R7.1 Polymerization

Flory mole fraction
373 Chap.
The number-average chain length, Equation (R7.1-26), can be rearranged as
The number-average molecular weight is
Recalling Equation (7-50) and rearranging, we have
The mass average molecular weight is
The variance is
The polydispersity index D is
NACL ∑ jPj ------------ ∑ j
∑ P j
P j
� � --------- �∑jyj
∑ P j
���820 structural (monomer) units
(RE7-2.1)
(RE7-2.2)
(RE7-2.4)
Flory Statistics of the Molecular Weight Distribution. The solution to the
complete set ( j � 1 to j � 100,000) of coupled-nonlinear ordinary differential
equations needed to calculate the distribution is an enormous undertaking even
with the fastest computers. However, we can use probability theory to estimate
the distribution. This theory was developed by Nobel laureate Paul Flory. We
have shown that for step polymerization and for free-radical polymerization in
which termination is by disproportionation the mole fraction of polymer with
chain length j is
distribution y j ( 1 � p)p
In terms of the polymer concentration
j�1
�
The number-average molecular weight
n
Mn ��nMM�820 � 25 �20,
500
∑ j
WACL �w 2P j ∑ j
--------------
∑ jPj 2 ( P j� ∑ P j)
� � � ---------------------------------
∑ j( Pj�∑P j)
∑ j2y 736, 000
� ----------- � ------------------- �897.5
monomer units.
∑ jy 820
Mw � MM�w �25 � 897.5 �22,
434
� n 2
� n
� ⎛ 2 � ⎞ 1
---- ⎜---- ⎟
�0 ⎝�0⎠ 2
� 736, 000 ( 820)
2
� � �
� 63, 600
� 252.2
(RE7-2.3)
22, 439
� � ---------------- �1.09
20, 500
D Mw
-------
Mn
P j y j M Mo( 1 � p)
2 p j�1
� �
(R7.1-6)
(R7.1-33)