Until quite recently, there was relatively little reliable quantitative information on the relationship of stress to structure, primarily because of the uncontrolled manner in which elastomeric networks were generally prepared. Segments close together in space were linked irrespective of their locations along the chain trajectories, thus resulting in a highly random network structure in which the number and locations of the cross-links were essentially unknown. Such a structure is shown in figure 10.1. New synthetic techniques are now available, however, for the preparation of “model” polymer networks of known structure. More specifically, if networks are formed by end linking functionally terminated chains instead of haphazardly joining chain segments at random, then the nature of this very specific chemical reaction provides the desired structural information. Thus, the functionality of the cross links is the same as that of the end-linking agent, and the molecular weight Mc between cross-links and the molecular weight distribution are the same as those of the starting chains prior to their being end-linked. An example is the reaction shown in figure 10.2, in which hydroxyl-terminated chains of poly(dimethylsiloxane) (PDMS) are end-linked using tetraethyl orthosilicate. Characterizing the un-cross-linked chains with respect to molecular weight Mn and molecular weight distribution, and then carrying out the specified reaction to completion, gives elastomers in which the network chains have these characteristics; in particular, a molecular weight Mc between cross-links equal to Mn, a network chain-length distribution equal to that of the starting chains, and cross-links having the functionality of the end-linking agent. It is also possible to use chains having a known number of potential cross-linking sites placed as side chains along the polymer backbone, so long as their distribution is known as well. Because of their known structures, such model elastomers are now the preferred materials for the quantitative characterization of rubberlike elasticity. Such very specific cross-linking reactions have also been shown to be useful in the preparation of liquid-crystalline elastomers. Trifunctional and tetrafunctional PDMS networks prepared in this way have been used to test the molecular theories of rubber elasticity with regard to the increase in non-affineness of the network deformation with increasing elongation.
Cytoskeletal Polymer Networks: Viscoelastic Properties are Determined by the Microscopic Interaction Potential of Cross-links