In a recent work we studied the use of hyperbranched poly(ethyleneimine)s as polymeric modifiers in DGEBA thermosetting formulations using 1-methylimidazole (MI) as anionic initiator (Fernández-Francos X, Santiago D, Ferrando F, Ramis X, Salla JM, Serra À, Sangermano M. Network structure and thermomechanical properties of hybrid DGEBA networks cured with 1-methylimidazole and hyperbranched poly(ethyleneimine)s. Journal of Polymer Science Part B: Polymer Physics 2012:50(21):1489-1503). We reported a complex effect of the different amine modifiers on the MI networks, determined by their incorporation into the network and their structure. However, some of the statements concerning the crosslinking density and the ideality of the networks were not accurate because of a misinterpretation of the rubber elasticity expression (5) (page 1492):
Where E′r is the relaxed modulus, R is the gas constant, T is the absolute temperature at the measurement, usually 50°C above Tg∞, ρT is the density of the material, ϕ is a factor reflecting all the nonidealities and deviations from the ideal behaviour, and νe is the concentration of elastically active network chains (EANCs) or strands between crosslinking points per unit mass. This term was confused with the crosslinking density and therefore the calculation of the deviation factor ϕ was wrong. In order to be consistent, the theoretical values of νe should be obtained from the theoretical amount of crosslinks one should expect and multiplying by a factor 3/2 (assuming 3 strands per crosslink, each strand shared by 2 crosslinks). The factor ϕ calculated using expression (5) has to be corrected using the same factor.
The main conclusions of the paper are not affected but some of the statements of the original paper concerning the interpretation of the ϕ factor should be reexamined. At the end of page 1495 it is stated that, because the ϕ factor is around 1, the epoxy-amine networks have an ideal behaviour in the rubbery state. In fact, the corrected ϕ factor is around 0.7. A perfect coincidence with the theoretical value of 1 is merely fortuitous, given the error in the experimental determination of E′r. One may hypothesize, however, that a value lower than 1, in the case of epoxy-amine networks, may reflect an unequal contribution of all the strands in the network, given completeness of curing. There are very short strands involving only two methylene units between N junctions (given by the amine structure) but there are also long strands (DGEBA chains) resulting from the condensation reaction. The contribution of the different strands to the entropic deformation of the network need not be equal and therefore deviations from the affine network behaviour are expected, hence the lower ϕ.
Although the values change, the trend in ϕ (as commented on pages 1497 to 1500) is not affected by this mistake. The interpretation of this trend and the discussion on the effect of the different modifiers or curing agents on the network mobility or network restrictions is still valid. The use of mixing rules and the discussion on the properties of the mixed networks are not affected by this error. The discussion on the dependence of the free-volume parameters derived from the TTS analysis on the crosslinking density is not affected either, although Figure 9 has been corrected using the strand density instead of the crosslinking density for νe.