Summary of networks and gels

Polymer networks are very important soft solids. As such, they find applications ranging from adhesives to automobile tires. The mechanical properties of network polymers arise primarily from the changes in entropy of the network strands when the network is macroscopically 

The number density of network strands determines and the plateau modulus caused by inter-chain entanglements is Cg. This plateau modulus is understood on a molecular level by imagining surrounding chains confining each network strand to an effective tube. 

Many models lead to a classical form for the variatipn of the true stress with uniaxial elongation  

Polymer gels are diluted polymer networks. The diluent can be other polymer chains or solvent. The modulus of gels decreases on dilution, in ways that depend on the details of the polymer-solvent interaction. When immersed in an excess of an appropriate solvent, polymer networks can often swell considerably. The swelling is driven by the favorable free energy 

Dynamics in polymer networks and also in polymer liquids can be studied by a variety of viscoelasticity experiments. For networks and gels, these methods determine the modulus from the long time (or low frequency) viscoelastic response and directly measure the relaxation of dangling structures and sol fraction at higher frequencies. For polymer 

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