Separation and fractionation of order and disorder in highly polydisperse systems

We study a polydisperse soft-spheres model for colloids by means of microcanonical Monte Carlo simulations. We consider a polydispersity as high as 24%. Although solidification occurs, neither a crystal nor an amorphous state are thermodynamically stable. A finite size scaling analysis reveals that in the thermodynamic limit: (a) the fluid-solid transition is rather a crystal-amorphous phase-separation, (b) such phase-separation is preceded by the dynamic glass transition, and (c) small and big particles arrange themselves in the two phases according to a complex pattern not predicted by any fractionation scenario.

Figure 1

(Color online) (pdf) of $\mathcal{F}$, Eq. (14) at various representative values of $e$. Data in panel (a) are computed at energy densities in the energy gap between the fluid and the solid phases. The double peak structure reveals phase coexistence (the position of the leftmost peak scales as $1/N$). Data in panel (b) are computed for $e$ in the solid phase (the $e$-dependency there is very mild).

Figure 2

(Color online) The (connected) time autocorrelation function for the energy in the PT can be fitted (dotted line) as $⟨e\left(t^{\prime }\right)e\left(t^{\prime }+t\right)⟩=a_{FS}{e}^{-t/{\tau }_{FS}}+a_{SS}{e}^{-t/{\tau }_{SS}}$.

Figure 3

(Color online) Finite size effects in the Maxwell construction. Main panel: the inverse temperature $\beta \left(e\right)$ as a function of the energy density $e$ for various sizes of the sample. Inset: $\delta -\beta$ phase diagram of the system obtained from the data in Ref. [8].

Figure 4

(Color online) Snapshot of a typical low energy configuration $\left(N=864,e=1.01\right)$. (a): whole system. (b): particles with index $i>725$ and $i∊\left[400,600\right]$. (c): particles $i<400$. (d): particles $i∊\left[600,725\right]$. The size of the circles are proportional to the particle sizes.

Figure 5

(Color online) The crystal order parameter $Q_6\left(x\right)$, Eq. (16) as a function of the particles size $x$, for different $N$ values.