Density time-cross-link

Time-Cross-Link Density Reduction for Use in Long Time Behavior Prediction... 

The compression set of sihcone mbber is similar to organic types of mbber at low (0—50°C) temperatures, ranging from 5 to 15% (380). Above 50°C, sihcone mbber is superior, but compression set increases with time and temperature. Sihcone mbber is more tear-sensitive than butyl mbber, and the degree of sensitivity is a function of filler size and dispersion, cross-link density, and curing conditions. The electrical properties of sihcone mbber are generally superior to organic mbbers and are retained over a temperature range from —50 to 250°C (51). Typical electrical values for a heat-cured sihcone mbber are shown in Table 9. 

Gel type Reaction time (hr) Equilibrium degree of swelling Shear modulus (g/cm2) Effective cross-link density (10 5 g/cm3)... 

The cross-link density obtained in this manner (p() is referenced to the swollen polymer volume at the time of compression. For comparison to theory or to similar polymers swollen to different extents, the cross-link density can be redefined in terms of moles of chains per unit volume of dry polymer (p,). This conversion is simply... 

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. 

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). 

Yc and t)c are the time and the degree of conversion at the gel point, respectively, v/V is the cross-linking density, a, e, and E are the strength, elongation at break and the tensile modulus, respectively. 

A careful study of the above tables and figure 12.1 will indicate why a rubber chemist spends a lot of time in designing compounds with various cross link densities for oil field service as well as for other critical applications. It can also be observed that tear strength, fatigue life and toughness, all important requirements for oil field, rubber seals pass through an optimum at low cross link density and fall off with increase in cross link, whereas the most important sealing properties such as hysteresis and compression set improve with increased cross link. 

In addition to forming the chains of polyacrylate, the chains are cross-linked. This is a process in which two or more chains are held together by other compounds in a network. Typical cross-linkers for this polymer include di- and tri-acrylate esters. The swelling and elasticity of the polyacrylate polymer depends on the structure of this network and the number of cross-links. The swelling capacity of the polymer decreases with increased cross-link density. After formation, the polyacrylate is dried and formed into microparticles of irregular shape that can be stored for a long time. 

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. 

Variations in cross-link density may arise from spatial variations in the rubber formulation, although short-scale variations are often smoothed by component diffusion during the vulcanisation process. Differences on the mm scale can lead to interfacial structures like those depicted in Figures 7.16 and 7.17. Another source of variations in cross-link density on the mm scale is the curing process in combination with the sample geometry. Heat is supplied to the sample for a certain time and after vulcanisation is removed from the sample in a certain time. Near the heat source vulcanisation sets in first, and near the heat sink it sets in last. Depending on how the heat is supplied to and withdrawn from the object, complicated time-dependent temperature profiles are established in the sample. 

Clearly, the basic imaging scheme can be extended to include relaxation-time contrast for discrimination of variations in cross-link density and strain, and the ID MRI-MOUSE (magnetic resonance imaging MOUSE) can be extended with further gradient coils to permit imaging in three dimensions. Numerous applications of the MRI-MOUSE can be envisioned in soft matter analysis, in particular in those areas, where imaging with conventional equipment has proven to be successful, and where smaller, less expensive, and mobile devices are in need. 

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