Polystyrene Linear viscoelastic behavior

Bailly, C., Stephanne, V., Muchtar, Z., Schappacher, M. Deffieux, A. Linear viscoelastic behavior of densely graftedpoly(chloroethyl vinyl ether)-g-polystyrene combs in the melt./. Rheol (2003) 47, pp.821-825... 

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

The five regions of viscoelastic behavior for linear amorphous polymers (3,7-9) are shown in Figure 8.2. In region 1 the polymer is glassy and frequently brittle. Typical examples at room temperature include polystyrene (plastic) drinking cups and poly(methyl methacrylate) (Plexiglas sheets). 

It is found empirically that the concentration dependence of 7 can be expressed by proportionality of n r) oo/Vs) to c, and the proportionality constant can be shown to be the high-frequency intrinsic viscosity [rf ]oo- An example is shown in Fig. 9-27 for five linear polystyrenes with widely different molecular weights and three branched samples.The high-frequency intrinsic viscosity is independent of branching as would be expected for a quantity which reflects a very local motion within the molecule it is also independent of molecular weight for M > 19,800. At M = 19,800, it is almost equal to the ordinary (steady-flow) intrinsic viscosity. However, W]oo does depend on detailed chemical structure as shown in Fig. 9-28, where data for several polymers are similarly plotted. Thus the high-frequency behavior is in a sense just the opposite of the low-frequency viscoelastic behavior... 

To illustrate the effect of temperature on mechanical properties, it is sometimes preferable to plot the property vs. temperature for constant values of time. For example, data of the type shown in Fig. 18.21 may be cross-plotted as (10) (the 10-second relaxation modulus) vs. T, Such a plot is given in Fig. 18.23 for several polystyrene samples," The five regions of viscoelastic behavior are evident in the linear, amorphous (atactic) samples (A) and (C) along with the effect of molecular weight in the flow region. The drop in modulus in the vicinity of Tg (100°C) is dearly seen. The crystalline (isotactic) sample maintains a fairly high modulus all the way up to (a 235 "C). Given values of one can convert data in the form vs, t at constant T (a master curve) to vs. T at constant t and vice versa. 

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