Solid-State Ionic Diodes Demonstrated in Conical Nanopores - The

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Solid-State Ionic Diodes Demonstrated in Conical Nanopores Timothy S. Plett, Wenjia Cai, Mya Le Thai, Ivan V. Vlassiouk, Reginald M. Penner, and Zuzanna S. Siwy J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b00258 • Publication Date (Web): 27 Feb 2017 Downloaded from http://pubs.acs.org on February 28, 2017

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The Journal of Physical Chemistry

Solid-State Ionic Diodes Demonstrated in Conical Nanopores Timothy S. Plett,1 Wenjia Cai,1 Mya Le Thai,2 Ivan V. Vlassiouk,3 Reginald M. Penner,2 Zuzanna S. Siwy*1,2,4 1

Department of Physics and Astronomy, University of California, Irvine, California 92697, United States 2 3

4

Department of Chemistry, University of California, Irvine, California 92697, United States

Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN, 37831, United States

Department of Biomedical Engineering, University of California, Irvine, California 92697, United States

Abstract. Ionic transport at the nanoscale features phenomena that are not observed in larger systems. Nonlinear current-voltage curves characteristics of ionic diodes as well as ion selectivity are examples of effects observed at the nanoscale. Many of men-made nanopore systems are inspired by biological channels in a cell membrane, thus measurements are often performed in aqueous solutions. Consequently, much less is known about ionic transport in non-aqueous systems, especially in solid-state electrolytes. Here we show ionic transport through single pores filled with gel electrolyte of poly(methyl methacrylate) (PMMA) doped with LiClO4 in propylene carbonate. The system has no liquid interface and the ionic transport occurs through the porous gel structure. We demonstrate that a conically shaped nanopore filled with the gel rectifies the current and works as a solid-state ionic diode.

*

Corresponding Author: [email protected], Tel. 949-824-8290, Fax 949-824-2174

ACS Paragon Plus Environment


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Introduction. Ionic circuitry has been a pursuit of nanofluidic research since its beginning.1 Ionic circuits are often inspired by biological channels embedded in a cell membrane; concerted action of the channels is the basis of many physiological processes including nerve signaling, vision and olfactory sense among others.2,3 Biomimetic nanopores with transport properties similar to these of biological channels have been reported.4-6 Among them, the ion current rectification characteristic of voltage-gated channels has been achieved in several types of synthetic nanopores.5-13 Ionic circuits also draw inspiration from electronic devices, so that nanopore ionic equivalents of pn junctions,

14-16

pnp- and npn-transistors,17,18 as well as diode and transistor-

based logic circuits were reported. 19-21 Many of the existing nanopore devices were designed for applications in biotechnology and biosensing22-24 thus the systems operate in liquid electrolytes similar to physiological conditions i.e. aqueous solutions of KCl and NaCl. Functioning ionic rectifiers and transistors require the presence of surface charges on the pore walls, thus ionic circuits also stimulated research aimed at quantitative description of ionic concentrations close to the charged surfaces, local electric potential in the solution, and current.25

In recent years, however, transport through porous media has started to be investigated for a very different set of applications, which demand solid rather than liquid electrolytes.26 One of the new directions of research is related to energy storage, specifically understanding the importance of porous structure in electrodes for power density and output. 27-30 In order to mitigate stability and safety issues of liquid electrolytes, batteries and supercapacitors often operate in solid electrolytes. One candidate material for solid electrolytes is LiClO4-doped PMMA gel, due to its relatively high conductivity (~10-3 S/cm) and tunable viscosity. 31,32 Recently, the gel has shown remarkable ability in preserving mesoscale battery electrodes past 100k cycles, demonstrating its stability for long-term application. 33

Here we present a system of a single nanopore filled with a solid-electrolyte of LiClO4-doped PMMA, which functions as a rectifier. The system does not contain any interface with a liquid electrolyte thus the gel-filled nanopore functions as a solid ionics diode. This system is very different from reported before organic diodes, which require organic semiconductors and electronic transfer within. 34 The solid-state diode presented here rectifies the current in a wide


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range of LiClO4 concentrations and produces stable ion current signals as well as fast switching. The solid-state ionic rectifier can find application to energy conversion from electrical fluctuating signals and storage procedures,35 and help understand ionic transport in solid electrolytes.

