Polymer energy elasticity

Almost every biological solution of low viscosity [but also viscous biopolymers like xanthane and dilute solutions of long-chain polymers, e.g., carbox-ymethyl-cellulose (CMC), polyacrylamide (PAA), polyacrylnitrile (PAN), etc.] displays not only viscous but also viscoelastic flow behavior. These liquids are capable of storing a part of the deformation energy elastically and reversibly. They evade mechanical stress by contracting like rubber bands. This behavior causes a secondary flow that often runs contrary to the flow produced by mass forces (e.g., the liquid climbs the shaft of a stirrer, the so-called Weissenberg effect ). 

Eq. (13.37) shows that the modulus of a rubber increases with temperature this is in contrast with the behaviour of polymers that are not cross-linked. The reason of this behaviour is that rubber elasticity is an entropy elasticity in contrast with the energy elasticity in "normal" solids the modulus increases with temperature because of the increased thermal or Brownian motion, which causes the stretched molecular segments to tug at their "anchor points" and try to assume a more probable coiled-up shape. 

The aim of any grafting is to increase the rubber efficiency, i.e. the ratio between the gel content and the rubber content, and to enable the rubber particles to bond to the polystyrene phase in order to ensure the transmission of external forces from the energy-elastic phase to the entropy-elastic phase. The graft polymer acts as emulsifier and stabilizes the dispersed rubber particles in the two-phase system. 

The development of a maximum in tan 5 or ihe loss modulus at the glass-to-rubber transition is explained as follows. At temperatures below Tg the polymer behaves elastically, and there is little or no flow to convert the applied energy into internal work in the material. Now It, the energy dissipated as heat per unit volume of material per unit time because of flow in shear deformation, is... 

Figure 12. Hypothetical increase in the internal osmotic swelling pressure, II, and counteractive polymer matrix elasticity (reflected in an increasing cohesive energy density, E), with increasing water content, n. n0 is the number of moles of water, per ionic sidechain, for which Tl-E = 0 (24).

Young s Modulus. Young s moduli, E, for several resins are plotted vs. temperature in Fig. 7. Young s moduli were determined from stress-strain diagrams. At 4K, their values are within 10%. Therefore, the low-temperature values of E do not depend markedly on the detailed chemical structure. It must be emphasized that epoxy resins are energy-elastic and have a nearly linear stress-strain behavior to fracture at low temperatures. No rate dependence was found over several decades. This is not true for many high polymers, such as polyethylene (PE), which are not cross-linked. PE behaves viscoelastically, even at 4 K [%... 

The moduli of elasticity determined by stress / strain measurements are generally much lower than the lattice moduli of the same polymers (Table 11-3). The difference is to be found in the effects of entropy elasticity and viscoelasticity. Since the majority of the polymer chains in such polymer samples do not lie in the stress direction, deformation can also occur by conformational changes. In addition, polymer chains may irreversibly slide past each other. Consequently, E moduli obtained from stress/strain measurements do not provide a measure of the energy elasticity. Such E moduli are no more than proportionality constants in the Hooke s law equation. The proportionality limit for polymers is about 0.l%-0.2% of the... 

Energy elastic components may be either positive or negative (Table 11-5). With polymers having a/ram conformation as lowest energy conformation, a transition from gauche to trans will therefore lead to an energy... 

Table 11-5. Energy-Elastic Component of Various Cross-Linked Polymers...

Polymers are not ideal energy elastic, but viscoelastic. In such cases, the deformation lags behind the applied stress. With ideal viscoelastic bodies, the resulting phase angle d in the corresponding vector diagram can be assumed constant, such that... 

Still further differences are observed for stress/strain diagrams of what are known as hard elastic or springy polymers. These polymeric states should exhibit a large energy-elastic component which is attributed to a special network structure (see Figure 38-10). However, electron microscopic studies do not provide any evidence for the proposed network structure. 

Friction coefficients, being not a physical property in the strict sense, but depending on the contact partners and many other external parameters, will be reported in the next section. The combination of low friction coefficients, typically < 0.2, with mechanical and surface properties which are partly polymer-like (elasticity, surface energy) and partly ceramic- or metal-like (hardness. Young modulus) qualitatively explains the outstanding position of DLC films as low-friction, highly wear-resistant coatings on which most of their present applications are based [77]. 

Finally, we consider theoretical or computational means of determining the ideal elastic constants of some polymers together with their temperatme dependences and compare these with experimental values, determined, as much as possible, under conditions that are free of viscoelastic relaxations. We then provide small-strain energy-elastic constants of a variety of both glassy and semi-crystalline polymers. 

Considerable information about elastic and viscoelastic parameters may be derived by measuring the response of a polymer to a small-amplitude cyclic deformation. Molecules perturbed in this way store a portion of the imparted energy elastically, and dissipate a portion in the form of heat (Ferry, 1970 Meares, 1965 Miller, M. L., 1966, pp. 243-253 Nielsen, 1962, Chapter 7 Rosen, 1971 Schultz, 1974, pp. 67-71 Williams, D. J., 1971), the ratio of dissipation to storage depending on the temperature and frequency. In dynamic mechanical spectroscopy experiments, a cyclic stress is applied to a specimen, and two fundamental parameters are measured the storage modulus E a measure of the energy stored elastically, and the loss modulus a measure of the energy dissipated. The loss modulus E" may be calculated as follows ... 

But other polymers such as it-poly(propylene) or poly(oxymethylene) can also be converted to what are known as hard-elastic fibers by suitable physical post-treatments (see also Section 38.3.1). At the present time, these energy elastic fibers are in the evaluation stage. 

E (o) and E" (o) are the dynamic storage modulus and the dynamic loss modulus, respectively. For a viscoelastic polymer E characterizes the ability of the polymer to store energy (elastic behaviour), while E" reveals the tendency of the material to dissipate energy (viscous behaviour). The phase angle is calculated from... 

Thus, in contrast to lattice moduli, moduli of elasticity obtained from stress/strain measurements are not measures of the energy elasticity, because of the effects of entropy-elasticity and viscoelasticity. Moduli of elasticity have more the character of being solely proportionality constants in a Hooke-type law. The proportionality limits are 0.05 % extension for steel and 0.1-0.2% for polymers. Above these so-called proportionality... 

The augend in (8.1) represents the pairwise repulsion energy of chain links in the self-consistent field approximation and the addend represents the polymer chain elastic energy determined via entropy (F =-TS) of its conformation in RW statistics. 

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