BEH. 462/3.962J Molecular Principles of Biomaterials Spring 2003 Second figure on right depicts a sorting valve that can determine whether fluid flow goes left or right based on pH of solution o Composed of one polybase gel(poly(dimethylaminoethyl methacrylate-co-hydroxyethyl methacrylate)cross-linked by ethylene glycol dimethacrylate and other gel poly(acrylic acid- co-hydroxyethyl methacrylate o Base gel swells at low pH, acid gel swells at high pH Surface modification agents: as described above for polylactide and other biomaterials Brannon-Peppas theory of swelling in ionic hydrogels Original theory for elastic networks developed by Flory and Mehrer, refined for treatment of ionic hydrogels by Other theoretical treatments 7 Derivation of ionic hydrogel swelling Model structure of the system Model of system ● Inorganic anion, e.g. Ch e Inorganic cation, e.g. Na* () System is composed of permanently cross-linked polymer chains, water, and salt We will derive the thermodynamic behavior of the ionic hydrogel using the model we previously developed for neutral hydrogels swelling in good solvent · Model parameters activity of cations in gel Boltzman constant activity of cations in solution absolute temperature(Kelvin) activity of anions in gel molar volume of solvent(water, volume/mole) activity of anions in solution molar volume of polymer(volume/mole concentration of cations in gel( moles/volume) Vsp,1 specific volume of solvent(water, volume/mass) concentration of cations in solution(moles/volume) specific volume of polymer(volume/mass) concentration of anions in solution(moles/volume) V2 total volume of polyme concentration of anions in solution( moles/volume) total volume of swollen hydrogel cs concentration of electrolyte total volume of relaxed hydrogel concentration of ionizable repeat units in gel umber of subchains in network (moles/volume) umber of 'effective subchains in network chemical potential of water in solution stoichiometric coefficient for eletrolyte cation chemical potential of water in the hydrogel chemical potential of pure water in standard state stoichiometric coefficient for eletrolyte anion volume fraction of water in swollen gel Molecular weight of polymer chains before cross-linking Molecular weight of cross-linked subchains volume fraction of polymer in swollen gel number of water molecules in swollen gel p2. r volume fraction of polymer in relaxed gel olymer-solvent interaction paramete mole fraction of water in swollen gel mole fraction of water in solution Lecture 9-polyelectrolyte hydrogels 11of17BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 • Second figure on right depicts a sorting valve that can determine whether fluid flow goes left or right based on pH of solution o Composed of one polybase gel (poly(dimethylaminoethyl methacrylate-co-hydroxyethyl methacrylate) cross-linked by ethylene glycol dimethacrylate and other gel poly(acrylic acid￾co-hydroxyethyl methacrylate) o Base gel swells at low pH, acid gel swells at high pH • Surface modification agents: as described above for polylactide and other biomaterials Brannon-Peppas theory of swelling in ionic hydrogels • Original theory for elastic networks developed by Flory and Mehrer12-14, refined for treatment of ionic hydrogels by Brannon-Peppas and Peppas15,16 • Other theoretical treatments17 Derivation of ionic hydrogel swelling • Model structure of the system: Model of system: Inorganic anion, e.g. Cl­ (-) (-) (-) (-) (-) (-) (-) (-) (-) Inorganic cation, e.g. Na+ water • System is composed of permanently cross-linked polymer chains, water, and salt • We will derive the thermodynamic behavior of the ionic hydrogel using the model we previously developed for neutral hydrogels swelling in good solvent • Model parameters: a+ activity of cations in gel a+* activity of cations in solution a- activity of anions in gel a-* activity of anions in solution c+ concentration of cations in gel (moles/volume) c+* concentration of cations in solution (moles/volume) c- concentration of anions in solution (moles/volume) c-* concentration of anions in solution (moles/volume) cs concentration of electrolyte c2 concentration of ionizable repeat units in gel (moles/volume) * µ1 chemical potential of water in solution µ1 chemical potential of water in the hydrogel µ1 0 chemical potential of pure water in standard state M Molecular weight of polymer chains before cross-linking Mc Molecular weight of cross-linked subchains n1 number of water molecules in swollen gel χ polymer-solvent interaction parameter kB Boltzman constant T absolute temperature (Kelvin) vm,1 molar volume of solvent (water, volume/mole) vm,2 molar volume of polymer (volume/mole) vsp,1 specific volume of solvent (water, volume/mass) vsp,2 specific volume of polymer (volume/mass) V2 total volume of polymer Vs total volume of swollen hydrogel Vr total volume of relaxed hydrogel ν number of subchains in network νe number of ‘effective’ subchains in network ν+ stoichiometric coefficient for eletrolyte cation ν− stoichiometric coefficient for eletrolyte anion φ1,s volume fraction of water in swollen gel φ2,s volume fraction of polymer in swollen gel φ2,r volume fraction of polymer in relaxed gel x1 mole fraction of water in swollen gel x1* mole fraction of water in solution Lecture 9 – polyelectrolyte hydrogels 11 of 17