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Weight Average Molecular Weight




\bar{M}_w= rac{\sum_i N_iM_i^2}{\sum_i N_iM_i}

where N_i is the number of molecules of molecular weight M_i.

Intuitively, if the weight average molecular weight is ''w'', and you pick a random monomer, then the polymer it belongs to will have a weight of ''w'' on average.

The weight average molecular weight can be determined by light scattering, Small Angle Neutron Scattering (SANS), X-ray scattering, and sedimentation velocity.

An alternative measure of molecular weight for a polymer is the Number Average Molecular Weight ; the ratio of the ''weight average'' to the ''number average'' is called the Polydispersity index.

The ''weight-average molecular weight'', ''M''w, is also related to the ''fractional monomer conversion'', ''p'', in Step-growth Polymerization as per Carothers' Equation :

:\bar{X}_w= rac{1+p}{1-p} \quad \bar{M}_w= rac{M_o\left(1+p ight)}{1-p}, where ''M''o is the molecular weight of the repeating unit.