Intrinsic viscosity terms

As expected, PB (Xx) exerted the main positive effect on the Izod, but this was balanced by a relatively small quadratic term. The ash content (X6) had a considerable negative quadratic term, balanced by a positive interaction term, X2X6. The latter became prominent at higher AN contents (X2). The X2X4 (AN x intrinsic viscosity) term had a positive effect on the Izod, and it was also present in the yield strength equation (Equation 5). Since ABS failure is ductile, under both the tensile and the impact tests at room temperature, the X2X4 term assumes greater importance. 

Figure 9.3 Intrinsic viscosity according to the Simha theory in terms of the axial ratio for prolate and oblate ellipsoids of revolution.

The relative viscosity of a dilute dispersion of rigid spherical particles is given by = 1 + ft0, where a is equal to [Tj], the limiting viscosity number (intrinsic viscosity) in terms of volume concentration, and ( ) is the volume fraction. Einstein has shown that, provided that the particle concentration is low enough and certain other conditions are met, [77] = 2.5, and the viscosity equation is then = 1 + 2.50. This expression is usually called the Einstein equation. 

In HOPC, a concentrated solution of polymer is injected. The concentration needs to be sufficiently higher than the overlap concentration c at which congestion of polymer chains occurs. The c is approximately equal to the reciprocal of the intrinsic viscosity of the polymer. In terms of mass concentration, c is quite low. For monodisperse polystyrene, c is given as (4)... 

As in the case of the Rouse relaxation time, it is possible to express x2 in term of the intrinsic viscosity either by using Eq. (24) or the Kirkwood-Riseman theory [24, 47] ... 

It was shown that the logarithm of the product of intrinsic viscosity and molecular weight of polymers of different chemical and stereochemical composition, configuration, or molecular weight is linearly related to the elution volume.81 A plot of log (r) M) vs. elution volume provides a single calibration curve, useful for samples of similar composition, and is termed a universal... 

The hydration of polyoxyethylene (POE) is dramatically affected by the anion present(J 0) in the aqueous phase. The adsorption of HEC (both 2.0 and 4.3 M.S.) was therefore studied in Na SO and Na PO, at equivalent normalities. The multivalent anions are more effective in precipitating POE than is the chloride ion. The amounts adsorbed and the interlayer expansions at normalities below precipitation conditions are given in Table III. The influence of multivalent anions on the intrinsic viscosity of variable M.S. HECs is illustrated in Figure 6. The increased amounts adsorbed are within experimental error, but the decrease in d. with the 4.3 M.S. HEC is notable. The d. changes in the absence of increased adsorption are not explainable in terms of solvation effects. 

This term has been suggested (compare Ref. 2) to replace intrinsic viscosity ... 

In this section alone, in order to avoid confusion the intrinsic viscosity [rf] represents that of a particle and is dimensionless and the intrinsic viscosity [rj] represents that of a polymer and has units of gem-3. From these expressions we know that as we increase the volume fraction above each of these values, the product demarcates the structural transition. For particles there are many situations where it is relatively easy to determine the volume fraction, but for polymers the situation is more complex and it is most convenient to use a mass concentration. We can rewrite this relationship in terms of the mass of added particles in gem-3 ... 

However, in such a high concentration regime we can no longer represent the relaxation times (Equation (5.92)) in terms of the intrinsic viscosity. In the low frequency limit, because there is no permanent crosslinking present, the loss modulus divided by the frequency should equate with ... 

Two approaches are common in modelling the SSP process. For the first approach, an overall reaction rate is used which describes the polycondensation rate in terms of the increase of intrinsic viscosity with time. Depending on the size and shape of the granules, the reaction temperature, the pressure, and the amount and type of co-monomers, the overall polycondensation rate lies between 0.01 and 0.03 dL/g/h. The reaction rate has to be determined experimentally and can be used for reactor scale-up, but cannot be extrapolated to differing particle geometry and reaction conditions. 

The shift in the intrinsic viscosity is easily understood in qualitative terms. Assuming validity of the Fox-Flory relationship also for branched macromolecules one can write... 

Alternatively, Eq. (295) can be rewritten in terms of the intrinsic viscosity given... 

Next, a plot is made for the terms and n(ri )/c as a function of c as was shown in Fig. 3.7. Extrapolation of the functions to a concentration of zero provides the intrinsic viscosity of 0.565 dl/g, as shown in Eig. 3.8. Using Mark-Houwink-Sakurada Eq. 3.22, the viscosity average molecular weight is calculated at 221,000 kg/kg-mole. 

It may seem confusing to introduce yet another type of viscosity. In fact, there are many other types of viscosity (see Table 4.5), but we will concentrate on the intrinsic viscosity for polymer solutions. The intrinsic viscosity is important because it has been found to correlate well with a number of important parameters, including polymer molecular weight and type of solvent. Note that if Eq. (4.23) is truncated to the first two terms, the intrinsic viscosity is the same as the reduced specific viscosity, r]sp, of Table 4.5. 

The effect of branching is to increase the segment density within the molecular coil. Thus a branched molecule occupies a smaller volume and has a lower intrinsic viscosity than a similar linear molecule of the same molecular weight. The degree of branching is often characterized in terms of the branching factor [1] in Eq. (14), where the subscripts B and L, respectively, refer to branched and linear polymers of the same molecular weight ... 

Benoit and co-workers [18] proposed that the hydrodynamic volume, Vr which is proportional to the product of [17] and M, where [17] is the intrinsic viscosity of the polymer in the SEC eluent, may be used as the universal calibration parameter (Fig. 18.3). For linear polymers, interpretation in terms of molecular weight is straightforward. If the Mark-Houwink-Sakurada constants K and a are known, log [t7]M can be written log M1+ + log K, and VT can be directly related to M. The size-average molecular weight, Mz, is defined by this process ... 

Equation (48) has been derived under the assumption that the volume fraction can reach unity as more and more particles are added to the dispersion. This is clearly physically impossible, and in practice one has an upper limit for , which we denote by max. This limit is approximately 0.64 for random close packing and roughly 0.71 for the closest possible arrangement of spheres (face-centered cubic packing or hexagonal close packing). In this case, d in Equation (46) is replaced by d(j>/[ 1 — (/m[Pg.169]

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