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If an electrode system, usually consisting of a gold cathode and a silver anode, is polarized under suitable conditions, any oxygen present in solution is reduced. The change in the polarization voltage that takes place as this occurs is directly proportional to the partial pressure of the oxygen (according to CLARK). The partial pressure and the volume of the gas are also proportional.

An electrochemical cell consisting of two electrodes and electrolytes, and that is covered with a membrane permeable to oxygen, produces an electric current. The current is proportional to the permeability of the membrane to oxygen, i.e., proportional to the partial pressure of oxygen in the medium. Oxygen reacts at the cathode of the cell, which normally consists of a precious metal (e.g., gold), according to the following equation:

O₂ + 2 H₂O + 4 e- → 4 OH^-

in which e^- means one electron in the metal. The electron flux over the course of the reaction produces the current that is then measured. In addition, the temperature also has an impact on the amount of current, which can be compensated for electronically.

The measurement using the Digox Analyzer occurs without a membrane using the potentiostatic 3-electrode measuring system according to TÖDT und TESKE.

The cathode performing the measurement consists of solid silver, while the anode is made of stainless steel and serves as an auxiliary electrode. The reference electrode consists of silver/silver chloride.

An electrochemical reaction occurs after applying a defined polarization voltage at the cathode. The oxygen molecules are reduced in this reaction.

Cathode (silver):
O₂ + 2 H₂O + 4 e^- → 4 OH^- (cathodic process)

Auxiliary electrode (VA):
4 OH^- → O₂ + 2 H₂O + 4 e^- (anodic process)

After a specific polarization voltage is applied, an electrochemical reaction takes place at the cathode. The current flowing while the reaction is taking place is directly proportional to the quantity of dissolved oxygen, i.e., if the polarization voltage remains as precise as possible at the level of the diffusion limited current.

If this is the case, the relationship is represented as follows:

I = K × C_O2, where K = n × F × A × 1/d

I      =    current measured
C_O2  =    oxygen concentration
n    =    number of electrons exchanged per molecule
F    =    Faraday constant
A    =    cathode surface
d    =    thickness of the natural convection boundary layer

The thickness of the natural convection boundary layer is defined by the hydrodynamic conditions at the cathode, while the movement of oxygen molecules through the barrier layer is determined by temperature-dependent diffusion processes. Those two clearly defined factors are measured precisely and are taken into consideration.

In order to adjust the polarization voltage between both electrodes in a defined manner, a third electrode, the auxiliary electrode, is employed for DIGOX analyzers. This auxiliary electrode remains in electrolytic contact with the surface of the cathode by means of a diaphragm but without the possibility of a mass transfer.

The analytical determination of oxygen using amperometric electrodes is achieved through measurement of the electrical current. The electrodes consist of a cathode and an anode, which are connected conductively through an electrolyte solution (KCl/KOH). Precious metals, such as platinum and gold are chosen for the cathode, and silver, for the anode. The gas-permeable membrane separates the two electrodes from the solution being measured. An appropriate polarization voltage causes diffusion of the oxygen across the membrane into the measurement cell, where it reaches the surface of the cathode and is reduced, producing hydroxide ions.

Reaction at the cathode:     O₂ + 4e^– + 2 H₂O      → 4 OH⁻

Reaction at the anode:        4 Ag + 4 Cl⁻               → 4 AgCI + 4e⁻

This chemical reaction creates an electrical current that is proportional to the partial pressure p_O2 of the oxygen. Oxygen must be steadily liberated from the solution being measured for the oxygen electrode to receive a constant supply. The concentration of oxygen in the medium can be determined using HENRY’s law and the solubility coefficient of oxygen [1]. Three different variations on the types of the equipment required for performing this analysis are present below.

CO₂ is introduced into the beer so that a specific volume of foam is produced. The mean retention time of the bubbles in the foam serves as a measure for the foam stability, which is calculated as the relationship between the time required for the foam to collapse and the logarithm of the relationship between the volume of the collapsed foam and the foam still present [1–3].

This method is frequently applied in instances when the influence of carbon dioxide content on foam formation in the beer is to be eliminated.

The measurement process using a Digox Analyzer works according to the principle of the potentiostatic three-electrode measurement system developed by TÖDT and TESKE and does not require a membrane.

The measuring electrode consists of solid silver, while the counter electrode is made of stainless steel. The reference electrode is composed of silver/silver chloride.

After generating a defined “polarization voltage”, an electrochemical reaction occurs at the measuring electrode, inducing a reduction of the oxygen molecules in the sample.

Measuring electrode (silver):

O₂ + 2 H₂O + 4 e⁻ → 4 OH⁻ (cathodic process)

Counter electrode (stainless steel):

4 OH⁻ → O₂ + 2 H₂O + 4 e⁻ (anodic process)

The flow of current as a result of this reaction is directly proportional to the amount of dissolved oxygen in the sample, if the polarization voltage is fixed as close to the level of the diffusion threshold current as possible.

In this case, the relationship can be represented as follows:

I = K × C_O2, whereupon K = n × F × A × 1/d

I = sensor current

C_O2 = oxygen concentration

F = Faraday constant

n = number of electrons per molecule

A = cathode surface

d = thickness of the “undisturbed layer” along the wall

The thickness of the undisturbed layer along the wall is determined by the hydrodynamic relationships at the measurement electrode and the transportation of oxygen molecules across the boundary layer brought about by temperature-dependent diffusion processes. Both of these clearly defined factors are precisely measured and compensated.

In order to adjust the polarization voltage between the two electrodes, a third electrode, the reference electrode, is employed in Digox measurement devices. This reference electrode remains in contact with the surface of the measuring electrode over a diaphragm in order to prevent mass transfer [1, 2, 3].

Active calibration:

In-line calibration is integrated into the device and is initiated by pressing a button. Taking advantage of Faraday’s Law, an exactly defined amount of oxygen is produced through the electrolysis of water.

I × t = m × F

I = current required for electrolysis

t = time

m = mass, g/mol

F = Faraday constant

The oxygen dissolves in the medium as it flows through and is detected at the measuring cell. The hydrogen liberated during the electrolysis reaction is not relevant for the measurement. The microprocessor monitors the calibration values and carries out any necessary corrective measures. The electrolysis enables the calibration of the device to be carried out under the same conditions and in the same medium as the analysis. Measurement operations are not disrupted during the calibration process [3].

The following applies to Digox 6.1 and all later models: In order to precisely determine the necessary potential for the measurement system, the Digox Analyzer possesses a scanner, which records the product-specific behavior of the medium subject to analysis. This can establish, whether the medium – due to the additives or supplements – must be measured at another potential. In this way, all types of beer-based beverages, non-alcoholic beverages and wine can be analyzed. Moreover, oxygen-reducing substances which can cause the calibration to be inaccurate may also be detected using the calibration scanning process. The device automatically implements the necessary compensative measures with the factors it has determined.