Experimental section Preparation of pores: Single pores in 12 µm thick films of polyethylene terephthalate were prepared by the track-etching technique, as reported before.36 The films were irradiated with single energetic heavy ions at the GSI Helmholtzzentrum fur Schwerionenforschung in Darmstadt, Germany. Cylindrical pores were obtained by etching the irradiated films in 0.5 M NaOH at 70 ˚C. Etching of the irradiated films in 9 M NaOH from one side at room temperature, while the other side was kept in contact with an acidic stopping medium, led to conical geometry.37 Pore opening diameter of each pore was characterized after etching by measuring current-voltage curves in 1 M KCl, and relating the pore resistance with its geometry.

Preparation of PMMA gels: The preparation of the gel started with the liquid electrolyte of LiClO4 in propylene carbonate (PC) in various concentrations (depending on the type of experiments). A 5 mL aliquot of LiClO4 in dry propylene carbonate (PC) was mixed with PMMA (with different w/w % mass- 2.6 g for 30% PMMA , and 2.0 g for 25% PMMA). The mixture was subjected to vigorous stirring at 115 °C. The mixture was left to cool down to room temperature in a desiccator and was subsequently transformed to the gel state.

Measurements of ion current: Current-voltage curves through all pores were recorded with 6487 picoammeter/voltage source and Ag/AgCl pellet electrodes (A-M Systems, Sequim, WA). In conical nanopores, the ground electrolyte was placed at the side of the membrane with the narrow opening. Some pores were also examined for the stability of ion current signals. Ion current in time was recorded using Axopatch 200B and 1322A Digidata (Molecular Devices, Inc.) at 20 kHz sampling frequency and 2 kHz low-pass Bessel filter. Voltage was changed between -2 V and +2 V with 200 mM steps and at each voltage level, the current was recorded for 20 s. Current-voltage curves were obtained by averaging the last 0.5 s of recordings at each voltage.



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Comsol modeling: Poisson-Nernst-Planck equations were solved using the Comsol Multiphysics 4.3 package.17,38 A single 12 µm long conically shaped nanopore had opening diameters of 50 nm and 500 nm, respectively. Predefined Comsol “extremely fine” meshing parameters were used with maximum element size fixed at 3.35·10-8 nm and minimum element size 10-10 nm. Dielectric constant of the pore interior was assumed 64 thus equal to the magnitude of ε of propylene carbonate.39 Diffusion coefficients of cations and anions was 2×10-10 m2/s, a magnitude reported before for Li+ ions in propylene carbonate.40

Results and Discussion Solid ionics diodes were based on single polyethylene terephthalate (PET) nanopores prepared in polymer films by the track-etching technique.36,37 Two pore geometries were used in the experiments, cylindrical and a tapered cone. Cylindrical pores ranged from 400nm-1100nm in diameter while conical pores varied from 340nm-1200nm at the base (wide opening) and 10nm60nm at the tip (narrow opening). Since the LiClO4-doped PMMA gel is based on propylene carbonate (PC), we tested first transport properties of the pores in propylene carbonate solutions of LiClO4 without any gel added. Figure 1 shows current-voltage curves through single cylindrical and conical pores in a range of LiClO4 concentrations. As found before, conically shaped nanopores in contact with LiClO4 in the organic solvent rectify the current in the opposite direction to the rectification in aqueous LiClO4.41 The experiments confirmed therefore the earlier report on the existence of net positive surface charge of the pore walls due to high dipole moment of PC, and possible adsorption of positively charged ions. 42,43 The rectifying properties are related with the conical shape of the pores,6-13 and as expected, the cylindrical pores exhibit linear I-V curves (Figure 1a,b, Figure S1). Note, rectification properties of conical nanopores in propylene carbonate solutions exhibit a non-monotonic dependence on salt concentration in the bulk; a similar effect was reported before for conically shaped nanopores in aqueous conditions.44 The observation can be understood by recalling that ion current rectification requires voltage modulation of ionic concentrations in the pore so that for one voltage polarity an enhancement of ionic concentrations is observed while for the other polarity a depletion zone is formed.6,7,10,13 In diluted salt solutions an overlap of the electrical double-layer occurs in the pore


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so that ionic concentrations are determined primarily by the pore surface charges and electroneutrality requirement, and only weakly by the external voltage. When the salt concentration is high, the surface charges are screened and the pore volume is filled with bulk solution independent of the applied voltage. Consequently, enhanced rectification properties occur at intermediate salt concentrations.

