Shear-stress fluctuations in self-assembled transient elastic networks

Area of Science:

• Soft Matter Physics
• Materials Science
• Network Theory

Background:

• Transient networks are crucial in soft matter, exhibiting complex mechanical properties.
• Understanding shear-stress fluctuations is key to characterizing network dynamics.
• Existing models often struggle to capture behavior across the liquid-to-solid transition.

Purpose of the Study:

• To develop and validate an efficient numerical method for determining the shear-stress relaxation modulus in transient networks.
• To investigate the behavior of these networks across a wide range of the dimensionless parameter Δx, spanning from the liquid to the solid limit.
• To generalize findings from permanent networks to transient systems.

Main Methods:

• Numerical investigation of a generic model for self-assembled transient networks.
• Systematic scanning of the dimensionless parameter Δx = Δt/t_{☆}(f), where Δt is sampling time and t_{☆}(f) is Maxwell relaxation time.
• Calculation of shear-stress relaxation modulus G(t) using a novel simple-average expression G(t) = μ_{A} - h(t).
• Comparison with the standard expression G(t) = c̃(t) based on shear-stress autocorrelation.

Main Results:

• An efficient method for determining the shear-stress relaxation modulus G(t) is established for all Δx values.
• The proposed method utilizes the simple-average expression G(t) = μ_{A} - h(t), involving the canonical-affine shear transformation and mean-square displacement of shear stress.
• Lower bounds for the number of configurations required for accurate calculations are provided for both the proposed and standard methods.
• The study demonstrates the applicability of the method across the liquid (Δx ≫ 1) and solid (Δx ≪ 1) limits.

Conclusions:

• The developed simple-average method provides an efficient way to calculate shear-stress relaxation modulus in transient networks.
• This approach is valid across the entire spectrum from liquid-like to solid-like network behavior.
• The findings offer a generalized understanding applicable to both transient and permanent network systems.