Rigidity of disordered networks with bond-bending forces

Area of Science:

• Condensed matter physics
• Materials science
• Statistical mechanics

Background:

• Disordered networks exhibit distinct critical behaviors based on inter-monomer forces.
• Central forces lead to rigidity percolation, while bond-bending forces relate to geometric percolation.

Purpose of the Study:

• Investigate the critical behavior of shear modulus in disordered networks with both central and bond-bending forces.
• Compare the findings with existing theories, particularly de Gennes' conjecture.

Main Methods:

• Extensive molecular dynamics simulations were performed on a model system.
• The simulations covered a range of temperatures (T).
• Analysis focused on the elastic constants and shear modulus near percolation thresholds.

Main Results:

• At zero temperature, elastic constants vanish at the geometric percolation point p(c) for networks with bond-bending forces.
• In contrast, networks with only central forces lose shear resistance at the rigidity percolation point p(r).
• At finite temperatures (T), the critical behavior of the shear modulus in the studied system aligns with that of purely central-force networks.

Conclusions:

• The critical behavior of the shear modulus in disordered networks with both force types is consistent with a purely central-force network at finite temperatures.
• These findings support the long-standing conjecture by de Gennes regarding network elasticity.
• The distinction between geometric and rigidity percolation is temperature-dependent.