Fig 1 - uploaded by Eric Bakker
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1: Experimental setup of the discussed amperometric ion sensor. The ionselective electrode shown on the left incorporates the ion-selective membrane, which is responsible for the sensing process.
Source publication
The heat equation posed on the half-line may be used as a simple mathematical model describing the operation of an amperometric ion sensor. These sensors represent the next generation of sensors that are in routine use today. Such sensors may be used to measure ion concentrations in the laboratory, for clinical analysis, environmental monitoring, p...
Citations
... Parabolic problems with nonhomogeneous flux jump condition and nonlinear jump condition are often encountered in scientific computing and engineering. For example, in Radu et al. [Radu, Meir and Bakker (2004); Hetzer and Meir (2007); Bakker and Meir (2003)], a numerical model is introduced to describe the concentration u of an ion I in aqueous solution Ω aq and adjoining polymeric membrane Ω org . Since the diffusion coefficients of the aqueous solution and of the membrane are different, this an interface problem with interface Γ at the membrane. ...
In this paper, we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton's method to handle nonlinearity. It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem. Numerical experiments show that our method is about second order accurate in the L∞ norm.
... Elliptic problems with nonhomogeneous flux jump condition and nonlinear jump condition are often encountered in scientific computing and engineering. For example, in [1][2][3], a numerical model is introduced to describe the concentration u of an ion I in aqueous solution K aq and adjoining polymeric membrane K org . (We adopt the notations from the above reference.) ...
In this paper, we propose a new method for solving two-dimensional elliptic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The method we used is traditional finite element method coupled with Newton’s method, it is very simple and easy to implement. The grid we used here is body-fitting grids based on the idea of semi-Cartesian grid. Numerical experiments show that this method is about second order accurate in the
... Therefore, the relaxation is incomplete (see Fig. 1), especially under the shorter time protocol. Similar results have been analyzed theoretically and obtained experimentally for ISEs in chronoamperometric mode [18]. External voltage was applied to ISEs to uptake electrolyte from solution , and then the electrolyte was striped back when the external voltage was off. ...
... External voltage was applied to ISEs to uptake electrolyte from solution , and then the electrolyte was striped back when the external voltage was off. In particular, it was shown that the stripping pulses must be about 25 times longer than the uptake pulses to ensure the reproducibility of the current signal (periodic mode) [18]. Shorter measuring time called for higher polarization current densities needed for setting the potentials at the Nernstian straight line. ...
A recently introduced tuned galvanostatic mode of measurements with ion-selective electrodes (ISEs) is utilized to perform analytical measurements in the nanomolar concentration range with the same or better selectivity than within the traditional ISE working range. Experimental evidence is provided for Ohmic behavior of ISEs when polarized with relatively large currents. Complete unified protocol of the optimization of the compensating current densities for a given ISE in a given solution is presented, as well as the complete unified protocol of analysis of extremely diluted samples. It is also demonstrated that tuned galvanostatic polarization has beneficial effect on the selectivity of ISEs. The problems related to incomplete relaxation of ISEs when the current is shut off are discussed as well.
... Chronopotentiometry delivered more detailed information. This method (as well as chronoamperometry) was successfully used in the mechanistic studies of ISEs [13,[35][36][37][38][39][40]and also in the practically-aimed research [13,[41][42][43][44][45][46]. For these measurements we recorded the signals for 20 s at the open circuit potential, and then the ISEs were polarized with a current of 10 nA for 60 s. ...
Potassium-selective solid-contact electrodes (ISEs) with various transducer layers are studied by means of the zero-current potentiometry, electrochemical impedance spectroscopy, chronopotentiometry, and SEM. The study is focused on the stability of the ISE potentials over time. A relatively good stability is shown by ISEs with (i) C-60 and C-70 fullerene-enriched carbon black (SD = 5.7 mV over 80 days) and with (ii) the combination of ordinary carbon black, poly(amidoacid) Cu(I) complex, and electron-ion exchanging resin in the transducer layer (SD = 3.3 mV over 80 days). Passing a current through the ISEs results in polarization which can be decomposed into a decaying exponent (slow redox reaction) and a diffusional polarization at the interface between the membrane and the transducer layer. There is no correlation between the exponential component of the polarization and the long-term stability of the ISE potentials, whereas the latter correlates with the diffusional part of the polarization. In turn, the diffusional polarization is low when the transducer layer contains the primary ion (K+), and/or the electronic conductor in the transducer layer has a higher specific surface area and/or smaller pores.
