The Viscosity of Polymer Solutions

if we measure the rate of flow of polymer solutions through capillaries we can get a measure of their viscosity. Two simple 

FIGURE 12-24 Which of these two molecules would display the highest viscous drag (diag—the ability to hold back the flow of the fluid)  

Furthermore, if what we want to determine is the frictional forces between a single polymer molecule and the solvent, then we need to make the measurements in dilute solution, so that there is no contribution from poly-mer/polymer interactions. In fact, just as in osmometry and light scattering, we measure the relative viscosity over a range of dilute solution concentrations and extrapolate to zero concentration. 

FIGURE 12-25 Schematic diagrams of (a) an Oswald viscometer and (b) an Ubbelholde or suspended-level viscometer. 

FIGURE 12 26 Plot of t kI versus c for poly-(metfayl methacrylate) in chloroform [replotted from the data of G. V. Schulz and F. Blashke, 

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In addition to thermodynamic appUcations, 62 values have also been related to the glass transition temperature of a polymer, and the difference 62-61 to the viscosity of polymer solutions. The best values of 6 have been analyzed into group contributions, the sum of which can be used to estimate 62 for polymers which have not been characterized experimentally. 

This chapter contains one of the more diverse assortments of topics of any chapter in the volume. In it we discuss the viscosity of polymer solutions, especially the intrinsic viscosity the diffusion and sedimentation behavior of polymers, including the equilibrium between the two and the analysis of polymers by gel permeation chromatography (GPC). At first glance these seem to be rather unrelated topics, but features they all share are a dependence on the spatial extension of the molecules in solution and applicability to molecular weight determination. 

This concludes our discussion of the viscosity of polymer solutions per se, although various aspects of the viscous resistance to particle motion continue to appear in the remainder of the chapter. We began this chapter by discussing the intrinsic viscosity and the friction factor for rigid spheres. Now that we have developed the intrinsic viscosity well beyond that first introduction, we shall do the same (more or less) for the friction factor. We turn to this in the next section, considering the relationship between the friction factor and diffusion. 

The viscosity of polymer solutions has been considered theoretically by Flory,130 but although this theory has been applied to cellulose esters,131 no applications have yet been made in the case of the starch components. Theoretical predictions of the effect, on [17], of branching in a polymer molecule have been made,132 and this may be of importance with regard to the viscometric behavior of amylopectin. 

In order to reduce production costs, high polymer concentrations are preferred in hydrogenation operations. However, the viscosity of polymer solutions rises rapidly as the polymer concentration increases. In present-day commercial processes, polymer concentrations do not normally exceed 15 wt.%. 

Miyata and Nakashio [77] studied the effect of frequency and intensity on the thermally initiated (AIBN) bulk polymerisation of styrene and found that whilst the mechanism of polymerisation was not affected by the presence of ultrasound, the overall rate constant, k, decreased linearly with increase in the intensity whilst the average R.M.M. increased slightly. The decrease in the overall value of k they interpreted as being caused by either an increase in the termination reaction, specifically the termination rate constant, k, or a decrease in the initiator efficiency. The increase in kj(= kj /ri is the more reasonable in that ultrasound is known to reduce the viscosity of polymer solutions. This reduction in viscosity and consequent increase in Iq could account for our observed reductions [78] in initial rate of polymerisation of N-vinyl-pyrrolidone in water. However this explanation does not account for the large rate increase observed for the pure monomer system. 

Polymer solutions are never ideal since dissolved macromolecules influence each other even at very low concentration. On the other hand, a reliable correlation of solution viscosity and molecular weight is only possible if the dissolved macromolecules are not affected by mutual interactions they must be actually independent of each other. Therefore, the viscosity of polymer solutions shoifld be determined at infinite dilution. However, such measurements are impossible in practice. So one works at an as low as possible polymer concentration and extrapolates the obtained values to zero concentration. To do so, the elution time... 

Branched chains occupy more volume than linear chains, and the viscosity of polymers with branched chains is less than that of those with linear chains. The viscosities of polymer solutions are greater than those of solvents. 

We then conclude the chapter with a brief discussion of the viscosity of polymer solutions. 

Here kH is the Huggins coefficient. The intrinsic viscosity decreases and the Huggins coefficient increases, as micelles become smaller. On micellization, ijsp/c has been observed to increase for some systems but to decrease for others, and unfortunately there are no firm rules governing which case will prevail for a given block copolymer solution. The viscosities of polymer solutions are measured in capillary flow viscometers, which are described in detail by Macosko (1994). 

It is not uncommon to encounter emulsions, foams, and suspensions, both in nature and in industry, that contain polymers. If the polymer concentration is high enough, and the dispersed species concentration low enough, the overall viscosity may be better described by the contribution from the polymer solution than that from the dispersed species. One commonly employed equation for describing the viscosity of polymer solutions is the Carreau equation,... 

