DE102017123647A1 - Method for calibrating a sensor - Google Patents

Abstract

The invention relates to a method for calibrating a sensor (1) having an ion-selective electrode (2) and a reference electrode (3), wherein the sensor (1) has an ideal calibration line which is linear, comprising the steps of determining a first and second ion concentration (c, c) of a sample taken from the measurement solution (4) at a first and second time (t, t), determining a first and second voltage (U, U) between the ion-selective electrode (2) and the reference electrode (3) at the first and second times (t, t), characterized by determining a spread (pX) of the ion selective electrode (2) with a theoretical slope (S), determining an interference ion concentration (c) of the measurement solution (4), determining an actual Calibration line based on the spread (pX) and the interference ion concentration (c), calibrating the sensor (1) using an actual calibration line instead of the ideal calibration line.

Description

The invention relates to a method for calibrating a sensor having an ion-selective electrode and a reference electrode.

Ion-selective electrodes (ISE) are often used in sewage treatment plants. The measurement of the activity or concentration of the desired ions takes place via a potentiometric measuring principle known from the prior art. In the following, the term "ion-selective electrode" is understood to mean a potentiometric electrode for determining an activity or concentration of ions other than H ₃ O ⁺ or H ⁺ ions. In the vast majority of applications of ion-selective electrodes in process or analytical measurement techniques concentration and activity can be equated with good approximation. The terms are therefore used synonymously below.

The ideal ion-selective electrode would be ion-specific if it responds selectively to the ion to be determined. In practice, however, this is not the case. Ion-selective electrodes often have a cross sensitivity to other interfering ions. A well-known example is the cross sensitivity of an ammonium ion selective electrode for potassium ions.

Another problem arises in the calibration of ion-selective electrodes with the aid of real samples. Frequently, the calibration of ion-selective electrodes is based on samples whose content of the ions to be determined is determined using a different measurement method in the laboratory. In order to produce standards with higher contents, the samples can also be supplemented with the ions to be determined. Since in such samples used as a calibration standard the interfering ions are contained in the same concentration as in the sample, the interference ion concentration must also be taken into account when calibrating the sensor.

Now, if an ion-selective electrode is calibrated, the interference ion concentration must also be known and taken into account. If the interference ion concentration is ignored during calibration, ie the measurement concentration and the apparent concentration are equated, the calibration process leads to incorrect results for the calibration parameters zero point, and in the case of a two-point calibration also the gradient.

The user works in the practice of the application of ion-selective electrodes with a mass concentration (mg / L) as a measured variable and not as in the supposedly analog potentiometric pH measurement with a logarithmic measure. As a result, terms such as slope, zero and offset known to the user from potentiometric pH determination are not readily transferable to the ammonium measurement and calibration of ISEs.

The invention has for its object to provide a method for calibrating a sensor with an ion-selective electrode, which leads to a sensor with more accurate readings.

mit einer theoretischen Steigung (S),
Bestimmen einer Störionenkonzentration (c_offset ) der Messlösung,
Bestimmen einer tatsächlichen Kalibriergeraden, die linear ist, anhand der Spreizung (pX) und der Störionenkonzentration (c_offset ),
Kalibrieren des Sensors anhand einer Verwendung der tatsächlichen Kalibriergeraden anstelle der idealen Kalibriergerade.This object is achieved by the subject matter of the invention. The invention relates to a method for calibrating a sensor having an ion-selective electrode and a reference electrode, wherein the sensor has an ideal calibration line which is linear, comprising the steps of immersing the sensor in a measurement solution having a time-varying ion concentration,
Determining a first ion concentration of a sample taken from the measurement solution at a first time,
Determining a first voltage between the ion-selective electrode and the reference electrode at the first time,
Determining a second ion concentration of a sample taken from the measurement solution at a second time,
Determining a second voltage between the ion-selective electrode and the reference electrode at the second time,
marked by,
Determining a spread ( pX ) of the ion-selective electrode $$pX=\text{log}\left(\frac{{10}^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102017123647A1\_0013.png,DE102017123647A1\_0014.png"\; state="\{\{state\}\}">U</figure-callout>}}_2/S}-{10}^{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="DE102017123647A1\_0014.png,DE102017123647A1\_0015.png"\; state="\{\{state\}\}">U</figure-callout>}}_1/S}}{c_2-c_1}\right)$$

with a theoretical slope ( S )
Determining an interference ion concentration ( c _offset ) of the measurement solution,
Determining an actual calibration line that is linear, based on the spread ( pX ) and the interference ion concentration ( c _offset )
Calibrate the sensor by using the actual calibration line instead of the ideal calibration line.

