BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Lecture 9: Polyelectrolyte Hydrogels Last Day: Physical hydrogels Structure and chemistry Today: polyelectrolyte hydrogels, complexes, and coacervates Polyelectrolyte multilayers theory of swelling in ionic hydrogels Reading: S.K. De et al., ‘Equilibrium swelling and kinetics of pH-responsive hydrogels: Models, experiments, and simulations,’ J. Microelectromech. Sys. 11(5) 544 (2002). Supplementary Reading: L. Brannon-Peppas and N.A. Peppas, ‘Equilibrium swelling behavior of pH-sensitive hydrogels,’ Chem. Eng. Sci. 46(3) 715-722 (1991). USE DEMO OF AMINOETHYL METHACRYLATE HYDROGEL TO SHOW PH-DEPENDENT SWELLING? Covalent polyelectrolyte hydrogels Response of polyelectrolyte gels to pH of environment o Reminder of the response of ionizable groups to pH changes: ionization of charged groups 1.2 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH o Presence of ionizable groups makes polyelectrolyte hydrogels sensitive to: o pH o Ionic strength o Electric fields o (T) Lecture 9 – polyelectrolyte hydrogels 1 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Observed swelling as a function of pH: o Data 1 for poly(2-hydroxyethyl methacrylate-co-acrylic acid) gels cross-linked with ethylene glycol dimethacrylate o Physical chemistry of swelling at high pH (example for anionic gels): o Stepwise process in basic solutions: 1 1. Ionization of carboxyl groups, releasing H + a. At high ionic group density, carboxylate anions repel one another, driving swelling- but this is not the main driving force for swelling in typical conditions i. Electrostatic force decays as 1/r 2 , too weak at typical charged group separation to have a significant effect ii. In water: F = q 1 q 2 /4πεr 2 = -e 2 /4τεr 2 = 2.04x10 -39 /r 2 (r in m) 1. ε = 80 in water 2. e = 1.602x10 -19 C iii. F1 nm/F0.2 nm = 0.04! 2. H + recombines with OH - to give water 3. Charge is compensated by diffusion of cations (e.g. Na + ) and OH - into gel 4. Influx of new ions creates osmotic pressure that drives swelling 2 Lecture 9 – polyelectrolyte hydrogels 2 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Kinetics: deswelling faster (~10X) than swelling ? Swelling in ~166 min. ? De-swelling in ~16 min. ? (300 μm thick gels) ? Theory based on diffusion of ions into and out of gel semi-quantitatively predicts observed swelling behavior o Implies that response time of gels will scale inversely with the size of the gel o Swelling rate inversely proportional to square of gel size 3 o Swelling rate can also be increased by creating greater porosity in gel- increase surface/volume ratio allows solute to diffuse into gel more rapidly Rapid swelling/deswelling of superporous gels: Low pH High pH (Zhao and Moore, 2001) o hydrogels containing basic groups show opposite pH sensitivity o swelling in acidic solutions o e.g. Peppas papers Lecture 9 – polyelectrolyte hydrogels 3 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Polyion complex hydrogels 4 Coacervates o complexation between two oppositely charged polyelectrolytes can lead to: 1. precipitation (insoluble solid phase) null driven by charge neutralization on hydrophobic polymers null driven by macro-aggregate formation 2. coacervate formation (dense liquid phase) 3. soluble complexes o mechanisms of formation 1. initial rapid Coulombic bonding 2. formation of new bonds/restructuring of chain distortions 3. aggregation of secondary complexes o mixing of two polyions can lead to 90% complex formation o Polyelectrolytes studied as coacervates for biomaterials: 4 o Polyanions o Carboxymethylcellulose o Alginate o Dextran sulfate o Carboxymethyl