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Figure 1. Current-voltage (I-V) measurements of a) a 790nm in diameter cylindrical pore and c) a conical pore with opening diameters of 560nm (base) and 23nm (tip) in solutions of LiClO4 in propylene carbonate. No gel was present in the pores. In b) and d), the currents at the positive and negative voltage extremes are compared over the different concentrations of LiClO4. The cylindrical pore (a, b) exhibits no rectification and a clear concentration dependence while the conical pore (c, d) rectifies over the different concentrations, and exhibits saturation of ion current at low concentrations. The pore inset texture represents LiClO4/PC liquid solution.



In order to test ion transport through pores filled with gel electrolytes, experiments were first performed with cylindrical pores. The measurements allowed us to provide evidence that continuous filling of a single pore with the LiClO4-doped PMMA gel is indeed possible. Figure 2a shows a recording for a single cylindrical pore with opening of 500 nm after drop-casting the gel, which had been warmed to 75-90oC, on both sides of the membrane; the gel was doped with 100 mM LiClO4. We found the best results for cylindrical pores using a gel containing 25% (by wt.) PMMA, and allowing the system to cool and set for at least 20h prior to testing. Two Ag/AgCl electrodes were placed directly into the gel as shown in the Figure S2. The measured current-voltage curves with known pore geometry allowed us to calculate the conductivity of the gel in the pore to be σ = 0.5 mS/cm, thus in good agreement with bulk studies. The recorded current is indeed due to the presence of ions in the gel since filling a pore with PMMA gel without LiClO4 led to significantly lower currents (Figure 2b, Figure S3). The finite values of the current with an undoped gel result from finite electronic conductivity of the PMMA gel.45 The ratio of ionic conductivities in the doped and undoped cases is 10. Thus, according to our measurements, the electronic contribution to the total measured current reaches ~10% when the gel is doped with LiClO4, again in excellent agreement with previous bulk studies.45 2

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Figure 2. I-V response of two cylindrical pores filled with PMMA gel. (a) A 500nm pore filled with 100mM LiClO4-doped PMMA, and b) a 790nm pore (the same as in Figure 1) with blank PMMA containing only propylene carbonate without salt. Despite the smaller pore size, it is clear the doped PMMA exhibits much higher conductivity than the blank PMMA (σdoped/σblank ~ 10). Conductivity was calculated relating the measured resistance with pore geometry, assuming cylindrical shape. The data were recorded using Keithley 6487 picoammeter/voltage source;


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voltage was changed with 0.1 V steps, and the currents shown represent values recorded at the end of 2 s long pulse. The cross-hatch texture is to represent PMMA gel inside the nanopore, with the red speckles in a) meant to indicate lithium doping.

Figure 3 shows recordings through a single conically shaped nanopore after drop-casting LiClO4doped PMMA gel on both sides of the membrane. Transport properties of the pore were examined using two experimental approaches. First, similar to the data shown in Figs. 1, 2, current-voltage curves were measured using Keithley picoammeter. The data revealed that the shape of the nanopore played a crucial role in the system behavior, so that the pore rectified. The character of the I-V curve was consistent with the presence of a net positive surface charge on the walls. We also wanted to probe stability of the ion current in time and recorded signals with sampling frequency of 10 kHz. The voltage was changed between -2V and +2V with 0.2 V steps; at each step, the current time series was measured for 20 s. The recordings revealed that the ionic diode is capable of providing stable rectifying signals; no decay or signal fluctuations were observed. We believe the excess of the gel on both sides of the membrane serves as ionic reservoir. Due to presence of only a single pore in the membrane, in the time frame of the experiments, the reservoir did not suffer ion depletion. Thus, the currents did not exhibit any decay even after minutes of recordings at one voltage. Averaging of the time signals allowed us to plot an I-V curve and compare it with the Keithley recordings. Excellent agreement of the two data sets confirms the system stability over long recordings. In order to confirm that the gel filled the entire volume of the pore, an I-V curve of a conical nanopore drop cast with an undoped PMMA gel was measured as well. Linear I-V curve and much smaller current (Figure S4) provided evidence that the I-V ion current data shown in Figure 3 present ionic movement through the PMMA gel in the pore. As in the case of cylindrical pores, the residual conductance observed with an undoped PMMA is due to electronic conduction, which is not rectified.



from picometer from time series

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b) Figure 3. (a) I-V curves through a conically shaped nanopore drop-cast with 1 M LiClO4 PMMA gel recorded with picoammeter/voltage source (black squares) and obtained by averaging ion current traces (recorded with 10 kHz sampling frequency) shown in (b) (green circles). Opening diameters of this pore were 610 nm and 22 nm, for base and tip, respectively. (b) 20 s long signals of ion current in time recorded between -2V and +2V with 200 mV steps. The crosshatch texture is to represent PMMA gel with the red speckles indicating lithium doping.

