fig2

Figure 2. Physical basis of the integration and leakage dynamics in the iontronic neuron. (A) A (9,9) single-walled CNT with a diameter d_(9,9) = 1.22 nm connects two reservoirs containing 1 mol/L KCl solution. An external electric field (E) is applied to drive ion transport, generating discrete ionbits; (B) The timeline is divided into three phases, including integration (ion accumulation without firing), firing (stochastic generation of ionbits under E), and leakage (ion dissipation after E is removed at t = 5 ns); (C) Driven by the field, ions migrate to the accumulation layer and become trapped in the Adsorption region due to the adsorption energy barrier (ΔG_ads). This process is analogous to charging a capacitor (q vs. t); (D) Probability density of ions near the entrance at different times, showing a clear build-up of concentration under an applied field; (E) Local ion concentration [c(t)] near the CNT entrance as a function of time, fitted to an exponential accumulation model ($$ c(t)=c_{\mathrm{T}}\left(1-e^{t / \tau_{\mathrm{I}}}\right) $$) with a characteristic timescale τ_I = 0.15 ns; (F) Illustration of the leakage process. When the field is off, accumulated ions dissipate and desorb back into the reservoir; (G) Local ion concentration decay over time, fitted with two exponential processes representing fast dissipation (τ_{L, dis} = 0.10 ns) and slower thermal desorption (τ_{L, des} = 0.45 ns); (H) The probability density of ion desorption times which follows an exponential distribution. The inset shows the calculation of the desorption rate k using the Arrhenius equation, and the derived adsorption energy barrier is ΔG_ads = 8.29 k_BT. CNT: Carbon nanotube; ΔG_ads: The desorption energy.