Problem Set 4 BE.462J/3.962J
Issued: Day 13 Spring 2003
Due: Day 15
(20 pts total)
1. Re-derive the equation for equilibrium swelling of a polyelectrolyte gel where the polymer chains
contain a basic ionizable group that becomes positively charged with decreasing pH:
+
R-NH
2
-> R-NH
3
Where R represents the polymer chain backbone. Show an example plot of the swelling ratio Q
of the gel vs. pH in water for a gel that has the following parameters:
c = 0.8
M
c
= 6000 g/mole
M = 100,000 g/mole
v
sp,2
= 0.8
f
2,r
= 0.4
pKa = 8.0
ionic strength = 0.2 mM (1:1 electrolyte)
2. An anionic polyelectrolyte gel is synthesized with the physical parameters given below, and
swollen in a solution with ionic strength = 0.5 mM and pH 7.4. What physical parameters of the
gel you could alter to obtain the same swelling ratio at pH 7.4 if the gel is to be used in an ionic
strength of 0.1 mM, assuming you must use the same polymer repeat units and you can’t add
organic solvents to the system? For one of the possible changes to the gel parameters, calculate
what new value the parameter would take to obtain the desired swelling ratio to show that it is
physically achievable.
c = 0.8
M
c
= 12,000 g/mole
M = 75,000 g/mole
v
sp,2
= 0.8
f
2,r
= 0.5
pKa = 6.0
(1:1 electrolyte)
BE.462 PS 4 1 of 1