BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Egn 8 k In P Ean 9 d=_pel, opening Pe, rome. o Where P*volume is the probability that a solute-sized volume of free space exists to jump into o P*opening is the probability that the network has a solute-sized gap to jump through gel, opening d qn o Where r is the size of the solute(drug) and s is the network mesh size The probability of a volume to jump into is an exponential of the ratio of the solute size to the available free volume per mole Eqn 11 ,volume e,ged Eqn 12 olme e bree,I o Where free is the specific free volume and v* is the volume of the solute(drug) o Refs for free volume theory applied here Yasuda et al. Makromol. Chem. 26, 177(1969) Peppas and Reinhart, J Membrane Sci. 15, 275(1983) Now Eqn 13 0. volume The free volume in a swollen gel is approximately free, 1 since the free volume contribution from polymer is extremely low(2.5% even in solid polymers at 25C) qn Free,gel=Q1vfree,1 92Vfree, 2 Therefore. n 15 Vfreegel-P1Vfree, 1=(1-92) Vree, 1=(1-1/Q) ree. o Where Q is the swelling degree =Swollen ge vary gel =1/02 Therefore. Lecture 10-Bioengineering Applications of Hydrogels 3 of 4  BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Eqn 8 ∆S*0 = k ln P*0 – k ln P0 * * * Eqn 9 D = Pgel = Pgel,openingPgel,volume ˆ * * P0 P0,volume o Where P*volume is the probability that a solute-sized volume of free space exists to jump into o P*opening is the probability that the network has a solute-sized gap to jump through P*gel,opening drug r drug P*gel,volume * ξ − r Eqn 10 Pgel,opening = ξ =1− r ξ o Where r is the size of the solute (drug) and ξ is the network mesh size ƒ The probability of a volume to jump into is an exponential of the ratio of the solute size to the available free volume per mole: v* − * Eqn 11 Pgel,volume ~ e v free,gel v* − * Eqn 12 P0,volume ~ e v free,1 o Where vfree is the specific free volume and v* is the volume of the solute (drug) o Refs for free volume theory applied here: ƒ Yasuda et al. Makromol. Chem. 26, 177 (1969) ƒ Peppas and Reinhart, J. Membrane Sci. 15, 275 (1983) ƒ Now: *  v* v*  Eqn 13 Pgel,volume = e −   v free,gel − v free,1   * P0,volume ƒ The free volume in a swollen gel is approximately vfree,1 since the free volume contribution from polymer is extremely low (2.5% even in solid polymers at 25°C) Eqn 14 vfree,gel = φ1vfree,1 + φ2vfree,2 ƒ Therefore: Eqn 15 vfree,gel ~ φ1vfree,1 = (1-φ2)vfree,1 = (1-1/Q)vfree,1 o Where Q is the swelling degree = Vswollen gel/Vdry gel = 1/φ2 ƒ Therefore: Lecture 10 – Bioengineering Applications of Hydrogels 3 of 4