Screening in Yukawa fluid mixtures

The effective pair potential between mesoscopic charged particles in a neutralizing background medium takes a Yukawa form $\exp (-\lambda r)∕r$ with screening length ${\lambda }^{-1}$. We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length $\xi <{\lambda }^{-1}$ and show that the Yukawa interaction is screened if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length ${\lambda }^{-1}$. However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particles is unscreened, i.e., the effective potential between the solute particles is equal to the bare potential at large particle separations.

Figure 1

The effective solute-solute potential ${\varphi }_{22}^{\mathit{eff}}\left(r\right)$ for solvent density ${\rho }_1{\lambda }^{-3}=3$ and ${\rho }_2\to 0$ calculated using the HNC closure. Solid line: system A, the point Yukawa mixture, with $\delta =0$ and dot-dashed line with nonideality parameter $\delta =0.1$. The dashed line is for system B $(\delta =0)$ where the solvent potentials decay faster than for the Yukawa case. Results are compared to the bare potential ${\varphi }_{22}\left(r\right)$ (dotted line). The inset displays the radial distribution functions $g_{11}\left(r\right)$ (solid line) and $g_{12}\left(r\right)$ (dashed line) for $\delta =0$. On this scale, there is no visible difference between results in systems A and B.

Figure 2

The effective potential ${\varphi }_{22}^{\mathit{eff}}\left(r\right)$ for solvent density ${\rho }_1{\sigma }^3=0.5$ and ${\rho }_2\to 0$ calculated using the PY closure for hard-core Yukawa mixtures. Dashed line, system C ($\beta {ϵ}_{11}=0.1$, $\beta {ϵ}_{22}=0.4$, $\beta {ϵ}_{12}=0.2$); dot-dashed line, system D $(\beta {ϵ}_{12}=-0.2)$; and solid line, system E ($\beta {ϵ}_{11}=0$, $\beta {ϵ}_{12}=0$, $\beta {ϵ}_{22}=0.4$). In systems C and D, ${\varphi }_{22}^{\mathit{eff}}\left(r\right)$ is shorter ranged than the bare potential ${\varphi }_{22}\left(r\right)$ (dotted line) but in system E, ${\varphi }_{22}^{\mathit{eff}}\left(r\right)\simeq {\varphi }_{22}\left(r\right)$ for $r\gtrsim 4\sigma$; there is no screening. The inset displays the corresponding total correlation function $h_{11}\left(r\right)$ for systems C, D, and E.