Modulus of polymers

Fig. 23.3. The way in which the modulus of polymers changes with the fraction of covalent bonds in the loading direction. Cross-linking increases this fraction a little drawing increases it much more.

To understand the global mechanical and statistical properties of polymeric systems as well as studying the conformational relaxation of melts and amorphous systems, it is important to go beyond the atomistic level. One of the central questions of the physics of polymer melts and networks throughout the last 20 years or so dealt with the role of chain topology for melt dynamics and the elastic modulus of polymer networks. The fact that the different polymer strands cannot cut through each other in the... 

The above examples show that we can describe the network modulus of polymer gels by using the concept of entropic springs making up the network. In some cases corrections to the network are required to... 

The modulus of polymers also increases as the cross-link density of network polymers is increased. Crystalline and filled polymers resemble polymers with low cross-link density at temperatures below the melting temperature rm. 

The simple theory presented accounts for the fall-off of the modulus of polymers with increased extension. The stiffening of the polymer at very large distortion results from interactions between the extended polymer chains, which is called strain-induced crystallization. 

Aharoni SM (1986) Correlation between chain parameters and the plateau modulus of polymers. Macromolecules 19(2) 426-434... 

Until the 1970s there was a substantial gap between the theoretical modulus of polymer chains and the practical stiffness achieved in the existing processes. Since then the fibres made by extended chain crystallisation have bridged this gap. Solution spun fibres of high molecular linear polyethylene have been prepared with a Young modulus (at low temperature) of 90% of the theoretical value. Tables 19.9 and 19.10 illustrate the whole extent of elastic moduli in the various materials. 

The technique of ultrasonic impedometry was developed by Mason and McSkimmin of Bell Telephone laboratories for measuring the complex mechanical shear modulus of polymer liquids (11, 12). They described three relaxation modes for the systems—configurational elasticity, long... 

Strength and Elastic Modulus of Polymer Impregnated Concrete, Cem. Concr. Res. (1971) 1, 631-644. 

Therefore, it is well established that topological entanglements dominate and control the modulus of polymer networks with long network strands. The Edwards tube model explains the non-zero intercept in plots of network modulus against number density of strands (see Figs 7.11 and 7.12). The modulus of networks with very long strands between crosslinks approaches the plateau modulus of the linear polymer melt. The modulus of the entangled polymer network can be approximated as a simple sum. 

Figure 3 illustrates how the wear varies with the hardness and modulus of polymer substrate. Figure 4 shows that the wear increases drastically with an increase of the effective frictional coefficient ( p ) between the particle and polymeric surface. As was mentioned earlier, the friction p depends not only on the bulk and surface properties of materials in contact but also on such parameters as contact geometry and surface roughness. The direct determination of y from the first principle has yet to be established. The present model can be used to estimate its value from experiment. When a surface becomes smoother and harder, the effective frictional coefficient usually decreases and so does the wear. 

Dynamic mechanical thermal analysers (DMTA) are semi-automated machines for determining the Young s or shear modulus of polymers as a... 

Reinforcement factor e=(E/E2)"1> where E and E2 are the moduli of blend and polymer matrix, respectively, as a function of volume fraction of the reinforcing material (v) is proposed for treatment of experimental data, as well as for comparison of different theoretical models for the elastic modulus of polymer blends. 

Simha, R., Rapazoglou, E., and Maurer, F. H. J., Thermal expansivity and bulk modulus of polymer composites experiment versus theory, Polym. Compos., 10, 409-413 (1989). 

In Sect. 2, we pointed out that for the plateau modulus of polymer melts an excellent quantitative agreement was achieved with the scaling representation of experimental results deduced by Graessley and Edwards (see Eq. (19)). Similary, from Eqs. (20, 51, 52) in the case of moderately crosslinked networks (Np 1) the relation... 

Another limit is governed by the deformation rate the latter cannot exceed the relative speed of sound c, which is defined as speed of sound divided by sample length (for solid polymers, c s (10 — 10 ) s ). This fact is confirmed by the previously mentioned data at v> 610 Hz, no dispersion occurs in Young s modulus of polymers [54]. 

---