Polar-solvation classical density-functional theory for electrolyte aqueous solutions near a wall

A precise description of the structural and dielectric properties of liquid water is critical to understanding the physicochemical properties of solutes in electrolyte solutions. In this article, a mixture of ionic and dipolar hard spheres is considered to account for water crowding and polarization effects on ionic electrical double layers near a uniformly charged hard wall. As a unique feature, solvent hard spheres carrying a dipole at their centers were used to model water molecules at experimentally known concentration, molecule size, and dipolar moment. The equilibrium ionic and dipole density profiles of this electrolyte aqueous model were calculated using a polar-solvation classical density-functional theory (PSCDFT). These profiles were used to calculate the charge density distribution, water polarization, dielectric permittivity function, and mean electric potential profiles as well as differential capacitance, excess adsorptions, and wall-fluid surface tension. These results were compared with those corresponding to the pure dipolar model and unpolar primitive solvent model of electrolyte aqueous solutions to understand the role that water crowding and polarization effects play on the structural and thermodynamic properties of these systems. Overall, PSCDFT predictions are in agreement with available experimental data.

Figure 1

The profiles of the orientational order parameter ${\eta }_{10}\left(z\right)=〈cos\theta 〉$ of a pure dipolar fluid near a charged plate for different values of the wall charge density ${\sigma }^{*}$. The number density in a bulk ${\rho }_b=0.033/{\text{Å}}^3$, the dipole moment strength $m=2.22\text{D}$.

Figure 2

The same as in Fig. 1, but for the profiles of the electric polarization $P\left(z\right)$.

Figure 3

The profiles of the dielectric permittivity $\varepsilon \left(z\right)$ of a pure dipolar fluid near a charged hard wall for different values of the dipole moment strength $m^{*}$ as calculated from Eq. (55). The number density in a bulk ${\rho }_b=0.033/{\text{Å}}^3$.

Figure 4

(a) The scaled number density profiles of three species of electrolyte solution near a charged hard wall. The results for PSCDFT are compared with the ones for USCDFT. The notations $+q$ and $-q$ mark the density profiles of positively charged ions ${\rho }_1\left(z\right)/{\rho }_{1,b}$ and negatively charged ions ${\rho }_2\left(z\right)/{\rho }_{2,b}$, correspondingly, whereas m and HS mark the ones of solvent species ${\rho }_3\left(z\right)/{\rho }_{3,b}$ for the dipole component in PSCDFT and for a neutral HS component in USCDFT, correspondingly. The ionic concentration $c=10\text{mM}$, the wall electric potential ${\phi }_0^{*}=6.4\text{mV}$. The dipole moment strength $m=2.22\text{D}$ in PSCDFT and the dielectric permittivity $\varepsilon =79.7$ in USCDFT; (b) The same as in (a). The oscillatory parts of density profiles are displayed with higher resolution.

Figure 5

The same as in Fig. 4, but for the wall electric potential ${\phi }_0=25.7\text{mV}$.

Figure 6

The profiles of the mean electrostatic potential ${\tilde{\phi }}^{*}\left(z\right)$ near a charged hard wall for two values of the wall electric potential ${\phi }_0=6.4$ and $25.7\text{mV}$. The results for PSCDFT are compared with the ones for USCDFT. The values of the parameters of an electrolyte solution are the same as the ones in Fig. 4.

Figure 7

The orientational order parameter profile ${\eta }_{10}\left(z\right)=〈cos\theta 〉$ of a dipole component of electrolyte solution near a charged hard wall. The ionic concentration $c=10\text{mM}$, the dipole moment strength $m^{*}=2.4$. The results are compared with the corresponding ones for pure dipole fluid (the curve $c=0$). (a) The wall electric potential ${\phi }_0=6.4\text{mV}$ (the corresponding wall charge density $\sigma =1.48\times {10}^{-4}\frac{C}{m^2}$); (b) ${\phi }_0=25.7\text{mV} \left(\sigma =6.26\times {10}^{-3}\frac{C}{m^2}\right)$.

Figure 8

The same as in Fig. 7, but for the dipole moment strength $m=0.93\text{D}$. (a) ${\phi }_0=6.4\text{mV} \left(\sigma =3.80\times {10}^{-4}\frac{C}{m^2}\right)$; (b) ${\phi }_0=25.7\text{mV} \left(\sigma =1.57\times {10}^{-3}\frac{C}{m^2}\right)$.

Figure 9

The dimensionless polarization profiles $P^{*}\left(z\right)$ for different values of the wall electric potential ${\phi }_0^{*}$. The values of the parameters of PSCDFT are the same as the ones in Fig. 4.

Figure 10

The dimensionless polarization profiles $P^{*}\left(z\right)$ for the wall electric potential ${\phi }_0^{*}=0.25$. The result for PSCDFT is compared to the corresponding one for USCDFT. The values of parameters are the same as the ones in Fig. 4.

Figure 11

The dependence of a wall charge density ${\sigma }^{*}$ on the wall electric potential ${\phi }_0^{*}$. The results for PSCDFT are compared with the ones for USCDFT. The values of parameters are the same as the ones in Fig. 4.

Figure 12

The same as in Fig. 11, but for the differential capacitance $C=d{\sigma }^{*}/d{\phi }_0^{*}$.

Figure 13

The scaled excess adsorptions ${\mathrm{\Gamma }}_i^{*} \left(i=1,2,3\right)$ as functions of the wall electric potential ${\phi }_0^{*}$. The results for PSCDFT are compared with the ones for USCDFT. The notations and the values of the parameters of the electrolyte solution are the same as the ones in Fig. 4.

Figure 14

The scaled wall-fluid surface tension $\gamma /{\gamma }_{\mathrm{HS}}$ as a function of the wall charge density ${\sigma }^{*}$. The result for PSCDFT are compared with the corresponding one for USCDFT. The values of parameters are the same as the ones in Fig. 4.

Figure 15

The ratio of wall-fluid PSCDFT surface tension ${\gamma }_{\mathrm{PSCDFT}}$ and USCDFT surface tension ${\gamma }_{\mathrm{USCDFT}}$ as a function of the wall charge density ${\sigma }^{*}$. The values of parameters are the same as the ones in Fig. 4.