The solution of the above object is thus achieved by calibrating the sensor in the measurement solution. Thus, the use of a separate calibration solution is not required. A further advantage of the method according to the invention is that the sensor constantly remains in the measurement solution, ie in the process, and continuously supplies measured values without being subject to a temperature fluctuation as a result of the removal.

For the method according to the invention, it is necessary at two different times each to take a sample with different ion concentration and to analyze them, for example, in a laboratory or on-site with a portable meter in terms of ion concentration. The interference ion concentration, in this case the potassium concentration, is determined by means of a laboratory method (cuvette test). The interference ion concentration or potassium concentration is then assigned a measured voltage.

For the method according to the invention, the concept of the zero point is renamed spread.

According to an advantageous development, the slope has a theoretical value of 59.15 mV for singly charged ions, a theoretical value of 118.3 mV for doubly charged ions, and a theoretical value of 177.45 mV for triply charged ions. The slope of an ion-selective electrode changes only slightly over time and, in the case of a small change, has only a negligible influence on the accuracy of the measurement result. Therefore, the slope of an ion-selective electrode does not necessarily need to be calibrated and adjusted.

According to an advantageous variant, the temperature is taken into account in the determination of the spread. During calibration, the temperature is directly proportional to the concentration of the ions to be measured. This follows from the Nernst equation. Therefore, there should be no large temperature differences between the measuring solution and the sensor.

• 1: einen Längsschnitt eines Sensors mit einer ionenselektiven Elektrode,
• 2: einen mehrere Konzentrationsdekaden umfassenden geraden Abschnitt eines Diagramms der Nernst-Gleichung,
• 3a/3b: Diagramme einer nicht kalibrierten ionenselektiven Elektrode,
• 4a/4b: Diagramme einer nach dem Stand der Technik kalibrierten Elektrode,
• 5a/5b: Diagramme einer nach dem erfindungsgemäßen Verfahren kalibrierten Elektrode,
• 6: ein Diagramm mit Verläufen der Konzentration von NH₄ ⁺ als Funktion der Zeit,
• 7: ein Diagramm entsprechend 6, aufgenommen mit einem nach dem Stand der Technik kalibrierten Sensor, und
• 8: ein Diagramm entsprechend 6, aufgenommen mit einem nach dem erfindungsgemäßen Verfahren kalibrierten Sensor.

The invention will be explained in more detail with reference to the following drawings. It shows:

• 1 FIG. 3: a longitudinal section of a sensor with an ion-selective electrode, FIG.
• 2 : a multiple-decade straight section of a diagram of the Nernst equation,
• 3a / 3b : Diagrams of an uncalibrated ion-selective electrode,
• 4a / 4b : Diagrams of an electrode calibrated according to the prior art,
• 5a / 5b : Diagrams of an electrode calibrated by the method according to the invention,
• 6 : a diagram with gradients of the concentration of NH ₄ ⁺ as a function of time,
• 7 : a diagram accordingly 6 , recorded with a calibrated according to the prior art sensor, and
• 8th : a diagram accordingly 6 taken with a calibrated by the method according to the invention sensor.

1 shows a longitudinal section of a sensor 1 with an ion-selective electrode 2 and a reference electrode 3 , A measuring circuit 5 measures an electrical voltage U between the ion-selective electrode 2 and the reference electrode 3 , wherein the reference electrode 3 has a constant electrode potential.

beschrieben, wobei S die Steigung und U₀ der Achsenschnittpunkt mit der x-Achse ist.Is in the measurement solution 4 an ion i with a concentration c _i present, the voltage changes U linear with the logarithm of the concentration c _i , This is done by the equation $$U={\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DE102017123647A1\_0013.png,DE102017123647A1\_0014.png"\; state="\{\{state\}\}">U</figure-callout>}}_0+S\text{log}\left(c_i\right)$$

described, wherein S the slope and U ₀ the intercept point with the x -Axis is.