dextran o Heparin o Carrageenan o Pectin o xanthan o Polycations o Chitosan (derived from crab shells) o Polyethyleneimine o Poly(4-vinyl-N-butylpyridinium) bromide o Quarternized polycations o Poly(vinylbenzyltrimethyl)ammonium hydroxide Lecture 9 – polyelectrolyte hydrogels 4 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Microstructure of coacervate hydrogels o Example structures: xanthan/chitosan coacervates (Dumitriu et al. 1998) o Pore sizes formed 0.1-1 μm; fiber diameters ~100 nm Polyelectrolyte multilayers (PEMs) Structure of PEMs Assembly ? Layer-by-layer deposition o How is it done o Surface properties change in digital fashion with adsorption of sequential layers 5 Lecture 9 – polyelectrolyte hydrogels 5 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Surface properties dominated by last layer deposited: θ null Assembly figure source: http://www.chem.fsu.edu/multilayers/ ? Assembly on complex surfaces o Polyelectrolytes will adsorb to surfaces with complex topography o Polyelectrolytes themselves may have complex geometries (e.g. particles or dendrimers) 6 Generation 7 poly(amidoamine) dendrimer: (Khopade and Caruso, 2002) null Dendrimer image source: http://www.foresight.org/Conferences/MNT7/Papers/Cagin3/ Lecture 9 – polyelectrolyte hydrogels 6 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Assembly on protein crystals to encapsulate proteins: 7 null Blah blah (Caruso et al., 2000) ? Cells as living PEM assembly substrates: SEM micrograph of multilayer-coated echinocyte blood cell (F. Caruso) (Source: http://www.chem.fsu.edu/multilayers/) o What else Building PEMs on biomaterials 8 ? Assembly of PEMs on amino-modified poly(lactide) 5 o Alternating adsorption of sulfonated polystyrene and chitosan (polycation) Lecture 9 – polyelectrolyte hydrogels 7 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 H 2N - C H CH 3 O -(CH -C-O) n - 2 - N H 2 CH 3 O H -CH -C-N-CH 2 CH 2 -NH 2 + HO- PEM-modified polylactide 2C H Lecture 9 – polyelectrolyte hydrogels 8 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Utility of polyeletrolyte gels in biomaterials/bioengineering o Cell encapsulation: In situ formation with no ‘additives’, no change in pH, no change in temperature, in physiological solutions o Useful for safe encapsulation of cells o Drug delivery: Ionic interactions for protein-polymer complexes prior to gel formation allow high protein entrapment efficiencies o PEMs can form hollow capsules Drug release from PSS/PAMAM PEM capsules: Fluorescent drug-loaded PEM capsules o Enzyme immobilization: binding to ionic groups for biosensors or active biomaterials o Protein separations/recovery: 9 some binding specificity can be achieved in certain situations to allow for selective sorption of a target protein o Addition of polycation or polyanion to solution of protein leads to protein-polyelectrolyte coacervate formation o Bound proteins released by adjustment of pH/ionic strength Lecture 9 – polyelectrolyte hydrogels 9 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Microvalves for bioMEMS and lab-on-a-chip applications: 10,11 Utilize fast response of swelling in microsized gels to control flow through microfluidics o Example: PHEMA-co-AA networks patterned in microfluidic channels: ? Schematic shows an example lab-on-a-chip analysis approach Lecture 9 – polyelectrolyte hydrogels 10 of 17 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 12-14 , refined for treatment of ionic hydrogels by Brannon-Peppas and Peppas 15,16 ? Other theoretical treatments 17 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) c s concentration of electrolyte c 2 concentration of ionizable