Chain in networks

Number-average molecular weights are Mn = 660 and 18,500 g/ mol, respectively (15,). Measurements were carried out on the unswollen networks, in elongation at 25°C. Data plotted as suggested by Mooney-Rivlin representation of reduced stress or modulus (Eq. 2). Short extensions of the linear portions of the isotherms locate the values of a at which upturn in [/ ] first becomes discernible. Linear portions of the isotherms were located by least-squares analysis. Each curve is labelled with mol percent of short chains in network structure. Vertical dotted lines indicate rupture points. Key O, results obtained using a series of increasing values of elongation 0, results obtained out of sequence to test for reversibility. 

Figure 1.9 Plot of concentration of polystyrene chains, Q, vs fraction p of monofunctional chains in networks swollen with benzene p = r mf...

These varied aspects of the C2 stress suggest that it is associated with entangled chains in networks (Fig. 6) and specifically that it arises from restrictions on the conformations available to entangled chains, different from those operating at crosslink sites [7-9], Prager and Frisch [10] have pointed out that chains involved in model entanglements are governed by different statistics their conclusions are quite consistent with what is known of the C2 stress. 

Terminal Relaxation Time of Pendant Chains in Networks with Approximateiy 20 wt% of iUlonofunctionai Chains... 

Neutron scattering is being used in a wide variety of applications in the study cf polymer structure. These include studies of dimensions of polymer chains in solution, conformation of chains in networks to test theories cf rubber elasticity, miscibility of blends, structure of block copolymws and semicrystalline polymers, and size and shape of bio-macromolecules. Adsorbed polymer layers can be studied by neutron reflectivity. 

Figure 4.13 Plot of ln[p(r)] vs at 298 K for polydimetbyl siloxane chains of 40 bonds compared with Gaussian and Langevin treatments of the freely jointed chain. (Reproduced from Stepto, R.F.T. and Taylor, D.J.R. (1995) Molecular modeling of the elastic behavior of polymer-chains in networks - comparison of polymethylene and poly(dimethylsiloxane). /. them. Soc. Faraday Trans., 91, 2639. Copyright (1995) Royal Society of Chemistry.)...

More recently, it has become apparent that polymer chains in networks are not as ideal as assumed in the formulation of statistical models, and there has been a shift in emphasis towards the less than ideal, perturbed and possibly inhomogeneous networks which are more frequently encountered in practice. The continuum approach, however, had to be developed before inhomogeneous systems could be described the present volume, therefore, contains both views. 

Chains in Networks. One of the first studies of chains in networks is by Gao and Weiner (235) where they performed extended simulations of short chains with fixed (affinely moving) end-to-end vectors. The first extensive molecular dynamics simulations of realistic networks were performed by Kremer and collaborators (236). These calculations were based on a molecular dynamics method that has been applied to study entanglement effects in polymer melts (237). The networks obtained by cross-linking the melts were then used to study the effect of entanglements on the motion of the cross-links and the moduU of the networks. The moduli calculated without any adjustable parameters were close to the phantom network model for short chains, and supported the Edwards tube model for long ones. Similar molecular dynamics analyses were used to understand the role of entanglements in deformed networks in subsequent studies (238-240). 

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