Normalized molecular weight function

As noted previously in this chapter, Eqs. (9.13)-(9.16) indicate that the line shape of the G t) curve is a universal function of the normalized molecular weight M/Me in the region covered by the pB t) and pc(t) processes. The relaxation times tb and tc can also be normalized with respect to the relaxation time of the lowest mode of the pA t) process, KM /6,... 

The fact that these two relaxation-time ratios are a universal function of M/Mg indicates that the universality of the G t) line shape extends to the PA t) process region, pxit) is situated between pA t) and the processes PB t) and pc t)- Thus, although we do not have the theoretical form for Px t), its characteristic time tx normalized with respect to should also be a function of the normalized molecular weight M/Mg- From the G t) line shape analysis in terms of Eq. (9.19) as discussed in detail in Chapter 10, it has been found that tx is best described by... 

Figure 8-6. Calculated W/A , ratios as a function of the exponents t, for a Schuiz-Flory (—) or a generalized logarithmic normal (--) molecular-weight distribution for. in cadi case. w/M, 2. SI may be A , or (After H.-G. Elias, R. Bareiss and J. G.

Prediction of the zero-shear viscosity rify normalized by the zero-shear viscosity of a polymer with molecular weight corresponding to one entanglement, as a function of normalized molecular weight Z=M/M for pure reptation (solid thin line), reptation with fluctuations, given by Eq. 6.33 with X = 1.3 (solid thick line), and the empirical formula t]q (dashed... 

Melt Viscosity. The study of the viscosity of polymer melts (43—55) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus melt viscosity as a function of temperature, pressure, rate of flow, and polymer molecular weight and stmcture is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extmsion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. 

Wax usually refers to a substance that is a plastic solid at ambient temperature and that, on being subjected to moderately elevated temperatures, becomes a low viscosity hquid. Because it is plastic, wax usually deforms under pressure without the appHcation of heat. The chemical composition of waxes is complex all of the products have relatively wide molecular weight profiles, with the functionaUty ranging from products that contain mainly normal alkanes to those that are mixtures of hydrocarbons and reactive functional species. 

There are many hundreds of raw material amines commercially available, and a wide variety are used for water treatment applications. They typically have low flash points and are therefore normally dissolved in water down to 20 to 40% strength, to minimize fire risks and permit blending. Additionally, each material has its own specific functional profile covering molecular weight, solubility, volatility, DR, basicity, thermal stability, and other parameters. The standard water treatment amines have all been known and used for 30 to 40 years or more. 

Fig. 50. Yield for chain scission as a function of strain rate for different fractions of polycarbonate (PC) in benzyl alcohol/dioxan (90 10 v.v) at 20 °C. A normal PC with Mp = 417000 B normal PC with Mp = 321000 C normal PC with Mp = 256000 D PC with weak bonds, Mp = 217000 Mp molecular weight at peak maximum sc critical strain rate for chain scission (extrapolated from the linear portion of the degradation curve)...

The molecular weight of a polymer will be reduced if either die extent of conversion or the average functionality is decreased. At 95% conversion of difunctional monomers, for example, Xn is only 20.25 The molecular weight is also related to a stoichiometric imbalance, r, which is normally defined to be less than 1.0 ... 

The sedimentation coefficient s°, or its normalized form 5 0 w function of the conformation and flexibility of a macromolecule (via its translational frictional property) and its mass. So if we are going to obtain conformation and flexibility information we need to know the molecular weight (molar mass)... 

Here the summation is over molecules k in the same smectic layer which are neighbours of i and 0 is the angle between the intermolecular vector (q—r ) projected onto the plane normal to the director and a reference axis. The weighting function w(rjk) is introduced to aid in the selection of the nearest neighbours used in the calculation of PsCq). For example w(rjk) might be unity for separations less than say 1.4 times the molecular width and zero for separations greater than 1.8 times the width with some interpolation between these two. The phase structure is then characterised via the bond orientational correlation function... 

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