How Do Pulsed Amperometric Ion Sensors Work? A Simple PDE Model
01 Jan 2003-Siam Review (Society for Industrial and Applied Mathematics)-Vol. 45, Iss: 2, pp 327-344
TL;DR: The heat equation posed on the half-line may be used as a simple mathematical model describing the operation of an amperometric ion sensor, used to measure ion concentrations in the laboratory.
Abstract: 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, process and quality control, biomedical analysis, and physiological applications. Study of the heat equation and its solutions provides insight into the operation of these ion sensors.
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TL;DR: A pulsed galvanostatic technique to interrogate ion-selective electrodes (ISEs) with no intrinsic ion-exchange properties is described, with the finding that the extent of concentration polarization near the membrane surface can be accurately controlled by this technique.
Abstract: This paper describes a pulsed galvanostatic technique to interrogate ion-selective electrodes (ISEs) with no intrinsic ion-exchange properties. Each applied current pulse is followed by a longer baseline potential pulse to regenerate the phase boundary region of the ion-selective membrane. The applied current fully controls the magnitude and sign of the ion flux into the membrane, thus offering instrumental control over an effect that has become very important in ion-selective electrode research in recent years. The resulting chronopotentiometric response curves essentially mimic traditional ISE behavior, with apparently Nernstian response slopes and selectivities that can be described with the Nicolsky equation. Additionally, the magnitude and sign of the current pulse may be used to tune sensor selectivity. Perhaps most important, however, appears to be the finding that the extent of concentration polarization near the membrane surface can be accurately controlled by this technique. A growing number of potentiometric techniques are starting to make use of nonequilibrium principles, and the method introduced here may prove to be very useful to advance these areas of research. The basic characteristics of this pulsed galvanostatic technique are here evaluated with plasticized poly(vinyl chloride) membranes containing the sodium-selective ionophore tert-butyl calix[4]arene tetramethyl ester and a lipophilic inert salt.
98 citations
TL;DR: A thin layer coulometric detection mode for ionophore based liquid ion-selective membranes, demonstrated here for the first time, with porous polypropylene tubing doped with the membrane material and which contains a chlorinated silver wire in the inner compartment.
Abstract: We are demonstrating here for the first time a thin layer coulometric detection mode for ionophore based liquid ion-selective membranes. Coulometry promises to achieve the design of robust, calibration free sensors that are especially attractive for applications where recalibration in situ is difficult or undesirable. This readout principle is here achieved with porous polypropylene tubing doped with the membrane material and which contains a chlorinated silver wire in the inner compartment, together with the fluidically delivered sample solution. The membrane material consists of the lipophilic plasticizer dodecyl 2-nitrophenyl ether, the lipophilic electrolyte ETH 500, and the calcium ionophore ETH 5234. Importantly and in contrast to earlier work on voltammetric liquid membrane electrodes, the membrane also contains a cation-exchanger salt, KTFPB. This renders the membrane permselective and allows one to observe open circuit potentiometric responses for the device, which is confirmed to follow the expe...
63 citations
TL;DR: A robust 10-20-fold sensitivity enhancement for calcium measurements is attained by departing from the classical response mechanism and operating in a non-Nernstian response mode, which may provide a significant increase in the accuracy and precision of electrolyte measurements in clinical analysis.
Abstract: Ion-selective electrodes ideally operate on the basis of the Nernst equation, which predicts less than 60- and 30-mV potential change for a 10-fold activity change of monovalent and divalent ions measured at room temperature, respectively. Typical concentration ranges in extracellular fluids are quite narrow for the electrolytes of key importance. A range of 2.2-2.6 mM for calcium ions, for instance, translates into just a 2.2-mV potential change. The direct potentiometric measurement of physiological electrolytes is certainly possible with direct potentiometry and is done routinely in clinical analyzers and handheld measuring devices. It places, however, strong demands on the precision of the reference electrode and requires careful temperature control and frequent calibration runs. In this paper, a robust 10-20-fold sensitivity enhancement for calcium measurements is attained by departing from the classical response mechanism and operating in a non-Nernstian response mode. Stable and reproducible super-Nernstian responses of these so-called pulstrodes in a narrow calcium activity range can be controlled by instrumental means in good agreement with theory. The potentials may be measured during a galvanostatic excitation pulse (mode I) or immediately after it (mode II), under open-circuit conditions. Subtraction of the potentials, sampled at different times during a single pulse, allows one to obtain a sensitive differential peak-shaped signal at a critical and fully adjustable analyte activity range. Calcium pulstrodes based on the diamide ionophore AU-1 were characterized and applied to the measurement in model physiological liquids. Super-Nernstian responses exceeding 700 mV/decade were observed in a physiological range of calcium concentration. Such remarkable sensitivity of the pulstrodes, complemented with the well-documented high selectivity of these potentiometric sensors, may provide a significant increase in the accuracy and precision of electrolyte measurements in clinical analysis.
46 citations
TL;DR: A pulsed galvanostatic technique is presented to distinguish free and total levels of calcium with a single membrane electrode by varying the magnitude of the applied current, which gives much more stable signals than with earlier work demonstrating the principle with zero-current potentiometry.
