Problem set 5 Solution BE462J/3962J Issued Day 15 Spring 2003 Day 17 5 points/problem(20 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 jel 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 crosslinks of 12, 500 g/mole. Separate measurements showed polymer chains of polymer a and polymer B that Finally, the hydrodynamic size r of the drug(IL-2)is one tenth the mesh size of gelao>) have the same molecular weight have the same unperturbed end-to-end distance(< 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 The diffusion of IL-2 through these gels will be slightly different, as assessed by the following calculation of the ratio of diffusion coefficients in ge/ A vs. gel B The measurement showing equal unperturbed end-to-end distances for A and B chains of equal molecular weight gives us 2M A ClI CinI M T2(2McB M Mo The above equation allows us to determine a relation between the mesh sizes of the two gels OCl 0.489 2M BE462J/3962JPs5 1 of 2Problem Set5 Solution BE.462J/3.962J Issued: Day15 Spring 2003 Due: Day 17 5 points/problem (20 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 crosslinks 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 ( < r0 2 >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. The diffusion of IL-2 through these gels will be slightly different, as assessed by the following calculation of the ratio of diffusion coefficients in gel A vs. gel B: QA = QB = Q The measurement showing equal unperturbed end-to-end distances for A and B chains of equal molecular weight gives us:  2Mc,A  1/ 2 1/ 2 lA   Mc  1/ 2 1/ 2 lA  1  1/ 2 1/ 2 lA < r0, 2 A >1/ 2   M0,A   Cn,A  M0,A   Cn,A   M0,A   Cn,A < r0, 2 B >1/ 2 =  2Mc,B  1/ 2 1/ 2 lB =  Mc  1/ 2 1/ 2 lB =  1  1/ 2 1/ 2 lB =1   M0,B   Cn,B   M0,B   Cn,B   M0,B   Cn,B The above equation allows us to determine a relation between the mesh sizes of the two gels:  2Mc,A   1/ 2 QA 1/ 2 lA ξ A   M0,A  1/ 3 Cn,A = ξ B   2Mc,B   1/ 2 QB 1/ 2 lB  M0,B  1/ 3 Cn,B 1/ 2 = Mc,A = 0.489 1/ 2 Mc,B BE.462J/3.962J PS 5 1 of 2