Electric-field-induced emergent electrical connectivity in graphene oxide

Understanding the appearance of local electrical connectivity in liquid filled layered graphene oxide subjected to an external electric field is important to design electrically controlled smart permeable devices and also to gain insight into the physics behind electrical effects on confined water permeation. Motivated by recent experiments [K. G. Zhou et al. Nature (London) 559, 236 (2018)], we introduce a new model with random percolating paths for electrical connectivity in micron thick water filled layered graphene oxide, which mimics parallel resistors connected across the top and bottom electrodes. We find that a strong nonuniform radial electric field of the order ∼10–50 mV/nm can be induced between layers depending on the current flow through the formed conducting paths. The maxima of the induced fields are not necessarily close to the electrodes and may be localized in the middle region of the layered material. The emergence of electrical connectivity and the associated electrical effects have a strong influence on the surrounding fluid in terms of ionization and wetting which subsequently determines the permeation properties.

Figure 1

A schematic of the emergence of global electrical connectivity in a porous layered GO device with thickness $L$ and “$n$” layers. The middle red wire with radius “$a$” is the simplest representation of a conducting route. The bottom figure represents the formed conducting filaments between the layers. The parallel resistors model causes the resistivity to be nonuniform across the membrane.

Figure 2

(a) The variation of $\varrho /{\varrho }_0$ with $z$. The solid line refers to no sinusoidal variation while the two dashed curves are the relative resistivity when a sinusoidal oscillation is added. (b) The variation of electric potential around the conducting cylinder at four different radial distances, i.e., $r=a,2a,4a,30a$ for $\alpha =3.0$, $a=10$ nm, and $L=1000$ nm.

Figure 3

(a) Contour plot of total electric field on the surface of a conducting wire ($r=a=10\text{nm}$) along the wire as function of $\alpha$ for $V_0=4\text{V}$. (b) 2D-plot of total electric field along wire as function of radius of wire $a$ for $\alpha =1$ and $V_0=4\text{V}$.

Figure 4

The variation of (a) $Z_{\text{max}}$ and (b) $Q_s$ with $\alpha$ for different wire radius.