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Ion Current Rectification in Extra-Long Nanofunnels

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Ion Current Rectification in Extra-Long Nanofunnels applied sciences Article Ion Current Rectification in Extra-Long Nanofunnels Diego Repetto, Elena Angeli * , Denise Pezzuoli, Patrizia Guida, Giuseppe Firpo and Luca Repetto Department of Physics, University of Genoa, via Dodecaneso 33, 16146 Genoa, Italy; [email protected] (D.R.); [email protected] (D.P.); [email protected] (P.G.); giuseppe.fi[email protected] (G.F.); [email protected] (L.R.) * Correspondence: [email protected] Received: 29 April 2020; Accepted: 25 May 2020; Published: 28 May 2020 Abstract: Nanofluidic systems offer new functionalities for the development of high sensitivity biosensors, but many of the interesting electrokinetic phenomena taking place inside or in the proximity of nanostructures are still not fully characterized. Here, to better understand the accumulation phenomena observed in fluidic systems with asymmetric nanostructures, we study the distribution of the ion concentration inside a long (more than 90 µm) micrometric funnel terminating with a nanochannel. We show numerical simulations, based on the finite element method, and analyze how the ion distribution changes depending on the average concentration of the working solutions. We also report on the effect of surface charge on the ion distribution inside a long funnel and analyze how the phenomena of ion current rectification depend on the applied voltage and on the working solution concentration. Our results can be used in the design and implementation of high-performance concentrators, which, if combined with high sensitivity detectors, could drive the development of a new class of miniaturized biosensors characterized by an improved sensitivity. Keywords: nanofunnel; FEM simulation; ionic current rectification; micro-nano structure interface 1. Introduction Nanofluidics has been attracting the attention of a wide scientific community for a long time [1,2]. Nevertheless, its potential has not yet been fully exploited [3]. This interest is motivated by the fact that nanofluidic systems offer functionalities in terms of control of ionic and molecular transport that occur only at a nanoscale [4,5]. Solid-state nanopores [6] and nanochannels [7] mimicking biological counterparts [8] have been investigated and exploited in many applications [9], e.g., the detection of molecules of biomedical interest, such as proteins [10], nucleic acids [11], viruses [12–14], and nanovesicles [15] or for developing new components of ionic circuits [16], such as transistors [17], diodes [18,19], and ion pumps [20–22]. A large number of nanofluidic devices exploit electric fields for handling fluids and nano-objects near or through functional nanostructures; for this reason, understanding electrokinetic phenomena occurring at the nanoscale is of paramount importance. Many researchers focused their efforts on modeling, either by analytical or numerical methods, the electrokinetic behavior of fluids in nanoconfinement conditions or at micro-nanointerfaces [23,24], but a comprehensive understanding of all the phenomena taking place and how they influence each other is still far off. This lack of understanding is due to the complexity of the problem, which involves coupled nonlinear fluid flow, charged species transport, and a dynamic evolution of the electric field in a multi-scale space spanning from nanometers to centimeters, as stated by Han and coworkers [25]. In addition to symmetric geometries, nanopores and nanochannels with asymmetric characteristics have also been studied due to their interesting functionalities [26,27], especially when electric fields are applied. In particular, electrostatic interactions between molecules and ions in aqueous solutions, and the electric double layer Appl. Sci. 2020, 10, 3749; doi:10.3390/app10113749 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 3749 2 of 13 (EDL), which forms on a nanostructure’s walls, can be exploited for creating ion-selective devices [28]. Concentration polarization (CP) [29] was observed at micro-nano interfaces [30], in nanochannels [17], and in ion current rectification (ICR) in nanostructures [31] with asymmetric surface charge distribution [32,33], geometry [20,26,27,33–40], or both [41]. Concerning conical nanochannels, many different parameters, such as length, cone angle, distribution of surface charge, size and shape, were analyzed to understand how they affect CP and ICR [34,42–44]. In particular, CP has been exploited to concentrate diluted analytes, such as proteins [29,45], to improve the sensitivity of biosensors. The challenging idea of combining accumulation capabilities with biological and chemical selectivity boosted the research of new methods and techniques for functionalizing the surface and/or immobilizing biomolecules. Nanochannel/nanopore surface functionalization was used for tuning the ion/molecule selectivity of the structure [46] and also for varying the rectification characteristics [46,47]. For example, Vlassiouk et al. [48] anchored biomolecules onto a conical nanopore