Electrodrying in nanopores: from fundamentals to iontronic and memristive applications

TL;DR

Electrodrying proposes a voltage-driven drying mechanism for hydrophobic nanopores, enabled by an intrinsic dipole that creates an asymmetric hydration landscape and bidirectional conductance control. The authors integrate an analytical free-energy framework with molecular dynamics simulations and experimental validation on engineered CytK pores to show that the interplay between $V$ and the intrinsic dipole $V_{\text{int}}$ can invert wet/dry states and generate hysteresis, including a shift to a nonzero crossing point indicative of a new memristor type. They demonstrate negative differential resistance and memristive behavior in nanopore arrays and illustrate neuromorphic and iontronic circuit concepts such as short-term plasticity and RLC oscillators. This work provides design principles for solid-state and biological nanopores, expanding the functional repertoire of nanopore gating for bio-inspired computing and nanofluidic devices.

Abstract

Iontronics is a burgeoning paradigm that employs ions in solution as information carriers for sensing and computing, e.g., in neuromorphic devices. The fundamentally different working principle as compared to electronics requires novel approaches and concepts to control the impedance of nanoscale fluidic circuit elements, such as nanopores. For instance, previous research has focused on voltage-induced pore wetting as a means to trigger conduction in nanopores. The present study explores the opposite counter-intuitive mechanism: using voltage to dry hydrophobic nanopores and, therefore, to turn off conduction. This "electrodrying" concept affords exquisite, bidirectional control over the conductance of nanopores additionally showing hysteresis in the current-voltage curve that is the fingerprint of memristors. Using an analytical model and free-energy molecular dynamics simulations, we explain the physical mechanism underlying electrodrying and provide clear design criteria for solid-state and biological nanopores with bidirectional control over conductance. The electrical behaviour of electrodrying nanopores shows two unique features: i) the hysteresis loop is shifted from the origin, accounting for the fifth, previously unreported memristor type and ii) negative differential resistance is observed over a broad voltage range in which the non-conductive state is favoured by electrodrying. These properties are demonstrated in a short-term memory task and in an iontronic oscillator circuit to showcase their potential in neuromorphic applications and iontronic devices. Finally, we validate our predictions through experiments on engineered dipolar hydrophobic CytK nanopores, whose voltage-dependent conductance substantiates the electrodrying concept.

Figures (11)

