Signature of electroconvective instability in transient galvanostatic and potentiostatic modes in a microchannel-nanoslot device

Experimental and numerical results reveal a distinct signature of electroconvective instability in the transient response for a microchannel-nanoslot system. We study the development of the electroconvective instability from equilibrium during the transient chronopotentiometric (galvanostatic operation) and chronoamperometric (potentiostatic operation) responses at overlimiting current conditions and observe a distinct signature of nonmonotonic transient response resulting from the emergence of electroconvective instability. This stands in contrast to previously reported experimental nonmonotonic transient responses in heterogeneous membrane systems associated with linear electro-osmotic flow.

Figure 1

(a) Schematic description of the chip design. (b) Steady-state I-V dependence. The blue line depicts a voltage sweep (5 mV/sec) while the dashed line connects between the steady-state values reached after the transient response. Inset: Magnification near the underlimiting-to-limiting current transition $\left(V_{lim}=2V,I_{lim}=6nA\right)$. (c), (d) The dimensionless chronopotentiometric (galvanostatic) and chronoamperometric (potentiostatic) responses upon a stepwise application of constant current and voltage, respectively. Insets: Magnification near the minima and maxima times ($t_{min}$ and $t_{max}$). (e) Galvanostatic operation: $t_{min}$ vs the steady-state voltage. Inset: $t_{min}$ vs the inverse of the applied current squared. (f) Potentiostatic operation: $t_{max}$ vs the applied voltage. Insets: $t_{max}$ vs the inverse steady-state current square.

Figure 2

(a) Chronoamperometric response. (b) Time evolution of the electroconvective instability vortex array wave number as extracted from the temporal evolution of the depletion region patterns (see Movie 2 in Supplemental Material [53]). (c) Time evolution of the vortex and depletion layer [imaged within the dashed-line rectangle in the inset of Fig. 1] at the times marked with black dots in (a). Here, the applied voltage is $30V_{\lim }$.

Figure 3

(a) Schematic description of the computational domain. (b) Dimensionless steady state I-V dependence. (c), (d) Chronopotentiometric (galvanostatic) and chronoamperometric (potentiostatic) responses upon a stepwise application of constant current (I = 2.4) and voltage (V = 25), respectively, for nonconfined (1-blue) and confined (2-red) systems, respectively, and without flow leading to 1D transport (3-black). Insets: Magnification near the minimum and maximum time ($t_{min}$ and $t_{max}$). (e) Galvanostatic operation: $t_{min}$ and Sand's time τ vs the inverse of the applied current squared. Insets: $t_{min}$ vs the steady-state voltage. (f) Potentiostatic operation: $t_{max}$ vs the applied voltage. Insets: $t_{max}$ vs the inverse steady-state current squared.

Figure 4

Chronoamperometric (dimensionless) response (a) and (c) and time evolution of the vortex and depletion layer (b) and (d) at the times marked with dots in I-t curves for $V=25$ in nonconfined (a) and (b) and confined (c) and (d) systems. In (b) and (d) we show the anions distribution (in color) and flow streamlines (black lines) where the white lines are equiconcentration contours.