Viscosities of polymers

Most properties of linear polymers are controlled by two different factors. The chemical constitution of tire monomers detennines tire interaction strengtli between tire chains, tire interactions of tire polymer witli host molecules or witli interfaces. The monomer stmcture also detennines tire possible local confonnations of tire polymer chain. This relationship between the molecular stmcture and any interaction witli surrounding molecules is similar to tliat found for low-molecular-weight compounds. The second important parameter tliat controls polymer properties is tire molecular weight. Contrary to tire situation for low-molecular-weight compounds, it plays a fimdamental role in polymer behaviour. It detennines tire slow-mode dynamics and tire viscosity of polymers in solutions and in tire melt. These properties are of utmost importance in polymer rheology and condition tlieir processability. The mechanical properties, solubility and miscibility of different polymers also depend on tlieir molecular weights. 

Common experimental evidence shows that the viscosity of polymers varies as they flow. Under certain conditions however, elastic effects in a polymeric flow can be neglected. In these situations the extra stress is again expressed, explicitly, in terms of the rate of deformation as... 

Before we are in a position to discuss the viscosity of polymer melts, we must first give a quantitative definition of what is meant by viscosity and then say something about how this property is measured. This will not be our only exposure to experimental viscosity in this volume—other methods for determining bulk viscosity will be taken up in the next chapter and the viscosity of solutions will be discussed in Chap. 9—so the discussion of viscometry will only be introductory. Throughout we shall be concerned with constant temperature experiments conducted under nonturbulent flow conditions. 

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. 

Polymer solutions are often characterized by their high viscosities compared to solutions of nonpolymeric solutes at similar mass concentrations. This is due to the mechanical entanglements formed between polymer chains. In fact, where entanglements dominate flow, the (zero-shear) viscosity of polymer melts and solutions varies with the 3.4 power of weight-average molecular weight. 

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. 

Melt Viscosity. The study of the viscosity of polymer melts (43—55) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus melt viscosity as a function of temperature, pressure, rate of flow, and polymer molecular weight and stmcture is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extmsion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. 

Piston Cylinder (Extrusion). Pressure-driven piston cylinder capillary viscometers, ie, extmsion rheometers (Fig. 25), are used primarily to measure the melt viscosity of polymers and other viscous materials (21,47,49,50). A reservoir is connected to a capillary tube, and molten polymer or another material is extmded through the capillary by means of a piston to which a constant force is appHed. Viscosity can be determined from the volumetric flow rate and the pressure drop along the capillary. The basic method and test conditions for a number of thermoplastics are described in ASTM D1238. Melt viscoelasticity can influence the results (160). 

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

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

As a starting point it is useful to plot the relationship between shear stress and shear rate as shown in Fig. 5.1 since this is similar to the stress-strain characteristics for a solid. However, in practice it is often more convenient to rearrange the variables and plot viscosity against strain rate as shown in Fig. 5.2. Logarithmic scales are common so that several decades of stress and viscosity can be included. Fig. 5.2 also illustrates the effect of temperature on the viscosity of polymer melts. 

One more fact, important in practice, lies in that a of the compositions based on heterogeneous blends of polymers obtained by the method 3, depends considerably on mixing temperature Tm. This is bound up with a variation of the polymer viscosity with the temperature on being introduced into the polymer mixture, a filler becomes distributed mostly in the less viscous polymer and, if the viscosity of polymers is almost the same, it is distributed comparatively uniformly and a of the composition decreases. Therefore, the dependence of a of the conducting polymer composite on Tm has a minimum (by a factor of 102 to 104) in the Tm region when the viscosities of the polymer components are close. 

To cold diionyl chloride (1.31 g, 11 mmol) in an ice-water bath, pyridine (10 mL) is added slowly for 10 min to keep the reaction temperature low. The reaction medium is stirred for 30 min. Then, a mixture of isophdialic acid (0.41 g, 2.5 mmol) and terephdialic acid (0.41 g, 2.5 mmol) in pyridine (10 mL) is added slowly for 10-20 min to control the reaction temperature. The cooling badi is then removed and the reaction mixture is stirred at room temperature for 20 min. 2,2-Bis(4-hydroxyphenyl)propane (bisphenol-A, 1.14 g, 5 mmol) in pyridine (10 mL) is added all at once to the mixture, and the whole solution is heated to 80°C (bath temperature) for 4 h. The resulting viscous solution is diluted with pyridine and poured into methanol to precipitate the polymer, which is washed in boiling methanol and dried. The inherent viscosity of polymer is 2.2 dL/g (determined in 60/40 phenol-1.1.2.2-tetrachloroethane at 30°C)... 

Salts of alkyl phosphates and types of other surfactants used as emulsifiers and dispersing agents in polymer dispersions are discussed with respect to the preparation of polymer dispersions for use in the manufactoring and finishing of textiles. Seven examples are presented to demonstrate the significance of surfactants on the properties, e.g., sedimentation, wetting behavior, hydrophilic characteristics, foaming behavior, metal adhesion, and viscosity, of polymer dispersions used in the textile industry [239]. 

Aggregation of particles may occur, in general, due to Brownian motion, buoyancy-induced motion (creaming), and relative motion between particles due to an applied flow. Flow-induced aggregation dominates in polymer processing applications because of the high viscosities of polymer melts. Controlled studies—the conterpart of the fragmentation studies described in the previous section—may be carried out in simple flows, such as in the shear field produced in a cone and plate device (Chimmili, 1996). The number of such studies appears to be small. 

Plasticizer or liquid diluents greatly reduce the melt viscosity of polymers (28.170-177). Small amounts of liquids at temperatures just above Tt produce an especially dramatic decrease in viscosity. Several factors are responsible for the decrease ... 

Since experimental and theoretical results show variations in viscosity that range all the way from the first power to the fourteenth power of the solvent concentration, it is nearly impossible to predict accurately the viscosity of polymers containing a solvent or plasticizer. As a rough approx-... 

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. 

ISO 1628-4 1999 Plastics - Determination of the viscosity of polymers in dilute solution using capillary viscometers - Part 4 Polycarbonate (PC) moulding and extrusion materials ISO 7391-1 1996 Plastics - Polycarbonate (PC) moulding and extrusion materials - Part 1 Designation system and basis for specifications ISO 7391-2 1996 Plastics - Polycarbonate (PC) moulding and extrusion materials - Part 2 Preparation of test specimens and determination of properties ISO 11963 1995 Plastics - Polycarbonate sheets - Types, dimensions and characteristics. 

The bulk viscosity referred to here (pg) should not be confused with the so-called bulk viscosity of polymers which refers to the steady flow shear viscosity of the bulk undiluted polymer. Here it represents all the causes of sound absorption other than those produced by shear viscosity or thermal conductivity. Typically these may be ... 

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. 

The z average molecular weight has been found to correlate with the shear viscosity of polymer melts when the molecular weight distribution is very broad and where very large molecules appear to dominate the resistance to fluid flow. 

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