We assess the nature of the chemical environment of free volume "holes" in polymers of different chemical compositions using positronium annihilation spectroscopy. After the subtraction of a narrow parapositronium component obtained from a three-Gaussian fit from the conventional Doppler broadened annihilation energy line, the remaining broad distribution can be related to the nature and density of the chemical species in the vicinity of the holes. Element specific information on the annihilation site can be expressed in terms of an integral parameter, e.g., the normalized peak height. This method has an advantage in that it can be used as a fast and routine method.