Absorbance spectra of two ionic liquids, the short alkyl chain N-trimethyl-N-propylammonium bis (trifluoromethanesulfonyl) imide (TMPA-TFSI) and the longer chain N-trimethyl-N-hexylammonium bis(trifluoromethanesulfonyl)imide (TMHA-TFSI) are reported as a function of pressure and temperature. The occurrence of various phase transitions is evidenced by the changes in the relative concentration of the cisoid and transoid conformers of their common TFSI anion. The infrared spectrum of TMPA-TFSI was measured at 300 K with an applied pressure varying over the 0-5 GPa range. Above 0.2 GPa only the trans conformer is detected, suggesting the occurrence of a pressure induced crystallization. When pressure is applied to TMHA-TFSI at T = 310 K, both TFSI conformers subsist up to similar to 11 GPa. However, the clear change of their intensity ratio observed around 2 GPa, suggests the onset of a glass phase as supported by measurements carried out at 4.2 GPa along a cooling/heating cycle. A careful analysis of the spectra collected along different p-T thermodynamic paths shows the occurrence of a cold crystallization at 295 K on heating from 139 K along the p = 0.5 GPa isobar. The rich phase diagrams of the two ionic liquids is the result of the competition among the anion cation intermolecular interactions, the lower energy of trans-TFSI with respect to cis-TFSI and the smaller volume of cis-TFSI with respect to trans-TFSI.