Rubber-plateau

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

Unfortunately, the method is based on a fairly large nunber of assumptions. If we want to relate GN to the pseudo-equilibrium rubber plateau modulus, G , and to the effect of chain entangling in ordinary networks produced by cross-linking in the unstrained state, the following assumptions are required ... 

Figure 3. Modulus contributions from chemical cross-links (Cx, filled triangles) and from chain entangling (Gx, unfilled symbols) plotted against the extension ratio during cross-linking, A0, for 1,2-polybutadiene. Key O, GN, equibiaxial extension , G.v, pure shear A, Gx, simple extension Gx°, pseudo-equilibrium rubber plateau modulus for a polybutadiene with a similar microstructure. See Ref. 10.

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

Figure 3.13 Polymer viscoelastic response as a function of temperature, showing the five regions glassy, glass to rubbery, rubber plateau, rubber flow, and liquid flow...

The large scale molecular motions which take place in the rubber plateau and terminal zones of an uncross-linked linear polymer give rise to stress relaxation and thereby energy dissipation. For narrow molecular weight distribution elastomers non-catastrophic rupture of the material is caused by the disentanglement processes which occur in the terminal zone, e.g., by the reptation process. In practical terms it means that the green strength of the elastomer is poor. 

The stress relaxation properties of a high molecular weight polybutadiene with a narrow molecular weight distribution are shown in Figure 1. The behavior is shown in terms of the apparent rubber elasticity stress relaxation modulus for three differrent extension ratios and the experiment is carried on until rupture in all three cases. A very wide rubber plateau extending over nearly 6 decades in time is observed for the smallest extension ratio. However, the plateau is observed to become narrower with increasing extension... 

Thus, the simplified Two-Network experiment shows by a direct comparison of forces at constant length that the trapped entangled structure of a well cross-linked elastomer contributes to the equilibrium modulus by an amount that is approximately equal to the rubber plateau modulus. The modulus contribution from the trapped entangled structure will be less for lower molecular weights and especially at low degrees of cross-linking (14). 

Chain entanglements are the cause of rubber-elastic properties in the liquid. Below the "critical" molecular mass (Mc) there are no indications of a rubbery plateau. The length of the latter is strongly dependent on the length of the molecular chains, i.e. on the molar mass of the polymer. From the shear modulus of the pseudo rubber plateau the molecular weight between entanglements may be calculated ... 

This result for (193) is quite different from Fig. 13.56, where f(193 K) is approximately equal to 3 x 10 12 h. If we take for the WLF constants not the universal values of 17.44 and 51.6 but those from Table 13.10 for polyisobutylene (cf = 16.85 and cf = 102.4), we then calculate (193 K) = 3 x 10-10 h which is slightly better in agreement with Fig. 13.56. However, as said before, because of the flatness of the pseudo-rubber plateau the determination of log aT is rather inaccurate, so that the shift from temperatures below to above this plateau, thus from 80 to 25 °C is rather problematic. This means that the value of 3 x 10-12 h will also be wrong. The values of 16.85 and 102.4 have been determined with the aid of the storage and loss moduli, by which these problems were bypassed, so that the value of f(193 K) = 3 x 10-10 h will be more realistic than the other two values for (193 K). 

Copoly(ester ester)s belong to the family of thermoplastic elastomers (TPEs) and consist in general of thermo-reversible hard and elastic soft domains [11]. The copoly(ester ester) used here consists of 60% poly(butylene terephthalate), 35% poly(butylene adipate) and 5% 4,4 -methylenebis(phenyl isocyanate), and shows domain sizes of about 20 nm [12]. The material possesses a rubber plateau between the glass transition temperature of the mixed amorphous PBA/PBT phase (the PBT phase is semi-crystalline) at about -30°C and the melting point of the PBT at about 220°C. Due to the vulnerability of the amorphous PBA/PBT soft domains towards water attack [13] the PBT/PBA copoly(ester ester) is used here to study the existence of ESC of a chemical rather than a physical nature. For the sake of clarity it should be emphasized that no additives have been used in the copoly(ester ester) described here. 

