Contribution of chain entangling

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. 

Batsberg W, Kramer O (1981) A direct experimental determination of the elastic contribution of chain entangling in a tightly cross-linked elastomer. J Chem Phys 74(ll) 6507-6508... 

In comparison with traditional cross-hnked polymers, in IPNs, due to the principle of their formation, there should be a strong contribution of chain entanglements into the effective network density. The effective network dens-... 

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. 

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. 

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. 

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). 

For melts of long chains containing short chains, the contribution of the unentangled component is in some cases non-negligible and has to be removed from the data of the blend in order to isolate the contribution of the entangled component ... 

The elastic modulus of networks with pendant chains, measured at low frequencies, shows very good agreement with values calculated from theory of elasticity when contribution of molecular entanglements is taken into account. 

In contact mode AFM, where the normal force is the detected signal, there can also be a large contribution from lateral or shear forces. These can be significant enough so as to lead to deformation, abrasion and wear. These are generally not desired, however, this behavior has been used to probe the role of chain entanglements in polystyrene films as a function of molecular weight [119]. 

Our understanding of networks is in a rather similar situation. It has been known for a long time, as Fig. 4.1 illustrates, that the noncrossability of the chains plays an important role. Experiments on the modulus of melts, cross-linked at different initial concentrations directly prove this point. However it is not clear how this comes about and what the actual contributions of the entanglement compared to the crosslinks are. The reason for this is twofold. First, experiments which allow good control of aU the microscopic parameters are very difficult to perform. Theoretical descriptions are very complicated and usually contain several adjustable parameters, which are related to microscopic details, which are almost impossible to determine uniquely from experiment. ... 

The deviations that are observed from either the free-growth or Avrami relations can be attributed in part to the general problem encountered in homopolymer crystallization, i.e. the role of chain entanglements. In addition, there is a major contribution to the deviations due to the decreasing availability of eligible sequences as the transformation proceeds. This is due to the decrease in the undercooling at constant temperature. As a consequence, in contrast to homopolymer crystallization, copolymer isotherms are not superposable. Deviations from theory are observed at much lower levels of crystallinity, although the same basic type of nucleation is involved with both homopolymers and copolymers. Nucleation catalysts influence copolymer crystallization in a similar manner to that of homopolymers.(33b)... 

Experimental determinations of the contributions above those predicted by the reference phantom network model have been controversial. Experiments of Rennar and Oppermann [45] on end-linked PDMS networks, indicate that contributions from trapped entanglements are significant for low degrees of endlinking but are not important when the network chains are shorter. Experimental results of Erman et al. [46] on randomly cross-linked poly(ethyl acrylate)... 

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