The annihilation of positrons in amorphous tetramethylpolycarbonate (TMPC) has been investigated in the temperature range from 30 to 300 K. The dependences of the mean lifetime of the ortho-positronium tau(3) and its relative intensity I-3 on temperature can be described by the empirical relations : tau(3) = 2.08(1 + 4.8 x 10(-4)T) (ns) and I-3 = 20.2(1 + 7.9 x 10(-4)T) (%). These dependencies are interpreted within the framework of the microstructural free volume concept. The comparison with the polycarbonate (PC) reveals that both values tau(3) and I-3 are larger for TMPC, indicating larger free volume realized through higher number (concentration) of larger free volume entities. The temperature dependencies of tau(3) and I-3 for TMPC exhibit a different character and a weaker dependence on the temperature. This different behaviour of the free volume is due to a different packing efficiency of chains and a different dominant mechanism of the free volume generation, as well as a decrease in the flip dynamics of the phenyl rings. The implications of different free volume microstructures on some mechanical properties (e.g. relaxation and fracture) as well as on the transport properties of gases in TMPC and PC are discussed.