Weight-Average Molecular Weight

$\left( {M_w ,\overline M _w } \right)$ For a sample with distributed molecular weights (all commercial polymers), the defining equation is

$$M_w {{\sum\limits_{i = 1}^\infty {(N_i M_i )(M_i )} } \over {\sum\limits_{i = 1}^\infty {N_i M_i } }} = {{\sum\limits_{i = 1}^\infty {N_i M_i^2 } } \over {\sum\limits_{i = 1}^\infty {N_i M_i } }}$$

where N _i is the number of individual molecules having molecular mass M _i and N _i M _i equals the mass of the N _i molecules in the sample with molecular mass M _i . The numerator and denominator quantities are also known as the second and first original moments of the distribution. M _w may be determined from measurements of Light Scattering or Size-Exclusion Chromatography. And it is M _w upon which melt viscosity in thermoplastics is strongly dependent. (Allcock HR, Mark J, Lampe F (2003) Contemporary Polymer Chemistry. Prentice Hall, New York; Slade, P. E., Polymer Molecular Weights, Vol. 4, Marcel Dekker, New York, 2001; Coleman, M. M., and Strauss,...