Effective potential theory for diffusion in binary ionic mixtures

Self-diffusion and interdiffusion coefficients of binary ionic mixtures are evaluated using the effective potential theory (EPT), and the predictions are compared with the results of molecular dynamics simulations. We find that EPT agrees with molecular dynamics from weak coupling well into the strong-coupling regime, which is a similar range of coupling strengths as previously observed in comparisons with the one-component plasma. Within this range, typical relative errors of approximately 20% and worst-case relative errors of approximately 40% are observed. We also examine the Darken model, which approximates the interdiffusion coefficients based on the self-diffusion coefficients.

Figure 1

Radial distribution functions in a 10% carbon (by mass) ${\mathrm{H}}^{+}{\mathrm{C}}^{6+}$ BIM. Solid lines represent hypernetted-chain predictions. Dotted lines show molecular dynamics results.

Figure 2

(a) Effective ion diameters and (b) modified Enskog correction factors (with and without virial cutoff) in a 36.8% helium (by mole) ${\mathrm{H}}^{+}{\mathrm{He}}^{2+}$ BIM. The dotted line in (a) shows $({\sigma }_1+{\sigma }_2)/2$.

Figure 3

Second-order correction factors for (a) 70% helium (by mass) ${\mathrm{H}}^{+}{\mathrm{He}}^{2+}$ BIM and (b) 10% carbon (by mass) ${\mathrm{H}}^{+}{\mathrm{C}}^{6+}$ BIM.

Figure 4

Diffusion coefficients versus BIM coupling parameter, $\overline{\mathrm{\Gamma }}$. (a–c) Self-diffusion coefficients, ${\mathfrak{D}}_i$. Solid lines represent the second-order effective potential theory (EPT); symbols, molecular dynamics results; and dashed lines, Landau-Spitzer theory. Dash-dotted lines represent EPT without the Enskog correction cutoff. (d–f) Interdiffusion coefficients, ${\mathfrak{D}}_{12}$. Solid lines represent second-order EPT; symbols, molecular dynamics; and crosses, the Darken approximation using MD self-diffusion coefficients as discussed in Sec. 4. Dash-dotted lines show EPT without the Enskog correction cutoff.

Figure 5

Errors in EPT diffusion coefficients, relative to MD values, for a 70% helium (by mass) ${\mathrm{H}}^{+}{\mathrm{He}}^{2+}$ BIM. Red circles: hydrogen self-diffusion coefficient. Blue squares: helium self-diffusion coefficient. Black triangles: interdiffusion coefficient. Dashed lines are included to guide the eye.

Figure 6

Errors in EPT diffusion coefficients, relative to MD, values for a 50-50 (by mole) ${\mathrm{H}}^{+}{\mathrm{D}}^{+}$ BIM. Red circles: hydrogen self-diffusion coefficient. Blue squares: deuterium self-diffusion coefficient. Black triangles: interdiffusion coefficient. Dashed lines are included to guide the eye.

Figure 7

Dependence of the diffusion coefficients on the deuterium mole fraction at selected coupling strengths for a ${\mathrm{H}}^{+}{\mathrm{D}}^{+}$ BIM. Lines represent EPT predictions for ${\mathfrak{D}}_1$ (solid red line) and ${\mathfrak{D}}_2$ (dashed blue line). Shapes show MD results.

Figure 8

(a) Effective ion diameters and (b) modified Enskog correction factors (both with and without virial cutoff) in a 0.9% carbon (by mole) ${\mathrm{H}}^{+}{\mathrm{C}}^{6+}$ BIM. The dotted line in (a) shows $({\sigma }_1+{\sigma }_2)/2$.

Figure 9

Errors in EPT diffusion coefficients, relative to MD values, for a 10% carbon (by mass) ${\mathrm{H}}^{+}{\mathrm{C}}^{6+}$ BIM. Red circles: hydrogen self-diffusion coefficient. Blue squares: carbon self-diffusion coefficient. Black triangles: interdiffusion coefficient. Dashed lines are included to guide the eye.

Figure 10

Test of the impurity-limit approximations, Eqs. (44) and (45), in a 0.9% (by mole) ${\mathrm{H}}^{+}{\mathrm{C}}^{6+}$ BIM. All diffusion coefficients plotted are second-order EPT results.