Dependence on cross-link density

Differing from the previous studies (5-7) where the parameters Goo, m, loay have been treated as constants, we find that they depend on cross-link density which is consistent with the measurements of Dickie and Ferry (4). Figure 5 shows the dependence of the viscoelastic relaxation on cross-link density. The solid curves are calculated from Equations 17, 19 and 20 by using a value of xq = 2.5 x 102 hrs at T = 25°C. Figure 5 resembles the corresponding figure in ref. 5. 

Regardless of the method of cross-linking, mechanical properties of a cross-linked elastomer depend on cross-link density. Modulus and hardness increase monotonically with cross-link density, and at the same time, the network becomes more elastic. Fracture properties, i.e., tensile and tear strength, pass through a maximum as the cross-link density increases (see Figure 5.4). 

Regardless of the method of cross-linking, mechanical properties of a cross-linked elastomer depend on cross-link density. Modulus and hardness increase mono-... 

From a fit of Equation (10) to spatially resolved relaxation curves, images of the parameters A, B, T2, q M2 have been obtained [3- - 32]. Here A/(A + B) can be interpreted as the concentration of cross-links and B/(A + B) as the concentration of dangling chains. In addition to A/(A + B) also q M2 is related to the cross-link density in this model. In practice also T2 has been found to depend on cross-link density and subsequently strain, an effect which has been exploited in calibration of the image in Figure 7.6. Interestingly, carbon-black as an active filler has little effect on the relaxation times, but silicate filler has. Consequently the chemical cross-link density of carbon-black filled elastomers can be determined by NMR. The apparent insensitivity of NMR to the interaction of the network chains with carbon black filler particles is explained with paramagnetic impurities of carbon black, which lead to rapid relaxation of the NMR signal in the vicinity of the filler particles. 

Hahn echo and solid echo produce different contrast in imaging, and the corresponding transverse relaxation times Tj and T2l- depend on cross-link density in a different fashion. 

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,... 

Within the limit of experimental errors scaled dynamic order parameters measured from the MQ experiments show a linear dependence on cross-link density (cf Fig. 11). 

In this case, one expects (cf equation 32) that (M2) has a polynomial dependence on cross-link density or shear modulus. 

The glass transition temperature is also dependent on cross-link density. According to Di Marzio (1964) ... 

A similar dependence of radical concentration on cross-link density was obtained for cis-polyisoprene tested below Tg by Natarajan and Reed ... 

It should be noted that, for all the resins considered, the specific heat does not depend on cross-linking or the chemical structure below 100 K. This can be explained by the Debye theory, which states that the specific heat is a function only of the oscillator density, N, and 0/T. 6 is the Debye temperature, which can be determined by elastic parameters, such as Young s modulus, E, N is approximately equal for all resins, since they have nearly equal densities. At low temperatures, roughly the same value of E is asymptotically reached by the epoxy resins. 

Bakule, R., Havranek, A. (1975). The dependence of dielectric properties on cross-linking density of rubbers. J. Polym. Sci. Polym. Symp, 53(1), 347-356. 

Fig. 12.5. Dependence of tensile strength (Ts) on cross-link density (vt) and cross-link structure for (a) EPDM (Royalene 301) and (b) EPM (Dutral). Tested using dumbell type 3 at 250mm/min elongation rate at 20 C. Cure systems (a) EPDM (1) tetramethylthiuram disulphide, bis (benzothiazolyl) disulphide (2) dicumyl peroxide, 1 phr sulphur (3) dicumyl peroxide, 0 3 phr sulphur (4) mercaptobenzothiazole (5) dicumyl peroxide (b) EPM (1) dicumyl peroxide, 1 phr sulphur (2) dicumyl peroxide, 0-3 phr sulphur (3) dicumyl peroxide. (From Imoto et al, 1%8.)...

FIGURE 12.2 The dependence of loosely packed matrix structure fractal dimension df" on cross-linking density n for epoxy polymers EP-2 (1) and EP-2-200 (2) [9],... 

During the vulcanization, the volatile species formed are by-products of the peroxide. Typical cure cycles are 3—8 min at 115—170°C, depending on the choice of peroxide. With most fluorosihcones (as well as other fluoroelastomers), a postcure of 4—24 h at 150—200°C is recommended to maximize long-term aging properties. This post-cure completes reactions of the side groups and results in an increased tensile strength, a higher cross-link density, and much lower compression set. 

Long-term compression set resistance is described in Figure 4. Lower set values are achievable by use of higher viscosity gumstock at comparable cross-link densities. Compression set resistance is also very dependent on the cure system chosen. The bisphenol cure system offers the best compression set resistance available today, as shown in Table 5. 

The conventionally covalently cross-linked rubbers and plastics cannot dissolve without chemical change. They will, however, swell in solvents of similar solubility parameter, the degree of swelling decreasing with increase in cross-link density. The solution properties of the thermoelastomers which are two-phase materials are much more complex, depending on whether or not the rubber phase and the resin domains are dissolved by the solvent. 

Whereas polymers of sufficiently high molecular weight may be soluble in the common solvents with some difficulty, network polymers do not dissolve, even at elevated temperature. They usually swell depending on the nature and cross-link density. Marcus [10] described the swelling of polystyrene cross-linked by divinylbenzene. 

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