2 shows a multiple concentration decades straight section of a graph of electrode voltage U as a function of concentration c _i , The straight section is slope through the calibration parameters S (Gradient triangle with dashed lines) and the voltage U ₀ characterized.

beschrieben, welche eine Erweiterung der Gl. 1 um den hier als c_offset bezeichneten Term darstellt. Die Störionenkonzentration c_offset beschreibt summarisch die Wirkung aller Störionen auf die ionenselektive Elektrode. Die Störionenkonzentration c_offset stellt also auch die Konzentration dar, um welche die Messung infolge der Wirkung aller Störionen verfälscht wird, d. h. zu hoch ausfällt. Die Summe $$c_{\text{schein}}=c_i+c_{offset}$$

aus der Konzentration der zu messenden Ionen c_i und der Störionenkonzentration c_offset wird hier als scheinbare oder wirksame Konzentration c_schein bezeichnet. Sie bestimmt die Spannung U, welche sich an einer ionenselektiven Elektrode einstellt. Wenn Störionen die Messung beeinflussen, muss für Gl. 1 korrekterweise $$U=U_0+S\text{ log}\left(c_{\text{schein}}\right)$$

geschrieben werden.Ion-selective electrodes very often respond to multiple ions than just the ion to be measured. This fact is approximated by the opposite of the equation in Eq. 1 extended Nikolsky equation $$U={\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DE102017123647A1\_0013.png,DE102017123647A1\_0014.png"\; state="\{\{state\}\}">U</figure-callout>}}_0+S\text{log}\left(c_i+c_{Offset}\right)$$

which describes an extension of Eq. 1 around here as c _offset represents designated term. The interference ion concentration c _offset summarizes the effect of all the interfering ions on the ion-selective electrode. The interference ion concentration c _offset So also represents the concentration by which the measurement is falsified due to the effect of all interference ions, that is too high. The sum $$c_{\text{bill}}=c_i+c_{Offset}$$

from the concentration of the ions to be measured c _i and the interference ion concentration c _offset is here as apparent or effective concentration c _shines designated. It determines the tension U , which adjusts to an ion-selective electrode. When interfering ions influence the measurement, Eq. 1 correctly $$U={\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DE102017123647A1\_0013.png,DE102017123647A1\_0014.png"\; state="\{\{state\}\}">U</figure-callout>}}_0+S\text{log}\left(c_{\text{bill}}\right)$$

to be written.

wobei pN = U₀ / S dem Schnittpunkt der Geraden aus Gl. 5 mit der log(c)-Achse entspricht und hier als der Nullpunkt der elektrochemischen Messzelle bezeichnet wird. Die Ermittlung dieser beiden Kalibrierparameter, nämlich pN und S kann durch die Messung der Spannung U in wenigstens zwei Kalibrierlösungen mit hinreichend unterschiedlichen Konzentrationen c_i des zu messenden Ions i erfolgen. For practical reasons, it is expedient, for the conversion of the measured voltage into a concentration value not the Eq. 4 to use, but the corresponding relationship $$U=S\left[\text{log}\left(c_{\text{bill}}\right)+pN\right]$$

where pN = U ₀ / S the intersection of the line from Eq. 5 corresponds to the log (c) axis and is referred to herein as the zero point of the electrochemical cell. The determination of these two calibration parameters, namely pN and S can by measuring the voltage U in at least two calibration solutions with sufficiently different concentrations c _i of the ion i to be measured.

verwendet werden. Die erfindungsgemäße Zwei-Punkt-Kalibrierung lässt sich folgendermaßen durchführen. Zuerst wird der Sensor 1 in eine Messlösung 4 mit sich zeitlich verändernder lonenkonzentration eingetaucht (siehe 1). Anschließend wird zu einem ersten und zweiten Zeitpunkt t₁ und t₂ eine erste und zweite lonenkonzentration c₁ und c₂ und eine erste und zweite Spannung U₁ und U₂ zwischen der ionenselektiven Elektrode 2 und der Bezugselektrode 3 bestimmt (siehe 1). Die Steigung S wird mit -59,15 mV für einfach geladene Ionen angenommen. Eine Spreizung pX des Sensors lässt sich gemäß $$pX=\text{log}\left(\frac{{10}^{U_2/S}-{10}^{U_1/S}}{c_2-c_1}\right)$$

