Density and temperature effects on electron mobility in gaseous, critical, and liquid ethane

Abstract

At applied electric-field strengths below a threshold value ${\left(\frac{E}{n}\right)}_{\mathrm{thr}}$ the mobility of electrons is independent of field strength. At strengths just above the threshold the sign of the mobility-field coefficient $\frac{d\mu }{\mathrm{dE}}$ is positive in the low-density gas, negative in the high-density gas and low-density liquid [$1.0<\left(\frac{n}{{10}^{21}}\right)<\mathrm{}8\mathrm{}$], and positive in the normal liquid. The temperature coefficient of mobility $\frac{d\mu }{\mathrm{dT}}$ is positive at all densities. The change of sign of $\frac{d\mu }{\mathrm{dE}}$ going from $n=0.9\mathrm{} \mathrm{to} 1.0$ (${10}^{21}$ molecule/${\mathrm{cm}}^3$) is attributed to destructive interference of long-range attractive interactions, which tends to reduce the effective scattering cross sections at the lower velocities. The sign of $\frac{d\mu }{\mathrm{dT}}$ remains positive because quasilocalization of electrons occurs at density fluctuations of suitable magnitude in this region of $n$. Quasilocalization is characterized by large negative values of $\Delta H^{\prime }$ and $\Delta S^{\prime }$, with $\Delta G^{\prime }\simeq 0$. The density-normalized mobility $\mu n$ changes by less than a factor of 2 while increasing $n$ from the low-density gas to the liquid at $n=7\mathrm{}\times {10}^{21}$ molecule/${\mathrm{cm}}^3$. At $n>\mathrm{}8\mathrm{}\times {10}^{21}$ the value of $\mu n$ plunges, due to the formation of more stable localized states; field-assisted delocalization of the electrons causes $\frac{d\mu }{\mathrm{dE}}$ to become positive again. Electron behavior in fluid ethane is quite different from that in fluid methane. The differences are attributed to the difference in molecular shape; methane is much more spherelike than ethane. The less spherelike molecule has a lower average scattering cross section for electrons at 300 K in the low-density gas, a Ramsauer-Townsend minimum in ${\sigma }_{\nu }$ lying at a lower energy, a larger ratio of threshold drift velocity to the speed of sound $\frac{v_d^{\mathrm{thr}}}{c_o}$, and more stable localized states of electrons in the liquid.