to fabricate a biosensor for avidin, streptavidin, and immunoassays. Although research activities focused on the exploitation of CP for biosensing have been very intensive in recent years, as demonstrated by three recent reviews [29,45,49], the main disadvantage of CP-based accumulation systems is still the inability to precisely control the location of the preconcentrated biomolecule plug, as stated by Park and Yossifon [50]. In fact, by controlling the position of the plug it would be possible to overlap target biomolecules with probe molecules anchored on the surface to enhance the detection sensitivity and promote the recognition mechanisms. With this idea in mind, we developed an immunosensor [51] to accumulate target biomolecules (e.g., antigens) inside a long funnel functionalized with probe molecules (e.g., antibodies). Exploiting the high surface-to-volume ratio of this structure, we succeeded in detecting, by fluorescence measurements, probe-target molecule interactions even for very dilute solutions (nearly 1 pg/mL). Moreover, we exploited the same geometry to implement ion current rectifiers [52] and studied how analytes accumulate inside the long funnel. The promising results we obtained in both fields (immunosensing and rectifiers) motivated us to further investigate the electrokinetic phenomena occurring inside such long structures in order to further improve the combination of accumulation and detection in the same area of a device. Here, we study the distribution of ions inside an extra-long (nearly 90 µm) funnel terminating with an 80 nm wide and nearly 1 µm long nanochannel. Our investigation was carried out by numerically solving the Poisson–Nernst-Planck equations in order to characterize the electrokinetic behavior of the structure for both positive and negative voltages and to estimate the rectification ratio (RR) in the range ( 10, 10 V). − 2. Methods It is well established that the distribution of the electrical potential and the flux of each ion species due to a gradient in concentration (diffusion) and electric potential (drift) through a micro-nano fluidic device is governed by the Poisson–Nernst-Planck (PNP) equations. We solved these equations by the finite element method. Details on the implementation in the COMSOL Multiphysics® Software and on the mesh structure used in the simulations are provided in the Supplementary Materials. In the following, we provide details on the geometry that we analyzed and on the imposed boundary conditions. 2.1. Funnel and Nanochannel Geometry Figure1 shows the geometry of the device used in the numerical finite element simulations. The 3D geometry of the system (reservoir + funnel + nanochannel + reservoir) was simplified to reduce computational effort by using a 2D axis-symmetric geometry. Two reservoirs (5 µm 20 µm), cis- on the left and trans- on the right, are connected by a × funnel-shaped microchannel, 90.32 µm long and 6 µm wide at the base (cis-side). At the other extremity, the funnel ends with a rectangular nanochannel (1 µm 80 nm) linked to the trans-reservoir. The total × distance between the two reservoirs (funnel + nanochannel) is therefore 91.32 µm. This geometry was inspired by the structure used by Pezzuoli et al. [51,52]. Appl. Sci. 2020, 10, 3749 3 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 14 Figure 1. Sketch of the system geometry used for the FEM calculations. The red numbers correspond Figureto walls 1. withSketch the of same the system boundary geometry conditions. used for the FEM calculations. The red numbers correspond to walls with the same boundary conditions. 2.2. Boundary Conditions Two reservoirs (5 µm × 20 µm), cis- on the left and trans- on the right, are connected by a funnel- We set a constant surface charge of σ = 1 mC/m2 on the walls of the funnel and the nanochannel shaped microchannel, 90.32 µm long and 6 µm− wide at the base (cis-side). At the other extremity, the (labeled 4 and 5 in Figure1). By changing the boundary conditions on wall 1 in the Poisson equation, funnel ends with a rectangular nanochannel (1 µm × 80 nm) linked to the trans-reservoir. The total we performed simulations for different applied voltages (V) between the cis- and trans- reservoirs. distance between the two reservoirs (funnel + nanochannel) is therefore 91.32 µm. This geometry was The trans-reservoir was set as grounded, while the potential for the cis- one was varied in a range of inspired by the structure used by Pezzuoli et al. [51,52]. between 10 and +10 V. We studied the system filled with electrolytic solutions of KCl with different − molarities (1–10 5 M). In the Nernst–Planck equations for both ion species, K+ and Cl , we set the same 2.2. Boundary Conditions− − concentration CBulk for boundaries 1 and 2 in both reservoirs. By solving the PNP equation system, + 2 we couldWe set model a constant the distribution surface charge of K of andσ = − Cl1 m− ionsC/m in on the the funnel walls of and the in funnel the nanochannel and the nanochannel as well as (labeledcalculate 4 theand ionic 5 in currentFigure 1) in. By the changing device as the a function boundary of Vcondition and CBulks on.
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