BEH. 462/3.962J Molecular Principles of Biomaterials Spring 2003 V C Cs c+2c(2,人c o Derivation of this equation in appendix o Now Eqn 27 becomes )-()2=2 o But definition of ionic strength I is C for a 1: 1 electrolyte Where z, is the charge on ion i o Therefore A)-(△A)m=(4= 4/v2,M o(Using relation C2=-=moles ionizable groups/volume) o Eqn 39 can be re-cast in terms of the solution pl RT (4A)n-() K K R 4(10m+Kn人(zV乎2 10P 41vs2MO o Returning to the equilibrium criterion Lecture 9-polyelectrolyte hydrogels 15of17      BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003   ν − ν +cs  ν +  *  Eqn 34    ν +c * s   =  ν −cs  ν −cs + ic2    ν −z−  ν −   ν +  *   c  c Eqn 35   c * s   =   s ic2    s   cs + ν − z−    ν −  ν + *  *  1    ic * 2    2 Eqn 36 c * s c − * s cs =1−     cs + cs ic2    =1 − cs + cs ic2 = ν ic2 * −   2z+z−ν2   cs ˆz−cs ˆ  ν −z−  ν −z− o Derivation of this equation in appendix o Now Eqn 27 becomes:  i 2 c2 2  ( )* Eqn 37 ∆µ ( )1 ion = vm,1RT  2z+z−ν *  1  ion − ∆µ ˆcs o But definition of ionic strength I is: all _ ions ˆcs * Eqn 38 I = 1 ∑zi 2 ci = z+z−ν …for a 1:1 electrolyte 2 i 2 ƒ Where zi is the charge on ion i o Therefore:  i 2 φ2  ( )* 2,s Eqn 39 ∆µ ( )1 ion = vm,1RT   i 2 c2 2    = vm,1RT   4Ivsp,2 M0 2  1 ion  − ∆µ 4I 2 φ2,s o (Using relation c2 = vsp,2 M0 =moles ionizable groups/volume) o Eqn 39 can be re-cast in terms of the solution pH: 2  ( )1 * ion − ∆( ) µ = vm,1RT  Ka  2  φ2,s  2  Ka  2  φ 2,s 2 Eqn 40 ∆µ 1 ion 4I   10− pH + Ka     z−vsp,2 M0   = vm,1RT  10− pH + Ka     4Ivsp,2 M0 2   o Returning to the equilibrium criterion: Lecture 9 – polyelectrolyte hydrogels 15 of 17