Dangling loops

AF3 is due to non-ionic interactions between dangling loops and the solvent and expressed by... 

These predictions need to be modified because real networks have defects. As shown in Fig. 7.7, some of the network strands are only attached to the network at one end. These dangling ends cannot bear stress and hence do not contribute to the modulus. Similarly, other structures in the network (such as dangling loops) are also not elastically effective. The phantom network prediction can be recast in terms of the number density of elastically effective strands v and the number density of elastically effective crosslinks ii. For a perfect network without defects, the phantom network modulus is proportional to the difference of the number densities of network strands v and crosslinks // = since there are fjl network strands per crosslink ... 

Both equalities are based on the following argument. The infinite cluster generated near Pc in general contains many dead ends and dangling loops that are connected to the backbone via a single path. Since the walk that visits such bonds is eventually terminated after a finite number of steps, the walks that survive in the limit N oo are those confined to the backbone. With Eq. (50) and the inequality ... 

An extensive Monte Carlo study was carried out by Zajac and Chakrabarti [25]. In this study the surface friction was assumed to be small. As a result, the chains adsorbing first on the bare surface rapidly unfolded to flat structures with many surface contacts and few dangling loops or ends. Late arrivals, however, were forced to adopt looser, more weakly bound conformations. Hence, one can consider the layer as consisting of two populations, one wifli the high bound fraction and one rather loosely attached. 

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. 

Mechanical properties of crosslinked elastomers are influenced not only by the volume-average crosslink density but also by network heterogeneity. The influence of structural defects (such as residual sol, dangling chains, chain loops and the heterogeneity of the junction distribution) on the viscoelastic properties and the equilibrium swelling data is still under discussion. Local methods which probe molecular properties are very suitable for the determination of the degree of network heterogeneity [11]. 

Fig. 1 Chemical and physical crosslinks associated with covalently bonded polymer gels. (A) Bi- and trifunctional chemical crosslinks (B) simple and trapped physical entanglements and (C) ineffective chemically bonded loop and dangling ends.

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