Lossless compression technique for digital signals in an embedded system
Compression is all about finding the redundancies in the data and removing them. Since you don't seem to be able to tell us much about your actual data sets, this answer will have to be very generic.
I gather that &quot;potentiostat&quot; data is continuous, varies slowly in general, but might have small deviations from sample to sample. One good way to encode this in 15-minute (450 sample) blocks would be to fit a first-, second- or third-order (or more, depending on the general nature of your data) polynomial to the block of data to capture its overall shape.1
The block would then be encoded as the parameters to that polynomial (perhaps four 16-bit numbers), plus the individual sample deviations from that polynomial, which presumably can be much smaller numbers — perhaps 450 3- or 4-bit numbers, for a total of 1414 or 1864 bits instead of the original 7200 bits — a compression ratio of roughly 4 or 5 to 1.
If you find that you can't use a fixed width for the sample deltas, consider using Huffman encoding to represent them — small values get short codes, while the presumably rarer large values get longer codes. You should still be able to get a compression ratio around 3 to 1, again, depending on your data.

1 If it turns out that the data has a cyclic component, it might be more useful to use autoregression or Fourier analysis to identify the key periodic components (frequency, phase and amplitude), and then record the individual sample deltas from the function defined by those parameters.