Heat capacity in the 1 K range and close to T-g was studied in a series of poly(n-alkyl methacrylate)s, PnAMA, including some random copolymers. We report on two findings: (i) The glass transition temperature T-g and the cooperativity of the a process that freezes-in at T-g, N-alpha(T-g), decrease smoothly between methyl (PMMA) and hexyl member (PnHNTA); the cooperativity from N-alpha(T-g) = 35 to N-alpha(T-g) approximate to 1. (ii) The tunnel density measured in the 1 K range as c(1) constant of the heat capacity function increases between PMMA and the ethyl member (PEMA), shows, after a maximum near PEMA, a sharp drop (factor of 6) to the butyl member (PnBMA), and remains constant at a low level up to the octyl member (PnOMA). The cooperativity of the a process near T-g and the tunnel density will be correlated assuming that freezing-in (vitrification) fixes the dynamic heterogeneity in the self-organized equilibrium liquid near T-g. We try to explain how freezing of dynamic heterogeneities in the PnAMA series is responsible for the trend in the tunnel density including the sharp drop: Freezing-in of cooperativity shells around Glarum defects forms some vaults that enlarge the free volume near these defects in comparison to a situation without vaults. The maximum in c(1) is promoted by this additional free volume; the drop in c(1) is caused by a vault breakdown effect if the cooperativity shell is too small for vault formation, N-alpha(T-g) < 15.