Chain entangling, contribution

Like PEO-LiCl04, a 6 1 crystalline compound is formed but, in this instance, the weakened interactions between polymer chains [18] contributes to the lowest melting point for any PEO-salt crystalline complex. A eutectic with composition 0 Li = 11 1 forms, provided the PEO molecular chain length is beyond the entanglement threshold [31]. For lower molecular weights, the 6 1 compound dose not crystallize in the presence of excess PEO and a crystallinity gap exists over the range 6 l < 0 Li < 12 1 [26]. 

In the perspective discussed in the present contribution, bundle formation occurs within the amorphous phase and in undercooled polymer solutions. It does not imply necessarily a phase separation process, which, however, may occur by bundle aggregation, typically at large undercoolings [mode (ii)]. In this case kinetic parameters relating to chain entanglements and to the viscous drag assume a paramount importance. Here again, molecular dynamics simulations can be expected to provide important parameters for theoretical developments in turn these could orient new simulations in a fruitful mutual interaction. 

For imperfect epoxy-amine or polyoxypropylene-urethane networks (Mc=103-10 ), the front factor, A, in the rubber elasticity theories was always higher than the phantom value which may be due to a contribution by trapped entanglements. The crosslinking density of the networks was controlled by excess amine or hydroxyl groups, respectively, or by addition of monoepoxide. The reduced equilibrium moduli (equal to the concentration of elastically active network chains) of epoxy networks were the same in dry and swollen states and fitted equally well the theory with chemical contribution and A 1 or the phantom network value of A and a trapped entanglement contribution due to the similar shape of both contributions. For polyurethane networks from polyoxypro-pylene triol (M=2700), A 2 if only the chemical contribution was considered which could be explained by a trapped entanglement contribution. 

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

Ronca and Allegra (12) and Flory ( 1, 2) assume explicitly in their new rubber elasticity theory that trapped entanglements make no contribution to the equilibrium elastic modulus. It is proposed that chain entangling merely serves to suppress junction fluctuations at small deformations, thereby making the network deform affinely at small deformations. This means that the limiting value of the front factor is one for complete suppression of junction fluctuations. 

Networks with tri- and tetra-functional cross-links produced by end-linking of short strands give moduli which are more in accord with the new theory if quantitative reaction can be assumed (3...13) However, the data on polydimethylsiloxane networks, may equally well be analyzed in terms of modulus contributions from chemical cross-links and chain entangling, both, if imperfect reaction is taken into account (J 4). Absence of a modulus contribution from chain entangling has therefore not been demonstrated by end-linked networks. 

Figure 3. Modulus contributions from chemical cross-links (Cx, filled triangles) and from chain entangling (Gx, unfilled symbols) plotted against the extension ratio during cross-linking, A0, for 1,2-polybutadiene. Key O, GN, equibiaxial extension , G.v, pure shear A, Gx, simple extension Gx°, pseudo-equilibrium rubber plateau modulus for a polybutadiene with a similar microstructure. See Ref. 10.

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

A new stress-relaxation two-network method is used for a more direct measurement of the equilibrium elastic contribution of chain entangling in highly cross-linked 1,2-polybutadiene. The new method shows clearly, without the need of any theory, that the equilibrium contribution is equal to the non-equilibrium stress-relaxation modulus of the uncross-linked polymer immediately prior to cross-linking. The new method also directly confirms six of the eight assumptions required for the original two-network method. 

If we accept an elastic contribution from chain entangling in cross-linked networks, the problem is to find the relative magnitudes of the contributions from chain entangling and from cross-links. 

Since the two effects work in parallel in ordinary networks, it is necessary to know the concentration of effective cross-links and to have a molecular theory which correctly relates the modulus to the concentration of cross-links. The contribution from chain entangling is then found as the difference between the observed and the calculated modulus. This seems to be an almost hopeless task unless the network structure is very simple and the contribution from chain entangling is large. 

The challenge is therefore to develop an experiment which allows an experimental separation of the contributions from chain entangling and cross-links. The Two-Network method developed by Ferry and coworkers (17,18) is such a method. Cross-linking of a linear polymer in the strained state creates a composite network in which the original network from chain entangling and the network created by cross-linking in the strained state have different reference states. We have simplified the Two-Network method by using such conditions that no molecular theory is needed (1,21). 

In addition to the contribution of intermolecular forces, chain entanglement is also an important contributory factor to the physical properties of polymers. While paraffin wax and HDPE are homologs with relatively high molecular weights, the chain length of paraffin is too short to permit chain entanglement, and hence lacks the strength and other characteristic properties of HDPE. 

During this same period, the equilibrium stress-strain properties of well characterized cross-linked networks were being studied intensively. More complex responses than the neo-Hookean behavior predicted by kinetic theory were observed. Among other possibilities it was speculated that, in some unspecified way, chain entanglements might be a contributing factor. 

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