Elastic properties of polymers

At aU technically relevant temperatures, polymers deform by creep. To describe the time-dependence of plastic deformation, we again exploit equation (8.3). In contrast to the viscoelastic deformation, there is no restoring force in viscoplasticity. Equation (8.3) is thus used to describe the dashpot element connected in series in the four-parameter model from figure 8.7(b). 

For large stresses, we can use the approximation 2 sinh x ss exp x in equation (8.3). This yields 

A simple form of this equation is obtained by solving for a/T  

---

If this is true, this should hold not only for polymer melts but, in the limit of long chains, also for polymer networks. In the simplest case the elastic properties of polymer networks are entirely governed by the entropic... 

See literature on visco-elasticity, for example J.D. Ferry, The Visco-elastic Properties of Polymers, 3rd Ed, Wiley, New York, 1980. 

Southwick, J.G. and Manke, C.W. "Molecular Degradation, Injectivity, and Elastic Properties of Polymer Solutions," SPE paper 15652, 1986 SPE Annual Technical Conference and Exhibition, New Orleans, October 5 8. 

After an introductory chapter we review in Chap. 2 the classical definition of stress, strain and modulus and summarize the commonly used solutions of the equations of elasticity. In Chap. 3 we show how these classical solutions are applied to various test methods and comment on the problems imposed by specimen size, shape and alignment and also by the methods by which loads are applied. In Chap. 4 we discuss non-homogeneous materials and die theories relating to them, pressing die analogies with composites and the value of the concept of the representative volume element (RVE). Chapter 5 is devoted to a discussion of the RVE for crystalline and non-crystalline polymers and scale effects in testing. In Chap. 6 we discuss the methods so far available for calculating the elastic properties of polymers and the relevance of scale effects in this context. 

The equilibrium (relaxed) elastic properties of polymers in the rubbery state display two very important features ... 

Of course, we haven t explained precisely what we mean by viscoelasticity yet and we won t for a while. We are going to approach the subject in the conventional way, first by looking at the elastic properties of polymer solids, then the rheological properties of polymer melts. This will remind you of some basic stuff you should know, but may have forgot, or, if you ve been really sneaky, managed to avoid altogether. 

This elastic property of polymer melts also... 

Hiergeist, C. and Lipowsky, R. (1996) Elastic properties of polymer decorated membranes. /. Phys. II France, 6, 1465-1481. 

Han, et al.. Molecular dynamics simulations of the elastic properties of polymer/ carbon nanotube composites. Comput Mater. Sci. 2007,39(8), 315-323. 

Table 6.1. Small-strain elastic properties of polymers compared with other materials E, p and v at room temperature, all values are approximate)...

T. Ocher changes occur at this temperature that can be monitored to identify the T experimentally. These include changes in specific volume of the polymer, index of refraction, gas diffusion coefficients, thermal expansion coefficients (measured by dilatomeCry), and specific heat (measured by differential scanning calorimetry (DSC) or by differential thermal analysis (DTA)). General discussions of the elastic properties of polymers can be found in references (4.2)-... 

These preliminary data demonstrate the sensitivity of the SAW device to the elastic properties of polymers. The SAW device has potential for use in the characterization of these materials. In addition to sensitivity, the SAW also represents a versatile and Inexpensive alternative to existing methods. Some of the parameters which ml t be studied using the SAW are discussed below. 

SOUTHWICK, J. G. and MANKE, C. W., "Molecular Degradation, Injectivity and Elastic Properties of Polymer Solutions", SPE 15652, presented at 61st SPE Annual Fall Conference, New Orleans, 5-8 October, 1986. 

Screen factor is a measure of the visco-elastic properties of polymer solutions and how they behave in porous media [50,51]. Figure 6 shows the screen factor monotonically increases with polymer concentration. According to Unsal, the shear rate encountered in a screen viscometer is nearly 1,000 s [52]. At such high shear rates, shear viscosities obtained by extrapolating the data shown in Figure 5 are much lower than those obtained from the screen viscometer. This difference... 

Improving Elastic Properties of Polymer-Reinforced Aerogels... 

Our present theories of rubber elasticity are mostly of the kinetic theory type. In some of these theories the elasticity of a single chain is multiplied by the number of effective chains in the network to provide the total elasticity. In these theories no information concerning the statistical properties of the network structure can be inferred since either no structural aspects are evaluated or a simple structural nature is assumed. These structuril properties should be of great interest in furthering our understanding of polymers in bulk. Thus the strain dependence of X-ray scattering measurements from networks, which have heavy atoms at the cross-links and/or the chain ends, should provide some correlation between the structural and elastic properties of polymer networks. 

The need for a fully statistical mechanical theory of polymers in bulk is more than just a question of rigor or elegance. We mentioned earlier the questions cancerning the relation between average structural and elastic properties of polymer networks. More important, the present statistical theories of bulk polymer elasticity fail to account for interactions between different chains in the network. Therefore they cannot be expected to provide a proper molecular basis for an understanding of elasticity at large deformations, of crystallization upon stretching, etc. A description of these phenc mena requires a fully statistical mechanical description of the polymer network. In such a description, the observable properties of the system are formally presented in terms of the properties of the constituent polymers and their mutual interactions. Thus all macroscopic-properties are expressed in terms of the microscopic properties of the individual polymer chains. 

The elastic melt extruder was developed in the late 1950s by Maxwell and Scalora [40, 41]. The extruder makes use of the viscoelastic, in particular the elastic, properties of polymer melts. When a viscoelastic fluid is exposed to a shearing deformation, normal stresses will develop in the fluid that are not equal in all directions, as opposed to a purely viscous fluid. In the elastic melt extruder, the polymer is sheared between two plates, one stationary and one rotating see Fig. 2.19. 

Correlation Between Steady-Shear and Oscillatory Data. The viscosity function is by far the most widely used and the easiest viscometric function determined experimentally. For dilute polymer solutions dynamic measurements are often preferred over steady-shear normal stress measurements for the determination of fluid elasticity at low deformation rates. The relationship between viscous and elastic properties of polymer liquids is of great interest to polymer rheologists. In recent years, several models have been proposed to predict fluid elasticity from shear viscosity data. 

Elastic Constants. For the polymers listed in Table 2 for which both longitudinal and shear sound speeds are given, the elastic constants have been calculated at room temperature, ambient pressure, and a frequency of 2 MHz these are listed in Table 7. The moduli values are approximately 1 order of magnitude lower than those for metals. The range of Poisson s ratio values is somewhat higher than that for metals. A review of elastic properties of polymers is given by Hartmann (130). 

As an example, Fig. 86 shows the tensile modulus of elasticity E vs temperature T plots, as measured for the 83PU-17PHEMA network and ND-containing composites based thereon (their CR spectra were described in Sects. 3.2 and 3.8). One can see a considerable and various (by a sign and magnitude) influence of small ND additives on the elastic properties of polymer matrix additionally, these changes are different in the different temperature regions. 

Ficheux, M.-F., Bellocq, A.-M., and Nallet, F. 2001. Elastic properties of polymer-doped dilute lamellar phases A small-angle neutron scattering study. Eur. Phys. J., E4, 315-326. 

---