A set of conically shaped nanopores with similar opening diameters and filled with PMMA gel with different LiCO4 concentrations (between 100 mM and 1 M) allowed us to understand the role of salt concentration on the ion current rectification. Figure 4 demonstrates system rectification over a range of ion concentrations but also seems to suggest rectification does not have strong dependence on bulk concentration as found in liquid electrolytes.8,13,44 The lack of clear dependence of rectification on the salt concentration in the gel is further evidenced by


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recordings obtained for six additional nanopores shown in Figure S5; the anomalously high rectification obtained with one nanopore in 250 mM LiClO4 (Figure 4b, Figure S5) stems most probably from favorable local arrangement of PMMA gel in this particular pore, and very small values of the current (few pA) for negative voltages. Presence of rectification even at high salt concentrations in the gel is consistent with earlier reports pointing to the formation of ion pairs when the salt concentration in PMMA is increased. 46 Consequently, the number of mobile ions does not increase with the increase of the salt concentration in the gel,45 providing less screening of the surface charges, and enabling rectification. Ion current rectification exhibited by conical nanopores filled with PMMA suggests that the structure of the PMMA gel matrix might play a significant role in transport properties of the gelnanopore system beyond the effects from surface charges on the pore wall. This is especially evident in recordings for a conical nanopore shown in Figure 4c; its opening diameter of 44 nm assures that the pore walls surface charges are screened, thus the pore’s transport properties are dominated by the gel. It is known that PMMA gel has mostly an amorphous character,47 which is partially dependent on its composition both in terms of PMMA and electrolyte concentration. Previous studies also revealed that even in bulk PMMA gels doped with salts, the measured current is primarily due to anions with transference numbers for lithium of ~0.2.32,48 The low transference numbers can be caused by interactions of Li+ with carbonyl groups in PMMA; complexation of Li+ ions with the gel was indeed demonstrated experimentally using e.g. XRD, FT-IR and Raman spectroscopy.47,49-51 We hypothesize that the complexed ions can lead to the formation of effective positive surface charge of the gel matrix, whose presence is suggested by I-V curves of nanopores filled with PMMA. 50

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Figure 4. I-V curves through three different conically shaped nanopores filled with PMMA gel doped with (a) 1 M, (b) 0.25 M, and (c) 100 mM LiClO4. Opening diameter of the pores (base & tip) were (a) 1170 nm &14 nm, (b) 680 nm & 14 nm, and (c) 350 nm & 44nm. All of these pores



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show significant rectification factor (ratio of currents at +2V and -2V exceeds 5) despite their differences in opening diameter and ionic concentration. The cross-hatch texture is to represent PMMA gel with the red speckles indicating lithium doping. The speckling frequency is not indicative of concentration.

Previous Brunauer-Emmett-Teller (BET) and X-ray powder diffraction (XRD) studies revealed that gel electrolytes contained pores/voids with effective diameter as large as ~10 nm.52,53 If the gel structure and ionic concentrations were homogeneous throughout the whole pore volume, the system would not rectify. Asymmetric current-voltage curves require breaking symmetry so that for one voltage polarity, enhancement of ionic concentration occurs, while for the opposite polarity, a depletion zone is formed.6-8,10,13

In order to probe the origin of rectification in the gel filled conically shaped nanopores, we consider a model of ionic conductivity consisting of two components: (i) the surface component that originates from counterions which neutralize the effective surface charge of the voids, and (ii) bulk conductivity through parts of the porous structure that is filled with bulk electrolyte. 54 We postulate the relative contribution of the surface and bulk conductivities to the measured ion current depends on the pore opening thus is different in the narrow and wide openings of the pore. Consequently, concentrations of charge carriers will vary along the pore axis. This hypothesis is supported by earlier experimental findings on the dependence of conductivity of gel electrolytes on the dimension of pores in which they were embedded.55 Gel electrolytes embedded in membranes with sub-100 nm pores were found to exhibit higher conductivity than in micron-sized pores; this observation could be caused e.g. by pore diameter dependent arrangement and concentration of the gel components56,57 as well as of mobile ions. Based on the studies of pore diameter dependent ionic conductivity,55 we assumed that due to the nano-constriction of the narrow opening of a conically shaped nanopore, the tip region features a higher density of mobile charges compared to the wide opening. This inhomogeneous distribution of mobile charges could be e.g. a result of a lower local PMMA concentration at the pore tip. A higher density of mobile charges at the tip could also be treated as a model of a system in which an enhanced ionic conductivity is caused by other effects such as higher


