Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids

Especially small values of the static structure factor $S\left(k\right)$ at long wavelengths, i.e., small $k$, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of $S\left(k\right)$ data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of $S\left(k\right)$ at small $k$ is typically in a range 0.02–0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that $S\left(k\right)$ at small $k$ generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of $S\left(0\right)$, so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

Figure 1

Example image from the top-view camera, in the experiment of HG [47, 48]. The field of view (FOV) was $23\times 17\mathrm{mm}$, which was smaller than the diameter of the entire cloud [20]. Individual microparticles appear as white dots that fill multiple pixels. The dashed circle indicates the region of interest (ROI) for our analysis, where the particle density was more uniform than in the corners of the FOV. This image is from the run with $T/T_m=1.19$.

Figure 2

Static structure factor $S\left(k\right)$ for the experimental run of HG with $T/T_m=1.19$. For this experimental run, the lowest data point in the curve is $S_{\min }=0.0154$, and the height of the first peak (obtained by fitting to a parabola) is $S_{\mathrm{peak}}=3.38\pm 0.01$. The horizontal axis is normalized by the 2D Wigner-Seitz radius $a$.

Figure 3

Lowest value $S_{\min }$ as a function of temperature $T/T_m$ for (a) experiment of HG with $N$ ranging from 820 to 870, depending on $T/T_m$, and (b) 2D Yukawa simulation with $N$ similar to that of the experiment. We find that $S_{\min }$ has its smallest value near the melting point $T_m$. The lowest experimental data point is $S_{\min }=0.0139$ at $T/T_m=1.15$. There is an upward trend for $S_{\min }$ to increase with $T/T_m$, as indicated by dotted lines. As our measure of the hyperuniformity index, $S_{\min }/S_{\mathrm{peak}}$ is also plotted with its values on the right axis. Temperature trends for $S_{\min }$ and $S_{\min }/S_{\mathrm{peak}}$ can be seen for both experiment and simulation. Data here are tabulated in the Supplemental Material [20].