I think you're asking about the volume of buffer to use OUTSIDE the D-Tube. The answer depends on how clean you want your sample. If you start with 100x the sample volume you'll theoretically remove 99% of the small molecule impurities at endpoint. If you replace the buffer and dialyze again, you'll remove 99.99% of impurities.

Millipore offers D-Tubes with various cutoff membranes. You need to use one with a cutoff that is larger than your unconjugated peptide MW yet smaller than your nanoconjugate. If your peptide is much smaller than the cutoff then the dialysis will reach equilibrium in 2-3 hours. If it's close you should run it overnight.

Thank you @ Dr. John Carter for the response nd suggestions.