Dear Sir;

dangling chain is another way to call branches, they are chains suspended laterally to the main backbone. Generally speaking it always related to the hysteresis of a polymeric matrix (repeated cycling under a given stress, ...and so on). Also it has a function of permanent spacer between chains insuring thus a certain free volume needed for the performance of a gel. This really a huge question, it answer constitute a big part in polymer physics science. there are so many books and book chapters on this topic. Regards

Just a small addition. As far as a polymer gel is in question, a dangling chain is in fact a defect of a polymer network structure leading to a number of deviations of the gel properties as compared to the case of ideal network. In particular, such chains are elastically inactive (thus reducing the equilibrium mechanical modulus of the material), and they can even give rise to a partially viscous low-frequency mechanical response instead if purely elastic response of an ideal network.

A hydrogel is generally a cross-linked polymer, forming a three dimensional network structure (gel) that is swelled by water (hydro). If the cross-linking reaction proceeds according to theory and stoichiometric amounts of functional groups are present, then all functional groups react to form the network. If some functional groups do not react due to incomplete polymerisation, inexact stoichiometry or reacting groups being unable to meet each other after gelation when molecular diffusion is constrained, then the unreacted groups with their chain segments will be dangling ends. As described by Evgeny Karpushkin, dangling end are elastically inactive because they are not constrained within the network, being held by only one segment end, and therefore do not return to their original conformation. As described by Abdelkader Bouaziz, dangling ends are essentially branches within the hydrogel network. Accurate stoichiometry, slow and complete polymerisation can minimise dangling chain ends, however all network polymers contain these defects.