End-linking networks

The SANS experiments of Clough et al. (21) on radiation crosslinked polystyrene are presented in Figure 9, and appear to fit the phantom network model well. However, these networks were prepared by random crosslinking, and the calculations given are for end-linked networks, which are not truly applicable. 

Figure 4. Frequency dependence of the storage modulus G at 303 K. Key PDMS-B11, (comblike crosslinks) , PDMS-C1, (tetrafunctional cross-links, randomly introduced) PDMS-A2 (tetrafunctional cross-links, end-linked network).

Figure 6. Sketch of expected variation of the initial (c0) and residual (cr) concentration of functional groups, reaction conversion , and the ratio ve/Te in end-linked networks as a function of molecular weight of elastomer component M. For discussion see text.

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. 

It is shown that model, end-linked networks cannot be perfect networks. Simply from the mechanism of formation, post-gel intramolecular reaction must occur and some of this leads to the formation of inelastic loops. Data on the small-strain, shear moduli of trifunctional and tetrafunctional polyurethane networks from polyols of various molar masses, and the extents of reaction at gelation occurring during their formation are considered in more detail than hitherto. The networks, prepared in bulk and at various dilutions in solvent, show extents of reaction at gelation which indicate pre-gel intramolecular reaction and small-strain moduli which are lower than those expected for perfect network structures. From the systematic variations of moduli and gel points with dilution of preparation, it is deduced that the networks follow affine behaviour at small strains and that even in the limit of no pre-gel intramolecular reaction, the occurrence of post-gel intramolecular reaction means that network defects still occur. In addition, from the variation of defects with polyol molar mass it is demonstrated that defects will still persist in the limit of infinite molar mass. In this limit, theoretical arguments are used to define the minimal significant structures which must be considered for the definition of the properties and structures of real networks. 

Segmental orientation in model networks of PDMS in uniaxial tension is measured by infrared dlchroism, Measurements are made for four tetrafunctlonal end-linked networks. Results of experiments are compared with predictions of calculations based in (i) the widely used Kuhn expression and (ii) the RIS formalism. The Kuhn expression is found to considerably overestimate the segmental orientation. The RIS approach leads to values of segmental orientation that fall between predictions of the affine and phantom network models. This indicates that the nematic-like Intermolecular contributions to orientation are not significant. 

To probe the 1/N dependence in the slope F, experiments were carried out on model end-linked networks with different precursor chain lengths (average molecular weight Mn varying from 3100 to 23000 g.mol 1) [55, 56]. As expected, the slope F decreases when N increases. However, it does not follow a 1/N variation F varies only by a factor of about 3 as N varies by a factor of 7. In an end-linked network, N should not be simply assimilated with the length of precursor chains, since trapped entanglements may play the role of effective crosslinks (often denoted as physical crosslinks), in addition to chemical... 

Filled squares and diamonds are data on vulcanized natural rubber from R. S. Rivlin and D. W. Saunders, Philos. Trans. R. Soc. London A 243,251 (1951). Filled and open circles are PDMS network data of H. Pak and P. J. Flory, J. Polym. Set, Polym. Phys. 17, 1845 (1979). Triangles and inverted triangles are PDMS network data of P. Xu and J. E. Mark, Rubber Chem. Technol. 63,276 (1990). Part (b) demonstrates the universal form of Eq. (7.65) and also includes simulation data on end-linked networks with Ng = 35 (open squares),... 

Constraint release effects are expected to be responsible for the different experimental results collected for end-linked networks and for networks made by the cross-linking of primary chains much longer than the resulting network chains. The different degree of completeness of the networks has to be considered as the main reason for these differences. 

Stepto, R. F. T. Cail, J. I. Taylor, D. J. R., Predicting the Modulus of End-Linked Networks from Formation Conditions. Macromol. Symp. 2003,200, 255-264. 

For a perfect end-linked network of functionality phantom modulus can be obtained from Eq. (5) ... 

F%. 9. Dependence of the ratio between 2C, and the phantom modulus on the number-average molecular weight of primary chains for imperfect tetrafunctional end-linked networks Mark (O) Llo-rente (x) Llorente (-I-) Meyers... 

The problem of counting the numbo of effective chains and junctions in an imperf t network has not yet been solved. In the case of end-linked networks, two points rf view can be considered. 

This Section is concerned with formulas to obtain p, v, T, and f from the sol fraction w, by the branching theory for end-linked networks. 

In the above, Hinkley et al. (99), Clough et al. (100,101), and Benoit et al. (94,95) utilized end-linked networks. Ullman (103,104) delineated the differences between the two types of network. He pointed out that randomly cross-linked chains deform to a greater extent than end-linked chains, that sensitivity to network functionality is much greater for end-linked chains, and that for high cross-linking levels, the randomly cross-linked chain approaches the macroscopic deformation of the sample. Ullman (105) recently reviewed these and other SANS experiments on the deformation of polymer networks. 

Knight, P.T., K.M. Lee, T. Chung, P.T. Mather (2009), PLGA-POSS end-linked networks with tailored degradation and shape memory behavior. Macromolecules, 42(17) pp. 6596-6605. 

Fig. 4.25 Sample conformations of five randomly taken strands from the end-linked network with N = 100. The first conformations are large spheres, while the subsequent conformations are only shown as points. The total time elapsed between the first and last conformation is ISOOOr. (From Ref. 162).

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