Respected Nebojsa Zec, if the presentation of the question is wrong, I am apologize for that!!
But unfortunately the answer is neither like a scientist nor like a researcher, not even like any professional.
May I humbly ask a question.....? " Does a answer in wrong way would help to rectify of a wrong question??" I will wait eagerly for your kind answer, Sir.
Dear Raja! I fully support Nebojsa! If you want to get a professional answer, learn how to ask a professional question. I friendly advise you to delete your posts.
In my experience, liquid-liquid extraction is the best way to purify IL. The starting compounds for synthesis (1-alkylimidazole, pyrrolidine, halogenoalkanes, etc.) are well-soluble in ethyl acetate, toluene, or some other organic solvent. The synthesized ionic liquid does not dissolve in them, so it is possible to extract the residual reactants thus. If synthesized IL is soluble in water (most of them are soluble, because IL are the molten salts), then extraction is possible with a solvent which is non-polar and water immiscible with non-water solvents (diethyl ether, toluene ...). Inorganic salts (sodium and potassium halide) are precipitate using acetone, usually. Of course, for each IL it is necessary to find the appropriate solvent (or a mixture).
Is it possible? Yes. You could probably do it on silica/ neutral alumina with solvents such as MeOH, some mixture of DCM/ MeOH (or a gradient) or what is called "magic solvent" first reported by the Stoddardt mechano chemistry group I believe. The classic ratio is 7:2:1 MeOH: 2M NH4Cl: MeNO2. You can vary the ratio of the three solvents. Obviously, this will convent your counter ion to Cl, so you do counter ion exchange after you've isolated your proper fractions.
Fair warning, Nitro methane is difficult to get rid of and that much methanol will dissolve some of your silica. So do not attempt to use this solvent mixture in a flash chromatography system. You'll ruin they system. Overall - do not recommend. I've done this when desperate. It's messy. But it works.
I'd advise making sure your starting materials are of high purity before you do your synthesis and then various washing/ liquid-liquid extractions as @Milan Vranes mentioned.
If you must do chromotography, I'd recommend reverse phase chomatography (after you've removed excess organics). Otherwise, there is a method called Dry vacuum chromatography (DVCC) or just dry column chromatogrphy (DCC) https://www.sorbtech.com/chromatography/dry-column-chromatography-dcc/ which I believe would work much better for charges organic compounds. It looks like it's basically prep scale TLC for larger amounts of compound. So it would not matter if you couldn't move your compound from the baseline. As long as everything else moves and you can extract it from your silica at the end you should be fine.