Rectification of Micro DC voltage levels?
That won't work.  It may detect ion flows and AC fields above a certain frequency, but it can't detect DC fields.  After all, the plates constitute a coupling capacitor in series with the fields you want to detect.   It's a high-pass filter.

The usual instrument for this is called a "field mill," where the detector plate is placed close behind a grounded metal propeller or rotating "sector disk."   The rotating disk chops any DC e-fields into low-freq AC, which is easily amplified/rectified/A-toD'd etc.    Perhaps even use low-pass filtering and a synchronous detector to reject any unwanted AC.

DIY e-field sensor field mill from Scientific American:  


Jul '99 The Amateur Scientist
More electrometer and Field Mill links
Besides "field mill," also search for "Electrometer"


Antenna without the field mill:  if your detector plate is 10 picofarad, and the amplifier's input is MOSFET with 100 giga-ohm Z-inp, then you've formed a high-pass filter which rejects all DC below ~1Hz (since RC is 1e11ohm * 1e-11farad)  It's possible to use a much higher-Z amplifier, plus a periodic shorting relay that "resets" the detector's input before taking data.  But then usually you'll run into unknown humidity leakage across plastic insulators, and a (drifting) high-pass period of ?tens? of seconds.   Better to just add a field mill, and measure true DC fields.

(edit) PS. Here's something I've not tried:  just build a non-fieldmill e-field antenna with well-known RC time constant of perhaps a few seconds, use high-res A/D input, then massage the numbers to cancel out the RC and restore the DC value.  Of course this includes a stage of integration, so any slight errors in zero-adjust would produce a constantly increasing drift.  The amplifier's DC-zero would need to be extremely stable across the environmental temperature changes involved.