berechnen. Anhand der Spreizung pX kann ein Sensor 1 mit einer ionenselektiven Elektrode als Messfühler für jede gemessene Spannung U den zugehörigen Konzentrationswert c_i berechnen.The slope S an ion-selective electrode changes little during the useful life in the practice of the ion-selective electrode. If the slope S Once an ion-selective electrode is known, it is sufficient, therefore, only the zero point pN z. B. by means of a simple one-point calibration to determine and once ascertained slope S maintain. For calculation, the formula $$pN=\frac{U}{S}-\text{log}\left(c_{\text{bill}}\right)$$

be used. The two-point calibration according to the invention can be carried out as follows. First, the sensor 1 into a measuring solution 4 immersed with time-varying ion concentration (see 1 ). Subsequently, at a first and second time t ₁ and t ₂ a first and second ion concentration c ₁ and c ₂ and a first and second voltage U ₁ and U ₂ between the ion-selective electrode 2 and the reference electrode 3 determined (see 1 ). The slope S is assumed to be -59.15 mV for singly charged ions. A spread pX the sensor can be adjusted according to $$pX=\text{log}\left(\frac{{10}^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102017123647A1\_0013.png,DE102017123647A1\_0014.png"\; state="\{\{state\}\}">U</figure-callout>}}_2/S}-{10}^{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="DE102017123647A1\_0014.png,DE102017123647A1\_0015.png"\; state="\{\{state\}\}">U</figure-callout>}}_1/S}}{c_2-c_1}\right)$$

to calculate. Based on the spread pX can be a sensor 1 with an ion-selective electrode as a sensor for each measured voltage U the associated concentration value c _i to calculate.

The first and second time t ₁ and t ₂ are different from each other, so that the first and second ion concentration c ₁ and c ₂ and the first and second voltages U ₁ and U ₂ are different from each other.

Is the interference ion concentration c _offset the ion-selective electrode 2 is known, an actual calibration line based on the spread pX and the interference ion concentration c _offset be determined. The sensor 1 can then be calibrated by fitting the actual calibration line to the ideal calibration line.

For a more detailed explanation of the method according to the invention, a calculation example of a measuring solution with a time-varying ion concentration of NH ₄ ⁺ carried out. The ion concentration of NH ₄ ⁺ varies in time between 0.1 and 10 mg / L.

Gl. 8 beschreibt gleichzeitig die Kalibriergerade eines fabrikneuen Sensors. Ist der Sensor gealtert, ergeben sich für die Spannungen U₁ und U₂ beispielsweise -222,58 mV und -104,26 mV. Daraus ergibt sich bei der Annahme einer unveränderten Steigung von S = -59,15 mV eine Spreizung von pX = 1,49. Somit ändert sich Gl. 4 zusammen mit pX = U₀ / S bei einem gealterten Sensor zu $$U=-\mathrm{59,16}\cdot \text{log}\left(c\right)+\mathrm{88,32}$$

At a first time t ₁ is z. B. based on a sample by means of a cuvette test or by means of a process photometer, a first ion concentration c ₁ from NH ₄ ⁺ to 0.1 mg / L. At this first time t ₁ becomes a tension U ₁ = -251.74 mV measured between the ion-selective electrode and the reference electrode. At a second time t ₂ is, for. Example, based on a sample by means of a Küvettentests or by means of a process photometer, a second ion concentration c ₂ from NH ₄ ⁺ to 10 mg / L. At this second time t ₂ becomes a tension U ₂ = -133.42 mV between the ion-selective electrode and the reference electrode. For the slope S a theoretical value of -59.15 mV is assumed. Thus, according to Eq. 7 for the spread pX = 1. Thus, according to Eq. 4 together with pX = U ₀ / S for the voltage to be measured $$U=-59.15\cdot \text{log}\left(c\right)+59.15$$

Eq. 8 simultaneously describes the calibration line of a brand new sensor. If the sensor aged, arise for the voltages U ₁ and U ₂ for example, -222.58 mV and -104.26 mV. This results in a spread of pX = 1.49 assuming an unchanged slope of S = -59.15 mV. Thus, Eq. 4 together with pX = U ₀ / S for an aged sensor too $$U=-59.16\cdot \text{log}\left(c\right)+88.32$$

A measurement of the ion concentration of NH ₄ ⁺ by means of Eq. 8 would lead to a time-varying ion concentration between 0.31 and 31.1 mg / L, which would not be accurate given the correct values of 0.1 and 10 mg / L. Therefore, the sensor must be calibrated by changing the spread pX from 1 to 1.49. An advantage of the method according to the invention is that only the spread pX and not in addition the slope S must be taken into account during calibration.

