Self-Assembly of Colloidal Superstructures in Coherently Fluctuating Fields

From microscopic fluid clusters to macroscopic droplets, the structure of fluids is governed by the van der Waals force, a force that acts between polarizable objects. In this Letter, we derive a general theory that describes the nonequilibrium counterpart to the van der Waals force, which emerges in spatially coherently fluctuating electromagnetic fields. We describe the formation of a novel and complex hierarchy of self-organized morphologies in magnetic and dielectric colloid systems. Most striking among these morphologies are dipolar foams—colloidal superstructures that swell against gravity and display a high sensitivity to the applied field. We discuss the dominance of many-body forces and derive the equation of state for a material formed by the coherent van der Waals force. Our theory is applied to recent experiments in paramagnetic colloidal systems and a new experiment is suggested to test the theory.

Figure 1

(a) The incoherent (van der Waals–like) interaction (ICFI) and (b) the spatially coherent fluctuation interaction (SCFI) are both induced by field fluctuations, but with different spatial correlations. (c), (d) While the two-body forces are similar in both cases, the three-body forces have different angular character and are longer ranged for SCFI; see Eq. (2). (e) The phase diagram of clusters of size $N$ and material susceptibility $\chi$. The colloidal clusters are growing over time [7, 8] and undergoing a transition from linear chains to membranes beyond a critical size $N_c(\chi )$.

Figure 2

(a) The SCFI is unexpectedly complex: The two-membrane interaction is attractive or repulsive depending on orientation, cf. Eq. (4), with a ground state in the “twisted” configuration. (b) The large scale structure of a dipolar foam (from 7, 8) in experiment (left) and in simulation (right). (c) The theoretical 3D shelf model for the foam structure.