquid membranes renormalization theory (Canham/Helfrich theory)1–3 is widely used for the study on the mechanical behavior of bio-membranes,1 after it has successfully illustrated the biconcave shape of the lipid bilayer red cell membranes.2,3 This theory has been used to study the temperature effect on the bending rigidity of graphene 2D membrane.4,5 it is still unclear whether this theory is appropriate to study the bending rigidity of graphene
Exchange and correlation are treated within the generalized gradient approximation (GGA) functional by Perdew-Burke-Ernzerhof (PBE)
We show that the bending rigidity graphene increases with increasing temperature based on molecular dynamics (MD) simulations and energy analysis
Summary
The liquid membranes renormalization theory (Canham/Helfrich theory) is widely used for the study on the mechanical behavior of bio-membranes, after it has successfully illustrated the biconcave shape of the lipid bilayer red cell membranes. This theory has been used to study the temperature effect on the bending rigidity of graphene 2D membrane (graphene). it is still unclear whether this theory is appropriate to study the bending rigidity of graphene. The liquid membranes renormalization theory (Canham/Helfrich theory) is widely used for the study on the mechanical behavior of bio-membranes, after it has successfully illustrated the biconcave shape of the lipid bilayer red cell membranes.. The liquid membranes renormalization theory (Canham/Helfrich theory) is widely used for the study on the mechanical behavior of bio-membranes, after it has successfully illustrated the biconcave shape of the lipid bilayer red cell membranes.2,3 This theory has been used to study the temperature effect on the bending rigidity of graphene 2D membrane (graphene).. In previous studies, the mechanism about the temperature effect on the bending rigidity is unclear, and the common explanations are that thermal fluctuation may soften or stiffen the bending rigidity of graphene.
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