Biomedical Engineering Reference
In-Depth Information
Unlike linear polymers, chemically cross-linked polymers
do not display flow behavior; the cross links inhibit flow at
all temperatures below the degradation temperature.
Thus, chemically cross-linked polymers cannot be melt
processed. Instead, these materials are processed as re-
active liquids or high-molecular-weight amorphous
gums that are cross-linked during molding to give the
desired product. SR is an example of this type of polymer.
Some cross-linked polymers are formed as networks
during polymerization, and then must be machined to
be formed into useful shapes. The soft contact lens,
PHEMA, is an example of this type of network polymer; it
is shaped in the dry state, and used when swollen with
water.
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
40 50
Elution time (minutes)
60
Fig. 3.2.2-12 A typical trace from a GPC run for a
poly(tetramethylene oxide)/toluene diisocyanate-based
polyurethane. The response of the ultraviolet detector is directly
proportional to the amount of polymer eluted at each time point.
Copolymers
In contrast to the thermal behavior of homopolymers
discussed earlier, copolymers can exhibit a number of
additional thermal transitions. If the copolymer is
random, it will exhibit a
T
g
that approximates the
weighted average of the
T
g
values of the two homopol-
ymers. Block copolymers of sufficient size and in-
compatible block types, such as the polyurethanes, will
exhibit two individual transitions, each one characteristic
of the homopolymer of one of the component blocks (in
addition to other thermal transitions) but slightly shifted
owing to incomplete phase separation.
of the solvent in solution with respect to that of the pure
solvent is compensated by applying a pressure p on the
solution. p is the osmotic pressure and is related to
M
n
by:
c
¼ RT
1
p
þ A
2
c þ A
3
c
2
þ
.
(3.2.2.3)
M
n
where
c
is the concentration of the polymer in solution,
R
is
the gas constant,
T
is temperature, and
A
2
and
A
3
are virial
coefficients relating to pairwise and triplet interactions of
the molecules in solution. In general, a number of polymer
solutions of decreasing concentration are prepared, and the
osmotic pressure is extrapolated to zero:
Characterization techniques
Determination of molecular weight
p
c
¼
RT
lim
c
/0
(3.2.2.4)
Gel permeation chromatography (GPC), a type of size
exclusion chromatography, involves passage of a dilute
polymer solution over a column of porous beads. High-
molecular-weight polymers are excluded from the beads
and elute first, whereas lower molecular-weight mole-
cules pass through the pores of the bead, increasing their
elution time. By monitoring the effluent of the column as
a function of time using an ultraviolet or refractive index
detector, the amount of polymer eluted during each time
interval can be determined. Comparison of the elution
time of the samples with those of monodisperse samples
of known molecular weight allows the entire molecular
weight distribution to be determined. A typical GPC
trace is shown in
Fig. 3.2.2-12.
Osmotic pressure measurements can be used to
measure
M
n
. A semipermeable membrane is placed be-
tween two chambers.
Only solvent molecules flow freely through the
membrane. Pure solvent is placed in one chamber, and
a dilute polymer solution of known concentration is
placed in the other chamber. The lowering of the activity
M
n
A plot of p
/c
versus
c
then gives as its intercept the
number average molecular weight.
A number of other techniques, including vapor pres-
sure osmometry, ebulliometry, cryoscopy, and end-group
analysis, can be used to determine the
M
n
of polymers up
to molecular weights of about 40,000.
Light-scattering techniques are used to determine
M
w
.
In dilute solution, the scattering of light is directly pro-
portional to the number of molecules. The scattered in-
tensity is observed at a distance
r
and an angle q from the
incident beam
I
o
is characterized by Rayleigh's ratio R
q
:
R
q
¼
i
o
r
2
(3.2.2.5)
I
o
The Rayleigh ratio is related to M
w
by:
K
c
R
q
1
M
w
þ
2
A
2
c þ
3
A
2
c
2
þ
.
¼
(3.2.2.6)
