End-linked

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. 

Alkyl halides, interaction with Lewis acids 207 Amination of polymer 156 Anionic end-linking 164... 

Emulsifiers (see also Surfactants) 27, 46 End-blockers 12, 18, 19, 76 End-capping 157 End-linking processes 163 End-stoppers (see also End-blockers) 10 End-to-end cyclization 159,160 Energy, cavitation 188,189 —, electrostatic interactions 188, 189... 

The pattern and efficiencies of strand cleavage at GG steps in duplex DNA reflect the ability of a radical cation to migrate from its initial position through a sequence of base pairs. In an illustrative example, we consider the photochemistry of AQ-DNA(l), which is shown in Fig. 4. AQ-DNA(l) is a 20-mer that contains an AQ group linked to the 5 -end of one strand and has two GG steps in the complementary strand. The proximal GG step is eight base pairs, ca. 27 A, from the 5 -end linked to the AQ, and the distal GG step is 13 base pairs (ca. 44 A) away. The complementary strand is labeled with 32P at its 5 -terminus (indicated by a in Fig. 4). 

The same relation is found for the end-linking of molecules of low functionality if = 3 or 4) and for the vulcanization of long molecular chains. The second-moment average number of cross-linking sites along the chain, f2, is defined as... 

The gel stiffness, S, was also found to depend on the molecular weight of the polymer precursor. For end-linking PDMS, S decreases with increasing... 

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)... 

If cyclic molecules of PDMS are present during the end linking, they are trapped within the network if they are large enough to be penetrated by any of the precursor chains [5]. This "incarceration" process has also been successfully simulated [51]. 

Figure 6 A network having a bimodal distribution of network chain lengths. The short chains are arbitrarily shown by heavier lines than the long chains, and the dots represent the crosslinks, typically resulting from the end linking of functionally terminated chains. 

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. 

The first SANS experiments on end-linked elastomers with a well-defined functionality were carried out by Hinkley et al, (22). Hydroxy-terminated polybutadiene was crosslinked by a trifunctional isocyanate, and the resultant polymer was uniaxially stretched. 

C. C. Han, H. Yu and their colleagues (23) have presented some new SANS data on end-linked trifunctional isoprene networks. These are shown in Figure 10. Those materials of low molecular weight between crosslinks exhibit greater chain deformation consistent with the thesis that the junction points are fixed. This is the reverse of that found by Beltzung et al. for siloxane networks. 

Figure 10. SANS measurements of Rn/R,° and RL/Re° for stretched trifunctional end-linked polyisoprene. Curves 1 through 4 are theoretical. Data from...

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).

There are now a number of techniques which may be used to prepare elastomeric networks of known structure Q-8). Two particularly useful and convenient ones involve the multi-functional end-linking of hydroxyl-terminated (4-16) or vinyl-terminated polydimethylsiloxane (PDMS) chains (3,17-21), and the cross-linking of PDMS chains through vinyl side groups present in known amounts and in known locations along the chains (4,18,22-25). A typical reaction of this type is... 

Figure 2. Typical stress-strain isotherms for PDMS networks prepared by tetra-functionally end-linking very short and relatively long chains.

Chains were vinyl-terminated, and end-linked using a silane having values of the functionality . 

Figure 3. Threshold tear energy T . Key O, A, , PDMS networks , A. PB networks , PI networks versus molecular weight Mc between cross-links calculated from Ct. O, , , random cross-linking A, A. trifunctional end-linking , tetrafunctional end-linking.

As is clear from the earlier discussions of pre-gel intramolecular reaction, such reaction in principle always occurs in random polymerisations, although its amount may be reduced by using reactants of higher molar mass, lower functionalities, and stiffer chain structures. Thus, the use of end-linking reactions to produce model networks (for example(35) and references quoted... 

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. 

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