27 citations
References
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Book•
23 Apr 19742,537 citations
2,105 citations
"How Do Pulsed Amperometric Ion Sens..." refers background in this paper
...Further, their application is widening to environmental and industrial analysis....
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Book•
26 Sep 1996
TL;DR: In this paper, the existence and compactness of solution semiflows of linear systems are investigated. But the authors focus on the nonhomogeneous systems and do not consider the linearized stability of non-homogeneous solutions.
Abstract: 1. Preliminaries.- 1.1 Semigroups and generators.- 1.2 Function spaces, elliptic operators, and maximal principles.- Bibliographical Notes.- 2. Existence and Compactness of Solution Semiflows.- 2.1 Existence and compactness.- 2.2 Local existence and global continuation.- 2.3 Extensions to neutral partial functional differential equations.- Bibliographical Notes.- 3. Generators and Decomposition of State Spaces for Linear Systems.- 3.1 Infinitesimal generators of solution semiflows of linear systems.- 3.2 Decomposition of state spaces by invariant subspaces.- 3.3 Computation of center, stable, and unstable subspaces.- 3.4 Extensions to equations with infinite delay.- 3.5 L2-stability and reduction of neutral equations.- Bibliographical Notes.- 4. Nonhomogeneous Systems and Linearized Stability.- 4.1 Dual operators and an alternative theorem.- 4.2 Variation of constants formula.- 4.3 Existence of periodic or almost periodic solutions.- 4.4 Principle of linearized stability.- 4.5 Fundamental transformations and representations of solutions.- Bibliographical Notes.- 5. Invariant Manifolds of Nonlinear Systems.- 5.1 Stable and unstable manifolds.- 5.2 Center manifolds.- 5.3 Flows on center manifolds.- 5.4 Global invariant manifolds of perturbed wave equations.- Bibliographical Notes.- 6. Hopf Bifurcations.- 6.1 Some classical Hopf bifurcation theorems for ODEs.- 6.2 Smooth local Hopf bifurcations: a special case.- 6.3 Some examples from population dynamics.- 6.4 Smooth local Hopf bifurcations: general situations.- 6.5 A topological global Hopf bifurcation theory.- 6.6 Global continuation of wave solutions.- Bibliographical Notes.- 7. Small and Large Diffusivity.- 7.1 Destablization of periodic solutions by small diffusivity.- 7.2 Large diffusivity under Neumann boundary conditions.- Bibliographical Notes.- 8. Invariance, Comparison, and Upper and Lower Solutions.- 8.1 Invariance and inequalities.- 8.2 Systems and strict inequalities.- 8.3 Applications to reaction diffusion equations with delay.- Bibliographical Notes.- 9. Convergence, Monotonicity, and Contracting Rectangles.- 9.1 Monotonicity and generic convergence.- 9.2 Stability and steady state solutions of quasimonotone systems.- 9.3 Comparison and convergence results.- 9.4 Applications to Lotka-Volterra competition models.- Bibliographical Notes.- 10. Dispativeness, Exponential Growth, and Invariance Principles.- 10.1 Point dispativeness in a scalar equation.- 10.2 Convergence in a scalar equation.- 10.3 Exponential growth in a scalar equation.- 10.4 An invariance principle.- Bibliographical Notes.- 11. Traveling Wave Solutions.- 11.1 Huxley nonlinearities and phase plane arguments.- 11.2 Delayed Fisher equation: sub-super solution method.- 11.3 Systems and monotone iteration method.- 11.4 Traveling oscillatory waves.- Bibliographical Notes.
1,747 citations
Book•
01 Jan 1984TL;DR: In this paper, Browder et al. considered the initial-boundary value problem for the semi-infinite strip with temperature and flux-flux-boundaries specification.
Abstract: Editor's statement Foreword Felix E. Browder Preface Preliminaries 1. Introduction 2. The Cauchy problem 3. The initial-value problem 4. The initial-boundary-value problem for the quarter plane with temperature-boundary specification 5. The initial-boundary-value problem for the quarter plane with heat-flux-boundary specification 6. The initial-boundary-value problem for the semi-infinite strip with temperature-boundary specification and heat-flux-boundary specification 7. The reduction of some initial-boundary-value problems for the semi-infinite strip, to integral equations: some exercises 8. Integral equations 9. Solutions of boundary-value problems for all times and periodic solutions 10. Analyticity of solutions 11. Continuous dependence upon the data for some state-estimation problems 12. Some numerical methods for some state-estimation problems 13. Determination of an unknown time-dependent diffusivity a(t) from overspecified data 14. Initial- and/or boundary-value problems for gneral regions with Holder continuous boundaries 15. Some properties of solutions in general domains 16. The solution in a general region with temperature-boundary specification: the method of perron-poincare 17. The one-phase stefan problem with temperature-boundary specification 18. The one-phase stefan problem with flux-boundary specification: some exercises 19. The inhomogeneous heat equation ut=uxx+f(x,t) 20. An application of the inhomogeneous heat equation: the equation ut=uxx+f(x,t,u,ux) Symbol index Subject index.
781 citations
Book•
01 Jan 1981
566 citations