JA is right. You can get truely split peaks, if your sample is injected in a buffer-type of environment at one pH and the mobile phase buffer is at another pH. His example is right on, and this is actually a not uncommon problem in dissolution testing. The analyte is dissolved in a rather strong acid at low pH, and you can get two peaks, if your mobile phase is in a rather weak buffer at a drastically different pH, where the analyte would be predominantly in a different form than at the acidic pH used in dissolution testing. This is equivalent to the injection of a sample dissolved in DMSO, where a large fraction of the analyte never gets out of the DMSO and is properly retained on the RP column. In this case, you also get two peaks: the analyte comigrating with the DMSO peak and the sampel properly retained by RPLC.
But this does not mean that you can separate the ionic form from the non-ionic form of the analyte. You have a situation where the analyte is not in equilibrium with the mobile phase, because it is migrating in an environment that is different from the mobile phase. You get two peaks that each depend on the local environment
To go back to Danko:
If you see a split at the peak top, or other strange peak shapes, they are in the case of simple ionizable analytes NOT due to a separation of the ionic from the non-ionic form, but due to differences in the mobile phase environment of your sample for at least some period of time during the migration process. If you get strange peak shapes, including double peaks, this does not mean that you have separated the ionic form from the nonionic form of the same substance. It only means that there was a mismatch between the injection solvent and the mobile phase. I guarantee you that I can generate a double peak for benzene, and I do not think that I will be able to make you believe that I managed to separate the benzene with the double bond on the right side from the benzene with the double bond on the left side...
And finally to YM3142: Your experiments are in agreement with expectation, including the low plate count at low retention, which is due to extra-column bandspreading.
The world of chromatography is completely intact...