Measurement of Intrinsic Viscosity

The measurement of intrinsic viscosity is simple and inexpensive when compared with other measurements related to the polymer MW. However, it can be time consuming, even if modern semiautomatic instruments are used for that purpose. As mentioned in Chapter 1, measurements of intrinsic viscosity were historically important in establishing the concept of macromolecules [29]. 

The determination of the intrinsic viscosity of a polymer essentially requires the measurement of the flow time of a polymer solution through a glass capillary at different solution concentrations. A polymer solution passing through a capillary obeys the Poiseuille s law for laminar flow through capillaries, which indicates that the pressure drop AP is directly proportional to the viscosity r] of the fluid [29, 30]. 

In order to get a simpler equation, some considerations are made. The bulb volume in the viscometer is fixed therefore, the flow rate Q is inversely proportional to the time between marks. Since AP is usually the hydrostatic pressure, which is proportional to the density p of the fluid, we have 

The above equation is valid if the whole pressure difference applied across the capillary is used in overcoming viscous forces. However, the potential energy of the liquid column imparts kinetic energy to the fluid. In order to correct the contribution of the kinetic energy, as the length of the capillary increases, the radius decreases [31, 32]. 

Several methods exist for characterization of the solution viscosity or, more specifically, the capacity of the solute to increase the viscosity of the solution. That capacity is quantified by using one of several different measures of solution viscosity. 

This determination is performed very easily with simple glass viscometers. Since the viscosity of a liquid depends markedly on temperature, viscosity measurements must be made at a carefully controlled temperature (within 0.1°C). Before a measurement, the viscometer is therefore equilibrated in a carefully controlled thermostatic bath at the required temperature. 

Two popular viscometers are of the Ostwald and Ubbelohde types, shown in Fig. 4.15. To operate the Ostwald viscometer, a given volume of liquid is introduced into bulb B through stem A and is drawn up by suction till it fills the 

With the assumption of a constant flow rate, the flow time t can be related to the viscosity rj of the liquid by the Hagen-Poiseuille equation (Moore, 1972) 

This equation is applicable if the flow is Newtonian or viscous and all of the potential energy of the driving force is expended in overcoming the frictional resistance. These conditions are usually satisfied (Allcock and Lampe, 1990) for the apparatus used and for measurement of relative viscosities 77/770 (see Table 4.2) which are of interest in polymer chemistry. 

Denoting the terms related to solvent with subscript zero, a ratio of viscosities of solution and solvent in terms of respective flow times for the same volume V through the same capillary is obtained from Eq. (4.97) as 

Two popirlar viscometers are of the Ostwald and Ubbelohde types, shown in Fig. 4.15. To operate the Ostwald viscometer, a given volirme of hqttid is introduced into bulb B through stem A and is drawn up by suction till it Us the bulb C and moves beyond the ducial mark a. The suction is then released and the time taken by the liquid meniscus to pass between the ducial marks a and b across the birlb C is measirred. The Uquid obviously ows under a varying driving force proportional to the changing difference (Ji) in the levels of the liquids in the two tubes. To ensure that this driving force is the same in all cases, the same amount of hquid must always be taken in bulb B. 

The above condition of always using the same volume of liquid does not apply, however, in the case of Ubbelohde suspended level viscometer (Ubbelohde, 1937), shown in Fig. 4.15(b). A modi ed design of the Ubbelohde viscometer is shown in Fig. 4.15(c). For measurement with the Ubbelohde viscometer a measured volume of polymer solution with known concentration is pipetted into bulb B through stem A. This solution is transferred into bulb C by applying a pressure on A with compressed air while column D is kept closed. When the pressure is released, the solution in bulb E and column D drains back into bulb B and the end of the capillary remains free of hquid. The solution ows from bulb C through the capillary and around the sides of the bulb E into bulb B. The volume of hquid in B has no effect on the rate of ow through the capillary because there is no back pressure on the liquid emerging from the capillary as the bulb E is open to atmosphere. The ow time t for the solution meniscus to pass between the ducial marks a and b 

---

The polymers dissolve in l,l,l,3,3,3-hexafluoro-2-propanol [920-66-1/, hot phenols, and /V, /V- dim ethyl form am i de [68-12-2] near its boiling point. The excellent solvent resistance notwithstanding, solvents suitable for measurement of intrinsic viscosity, useflil for estimation of molecular weight, are known (13,15). 

Molecular Weight. Measurement of intrinsic viscosity in water is the most commonly used method to determine the molecular weight of poly(ethylene oxide) resins. However, there are several problems associated with these measurements (86,87). The dissolved polymer is susceptible to oxidative and shear degradation, which is accelerated by filtration or dialysis. If the solution is purified by centrifiigation, precipitation of the highest molecular weight polymers can occur and the presence of residual catalyst by-products, which remain as dispersed, insoluble soHds, further compHcates purification. 

