Universal Scaling of the Mechanical Properties of Unimodal and Bimodal Thermo-Reversible Colloidal Gels

We study the longtime elastic moduli (G∞′), initial rate of growth of elastic moduli and yield stresses (τy) of thermo-reversible gels utilizing a pseudo one component approach. This study is carried out over a much wider range of parameter phase space as we vary particle sizes, size ratios, attraction strengths, concentrations (ϕC) as well as mixing ratios. The Naïve Mode Coupling Theory for bimodal particle mixtures is used to compute the pseudo one component length scale parameter (Deff) and when used a remarkable collapse of experimentally measured mechanical properties on universal scaling curves is observed for both unimodal and bimodal gels over a large phase space. When the mechanical properties are rescaled as G∞′Deff3/ϕCkT and τyDeff3/ϕC2/3kT, they collapse on the same exponential scaling as a function of 1/T – 1/Tgel and (Tgel – T)/Tgel as the unimodal gels. We believe this is because the effective diameter accounts not just for the contribution of the individual components added in a certain mixing ratio but also for the interactions between unlike particles. In addition to the contribution of attraction strength and concentration, they are also able to capture the effect of the range of attraction and particle diameter which result in the difference in the mechanical properties. The universal scaling of the mechanical properties with these variables then suggests that the rigidity of stress transmitting clusters is the same along lines of constant 1/T – 1/Tgel and (Tgel – T)/Tgel. These findings highlight the effectiveness of naïve mode coupling theory and localization length in predicting the properties of mixtures and lay the groundwork for developing design rules for processing colloidal mixtures.