Viscoelastic Scaling Regimes for Marginally Rigid Fractal Spring Networks

A family of marginally rigid (isostatic) spring networks with fractal structure up to a controllable length was devised, and the viscoelastic spectra G*(co) calculated. Two nontrivial scaling regimes were observed, (i) G' ??? G'' ?? coA at low frequencies, consistent with A = 1/2, and (ii) G' ?? G'' ?? coA' for intermediate frequencies corresponding to fractal structure, consistent with a theoretical prediction A' = (ln 3 ??? ln 2)/(ln 3 + ln 2). The crossover between these two regimes occurred at lower frequencies for larger fractals in a manner suggesting diffusivelike dispersion. Solid gels generated by introducing internal stresses exhibited similar behavior above a low-frequency cutoff, indicating the relevance of these findings to real-world applications.

Automated summary

A family of marginally rigid spring networks with fractal structure was created and their viscoelastic spectra were calculated. Two scaling regimes were observed at different frequencies, consistent with theoretical predictions. The findings were shown to be relevant in real-world applications.