麻省理工大学：《生物材料的分子结构》教学讲义（英文版）Problem set 5

Problem set 5 BE462J3.962J Issued: Day 15 Spring 2003 (10 points total 1. Two hydrogels are prepared from two different candidate polymers for controlled release of a protein drug, interleukin-2(IL-2). The gels exhibit the same swelling ratio at equilibrium, but gel A(formed by cross-linked polymer A, repeat unit molecular weight Mo= 100 g/mole)has a molecular weight between cross-links of 3, 000 g/mole, while gel B(formed from cross linked polymer B, Mo= 95 g/mole) has a molecular weight between cross-links of 12, 500 g/mole. Separate measurements showed polymer chains of polymer a and polymer B that have the same molecular weight have the same unperturbed end-to-end distance() Finally, the hydrodynamic size r of the drug(IL-2)is one tenth the mesh size of gel B a. Will diffusion of IL-2 through these two gels be the same or different? Calculate the atio of the diffusion coefficient in gel a to that in gel B mesh sizes and diffusion rates for an entrapped drug. (It may be helpful to try b ent b. Explain in physical terms how two gels could have equal swelling ratios but differ sketch the physical situation to explain the case described above where two gels have different molecular weights between cross-links but equivalent swelling ratios. BE4623.962JPs5 1 of 1

Problem Set 5 BE.462J/3.962J Issued: Day 15 Spring 2003 Due: Day 17 (10 points total) 1. Two hydrogels are prepared from two different candidate polymers for controlled release of a protein drug, interleukin-2 (IL-2). The gels exhibit the same swelling ratio at equilibrium, but gel A (formed by cross-linked polymer A, repeat unit molecular weight M0 = 100 g/mole) has a molecular weight between cross-links of 3,000 g/mole, while gel B (formed from cross￾linked polymer B, M0 = 95 g/mole) has a molecular weight between cross-links of 12,500 g/mole. Separate measurements showed polymer chains of polymer A and polymer B that have the same molecular weight have the same unperturbed end-to-end distance (1/ 2 ). Finally, the hydrodynamic size r of the drug (IL-2) is one tenth the mesh size of gel B. a. Will diffusion of IL-2 through these two gels be the same or different? Calculate the ratio of the diffusion coefficient in gel A to that in gel B. b. Explain in physical terms how two gels could have equal swelling ratios but different mesh sizes and diffusion rates for an entrapped drug. (It may be helpful to try to sketch the physical situation to explain the case described above where two gels have different molecular weights between cross-links but equivalent swelling ratios.) BE.462J/3.962J PS 5 1 of 1