Abstract
Colloidal gels formed by arrested phase separation are found widely in agriculture, biotechnology, and advanced manufacturing; yet, the emergence of elasticity and the nature of the arrested state in these abundant materials remains unresolved. Here, the quantitative agreement between integrated experimental, computational, and graph theoretic approaches are used to understand the arrested state and the origins of the gel elastic response. The micro-structural source of elasticity is identified by the l-balanced graph partition of the gels into minimally interconnected clusters that act as rigid, load bearing units. The number density of cluster-cluster connections grows with increasing attraction, and explains the emergence of elasticity in the network through the classic Cauchy-Born theory. Clusters are amorphous and iso-static. The internal cluster concentration maps onto the known attractive glass line of sticky colloids at low attraction strengths and extends it to higher strengths and lower particle volume fractions.
Highlights
Colloidal gels formed by arrested phase separation are found widely in agriculture, biotechnology, and advanced manufacturing; yet, the emergence of elasticity and the nature of the arrested state in these abundant materials remains unresolved
The volume fraction of colloids within the clusters falls on and extends the attractive glass line (AGL) of colloids determined via mode coupling theory (MCT), suggesting that the arrest of the gel forming process is due to glassy physics within the fundamental elastic units
A recently developed model depletion gel is employed, which enables the rheology, microstructure, and particle interactions to be measured in concert for complete determination of the microscopic properties and macroscopic elastic response[22]
Summary
Colloidal gels formed by arrested phase separation are found widely in agriculture, biotechnology, and advanced manufacturing; yet, the emergence of elasticity and the nature of the arrested state in these abundant materials remains unresolved. This property cannot be accounted for by any macroscopic structural change or the change in inter-particle bond stiffness To resolve this important puzzle, we use a graph theoretic approach to identify the fundamental elastic units of the gels, a set of clusters, and to measure the density of cluster-cluster contacts. The physical size of the clusters is independent of the strength of the depletion attraction, but their number density and the number of cluster-cluster contacts grows with increased attractive strength These changes, when combined with the Cauchy-Born theory, yield a prediction of the elastic modulus with the correct convexity and in quantitative agreement with experimental measurements and calculations from simulations. There is a striking similarity to polycrystalline solids: elasticity and, potentially, plasticity emerges from the few weak bonds between clusters[21]
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