Colloidal gelation with non-sticky particles

Abstract

Colloidal gels are widely applied in industry due to their rheological character-no flow takes place below the yield stress. Such property enables gels to maintain uniform distribution in practical formulations; otherwise, solid components may quickly sediment without the support of gel matrix. Compared with pure gels of sticky colloids, therefore, the composites of gel and non-sticky inclusions are more commonly encountered in reality. Through numerical simulations, we investigate the gelation process in such binary composites. We find that the non-sticky particles not only confine gelation in the form of an effective volume fraction, but also introduce another lengthscale that competes with the size of growing clusters in gel. The ratio of two key lengthscales in general controls the two effects. Using different gel models, we verify such a scenario within a wide range of parameter space, suggesting a potential universality in all classes of colloidal composites.

Fig. 1. Gelation dynamics of colloidal gels.

a Sketches of possible pairwise motions and two contact models with constraints shown in red crosses. b Schematic gelation determination. See details in the Methods section. c Gelation times t_g as functions of volume fraction ϕ in different gels. The blue dashed line and red dotted line are power-law fittings with results shown in Eqs. (1) and (2). The gray region denotes the attractive glass (AG) regime. d Evolution of structure factors S(q) in an attractive gel (ϕ = 0.1, top) and an adhesive gel (ϕ = 0.05, bottom). The open and filled symbols represent S(q) of snapshots before and upon gelation, respectively, and the arrows indicate time evolutions (from bottom to top: t/τ_B = 0, 1, 10, 100, and 1000). Solid lines indicate the slope at intermediate wavenumbers.

Fig. 2. Colloidal gelation with non-sticky particles.

a 3D rendering of a gelled attractive system of d_NS = 8d at ϕ_g = 0.05 and ϕ_NS = 0.1. Red and gray spheres represent sticky colloids and non-sticky particles, respectively. b Gelation times t_g of attractive (top) and adhesive (bottom) systems of d_NS = 8d vary as functions of ϕ_NS at different ϕ_g. Data with ϕ_NS = 0 refer to colloidal gels. c Plot of the same data in b with t_g versus ϕ_eff (defined in Eq. (3)). The dashed blue line and dotted red line are the power-law fittings of gel data in Fig. 1b, also see Eqs. (1) and (2).

Fig. 3. Interplay between lengthscales affects gelation with NS particles.

a Characteristic lengthscale ξ_g as a function of volume fraction ϕ in colloidal gels. Dashed and dotted lines are power-law fittings with results shown in Eqs. (4) and (5). b Average spacing δ between NS particles as a function of ϕ_NS. Gray stars are from individual simulations of only NS particles, while black filled circles are from binary composites with various ϕ_g and d_NS. The NS spacing δ is determined through Voronoi analysis in both cases (see the Methods section). c ϕ_g–ϕ_NS diagrams in attractive (left) and adhesive (right) systems with d_NS = 8d. Color indicates the value of dev[t_g]. Gray region refers to AG regime with ϕ_eff > 0.4. Lines refer to the iso-γ lines with values shown on each of them. d, e are diagrams in attractive systems and adhesive systems with various d_NS shown on the upper-left corner of each diagram. Dashed and dotted lines refer to γ = 2. f Plot of dev[t_g] versus γ, including all the data presented in c–e. Deviations below the dotted line (dev[t_g] = 0.05) are considered as random error only.

Fig. 4. Lengthscale ratio γ controls cluster growth.

a Time evolutions of particle fraction in the largest cluster N_lc/N of attractive systems with ϕ_eff = 0.2. b Time evolutions of N_lc/N in adhesive systems with ϕ_eff = 0.1. In each plot, data of pure gels (ϕ = ϕ_eff) are shown in black. Detailed compositions are not shown; instead, we use γ represented by the color. Arrows indicate increasing γ.

Fig. 5. Behavior of NS particles during gelation.

a Normalized MSD of colloids (lines) and NS particles (symbols). While varying ϕ_g (left), d_NS (middle), and ϕ_NS (right) individually, the other two parameters are fixed with values shown in the upper left corner. For better comparison, data in red and black are shifted by 100 and 10, respectively. b RDF of NS particles in composites of ϕ_g = 0.1 and ϕ_NS = 0.3. Visible peaks are highlighted by arrows. Lines and symbols represent data before and after gelation. For better comparison, data of d_NS = d, 3d, and 5d are shifted by 15, 10, and 5, respectively.

Fig. 6. Schematic illustration of two limit cases in binary systems.

Left: d_NS → ∞ (γ → 0). Right: d_NS → 0 (γ → ∞).