Entropic Identification of the First Order Freezing Transition of a Suspension of Hard Sphere Particles

We analyze the experimental particle current autocorrelation function of suspensions of hard spheres. Interactions between the particles are mediated by thermally activated acoustic excitations in the solvent. Those acoustic modes are tantamount to the system’s (energy) microstates and by their orthogonality, each of those modes can be identified with an independent Brownian particle current. Accordingly, partitioning of the system’s energy states is impressed on the current autocorrelation function. This impression provides a novel measure of the entropy and location of a partitioning or entropy limit at a packing fraction that coincides with that of the observed suspension’s first order freezing transition.

Figure 1

(a) The scaled current correlator for suspension $M2$ for values of $q$ indicated. The best fitting SE, Eq. (5) ($A=0.7$, ${\tau }_x=0.07$, $\gamma =0.44$) cannot be distinguished from the data. To illustrate the degree of stretching the basic exponential decay (SE with $\gamma =1$) is shown by the red dashed curve. (b) Parameters $A$, ${\tau }_x$, and $\gamma$ of the SE defined by Eq. (5). The vertical dashed line is located at ${\varphi }_f=0.494$. The two dashed curves are power laws $A=A_o|{\varphi }_a-\varphi {|}^{-\alpha }$ (top) and ${\tau }_x=T_o|{\varphi }_b-\varphi {|}^{\beta }$ fitted to $A$ and ${\tau }_x$, respectively. Fitting parameters are listed in Table 2. The small (black) horizontal bars at the right of the figure indicate average values of the SE parameters fitted to $C^{*}(q\ne q*,\tau *;\varphi >{\varphi }_f)$. See text for explanation.

Figure 2

Triangles: suspension $P$; squares, suspension $M1$; circles, suspension $M2$. (a) Moments of the distribution, $g({\tau }_t)$, of decay times in Eq. (7); mean, $⟨{\tau }_t⟩$ (closed symbols). Spread, $\sigma$ (open symbols). Skewness, $\zeta$ (half-filled symbols). The (magenta) vertical bar is an estimate of the error in $⟨{\tau }_t⟩$. (b) Products, $A{\tau }_x$, (closed symbols) and $A⟨{\tau }_t⟩$, (open symbols). See text for details.