Dilute solution viscometry

A characteristic feature of a dilute polymer solution is that its viscosity is considerably higher than that of either the pure solvent or similarly dilute solutions of small molecules. This arises because of the large differences in size between polymer and solvent molecules, and the magnitude of the viscosity increase is related to the dimensions of the polymer molecules in solution. Therefore, measurements of the viscosities of dilute polymer solutions can be used to provide information concerning the effects upon chain dimensions of polymer structure (chemical and skeletal), molecular shape, degree of polymerization (hence molar mass) and polymer-solvent interactions. Most commonly, however, such measurements are used to determine the molar mass of a polymer. 

The quantities required and terminology used in dilute solution viscometry are summarized in Table 3.7. The terminology proposed by lUPAC was an attempt to eliminate the inconsistences associated with the common names, which define as viscosities, quantities that do not have the dimensions (ML T ) of viscosity. However, the common names were well established when the lUPAC recommendations were published and the new terminology has largely been ignored. 

The quantity of greatest importance for the purposes of polymer characterization is the intrinsic viscosity [rj] since it relates to the intrinsic ability of a polymer to increase the viscosity of a particular solvent at a given temperature. The specific viscosity of a solution of concentration c is related to [tj] by a power series in [t]]c 

TABLE 3.7 Quantities and terminology used in dilute solution viscometry 

Common name Name proposed by lUPAC Symbol and definition  

The dependence of viscosity on size permits estimation of an average molecular weight from solution viscosity. The average molecular weight that is measured is ihe viscosity average Mj, which differs from M and Mw described so far in this chapter. The relation between viscosity increase and molecular weight that is used for the calculation of is given by the Mark-Houwink- 

Sakurada (MHS) equation (see below). Before viscosity increase data are used to calculate of the polymer, it is necessary to eUminate the effects of polymer concentration. The methods whereby this is achieved are described in a later section. These methods, however, do not remove the effects of polymer-solvent interactions, and so of a given polymer sample will depend to some extent on the solvent used in the solution viscosity measurements. 

The nomenclature commonly used for solution viscosity is represented in Table 4.2. It may be noted that the viscosity terms listed in it are not viscosities at all. Thus T]r and ijsp are actually unitless ratios of viscosities. The intrinsic viscosity [ ] is a ratio of viscosities divided by concentration and so has the units of reciprocal concentration, commonly quoted in cm /g or dL/g. 

The Mark-Houwink-Sakurada (MHS) equation for the calculation of Mj, is written as 

Problem 4.17 Assuming that the MHS constants K and a are independent of molecular weight, derive the de nitions of Mv provided by Eq. (4.93). 

Polypropyleneimines have been examined by dilute solution viscometry by several groups of investigators [17-19, 22], For example, Scherrenberg and 

Consider a polymer sample to be made up of a series (i) of monodisperse macromolecules each with concentration (weight/volume) c/ and molecular weight M/. Then, 

We may regard the viscosity of the solution of a whole polymer as the sum of the contributions of the monodisperse species that make up-the polymer. That is, 

---

Dilute Solution Viscometry - The hydrogenated and hydroformyl ated (10%) PBD were completely soluble in toluene. Intrinsic viscosity measurements were carried out in toluene at 30°C using a Cannon-Ubbelohde viscometer. 

Chain Length Properties of the Modified Polymers. A number of partially hydrogenated and hydroxymethyl ated polybutadienes were analyzed using vapour pressure osmometry, dilute solution viscometry and gel permeation chromatography. The parent polybutadiene had Mn in the range of 9,000 to 50,000. In the case of vapour pressure osmometry, the data were reproducible for polymers with Mn less than 20,000. All the polymers obtained (hydrogenated and... 

The viscosities of products in solution (0.5 Weight %/volume) were measured by dilute solution viscometry using a Cannon Ubellohde viscometer at 35 °C. 

Sections of several packages were tested by dilute solution viscometry in decahydronaphthalene at 135°C to determine if the failures are consistent with UV degradation. The top surface of each package was partially covered by a paper label. This label should have shielded the underlying film from UV exposure, and there should be a difference in the solution viscosity of material taken from the shielded center of the package and material taken from the UV-exposed edge. Sections from the center and edge of three samples were... 

