Weight Average MolecularWeight

The weight average molecular weight (M_w) is the sum of the products of the weight of each species present and its molecular weight, divided by the sum of all the species’ weights:

W_i = weight of each polymeric species

M_i = molecular weight of each polymeric species

Substituting N_iM_i = W_i, the weight average molecular weight can be defined as Larger, heavier molecules contribute more to Mw than to M_n. Light scattering techniques and ultracentrifugation can determine M_w.

The following simple example illustrates the difference between M_n and M_w: Suppose a sample has six macro-molecules. Three of them have a molecular weight = 1.0 × 10⁴, two have a molecular weight = 2.0 × 10⁴, and one has a molecular weight = 3.0 × 10⁴:

In monodispersed systems M_n = M_w.

The difference in the value between M_n and M_w. indicates the polydispersity of the polymer system. The closer M_n is to Mw, the narrower the molecular weight spread. Molecular weight distribution curves for polydispersed systems can be obtained by plotting the degree of polymerization i versus either the number fraction, _Ni, or the weight fraction, W_i.