Polyhydroxamic acid (PHA) from polymethacrylamide (PMAA) was prepared. Chromium chloride (CrCl3) and ferric chloride (FeCl3) salts were added to the polymer in order to increase its electrical conductivity, i.e., the dopants help produce semiconducting properties. The positron annihilation lifetime technique spectroscopy (PALS) was used to study the changes in the free volume as a function of FeCl3 and CrCl3 concentrations. ortho-Positronium lifetime components were used to estimate the free volume parameters. It was found that the hole size and the total free volume fraction decreased with FeCl3 concentration. On the other hand, the hole size increased slightly with CrCl3 concentration and then decreased, while the total free volume fraction increased continuously. The free volume distributions were determined from ortho-positronium distributions. The electric conductivity as a function of FeCl3 and CrCl3 concentrations showed fluctuation behavior and showed a continuous increase with the increase in temperature. The correlation between positron annihilation parameters and electric conductivity were discussed.