Page 400 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.3: Polymerization 371

Properties of the Distribution. From the distribution of molecular weights
of polymers, some of the parameters one can use to quantify the distribution
shown in Figure 7-6 and their relationships are given below.

1. The moments of the distribution
11
A, = %j.P, (7-44)
n= 1
2. The zeroth moment is just the total polymer concentration:
m
h,= CP,=P (7-45)
J=1
3. The first moment is related to total number of monomer units (Le.,
mass):

03
X, = C jp, (7-46)
n=l
4. The first moment divided by the zeroth moment gives the num-
ber-average chain length (NACL), pn :

(7-47)

For step-reaction polymerization, the NACL is also sometimes referred
to as the degree ofpolymerization. It is the average number of struc-
tural units per chain and can also be calculated from

5. The number-average molecular weight,

M, = p,Ms (7-48)
where MS is the average molecular weight of the structural units. In
chain polymerization, the average molecular weight of the structural
unit is just the molecular weight of the monomer, MM.
6, The second moment gives emphasis to the larger chains:

h, = j2P, (7-49)

7. The mass per unit volume of each polymer species is just as jP,. The
mass aveirage chain length is just the ratio of moment 2 to moment L :

(7-50)