Quantifying primary loops in polymer gels by linear viscoelasticity.

In polymeric gels, basically two species of cross-links exist: those contributing to the network and those that don’t. Zhou et al. (1) suggested network disassembly spectrometry to determine the content of loops— the simplest kind of network defects in gels. Although cross-links contributing to the network hold the gel together and are thus desirable, the noncontributing links (e.g., the loops on which the article focuses) are weak points in the gel. However, the plateau modulus G0 by rheology can yield comparable information, directly related to the concentration of cross-linkers n by G0 = nkT, where k is the Boltzmann-constant and T is the temperature. Using n, a theoretical value G0 theor can be determined, which in relation to the experimental G0 suggests which fraction of cross-linkers contributes to the network. To determine G0 theor from composition, n must be determined, which for hydrogels and other soft matter systems is not obvious because of solvent (and fillers). The work on polymer solutions (2) can be transferred to chemical and supramolecular cross-links as well because of equivalence with entanglements (3). For homogeneous soft matter, n = φnbulk can be assumed analogous to ref. 2, where φ is the polymer fraction and α the dilution exponent (α = 1.0-1.3). Furthermore, n can be determined by analytical methods. The most interesting question is, however, to what the degradation product and the rheological method are sensitive. As there is no direct comparison so far, theoretical considerations have to be applied. Basically, three kinds of errors in the network have to be distinguished: loops, isolated chains, and dangling ends (segments connected to the network on one end). Although the rheological behavior will be sensitive to all three categories (lowering G0 below G0 theor and increasing the phase angle δ), network disassembly spectrometry, although successfully detecting loops, might fail at the two other categories depending on the size of molecule or chain end. On the other hand, conventional spectroscopy will fail at loops but will theoretically be able to find the chemical signature of chain ends, if present in sufficient concentration. For this reason, a combination of rheology with conventional spectroscopy should reach roughly the same results for the loop content as network disassembly spectrometry, but with lower experimental challenges, as only established experimental methods—which are usually applied for soft matter systems— need to be combined. In the future, it would be interesting to compare the methods of network disassembly spectrometry and rheology/spectroscopy.