^{1,a)}, Ronald Blaak

^{2}, Craig N. Lumb

^{1}and Jean-Pierre Hansen

^{1,3}

### Abstract

We report the results of extensive molecular dynamics simulations of a simple, but experimentally achievable model of dipolar colloids. It is shown that a modest elongation of the particles and dipoles to make dipolar dumbbells favors branching of the dipolar strings that are routinely observed for point dipolar spheres (e.g., ferrofluids). This branching triggers the formation of a percolating transient network when the effective temperature is lowered along low packing fraction isochores . Well below the percolation temperature the evolution of various dynamical correlation functions becomes arrested over a rapidly increasing period of time, indicating that a gel has formed. The onset of arrest is closely linked to ongoing structural and topological changes, which we monitor using a variety of diagnostics, including the Euler characteristic. The present system, dominated by long-range interactions between particles, shows similarities to, but also some significant differences from the behavior of previously studied model systems involving short-range attractive interactions between colloids. In particular, we discuss the relation of gelformation to fluid–fluid phase separation and spinodal decomposition in the light of current knowledge of dipolar fluid phase diagrams.

The authors are grateful to Dr. Philip Camp for helpful discussions on the phase diagrams of dipolar systems. M.A.M. thanks EPSRC (U.K.) (contract EP/D072751/1) for financial support.

I. INTRODUCTION

II. DIPOLAR DUMBBELLS

III. PERCOLATION

IV. NETWORK STRUCTURE AND TOPOLOGY

V. DYNAMICAL ARREST

VI. DISCUSSION AND CONCLUSIONS

### Key Topics

- Percolation
- 32.0
- Colloidal systems
- 18.0
- Gels
- 18.0
- Molecular dynamics
- 16.0
- Bond formation
- 7.0

## Figures

Potential energy in units of of two dipolar dumbbells with center-to-center separation in various orientations with respect to each other and to the center-to-center vector .

Potential energy in units of of two dipolar dumbbells with center-to-center separation in various orientations with respect to each other and to the center-to-center vector .

Interaction energy per particle of two parallel idealized chains of 20 head-to-tail dipoles, shifted with respect to each other by along their axes, as a function of the separation of the chain axes. The four curves correspond to different dumbbell extensions, . Each curve has been scaled in length by the equilibrium pair separation and in energy by the minimum pair energy [see Eq. (2)] for the relevant value of . The thick line corresponds to the adopted in the present work.

Interaction energy per particle of two parallel idealized chains of 20 head-to-tail dipoles, shifted with respect to each other by along their axes, as a function of the separation of the chain axes. The four curves correspond to different dumbbell extensions, . Each curve has been scaled in length by the equilibrium pair separation and in energy by the minimum pair energy [see Eq. (2)] for the relevant value of . The thick line corresponds to the adopted in the present work.

Snapshot configurations at and temperatures of (a) , above the percolation threshold, and (b) (just below the percolation threshold). Particles belonging to a given cluster in the periodic system are shown in the same color.

Snapshot configurations at and temperatures of (a) , above the percolation threshold, and (b) (just below the percolation threshold). Particles belonging to a given cluster in the periodic system are shown in the same color.

Percolation probability (fraction of percolating configurations) along the isochore . The inset shows the probability as a simple function of for three linear system sizes . The main plot shows the same data as a function of the shifted and scaled density (see text).

Percolation probability (fraction of percolating configurations) along the isochore . The inset shows the probability as a simple function of for three linear system sizes . The main plot shows the same data as a function of the shifted and scaled density (see text).

Radial distribution function and coordination number distribution (inset) at packing fraction . The lines in the inset are a guide to the eye.

Radial distribution function and coordination number distribution (inset) at packing fraction . The lines in the inset are a guide to the eye.

Static structure factor at packing fraction . The inset shows the same data on a semi-log plot.

Static structure factor at packing fraction . The inset shows the same data on a semi-log plot.

Convergence of the dielectric permittivity with the progress of simulations at packing fraction and the reduced temperatures indicated.

Convergence of the dielectric permittivity with the progress of simulations at packing fraction and the reduced temperatures indicated.

Profile of the normalized EC as a function of length scale at packing fractions (a) and (b) at the temperatures indicated in (a).

Profile of the normalized EC as a function of length scale at packing fractions (a) and (b) at the temperatures indicated in (a).

Distribution of void sizes at measured by the probability of the maximum diameter of a sphere that can be inserted at a random point in space without overlapping with a particle.

Distribution of void sizes at measured by the probability of the maximum diameter of a sphere that can be inserted at a random point in space without overlapping with a particle.

Arrhenius plots of the self-diffusion constant and the rate constant for bond breaking at packing fraction . The lines joining the symbols are a guide to the eye.

Arrhenius plots of the self-diffusion constant and the rate constant for bond breaking at packing fraction . The lines joining the symbols are a guide to the eye.

MSD of particles at packing fraction .

MSD of particles at packing fraction .

Velocity autocorrelation function as a function of reduced time and its Fourier transform as a function of reduced frequency at packing fraction .

Velocity autocorrelation function as a function of reduced time and its Fourier transform as a function of reduced frequency at packing fraction .

Self-part of the intermediate scattering function, . (a) Packing fraction and wavenumber at selected temperatures as marked. Inset: expanded plot of the curve. (b) Wavenumber , temperature , and three packing fractions, as marked.

Self-part of the intermediate scattering function, . (a) Packing fraction and wavenumber at selected temperatures as marked. Inset: expanded plot of the curve. (b) Wavenumber , temperature , and three packing fractions, as marked.

Non-Gaussian parameter of the self-part of the van Hove correlation function at packing fraction .

Non-Gaussian parameter of the self-part of the van Hove correlation function at packing fraction .

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