Structural-mechanical model of wax crystal networks—a mesoscale cellular solid approach

Abstract

Mineral waxes are widely used materials in industrial applications; however, the relationship between structure and mechanical properties is poorly understood. In this work, mineral wax-oil networks were characterized as closed-cell cellular solids, and differences in their mechanical response predicted from structural data. The systems studied included straight-chain paraffin wax (SW)-oil mixtures and polyethylene wax (PW)-oil mixtures. Analysis of cryogenic-SEM images of wax-oil networks allowed for the determination of the length (l) and thickness (t) of the wax cell walls as a function of wax mass fraction (Φ). A linear relationship between t/l and Φ (t/l ∼ Φ0.89) suggested that wax-oil networks were cellular solids of the closed-cell type. However, the scaling behavior of the elastic modulus with the volume fraction of solids did not agree with theoretical predictions, yielding the same scaling exponent, μ = 0.84, for both waxes. This scaling exponent obtained from mechanical measurements could be predicted from the scaling behavior of the effective wax cell size as a function of wax mass fraction in oil obtained by cryogenic scanning electron microscopy. Microscopy studies allowed us to propose that wax-oil networks are structured as an ensemble of close-packed spherical cells filled with oil, and that it is the links between cells that yield under simple uniaxial compression. Thus, the Young’s moduli for the links between cells in SW and PW wax systems could be estimated as EL(SW) = 2.76 × 109 Pa and EL(PW) = 1.64 × 109 Pa, respectively. The structural parameter responsible for the observed differences in the mechanical strength between the two wax-oil systems is the size of the cells. Polyethylene wax has much smaller cell sizes than the straight chain wax and thus displays a higher Young’s modulus and yield stress.