MEMBRANE COVERED POLAROGRAPHIC OXYGEN SENSOR MANUFACTURING THEORETICAL CONSIDERATIONS

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1 ANALELE ŞTIINŢIFICE ALE UNIVERSITĂŢII AL. I. CUZA IAŞI Tomul II, s. Biofizică, Fizică medicală şi Fizica mediului 006 MEMBRANE COVERED POLAROGRAPHIC OXYGEN SENSOR MANUFACTURING THEORETICAL CONSIDERATIONS Alina Manole 1, I. Neacsu, M-O. Apostu 3, V. Melnig 1 KEYWORDS: Clark electrode, polarography, diffusion oxygen models The operating principle of the Clark type polarographic oxygen electrode is based on the use of an electrolyte solution contained within the electrode assembly to transport oxygen from an oxygen-permeable membrane to the metal cathode. In this paper are reconsidered theoretical assumption of one layer and two layer diffusion models and the evaluation of optimal calibration and error measurements. 1. INTRODUCTION Electrochemical oxygen analysers are based on electrochemical reduction of O at a negatively polarized electrode. This principle lies in the bases of the Clark-type oxygen-sensitive electrode which was proposed in 1956 by Leland Clark [1, ]. Clark studied the electrochemistry of oxygen gas reduction at platinum (Pt) metal electrodes, pioneering the use of Pt electrodes as an oxygen sensor. (Pt electrodes used to detect oxygen electrochemically are often referred as Clark electrodes. ) An electrode is an electrical conductor used to make contact with a metallic part of a circuit (e.g. a semiconductor, an electrolyte or ionised gases). The word was coined by the scientist Michael Faraday from the Greek words elektron (meaning amber, from which the word electricity is derived) and hodos, a way. An electrode in an electrochemical cell is referred to as either an anode or a cathode, words that were also coined by Faraday. The anode is defined as the electrode at which electrons leave the cell and oxidation occurs, and the cathode as the electrode at which electrons enter the cell and reduction occurs. Each electrode may become either the anode or the cathode depending on the voltage applied to the cell. A bipolar electrode is an electrode that functions as the anode of one cell and the cathode of another cell. 1 Faculty of Physics, Al. I. Cuza University, Bd. Carol I, Nr. 11A, , Iasi Faculty of Biology, Al. I. Cuza University, Bd. Carol I, Nr. 0A, , Iasi 3 Faculty of Chemistry, Al. I. Cuza University, Bd. Carol I, Nr. 11A, , Iasi

2 ALINA MANOLE, I. NEACSU, M-O. APOSTU, V. MELNIG 6. THEORETICAL CONSIDERATIONS If an electrode of noble metal such as platinum or gold is made 0.6 to 0.8 V negative with respect to a suitable reference electrode such as Ag/AgCl or an calomel electrode in a neutral KCl solution (Fig. 1), the oxygen dissolved in the liquid is reduced at the surface of the noble metal following the reactions [3]: Cathodic reaction: O + H O + e - H O + OH H O + e - OH Anodic reaction: Ag + Cl - AgCl + e - Overall reaction: 4 Ag + O + H O + 4 Cl - 4 AgCl + 4 OH - Fig. 1 Setup for polarography. The oxygen reduction at the noble metal surface can follow two pathways: 4 electron pathway - the oxygen in the bulk diffuses to the surface of the cathode and is converted to OH - via H O (path a in Fig. ) electron pathway - the intermediate H O diffuses directly out of the cathode surface into the bulk liquid (path b in Fig. ). The oxygen reduction path may change depending on surface condition of the noble metal. This is probably the cause for time-dependent current drift of polarographic probes. Since the hydroxyl ions are constantly being substituted for chloride ions as the reaction starts, KCl or NaCl has to be used as the electrolyte. When the electrolyte is depleted of Cl -, it has to be replenished. Fig. Alternative pathways of oxygen reduction at cathode surface.

