*1.5c.3c Viscosity-Average Molecular Weight*. The *viscosity average molecular weight* ${{\displaystyle \overline{M}}}_{vis}$ is written as

${{\displaystyle \overline{M}}}_{vis}={\left(\frac{{\text{\Sigma}}_{i}{n}_{i}{M}_{i}^{1+a}}{{\text{\Sigma}}_{i}{n}_{i}{M}_{i}}\right)}^{1/a}$ |
(20) |

The logic of this definition follows the logic used in defining average diameters based on surface area or volume discussed above and, as its name implies, ${{\displaystyle \overline{M}}}_{vis}$ is a molecular weight average determined from viscosity measurements on polydisperse polymer samples. The exponent *a* in this definition is called the *Mark-Houwink coefficient*, generally 0.5 < *a* < 1.0. The exponent is characteristic of the polymer-solvent-temperature conditions of the experiment. We see how these experiments are conducted and the significance of the Mark-Houwink coefficient in Chapter 4. For now, we may take Equation (20) as merely ...

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