On the universality of the scaling relations during sol-gel transition

Abstract

The evolution of viscoelastic properties near the sol-gel transition is studied by performing oscillatory rheological measurements on two different types of systems: a colloidal dispersion and a thermo-responsive polymer solution under isothermal and nonisothermal conditions. While undergoing sol-gel transition, both the systems pass through a critical point. An approach to the critical point is characterized in terms of divergence of zero shear viscosity and the subsequent appearance of the low frequency modulus. In the vicinity of the critical gel state, both the viscosity and the modulus show a power-law dependence on relative distance from the critical point. Interestingly, the longest relaxation time has been observed to diverge symmetrically on both the sides of the critical point and also shows a power-law dependence on relative distance from the critical point.The critical (power-law) exponents of the zero-shear viscosity and modulus are observed to be related to the exponents of the longest relaxation time by the hyper scaling laws.The dynamic critical exponent has also been calculated from the growth of the dynamic moduli. Remarkably, the critical relaxation exponent and dynamic critical exponent predicted from the scaling laws precisely agree with the experimental values from the isothermal as well as non-isothermal experiments. The associated critical exponents show remarkable internal consistency and universality for different kinds of systems undergoing the sol-gel transition.

ATP:Mg2+shapes condensate properties of rRNA-NPM1in vitronucleolus model and its partitioning of ribosomes

“…At Mg 2+ concentrations higher than 7 mM, rRNA is fully arrested with τ >1500 s and percentage recoveries decreased to <10% ( Figure 1E ). These findings suggest a gradual transition from liquid to an arrested, gel state of the RNA component of the nucleolus, which is supported by the scaling behavior of the relaxation times near the critical point ( Figure 1D ) (18, 19). The NPM1 component remained astonishingly mobile within the rRNA gel network as the Mg 2+ concentration increased, with low τ ( Figure 1D ), which is consistent with other reported FRAP recoveries (2, 4).…”

Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction

“…Finally, we can compare the fractal dimension determined experimentally with the value estimated from the hyperscaling relation of standard percolation τ = ( d / d f ) + 1, where τ is the power-law exponent of the cluster-mass distribution at percolation, assuming that this relation holds also for the nonequilibrium case studied here (recent experimental evidence supporting the validity of hyperscaling relations in colloidal gelation has been shown in ref. 46 ). Using τ = 5/2 as predicted by the model and confirmed in both experiments and simulations, we obtain the prediction d f = 2.…”

Scaling relations in rheology of concentrated starches and maltodextrins

“…The collected data is only in the shearthinning regime, with an exponent different from the MDX18 -namely n = 0.2. Note that the rescaled data of starch exceeds the value η/η 0 , meaning that the actual zero-shear viscosity of starch is higher than MDX DE2, or that the viscosity is diverging due to gelation of the starch via the amylose junctions, as observed for other polymer systemsshowing critical gel behaviour (Li et al, 1997;Suman & Joshi, 2020;Winter 1987). )…”