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Gel electrophoresis is a method that separates biological macromolecules like nucleic acids or proteins by forcing them to pass through a gel matrix under an electric field.
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Rigid m-percolation in limited-valence gels.

J C Neves1,2, J M Tavares1,3, N A M Araújo1,2

  • 1Universidade de Lisboa, Centro de Física Teórica e Computacional, Faculdade de Ciências, 1749-016 Lisboa, Portugal.

Physical Review. E
|October 21, 2025
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Summary
This summary is machine-generated.

Rigidity in gels emerges when particles form an infinite, three-bonded cluster. This study uses m-percolation theory to map gel rigidity, finding valence impacts the connectivity-rigidity gap.

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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.