Polymer Crosslink Networks

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CROSS-LINKED POLYMERSAND RUBBER ELASTICITY

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An elastomer is defined as a cross-linked amorphous polymer above its glasstransition temperature. Elastomers may be stretched substantially reversiblyto several hundred percent. While most of this chapter explores the behaviorof elastomers, the study of cross-linking is more general. If the cross-linkedpolymer is glassy, it is often called a thermoset. Below, the terms elastomer

and rubber are often used interchangably.

9.1 CROSS-LINKS AND NETWORKS

During reaction, polymers may be cross-linked to several distinguishablelevels. At the lowest level, branched polymers are formed. At this stage thepolymers remain soluble, sometimes known as the sol stage.As cross-links areadded, clusters form, and cluster size increases. Eventually the structurebecomes infinite in size;that is, the composition gels.At this stage a Maxwelliandemon could, in principle, traverse the entire macroscopic system stepping onone covalent bond after another. Continued cross-linking produces composi-tions where, eventually, all the polymer chains are linked to other chains at

multiple points, producing, in principle, one giant covalently bonded molecule.This is commonly called a polymer network.

9.1.1 The SolGel Transition

The reaction stage referred to as the solgel transition (13) is called the gelpoint. At the gel point the viscosity of the system becomes infinite, and the

Introduction to Physical Polymer Science, by L.H. SperlingISBN 0-471-70606-X Copyright 2006 by John Wiley & Sons, Inc.


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equilibrium modulus climbs from zero to finite values. In simple terms thepolymer goes from being a liquid to being a solid. There are three differentroutes for producing cross-linked polymers:

1. Step polymerization reactions, where little molecules such as epoxies(oxiranes) react with amines, or isocyanates react with polyols with func-tionality greater than two to form short,branched chains, eventually con-densing it into epoxies or polyurethanes, respectively. Schematically

(9.1)

2. Chain polymerization, with multifunctional molecules present. Anexample is styrene polymerized with divinyl benzene.

3. Postpolymerization reactions, where a linear (or branched) polymer iscross-linked after synthesis is complete.An example is the vulcanizationof rubber with sulfur, which will be considered further below.

The general features of structural evolution during gelation are describedby percolation (or connectivity) theory, where one simply connects bonds (or

fills sites) on a lattice of arbitrary dimension and coordination number (46).Figure 9.1 (6) illustrates a two-dimensional system at the gel point. It must benoted that gels at and just beyond the gel point usually coexist with sol clus-ters. These can also be seen in Figure 9.1. It is common to speak of the con-

BnA A+mB

B

AB ABBA

BA AB

428 CROSS-LINKED POLYMERS AND RUBBER ELASTICITY

Figure 9.1 A square lattice example of percolation, at the gel point (6). Note structures that

span the whole sample.


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version factor, p, which is the fraction of bonds that have been formedbetween the mers of the system; see Section 3.7. For the two-dimensionalschematic illustrated in Figure 9.1,p = 1

2yields the gel point.

9.1.2 Micronetworks

A special type of network exists that involves only one or a few polymerchains. Thus microgels may form during specialized reaction conditions whereonly a few chains are interconnected.

Globular proteins constitute excellent examples of one-molecule micronet-works (7), where a single polymer chain is intramolecularly cross-linked; see

Figure 9.2 (8). Here, disulfide bonds help keep the three-dimensional struc-ture required for protein biopolymer activity.Such proteins may be denatured by any of several mechanisms, especially

heat. Thus, when globular proteins are cooked, the intramolecular cross-linksbecome delocalized, forming intermolecular bonds instead. This is the majordifference between raw egg white and hard-boiled egg white, for example.

Fully cross-linked on a macroscopic scale, polymer networks fall into dif-ferent categories. It is convenient to call such polymers, which are used below

9.1 CROSS-LINKS AND NETWORKS 429

Figure 9.2 The structure of ribonuclease A, a micronetwork of one chain. Note cysteine

cysteine bonds (8).


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their glass transition temperature, thermosets, since they are usually plasticsincapable of further flow. On the other hand, those networks that are abovetheir glass transition temperature are rubbery unless very heavily cross-linked.While all these kinds of cross-linked polymers are important, the remainderof this chapter is devoted primarily to amorphous, continuous polymernetworks above their glass transition temperature, the regime of rubberelasticity.

While the rubber elasticity theory to be described below presumes a ran-domly cross-linked polymer, it must be noted that each method of networkformation described above has distinctive nonuniformities, which can lead tosignificant deviation of experiment from theory. For example, chain polymer-

ization leads first to microgel formation (9,10), where several chains bondedtogether remain dissolved in the monomer. On continued polymerization, themicrogels grow in number and size, eventually forming a macroscopic gel.However, excluded volume effects, slight differences in reactivity between themonomer and cross-linker, and so on lead to systematic variations in cross-link densities at the 100- to 500- level.

9.2 HISTORICAL DEVELOPMENT OF RUBBER

9.2.1 Early Developments

A simple rubber band may be stretched several hundred percent; yet on being

released, it snaps back substantially to its original dimensions. By contrast, asteel wire can be stretched reversibly for only about a 1% extension. Abovethat level, it undergoes an irreversible deformation and then breaks.This long-range, reversible elasticity constitutes the most striking property of rubberymaterials. Rubber elasticity takes place in the third region of polymer vis-coelasticity (see Section 8.2) and is especially concerned with cross-linkedamorphous polymers in that region.