3 7 THEORETICAL AND PRACTICAL If we study the current-voltage diagram of the electrode (called a polarogram) we can observe that the current output of the electrode increases, in the beginning, with the increase of the negative voltage applied to the noble metal electrode (the cathode) and because the reaction of oxygen at the cathode is very fast and the rate of reaction is limited by the diffusion of oxygen to the cathode surface, the current becomes saturated (Fig. 3a). When the negative voltage is further increased, the current output of the electrode increases rapidly due to other reactions, mainly, the reduction of water to hydrogen. If a fixed voltage in the plateau region (for example, - 0.6V) is applied to the cathode, the current output of the electrode can be linearly calibrated to the dissolved oxygen (Fig. 3b). It has to be noted that the current is proportional not to the actual concentration but to the activity or equivalent partial pressure of dissolved oxygen, which is often referred to as oxygen tension. Originally developed for measuring oxygen gas, it is only a matter of polarity, whether the electrode senses hydrogen or oxygen gas. For hydrogen measurements +600 mv (vs. Ag/AgCl) are supplied. The electrode is calibrated using two gas mixtures of known oxygen (or hydrogen) concentration. (a) (b) Fig. 3 (a) Current-to-voltage diagram at different oxygen tensions; (b) Calibration obtained at a fixed polarization voltage of -0.6V. Sensor Output and Design Variables. One Layer Model A first-order diffusion model of the Clark electrode is illustrated in Fig. 4 []. The membrane electrolyte electrode system is considered to act as a one-dimensional diffusion system with the partial pressure at the membrane surface equal to the equilibrium partial pressure p 0 and that at the cathode equal to zero.

4 ALINA MANOLE, I. NEACSU, M-O. APOSTU, V. MELNIG 8 The following assumptions are made [4]: 1. The cathode is well polished and the membrane is tightly fit over the cathode surface such that the thickness of the electrolyte layer between the membrane and the cathode is negligible.. The liquid around the sensor is well agitated that the partial pressure of oxygen at the membrane surface is the same as that of the bulk liquid. 3. Oxygen diffusion occurs only in one direction, perpendicular to the cathode surface. Fick s nd law describes the unsteady-state diffusion in the membrane: p p = D m (1) t x D m - the oxygen diffusivity in the membrane; x - the distance from the cathode surface. The initial and boundary conditions are: p = 0 at t = 0 () p = 0 at x = 0 (3) p = p o at x = d m (4) d m - the membrane thickness; p o - the partial pressure of oxygen in the bulk liquid The solution of eq. (1) with the boundary conditions is: p x = + m m (5) p 0 d m n= 1 nπ d m The current output of the electrode is proportional to the oxygen flux at the cathode surface: I = NFADm ( C/ x) x= 0 (6) = NFAP ( p/ x) n nπx ( 1) sin exp( n π D t d ) m N - number of electrons per mole of oxygen reduced; F - Faraday constant (= 96,500 C/mol); A - surface area of the cathode; P m - oxygen permeability of the membrane The permeability P m is related to diffusivity by: P m = D msm (7) S m - the oxygen solubility of the membrane From eqs. (5) and (6), the current output I t of the electrode is: P = + m n I t NFA p 0 1 ( 1) exp( n π D mt d m ) (8) d m n=1 The pressure profile within the membrane and the current output under steady-state conditions can be obtained from eqs. (5) and (8), respectively: p d = (9) p and 0 d m p x= 0 m I s = NFA p 0 (10) d m

(8) shows that the rapidness of the sensor response is characterized by the response time parameter: d m τ = (11) D m For a rapid response (small τ) the membrane must be thin and/or diffusion

(10) and (11) indicate that the design variables for a diffusion oxygen sensor (DO sensor) are P m, d m, D m and A. Fig.

5 9 THEORETICAL AND PRACTICAL At steady state, the pressure profile is linear and the current output is proportional to the oxygen partial pressure in the bulk liquid. Eq. (10) forms the basis for oxygen diffusion measurement by the sensor. Eq. (8) shows that the rapidness of the sensor response is characterized by the response time parameter: d m τ = (11) D m For a rapid response (small τ) the membrane must be thin and/or diffusion coefficient, D m, high. Adjusting d m (rather than D m ) is more effective in adjusting τ (because τ depends on the square of d m ). Eqs. (10) and (11) indicate that the design variables for a diffusion oxygen sensor (DO sensor) are P m, d m, D m and A. Fig. 4 One layer electrode model. Fig. 5 Two layer electrodemodel Two Layer Model In reality, the assumption made earlier is not entirely satisfactory, because when a DO sensor is used to measure DO concentration in two different liquids at the same partial pressure of oxygen, the readings are not the same. This indicates that the sensor output depends, to a certain extent, on the properties of the liquid. The effect of liquid layer on sensor current output can be estimated using the two layer model witch considers the membrane and the liquid film as shown in Fig. 5. At steady state, the oxygen flux J through each layer in Fig. 5 should be the same: J = Kp 0 = k L ( p 0 p m ) (1) = k mp m K - the overall mass transfer coefficient; k L - mass transfer coefficient for liquid film; k m - mass transfer coefficient for membrane The inverse of the mass transfer coefficient can be termed as the mass transfer resistance:

