What is the purpose of this op amp?
Amplifier U1 helps to make the circuit as close to "ideal" as possible. In the pH cell the impedances involved re very high and any variations from ideality are reflected in the results.
The "challenge" is given in the following section from the application note:
The output of amplifier U1, which is set up in a unity-gain configuration, biases the reference electrode of the pH electrode with the same voltage, 512 mV, at low impedance.
The pH-measuring electrode will produce a voltage which rides on top of this 512 mV bias voltage. In effect, the circuit shifts the bipolar pH-electrode signal to a unipolar signal for use in a single-supply system.
ie any error in this voltage is directly reflected in the output voltage as an error in pH reading.
The source impedance of the 2 x 10 k resistors in series is 5 K ( Reffective = R1 x R2 / (R1+ R2)). If the cell were to load this with a 1 megohm impedance the change in actual voltage would be 5k // 1 M = 0.005 = 0.5%. Loading with 10 Megohm would give 0.05% error etc. This does not sound much (& isn't much) but the sensitivity of the cell is 1 mV per pH. So 5/1000 x 512 mV ~= 2.5 mV or 2.5 pH error. And 10 megohm loading = 0.25 pH error. Even 100 megohm loading = 0.025 pH error.
If pH is read to even 0.1 pH units an error of 0.025 pH is 1/4 of a "bit". If pH was read to 0.01 units then 0.025 pH = 2.5 "bits " - and that's with 100 only megohm load!
Reducing R1 & R2 to 1 k or 100 ohms would help, at the expense of increased current drain U1 provides a better solution at acceptable cost.
The LMP7721 opamp datasheet advertises with it's extremely low input bias current. The input bias current is the current going into the input terminals of an opamp. The ideal opamp model says that's zero, but it isn't in practice.
In most cases it isn't a problem. But you're dealing here with very high impedance sources. High impedance sources means you can't draw any current out of them. As I just said, an opamp draws current as well. Why would I bother?
Well, the pH electrode is probably very very high impedance (I expect mega ohms). The input impedance of a simple ADC of a PIC or AVR microcontroller is like 10k. If you imagine a voltage source, a resistor divider of 1M and 10k and connect the 'output' of that divider to the real sampler of the ADC, what voltages do you think you will measure? I think not a whole lot..
Also, if you draw 50nA through a 1MEG resistor, it causes a voltage (drop) of 50mV. This can be very significant.
This particular opamp has a huge input impedance. The error this opamp causes with it's input bias current is very very small. The opamp is able to provide enough current to drive your ADC.
The resistor divider of the reference is a similar story. 1uA load current on R1 will mean 10mV drop, which is over 2%! Using an opamp will solve this problem.