Unveiling the capabilities of bipolar conical channels in neuromorphic iontronics

Abstract

Conical channels filled with an aqueous electrolyte have been proposed as promising candidates for iontronic neuromorphic circuits. This is facilitated by a novel analytical model for the internal channel dynamics [T. M. Kamsma, W. Q. Boon, T. ter Rele, C. Spitoni and R. van Roij, Phys. Rev. Lett., 2023, 130(26), 268401], the relative ease of fabrication of conical channels, and the wide range of achievable memory retention times by varying the channel lengths. In this work, we demonstrate that the analytical model for conical channels can be generalized to channels with an inhomogeneous surface charge distribution, which we predict to exhibit significantly stronger current rectification and more pronounced memristive properties in the case of bipolar channels, i.e. channels where the tip and base carry a surface charge of opposite sign. Additionally, we show that the use of bipolar conical channels in a previously proposed iontronic circuit features hallmarks of neuronal communication, such as all-or-none action potentials and spike train generation. Bipolar channels allow, however, for circuit parameters in the range of their biological analogues, and exhibit membrane potentials that match well with biological mammalian action potentials, further supporting their potential biocompatibility.

Fig. 1. (a) Schematic representation of the azimuthally symmetric bipolar (BP) conical channel (not to scale), with channel length L, base radius R_b, and tip radius R_t < R_b, connecting two bulk reservoirs of a 1 : 1 aqueous electrolyte, with bulk concentration ρ_b. The channel wall carries a surface charge density eσ(x), with . Here σ′ = −3σ₀/2 with eσ₀ = 0.1e nm⁻² such that the surface charge is positive at the base (eσ(0) = eσ₀) and negative at the tip (eσ(L) = −eσ₀/2). A possibly time-dependent electric potential drop V(t) is applied over the channel, driving an ionic charge current I(t) = g(V(t),t)V(t) with g(V(t),t) being the channel conductance that we calculate in this paper. (b) Steady-state current I as a function of the static potential V as predicted by full FE calculations of the PNPS eqn (2)–(5), for a bipolar (BP) channel (blue) and otherwise identical unipolar (UP) channels with uniform surface charges −σ₀/2 (green) and −σ₀ (red). An applied positive (negative) voltage over the channel results in ion depletion (accumulation) as depicted in the insets of (b), responsible for the steady-state diodic behaviour of the cones.

Fig. 2. Comparisons of finite-element calculations (FE) of the full PNPS eqn (2)–(5) and our analytical approximation (AA) of eqn (8), (10) and (15), all for our standard parameter set of a bipolar conical channel (see text). (a) The radially averaged salt concentration profiles as determined using eqn (8) (solid lines) and the FE calculation (circles) for various static potentials V ∈ [−200, 200] mV as indicated by the colours. (b) Steady-state current–voltage relation as predicted by our AA of eqn (9) and (10) (red) and by the FE calculations (blue), featuring strong (diodic) current rectification. (c) Current–voltage diagram for an applied periodic triangle potential V(t) with amplitudes ± 1 V and frequency f = 45 Hz, revealing a clear pinched hysteresis loop.

Fig. 3. (a) Steady-state electric field −∂_x(x) inside the channel as predicted by eqn (6) (solid lines) and as measured on the central axis of the channel through the FE calculations (circles) of the PNPS eqn (2)–(5) for various static applied potentials V. (b) Steady-state fluid volume flow Q(V) as a function of the static potential V as predicted by Q(V) = −πR_tR_bεψ_effV/(ηL) with ψ_eff = −25 mV a fit parameter for the linear regime (V ≲ 0.4 V) of Q(V) (red) and as determined by FE calculations (blue).

Fig. 4. (a) Schematic representation of the circuit proposed in ref. , but now with three bipolar rather than three unipolar channels, connected in series to individual batteries and in parallel to a capacitor. The electric potential difference V_m(t) over the capacitor can be driven by an imposed stimulus current I(t). (b) The membrane potential V_m(t) resulting from an imposed subcritical (red) and supercritical (blue) current pulse I(t) of duration 20 ms and strengths 17.5 pA and 17.6 pA, respectively, as determined using eqn (16), displaying an all-or-none action potential, as can be seen by the jump in spike amplitude around I_AP = 17.5 pA shown in the inset. (c) The membrane potential V_m(t) as a result of an imposed subcritical (red) and supercritical (blue) sustained current I(t) of strengths 18 pA and 18.1 pA, respectively, where a spike train emerges for I(t) > I_train = 18 pA. The magnitudes of the membrane potentials before and during the APs are similar to those observed in mammalian APs.