Viscosity Methods of Determining Relative Molar Mass

4 VISCOSITY METHODS OF DETERMINING RELATIVE MOLAR MASS 

For the determination of polymer molar masses, very dilute solutions are used, typically of the order of 1% by mass. In using viscosity techniques, a number of functions are used. These are  

Equation (6.20) is known as the Huggins equation. From it, we can see that the limiting case as c tends to zero is that the term (p - PoVho c tends to a 

We determine the value of [rj] experimentally by making measurements on a series of polymer solutions and plotting a graph of (p - iift/riQ c against c. This gives a straight line with intercept at [p]. The value of [p] is characteristic of the isolated polymer molecule in solution, because of the extrapolation to infinite dilution, and is a fimction of temperature, pressure, polymer type, solvent, and (most important of all in the present context) relative molar mass. 

In practice we do not measure viscosity directly. Instead, what is measured is time of flow for solutions and pure solvent in a capillary viscometer, the so-called efflux time. If the same average hydrostatic head is used in all cases, and since for very dilute solutions the density differences between the different concentrations are negligible, then the ratio of the efflux time of the solution, t, to that of the pure solvent, tg, may be taken as a measure of the ratio of the viscosities, i.e. 

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The intrinsic viscosity of each sample has to be measured (as described in Chap. 4). In addition to this, the molar mass M of each sample has to be determined. For commercial samples, the molar mass is often already measured and supplied with the sample (as well as the polydispersity Q). If these parameters are not known for a polymer sample, they have to be determined. Different methods (absolute and relative) of determining the molar mass of a polymer sample are listed in Table 6.1. 

One of the easiest means of determining the molar mass of a polymer is via viscometry. This yields the viscosity average molar mass, Mt . The viscosity of a polymer solution can be measured using capillary viscometers. The time for flow of the polymer solution through a given distance is measured and this is proportional to viscosity. The viscosity obtained by this method is expressed relative to that of the pure solvent. To determine molar mass, the intrinsic viscosity is required. It has this name because it relates to the intrinsic ability of a polymer to increase the viscosity of a solvent. The intrinsic viscosity [ j] is related to the specific viscosity jsp = 1 — rj/rjo, where rj is the viscosity of the polymer solution and rjo is that of the solvent via a virial equation in concentration resembling Eq. (2.9). It has been found empirically that for many polymer solutions the Mark-Houwink equation for intrinsic viscosity is obeyed ... 

Polymer scientists are normally interested in the variation of the solution viscosity with molar mass. Unfortunately no theories have been developed to relate them to each other and empirical relationships are used to determine the molar mass of a polymer sample from measurements of solution viscosity. However, this method does have the distinct advantage of being a rapid technique that can be carried out quickly using relatively simple apparatus. 

Several authors have published the method for determining molar masses of DADMAC polymers, primarily in connection with practical applications [1]. In Table 11 intrinsic viscosity-molar mass relations of PDADMAC are summarized in the form of the Mark-Kuhn-Houwink-Sakurada (MKHS) relationship. The relatively high exponent of the relationships is attributed to the greater chain stiffness in comparison with vinyl backbones. One has to look quite skeptically at the values from reference [59] given its deviation from the remainder of the published data. 

Of all the methods used for the determination of molar masses of macromolecules, the viscosity method, introduced by H. Staudinger, is the one most commonly employed in research. Accurate measurement of absolute viscosity being difficult, it is convenient to measure relative viscosity, x e denned as... 

Knowledge of the molar mass and of the molar mass distribution of a polymeric material is indispensable for scientific studies and for many technical applications of polymers. They affect the solution and melt viscosity, the self-assembly behavior, the processability, and the resulting mechanical properties tremendously. Therefore, we will give a short introduction into methods that allow us to determine the required information. Roughly, the methods developed for the determination of molecular weights are subdivided into absolute and relative methods ... 

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