6 ALINA MANOLE, I. NEACSU, M-O. APOSTU, V. MELNIG 30 1 K 1 1 = + (13) k L k m Equation (13) says that the overall mass transfer resistance, 1/K, is the sum of the liquid phase mass transfer resistance, 1/k L, and the membrane phase mass transfer resistance, 1/k m. The derivation is based on Ohm s law analogy; J is considered the current and p the voltage. The individual resistances can be replaced by: 1 d L d m = + (14) K PL Pm d L- liquid film thickness; P L - the oxygen permeability of the liquid film When the individual mass transfer resistances are considered the steady state sensor output becomes: p m I s = NFA p 0 (15) d where d is defined by: Alternatively, I s can be written as: d + I d L = d m Pm (16) PL p 0 s = NFA (17) d m Pm + d L PL The time constant τ of eq. (11) can be modified to: d τ = (18) D m where d is defined by: D m d = d m + d L (19) D L When placed in a stagnant liquid, the DO sensor produces a diffusion gradient extending outside the membrane and into the liquid. When the liquid is stirred, the diffusion gradient can no longer be extended beyond the liquid film around the membrane. Since the diffusion gradient becomes steeper with decreasing liquid film thickness, the current output of the sensor increases with increase in liquid velocity as shown in Fig. 6. Also, the response time of the sensor increases as the liquid velocity decreases. This so-called "flow sensitivity" is greater for a sensor with a larger cathode because the size of the stagnant diffusion field is proportionally with the size of the cathode. For proper operation of the sensor, the liquid has to be stirred beyond a certain level to maintain membrane control of oxygen diffusion. The critical velocity, V c, of the liquid is the velocity where the probe output reaches 95% (95-99% depending on the definition) of the steady state value. For a given liquid, V c is smaller for smaller cathodes. For example, with a 5 μm Teflon membrane, a cathode of 5 mm diameter requires V c of 70 cm/s in water, whereas only 5 cm/s is required for 5 μm

7 31 THEORETICAL AND PRACTICAL cathode. When the cathode diameter is less than 1 μm, the sensor becomes insensitive to liquid flow even without the membrane because, the diffusion field of the cathode is so small that it is always contained inside the minimum liquid boundary layer around the cathode. One obvious effect of the cathode size is the area effect. Eq. (17) shows that the current output is directly proportional to the sensor area A. When the current produced by the sensor is too small (when the cathode area is small), the sensor signal tends to be more susceptible to noise. The current output should be greater than 10-6 to 10-7 range for ease of signal amplification. From eq. (17), the condition for a membrane-controlled diffusion becomes: d m /Pm >> d L/PL (0) To achieve this condition, a relatively thick membrane with low oxygen permeability has to be used (this contradicts the requirement for a fast sensor response). In this case the oxygen sensor output depends only on membrane properties as given by eq. (10) and the sensor calibrated in one liquid can be used in other liquids without recalibration. In reality, however, there is always a liquid film (however thin it may be) and this causes variations in calibration in different liquids. Fig. 6 Effect of cathode diameter on flow dependency of DO sensor. Running experiments it has been observed that there is 1 to 5% increase in sensor output current per Celsius degree increase in temperature (Fig. 7a). From eq. (17) we can see that the temperature effect comes from P m and P L because they are functions of temperature. In the case of membrane diffusion control, the temperature dependency of I s should come entirely from P m and when the liquid film resistance is not negligible, both P m and P L contribute to the temperature dependency. Generally, P m is expressed as: Pm = Pm *exp(-e/rt) (1) E - the activation energy for the permeation (8.8 kcal/g-mol for polyethylene and kcal/g-mol for polypropylene membranes) [5].

