Sub-THz complex dielectric constants of montmorillionite clay thin samples with Na$^{+}$/Ca$^{++}$-ions

We implement a technique to characterize electromagnetic properties at frequencies 100 to 165 GHz (3 cm$^{-1}$ to 4.95 cm$^{-1}$) of oriented montmorillionite samples using an open cavity resonator connected to a sub-millimeter wave VNA (Vector Network Analyzer). We measured dielectric constants perpendicular to the bedding plane on oriented Na$^{+}$ and Ca$^{++}$-ion stabilized montmorillionite samples deposited on a glass slide at ambient laboratory conditions (room temperature and room light). The clay layer is much thinner ($\sim$ 30 $\mu$m) than the glass substrate ($\sim$ 2.18 mm). The real part of dielectric constant,$\epsilon_{re}$, is essentially constant over this frequency range but is larger in Na$^{+}$- than in Ca$^{++}$-ioned clay. The total electrical conductivity (associated with the imaginary part of dielectric constant, $\epsilon_{im}$) of both samples increases monotonically at lower frequencies ($<$ 110 GHz), but shows rapid increase for Na$^{+}$ ions in the regime $>$ 110 GHz. The dispersion of the samples display a dependence on the ionic strength in the clay interlayers, i.e., $\zeta$-potential in the Stern layers.