Tetrabutylammonium iodide is used to catalyze the C-alkylation of a substituted cyclohexanone shown in the diagram.
It is reasonable to assume that the role of the iodide is to form in situ the more reactive 3-iodo-1,1-dimethoxypropane from the bromo derivative.
It is also reasonable to assume that t-butoxide was chosen as the base to avoid hydrolysis of the ester if a base such as NaOH would have been used. The pKa of the methylene alpha to the carbonyl being deprotonated should be within the range of 16-23 for which PTC-NaOH reactions excel. This is taught in the 2-day course “Industrial Phase-Transfer Catalysis.”
Since the reaction is performed in t-butanol, it is likely that the tetrabutyl ammonium iodide is simply a source of soluble iodide and not an actual phase-transfer catalyst from a mechanistic standpoint, since the reactants are likely soluble in t-butanol.
One interesting aspect of the procedure is that the cyclohexanone substrate, the t-butoxide in t-butanol and the tetrabutylammonium iodide were mixed for hours with heating before starting to add the 3-bromo-1,1-dimethoxypropane. This is curious since the acid-base neutralization should be instantaneous and there would be no need for the tetrabutylammonium iodide to be present for the neutralization.
In fact, the more that the tetrabutylammonium cation is needlessly exposed to strong base and heat, the higher the probability of experiencing Hofmann Elimination that decomposes the quat cation. Then again, the reaction appears to proceed in the presence of only 1.3% quat iodide. So, maybe the quat survives this heat history.
We do not know if the 51.5% isolated yield is due to taking a high quality distillation cut or if the conversion was low. If the conversion was low, it would be worthwhile to observe whether the quat cation decomposed during the exposure to the butoxide base which doesn’t have a readily apparent reason for being present during the 4 hours of heat history.