Glass-transition properties of Yukawa potentials: From charged point particles to hard spheres

The glass transition is investigated in three dimensions for single and double Yukawa potentials for the full range of control parameters. For vanishing screening parameter, the limit of the one-component plasma is obtained; for large screening parameters and high coupling strengths, the glass-transition properties cross over to the hard-sphere system. Between the two limits, the entire transition diagram can be described by analytical functions. Unlike other potentials, the glass-transition and melting lines for Yukawa potentials are found to follow shifted but otherwise identical curves in control-parameter space.

Figure 1

Glass-transition diagram for the single Yukawa potential (filled circles). Transition points are shown together with the full curve exhibiting Eq. (7). For comparison, a similar curve is shown for the melting of the crystal.

Figure 2

Critical glass-form factors $f_q$ for the glass transition in the single Yukawa system. For increasing screening parameter $\kappa$, the inset shows the location of the respective transition points on the MCT-transition line, cf. Fig. 1, with the same symbols as in the main panel. The full curve shows the solution for the HSS within the HNC approximation. The result for HSS within the PY approximation [14] is shown as a dashed line.

Figure 3

Comparison in the glass-transition line between HNC (bullets) and PY (triangles) for the structure-factor input to the glass-transition calculations. Equation (7) is shown as a dashed curve.

Figure 4

Evolution of the single Yukawa potential along the glass-transition line in Fig. 1. The potentials are shown from right to left for $(\kappa ,\Gamma )=(1.01,396)$, $(3.87,1240)$, $(9.87,1.34\times {10}^5)$, and $(38.71,1.06\times {10}^{17})$.

Figure 5

Effective packing fraction ${\phi }_{\mathrm{eff}}^c$ for Yukawa potentials along the transition line in Fig. 1. The horizontal dashed line shows the HSS-HNC limit of ${\phi }_{\mathrm{HSS}}^c=0.525$. The inset shows the effective hard-sphere diameter, $d_{\mathrm{eff}}^c=ln{\Gamma }^c/\kappa$ equivalent to the effective densities. In both plots, the dotted curves display the small-$\kappa$ asymptotes derived from Eq. (7).

Figure 6

Glass-transition diagram for double Yukawa potentials with $\alpha =0.125$, $\epsilon =0.2$ (diamonds) and 0.01 (squares). The single Yukawa data (filled circles) are shown together with the analytical description by Eq. (7) (solid curve labeled $\epsilon =0$). The single Yukawa points are scaled according to Eq. (13) for $\epsilon =0.2$ and shown by open circles. Dotted and dashed curves represent scaled versions of Eq. (7) for $\epsilon =0.01$ and $\epsilon =0.2$, respectively. The solid curves labeled $\epsilon =0.01$ and $\epsilon =0.2$, respectively, show the solution of Eq. (14).

Figure 7

Localization length for single Yukawa (full circles) and double Yukawa (diamonds) potential with $\alpha =0.125$ and $\epsilon =0.2$. The open circles show the single Yukawa data scaled according to Eq. (13). The horizontal dashed line shows the HSS limit for $r_s^c$.