3a / 3b show diagrams of an uncalibrated ion-selective electrode. 3a shows a diagram in which the voltage U plotted against the concentration c in logarithmic representation. The solid curve describes a measured and the dashed curve describes an idealized curve of the voltage U , 3a represents the actual calibration with the logarithmic relationship between signal and concentration acc. Nernst equation.

3b shows a graph at which the measured concentration c _acc against the actual concentration c _real is applied. The solid curve describes a measured and the dashed curve an idealized course of the concentrations c _acc and c _real , 3b represents the view of the user.

Calibration of the uncalibrated electrode accordingly 3a and 3b leads to the in 4a / 4b shown diagrams.

4a / 4b show diagrams of a calibrated according to the prior art electrode. Clearly visible is the too great deviation between the measured (continuous line) and the desired course (dashed line). It can be seen that the measured and the desired line coincide at only two points, namely at the zero point and the one calibration point.

5a / 5b show diagrams of a calibrated according to the inventive electrode. Clearly recognizable is the great agreement between the measured and the desired course.

6 shows a diagram with courses of the concentration of NH ₄ ⁺ recorded as a function of time in hours with a non-calibrated potentiometric sensor with an ion-selective electrode (solid line) and a reference measurement of a photometric analyzer (dotted line). When a sewage treatment plant is aerated, the concentration of ammonium falls to a minimum. The course shows an alternating ventilation and filling of the treatment plant, which is noticeable by the up and down of the course or the ammonium concentration. This course can be exploited by using a time of high as the first time to acquire a first calibration reading NH ₄ ⁺ -Concentration (ventilation off) and a time of low concentration (ventilation on) is selected as the second time to acquire a second calibration value.

7 shows a diagram accordingly 6 , recorded with a calibrated according to the prior art sensor (solid line) and a reference measurement (dotted line, see 6 ).

8th shows a diagram accordingly 6 , recorded with a calibrated by the inventive method sensor (solid line) and a reference measurement (dotted line, see 6 ).

LIST OF REFERENCE NUMBERS

1

sensor

2

Ion-selective electrode

3

reference electrode

4

measurement solution

5

measuring circuit

c ₁

First ion concentration

c ₂

Second ion concentration

t ₁

First time

t ₂

Second time

U ₁

First tension

U ₂

Second tension

pN

intersection

pX

spread

S

pitch

c _offset

Störionenkonzentration

Claims (3)

A method of calibrating a sensor (1) having an ion selective electrode (2) and a reference electrode (3), the sensor (1) having an ideal calibration straight line, comprising the steps of immersing the sensor (1) in a sensing solution (4) with a time-varying ion concentration, determining a first ion concentration (c ₁ ) of a sample taken from the measurement solution (4) at a first time (t ₁ ), determining a first voltage (U ₁ ) between the ion-selective electrode (2) and the Reference electrode (3) at the first time (t ₁ ), determining a second ion concentration (c ₂ ) of the sample (4) at a second time (t ₂ ) taken sample, determining a second voltage (U ₂ ) between the ion-selective electrode (2) and the reference electrode (3) at the second time (t ₂ ), characterized by determining a spread (pX) of the ion-selective electrode (2) $$pX=\text{log}\left(\frac{{10}^{U_2/S}-{10}^{U_1/S}}{c_2-c_1}\right).$$

with a theoretical slope (S), determination of an interference ion concentration (c _offset ) of the measurement solution (4), determination of an actual calibration straight line, based on the spread (pX) and the interference ion concentration (c _offset ), calibration of the sensor (1) by using the actual calibration line instead of the ideal calibration line. Method according to Claim 1 wherein the slope (S) has a theoretical value of 59.15 mV for singly charged ions, a theoretical value of 118.3 mV for doubly charged ions, a theoretical value of 177.45 mV for triply charged ions. Method according to Claim 1 or 2 , wherein the temperature is taken into account in the determination of the spread (pX).

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