Functionality of cross-links

Statistical theories which predict the gel point as a function of cross-linking have been developed. While the theoretical analysis of gelation caused by the... 

Plot (7 x - TA) as a function of cross-linking using DiBencdetto s equation for poly(l,4-buladicnc) and for polystyrene. 

Plazek (183) carried out very accurate creep experiments on natural rubber as a function of cross-linking. He found that data at different temperatures could be superimposed by the usual WLF shift factors which were developed for non-cross-linkcd poiymers (27). Temperature-superposed... 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

The function of cross link requires no elaborative discussions in the matter of product design since the implications of the same on the physical properties are quite obviously mentioned in many textual treatises on cross linking of rubbers. The cross link density directly affects physical properties such as heat build up, tear strength and elongation, too. 

Fillers serve numerous functions but common to all events is their effect brought about by increasing the viscosity of the formulation. There is the strong possibility of a vigorous attack by the operating environment on what is basically the reinforcing mechanism of the elastomer in highly loaded compounds. The function of cross links requires no elaboration. How they are created and how they subsequently perform is another story told in chapter 10. 

A new area that has been examined is that of molecular dynamics in polyelectrolytes,106 where the molecular motions responsible for the glass transition have been identified. Another interesting study is the effect of molecular motion upon the ingress of solvent into polymer material, as a function of cross-linking density.107 In the particular case studied, of dioxane... 

Polymeric supports can also be used with advantage to form monofunctional moieties from difunctional (Hies. Leznoff has used this principal in the synthesis of sex attractants on polymer supports (67). Starting from a sheap symmetrical diol he blocked one hydroxyl group by the polymer. Functionalization of cross-linked polymers is mostly performed by chloromethylation (65). A very promising method to introduce functional groups into crosslinked styrene-divinylbenzene copolymers is the direct lithiation with butyllithium in presence of N,N,N, N -tetramethyl-ethylenediamine (TMEDA) (69, 70). Metalation of linear polystyrene with butyl-lithium/TMEDA showed no exchange of benzylic hydrogen and a ratio of attack at m/p-position of 2 1 (71). In the model reaction of cumene with amylsodium, a kinetic control of the reaction path is established. After 3h of treatment with amyl-sodiuni, cumene is metalated 42% in a-, 39% m-, and 19% p-position. After 20h the mixture equilibrates to affort 100% of the thermodynamically more stable a-prod-uct (72). 

A network is formed by network chains (N number of net chains) which are connected in the cross-links (junction points). The functionality / of cross-links (number of chains connected in a junction point) depends on their chemical nature, e.g., on the cross-linker. In a perfect network each network chain starts in one junction point and ends in another one. A real network is imperfect, but it can be described by two quantities, the network cycle rank and the number of junction points p/. 

For temperature function of cross-linked polymers a-relaxation times was suggested following equation ... 

FIGURE 60.6. (a) Phonon velocity in linear polydimethylsiloxane as a function of the molecular weight, (b) Phonon velocity in rubbery PDMS as a function of cross-link density. Here Oc is the average number of monomer units between cross-links and is directly proportional to Me [11]. Reprinted with permission from Shingo Kondo and Takashi Igarashi, Journal of Applied Physics, 51, 1514 (1980). Copyright 1980, American Institute of Physics. 

From this point of view, degraded networks differ from ideal networks in which fracture properties are generally a decreasing function of cross-link density (Crawford and Lesser, 1999 Pascault et al., 2002). Little is known on the quantitative relationships between chain scission and embrittlement in networks. 

FIGURE 8.37 Dependence of TVEX capacity on TBP content as a function of cross-linking degree 1-10% DVB, 2-20% DVB, 3-30% DVB. 

Figure 1 shows a schematic representation of a polymer gel. Black circles denote cross-links between polymer chains. The number of chains bound to a given cross-link is called the functionality of the cross-link. Often the functionality of cross-links equals to 4 like in the gel depicted in Figure 1. 

Perez-Baena et al. expanded on this work and determined the relationship between intrinsic viscosity and molecular weight of SCNPs as a function of cross-linking density. ... 

The polymer is located not only around and between the microfibrils and matrices, but also at the interprotofibrillar and interstitial regions of microfibrils. In terms of either histological or supramolecular structure, the distribution of pol3nners is characteristic of the structure of wool itself as a function of cross-link density in many type of aggregates in wool. 

Coneski, P.N., Rao, K.S., Schoenfisch, M.H. Degradable nitric oxide-releasing biomaterials via post-polymerization functionalization of cross-linked polyesters. Biomacromolecules 11(11), 3208-3215 (2010)... 

Polymeric reagents and catalysts have evolved from the polymers used in ion exchange and in solid phase peptide synthesis. Most ion exchange resins are prepared by functionalization of cross-linked polystyrenes, and are used for water purification and as acidic and basic catalysts. Peptides are synthesized on similar polystyrene supports. Multistep modifications of polymers are used to produce non-commercial reagents and catalysts. However, peptide and nucleotide syntheses still provide the best-developed examples of polymeric reagents, and ion exchange resins are the most widely used polymer-supported catalysts. 

Figure 1. The polymer-solvent interaction parameter % in reduced form as a function of cross-link density for poly(isoprene) rubber cross-linked with dicumyl peroxide and showing the effect of cross-link density on x- (After reference 4).

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