Effect of surface modifier on flow properties of epoxy suspensions containing model plate-like nanoparticles

Abstract

The influence of inter-particle interaction on the rheology of an uncured epoxy containing model α-zirconium phosphate (ZrP) nanoplatelets with aspect ratio of 160 is reported. Epoxy suspensions containing nanoplatelets exfoliated with tetra-n-butyl ammonium hydroxide (TBA), a low molecular weight quaternary ammonium cation, show short-range repulsive potential with weak elastic response at low concentration. At semi-dilute concentrations, the suspensions are solid-like at intermediate frequency and transition to viscous flow for time scales longer than the rotary diffusion process. The weak elasticity at intermediate frequency is attributed to the effect of Brownian motion on the rotational motion of the isolated plates. Suspensions containing nanoplatelets exfoliated with hydrophilic polyetheramine oligomers show similar behaviour to the ZrP-TBA system, but shifted to lower concentration. The rheological behaviour is attributed to steric stabilization of the nanoplatelets by extended oligomer brushes with short-range repulsive interactions. For suspensions containing nanoplatelets exfoliated with hydrophobic polyetheramines with shorter length, there is evidence for elastic response on local length scales and the flow behaviour shows strong history and temperature dependence. Rheological signatures associated with equilibrium nanoplatelet dispersions with repulsive interactions are discussed.

Appendix: Calculation of rotary diffusion coefficients

The rotary diffusion coefficients were calculated following the detailed framework of dilute suspension rheology for dilute spheroids described by Brenner (1974). The rotary diffusivity of a spheroid perpendicular to its symmetry axis (i.e., tumbling motion) is given by D ^⊥ _r  = k _B T/6V η _m ^r K _⊥, where k _B T is the thermal energy, V is the particle volume, and η _m is the viscosity of the unfilled solvent. The rotary diffusivity of a spheroid parallel to its symmetry axis (i.e., spinning motion) is D ^∥ _r  = k _B T/6V _p η _s ^r K _∥. The dimensionless material constants ^r K _⊥ and ^r K _∥ are scalars that depend only on geometry. For an isolated spheroid with axial ratio r = a/b, where a and b are the polar and equatorial radii of the spheroid, respectively, ^r K _⊥ = 2(r ² + 1)/3(r ² α _∥ + α _⊥) and ^r K _∥ = 2/3α _⊥, where the α terms are shape integrals related to the geometry of the spheroids and are given by Brenner (1974). The volume of a spheroid is V = 4πab ²/3. For convenience, in the main text we define the aspect ratio of the nanoplatelets to be r _p  = L/t > 1 and the aspect ratio of the equivalent oblate spheroids to be r = a/b < 1.

To determine the hydrodynamic properties of a real particle, it is necessary to define an effective spheroid with equivalent hydrodynamic properties. The particles used in this work are hexagonal sheets with diameter, L, and monodisperse thickness, t. The volume of a hexagonal sheet is $V=\sqrt{3}{L}^2t/2$. Since the length scale for hydrodynamic perturbation will be determined by the diameter of a high aspect ratio plate, the equatorial radius of the equivalent spheroid was defined as b = L/2, where L is the nanoplatelet diameter.

For real particles, edge effects are generally accounted for by defining a spheroid with equivalent hydrodynamic properties to the real plate-like particles of interest using a correlation function. However, for plate-like particles, the available correlations are empirical functions based on visual evidence of rotational period for micron-scale plate-like particles of moderate aspect ratio (c.f. (Anczurowski and Mason 1967; Okagawa and Mason 1973)). There are no relevant correlation functions available for high aspect ratio nanoparticles, so it was assumed that the diameter and volume of the nanoplatelet and effective spheroid were equivalent.