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Figure 39. Two polymers of the same size (DP) but different R
G
Even if M
1
= M
2
(not easy to see in the figure), then it should be obvious that
R
G,1
> R
G,2
.
2.2.3. The R
G
-‐M
relationships
for
solid
spheres.
A solid sphere is an extremely simple geometry. Since the volume V =
(4/3)
π
R
3
, and the mass M is proportional to the volume, it follows that M
∝
V.
Thus: M
∝
R
3
, or R
∝
M
1/3
. Further, since
G
3 R R 0.775R
5
= =
(see chapter
6.4.1 in textbook for strict mathematical proof)
it simply follows that for a solid
sphere:
1/ 3
log (1/ 3) log
.
G
G
R M
R
M const
∝
=
+
Therefore, if we plot log R
G
as a function of log M should give a straight line
with slope 0.333, as shown in Figure 8: