麻省理工大学：《生物材料的分子结构》教学讲义（英文版）Problem set 4

Problem set 4 BE462J3.962J Issued Day 13 Spring 2003 (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 RNH2→>RNH3 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 0.8 Mc=6000 g/mole M=100.000g/moe vsp2=0.8 中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 cant 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 0.8 M=12,000g/moe M=75,000 g/mole 0.8 pKa=6.0 (1: 1 electrolyte) BE.462 PS 4 1 of 1

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-NH2 -> R-NH3 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 Mc = 6000 g/mole M = 100,000 g/mole vsp,2 = 0.8 f2,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 Mc = 12,000 g/mole M = 75,000 g/mole vsp,2 = 0.8 f2,r = 0.5 pKa = 6.0 (1:1 electrolyte) BE.462 PS 4 1 of 1