• Figure 1: Electrodrying working principle.a) Schematic of the nanopore system with membrane height $h$, pore radius $R$, and applied potential $V$. Positive and negative charged rings at the pore entrances are indicated in blue and red, respectively. The hydrophobic pore can be either dry (left) or wet (right) due to the presence of a metastable vapour bubble. b) Electric potential along the $z$-axis for the wet state. An intrinsic voltage drop $V_{int}$ is present at equilibrium ($V=0$). When an external potential is applied, most of the voltage drop $V$ occurs across the membrane, resulting in an approximated $\Delta \phi_{wet} \approx V_{\text{int}} - V$. The electric field $E_z = -\nabla_z \phi(z)$ varies asymmetrically with $V$. For $V < 0$, $|E_z|$ increases, and for $0< V < 2V_\text{int}$, $|E_z|$ decreases to zero, then increases again. c) Hydration free-energy profile as a function of the number of water molecules in the pore. At equilibrium, two local minima correspond to the dry and wet states, with the wet state being more stable ($\Delta F_{wet,0}<0$). For $V < 0$, the wet state is stabilised, while for $V > 0$, decreased water polarisation leads to a positive variation in $\Delta \Delta F_\mathrm{wet}$, potentially making the pore stably dry. d) Hydration free-energy difference between the wet and dry state as a function of $V$, normalised over the intrinsic equilibrium voltage drop $V_\mathrm{int}=1$ Volt, computed via Eqs. (\ref{['eq:dFwet']}-\ref{['eq:ddF']}) for a pore of length $h=3$ nm and radius $R=0.5$ nm, water relative permittivity $\epsilon_L=80$ and charge of the rings $\pm 7e$.
• Figure 2: Simulations of electrodrying in hydrophobic dipolar pores.a) The molecular dynamics system consists of an hydrophobic nanopore with oppositely charged rings at the entrances. The top entrance (blue) has a total charge of $+5e$, while the bottom one (red) $-5e$. The pore presents a metastable dry state (left) and a stable wet one (right). The pictures are realized using VMD vmd, using the last frame of each state respective RMD simulations; water is represented in transparency. A constant and homogeneous electric field $E_z=-V/L_z$ is applied to the system, with $L_z$ the simulation box size in the direction of the pore axis. This setup mimics a potential difference $V$ across the two sides of the membrane. b) When no external voltage is applied ($V = 0$), an intrinsic potential difference is present across the pore entrances, $V_\mathrm{int} \approx 0.8\,V$. As a positive voltage is applied, this field is cancelled out, eventually drying the pore. c) Free energy profiles obtained using RMD. When no voltage is applied the wet state is more favourable. While negative applied voltages increase the stability of the wet state, positive voltages make the dry state more favourable. d) Probability to find the system in the wet state for the uncharged hydrophobic nanopore (gray) and for the dipolar pore (blue). The effect of voltage is no longer symmetric around zero, and applying voltage reduces the probability of finding the pore in the wet state to as low as $\sim 10\%$. Increasing the applied voltage wets the pore again. The curve is obtained interpolating the data obtained from eleven free energy profiles computed at different voltages, from $V = -0.75$ to $2.0$ V, using the procedure exposed in paulo2024voltage.
• Figure 3: Atypical electrical characteristics of electrodrying nanopores.a) Conductance of an array of electrodrying nanopores as a function of voltage. The conductance is computed as $G_o n_\mathrm{wet}(V)$, where $G_o$ is the open-pore conductance and $n_w$ is the probability of the wet (conductive) state. The wetting and drying rates are estimated as the voltage is cycled at different frequencies using the procedure in paulo2024voltagepaulo2023hydrophobically. The open-pore conductance is assumed to be constant with voltage and equal to $1$. b) Current as a function of voltage, computed by multiplying the conductance by the voltage. Real units for conductance and current can be obtained by multiplying the single pore conductance (usually in the order of 1 nS) at a given voltage for an arbitrary number of pores (tens to hundreds).
• Figure 4: Memristive and iontronic applications of electrodrying nanopores.a) Learning-forgetting task on an array of model electrodrying nanopores. A train of voltage spikes composed of two excitatory pulses, five inhibitory pulses, and four excitatory pulses is used to program the conductance of the nanopore array. Current is measured as a function of time (top panel), while memory in the response is estimated as $\Delta G_i(\%) = \left(G_i-G_0\right)/G_0 \cdot 100$ where $G_i$ is the time averaged conductance over a pulse and $G_0$ is the value for the first pulse (bottom panel). Current evolution in time is computed from the wetting and drying rates as explained in paulo2023hydrophobically. b) RLC oscillator with electrodrying nanopores. Plots show two different possible oscillating responses of the circuit depending on the model parameters. The blue curve (undamped oscillator) is obtained with an open pore capacitance $g_0 = 100 \ mS/cm^2$ while the inverse of the circuit resistance is $1/R = 1 \ mS/cm^2$. The orange curve (damped oscillator) is produced with $g_0 = 1/R$. The other circuit parameters for the curves are $I_{ext} = 1 \ mA/cm^2$, $L = 1 \ mH/cm^2$, $C = 1 \ mF/cm^2$, $V_n = -1.5 \ V$
• Figure 5: Engineered dipolar hydrophobic CytK nanopore. a) Schematic illustration of the transmembrane barrel and 3D renderings of CytK nanopore, showing the spatial arrangement of engineered hydrophobic mutations (gray) alongside charged residues (blue, red) designed to induce electrodrying. b) Representative experimental conductance–voltage measurements at 140 mV for the Cytk WT (black), M3IK (pink), and M2IFK (orange) mutants. The presence of pronounced current blockades for the mutants indicate the presence of hydrophobic gating. Dashed lines represents the average conductance between 40 and 100 ms; the voltage is applied at $t=2.5$ ms, see the inital spike. c) Mean conductance for different applied voltages, computed by averaging the current traces of >20 voltage sweeps, from two independent experiments per system. Supplementary Fig. S5 reports additional current traces for other voltages. Overlay of experimental data (symbols) and predictions based on MD results (purple dot-dashed line) for the M3IK mutant confirms that the observed conductance modulation accurately follows the theoretical predictions for hydrophobic electro‑drying. d) Free-energy profiles as a function of the water filling $N_w$ of the nanopore, for positive and negative applied voltages, show how the external field alters the barrier and well depths. e) Voltage-dependent shifts $\Delta \Delta F$ of the free-energy difference between minima, using the $V=0$ case as a reference. The parabolic fit (purple dot-dashed line) illustrates the asymmetric electrodrying trend of Eq. \ref{['eq:ddF']} for reference.