Effective potential and interdiffusion in binary ionic mixtures

We calculate interdiffusion coefficients in a two-component, weakly or strongly coupled ion plasma (gas or liquid, composed of two ion species immersed into a neutralizing electron background). We use an effective potential method proposed recently by Baalrud and Daligaut [Phys. Rev. Lett. 110, 235001 (2013)]. It allows us to extend the standard Chapman-Enskog procedure of calculating the interdiffusion coefficients to the case of strong Coulomb coupling. We compute binary diffusion coefficients for several ionic mixtures and fit them by convenient expressions in terms of the generalized Coulomb logarithm. These fits cover a wide range of plasma parameters spanning from weak to strong Coulomb couplings. They can be used to simulate diffusion of ions in ordinary stars as well as in white dwarfs and neutron stars.

Figure 1

Radial distribution functions for a mixture composed of 30% ${}^1\mathrm{H}$ and 70% ${}^{12}\mathrm{C}$ (by numbers), with ${\Gamma }_0=5(\overline{\Gamma }\approx 117)$.

Figure 2

Absolute values of effective potentials for the same mixture of ${}^1\mathrm{H}$ and ${}^{12}\mathrm{C}$ as in Fig. 1. For a better visualization, ${\Phi }_{12}$ is multiplied by 10 and ${\Phi }_{22}$ by 100.

Figure 3

Effective Coulomb logarithm ${\Lambda }_{\mathrm{eff}}$ calculated from Eq. (38) for the ${}^1\mathrm{H}-{}^{12}\mathrm{C}$ mixture. Regions of weak and strong couplings can be clearly seen as well as a transition region between them.

Figure 4

Interdiffusion coefficient $D_{12}^{*}$ for ${}^1\mathrm{H}-{}^4\mathrm{He}$ mixture ($x_1=0.5$) and its comparison with MD data of Ref. [23]. Weak, strong, and intermediate coupling regions are distinguishable (cf. Fig. 3). Exact values of $D_{12}^{*}$ are given in Table 3.