Wide Ratio O2 Sensor

[ptimmerm at mashtun.JPL.NASA.GOV]

>
>Gar Wrote:
>
>P.S. To any electrochem guys that read my words and wince, get off yer
>duff and eXplain it to the rest of us lower lifeforms; otherwise, quit
>yer complainin.
>

You may regret having asked, cause this is no short note!

Our God of Electrochemistry, Prof. John S. Newman, wrote this
about concentration cells in Electrochemical Systems, Vol. 2.

1.6 Concentration Cells

We need to examine further the consequences of the concentration variation...

Envision a cell  "consistint of two copper electrodes partially immersed in 
two cupric sulfate solutions of different concentrations, with the two 
solutions separated by a porous glass disk that prevents rapid mixing of the 
solution, while allowing the passage of current and slow diffusion between 
solutions.

Because of the concentration differentces, there is a tendancey for cupric ions to dischare from the 0.1 M solution and for copper to dissolve into the 0.05 M 
solution.  This manifests itself as a potential difference between the 
electrodes in order to prevent current flow, the electrode in the more 
concentrated solution being more positive relative to the other electrode.
If these electrodes were connected through an external resistor, current
would flow through the resistor from the positive to the negative electrode
and through the solution from the negative to the positive.  

In the absence of current flow, the potential difference between
the electrodes can be expressed approximatly as

	U  =  Phi I - Phi II  =  (1-t+) * (RT/F) * ln (C1/C2)

Where t+ is the transference number of cupric ions, R is the gas constant
and and C1 and C2 are the solution concentrations, (ignoring activities)."
(also lets skip the transference number thing)

***********

So here we have a description of the classic concnetration cell.  You can
leave it open circuit, or probe with a high Imp. Voltmeter and get the voltage,
or you can add current and "pump ions".  We call that electroplating copper
in this case.  

Standard O2 Sensor

Now lets look at O2 sensor, a solid oxide based concentration cell.  Instead 
of having a porous frit, you can have a sintered Al2O3 disk that acts as both
electrolyte and separator at high temperature.  Certian oxides allow for
conduction of oxygen ions, yet are not electronically conductive.  If you
vapor deposit some metal film on both surfaces and mount with one side
facing the exhaust and one side facing atmosphere you have a 

	metal//gas//solid//gas//metal
 
concentration cell.  Wires must go to these metalized surfaces.  There you 
take atmospheric diatomic oxygen and it reacts at the metal to go to oxygen 
ions in the solid solution (cermaic).  From there it diffuses to the other 
side and the reverse reaction occurs.  Phi I occurs at the first side and 
Phi II at the other, giving a net potential U.

That is our 0.1 to 1.0 volt signal.  Obviously the ratio of ln(C1/C2) is 
important to the U that you get out, and it could vary with thickness
and temperature.  If you get the thing hot enough, diffusion of oxygen
ions will be fast, and then you only have reaction rate limitations,
or likely some mixture of both kinetics and diffusion rate.  This is
where electrochemistry begins to get complicated, mixed control modes.
Note that reaction rate, (kinetics) is also a function of temperature.
Generally there is an exponetial relationship, with an activation energy
defined by the arhenius relation.  Enough of that!

Wide ration O2 sensor

Now you want to talk about a cell with three electrodes and two
separator/electrolyte disks giving us something like this: 

	gas//metal//solid//metal//solid/metal//gas.	Phase
	CI	    	    CII			CIII	O- Concentration
		Phi I	   Phi II	Phi III		Chemcial Potential

			
Obviously we have three chemical potentials as well, well call Phi I, Phi II, 
and Phi III.  From these three taps we will make two potential measurements 
VI & VII Where VI = PhiI - Phi II and VII = Phi III - Phi II give us cell 
potentials. We always have to measure agianst something like a ground, ~kinda.
If you ran this thing in the passive mode, oxygen would react  at the location 
of more oxygen (atmosphere) diffuse first to the center tap, creating some   
and Phi II, and then continue on to the inside surface where CIII and PhiIII
would be established.  

The active mode described in this forum was an ion pump, maintaining a
fixed potential VII of 0.45 volts.  When you are at stoich, the simple 
cell is calibrated to give 0.45 volts when you have one atmoshpere with 
12% oxygen near sea level.  Now you want to run the  thing across a wider 
range.  So what you have to do is run the external cell (ion pump) by 
applying current to maintian the CII value.  This is controlling you reference 
concentration CII = CI and allows you operate at much higher or lower
CIII levels without having your V II go off exactly at 0.45 volts.  
Because there is some work required for O- ions to diffuse from CI to CII, 
leaving the pump off gives a lower range calibration, turning it up to the 
level of current where CI = CII gives you "normal"operation, and flowing 
more than this level allows for measuring higher oxygen levels without 
going exponential.(or leaving VII = 0.45 volts)

So we can now just vary the current into the C1-CII cell, using the
V II reference voltage as the control signal.  Then the temperature 
compenstation must be done.  This is where some speculation was done.
I suggest that if you're dumping x current into the ion pump, and are 
measuring the voltage PhiI, you can relate the Voltage drop to the 
temperature. This transport rate changes for both of the cells, but it
should vary exponentially with temperature as per an arhenius relationship, 
doubling about every ten degrees. Remember that T is found in our nerst 
equation, so there another clue.

If I was a genius at this I could have done it in two lines, sorry about
the length.  I hope a cheap DIY circuit does surface on this list.
I will be happy to continue contributing to the development as best I can.
If your head hurts by now, I feel your pain! 8-}

paul timmerman