Columbus, on his second trip to America, found the American Indiansplaying a game with rubber balls (11,12) made of natural rubber.These crudematerials were un-cross-linked but of high molecular weight and hence wereable to hold their shape for significant periods of time.

The development of rubber and rubber elasticity theory can be traced

through several stages. Perhaps the first scientific investigation of rubber wasby Gough in 1805 (13). Working with unvulcanized rubber, Gough reachedthree conclusions of far-reaching thermodynamic impact:

1. A strip of rubber warms on stretching and cools on being allowed to con-tract. (This experiment can easily be confirmed by a student using arubber band. The rubber is brought into contact with the lips andstretched rapidly, constituting an adiabatic extension. The warming iseasily perceived by the temperature-sensitive lips.)



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2. Under conditions of constant load, the stretched length decreases onheating and increases on cooling.Thus it has more retractive strength athigher temperatures.This is the opposite of that observed for most othermaterials.

3. On stretching a strip of rubber and putting it in cold water, the rubberloses some of its retractile power, and its relative density increases. Onwarming, however, the rubber regains its original shape. In the light ofpresent-day knowledge, this last set of experiments involved the phe-nomenon known as strain-induced crystallization, since unvulcanizednatural rubber crystallizes easily under these conditions.

In 1844 Goodyear vulcanized rubber by heating it with sulfur (14). Inmodern terminology, he cross-linked the rubber. (Other terms meaning cross-linking include tanning of leather, drying of oil-based paints, and curingof inks.) Vulcanization introduced dimensional stability, reduced creep andflow, and permitted the manufacture of a wide range of rubber articles, wherebefore only limited uses, such as waterproofing, were available (15). (TheMacIntosh raincoat of that day consisted of a sandwich of two layers offabric held together by a layer of unvulcanized natural rubber.)

Using the newly vulcanized materials, Goughs line of research was contin-ued by Kelvin (16). He tested the newly established second law of thermody-namics with rubber and calculated temperature changes for adiabaticstretching. The early history of rubber research has been widely reviewed(17,18).

All of the applications above, of course, were accomplished withoutan understanding of the molecular structure of polymers or of rubber inparticular. Beginning in 1920, Staudinger developed his theory of thelong-chain structure of polymers (19,20). [Interestingly Staudingers viewwas repeatedly challenged by many investigators tenaciously adhering to ringformulas or colloid structures held together by partial valences (21).] SeeAppendix 5.1.

9.2.2 Modern Developments

In the early days the only elastomer was natural rubber. Starting around 1914,a polymer of 2,3-dimethylbutadiene known as methyl rubber was made in

Germany. This was replaced by a styrenebutadiene copolymer calledBuna-S (butadienenatriumstyrene), where natrium is, of course, sodium.This sodium-catalyzed copolymer, as manufactured in Germany in the periodfrom about 1936 to 1945 had about 32% styrene monomer (22).

In 1939 the U.S. government started a crash program to develop a manu-factured elastomer, called the Synthetic Rubber Program (23).The new mate-rial was called GR-S (government rubber-styrene). GR-S was made byemulsion polymerization.While the Bunas was catalyzed by sodium, the latterwas catalyzed by potassium persulfate. Incidentally, the emulsifier in those

9.2 HISTORICAL DEVELOPMENT OF RUBBER 431


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days was ordinary soap flakes. Both materials played crucial roles in WorldWar II, a story told many times (2325).

While Buna-S had about 32% styrene monomer (22), the GR-S material,started a few years later with the benefit of the German recipe, had about 25%styrene (26). This difference in the composition was important for loweringthe glass transition temperature. Using the Fox equation,equation (8.73), witha Tg of polystyrene of 373 K, and that of polybutadiene of 188 K, Table 8.7,values ofTg for Buna-S and GR-S are estimated at -47 and -58C, respec-tively. Noting that winter temperatures in European Russia reach -40 to-51C (27), lore has it that use of Buna-S seriously influenced the winterRussian campaigns.

Today, SBR elastomers are widely manufactured with only minor improve-ments in the GR-S recipe.One such is the use of synthetic surfactants as emul-sifiers. These and other improvements allow the production of more uniformlatex particles.

9.3 RUBBER NETWORK STRUCTURE

Once the macromolecular hypothesis of Staudinger was accepted, a basicunderstanding of the molecular structure was possible. Before cross-linking,rubber (natural rubber in those days) consists of linear chains of high molec-ular weight. With no molecular bonds between the chains, the polymer may

flow under stress if it is above Tg.The original method of cross-linking rubber,via sulfur vulcanization,results

in many reactions. One such may be written

(9.1a)

where R represents other rubber chains.Two other methods of cross-linking polymers must be mentioned here. One

is radiation cross-linking, with an electron beam or gamma irradiation. Usingpolyethylene as an example,

C2 CH2

CH3

CH CH2 + sulfur

CCH

S

CH3

CH CH2

S

S

CH CH CHC

S R

CH3


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