Monte Carlo study of coherent scattering effects of low-energy charged particle transport in Percus-Yevick liquids

We generalize a simple Monte Carlo (MC) model for dilute gases to consider the transport behavior of positrons and electrons in Percus-Yevick model liquids under highly nonequilibrium conditions, accounting rigorously for coherent scattering processes. The procedure extends an existing technique [Wojcik and Tachiya, Chem. Phys. Lett. 363, 381 (2002)], using the static structure factor to account for the altered anisotropy of coherent scattering in structured material. We identify the effects of the approximation used in the original method, and we develop a modified method that does not require that approximation. We also present an enhanced MC technique that has been designed to improve the accuracy and flexibility of simulations in spatially varying electric fields. All of the results are found to be in excellent agreement with an independent multiterm Boltzmann equation solution, providing benchmarks for future transport models in liquids and structured systems.

Figure 1

Flowchart detailing how electric fields and coherent scattering are implemented in the SSMC code.

Figure 2

Schematic diagram of the various elastic cross sections used in simulating a Percus-Yevick liquid $\left(\varphi =0.4\right)$. All quantities are given relative to the elastic cross section for a single particle. Note that ${\sigma }_{\mathrm{tot}}\ge {\sigma }_{\mathrm{sp}}$.

Figure 3

Angle-integrated Percus-Yevick structure factors, from Eqs. (11) and (5), as a function of particle energy and volume fraction.

Figure 4

Mean energy $\epsilon$, drift velocity $W$, and diffusion coefficients $D_L$ and $D_T$ for Percus-Yevick model simulations, as a function of reduced electric field $E/n_0$ and Percus-Yevick packing ratio $\varphi$. Error bars are not visible at this scale.

Figure 5

Ratio of diffusion coefficients as a function of reduced electric-field strength $E/n_0$ and packing ratio $\varphi$. Note that the ratio for $\varphi \sim 0$ is 0.5, as required.

Figure 6

Mean energy $\epsilon$ and longitudinal diffusion $D_L$ percentage difference for each Monte Carlo model vs the Boltzmann equation (BE) model, for the Percus-Yevick structure factor at $\varphi =0.4$.