8 ALINA MANOLE, I. NEACSU, M-O. APOSTU, V. MELNIG 3 (a) (b) Fig. 7 Temperature dependency of DO sensor. From Fig. 7b we can observe that as the temperature increases, the diffusivity increases and this makes the sensor respond faster. Calibration and k L a Measurement For liquid phase calibration an air saturated and also a nitrogen saturated water is prepared by passing air bubbles into a small volume (100 ml) of water, then the voltage output for both water solutions is measured. To obtain proper calibration the liquids have to be stirred at high speed. This is so-called a two point calibration. To perform gas phase calibration the sensor is exposed to air and also to nitrogen, as the gas phase, and then the two calibrations are compared [6]. For measuring the response time a step change in oxygen partial pressure in the measurement medium has to be done and then the sensor response is determined. The sensor can be approximated as a first order system: c c p = τ p (dc p / dt) () c - the oxygen concentration in the measurement sample; c p - the oxygen concentration measured by the sensor; τ p - the sensor time constant When a step change is made in c (by transferring the sensor from air into nitrogen saturated, stirred water), the sensor output decreases roughly exponentially (not exactly exponentially because the sensor may not be a true first order system). The time constant τ p is the time when the sensor response reaches 63.7% of the ultimate response (Fig. 8a). The solution to eq. () with the following boundary condition is an exponential function: c = 1 at t = 0 (3) c c p = 1 exp( t / τ p ) (4) A normalized concentration is used: c of 1 means 100% air saturation and 0 means nitrogen saturation. Eq. (4) indicates that when t = τ p, c/c p will be The time constant τ p can also be determined conveniently by using an integral method - the area above the response curve is equal to τ p (see Fig. 8b). This method is especially useful when there is a lot of noise in the measured signal.

9 33 THEORETICAL AND PRACTICAL Fig. 8 (a) Sensor response time measurement; (b) integral method for measuring the sensor time constant. Measurement of k L a k L a, the liquid phase overall volumetric mass transfer coefficient, represents the oxygen absorption capability of a bioreactor [4]. A DO sensor is used frequently to measure k L a. The reactor is first sparged with nitrogen and at time zero, the nitrogen is switched to air. The oxygen mass balance in the reactor yields: * dc dt = k La( c c) (5) c - the oxygen concentration in the reactor; c* - the oxygen concentration at the gasliquid interface. This equation can be rearranged to: * c c = τ k ( dc dt) (6) where τ k =1 k L a (7) Eqs. () and (6) can be solved simultaneously to obtain an expression for k L a and τ k can be obtained graphically as shown in Fig. 9 when τ p is known. Fig. 9 Measurement of k L a by integral method. It is very important to know that the magnitude of τ p depends on the liquid velocity in the vicinity of the sensor. Therefore, if a τ p measured at one agitation rate is used for measuring k L a for different agitation rates, the results will be in error. A safe

10 ALINA MANOLE, I. NEACSU, M-O. APOSTU, V. MELNIG 34 way is to used the same agitation rate for both τ p and τ k measurements. However, if τ k is much greater than τ p, such a precaution is not necessary. 3.CONCLUSIONS As the models reveals, there is the possibility of constructing an oxygen sensor, based on oxygen diffusion limited process (the Clark electrode), that consists of an anode and cathode in contact with an electrolyte solution (usually potassium chloride, 1 M). It is covered at the tip by a semi-permeable polymer membrane, which is permeable to gases but not contaminants and reducible ions of the sample. The cathode is in a glass envelope in the body of the electrode. The anode has a larger surface that provides stability and guards against drift due to concentration of the po electrolyte. This silver/silver chloride (Ag/AgCl) anode provides electrons for the cathode reaction. When most of the mass transfer resistance is confined in the membrane, the electrode system can measure oxygen tension in various liquids. This is the basic operating principle of the membrane covered polarographic DO probe (DO sensor) (Fig. 10) [7]. Fig. 10 A Clark-type oxygen-sensitive electrode. REFERENCES 1. T.C. Tan, and C.C. Liu, 1991, Principles and fabrication materials of electrochemical sensors. In: Chemical Sensor Technology. Kodansha Ltd., Vol. 3.. L.C. Clark, Monitor and control of blood and tissue oxygen tension. Trans. Am.Soc. Artif. Internal Org., Magda Aflori, I. Neacşu, V. Melnig, 006. Analysis methods of oxygen consumption in biological systems, Scientific Annals of University of Agricultural Sciences and Veterinary Medicine Ion Ionescu de la Brad IA I, Tom XLIX. 4. Young H. Lee, Biosensors, Engineering Biotechnology Gateway Project, Drexel University, 5. Park, J.H., N.O. Kaplan, E.P. Kennedy, 1966.Current Aspects of Biochemical Energetics, Academic Press, New York, David R. Caprette, Experimental Biosciences, Introductory Laboratory Bios 11, Rice University. 7. Trinity College Dublin, Biochemistry Laboratory: Manual for Senior Freshman Science.

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