Molar viscosity average

For polydisperse samples, the weight average intrinsic viscosity [p])w is measured (Equation (8)) and the so-called viscosity averaged molar mass is obtained ... 

From the results of the light scattering experiments it follows that A and B have the sameM. The viscosity average,My, is for A higher than for B, and is thus closer toMw. A has, therefore, a narrower molar mass distribution and a higher M. The osmotic pressure IT is therefore lower. 

FIGURE 16.1 Schematic differential (—) and integral (—) representations of amount of polymer with certain molar mass present in the sample. The narrow, broad, and bimodal molar mass distributions are shown. The typical positions of weight, viscosity, number, and z-molar mass averages are depicted. 

The second average is viscosity average molecular weight, M . This expression is obtained by using the exponent from the limiting viscosity number-molar mass relationship, a, as a power for the molecular weight of each molecule in the distribution. The formula for this average is... 

The viscosity average,Mv, does not belong to the series Mn, MW,MZ etc. The measurement does not supply an absolute value of the molar mass, but can, by contrast with the other methods mentioned so far, be carried out in an easy way. Its principle is, that a polymer, even at very low concentrations, brings about a significant viscosity increase of the solvent. This increase is not only dependent on the concentration but also on the molar mass. The measurement is carried out as follows (see also Qu. 2.14 - 2.18 and 2.31 - 2.34) ... 

Our calculation of (ro2) is therefore, for polymer solutions, only valid for theta conditions. We shall consider this case in somewhat more detail. We have seen that for the determination of the viscosity average molar mass, the Mark-Houwink... 

This is the Mark-Houwink equation, where the formal dimension of K is equal to cm3/g x (g/mol)a. In general, however, K is tacitly expressed and tabulated in the same dimension as [r ] and the resulting polymer molecular weight M is then expressed in g/mol. For polydis-perse polymers, M is replaced by Mv the so-called viscosity-average molar mass, so that... 

Knowing the values of a and K, for a polymer-solvent system, the viscosity-average molar mass Mvis can be easily determined from intrinsic viscosity measurements. 

Find the intrinsic viscosity and viscosity average molar mass on the basis that the viscosity of the system obeys [r ] = K Mvisa with K = 3.80 10"5 dm3 g-1 and a = 0.63. 

Example The following data were obtained for the intrinsic viscosity of poly isobutylene in CC14 solution at 30 C as a function of viscosity average molar mass... 

We shall now comment on the viscosity-average molar mass, Mvigc If the exponent a in the Mark-Houwink equation, we, [ri]... 

Therefore, the viscosity-average molar mass can be written as... 

The sample amount can be easily determined from the injection volume and the sample concentration, and no information from a concentration detector is required. With this approach, the Mn value of any polymer sample can be determined by SEC using only a viscosity detector. Other molar mass averages, however, cannot be determined. The advantage of the Goldwasser Mn method is that it can access much wider molar mass ranges than other existing methods like osmometry or end-group methods. 

Equation (7) also holds for a polydisperse sample of PVOH, but the molar mass in this case is, the viscosity-average molar mass defined below. 

Number-Average and Viscosity-Average Molar Mass. For a polydisperse polymer, any determination of molar mass must yield an average of some sort. When a col-ligative property such as osmotic pressure is used, the average is a number average ... 

Viscosity average molar mass, as measured in CC14 at 25° C, is related to intrinsic viscosity by the following relationship [64] ... 

Gel permeation chromatography (GPC) is the established method for the determination of molar mass averages and the molar mass distributions of polymers. GPC retention is based on the separation of macromolecules in solution by molecular sizes and, therefore, requires a molar mass calibration to transform elution time or elution volume into molar mass information. This kind of calibration is typically performed with narrow molecular mass distribution polymer standards, universal, or broad calibration methods or molar-mass-sensitive detectors like light-scattering or viscosity detectors. 

The average molecular weight, polydispersity, temperature, hydrostatic pressure, and shear rate dependences of polymer melt viscosity will be discussed in Chapter 13, resulting in a set of correlations which can be used to obtain a rough estimate of melt viscosity as a function of all of these variables. A new correlation will be presented for the molar viscosity-temperature function. The dependences of the zero-shear viscosity of concentrated polymer solutions on the average molecular weight and on the temperature will also be discussed. Finally, a new model that was developed to predict the shear viscosities of dispersions of particles in both polymeric fluids and ordinary molecular fluids will be presented. 

Figure 3.41 Concentration of hydroxyethyl cellulose at which depletion flocculation occurred, Cf, as a function of the viscosity-average molar mass of the polymer. Reproduced by permission of The Royal Society of Chemistry from ref. [133]...

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