Reversible gelation and dynamical arrest of dipolar colloids

We use molecular dynamics simulations of a simple model to show that dispersions of slightly elongated colloidal particles with long-range dipolar interactions, like ferrofluids, can form a physical (reversible) gel at low volume fractions. On cooling, the particles first self-assemble into a transient percolating network of cross-linked chains, which, at much lower temperatures, then undergoes a kinetic transition to a dynamically arrested state with broken ergodicity. This transition from a transient to a frozen gel is characterised by dynamical signatures reminiscent of jamming in much denser dispersions. Colloidal dispersions have been observed to undergo a glass transition to a disordered solid upon increasing their volume fraction φ [1], or to undergo clustering and then gelation at low φ upon increasing the mutual attraction between particles [2]. Reversible gelation of colloidal dispersions is characterised by long-lived physical (rather than irreversible chemical) bonding between particles [3], which leads to the formation of sample-spanning networks capable of sustaining weak stresses at low volume fractions. In recent experimental and theoretical investigations the gelation process is almost invariably associated with short-range attractive interactions between particles, induced, e.g., by the polymer-driven depletion mechanism, which lead to low coordination clustering or jamming of preformed clusters [2, 4–7]. In this Letter we explore an alternative gelation mechanism driven by long-range anisotropic interactions resulting from electric or magnetic dipoles as in the technologically important ferrofluids. Spherical particles with a point dipole are known to form a “string phase” at low volume fraction, comprising long transient chains of particles concatenated in energetically favourable head-to-tail configurations [8]. Individual chains percolate in such a phase, i.e., the average chain length diverges and in simulations the particles become connected to their own periodic images through the boundary conditions on the simulation cell. However, the chains do not appear to be sufficiently interconnected to form a genuine gel-like network. Here, we show that network formation may be achieved at low φ by a modest elongation of the particles and their dipoles to make short dipolar dumbbells. Chain formation in dipolar colloids is a natural consequence of the anisotropy of the long-ranged dipole–dipole interactions. Colloidal chaining can also be achieved using short-ranged attraction, by limiting each particle to a maximum of two (reversible) bonds at specified sticky patches on their surface. To form networks of such particles, it is necessary to introduce a second type of particle with higher valency to act as chain junctions [7]. Alternatively, a low coordination number can be enforced by the introduction of three-body forces that discourage small angles between the bonds to any given particle [6]. In contrast, junctions arise with decreasing temperature in our one-component dipolar dumbbell fluid simply because their statistical weight increases relative to that of disconnected chains. The nature [9] and location of any first-order fluid– fluid phase transition in dipolar spheres is still not completely resolved. The critical point of the Stockmayer fluid (Lennard-Jones particles with a point dipole) has been shown to drop rapidly in temperature as the isotropic attraction is switched off, leaving soft dipolar spheres [10]. In contrast, Monte Carlo simulations of dipolar hard spheres indicate as many as three disordered phases at low temperature [11]. Less controversially, it has been shown that hard spherocylinders [12] or dumbbells [13] with an axial point dipole exhibit a gas–liquid transition within a limited range of particle elongations. However, the present simulations of soft-core dumbbells with an extended dipole showed no sign of such a transition within the range of