0.15 04895B)=0884 0.15 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. As we saw in our derivation of the equilibrium expression for the swelling of neutral hydrogels, Q depends on multiple factors- in addition to the molecular weight between crosslinks, it also notably depends on the polymer-solvent interaction parameter x. Thus two gels may have the same swelling ratio but different molecular weights between cross-links. The physical interpretation of this result is that a polymer which does not have highly favorable interactions with water may have less swollen chains (chains more collapsed to provide more polymer-polymer contacts). This gel may have a significantly higher Mc than a gel that has the same degree of swelling but which has more expanded chains(more favorable water-polymer interaction, lower x). This situation is schematically llustrated below. Gel diffusion theory( as illustrated by the calculation above) says that when the swelling ratio is equal between two gels, the gel with the higher molecular weight between cross- links(drawing on left below), and thus larger mesh size, will allow faster diffusion of a drug through its structure. Though the local concentration of polymer per unit volume within the gel in these two cases can be equal, the constraint to diffusion presented by cross-links slows diffusion in the gel with lower Mc 80p2p BE462J/3962JPs5 20f2BE.462J/3.962J PS 5 2 of 2 DA DB = 1− r ξ A       e −1 QA −1       1− r ξ B       e −1 QB −1       = 1− r ξ A       1− r ξ B       = 1− 0.1ξ B 0.489ξ B       1− 0.1ξ B ξ B       = 0.884 b. Explain in physical terms how two gels could have equal swelling ratios but different mesh sizes and diffusion rates for an entrapped drug. sketch the physical situation to explain the case described above where two gels have different molecular weights between cross-links but equivalent swelling ratios.). As we saw in our derivation of the equilibrium expression for the swelling of neutral hydrogels, Q depends on multiple factors- in addition to the molecular weight between crosslinks, it also notably depends on the polymer-solvent interaction parameter χ. us two gels may have the same swelling ratio but different molecular weights between cross-links. he physical interpretation of this result is that a polymer which does not have highly favorable interactions with water may have less swollen chains (chains more collapsed to provide more polymer-polymer contacts). This gel may have a significantly higher Mc than a gel that has the same degree of swelling but which has more expanded chains (more favorable water-polymer interaction, lower χ). tion is schematically illustrated below. y ( as illustrated by the calculation above) says that when the swelling ratio is equal between two gels, the gel with the higher molecular weight between cross￾links (drawing on left below), and thus larger mesh size, will allow faster diffusion of a drug through its structure. Though the local concentration of polymer per unit volume within the gel in these two cases can be equal, the constraint to diffusion presented by cross-links slows diffusion in the gel with lower Mc. (It may be helpful to try to Th T This situa Gel diffusion theor