Erratum : Dominance of Chain Entanglement over Transient Sticking on Chain Dynamics in Hydrogen-Bonded Supramolecular Polymer Networks in the Melt (Macromolecules (2018) 51 L 8 (2859−2871) DOI: 10.1021/acs.macromol.7b02180)

Abstract

In our article, our conclusion was that the diffusive mobility of chains in hydrogen-bonding transient networks is more decelerated by chain entanglement than by associative interactions between the chains. We came to this conclusion by the results of fluorescence recovery after photobleaching (FRAP) experiments on a series of such networks containing a small amount of fluorescently labeled chains. These tracer chains had identical molar mass and associative-group contents as the unlabeled polymer matrixes. We observed that the deceleration of the tracer diffusion by an increasing mole percentage of associative groups due to the formation of transient bonds to the matrix appeared to be weaker at stronger extent of chain entanglement, which led us to the conclusion named above. To further investigate the physical basis of these observations, we then performed additional research on supramolecular associative networks, which was later published in the Journal of Polymer Science, Part B: Polymer Physics (2019, (Figure presented) 57 (18), 1209-1223). In this research, a series of supramolecular associative polymer networks based on random copolymers of lauryl methacrylate and hydroxyl ethyl methacrylate, functionalized with pendant ureidopyrimidinone (UPy) groups, was studied by rheology and wide-angle X-ray scattering. In these samples, the molar mass of the precursor copolymers was varied to have 2-11 entanglements. Each precursor was then functionalized with 3-10 mol % UPy groups, which increased the mid-frequency plateau in rheology; this increase, however, was less promoted for samples with higher extents of entanglement (see Figure 1A,B). Moreover, we observed a shallowing of the power-law frequency dependence of the moduli in the flow region for samples with high entanglement and/or UPy content. We found that if the total number of UPy groups plus entanglements per polymer chain is higher than a threshold (13 for our samples), the frequency-dependent storage and loss moduli curves are parallel in the very low frequency region, with a log-log slope of ~0.5. This parallel region is accompanied by a second low-frequency plateau of the storage modulus for samples with maximum UPy content (10 mol %; see Figure 1A,B), which can be assigned to trapped segments between stable supramolecular junctions that can hold stress. This assumption was confirmed by comparison of the wideangle X-ray scattering (WAXS) patterns of samples with different total numbers of entanglements plus UPy groups. We found that only a sample with a total extent of entanglement plus UPy-association larger than the threshold named above (which then has a low-frequency plateau of its storage modulus) showed a peak at q = 4.28 nm-1, corresponding to a length of 1.4 nm (Figure 1C). This peak is interpretable as the distance of two UPy stacks aligned next to each other. On the basis of these results, we concluded that phase separation of UPy binary assemblies from the (nonpolar) precursor chain backbones and formation of stable, long-living clusters is controlled by the total number of the network junctions formed by both UPy association and chain entanglement. The formation of long-lifetime UPy clusters can be further investigated by FRAP experiments on these samples. In these experiments, again, all tracers have molar mass and associativegroup contents identical to those of the unlabeled polymer matrixes. The results show that each tracer has in fact two distinct fractions of diffusion coefficients (D) differing from one another by 2-4 orders of magnitude. The slow-D fraction can be assigned to tracers involved in stable UPy clustering, whereas the fast-D fraction can be attributed to sticky tracers in short-living binary assemblies. As an example, we compare the diffusivity of two samples with ~3 mol % UPy groups, but two different precursor molar masses (42.5 and 165.5 kg mol-1). Even for the sample made from the low molar mass precursor, with only 2 entanglements per chain, ~76% of the tracer chains are involved in the UPy clustering, and just ~24% form binary associations only (Figure 1D). At higher molar mass, with 11 entanglements per chain, ~98% of the tracers are involved in the UPy clustering. This observation is in agreement with the rheology results of these samples. The dynamic moduli of the network made from the low molar mass precursor show a crossover in the low-frequency region followed by a terminal flow process. By contrast, the dynamic moduli of the high molar mass sample show no low-frequency crossover and instead are parallel with a log-log slope of ~0.5, which confirms the dominance of long-living UPy clustering as explained above. Combination of the FRAP and rheology results therefore illustrates that upon increasing the molar mass and, with that, the extent of entanglement of the precursor polymer chains, the probability of the clustering of the UPy groups (collective assemblies) increases. In a conceptual view, this is understandable: in a sample with a high degree of chain entanglement and therefore with slow chain dynamics, the probability of a (temporarily) nonassociated UPy group to find another free UPy to form a network junction is low. Therefore, such unassociated UPy groups have a high tendency to associate to the existing network junctions, that is, to undergo clustering, by hydrogen bonding to the urethane linkers between them and the polymer backbone. According to this conclusion, we reasoned that our FRAP results can be explained in a different way instead of “dominance of chain entanglement over transient sticking”: In our original paper, we actually even mentioned that each tracer has two distinct fractions of diffusion coefficients (D) differing from one another by 2-4 orders of magnitude (see Figure 2). Just as mentioned above, the slow-D fraction can be assigned to tracers involved in stable UPy clustering, whereas the fast-D fraction can be attributed to sticky tracers in shortliving binary assemblies. Our original analysis focus and conclusion, though, was based only on the data of the latter tracers. In the limit of high molar mass, however, the probability of clustering of the UPy groups is high. Consequently, the content of UPy groups that form just binary associations is lower in comparison to samples with a similar UPy content but a lower molar mass. Correspondingly, at high molar mass, the fraction of the tracers that associate with the polymer matrix only through binary assemblies, and which therefore diffuse comparably fast, is lower than the fraction of tracers trapped by partition in stable UPy clusters (see Figure 2). Considering that our conclusion was based on the fast diffusion of these tracers only suggests that our observation of an apparently weaker dependence of the chain dynamics on the UPy content upon increase of the extent of chain entanglement should be reflected critically. The major effect of an increase of the extent of entanglement is actually that it makes chains participate in clusters and, therefore, in fact drastically reduces their mobility. Our original analysis, though, was focused only on those few chains in the ensemble that do not yet participate in that, which is because their total number of entanglements plus associations is lower than a threshold. These few chains are of course comparably fast, and an increase of their UPy content makes them just moderately slower, which is more pronounced for low than for high molar masses, because for the latter, the main effect of an increase of the UPy content is actually a different one, namely, a pronounced participation in nearly immobile clusters, that, however, were disregarded in our original analysis.