by Kathryn R. Williams

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1. Introduction

Rubber objects are common in daily life, and everyone is familiar with at least some of the physical properties of the class of polymers called elastomers:

1) They are capable of being stretched to several times their original length with relatively little applied force.

2) When the force is released they retract rapidly to the unstressed length (property of snap or rebound). The heat transfer on rebound is very close to zero.

3) They suffer no permanent deformation as a result of the extension process (property of resilience).

4) When they are fully elongated (or nearly so), they exhibit very high tensile strengths and stiffness (modulus).

The properties described above are all observable on the macroscopic level, which is the realm of classical thermodynamics. The classical treatment requires no knowledge or assumptions of molecular structure. However, in order to exhibit such behavior, the polymer must have certain molecular properties:

1) The polymer must have a large molecular weight, with, for the most part, very weak interactions between chains. For example, natural rubber, which is also called Hevea rubber after its source as the sap of the Hevea brasiliensis tree, has a molecular weight of about 350,000. Its chemical composition is poly(cisisoprene) (Figure 1), which in the untreated material has only weak intermolecular forces.

2) The polymer must be amorphous (i.e., noncrystalline) and must be above its glass transition temperature, Tg. The Tg is the temperature, or range of temperatures, over which the polymer exhibits a marked change in several physical properties, most notably specific volume, thermal coefficient of expansion, specific heat capacity, and refractive index. Below the Tg, there may be small local rotations (e.g., rotation around the C-C bond to a side-chain methyl group), but the polymer chains themselves are frozen into fixed positions (albeit not in a regular crystalline array), and the polymer is a hard, brittle glass. Above the glass transition temperature, the thermal energy is sufficient to allow rotations and limited translations of large segments of the polymer chain. On the macroscopic scale the polymer has the dimensional constancy of a solid, but on the molecular level the chain segments exhibit liquid-like properties.

A polymer with these properties can be envisaged as a disordered tangle of relatively compact random coils, as shown in Figure 2a. Because of their local mobility and lack of strong intermolecular attractions, the chains can be extended with essentially zero change in internal energy (Figure 2b). That they do not spontaneously revert to the stretched form is dictated by the entropy of the system. The elongated chains are more highly ordered than the random coils. In order to overcome the negative entropy effect, work must be performed to elongate the chains, and when the force is removed, the chains return to their disordered 'spaghetti-like' state. The polymer will usually not regain its original dimensions, unless there is some overall network structure, and this leads to another requirement:

3) To prevent long-range movements, the polymer chains must be joined at a few points (about once in every one hundred C-C linkages) by chemical bonds, usually via a short segment called a cross-link. Figure 1 shows a disulfide group connecting two poly(cis-isoprene) molecules. The development of the process of vulcanization which was discovered in 1839 independently by the Englishman Thomas Hancock and Charles Goodyear of the United States, made it possible to manufacture resilient rubber products, and led eventually to the large-scale usage of rubber in bicycle and automobile tires at the end of the nineteenth century. The fourth characteristic listed above (high modulus at full extention) accrues from another molecular property:

4) The molecular order brought about by the stretching process induces formation of crystalline regions within the polymer at high elongations. The crystallites act as physical cross-links and the stiffness is increased as a result.

The commercial importance of rubber became evident soon after the discovery of vulcanization, and scientific investigations of the product began shortly thereafter. The classical thermodynamics were studied by such masters as Lord Kelvin and Joule. In the 1920's and '30's the molecular interpretation was developed by early polymer chemists, such as Staudinger, Meyer, Kuhn, Guth and Herman Mark. The study of rubber elasticity provides an excellent opportunity to demonstrate the utility of statistical mechanics, as well as to review the basic relationships of classical thermodynamics.

In this experiment the dimensional properties of a rubber band will be studied using both a simple home-built apparatus and a Thermomechanical Analyzer. The data will be related to the change in entropy with elongation by the equations of classical thermodynamics. The results may also be used to validate the predictions of the statistical mechanical model of rubber elasticity and to calculate the number of active chain segments at the molecular level.

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This document originated from Professor Kathryn R. Williams

Copyright 1996 / Innovative Teaching Lab / 18.8.1996