Scaling behavior of free-volume holes in polymers probed by positron annihilation

Positron lifetimes in polybutadiene (PB) and polypropylene (PP) are measured as functions of temperature in the range 95--305 K and 95--370 K, respectively. From the variations of ortho-positronium (o-Ps) lifetime τ₃, we have determined the glass transition temperatures Tg in PB and PP and the excluding temperature Tₑ in PB, beyond which the o-Ps lifetime τ₃ in PB is saturated. From the analogy of the temperature-dependent o-Ps intensity I₃ in PB and PP, high- and low-density polyethylene (HDPE and LDPE), we propose that above the glass transition temperature Tg the o-Ps intensity I₃ exhibits the scaling relation I₃{~}(T-Tg{)}^{{{β}}}$ in these polymers. The data also indicate the existence of a crossover temperature ${T}c$, located above ${T}g, where the β value changes greatly. When{T}gT≤{T}c, β has the order of magnitude of{10}^{{{-}}2}$. When ${T}c≤T{T}ₑ$, {β}=0.346±{}0.035 and 0.297±{}0.037 for linear polymers PB and PP. Similar features are also observed for previous results of HDPE and LDPE [D. Lin and S. J. Wang, J. Phys. Condens. Matter 4, 3331 (1992)]. The {β} values in the region of Tc{≤}TTₑ are found to be 0.336±{}0.038 and 0.507±{}0.059 for linear polymers HDPE and branched LDPE, respectively. These results reveal a common picture of hole creation above Tg in polymers, however, the concrete value of {β} may be associated with the branching structure of macromolecules.