Measuring potential difference between electrodes

[johnerrington]

generally +-12V supplies are inconvenient.
You need to condition the signal from your sensor to a voltage that lies within the range of the ADC.
The sensor can produce a voltage in either direction.
The easy way to do this is to use a circuit like this:

Using Operational Amplifiers in your Arduino project

8: Example 2. Amplifying a signal from a sensor when it has an offset voltage Many common sensors will produce a voltage that does not "sit" on the 0V rail, as shown in the blue line in this example. [opamp signals3.png] The green signal is too small (say 0.04V) to measure with any accuracy; however by amplifying it by 100 we get a signal of around 0.04*100 = 4V that can be measured. However the signal on the blue line is small, but has a dc offset of about 2.5V; multipling that by 100 gives…

that will give a value of 3.3V /2 for 0V input.
You can choose R2/R1 to give the gain you need, that will keep the voltage within the ADC range.
To get a higher input resistance you could go to R2=100M.

I'd suggest you choose an op amp from the table in that tutorial - say an MCP6002

A 741 will not give a suitable output with single ended or even +-3.3V supplies. Dont bother generating a negative supply, there is no need with modern rail-rail op amps.