Natural rubber, cross-link density

Fig. 98.— r/(a —l/a ) for natural rubber, cross-linked to the densities (pXlOO) indicated with each curve using a bis-azo cross-linking agent. (Flory, Rabjohn, and Shaffer. )... 

Many of the most floppy polymers have half-melted in this way at room temperature. The temperature at which this happens is called the glass temperature, Tq, for the polymer. Some polymers, which have no cross-links, melt completely at temperatures above T, becoming viscous liquids. Others, containing cross-links, become leathery (like PVC) or rubbery (as polystyrene butadiene does). Some typical values for Tg are polymethylmethacrylate (PMMA, or perspex), 100°C polystyrene (PS), 90°C polyethylene (low-density form), -20°C natural rubber, -40°C. To summarise, above Tc. the polymer is leathery, rubbery or molten below, it is a true solid with a modulus of at least 2GNm . This behaviour is shown in Fig. 6.2 which also shows how the stiffness of polymers increases as the covalent cross-link density increases, towards the value for diamond (which is simply a polymer with 100% of its bonds cross-linked. Fig. 4.7). Stiff polymers, then, are possible the stiffest now available have moduli comparable with that of aluminium. 

Figure 3. Cross-link density versus curing temperature. Straight lines are drawn through data points of nature rubber (NR). ...

Both linear and branched polymers are thermoplastics. However, cross-linked three-dimensional, or network-polymers are thermoset polymers. The cross-linked density may vary from the low cross-linked density in vulcanized rubber to high cross-linked density observed in ebonite (hard rubber highly cross-linked natural rubber). 

On the other hand, if the cross-link density is low (the length of the chains between cross-links is large) and the mobility of the chains is high, the cross-linked material is called an elastomer. An example of a typical elastomer is cw-l,4-polyisoprene (natural rubber), which, by means of a cross-linking reaction with sulfur (vulcanization), gives rise to a network structure (see Fig. 1.4). 

The rate at which coals swell is dictated by the rate at which the solvent diffuses into the coal. This is controlled by solvent properties, the size of the coal particles, and the average molecular weight between the cross-links of the coal matrix (Olivares and Peppas, 1992). Coal is a glassy solid at room temperature, but transitions to a flexible state as it absorbs solvent and the flexible nature of the swollen coal suggested lower effective cross-link density, and suggested that the elasticity of the solvent swollen coal may be predominantly rubber-like. The transition from the glassy to rubbery state is generally very sharp (Olivares and Peppas, 1992). 

A typical entropy-elastic material is cross-linked natural rubber, ds-poly(l-methyl-1-butenylene) or cts-l,4-polyisoprene, as summarized in Fig. 5.166 (see also Fig. 1.15). Its extensibility is 500 to 1,000%, in contrast to the 1% of typical energy-elastic sohds. Natural rubber has a molar mass of perhaps 350,000 Da (about 5,000 isoprene monomers or 20,000 carbon backbone bonds) and is then vulcanized to have about 1% cross-links (see Fig. 3.50). A rubber with a Young s modulus of 10 Pa (depending on cross-link density) must be compared to its bulk modulus (= 1/p,... 

TABLE 15.2 The effect of UV ageing on mechanical properties and the cross-linking density of natural rubber vulcanizates containing different fillers... 

The cross-link density of the polymer network, as well as its properties, depend on the functionality, the length and the chemical nature of the polyene (R ) and thiol (R) prepolymer chains, and it can thus be tailored as desired. Low-modulus polymers suitable for adhesive applications were obtained by using aliphatic prepolymer chains, in particular with polybutadiene-based elastomers which were cross-linked very efficiently by UV-irradiation in the presence of a tri- or tetrathiol [45-48]. As only a few cross-links need to be formed between the polymer chains to make the rubber insoluble, low concentrations of thiol (2 wt%) proved to be sufficient to achieve an effective and fast cross-finking. Hardening was found to hardly occur upon UV-curing (increase of the Persoz hardness from 40 to 55 s), which is essential to ensure outstanding adhesion. At the same time, the shear adhesion failure temperature (SAFT) increased from 80 to 160°C, due to the formation of the chemical network (Fig. 4). 

Wide-angle x-ray diffraction studies of crystalline networks of both polyethylene and natural rubber show that with increasing cross-linking density there is a progressive broadening of the reflections from various crystalline planes.( 13,14,23) This broadening can be attributed to either a decrease in crystallite size, the development of ftuther imperfections in the crystals, or to strain. Irrespective of which of these... 

Bliimieh et al. have published a paper devoted to the application of the residual heteronuclear dipolar couplings in elucidation of the segmental and loeal ehain mobilities in a series of natural rubber samples with different cross-links densities. 

Andrews and Reed [31] observed an increase in radical intensity with increasing cross-link density of sulphur cured natural rubber (Fig. 7.24) using the preorientation-technique described above. This observation is well in keeping with the fact that... 

The general effect of cross-link density on the elastic modulus of an elastomer is indicated by Eq. 2.3. In their paper Landel and Fedors [189] consider the influence of a time-dependent cross-link density on the shape of the stress-strain curves of silicon, butyl, natural, and fluorinated rubbers. Introducing an additional shift-factor a related to the cross-link density, they were able to represent reduced breaking stresses as a function of reduced time in one common master curve. 

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