... Recently, the authors of [9] considered a spherical interfaces dynamos modeling where the interfaces are known spheres in the universe, and our 3D linear IFE constructed in [21] can be extended to this case to provide a useful alternative approach for such important problems in astrophysics. The authors of [5] studied a simple PDE model for a pulsed amperometric ion working mechanism, where the quadratic jump interface conditions are derived, the solution decomposition and numerical method are provided in [17], our IFE here can also be employed in such case to give a more accurate numerical solution techniques. The so-called WPE method [31] is proposed for Fokker-Planck equations in bimolecular transport process with interfaces when the motor potential is discontinuous function, IFE discussed below can also be used for such equation with a proper homogeneity. ...
... The model describes the concentration u of an ion I in an aqueous solution (sample) and in an adjoining polymeric membrane, the interface being the point at which the membrane contacts the solution, see [5] and [4] for details. A general description of the operating principle, as well as a simpler model, of such ion sensors may be found in [1]. ...
... In the absence of sources or sinks the diffusion of ions in the aqueous solution and membrane is governed by (6) u t − (ku x ) x = 0 in Ω × (0, T ) where now Ω = Ω aq ∪Ω org (using notation similar to that introduced in the previous section). The ion concentration satisfies the boundary conditions (7) u(−δ aq , t) = u b aq (t) and u(δ org , t) = u b org (t) in (0, T ) where the first condition is given by the sample bulk concentration, and the second is given by the ion concentration in the, so-called, inner solution (a reference solution on the other side of the membrane, see [1]), and the initial condition ...
In this paper we describe a one-dimensional interface problem for the heat equation, with a nonlinear (quadratic) jump condition at the interface. We derive a numerical method for approximating solutions of this nonlinear problem and provide some results from numerical experiments. The novelty of this problem is precisely this nonlinear (quadratic) jump condition, and it arises in the study of polymeric ion-selective electrodes and ion sensors.
Health monitoring is experiencing a radical shift from clinic‐based to point‐of‐care and wearable technologies, and a variety of nanomaterials and transducers have been employed for this purpose. 2D materials (2DMs) hold enormous potential for novel electronics, yet they struggle to meet the requirements of wearable technologies. Here, aiming to foster the development of 2DM‐based wearable technologies, reduced graphene oxide (rGO)‐based liquid‐gated transistors (LGTs) for cation sensing in artificial sweat endowed with distinguished performance and great potential for scalable manufacturing is reported. Laser micromachining is employed to produce flexible transistor test patterns employing rGO as the electronic transducer. Analyte selectivity is achieved by functionalizing the transistor channel with ion‐selective membranes (ISMs) via a simple casting method. Real‐time monitoring of K⁺ and Na⁺ in artificial sweat is carried out employing a gate voltage pulsed stimulus to take advantage of the fast responsivity of rGO. The sensors show excellent selectivity toward the target analyte, low working voltages (<0.5 V), fast (5–15 s), linear response at a wide range of concentrations (10 µm to 100 mm), and sensitivities of 1 µA/decade. The reported strategy is an important step forward toward the development of wearable sensors based on 2DMs for future health monitoring technologies.
The structure and ion-selective properties of some 2-phosphorylphenols were studied. It was shown that, irrespective of the nature of the substituents on the benzene ring and on the phosphorus atom, these compounds exhibit potentiometric selectivity to cesium cation. The crystal structures of 2-(diphenylphosphoryl)-4-ethylphenol and 2-[(diphenylphosphoryl)methyl]phenol were established.
We carry out error estimation of a class of immersed finite element (IFE) methods for elliptic interface problems with both perfect and imperfect interface jump conditions. A key feature of these methods is that their partitions can be independent of the location of the interface. These quadratic IFE spaces reduce to the standard quadratic finite element space when the interface is not in the interior of any element. More importantly, we demonstrate that these IFE spaces have the optimal (slightly lower order in one case) approximation capability expected from a finite element space using quadratic polynomials.
Simple expressions corresponding to the current-potential-time-curves and to the profiles of a target ion in the organic and aqueous phase when any multipotential pulse is applied to an ITIES, are given and applied to the determination of the diffusion coefficients of both phases. The special situation of solvent polymeric membrane ion sensors, for which it can be considered that the ionic transport is only controlled by diffusion in the organic phase, has also been treated in a very simple and elegant form.
