Entanglement and network formation

Saccharide Polymers Entanglement and Network Formation - Network Tg... 

Figure 9. Plot of log viscosity + constant vs. log MW + normalization constant for a series of synthetic polymers, illustrating the generic behavior of polymers with MWs above and below the critical DP required for intermolecular entanglement and network formation. (Reproduced with permission from reference 10. Copyright 1980 John Wiley Sons.)...

An important consequence of entanglement and network formation is the effect on the Tg that determines all diffusion-limited structural and mechanical relaxation processes of the system. As shown schematically in Figure 10 (2), while the molecular or segmental Tg remains constant above the entanglement MW limit, the network Tg, i.e. the macroscopic, controlling Tg of the supramolecular network (that would affect Instron measurements of the modulus, for instance (D). continues to increase with increasing MW above the entanglement MW, because of the increased probability of crosslinks (97.101). 

Saccharide Oligomers and Polymers as Moisture Management Agents. The relationship between the solute concentration and linear DP requirements for entanglement and network formation, and its resultant effect on Tg (molecular vs. network), also has important implications for moisture management by saccharide oligomers and polymers (6.7). ... 

G and G increase as molecular weight (cure) advances. G eventually exceeds G"" as the polymer system gains elasticity due to molecular entanglement and network formation. The crossover of the G" and G " curves has been related to the gel point for these materials. 

Networks obtained by anionic end-linking processes are not necessarily free of defects 106). There are always some dangling chains — which do not contribute to the elasticity of the network — and the formation of loops and of double connections cannot be excluded either. The probability of occurrence, of such defects decreases as the concentration of the reaction medium increases. Conversely, when the concentration is very high the network may contain entrapped entanglements which act as additional crosslinks. It remains that, upon reaction, the linear precursor chains (which are characterized independently) become elastically effective network chains, even though their number may be slightly lower than expected because of the defects. 

The deformation of polymer chains in stretched and swollen networks can be investigated by SANS, A few such studies have been carried out, and some theoretical results based on Gaussian models of networks have been presented. The possible defects in network formation may invalidate an otherwise well planned experiment, and because of this uncertainty, conclusions based on current experiments must be viewed as tentative. It is also true that theoretical calculations have been restricted thus far to only a few simple models of an elastomeric network. An appropriate method of calculation for trapped entanglements has not been constructed, nor has any calculation of the SANS pattern of a network which is constrained according to the reptation models of de Gennes (24) or Doi-Edwards (25,26) appeared. 

In this case the concentration of chemically introduced crosslinks, vf, was accurately known. Assuming that there are no entanglements and no wasted crosslinks through loop formation the concentration of chemically formed network chains equals the effective number of chains, v. Proceeding in this way Van de Kraats found for a series of three gels that B = 0.5 0.1. Of course, this result should be viewed with caution because the assumption vf — r is open to some doubt. An estimate of the error on the basis of the considerations of Chapter II, Section 2.2 is not reasonably feasible. The data, of course, also yield A /B. 

Epoxy networks may be expected to differ from typical elastomer networks as a consequence of their much higher crosslink density. However, the same microstructural features which influence the properties of elastomers also exist in epoxy networks. These include the number average molecular weight and distribution of network chains, the extent of chain branching, the concentration of trapped entanglements, and the soluble fraction (i.e., molecular species not attached to the network). These parameters are typically difficult to isolate and control in epoxy systems. Recently, however, the development of accurate network formation theories, and the use of unique systems, have resulted in the synthesis of epoxies with specifically controlled microstructures Structure-property studies on these materials are just starting to provide meaningful quantitative information, and some of these will be discussed in this chapter. 

---