Viscosity parameters

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

The constant 0, called the Flory-Fox viscosity parameter, has an experimental value of x2.5 x 1023 mol-1 [44]. The corresponding value for x2 is then ... 

The advantage of this simplified case is that the conversion and velocity profiles for all reactors can be represented in terms of the viscosity parameter, a, a... 

Figure 1. Cup average conversion as a function of the Theile modulus, < ), and the viscosity parameter, a, at a dimensionless length, = 3.0.

Since [n] is a physically measurable quantity and is more directly relatable than the usual SEC calculated Mn and Mw values to the macroscopic viscosity parameters of the polymer solution, a routine SEC-[n] method brings SEC a step closer to practical evaluation of the strength and processibility of different polymer samples. 

Frechet [49, 89] was the first to compare viscosity parameters for (A) linear topologies, as well as (B) random hyperbranched polymers and (C) dendrimers. More recently, we reported such parameters for (D) dendrigraft polymers [111] as shown in Figure 1.19. It is clear that all three dendritic topologies behave differently than the linear. There is, however, a continuum of behavior wherein random hyperbranched polymers behave most nearly like the linear systems. Dendrigrafts exhibit intermediary behavior, whereas dendrimers show a completely different relationship as a function of molecular weight. 

The following is a brief review of the viscosity pareimeters that are commonly used in polymer analyses. The relative viscosity (ripgi) of a polymer saitple solution as defined in Equation 1 can be determined experimentally from the measured viscosity value for the polymer saitple solution (h) and that of the solvent (h )- From the h -1 value and the polymer sanple concentration (c), tne calculations for the other viscosity parameters are possible in accordance to Equations 2 through 5 ... 

It is clear that if a - 0 and by denoting b = T, from Eq. (5.12) we shall obtain Eq. (4.10). Since the viscosity parameters a and b depend on the temperature differential AT = Tm - T0, the dependence of tf on AT may be readily analyzed. This seems reasonable only upon determining the characteristic time for the stage of feeding-up (with the viscosity change in the course of gelatination taken into account). 

There are theoretical expressions for the effect of the solvent on the reaction rate using dielectric constant (e) and viscosity parameters. Grissom et al. [95] have reported the increase in photostability of Vitamin B-12 by addition of viscogens, such as glycerol and Ficoll. However, in this section the focus will be on the inLuence of the dielectric constant of the solvent. 

Therein, D-1 is the positive definite, isotropic, fourth order viscous compliance, where r/ s and (s are the macroscopic viscosity parameters, D, , is the inelastic solid deformation rate and = F, 1 rfEQ F 71 is the corresponding non-equilibrium stress tensor. Furthermore, the superscript ( ) indicates the belonging to the intermediate configuration. 

Where tube methods are used, an often-encountered viscosity parameter is the kinematic viscosity. It is determined from the same measurement as above, but without requiring any knowledge of the density ... 

Pokrovskii and Kokorin (1987) extended the results to the more general case where the internal viscosity parameter assume arbitrary values and the excluded-volume effects are taken into account. 

An important aspect of magnetic viscosity is its field dependence. For example, S(H) tends to exhibit a maximum near the coercivity. This reflects the close relationship between the energy-barrier distribution and the irreversible part x>n of the susceptibility, and leads to S = x where the viscosity parameter Sv is only weakly field-dependent [5, 133, 159, 167, 169-172],... 

The highly viscous spray fluids used in pesticide application have been either water-in-oil emulsions or solutions of macromolecules both systems are non-Newtonian since their viscosity varies with the applied shear. While a viscosity parameter which is suitable for studies on drop formation was subsequently devised for such systems (II), it was necessary to use Newtonian liquids in the initial studies on the effect of viscosity on drop size. Sugar solutions behave as Newtonian liquids and provide a suitable means of varying viscosity over a wide range. These were prepared from a commercially available syrup by dilution with distilled water 1% w/v of a black dye (Nigrosine G140) was added to each solution to render the spray drops visible for sizing. 

Other aspects of transport phenomena including activation energies for viscosity parameters and Washburn transport numbers (Feakins, 1974a Feakins and Lorimer, 1974) have also been measured to probe ion-solvent interactions in mixed solvent systems. 

Fig. 8. Variations of viscosity parameter with expansion factor. Experimental data of Schulz (229) (circles) and Krigbaum and Carpenter (146) (crosses) Theoretical curves according to Eqs. (55) and (56) for homogeneous polymers (broken curve and chain curve) and for broad fractions (dotted curve and full curve)...

The third mechanism by which proteins affect the stability of emulsions is rheological. This mechanism derives fundamentally from electrostatic and steric effects. The importance of viscosity has been described earlier. The viscosity of a caseinate solution is, inter alia, an indicator of the degree of bound water absorbed by the hydrophilic groups, as well as the water trapped inside the molecular aggregates (Korolczuk, 1982). The viscosity parameters (K, apparent viscosity at zero shear stress n, the power law factor and o-y, the yield stress) of sodium caseinate have been studied and found to be affected by concentration (Hermansson, 1975), precipitation and solution pH of caseinate (Hayes and Muller, 1961 Korolczuk, 1982), de-naturation (Hayes and Muller, 1961 Canton and Mulvihill, 1982), sodium chloride (Hermansson, 1975 Creamer, 1985), calcium chloride (Hayes and Muller, 1961) and temperature (Korolczuk, 1982). 

Table 9.3. Main effects of the ingredients on the viscosity parameters of the aqueous phase of emulsions (Keogh, 1993)a... 

Aqueous phase viscosity parameters and percentage variance... 

V 14. Molar intrinsic viscosity J K -M - 4.2Z Intrinsic viscosity parameter K1/2 Ae... 

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