Chemistry Reference
In-Depth Information
where k
1
and k
2
are constants.
(a) Sketch qualitatively the distribution function.
(b) Sketch qualitatively the corresponding normalized integral number
distribution curve (i.e., cumulative mole fraction against molecular
weight).
(c) How would you calculate M
n
and M
w
of the polymer sample using the
given distribution (show the relevant equations but do not do the
calculations)?
(d) Assuming that you do not know how to do the calculations in part (c),
can you determine the variance of the distribution if the polydispersity
index of the sample is given? Why or why not?
(e) Given that the variance of the weight distribution (i.e.,
2
σ
w
) is given
by
P
i
w
i
ð
M
i
2
M
w
Þ
2
, show that
2
w
=
M
w
5 ð
M
z
=
M
w
Þ 2
σ
1 (note that
P
i
w
i
M
i
5
M
z
M
w
).
Reference
[1] G. Herdan, Small Particle Statistics: An Account of Statistical Methods for the
Investigation of Finely Divided Materials, second ed., Academic Press, London, 1960
(p. 281).