The measurements of chain stiffness of denatured proteins are made in the presence of a strong denaturant, such as 8 M urea or 6 M GdmCl, in which peptide H-bonds are weak and peptide helices unfold (Scholtz et al., 1995 Smith and Scholtz, 1996), and the possible presence of (/-helices or /3-hairpins is not an issue in these denaturants. The careful and thorough measurements of intrinsic viscosities made by Tanford and co-workers (1968), discussed above, yield a substantially lower estimate for chain stiffness than the work of Flory and co-workers. A comparison is made by Tanford (1968) between the proportionality coefficient... 

The measurements of intrinsic viscosity [ij] have been carried out at 135° in tetralin. Under these conditions, the relationship between [ij] and vis-cosimetric molecular weight M, for isotactic polypropylene is (41) ... 

The present paper describes a procedure by which the average DP values can be obtained by GPC without making measurements of intrinsic viscosity, thereby drastically reducing the time necessary for GPC characterization of samples as well as increasing the accuracy and reproducibility of average DP values as compared with those obtained by other experimental methods. 

An example illustrating the application of Eq. (2.4) for calculating Mn is shown in Fig. 2.2. The position of the line at 45° reflects the exact equality of the Mn values calculated from the concentration of active centers and those determined by measurement of intrinsic viscosity, [r ]. Bearing in mind possible experimental errors and the accuracy of the equation relating [tj] and Mn, we can conclude that the correspondence between the two series of Mn values is satisfactory. 

Calculated from the rate expression Rp = fcP[NVC][C7H7+SbCl6 ]. b Estimated from measurements of intrinsic viscosity in benzene at 25°C. (38). 

Investigators have been cautioned that the weak links can be broken at the time the cellulose is put into solution in preparation for the measurement of intrinsic viscosity rather than at the time of its exposure to ultraviolet radiation (8,13). Nevertheless, regardless of the immediate cause of rupture, the existence of links weaker than normal bond strength can be detected through the use of Equation 1. 

The Mark-Houwink equation provides an indirect estimate of molar mass from a measurement of intrinsic viscosity [r ], if the two Mark-Houwink constants K and a, are known. The predictions of Mark-Houwink constants are summarized in Table 8.1. Comparison with Table 1.4 shows that the Zimm model agrees reasonably well with experimental results, as a = 0.50 is observed in 0-solvent and 0.7 < a < 0.8 is usually observed in good solvents. 

Cross-linking. When it is heated in solution, as described above, PVC not only loses HCl, but also undergoes cross-linking and thereby results eventually in an insoluble gel. Initial stages of this cross-linking reaction can be followed by measurement of Intrinsic viscosity. However, because of simultaneously occurring chain-scission reactions and because the molecular weight of the branched molecules formed cannot be reliably calculated,interpretation of results is very difficult. 

Detailed Sample Preparation and Measurement of Intrinsic Viscosity In order to obtain the intrinsic viscosity of a polymer in a dilute solution, different concentrations of a polymer in a solvent are prepared. A small amount of polymer is weighed and dissolved in a solvent during a few hours using a stirrer in order to improve the solubility of the polymer. It is recommended to prepare at least six different concentrations of a polymer in a solvent. The highest concentration could be in the order of 30 mg in 10 ml of solvent and the rest of the concentrations should be more dilute however, the concentrations will depend on the type of polymer. There are different ASTM (American Society for Testing and Materials) methods recommended to measure the intrinsic viscosity of different polymers. 

Meanwhile a quantity of methanol was cooled in dry ice-acetone. To the reaction tube, 10 ml of the precooled methanol was added. This terminated the polymerization. The precipitated polymer was collected on a sintered glass filter and washed with additional quantities of methanol. The product was dried under reduced pressure at 80°C. Yield was 0.70 gm (95.8% of theory). The polymer was purified by dissolution in -pentane and precipitation of the product by the dropwise addition of this solution to methanol. Then the polymer was again dried under reduced pressure. The product was used for the measurement of intrinsic viscosities and specific rotation [a]589 = + 0.05° intrinsic viscosity = 0.20 dl/gm. 

The tertiary structure of the macromolecule and its molecular weight can be ascertained from measurements of intrinsic viscosity and diffusion, from ultracentrifugation studies, and from light scattering determinations. These methods can... 

The measurement of intrinsic viscosity is performed in a capillary viscom-... 

Hence, measurements of intrinsic viscosity yield the hydrodynamic radius (or volume) of the chain molecule. Under 0 conditions and in a good solvent, respectively, we expect for solutions of flexible chain molecules after relationships Equations (36) and (37) of chapter 3... 

The measurement of intrinsic viscosity can be readily obtained by extrapolation of experimental results, as shown in Figure 2.23. 

Measurement of intrinsic viscosities which are less than 5 dl/g are not difficult. Solution and solvent viscosities can be determined with simple and inexpensive capillary viscometers. These viscometers usually make measurements at fluid shear rates greater than 50 sec . These shear rates do not greatly perturb small polymer coils. However, large polymer coils are perturbed by large-fluid flow shear fields and equation (1) would not be valid. For EOR polymers with larger intrinsic viscosities, more sophisticated rheometers must be... 

---