Density and temperature effects on electron mobility in fluid methane

Abstract

The mobility $\mu$ electrons in methane at $n<\mathrm{}6\mathrm{}\times {10}^{20}$ molecule/${\mathrm{cm}}^3$ is field dependent at $\frac{E}{n}>0.012\mathrm{}$ Td (1 Td = 1×${10}^{-17\mathrm{}}$ V ${\mathrm{cm}}^2$/molecule). The temperature dependence of the thermal-electron mobility in the low-density vapor is $\mu n\propto T^{0.45}$. The threshold field and temperature dependence are much lower than reported previously. In the electron energy region $0.002<\mathrm{}\epsilon <0.2\mathrm{}$ eV the momentum-transfer cross section of methane molecules is well approximated by ${\sigma }_{\nu }=0.014\mathrm{}{v}^{-1.9\mathrm{}}$ ${\mathrm{cm}}^2$. In the low-density gas the electron drift velocity $v_d$ becomes superlinear with field strength at threshold velocity $v_d^{\mathrm{thr}}=c_0$, the speed of low-frequency sound. At $n>\mathrm{}6\mathrm{}\times {10}^{20}$ the value of $\mu n$ in the coexistence gas decreases slightly, while $\frac{d\left(\mu n\right)}{\mathrm{dT}}$, ${\left(\frac{E}{n}\right)}_{\mathrm{thr}}$, and $\frac{v_d^{\mathrm{thr}}}{c_0}$ increase. The effects are due to quasilocation of the electrons by density fluctuations in the dense gas. The entropy $\Delta S^{\prime }$ and enthalpy $\Delta H^{\prime }$ of activation of electron transport correlate with the structure factor $S\left(0\right)\mathrm{}$ of the dense gas: $\frac{\Delta S^{\prime }}{S\left(0\right)\mathrm{}}=19\mathrm{}$ J/mol K and $\Delta H^{\prime }\approx T\Delta S^{\prime }$ near the vapor-liquid coexistence region. At $n>\mathrm{}6\mathrm{}\times {10}^{21}$ there is a rapid increase in $\mu n$ due to conduction-band formation. ${\left(\frac{E}{n}\right)}_{\mathrm{thr}}$ passes through a cusp >0.04 Td at $n=8\mathrm{}\times {10}^{21}$, where $\frac{d\mu }{\mathrm{dE}}$ changes sign, then decreases again to 0.01 Td at $n>\mathrm{}1.0\mathrm{}\times {10}^{22}$ molecule/${\mathrm{cm}}^3$. The threshold $\frac{E}{n}$ in the normal liquid is similar to that in the low-density gas. At low field strengths the electron energy is moderated mainly by elastic collisions in the low-density gas, and by inelastic collisions in the liquid.