ABSTRACT
In many instances, average molar masses and their ratios (i.e. molar mass dispersities) are insufficient to describe the properties of a polymer, and more complete information on the molar mass distribution (MMD) is required. This is particularly important for polymers that have MMDs which are broad, non-uniform (e.g. having low or high molar mass shoulders) and/or multimodal. Even for polymers with relatively simple MMDs, there is advantage in knowing the complete MMD. Furthermore, any molar mass average can be calculated from the moments of the distribution curve. For example, if w(M) is the weight-fraction MMD function, then the number-average molar mass M –
n can be defined in integral form (cf. Equation 1.7) as
M w M M M
/ d =
1 0
( )( ) (14.1)
the weight-average molar mass M –
w (cf. Equation 1.8) as
M w M M Mw d=
∞∫ ( ) 0
(14.2)
and the z-average molar mass M –
z (cf. Equation 1.10) as
M w M M M
w M M M z
d
d =
( )
( )
(14.3)
Similarly from Equation 13.6 (recognizing that wi = niMi and that w M M( )d
0 1
∞∫ = , i.e. w(M) is normalized), an expression for the viscosity-average molar mass M
– v is obtained
M w M M Ma a
d=
∞∫ ( ) 0
(14.4)
where a is the exponent in the Mark-Houwink-Sakurada Equation 13.5.
