Moduli and modes in the Mikado model.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 34151919.
- Also identified by DOI 10.1039/d1sm00551k and PMC identifier 8612360.
- Licence recorded as CC BY-NC.
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Abstract
We determine how low frequency vibrational modes control the elastic shear modulus of Mikado networks, a minimal mechanical model for semi-flexible fiber networks. From prior work it is known that when the fiber bending modulus is sufficiently small, (i) the shear modulus of 2D Mikado networks scales as a power law in the fiber line density, <i>G</i> ∼ <i>ρ</i><sup><i>α</i>+1</sup>, and (ii) the networks also possess an anomalous abundance of soft (low-frequency) vibrational modes with a characteristic frequency <i>ω</i><sub><i>κ</i></sub> ∼ <i>ρ</i><sup><i>β</i>/2</sup>. While it has been suggested that <i>α</i> and <i>β</i> are identical, the preponderance of evidence indicates that <i>α</i> is larger than theoretical predictions for <i>β</i>. We resolve this inconsistency by measuring the vibrational density of states in Mikado networks for the first time. Supported by these results, we then demonstrate analytically that <i>α</i> = <i>β</i> + 1. In so doing, we uncover new insights into the coupling between soft modes and shear, as well as the origin of the crossover from bending- to stretching-dominated response.