AbstractTemperature dependences of diffusion and permeation coefficients of hydrogen and deuterium in glassy and rubbery polymer films have been measured. The size of the free volume element in rubbery polymers has been calculated according to the theory of Frisch and Rogers for the quantum isotope effect, but the free volume is too large for precise calculation below the glass‐transition temperature. The cooperative movement of segments is also discussed using the ratio of preexponential factors for diffusion mechanisms above and below the glass‐transition temperat