Rigid m-percolation in limited-valence gels

Area of Science:

• Soft Matter Physics
• Colloid Science
• Materials Science

Background:

• Determining gel rigidity onset is crucial for applications.
• Patchy-particle systems model microscopic interactions and macroscopic properties.
• Rigidity is hypothesized to link with infinite clusters of particles with >= 3 bonds.

Purpose of the Study:

• To test the hypothesis linking gel rigidity to 3-bonded infinite clusters.
• To explore the implications of this hypothesis across system parameters.
• To associate rigidity emergence with m-percolation transitions (m=3).

Main Methods:

• Developed m-percolation properties using mean-field theory.
• Validated theoretical approach with numerical simulations.
• Constructed phase and rigidity diagrams for various patchy particle systems.

Main Results:

• The difference between connectivity and rigidity percolation thresholds decreases with increasing particle valence.
• This finding explains experimental difficulties in distinguishing connectivity from rigidity.
• A minimum average valence is identified for rigidity in binary mixtures.

Conclusions:

• The m=3 percolation model accurately describes gel rigidity onset.
• Particle valence is a key factor controlling the relationship between connectivity and rigidity.
• Understanding valence is critical for designing rigid gels, especially in binary mixtures.