Anisotropic self-assembly of soft particles mediated by elliptically polarized AC fields

TL;DR

The paper addresses how elliptically polarized AC fields mediate anisotropic self-assembly of soft particles, bridging previously studied linear and circular polarization regimes. It develops a coarse-grained dipole interaction framework by time-averaging field-induced dipoles and expanding in spherical harmonics, enabling direct mapping to linear and circular cases via the parameters $u_0(r)$, $u_2(r)$, and the anisotropy $\alpha$. The model is specialized to ionic soft microgels with monopole charges and field-induced polarization, incorporating Debye screening lengths $\kappa$ and $\kappa_d$, yielding a total potential $u(\mathbf{r})=u_M(r)+\bar{u}_{dd}(\mathbf{r})+u_H(r)$ that drives aggregation. MD simulations reveal a transition from linear chains to planar, isotropic aggregates as $\alpha$ increases, with the dipole range ratio $f=\kappa_d/\kappa$ strongly shaping morphologies. The framework offers a tunable route to design field-directed self-assembly of soft nanomaterials and can be extended to related systems, including magnetic analogs.

Abstract

Attractive dipole interactions can be induced between equally charged soft nanoparticles under the influence of AC electric fields. The combination of charge repulsion and dipole attraction, along with different screening responses from an underlying electrolyte, lead to complex aggregations ranging from chain-like formation for linear polarizations to isotropic planar structures in the case of circular polarizations. In this work, we analyze the role of varying field anisotropies in these self-assembled structures. To this end, the formalism previously developed for the coarse-grained interactions of soft particles in the presence of linear [T.~Colla {\it et al.}, ACS Nano {\bf 12}, 4321-4337 (2018)] and circular [M.~Reich {\it et al.}, Soft Matter {\bf 21}, 1516-1528 (2025)] field polarizations is naturally extended to incorporate elliptical polarizations of arbitrary asymmetries. A rich variety of self-assembly formations is found at intermediate field anisotropies, thus bridging the gap between linear and circular field-induced self-assembly scenarios.

Figures (9)

• Figure 1: Sketch of our model system. Two spherical particles of center-to-center separation $\bm{r}$ are polarized by an elliptically polarized field, lying along the $x$-$y$ plane. The origin of the coordinate system is placed at the center of colloid 1 and colloid 2 has its center at position ${\bm r}$. The induced dipole interactions are obtained by considering the interactions between bound charges at points located at positions $\bm{r}_1$ and $\bm{r}_2$ from the particle centers $1$ and $2$, respectively, and separated by a distance $\bm{R}=\bm{r}-(\bm{r}_1 - {\bm r}_2)$. The electrostatic interaction is mediated by a response function $G(R)$ which incorporates the implicit effects of a underlying electrolyte.
• Figure 2: Sketch of the polarizing mechanism of soft particles driven by an alternating field $\bm{E}(t)$, given rise to uniform polarizations. Under the influence of this field, some fixed charges of magnitude $\rho_0$ undergo rigid displacements of amplitude $d$ along the instantaneous field direction. Such a charge displacement leads to the building-up of net charges at the particle boundaries, bearing opposite signs along the field direction.
• Figure 3: The time-averaged dipole-dipole pair potential of ionic microgels, $\bar{u}_{dd}(\bm{r})$, induced by the elliptically polarized field, Eq. (\ref{['E1']}). The reduced polarization is $\tau=P_0/(qa)=400$. In (a), the field is linearly polarized along the $x$ direction ($\alpha=0$), and the potential is isotropic along the $yz$ plane. In (b), the the elliptic polarization angle is $\alpha=\pi/8$, and the interactions are fully anisotropic, whereas in (c) the field is circularly polarized, $\alpha=\pi/4$, and the interactions are isotropic along the $xy$ plane.
• Figure 4: Equilibrium positions (left panels) and depth (right panels) of dipole pair correlations along the $x$ (top panels) and $y$ (bottom panels) directions, as a function of polarization angles $\alpha$ for different fractions $f$ that determine the ratio between dipole and monopole inverse screening lengths. In all cases, the dimensionless dipole interaction strength is fixed at $\tau=400$.
• Figure 5: Total pair potential $u(\bm{r}) = u_M(r) + \bar{u}_{dd}(\bm{r}) + u_{\mathrm H}(r)$ for two representative systems. In panels (a), (b), and (c), microgels have charge $Z=50$ and polarizations $\tau=400$, whereas panels (d), (e), and (f) pertain to microgels with larger charges, $Z=100$, and polarizations $\tau=800$. In all cases, the screening lengths for monopole and dipole interactions are the same, $\kappa=\kappa_d=2.79a^{-1}$, i.e., $f = 1$.