Universal law of hierarchical dynamics in gels arising from confluence of local physically dynamic bonds

Gels comprised of dynamic bonds are important candidates for the emerging 'intelligent' gels due to their unique characteristics. We report a universal law of hierarchical gel dynamics arising from association-dissociation of physical crosslinks, as discerned from dynamic light scattering (DLS) on diverse sets of complex gels. It is the first experimental evidence of a stretched exponential decay with a universal exponent 1/3 in DLS for all the physical gels, complementing more than five decades of DLS studies on conventional chemical gels. Here we show that diversely different chemistries of dynamic bonds map into the observed unifying law for large-scale collective dynamical properties of physical gels. This discovery allows identification of whether physical or chemical bonds dominate the crosslinks in complex gels, as well as extraction of local energetics of the constituent physical crosslinks by their characteristic relaxation times. It also elicits large-scale functional properties applicable in smart gels.