We present a new method to accurately describe the ionization fraction and the size distribution of polycyclic aromatic hydrocarbons (PAHs) within astrophysical sources. To this purpose, we have computed the mid-infrared emission spectra of 308 PAH molecules of varying sizes, symmetries, and compactness, generated in a range of radiation fields. We show that the intensity ratio of the solo CH out-of-plane bending mode in PAH cations and anions (referred to as the 11.0 $mu$m band, falling in the 11.0-11.3 $mu$m region for cations and anions) to their 3.3 $mu$m emission, scales with PAH size, similarly to the scaling of the 11.2/3.3 ratio with the number of carbon atoms (N$_{mathrm{C}}$) for neutral molecules. Among the different PAH emission bands, it is the 3.3 $mu$m band intensity which has the strongest correlation with N$_{mathrm{C}}$, and drives the reported PAH intensity ratio correlations with N$_{mathrm{C}}$ for both neutral and ionized PAHs. The 6.2/7.7 intensity ratio, previously adopted to track PAH size, shows no evident scaling with N$_{mathrm{C}}$ in our large sample. We define a new diagnostic grid space to probe PAH charge and size, using the (11.2+11.0)/7.7 and (11.2+11.0)/3.3 PAH intensity ratios respectively. We demonstrate the application of the (11.2+11.0)/7.7 - (11.2+11.0)/3.3 diagnostic grid for galaxies M82 and NGC 253, for the planetary nebula NGC 7027, and the reflection nebulae NGC 2023 and NGC 7023. Finally, we provide quantitative relations for PAH size determination depending on the ionization fraction of the PAHs and the radiation field they are exposed to.
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