The Mechanical Properties of Polymers

A common characteristic of soft materials is that while slow deformations produce viscous behavior, fast deformations yield an elastic response. 

FIGURE 4.17 Cross-linking the entangled polymer chains in a rubber improves durability and elastic properties. 

Polymers can form materials that are purely elastic, viscoelastic, or viscous, and an entangled polymer network is a good example of this phenomenon. Different relaxation times result from the different kinds of mechanical deformation that can take place in the material. On very small length scales, the bonds between atoms in a polymer chain can be stretched. This deformation relaxes back to its equilibrium state quickly. In the same material on a larger, molecular level length scale, the elastic network itself can be deformed but in this case will relax back to equilibrium slowly as polymer chains must move around each other in the network. 

The length of the polymer chains in a material has a strong impact on viscoelastic properties with a relaxation time t, related to chain length by the expression 

The viscoelastic properties of polymeric materials also vary with temperature. Far below the glass transition temperature 7 (see Table 4.1), polymers behave like elastic solids under small deformations. In the glassy phase, polymer chain conformations are effectively frozen in, and the material requires a large force to deform. Think about a piece of hard plastic it does not seem very elastic, but plastics, like other solids, including crystalline materials, obey Hooke s law under small deformations, so 

---

In this section we resume our examination of the equivalency of time and temperature in the determination of the mechanical properties of polymers. In the last chapter we had several occasions to mention this equivalency, but never developed it in detail. In examining this, we shall not only acquire some practical knowledge for the collection and representation of experimental data, but also shall gain additional insight into the free-volume aspect of the glass transition. 

Glass Transition. The glass-transition temperature T reflects the mechanical properties of polymers over a specified temperature range. 

Molecular Weight. The values of the mechanical properties of polymers increase as the molecular weight increases. However, beyond some critical molecular weight, often about 100,000 to 200,000 for amorphous polymers, the increase in property values is slight and levels off asymptotically. As an example, the glass-transition temperature of a polymer usually follows the relationship... 

And we are still learning how best to fabricate and use them. As emphasised in the last chapter, the mechanical properties of polymers differ in certain fundamental ways from those of metals and ceramics, and the methods used to design with them (Chapter 27) differ accordingly. Their special properties also need special methods of fabrication. This chapter outlines how polymers are fabricated and joined. To understand this, we must first look, in slightly more detail, at their synthesis. 

The mechanical properties of polymers are of interest in all applications where they are used as structural materials. The analysis of the mechanical behavior involves the deformation of a material under the influence of applied forces, and the most important and characteristic mechanical property is the modulus. A modulus is the ratio between the applied stress and the corresponding deformation, the nature of the modulus depending on that of the deformation. Polymers are viscoelastic materials and the high frequencies of most adiabatic techniques do not allow equilibrium to be reached in viscoelastic materials. Therefore, values of moduli obtained by different techniques do not always agree in the literature. 

Usually, crystallization of flexible-chain polymers from undeformed solutions and melts involves chain folding. Spherulite structures without a preferred orientation are generally formed. The structure of the sample as a whole is isotropic it is a system with a large number of folded-chain crystals distributed in an amorphous matrix and connected by a small number of tie chains (and an even smaller number of strained chains called loaded chains). In this case, the mechanical properties of polymer materials are determined by the small number of these ties and, hence, the tensile strength and elastic moduli of these polymers are not high. 

The mechanical properties of polymers also depend on the extent of crosslinking. Uncrosslinked or lightly crosslinked materials tend to be soft and reasonably flexible, particularly above the glass transition temperature. 

In order to understand the mechanical properties of polymers it is useful to think of them in terms of their viscoelastic nature. Conceptually we can consider a polymeric item as a collection of viscous and elastic sub-components. When a deforming force is applied, the elastic elements deform reversibly, while the viscous elements flow. The balance between the number and arrangement of the different components and their physical constants controls the overall properties. We can exploit these relationships to create materials with a broad array of mechanical properties, as illustrated briefly by the following examples. 

Besides the ASTM standard tests, a number of general reference books have been published on testing and on the mechanical properties of polymers and viscoelastic materials (2-7). Unfortunately, a great variety of units are used in reporting values of mechanical tests. Stresses, moduli of elasticity, and other properties are given in such units as MK.S (SI), cgs, and English units. A table of conversion factors is given in Appendix II. 

The modulus-time or modulus-frequency relationship (or, graphically, the corresponding curve) at a fixed Temperature is basic to an understanding of the mechanical properties of polymers. Either can be converted directly to the other. By combining one.of these relations (curves) with a second major response curve or description which gives the temperature dependence of these time-dependent curves, one can cither predict much of the response of a given polymer under widely varying conditions or make rather... 

While a number of introductory or comprehensive texts dealing with polymer chemistry were written, the most influential was probably Paul J. Flory s textbook "Principles of Polymer Chemistry", published in 1954. No prior knowledge of polymers was assumed with particular chapters directed at the beginner. It also contained much information useful to the experienced investigator. A wealth of experimental data was included to illustrate the applicability of the presented concepts and conclusions. Admittedly missing are topics related to the mechanical properties of polymers and to the application of polymers in industry - i.e. fabrication, synthesis, etc. Even so Flory s text is a landmark book in science. 

The experimental design was to study both the carbon-13 and proton relaxation as a function of temperature for both polymer and solvent, and to extend these to as high a polymer concentration as the available equipment permitted. Inasmuch as the mechanical properties of polymers can be affected considerably by small amounts of diluents, we would ultimately like to approach the bulk polymer state, where use of strong dipolar decoupling and magic angle spinning are necessary. ... 

