Reply to Stadler: Combining network disassembly spectrometry with rheology/spectroscopy

We thank F. Stadler for his comments (1) regarding our report (2); we agree with his assessment in many ways. For example, as suggested in the last line of Stadler’s letter, we completely agree that it will be interesting to compare network disassembly spectrometry (NDS) to rheology/spectroscopy. In fact, those experiments are currently ongoing in our laboratories. We agree with Stadler that measurement of the plateau modulus, G₀, by rheology can “yield comparable information” to NDS, with a combination of rheology and spectroscopy reaching “roughly the same results for the loop content as network disassembly spectrometry…” Both this rheology method and the related gel-point delay method have been carried out for many decades as methods to estimate loop fraction (3, 4).

The key problem with both rheology/spectroscopy and gel-point delay are that these methods rely on unproven assumptions about network structure to estimate, rather than directly measure, the loop fraction. Both methods assume knowledge of the value of a theoretical parameter (e.g., the modulus of an ideal network, G₀^ideal, for rheology), and they then assume that deviations from this value arise solely from the presence of loops in the network. Clearly, such methods will depend on the model chosen to obtain the theoretical parameters. In the case of rheological measurements, one could use affine network theory, as proposed by Stadler, or phantom network theory, which is advocated by other researchers. Regardless of the choice of model, the assumption is made that all bridges are elastically effective and all loops are elastically ineffective, ignoring the potential effects of higher-order topological structures or physical chain entanglements (e.g., concatenated loops). Because of these higher-order topological effects, there are many ways one can envision preparing polymer networks with identical mechanical properties but varying loop fractions. Therefore, these classic methods can only provide an estimate of the loop fraction within a gel.

In contrast, NDS is a direct method for counting loops and dangling chains in polymer networks. There is no need to use concepts or assumptions from theory to, for example, calculate a maximum theoretical modulus, G₀^ideal. The product ratio measured by NDS directly yields the number of loops independent of the modulus and independent of any assumptions about the structure or higher-order topology of the gel.

We reiterate that NDS provides both the loop and dangling chain content in the same experiment. NDS even provides the type of dangling chain. As shown in figure 2C of our report (2), the disassembly products for each dangling chain have unique masses: they can be separately identified. We show examples in figure 4 B and D of our report (2). As Stadler points out, spectroscopy is “able to find the chemical signature of chain ends, if present in sufficient concentration” (1). We wish to note that we were unable to measure the number of dangling chains in these materials by absorbance spectroscopy; NDS showed that they were indeed present.

Again, we are most excited about the potential for NDS to provide interesting insights when used in combination with classic methods, like rheology and modern spectroscopic techniques (5). We thank F. Stadler for pointing out this intersection, and for the opportunity to further discuss NDS in the open literature.