Onset of Entanglement Coupling

Logarithmic plots of G (black circles) and G - wris (open circles) against frequency reduced to a reference temperature of 25.0°C for polystyrene with M = 261,000 in chlorinated diphenyl (Aroclor 1232). Ordinates displaced as shown by respective locations of 4 on the vertical scale. Numbers refer to concentrations c in g/cm tags on points to different temperatures of measurement, between 0° and 25°C. Reproduced, by permission, from the Journal of Polymer Science. 

Schematic delineation of dilute, semidilute, and entangled regions on a logarithmic map of M against c for polystyrenes in a good solvent. 

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The terminal relaxation time t can be roughly estimated from equation 7 of Chapter 10, derived from the Rouse theory it may be expected to be nearly correct since the molecular weight is only moderately greater than that for onset of entanglement coupling effects. The result is ti = 1.2 X 10 sec, which happens to be very close to the observed value of 1.3 X 10 sec. 

Each of the viscoelastic parameters G°, rj0, and Je° has associated with it a characteristic molecular weight which either measures an equivalent spacing of entanglement couples along the chain (Me, deduced from G with the kinetic theory of rubber elasticity), or marks the onset of behavior attributed to the presence of entanglements (Mc and AT, deduced from r/0 and Je° as functions of molecular weight). Table 5.2 lists Me, Mc, and M c for several polymers. Aside from certain difficulties in their evaluation, each is a rather direct and independent reflection of experimental fact. 

Bates et al. 1990 Rosedale and Bates 1990). It was pointed out that the onset of measurable fluctuation effects depends on molecular weight in a manner that suggests that entanglements play an important role in coupling fluctuations... 

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