Competing structures in a minimal double-well potential model of condensed matter

TL;DR

This work demonstrates that a minimal athermal two-dimensional model with isotropic interactions, implemented as a double-well bonding potential plus an excluded volume and a valence cap, can reproduce key features of polyamorphic amorphous materials without thermodynamic assumptions. By depositing particles and allowing relaxation, the model yields g(r) with two principal peaks at $r_a$ and $r_b$ and a structure factor S(q) with corresponding peaks and low-$q$ plateaus that signal long-range heterogeneity, particularly at intermediate packing fractions and high coordination $n$. Local orientational statistics show well-defined angular motifs (e.g., near $\pi/4$, $\pi/3$, $2\pi/5$, $\pi/2$) consistent with emerging polycrystallinity in an isotropically bonded network. Overall, the results suggest that a simple double-well interaction, constrained by a maximum number of bonds, can capture a broad range of amorphous behaviors observed in materials such as water, silicon, and other glasses, with potential extensions to 3D and targeted inverse design.

Abstract

The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate a refined description of the particle interaction that includes an ad hoc design of the inside of the system constituents, and use temperature as a control parameter. We show that all these features can emerge from a minimal athermal two-dimensional model where particles interact isotropically by a double-well potential, which includes an excluded volume and a maximum coordination number. The rich variety of structural patterns shown by this simple geometrical model apply to a wide range of real systems including water, silicon, and different amorphous materials.

Figures (5)

• Figure 1: Double-well potential with excluded volume. The blue line represents the potential $V(r)$ for bonded interactions with a maximum coordination limit, $n$. The red line represents the unbonded interaction potential $V_{unbonded}(r)$ in the form of an excluded volume.
• Figure 2: Radial distribution function$g(r)$ as a function of $\phi$ and $n$. Dashed lines mark the height of the two main peaks, at $r_a$ and $r_b$, for clarity. Inset show a zoom with a detail of the medium-range order for $r>2$.
• Figure 3: Structure factor$S(q)$ as a function of $\phi$ and $n$. Insets show, for each $\phi$, the energy per particle, $V/$particle, as well as the mean number of bonds per particle, as a function of $n$. Insets show a zoom of the long-range order manifest at low $q$.
• Figure 4: Snapshots (top) for $\phi=0.3$ and $n=3$ (left) and $6$ (right). Black (red) lines between particles represent bonds in the first (second) potential well. Contour maps (bottom) of the snapshots colored according to the number of particles per square; contour lines join points at constant density; lines are smoothed for clarity using B-splines. Two particularly long contour lines of low particle density have been highlighted for $n=6$.
• Figure 5: Angle distribution shown by a normalized histogram for $\phi$=0.3 as a function of $n$ of the angles associated with the non-overlapping triangles each particle forms with any pair of its adjacent neighbors. Sketches show (left) a generic particle (red) with four neighbors (lines represent bonds as in Fig. \ref{['snapshots']}), and (right) the corresponding four blue triangles (numbered from 1 to 4) that the red particle forms with any pair of its adjacent neighbors, from which we obtain the angles to construct the histograms.