The relaxation spectra of polymer networks with different types of topology, ordering, heterogeneity

Abstract

Many characteristic features of the relaxation spectra of the different types of polymer networks (meshlike and tree‐like) manifesting in experimental behaviour are determined by manifold types of local and long‐range irregularities or inclusions existing even in the simplest network structures. These irregularities in the local topology, in the fluctuations of the local orientational order existing due to stretching of the chains in the bulk elastomers (even in the non‐ordered elastomers), also due to possible LC‐ordering, the distribution of chain lengths between junctions and possible existence of cross‐link agglomerations and domains at random cross‐linking and the influence of the position of the chain element relative to junctions lead to variety of relaxation spectra, frequency and time‐dependencies. The long‐range hydrodynamic effects in bulk network can also lead to drastic variation of relaxation spectra. The inclusion of elongated rigid particles in polymer gels and network leads to the appearance of new branches of relaxation spectra changing and overlapping the relaxation spectra of the primary network system.

Effects of Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included rod‐like Particles: Mean‐Field Approximation

“…The use of rigid rod‐like chain segments leads to an additional splitting of branches in the relaxation spectrum of a nematic elastomer at small order parameters as compared with the spectrum predicted by the modified Gaussian subchain model 33,34,45. At high values of the order parameter, however, the above‐mentioned splitting becomes weak and “soft” Gaussian chain segments with fixed mean‐square lengths behave like rigid rods at strong ordering 33,34,45…”

“…The rods can be absorbed by network fragments and move together with them. This effect has been described in ref 33,34. by “effective” quasi‐elastic interactions between rods and network fragments.…”

“…Equilibrium and dynamic properties of rod‐like rigid segments of network strands are described here by a freely‐jointed chain model consisting of $N$ elastic elements (Gaussian subchains) 33,34,45. The energy of a single Gaussian element included in a chain stretched along the n ‐axis ( n = X , Y , or Z ) is given by where b x , b y and b z are the components of a vector $\vec b$ which connects the elastic element ends (Figure 1).…”

“…Moreover, the authors have recently considered33,34,45 the mean‐square characteristics determining relaxation times of a nematic elastomer using both the Gaussian subchain model for network strands and the chain model consisting of rigid rod‐like segments. The use of rigid rod‐like chain segments leads to an additional splitting of branches in the relaxation spectrum of a nematic elastomer at small order parameters as compared with the spectrum predicted by the modified Gaussian subchain model 33,34,45. At high values of the order parameter, however, the above‐mentioned splitting becomes weak and “soft” Gaussian chain segments with fixed mean‐square lengths behave like rigid rods at strong ordering 33,34,45…”

“…Effects of external stress on phase transitions in polymer networks with nematic fillers have been investigated by Wang 19. Although the equilibrium properties of ordered polymer networks have been considered in detail (phase separation, stress‐strain behaviour19 for both nematic elastomers,15–19 and polymer networks with nematic fillers19), there are only few studies33,34,45 devoted to the theory of local molecular mobility in ordered polymer networks. According to the theory of dynamic properties of isotropic polymer networks,6–8 local motions in a network can be represented as a superposition of two main types of motions.…”