Ionic Memcapacitive Effects in Nanopores $^{1}$Department of Physics, University of California, San Diego, La Jolla, CA 92093 $^{2}$Department of Physics and Astronomy and USC Nanocenter, (Dated: November 8, 2018) University of South Carolina, Columbia, SC 29208 Using molecular dynamics simulations, we show that, when subject to a periodic external elec- tric field, a nanopore in ionic solution acts as a capacitor with memory (memcapacitor) at various frequencies and strengths of the electric field. Most importantly, the hysteresis loop of this mem- capacitor shows both negative and diverging capacitance as a function of the voltage. The origin of this effect stems from the slow polarizability of the ionic solution due to the finite mobility of ions in water. We develop a microscopic quantitative model which captures the main features we observe in the simulations and suggest experimental tests of our predictions. We also suggest a possible memory mechanism due to the transport of ions through the nanopore itself, which may be observed at small frequencies. These effects may be important in both DNA sequencing proposals using nanopores and possibly in the dynamics of action potentials in neurons. A nanopore is an aperture of nanoscale dimensions across an insulating membrane. This way, if immersed in an ionic solution, ions can enter the nanopore, and if sub- ject to an electric field of given strength, they may enter it from one side of the opening and emerge on the other side. The membrane can be made of either biological or solid-state materials. Nanopores are ubiquitous in biolog- ical systems as they regulate the flow of ions across cell membranes (of, e.g., neurons). At present, they are also actively investigated for potential applications in DNA sequencing [1, 2]. Despite its apparent simplicity, ion dy- namics in nanopores is far from trivial. An example of this is provided by the recently predicted phenomenon of “quantized ionic conductance”, namely the presence of current steps occurring at effective pore radii that match the radii of the water hydration layers that form around the ions [3]. Here, we predict another intriguing property of ion dy- namics in nanopores, when the latter are subject to a periodic external electric field. In particular, we show that the electric field forces ions to accumulate at the two surfaces of the nanopore membrane, creating an ef- fective capacitor. However, this capacitor shows inter- esting features as a function of the frequency of the field, namely a hysteresis loop of the capacitance (memory- capacitance or memcapacitance for short [4]) as a func- tion of voltage which diverges at zero voltage and dis- plays negative-capacitance properties. Memcapacitors have been theoretically formulated in Ref. [4] and be- long to the wider class of memory-circuit elements, which includes also memristors and meminductors, namely re- sistors and inductors with memory. Following Ref. [4] we define a voltage-controlled memcapacitive system by the set of equations Ionic memcapacitors — In order to show that a nanopore in solution indeed acts as a memcapacitive sys- tem (Eqs. (1) and (2)), let us be more specific and con- sider the experimental situation as depicted in Fig. 1 which we suggest as a way to observe the effects pre- dicted here. An external (time-dependent) voltage V ( t ) is applied to electrodes which form an effective capaci- tor with the ionic solution and the nanopore at its inte- rior. In this paper we consider a typical setup for, e.g., DNA sequencing devices [5–7] with KCl ionic solution and a Si$_{3}$N$_{4}$ nanopore 25 Å thick and 88 Å wide with a 7 Å radius cylindrical hole drilled through the center of the membrane. However, the specific dimensions of the pore are irrelevant for the overall conclusions of this paper and similar considerations would apply also to biologi- cal pores. When a global time-dependent bias is applied to the system, the ionic solution is polarized and ions are forced to accumulate at the surfaces of the pore (see Fig. 1). First, we consider relatively short time scales where Q ( t ) is the charge on the capacitor at time t , V ( t ) is the voltage across it, and C is the time-dependent mem- capacitance which depends on the internal state of the system described by a set of n state variables x , with f a continuous n -dimensional vector function. Using all- atom molecular dynamics (MD) simulations, we indeed demonstrate that memory characteristics of nanopores in solution originate from the finite mobility of ions in water with consequent slow polarizability of the ionic so- lution. We also develop a simple microscopic model that captures the main properties observed in the simulations and allows us to extend our results to regimes beyond the reach of MD simulations. Additionally, we use an equivalent circuit formulation to discuss how ionic trans- port through the nanopore itself may lead to an addi- tional memory mechanism. We also propose ways our predictions could be tested with available experimental capabilities. arXiv:1001.0796v3 [cond-mat.soft] 16 Jun 2010 Q ( t ) = C ( x, V, t ) V ( t ) (1) ˙ x = f ( x, V, t ) (2) Matt Krems $^{1}$, Yuriy V. Pershin$^{2}$, Massimiliano Di Ventra1