Solution Viscosity of Polymers

The bulk viscosity of polymer solution is an important parameter also when polymers are being used as suspending agents to maintain solid particles in suspension by prevention of settling (see Chapter 7) and when they are used to modify the properties of liquid medicines for oral and topical use. 

Departure of the limiting value of rj j4 from the theoretical value of 2.5 may result from either hydration of the particles, or from particle asymmetry, or from both as discussed in Box 8.1. 

The presence in solution of large macromol-ecular solutes may have an appreciable effect on the viscosity of the solution. From a study of the concentration dependence of the viscosity it is possible to gain information on the shape or hydration of these polymers in solution and also their average molecular weight. The assumption is made in this section that the solution exhibits Newtonian flow characteristics. 

The viscosity of solutions of macromolecules is conveniently expressed by the relative viscosity, defined as the ratio of the viscosity of the solution, t], to the viscosity of the pure solvent t]Q  

Another useful expression is the specific viscosity, 7sp, of the solution, defined by 

An important empirical generalization about the intrinsic viscosity of polymer solutions is given by 

EXAMPLE 4.5 Empirical Determination of the Mark-Houwink Coefficients for a Polymer Solution. The molecular weights of various polycaprolactam preparations were determined by end-group analysis (see Example 3.2) intrinsic viscosities of the various fractions in m-cresol were measured at 25°C. The following values are representative of the results obtained (Reim-schussel and Dege 1971)  

Solution By taking the logarithms of Equation (71), a linear form is obtained  

This could be plotted with a and In k evaluated from the slope and intercept, respectively. Alternatively, a least squares analysis of the data can be performed. When this is carried out using the logarithms of the above results, it is found that a = 0.683 and In k = -6.593, or k = 1.37 10 3. The units of k are consistent with the concentration units dl/g. This result can be inverted to give M directly M = 1.51 104[tj]146.  

The practical significance of the result of this example lies in the great ease with which viscosity measurements can be made. Once the k and a values for an experimental system have been established by an appropriate calibration, molecular weights may readily be determined for unknowns measured under the same conditions. Extensive tabulations of Mark-Houwink coefficients are available, so the calibration is often unnecessary for well-characterized polymers (see Table 4.5). 

---

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

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. 

M. Bohdanecky and J. Kovar, Viscosity of Polymer Solutions, Elsevier, Amsterdam, the Netherlands, 1982. 

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.%. 

The empirical dependence that is established for a polymer of a specified chemical structure is only valid for a given solvent and temperature. Viscosity of polymer solutions are generally higher as compared to those of pure solvent. A number of viscosity designation have been defined for dilute polymer solutions. For the sake of consistency, the more common usage is adopted in present discussion. 

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... 

Viscosity of Polymer Solutions. Polymer solutions are very common. Glues, pastes, and paints are just a few examples of commercially available aqueous suspensions of organic macromolecules. Also, recall from Chapter 3 that certain types of polymerization reactions are carried out in solution to assist in heat removal. The resulting polymers are also in solution, and their behavior must be fully understand in order to properly transport them and effect solvent removal, if necessary. 

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. 

O, adsorption of Cu(II) on partially quaternized poly(4-vinylpyridine), Cu-tempelate DBQP resin (erosslinking 42%), viscosity of polymer solution... 

Flow and rheology of dispersions and viscosity of polymer solutions and how viscosity is used to characterize dispersions (Chapter 4)... 

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

What is meant by free-draining model and nondraining model in the case of viscosities of polymer solutions ... 

Thurston, G.B., Peterlin,A, Influence of finite numbers of chain segments, hydro-dynamic interaction, and internal viscosity on intrinsic birefringence and viscosity of polymer solutions in an oscillating laminar flow field. J. Chem. Phys. 46, 4881-4885 (1967). 

Peterlin,A. Gradient and time dependence of viscosity of polymer solutions in very viscous solvents. J. Lubrication Tech. 90,571-576 (1968). 

Burow.S. P., Peterlin, A., Turner, D.T. The upturn effect in the non-newtonian viscosity of polymer solutions. Polymer (London) 6. 35-47 (1965). 

Curves 2-4 in Fig. 5 give the dependence of Tcl on intrinsic viscosity of polymer solutions, which is in a first approximation proportional to the degree of polymerization. 

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). 

Reports on reductions in viscosity of polymer solutions by ultrasound... 

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,... 

Edwards SF, Freed KF (1974) Theory of the dynamical viscosity of polymer solutions. J Chem Phys 61(3) 1189-1202... 

K 12 — L. Mandelkern and P. J. Flory Molecular weight dependence of intrinsic viscosity of polymer solutions. J. Polymer Sci. 9,381 (1952). 

Figure 2. Viscosities of polymer solutions as a function of time...

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. 

---