Many aromatic molecules self-associate in aqueous solutions into dimers, trimers, and higher order one-dimensional aggregates. They self-assemble due to the pi-pi stacking interactions in supramolecular structures with a length distribution determined by the size-dependent association equilibrium constants. Due to their low solubility, in many experiments the aromatic molecules are dissolved in their cationic form. The presence of the localized positive charge promotes a new type of binding led by the cation-pi interaction. Accordingly, in the case of aromatic molecules dissolved in water in their cationic form, at least two types of aggregates may appear: the rodlike aggregates stabilized by pi-pi stacking, and dimers coupled by the cation-pi interaction. The heat exchange which accompanies the association (dissociation) processes offers the most direct way to determine the characteristic thermodynamic parameters. The heat exchange that arises at each dissociation event has been measured by isothermal titration calorimetry (ITC) on a test molecule whose self-association properties are already known: ciprofloxacin hydrochloride. The fitting protocol relies on the recently developed DK self-association model which describes in a rigorous manner the size distribution of molecular aggregates in solution.