Elastic response of wire frame glasses. I. Two dimensional model

Area of Science:

• Soft Matter Physics
• Materials Science
• Rheology

Background:

• Understanding the mechanical behavior of concentrated particle suspensions is crucial for various applications.
• Topological entanglements in dense suspensions of complex particles can significantly influence their elastic response.
• Previous studies have focused on simple particle shapes like rods, with limited understanding of complex geometries.

Purpose of the Study:

• To investigate the elastic response of concentrated suspensions of rigid wire frame particles under step strain.
• To compare the mechanical properties of wire frame particles with straight rod-like particles.
• To develop a geometric method for predicting the scaling of elastic stress with particle concentration.

Main Methods:

• A simple, geometric approach was employed to analyze the elastic stress scaling in glassy systems.
• A 2D model system was used, involving a test particle constrained by a random distribution of points.
• Numerical calculations were performed to validate the theoretical predictions for the 2D system.

Main Results:

• Wire frame suspensions display significantly higher linear elasticity, scaling as concentration squared and length to the fourth power (ν²L⁴).
• Unlike rods, wire frames exhibit shear hardening at lower concentrations, dependent on particle bending modulus (K/kBT L⁴).
• Particle deformation in wire frames is significant even at small strains, proportional to (νL²)²γ².

Conclusions:

• Rigid wire frame particles in concentrated suspensions possess distinct elastic and rheological properties compared to rod-like particles.
• The developed geometric method provides a scalable approach to understand elastic stress in these complex glassy systems.
• The findings highlight the importance of particle architecture in determining the macroscopic mechanical response of suspensions.