Monte Carlo calculations of hole size distributions: Simulation of positron annihilation spectroscopy

Consequences are explored of a hole size distribution in an amorphous polymer for the ortho‐positronium (o‐Ps) lifetime (τ3) and intensity (I3), determined by positron annihilation lifetime spectroscopy. The disordered lattice model, with a vacancy fraction h as a central quantity, is used to represent the equation‐of‐state behavior of the polymer. By means of Monte Carlo simulations, we obtain the cluster size distribution as a function of h and hence temperature. The predicted average cluster size and the cluster concentration are compared to τ3 and I3 data, respectively, for bisphenol‐a polycarbonate. Furthermore, the influence of an o‐Ps lifetime distribution on the experimental mean τ3 is investigated. By mimicking the computational methods used in experimental analysis, agreement between experiment and theory in respect to τ3 and to I3 in the melt ensues. In the glass, however, the experimental I3 becomes increasingly smaller with decreasing temperature than is computed. These deviations may result from a distortion of the equilibrium free volume.