Structure formation in suspensions with a liquid crystalline medium: percolation phenomena

Abstract

Measurements of the storage modulus of suspensions of marble particles in a surfactant-based lyotropic liquid-crystalline medium (lamellar, smectic B) are reported. The suspension is a model system for several food and consumer products. The storage modulus is found to remain nearly constant with an increase in the particle volume fraction until a critical value is reached, beyond which a sharp increase in the storage modulus is obtained. The critical volume fraction is found to increase with an increase in particle size. The storage modulus of the suspensions exhibits a power law dependence on the oscillation frequency, and the power law exponent decreases sharply near the critical volume fraction. The experimental data indicate a transition from a multidomain lamellar liquid-crystalline structure to a structure with a rigid sample spanning network. A network model for the suspension is proposed in which a large number of parallel lamellae bridge randomly placed particles with surfaces closer than a specified distance, the maximum layer size (s_m). The network formation is essentially a continuum percolation problem, for which the dimensionless critical number density is found by numerical simulations to be α_c=ρ_c^1/3 L_m ≈ 0.87 where L_m is the maximum distance between the centers of bonded particles and ρ_c is the critical number density. The modulus (G_c) of the percolation network is obtained computationally as the stress required for a small tensile deformation of the network. The computed modulus is found to be of the form G_c ∝ ρ^2/3(α - α_c)^2.5, which is in good agreement with experimental data.