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4) coordinated particles strongly increases. C3b(t)is plotted as a function of time in the inset of Fig.10 and displays a similar abrupt change for E $ 0.7 but in the opposite direction: interestingly the presence of a strong external field enhances time correlations of multiply connected particles, as effect of the bundling. Moreover, we also notice a non-monotonic dependence of C3b(t) on time, which hints to correlations under the action of strong fields (E $ 0.5), that are probably caused by the dynamics of the bundled chains. In particular, due to the lateral diffusion of chains perpendicular to the field direction, particle coordination can increase (n $ 4) and decrease (n ¼ 2) due to presence or absence of nearby chains. These results overall confirm our interpretation of a complex and rather dramatic structural transition underlying the highly non-linear dielectric response. They also suggest that the nonlinear dielectric response of the gel network should correspond to an abrupt transition in the viscoelastic response of the material due to the transition from the connected network to bundled chains. The latter are characterized by strongly anisotropic magnetoviscous behavior,11,40,43 while the former behave as soft solids with a field-dependent yield stress.44 In the network phase, we also expect field-induced hardening as recently reported for a copolymer gel.45

E. Particle dynamics We have also studied the effect of the field on the particle mean square displacements. At high temperature, the anisotropy in the particle motion smoothly increases with increasing field strength, similar to previous studies and theoretical expectations.46 In Fig. 11 we show the particle mean square displacement under the action of a strong field (E ¼ 0.75) as a function of time in the gel. The same conditions as in Fig. 10 are chosen. In particular we distinguish the different contributions along the directions parallel (^ z) and perpendicular to the external field. For these low temperatures, we find that the mean square displacement is isotropic not only in the absence of a field (solid line) but also for field amplitudes E ( 0.5 (not shown). Even the values of the

Fig. 11 Dumbbell mean square displacement under the effect of a field E ¼ 0.75 (symbols) at f ¼ 0.0484 and T ¼ 0.06. The solid line is the result in the absence of a field.

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mean square displacements are very similar in these two cases. It is clear from the figure that a strong anisotropy is instead induced beyond a critical field strength. Particle motion slows down significantly in the presence of such a strong field, especially at intermediate times 100 < t < 102 where the mean square displacement develops a plateau. The motion parallel to the field direction is hindered even more, probably due to the presence of chain-like structures. In fact, we notice that the localization time associated with the plateau in the mean square displacement in a strong field is roughly the time where C3b(t) displays the minimum mentioned above (see Sect. IV.D). This suggest that the strong localization of the particle motion along the chains due to strong fields also affects the change toward higher or lower connectivity typical of different relative configurations of chains in the bundles. Only for very long times does the mean square displacement become isotropic again and diffusive behavior might set in at even later times, beyond the simulated time window. Similar conclusions can be drawn from the anisotropy in the intermediate scattering function Fs(~ q,t), when orienting the wave vector ~ q parallel and perpendicular to the field direction. F.

Hysteresis effects

In order to further investigate the dramatic structural transition just described, starting from the configurations at E ¼ 1.0 we have then reduced the intensity of the field to E ¼ 0.0, with steps of DE ¼ 0.05. The system is subjected to the reduced field for 2 106 MD steps, before the analysis starts. In Fig. 6, also the normalized polarization P/Psat obtained upon decreasing the field is shown. In contrast to what is observed at higher temperatures where the field induced changes are totally reversible, the gel displays a strong hysteresis in the response to the external field. This feature becomes evident as soon as the system enters the gelation regime. The coordination number c(n), measured upon reducing the external field, clearly confirms that the field-induced structural transition taking place in the gel is strongly hysteretic and the original structure can be by no means recovered upon reducing the external field.

V. Conclusions We have studied the equilibrium and field-induced structural properties of soft dumbbells, carrying a finite dipole moment. For moderate temperatures 0.2 ( T ( 0.5, where dipolar and thermal energies are comparable, the system is characterized by chain-like structures with an exponential distribution of chain lengths. An external magnetic field orients not only the particle’s dipole moments but also the chain-like structures as a whole. These features are typical for many dipolar systems. For even lower temperatures instead, where the dipolar interactions are more dominant, the system undergoes a percolation transition to an interconnected network of particle chains showing a powerlaw distribution of cluster sizes. Below the percolation transition, almost all particles belong to the same sample-spanning network. In the network regime, we find a much longer bond life time together with a much slower relaxational dynamics compared to the chain regime. Thus, the network is rather persistent and therefore has a big influence on the system’s mechanical properties. These properties are typically observed in colloidal gels. Soft Matter, 2011, 7, 163–171 | 169

Here we have shown that gelation dramatically, and rather irreversibly, changes the response of the material to an external electric field. In fact, since particles are strongly bound in the network, they can not easily reorient according to the field. Hence the polarizability of the gel network is initially relatively weak, as compared to the initial dipolar fluid. When the external field strength reaches a critical value, however, the particle’s dipole moments orient rather abruptly along the field direction, with a strongly non linear increase of the polarization. This reorientation breaks the network structure and particles rearrange into oriented, bundled chains. Such significant structural reorganizations beyond a critical field strength allows to change the mechanics and the dielectric properties at the same time, and could offer new applications for dipolar colloidal suspensions as field-responsive, smart materials. Because of this field-induced structural transition, the gel dielectric response displays a significant hysteresis, which is stronger for the more persistent network structures. A similar ferromagnetic hysteresis is known for ferrogels, where superparamagnetic particles are incorporated into a chemical gel.47,48 Since there is no underlying chemical gel here, the present system is much more susceptible to external fields and therefore might have an even greater potential for several applications. An experimental realisation of this model system would therefore be highly promising.

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