Binary colloidal systems with competing interactions: structural transitions and ordering

Colloidal systems with competing interactions exhibit a diverse range of self-assembled structures, making them fundamental for both theoretical and experimental research in soft matter physics. In this work, we investigate a binary colloidal system confined by a harmonic potential, where particles interact via a modified short-range attraction and long-range repulsion (SALR) potential. The proposed<i>modified mermaid potential</i>incorporates three characteristic interaction scales: (i) a short-range neutral zone where the force is zero, (ii) an intermediate attractive well, and (iii) a long-range repulsive barrier. Particles of type A and B differ in their polymer coating thickness, leading to distinct interaction ranges and asymmetric pair interactions. Using overdamped Langevin dynamics simulations, we explore the system's structural transitions as a function of the interaction parameters and confinement strength. Our results reveal a rich phase behavior, including alternating stripe patterns composed of A- and B-type particles, which reflect interaction asymmetry; locally ordered square motifs where A-type particles are surrounded by B-type neighbors; and radial phase segregation in which B-type particles accumulate near the system boundary while A-type particles dominate the central region. The competition between interparticle interaction asymmetry and confinement gives rise to structural motifs such as alternating peripheral radial stripes, central crystalline domains, and mixed arrangements with short-range hexagonal order. These findings not only extend our understanding of SALR systems, but also provide valuable guidance for experimental efforts aimed at realizing such interaction potentials-particularly in regimes with smalllAandlB, the effective interaction ranges for species A and B-where the neutral-force zone acts predominantly between nearest neighbors.