Dependence of the Shear Modulus on the Concentration. The experimental results of Figure 3a show that the plateau values increase with the detergent concentration. Unfortunately, we were not able to reach the rubber plateau for all concentrations for lack of the frequency range. From the theory of networks it is possible to calculate the number of elastically effective chains between the crosslinks from the shear modulus Gq of the rubber plateau (12). If the network... 

Viscoelastic measurements of ionomers have been used to indirectly characterize the microstructure and to establish property structure relationships. Forming an ionomer results in three important changes in the viscoelastic properties of a polymer. First, T usually increases with increasing ionization. This is a conseqi nce of the reduced mobility of the polymer backbone as a result of the formation of physical, ionic crosslinks. Second, an extended rubber plateau is observed in the modulus above T, again as a result of the ionic network. Third, a high temperaturi mechanical loss is observed above T, which is due to motion in the ion-rich phase. The dynamic mechan cal curves for SPS ionomers shown in Fig. 9 clearly demonstrate these three characteristics. 

Blends of atactic poly(methyl methacrylate) with poly(ethylene glycol), PMMA/PEG, were reported miscible [Colby, 1989]. Their rheology, PMMA/PEG = 50/50 and 80/20 at T = 160-210°C, was studied in a dynamic shear field [Booij and Palmen, 1992]. By contrast with homopolymers, the blends did not follow the time-temperature superposition. The deviation was particularly large at low temperatures. The reason for the deviation is most likely based on the different temperamre dependence of the relaxation functions. The authors concluded that in miscible blends, the temperature dependence of the relaxation times of individual macromolecules depends on composition. This leads to different degrees of mutual entanglement and hence the rubber plateau moduli. 

Figure 38 Master curves of elastic storage (S, ) and viscous loss (S", o) linear viscoelastic moduli of the 12-arm 12 828 (a) and 64-am 6430 (b) star-PBd polymers in the temperature range from 150 up to -103°C, with reference temperature-83 °C. Solid arrows represent the various transitions and corresponding crossover frequencies (cos. glass to Rouse-like transition cof.. transition to rubber plateau

Nanocomposites were prepared from epoxidised linseed oil after copolymerisation with 3-glycidyl propyl heptaisobutyl-T8-polyhedral oUgomeric sUsesquioxanes (G-POSS). Owing to reinforcement by inorganic POSS derivatives, enhanced values and storage moduli of the networks in the glassy state and rubber plateau were observed compared to pristine epoxy. ... 

Fig. 5.7 Illustration of the rubber plateau for the creep compliance within the time scale shorter than the characteristic time of the reptation chain in the melt phase at a given temperature...

Why do polymers have a rubber plateau between the glass state and the liquid... 

The storage modulus of a 3wt% solution shows almost rubber elastic behaviour with a slope of approximately 0.035. The slope of the i] curve, i.e. 0.94, is in reasonable agreement with the slope of G. The rubber plateau decreases gradually (almost monotonically) with increasing temperature, although a weak transition is perceptible at about 40 °C, where the slope changes little. 

The exponent n in the concentration dependence of the storage modulus, E = Ac , is much larger than 2. However, the values of E measured at 2.5 Hz are in general not the equilibrium rubber plateau values. Hence, it is difficult to interpret these high values of n. 

Jong et prepared NR composites reinforced with hybrid filler consisting of defatted soy flour (DSF) and CB. Aqueous dispersions of DSF and CB were first mixed, and then blended with NR latex and sulfur dispersion, respectively. The homogenous composite mixtures were quickly freeze-dried and compression moulded to offer the NR composites. They found that the NR composites reinforced with 40% of hybrid filler (the ratio of DSF to CB was 1 1) exhibited a 90-fold improvement in the rubber plateau modulus compared with unfilled NR, showing a significant reinforcement effect by the hybrid filler. 

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