Elongation, network moduli

The Phantom Network Model. The theory of James and Guth, which has subsequently been termed the phantom network theory, was first outlined in two papers (186,187), followed by a mathematically more rigorous treatment (188-190). More recent work has been carried out by Duiser and Staverman (191), Eichinger (192), Graessley (193,194), Flory (82), Pearson (195), and Kloczkowski and co-workers (196,197). The most important physical feature is the occurrence of junction fluctuations, which occur asymmetrically in an elongated network in such a manner that the network chains sense less of a deformation than that imposed macroscopically. As a result, the modulus predicted in this theory is substantially less than that predicted in the affine theory. 

Vulcanization changes the physical properties of rubbers. It increases viscosity, hardness, modulus, tensile strength, abrasion resistance, and decreases elongation at break, compression set and solubility in solvents. All those changes, except tensile strength, are proportional to the degree of cross-linking (number of crosslinks) in the rubber network. On the other hand, rubbers differ in their ease of vulcanization. Since cross-links form next to carbon-carbon double bonds. 

Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or "creep" in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122], Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5] ... 

Number-average molecular weights are Mn = 660 and 18,500 g/ mol, respectively (15,). Measurements were carried out on the unswollen networks, in elongation at 25°C. Data plotted as suggested by Mooney-Rivlin representation of reduced stress or modulus (Eq. 2). Short extensions of the linear portions of the isotherms locate the values of a at which upturn in [/ ] first becomes discernible. Linear portions of the isotherms were located by least-squares analysis. Each curve is labelled with mol percent of short chains in network structure. Vertical dotted lines indicate rupture points. Key O, results obtained using a series of increasing values of elongation 0, results obtained out of sequence to test for reversibility. 

Only one of the approaches considered here, chain-extension with propylene oxide of hydroxypropyl lignins, allowed for the preparation of networks with substantial elongation at break. Typical of most polyurethanes, an increase in the elongation at break resulted in a corresponding decrease in modulus and strength. This represents the most complex modification procedure of those discussed, although process development could probably simplify this modification for adoption on industrial scale. 

In view of the similarity in behavior of the networks in the ionomer and low density resin, we are able to deduce from modulus and elongation at rupture measurements the relative crosslinking rates. It appears that Surlyn A crosslinks 50 to 60% more rapidly than DFD 6040. The increased crosslinking in the ionomer may be associated with the radio-... 

In the simplest study of this type, Al-ghamdi and Mark [138] studied reinforcement of PDMS by two zeolites of different pore sizes. The zeolites were a zeolite 3A (pore diameter 3 A) and a zeolite 13X (pore diameter 10 A), both with a cubic crystalline structure. They were simply blended into hydroxyl-terminated chains of PDMS which were subsequently end-linked with tetraethoxysilane to form an elastomeric network. These elastomers were studied by equilibrium stress-strain measurements in elongation at 25°C. Both zeolites increased the modulus and related mechanical properties of the elastomer, but the effect was larger for the zeolite with the larger pore size. 

In the case of siloxane elastomers, the testing of mechanical properties is of particular importance. Elongation or tensile measurements are used almost to the exclusion of other types of mechanical tests, probably because of their simplicity. In this way, structural information is obtained about the networks, such as their degrees of cross-linking.92 Measurements of the ultimate strength (modulus at rupture), and the maximum... 

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