Table 16 Summary of dilute solution viscometry results ...

Values calculated from dilute solution viscometry (DSV) data for PAMAMs obtained in the same solution as in a for PPIs from ref. 19 for PBzEs from ref. 15. 

Compared to dilute solution viscometry and to some extent to bulk rheology, the flow properties of dendrimers in concentrated solutions have been the least investigated area of dendrimer rheology. In fact, with the notable exception of some recent data on generation 4 PPI in water [22] the only [32] reported... 

It should be noted that discrepancies amidst available data may result from different methods of determination. For example, selected hydrodynamic radii of PAMAM dendrimers of Table 14.1 were obtained by two different experimental methods for generations 1 through 4 by dilute solution viscometry, while for generations 5 through 10 by size exclusion chromatography. 

Physical Measurements. Intrinsic Viscosities. Intrinsic viscosities were obtained using dilute solution viscometry (Cannon-Ubbelohde viscometers). 

Physical Measurements. Molecular Weight. Intrinsic viscosities were determined using dilute solution viscometry (Cannon-Ubbelohde viscometers). For the poly (methyl methacrylate) polymer the following empirical expressions were used to obtain molecular weights (4) ... 

In addition, more complex exponent averages can be obtained (e.g., by dilute Solution viscometry and sedimentation measurements). 

In this Investigation we have shown, with the use of dilute solution viscometry and gel permeation chromatography, that the molecular weight does remain constant for both polystyrene and poly(methyl methacrylate) during the period of constant rate in mul slon polymerization. It also appears that the ratio of M /M is very close to the most probable distribution, i.e.,... 

Intrinsic Viscosity. Dilute-solution viscometry of samples in toluene was carried out in a Cannon-Ubbelohde semimicrodilution viscometer (size 25) in a temperature-controlled bath (25.0 0.2 °C). At least three concentrations were measured, and the results were extrapolated to infinite dilution by using the Huggins and Kramers relations... 

Problems 3.4 and 3.5 test your understanding of dilute-solution viscometry. 

Lovell, P. A., Dilute solution viscometry, in Comprehensive Polymer Science (C. Booth and C. Price, eds.), Pergamon Press, New York, 1989, pp. 173-197. 

The intrinsic viscosity of each polymer was determined by dilute solution viscometry using distilled methyl ethyl ketone as the solvent at a constant temperature of 30 C. The MEK was distilled onto p-methoxyphenol to prevent peroxide formation. 

The unperturbed dimensions for a number of stereoregular polymers have been studied by dilute solution viscometry in theta solvents. Given in Tables (1—8) are... 

Size exclusion chromatography relative to linear PEO standards. Dilute solution viscometry. 

Differentiai scanning caiorimetry (ASTM D34i7) > Dilute solution viscometry (ASTM D2857, F4020) Fatigue (ASTM E647) - > ... 

Another parameter that is sensitive to the macromolecular architecture is the Huggins constant, / h, calculated by dilute solution viscometry measurements. For linear polymers, kn varies between 0.5 and 0.6 in 0-solvents and is equal to 0.3 in good solvents. For star polymers, in both good and 0-solvents, the values of fen increase with inaeasing / from the value obtained for linear polymers and reach values slightly lower than unity, which is the hard sphere limit (Tables 3 and 4). 

However, the application of eqn [1] to the SPEB is less straightforward than anticipated. In principle, the counterion cloud of the polyelectrolyte brushes will be disturbed by the motion of the maaoions leading to electroviscous effects. However, the number of counterions that may leave the brash is small compared to the total number of counterions. When this assumption is valid, this effect can be dismissed and Rh can be determined directly by use of eqn [1]. ° This is also justified when considering Rh which has been determined by dilute solution viscometry. 

KAV Kavlak, S., Can, H.K., and Guener, A., Miscibility studies on poly(ethylene glycol)/dextran blends in aqueous solutions by dilute solution viscometry, J. Appl. Polym. Sci., 94, 453, 2004. 

---