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mobility of ions due to nano-scale induced arrangement of PMMA molecules, shown before for other polymer electrolytes.55-57 Current-voltage curve through a conically shaped pore filled with a gel can be predicted by solving the following set of Poisson-Nernst-Planck (PNP) equations: J i = − Di (∇Ci +

zi eCi ∇ϕ ) k BT

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ε oε∆ϕ = −[e(C+ − C− ) + ρ (z )]

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where J i is a flux due to one type of ions, characterized by diffusion coefficient, Di , ε o is vacuum permittivity, and ε is dielectric constant of the medium assumed to be equal to 64.39 Note that the Poisson equation (eq. 1c) has been modified to include space charge, ρ(z), in the pore volume due to the presence of charged porous gel. In order to consider the dependence of the concentration of mobile charges on the pore diameter, we assumed the density of the space charge, ρ(z), changes according to the following function:17 n

 dL   n=0.5, 1, 2, 4  Dz + dL 

ρ (z ) = ρ0 

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where ρ0 is the concentration of space charge at the tip, and d and D and the diameters of the tip and the base opening, respectively. ρ0 was taken equal to 107 C/m3 which corresponds to charge concentration of ~ 0.1M. The general equation of ρ(z) with four values of n allowed us to verify that the effect of ion current rectification in pores with axially changing space charges is robust, and only weakly dependent on the details of space charge distribution (captured by changing n). Figure 5 shows the predicted current-voltage curves for a pore with diameters of 50 and 500 nm obtained by solving eqs. (1, 2) numerically using Comsol Multiphysics 4.3 package. The modeled current-voltage curves are in qualitative agreement with the experimental data (Figure 3) and predict ion current rectification for all values of n considered.



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Figure 5. Numerically modeled I-V curves through a conically shaped nanopore with opening diameters of 50 and 500 nm. Presence of the charged PMMA gel was modeled by introduction of additional space charge term, ρ(z), whose dependence on the axial position, z, is given in eq. (2). The legend gives values of the coefficient, n, in eq. (2).

Conclusions We presented a single nanopore system filled with a PMMA-based gel electrolyte that is relevant for energy-storage devices.33,35 The system does not contain any external liquid interface thus can be considered an example of an ionic solid device and diode. Our future experiments will be aimed at probing the nature of inhomogeneity of concentration of mobile ions in conical pores, we assumed in the modeling and explanation of asymmetric transport. These studies will be aided by structural characterization of the embedded gel as well as dependence of ionic transport on temperature. Our future efforts will also focus on testing other solid electrolytes at the nanoscale, to contribute to understanding of ion current, charge screening and selectivity in these largely unexplored systems. Finally, we would like to probe ionic transport in solid electrolytes using even more nanoscopic structures with opening diameters less than 10 nm. The studies will allow us to identify optimal conditions for asymmetric transport, and probe systems which are expected to have only a few polymer molecules at the narrow opening. The experiments might have to be performed with nanopores in silicon nitride,58,59 which feature small opening diameters and smaller lengths (see low signals of ion current for the 14 nm in diameter conical pore in Figure 3b); such short aspect ratio nanopores will allow us to record detectable ionic signals even for pores as small as few nanometers.


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Supporting Information. Additional recordings of ion current through pores with and without PMMA gel, as discussed in the text as well as details of the experimental set-up.

Acknowledgements. This work was funded by the Nanostructures for Electrical Energy Storage (NEES), an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DESC001160. We also acknowledge GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany for providing irradiated membranes as well as Dr. Phil Collins for valuable conversations during the course of the research. We also thank Prof. Salvador Mafe and Prof. Patricio Ramirez from the University of Valencia, Spain for insights on modeling of ionic transport at the nanoscale.

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Solid-State Ionic Diodes Demonstrated in Conical Nanopores - The

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