Properties of the Plateau Modulus

The values of Mc [defined by Eq.(5.19)] are those reported by Ferry (15) and Berry and Fox (16), except that for polystyrene (124) and the values in parentheses for poly-methyl methacrylate (146), polybutadiene (79,197), and ds-polyisoprene (79, 197). The values of (defined as described in 5.4.1) are from the same compilations, except that for poly (a-methyl styrene) (161). The values of Mc were obtained as described in Section 5.4.4. 

As molecular weight increases, the slow relaxations shift progressively to longer times while the fast relaxations remain essentially unchanged. 

For long chains, the modulus at about 106-107 dynes/cm2 passes into a domain of much slower relaxation (the plateau region). The width of the plateau depends strongly on molecular weight, while the characteristic modulus of the plateau region G is independent of molecular weight. The presence of the plateau confers rubber-like elastic properties over an intermediate range of frequencies or times. 

The plateau region appears when the molecular weight exceeds Mc [(Mc)soln. for solutions], and is taken to be a direct indication of chain entanglement. Indeed the presence of a plateau may be a more reliable criterion than r 0 vs M behavior, especially in solutions of moderate concentration where viscosity may exhibit quite complex concentration and molecular weight behavior. It is postulated that when M greatly exceeds Mc, a temporary network structure exists due to rope-like interlooping of the chains. Rubber-like response to rapid deformations is obtained because the strands between coupling points can adjust rapidly, while considerably more time is required for entire molecules to slip around one another s contours and allow flow or the completion of stress relaxation. 

Plateau moduli are commonly expressed in terms of Me, the apparent average molecular weight between coupling junctions. The modulus equation from the 

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