Shape-specific fluctuations of an active colloidal interface

Motivated by a recently synthesizable class of active interfaces formed by linked self–propelled colloids, we investigate the dynamics and fluctuations of a phoretically (chemically) interacting active interface with roto–translational coupling. We enumerate all steady–state shapes of the interface across parameter space and identify a regime where the interface acquires a finite curvature, leading to a characteristic ‘‘C–shaped’’ topology, along with persistent self–propulsion. In this phase, the interface height fluctuations obey Family–Vicsek scaling but with novel exponents: a dynamic exponent $z_h \approx 0.5$, a roughness exponent $α_h \approx 0.9$ and a super–ballistic growth exponent $β_h \approx 1.7$. In contrast, the orientational fluctuations of the colloidal monomers exhibit a negative roughness exponent, reflecting a surprising smoothness law, where steady–state fluctuations diminish with increasing system size. Together, these findings point towards a unique non–equilibrium universality class associated with self–propelled interfaces of non–standard shape.

💡 Research Summary

The authors investigate a novel class of active interfaces formed by a chain of chemically interacting self‑propelled colloids. Each particle moves in two dimensions with a self‑propulsion speed (v_s) along its orientation (\mathbf e_i=(\cos\theta_i,\sin\theta_i)) and experiences a force derived from a harmonic bond potential that keeps the chain together. In addition, the particles generate a phoretic field (c(\mathbf r)) that diffuses instantly (Laplace equation with point sources) and creates a gradient (\mathbf J_i=-\nabla c(\mathbf r_i)). This gradient exerts a torque on each particle proportional to a coupling constant (\chi_r), producing a roto‑translational coupling: the orientation dynamics (\dot\theta_i = \chi_r (\mathbf e_i\times \mathbf J_i) + \sqrt{2D_r},\xi_i^r) is directly linked to the positions. Translational and rotational noises ((D_t, D_r)) are also present.

Two dimensionless groups are introduced:
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