Figure 1

Schematic of a QA system. Equal-sized filled and empty circles are matrix and fluid particles, respectively. The bigger circle is a window with radius equal to one particle diameter. ${\Pi }_i$ is the probability that it will be occupied by exactly $i$ matrix or fluid particle centers.Reuse & Permissions

Figure 2

(Color online) The fractional available volume $V_0∕V$ in HS QA-FM matrices computed using the IT approach of Eqs. (3, 4) (curves) and “exact” results (filled circles) using the available space algorithm of Ref. 12.Reuse & Permissions

Figure 3

(Color online) Fluid self-diffusivity $D$ versus fluid density ${\rho }_{\mathrm{F}}$ for (a) HS QA-FM and (b) HS QA-M systems with matrix densities ${\rho }_{\mathrm{M}}=0.0$, 0.05, 0.15, 0.25, 0.30, and 0.35. In both (a) and (b), matrix density increases from the top to bottom. Curves are predictions of Eq. (1) and circles are molecular dynamics simulation results.Reuse & Permissions

Figure 4

(Color online) (a) Fluid self-diffusivity $D$ versus fluid density ${\rho }_{\mathrm{F}}$ for HS QA-FM (circles) and LJ QA-FM (diamonds) systems obtained via molecular dynamics simulations. The LJ QA-FM system is at $T=ϵ∕k_{\mathrm{B}}$. Matrix densities of ${\rho }_{\mathrm{M}}=0.05$, 0.15, 0.25, and 0.35 are presented. (b) Results for the LJ QA-FM system at $T=3ϵ∕k_{\mathrm{B}}$: molecular dynamics simulations (circles) and Eq. (1) (curves). Matrix densities of ${\rho }_{\mathrm{M}}=0.043$, 0.128, 0.214, and 0.3 are presented. In both (a) and (b), matrix and mobile densities for the LJ QA-FM systems are defined as ${\rho }_{\mathrm{M}}=N_{\mathrm{M}}\sigma {\left(T\right)}^3∕V$ and ${\rho }_{\mathrm{F}}=N_{\mathrm{F}}\sigma {\left(T\right)}^3∕V$, respectively. The effective HS diameter $\sigma \left(T\right)$ is determined by a Boltzmann factor criterion described in the text. In both (a) and (b), matrix density increases from the top to bottom.Reuse & Permissions