Polymerization transitions in two-dimensional systems of dipolar spheres

We investigate the self-organization of dipolar spheres into polymer chains as a fundamental model of the self-assembly of particles having anisotropic interparticle interactions. Our study involves a combination of modeling with vertically vibrated magnetic beads simulating a quasi-two-dimensional fluid at equilibrium and corresponding Monte Carlo simulations of hard spheres with embedded extended dipoles. We find a transition from a gas-like phase to a polymerized phase upon cooling, in accord with the analytic theory of equilibrium polymerization.

Figure 1

(Color online) (a),(b),(c) Images of an experimental system where $C=0.026$ at three different temperatures: $T∕T_{\Phi }>1$ (a), $T∕T_{\Phi }\approx 1$ (b), and $T∕T_{\Phi }<1$ (c). Particles were constructed to have differently colored northern and southern hemispheres so that dipole orientations could be discerned. (d),(e),(f) Simulated particle realizations with $C=0.026$ and: $T∕T_{\Phi }>1$ (d), $T∕T_{\Phi }\approx 1$ (e), and $T∕T_{\Phi }<1$ (f).

Figure 2

(Color online) (a) A plot of $\Phi$ vs $T∕T_{\Phi }$ for experimental systems where $C=0.020$, 0.026, 0.039, 0.052, 0.078, and 0.104; (b) a similar plot of $\Phi$ vs $T∕T_{\Phi }$ for similar simulated systems.

Figure 3

(Color online) (a) A plot of $L$ as a function of $T$ for experimental systems where $C=0.020$, 0.052, and 0.104. Inset is a plot of $L$ vs $T∕T_{\Phi }$; (b) plot of $L$ as a function of $T$ for similar simulated systems. Inset is a plot of $L$ vs $T∕T_{\Phi }$.

Figure 4

$T_{\Phi }$ for the simulation (open circles) and the experiment (filled circles). Solid line is a fit of $T_{\Phi }$ to the Dainton-Ivin equation.