Can anybody explain me (molecularly) what happens in chromatography when the stationary phase interacts with compounds. What type of interaction the column achieve with the analyte?
As general rule non-polar stationary phase tends to interact better with non-polar compounds, How?

Whew! That's a question that whole textbooks have been written about!

Probably the easiest to visualize explanation is the old "like dissolves like" rule.

If you want to take it one level deeper than that, the rule is that the total free energy of a two-immiscible-phase system is minimized when the interface surface area is minimized. If you shake oil in water, the small droplets will eventually coalesce because that minimizes the contact area. Think of a non-polar sample molecule as a little droplet of oil and the stationary phase surface as a larger drop of oil.

At one level deeper, we can start to talk about hydrophobicity (more generally, "solvophobicity") of analytes and stationary phase surfaces, but at that point, we have to rely less and less on analogies and more and more on mathematical models.

When all is said and done, all of these explanations are mental constructs (analogies) that we use to impose conceptual order on a set of complex phenomena.

-- Tom Jupille / LC Resources Inc.

There is a nice book that systhematically explains the molecular level of intermolecular interaction between the LC components and an analyte. It is "Quantitative Structure-Chromatographic Retention Relationships" written by Roman Kaliszan, published by Wiley Interscience in 1987. I recommend you the chapter 2.
Best regards,
Maciej Turowski
Kyoto Institute of Technology

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