Molecular Relaxation modulus, effect

The above discussion easily motivates the notion that reorientation times will become long as the liquid is cooled towards the glass transition, but it does not explain the shape of the observed relaxation function. Part of the shear viscosity in fluids is due to coupling to molecular reorientation. This effect has been studied in detail in alkane liquids26,27. At low viscosities the shear modulus can be described by... 

These points can be illustrated by comparing the elastic relaxation modulus ,(0 for crystalline (isotactic), amorphous, and chemically cross-hnked (atactic) polystyrene samples, as shown in Figure 15.9. Crystalhnity has little effect below Tg, but as the molecular motion increases above T, the modulus of the amorphous polymCT drops more sharply. The value of E t) remains high for the crystalline polymer throughout this range until the rapid decrease at the melting temperature is recorded. The cross-hnked sample maintains its modulus level at this temperature as the crosslinks are not thermally labile and do not melt. 

Another strong indication of the entanglement effect is the observation of a clear plateau in the linear relaxation modulus amj storage modulus spectrum when the polymer has a sufficiently high molecular... 

What has been said above about the effect of molecular-weight distribution on rjo and J° is similarly applicable to the low-molecular-weight region where the contributions of the p,A t) and px t) processes cannot be neglected. The analjTical expressions for 770 and J° cannot be obtained from the full expression of the relaxation modulus (Eq. (9.19)). Yet theoretical values of rjo and J°, including the contributions of PA t) and px(f)> can be numerically calculated with a computer program. 

Two samples of the same polymer equal in weight average molecular weight may exhibit different physical properties, if they differ in the molecular weight distributions. Many effects of the molecular weight distribution on such properties as elongation, relaxation modulus, tensile strength, and tenacity were reported. ... 

Inspection of Figure 5 shows a very broad glass-to-rubber transition range which extends from below -100°C to above 0°C for the polyurethane adhesive. The relaxation modulus E(t) - 400 Kg/cm which occurs at the rubbery inflection temperature - 40°C - 313 K describes an effective molecular weight M as defined by kinetic theory of rubber elasticity ... 

For higher extrusion temperatures, the annealing effect is favoured and molecular relaxation and recrystallisation are more likely to occur. Because of the variation in crystallinity with increasing draw ratio, tensile strength and modulus significantly increase as a fibrillar structure is formed starting from the spherulitic material. An increase of these properties with molecular weight also... 

This result implies that a temperature-independent master curve can be constructed simply by plotting the storage and moduli as functions of the product of frequency times the zero-shear viscosity. Likewise, a master curve of the relaxation modulus can be made by plotting G as a function of t/rjQ. We will see in Chapter 5 that molecular weight has very little effect on the short-time or high-frequency behavior of polymers, i.e., in the transition region, so if the same shift factor is really valid at all relaxation times, it should be independent of molecular weight. 

The study that produced the data shown in Fig. 10.2 [2] included several other solutions, and it was found that molecular weight and concentration had little effect on the damping function for cM around 5 lO. Todemonstrate the degree of time-strain separability, the data ofFig. 10.2 are replotted in Fig. 10.5 as relaxation modulus divided by the vertical shift factor required to superpose them, i.e., The superposibility is excellent for times longer than a... 

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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