Most polymers are applied either as elastomers or as solids. Here, their mechanical properties are the predominant characteristics quantities like the elasticity modulus (Young modulus) E, the shear modulus G, and the temperature-and frequency dependences thereof are of special interest when a material is selected for an application. The mechanical properties of polymers sometimes follow rules which are quite different from those of non-polymeric materials. For example, most polymers do not follow a sudden mechanical load immediately but rather yield slowly, i.e., the deformation increases with time ( retardation ). If the shape of a polymeric item is changed suddenly, the initially high internal stress decreases slowly ( relaxation ). Finally, when an external force (an enforced deformation) is applied to a polymeric material which changes over time with constant (sinus-like) frequency, a phase shift is observed between the force (deformation) and the deformation (internal stress). Therefore, mechanic modules of polymers have to be expressed as complex quantities (see Sect. 2.3.5). 

Describe temperature, molecular weight, and strain-rate effects on the mechanical properties of polymers. 

To a much greater extent than either metals or ceramics, the mechanical properties of polymers show a marked dependence on a nnmber of parameters, inclnding temper-atnre, strain rate, and morphology. In addition, factors snch as molecnlar weight and temperature relative to the glass transition play important roles that are not present in other types of materials. Needless to say, it is impossible to cover, even briefly, all of these effects. We concentrate here on the most important effects that can affect selection of polymers from a mechanical design point of view. 

Selected factors affecting crystallinity regarding Tg and Tm are described in Chapter 2. Here we discuss the influence of crystallinity on the mechanical properties of polymers. For thermoplastics the relation between the degree of crystallinity and the physical nature is shown in Table 5.1. The general lack of difference in physical nature shown by largely crystalline polymers at... 

Thus, although some degree of local organization may indeed occur in amorphous systems, and may even have some effect on the mechanical properties of polymers in the glassy state, the influence on the mechanical properties of melts, concentrated solutions and networks appears to be negligible. 

PE-PEP diblock were similar to each other at high PE content (50-90%). This was because the mechanical properties were determined predominantly by the behaviour of the more continuous PE phase. For lower PE contents (7-29%) there were major differences in the mechanical properties of polymers with different architectures, all of which formed a cubic-packed sphere phase. PE-PEP-PE triblocks were found to be thermoplastic elastomers, whereas PEP-PE-PEP triblocks behaved like particulate filled rubber.The difference was proposed to result from bridging of PE domains across spheres in PE-PEP-PE triblocks, which acted as physical cross-links due to anchorage of the PE blocks in the semicrystalline domains. No such arrangement is possible for the PEP-PE-PEP or PE-PEP copolymers (Mohajer et al. 1982). 

This section contains two primary topics. The first is polymer rheology, which is concerned with how polymeric materials flow when they are placed under stress. Also of interest are the mechanical properties of polymers, particularly their elasticity. The combination of viscous effects with elastic phenomena is called viscoelasticity. 

As it was mentioned above mechanical properties of polymers are strongly dependent on the temperature. Therefore, E and D, for a polymeric sample are dependent on the temperature at which the experiment is performed. On the other hand the mechanical properties of polymers are also dependent on time. Therefore E and D are not constant at one temperature but evolve with time i.e. E(t), D(t) [7], The complex relationship between the configurational distorsion produced by a perturbation field in polymers and the Brownian motion that relaxes that distorsion make it difficult to establish stress-strain relationships. In fact, the stress at that point in the system depends not only on the actual deformation but also on the previous history of the deformation of the material. 

The mechanical properties of polymer chains that do not exhibit interactions between the side chains and the backbone, or one part of the backbone and another part of the backbone, are related to the number of available conformations and hence the chain entropy. As we discuss later, the stiffness of a polymer chain that does not exhibit bonding with other parts of the chain is related to the change in the number of available conformations. It turns out this refers to random chain polymers of which elastin, poly(ethylene) at high temperatures, and natural rubber are discussed in this text. As we stretch a polymeric chain we reduce the number... 

We have just discussed several methods for improving the mechanical properties of polymers. In addition to these techniques, one could think about synthesizing copolymers of styrene and less brittle monomer(s). Actually, we have already seen that this approach has been used with considerable success (see Chapter 5 and Table 5-2). Styrene-acrylonitrile (SAN) copolymers and acrylonitrile-butadiene-styrene (ABS) terpolymers have excellent impact strength. Although sometimes copolymerization is a viable option, oftentimes a completely different approach is called for. Let s see how. 

The mechanical properties of polymers can be expressed in a number of ways. Tensile modulus describes the stiffness of a material and provides information about its potential usefulness. Toughness is defined as the work required to elongate a sample to the breaking point. Polymers with high impact strength resist cracking or breaking when struck by a hard object. 

The available data on the mechanical properties of polymer materials at cryogenic temperatures have been reported for the last few decades mainly in close connection with space technology. 

The mechanical properties of polymers are controlled by the elastic parameters the three moduli and the Poisson ratio these four parameters are theoretically interrelated. If two of them are known, the other two can be calculated. The moduli are also related to the different sound velocities. Since the latter are again correlated with additive molar functions (the molar elastic wave velocity functions, to be treated in Chap. 14), the elastic part of the mechanical properties can be estimated or predicted by means of the additive group contribution technique. 

The mechanical properties of polymers are of interest, in particular in all applications where polymers are used as structural materials. Mechanical behaviour involves the deformation of a material under the influence of applied forces. 

---