Polymer notations Viscosity

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

Universal SEC calibration reflects differences in the excluded volume of polymer molecules with identical molecular weight caused by varying coil conformation, coil geometry, and interactive propenies. Intrinsic viscosity, in the notation of Staudinger/ Mark/Houwink power law ([77]=fC.M ), summarizes these phenom-... 

In Section 6.3.3 some of the experimental evidence for and theoretical interpretation of a depleted layer effect close to the pore wall was reviewed. This is discussed here in the context of a narrow cylindrical capillary in which the hydrodynamic problem can be formulated. Figure 6.7 shows that there is a polymer concentration profile, C(r), across the capillary and that the depleted layer extends over a distance S from the wall. Some notation is introduced in Figure 6.6 r is the radial co-ordinate, i 2 is the tube radius, is the radius of the inner bulk region, and the depleted layer thickness, d, is given by d = R2 — Ri). In order to perform calculations on the hydrodynamic effects which are caused by this profile, it is necessary to have a single analytic form for either the concentration profile, C(r), or the resulting viscosity profile, rj r), directly. The latter quantity must be derived in the calculations if it is not directly available. In the absence of a depleted layer. 

There are basically two difficulties associated with the determination of for immiscible polymer blends using a plunger-type capillary rheometer. One difficulty lies in the determination of shear rate of dispersed two-phase polymer blends (see Figures 11.1-11.3 for PMMA/PS blends). This is because one cannot define the shear rate (velocity gradient) of a dispersed two-phase polymer blend inside a capillary die. Thus, at best what one can do is to calculate an apparent shear rate from Tapp = 32 2/tt with Q being the volumetric flow rate and D being the capillary diameter. One can then only calculate an apparent shear viscosity from the definition = a/)>app. Thus, to be precise, in Figure 11.4 we should have used the notation rj... 

Many time-dependent flows have been studied by polymer chemists. A particularly important one is the small-amplitude sinusoidal shear flow (Figure 2b) where = Re(y e " y, Vy = 0, v = 0, in which is in general a complex quantity and co is the frequency of oscillation the notation Re means the real part of . Then because the amplitude of the oscillation is vanishingly small, the shear stress is also sinusoidal Ty = Reltyj e, where Zy is complex. We now define a complex viscosity by... 

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