Colloids and polymers in random colloidal matrices: Demixing under good-solvent conditions

We consider a simplified coarse-grained model for colloid-polymer mixtures, in which polymers are represented as monoatomic molecules interacting by means of pair potentials. We use it to study polymer-colloid segregation in the presence of a quenched matrix of colloidal hard spheres. We fix the polymer-to-colloid size ratio to 0.8 and consider matrices such that the fraction $f$ of the volume that is not accessible to the colloids due to the matrix is equal to 40$\%$. As in the Asakura-Oosawa-Vrij (AOV) case, we find that binodal curves in the polymer and colloid volume-fraction plane have a small dependence on disorder. As for the position of the critical point, the behavior differs from that observed in the AOV case: While the critical colloid volume fraction is essentially the same in the bulk and in the presence of the matrix, the polymer volume fraction at criticality increases as $f$ increases. At variance with the AOV case, no capillary colloid condensation or evaporation is generically observed.

Figure 1

Bulk demixing curve (solid symbols) and coexistence diameter (empty symbols) in the $({\eta }_c,{\eta }_p)$ system representation for $L/R_c=14,16$. We also report the demixing curve of the AOV model, solid line, from Ref. [18]; the solid circle gives the position of the critical point.

Figure 2

Bulk demixing curve in the reservoir representation for $L/R_c=14,16$. ${\eta }_p^{r,\mathrm{id}}$ is the ideal reservoir packing fraction, while ${\eta }_p^r$ is the true reservoir packing fraction.

Figure 3

Cumulant ratios $M$ and $U$ at coexistence as a function of ${\eta }_p^{r,\mathrm{id}}$ for several values of $L/R_c$.

Figure 4

Colloid (left) and polymer (right) volume fraction histograms at coexistence for several values of ${\eta }_p^{r,\mathrm{id}}$ for $(f,R_{\mathrm{dis}}/R_c)=(0.4,1.0)$, $L/R_c=14$.

Figure 5

Fluid-fluid binodal curves for $f=0.4$, $R_{\mathrm{dis}}/R_c=0.2$ (left), $f=0.4$, $R_{\mathrm{dis}}/R_c=1.0$ (right). We report the results for $L/R_c=12$ and $L/R_c=16$ in terms of ${\eta }_c$ and ${\eta }_p$.

Figure 6

Fluid-fluid binodal curves for $f=0.4$, $R_{\mathrm{dis}}/R_c=0.2$ (top) and $f=0.4$, $R_{\mathrm{dis}}/R_c=1.0$ (bottom). We report the results for $L/R_c=12$ and $L/R_c=16$ in terms of ${\eta }_c,{\eta }_p^{r,\mathrm{id}}$ (left) and ${\eta }_c,{\eta }_p^r$ (right).

Figure 7

Estimates of $z_c^{*}{R}_c^3$ as a function of the reservoir polymer volume fraction ${\eta }_p^r$ (left) and of ${\eta }_p^{r*}$ at coexistence in terms of the reservoir colloid volume fraction ${\eta }_c^r$ (right). Results for $L/R_c=14$.

Figure 8

Connected susceptibilities $\chi$ in the colloid-vapor (left) and in the colloid-liquid (right) phases for $f=0.4$, $R_{\mathrm{dis}}/R_c=0.2$ (top), and $R_{\mathrm{dis}}/R_c=1$ (bottom). We report the results for $L/R_c=12,14,16$ as a function of ${\eta }_p^r$.

Figure 9

Rescaled connected susceptibilities ${(L/R_c)}^{-\gamma /\nu }\chi$ as a function of $t{(L/R_c)}^{1/\nu }$, where $t\equiv {\eta }_p^r/{\eta }_{p,\mathrm{crit}}^r-1$, for $L/R_c=12,14,16$. Data for $f=0.4$, $R_{\mathrm{dis}}/R_c=0.2$ (top) and $R_{\mathrm{dis}}/R_c=1$ (bottom). We use [50] $\gamma /\nu =1.5$, $\nu =0.9$.

Figure 10

Binodal curves for the interacting-polymer model (solid symbols) and for the AOV model (lines). Empty symbols give the critical points.