The advantage of these models is that they predict a Newtonian plateau at low shear rates and thus at low shear stresses. We will see back these models in Chap. 16 where an extra term 7700 is added to the equations to account for the viscosity of polymer solutions at high shear rates. At high shear rates the limiting slopes at high shear rates in log r) vs. log y curves are for the Cross, the Carreau and the Yasuda et al. models —m, (n-1) and (n-1), respectively. 

For this reason the effects of concentration and temperature on the viscosity of polymer solutions cannot be separated. 

Equations for the viscosity of polymer solutions over the whole concentration range... 

Nevertheless, Lyons and Tobolsky (1970) proposed an equation for the concentration dependence of the viscosity of polymer solutions, which is claimed to be valid for the whole concentration range from very dilute solutions to pure polymer. The equation reads ... 

A certain generalisation is permitted with respect to the relationship between the effects of concentration and molecular mass on the viscosity of polymer solutions. It is restricted to solutions of polymers with M > Mcr in good solvents. 

The relative viscosities of polymer solutions are measured at different concentrations and a plot of the reduced viscosity versus concentration is made, in order to extrapolate to zero concentration. The concentration dependence of the viscosity of polymer solutions, in the dilute regime, may be expressed by several linear equations. For practical extrapolation to zero concentration, the most commonly employed are the Huggins equation ... 

The problem is that if produced water with higher salinity is used, the viscosity of polymer solution will be lower. For example, if produced water is used instead of fresh water, the polymer concentration has to be increased by 55% to reach the same viscosity. To solve this problem, we need a polymer that can tolerate high salinity. A polymer with 30 million MW was used for this purpose in a Daqing pilot test (Niu et al., 2006). 

The grid blocks used are 100 x 1 x 1, which is a ID model, and the length is 0.75 ft. Some of the reservoir and fluid properties and some of the surfactant data are listed in Table 8.1. The viscosity of polymer solutions at different concentrations is presented in Figure 8.5. The polymer adsorption data are shown in Figure 8.6. The microemulsion viscosity is shown in Figure 8.7, and the capillary desaturation curves are shown in Figure 8.8. 

It may be assumed that under the action of a shear stress the polymer coil with the solvent enclosed by it behaves like an Einsteinian sphere, and hence, the viscosity of polymer solution should obey Eq. (3.172) for noninteracting spherical particles. Noninteraction of the polymer coils requires infinite dilution and this is achieved mathematically by defining a quantity called the intrinsic viscosity, [77], according to equation... 

This condition is readily satisfied for the apparatus and liquids usually used for measurements of the viscosities of polymer solutions. However, in addition to the requirements of viscous flow, the derivation of Eq. (4.128) relies on the following assumptions. 

The viscosities of polymer solutions and of polymer melts have some very important common features, which are related to the fundamental nature of the motions of polymer chain segments [4,8,10] resulting in the flow of macromolecular chains. At an empirical level, one manifestation of these interrelationships is that Mcp which is the key material parameter determining the molecular weight dependence of the melt viscosity, can be estimated from the intrinsic viscosity of the polymer under 0 conditions, which was discussed in Chapter 12. If K -Mci.0-5 is expressed in units of cc/grams, then Mcr can be predicted [7] (but only to within a factor of two) by using Equation 13.6. 

Various theories have been proposed which take into account the effects of aggregation on the viscosities of polymer solutions (2). These theories generally require a detailed knowledge of the mechanism and energetics of association. Further, they are considered applicable only to moderately concentrated solutions. 

The viscosity of polymer solutions is usually determined by measuring the flow time of a definite quantity of solution through a capillary. The driving force is the height of the fluid in the viscometer. A difficulty arises because polymer solutions are sufficiently oriented in ordinary capillary viscometers so that even at a low rate of shear the viscosity determined does not correspond to its real value at zero shear. In order to get values which are reproducible, regardless of the viscometer used, the viscosities, therefore, have to be determined at several rates of shear and extrapolated to zero shear rate as well as to zero concentration. This is particularly import t for high molecular-weight polymers where the shear dependence of viscosity is most pronounced. 

In bulk and solution polymerizations, the reaction mixture is homogenous (single phase) and thus the viscosity at any time is given by the viscosity of polymer solution at the given reactor temperature. During the polymerization, high solution viscosity can constrain mixing, heat and mass... 

In nonaqueous solvents, the viscosities of polymer solutions is often well described by a simple relationship with temperature, solids and and can be fit to a general semiempirical expression as described by Pezzin... 

Perhaps the most important factor to a process engineer in predicting extrusion or molding behavior is melt viscosity. Several methods are used to obtain the viscosity of polymer solutions and melts experimentally as a function of shear rate [19]. Instruments for making such measurements must necessarily accomplish two things (1) the fluid must be sheared at measurable rates, and (2) the stress developed must be known. Two kinds of instruments having simple geometry and wide use a rotational viscometer and capillary or extrusion rheometer. 

The viscosity of polymer solution, at the molecular level, is a direct measure of the hydrodynamic volume of the polymer molecules which in turn is governed by the molecular size or chain... 

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