Tetrafunctionally end-linked

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.

End linking by a condensation reaction between hydroxyl groups at the ends of a polymer chain and the alkoxy groups on a tetrafunctional end-linking agent. The number-average molecular weight of the precursor chains becomes the critically important molecular... 

Fig. 2. Dependence of the structure factor at infinite deformation on M for perfect tetrafunctional end-linked PDMS netwodcs. Mark (O) Llorente (+) Fatento (V)...

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 polymer used typically has end groups, such as hydro grls, that can participate in the hydrolysis-condensation reactions (5,9,292). Such end groups provide better bonding between the two rather disparate phases, but bonding agents may also be introduced for this purpose (293). It is thus possible to mix hydroxyl-terminated chains (such as those of PDMS) with excess TEOS, which then serves simultaneously to tetrafunctionally end link the PDMS into a network structure and to act as the source of silica upon hydrolysis (5). 

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).

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. 

Compare random crosslinking of linear precursor (with/rs A/q) and end-linking of linear precursor A o-mers with tetrafunctional crosslinkers. 

Mark and Semiyen, in a series of papers, have studied the mechanism and the effect of trapping cyclics in end-linked elatomeric networks [100-103], Sharp fractions of cyclics of polyfdimethylsiloxane) (PDMS), varying in size from 31 to 517 skeletal atoms, were mixed with linear chains for different periods of time and the linear chains were then end-linked using a tetrafunctional silane. The untrapped cyclics were extracted to determine the amount trapped. It was found that while cyclics with less than 38 skeletal atoms were not at all trapped, for n>38, the percentage of cycUcs trapped increased with size, with 94% trapped in the case of the cychc with 517 skeletal atoms. In effect, the system of trapped cycUcs in the end linked PDMS network is a polymeric catenane. It is thus possible to control the elastomeric properties of the network by incorporating the appropriate sized cyclics. This study has been extended to cyclic PDMS in poly(2,6-dimethyl-l,4-phenylene oxide) [104,105] and cyclic polyesters in PDMS [106]. 

A tetrafunctional network containing cyclics (heavy lines). Cyclics a and b were trapped by linear chains that passed through them prior to end linking into a network structure. 

If the tetrafunctional cross-links to which are connected four clmins leading to the network are suppressed, the network (first-stage) is formed only with the crosslinks having three chains connected to the mesh. Each chain end is connected to this type of cross-link, whose number density is therefore... 

The question arose whether polymer chains in a network had the same conformation as in the melt before cross-linking. Beltzung et al. (93) prepared well-defined poly(dimethyl siloxane) (PDMS) chains containing Si—H linkages in the a and positions. Blends of PDMS(H) and PDMS(D) were prepared, where H and D, of course, represent the protonated and deuterated analogues. These blends were end-linked by tetrafunctional or hexafunctional cross-linkers under stoichiometric conditions. 

Table A9.1.2 also demonstrates that at each gelatin concentration, the number of bonds per gelatin molecule is relatively constant. This number, of course, is the number of bonds taking part in three-dimensional network formation. Not all the gelatin chains are bound in a true tetrafunctionally cross-linked network. Many dangling chain ends exist at these low concentrations, and the network must be very imperfect.

This material, because of its hydrocarbon character, can be easily maintained in a dry state and interactions of SiH with moisture during end-linking will be minimized. Further, any new siloxane structures formed during end-linking can be readily detected by NMR. Bifunctional (A ) or tetrafunctional (A ) endlinkers are used with a dry catalyst, cis-[(C2H )2S]2PtCl2 dissolved in toluene solutions. 

Fig. 1.32. The ultimate strength shown as a function of the high-deformation modulus for tetrafunctional PDMS networks containing a negligible number of dangling ends (o) and dangling ends introduced by using less than the stoichio-metrically required amount of end-linking agent ( ) [130]. In the latter case, a decrease in 2C corresponds to an increase in the number of dangling ends [130]. (Reproduced with permission copyright 1981, John Wiley Sons, Inc.)...

Llorente, M. A. Mark, J. E. (1979). Model Networks of end-Linked Polydimethylsiloxane chains. IV Elastomeric Properties of the Tetrafunctional Networks Prepared at Different Degrees of Dilution. Journal of Chemical Physics, Vol. 71, No. 2, pp. 682-689, ISSN 0021-9606... 

Effects of Junction Functionality. End linking of chains with linkers of a known functionality is used to control the structure in this way. Increasing the junction functionality decreases the fluctuation amplitudes of the junctions in the undeformed state. A network with suppressed junctions behaves close to an affine network under deformation. However, the affineness diminishes under increasing extension. Trifimctional and tetrafunctional PDMS networks prepared in this way have been used to test the molecular theories of rubber... 

A typical end-linking reaction producing a tetrafunctional network is given by ... 

Fig. 11. Values of the maximum extensibility (elongation at rupture) shown as a function of the molecular weight M between cross-links for unfilled) tetrafunctional PDMS networks at 25 The results pertain to networks prepared and studied in a series of investigations and are typical for the types of cross-linking techniques employed (i) selectively end-linking a mixture of relatively long and very short chains to give a bimodal network (--X--), (ii) selectively linking a (unimodal) sample of chains either through their ends or side-chains (-0-), (iii) peroxide curing (C), and radiation curing (- -)...

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