Fragility and Strength in Nanoparticle Glasses

Abstract

Glasses formed from nano- and microparticles form a fascinating testing ground to explore and understand the origins of vitrification. For atomic and molecular glasses, a wide range of fragilities have been observed; in colloidal systems, these effects can be emulated by adjusting the particle softness. The colloidal glass transition can range from a superexponential, fragile increase in viscosity with increasing density for hard spheres to a strong, Arrhenius-like transition for compressible particles. However, the microscopic origin of fragility and strength remains elusive, both in the colloidal and in the atomic domains. Here, we propose a simple model that explains fragility changes in colloidal glasses by describing the volume regulation of compressible colloids in order to maintain osmotic equilibrium. Our simple model provides a microscopic explanation for fragility, and we show that it can describe experimental data for a variety of soft colloidal systems, ranging from microgels to star polymers and proteins. Our results highlight that the elastic energy per particle acts as an effective fragility order parameter, leading to a universal description of the colloidal glass transition.

Keywords: colloids; fragility; glasses; microgels; nanoparticles.

Figure 1

(a) Real volume fraction ϕ versus experimental control parameter ζ as a function of particle elasticity, for (top to bottom) k = 1 × 10⁴, 1 × 10³, 5 × 10², 2 × 10², 1 × 10², and 5 × 10¹ Pa, with a₀ = 50 nm and ϕ_p,0 = 0.1. (b) Extent of osmotic deswelling a/a₀ with increasing particle volume fraction for the same settings as in (a).

Figure 2

(a) Structural relaxation time τ, normalized to the Brownian time scale τ₀, as a function of extrapolated particle packing fraction ζ for (solid lines, top to bottom) k̅ = 20, 10, 5, 3.5, 2, and 1 Pa, with a₀ = 50 nm, using eq 7. Symbols: experimental data for colloidal hard spheres from fitted to the VFT equation as described in the text (dotted line). (b) Same data as in (a) in the so-called Angell representation where the packing fraction is normalized to the glass transition ζ_g. (c) Angell plot for theoretical predictions using the harmonic approximation for Π_in (eq 11) for κ = 350, 400, 500, 600, 1000, and 5000 J/m². (d) Angell plot for theoretical predictions using the Flory–Rehner equation-of-state (eq 12) for N_x = 100, 500, 1000, 2000, 3000, and 4000.

Figure 3

(a) Angell plot for various systems of compressible spheres, symbols (defined in legend): experimental data for hard spheres (a₀ ∼ 130 nm), various microgels (a₀ ∼ 90 nm),^, star polymers (a₀ ∼ 20 nm), and the globular protein bovine serum albumin (a₀ ∼ 5 nm), drawn lines: predictions from the model as outlined in the text with k̅ as the adjustable parameter. (b) Fragility index m as a function of k̅a₀³ as predicted by the model (line) and for the data sets in (a) (symbols). (c) Intensity correlation functions from dynamic light scattering for uncharged polystyrene microgels with (from left to right) ζ = 0.64, 0.88, 1.02, 1.03, 1.19, 1.25, 1.30, 1.35. (d) Angell plot for compressible colloids of varying charge density: hard spheres, weakly charged microgels,^, uncharged microgels from (c), and highly charged microgels, drawn lines: predictions from the model.