repeat units in gel (moles/volume) * μ 1 chemical potential of water in solution μ 1 chemical potential of water in the hydrogel μ 1 0 chemical potential of pure water in standard state M Molecular weight of polymer chains before cross-linking M c Molecular weight of cross-linked subchains n 1 number of water molecules in swollen gel χ polymer-solvent interaction parameter k B Boltzman constant T absolute temperature (Kelvin) v m , 1 molar volume of solvent (water, volume/mole) v m,2 molar volume of polymer (volume/mole) v sp , 1 specific volume of solvent (water, volume/mass) v sp,2 specific volume of polymer (volume/mass) V 2 total volume of polymer V s total volume of swollen hydrogel V r total volume of relaxed hydrogel ν number of subchains in network ν e number of ‘effective’ subchains in network ν + stoichiometric coefficient for eletrolyte cation ν ? stoichiometric coefficient for eletrolyte anion φ 1,s volume fraction of water in swollen gel φ 2,s volume fraction of polymer in swollen gel φ 2,r volume fraction of polymer in relaxed gel x 1 mole fraction of water in swollen gel x 1 * mole fraction of water in solution Lecture 9 – polyelectrolyte hydrogels 11 of 17 ? ? ? ? ? ? BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Asterisks denote parameters in solution o Free energy has 3 components: free energy of mixing, elastic free energy, and ionic free energy Eqn 1 ?G total =?G mix +?G el +?G ion o At equilibrium, the chemical potential of water inside and outside the gel are equal: Eqn 2 μ 1 * = μ 1 Eqn 3 μ 1 * - μ 1 0 = μ 1 – μ 1 0 o Solution contains ions so μ 1 * is not equal to μ 1 0 Eqn 4 (?μ 1 *) TOTAL = (?μ 1 ) TOTAL Eqn 5 (?μ 1 *) ion = (?μ 1 ) mix + (?μ 1 ) el + (?μ 1 ) ion o The equation we’ll try to solve is a rearrangement of this: Eqn 6 (?μ 1 *) ion - (?μ 1 ) ion = (?μ 1 ) mix + (?μ 1 ) el o Contributions to the free energy: o Free energy of mixing: Eqn 7 ?G mix = ?H mix – T?S mix o We previously derived the contribution from mixing using the Flory-Rehner lattice model: Eqn 8 ?G mix = k B T[n 1 ln (1-φ 2,s ) + χn 1 φ 2,s ] () 1 mix = ? ? ? ?(?G mix ) ? ? ? = k B T[ln(1?φ 2,s ) +φ 2,s +χφ 2,s 2,s Eqn 9 ?μ ?n 1 T ,P 2 ] = RT[ln(1?φ 2,s ) +φ 2,s +χφ 2 ] o Second expression puts us on a molar basis instead of per molecule o Elastic free energy: Eqn 10 ?G el = (3/2)k B Tν e (α 2 – 1 – ln α) Eqn 11 () ?μ = ? ?(?G el ) ? = ? ?(?G el ) ? ? ?α ? ? ? v m,1 ? ? ? φ 2,s ? 1/3 ? 1 ? φ 2,s ? ? ? M 1 el ? ? ?n 1 ? ? T ,P ? ? ?α ? ? T ,P ? ? ?n 1 ? ? T ,P = RTν ? ? ? 1? 2 M c ? V r ?? ? φ 2rs ? ? 2 ? ? φ 2rs ? ? ? ? v m,1 = RT ? ? v sp,2 M c ? ? ? ? ? ? 1? 2M c ? ? ? φ 2,s ? 1/3 ? 1 ? φ 2,s ? ? ? M ? ? φ 2,r ? ?? ? φ 2rs ? ? 2 ? ? φ 2rs ? ? ? ? Last equality uses: o ν = V 2 /v sp , 2 M c (on handout) o V r = V 2 /φ 2 , r (on handout) o Thus ν/V r = φ 2 , r /v sp,2 M c o Ionic free energy: o Term driving dilution of ions diffusing into gel to maintain charge neutrality Lecture 9 – polyelectrolyte hydrogels 12 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Chemical potential change in solution: all _ solutes () * Eqn 12 ?μ 1 11 ion =μ * ?μ 0 = RT ln a 1 * ? RT ln x 1 * = RT ln(1? ∑ x * j ) j o approximation in third equality is used for dilute solutions all _ ions all _ ions all _ ions all _ ions Eqn 13 () ?μ 1 * ion ??RT ∑ x * j =? RT ∑ n * j =? v m,1 RT ∑ n * j ??v m,1 RT ∑ c * j j n j v m,1 n j j o The first approximation holds if Σx j * is small o Fourth equality holds because we assume in the liquid lattice model that the molar volume of all species is the same, thus v m , 1 n = V, the total volume of the system o Chemical potential change in gel: all?ions Eqn 14 (?μ 1 ) ion = μ 1 ?μ 1 0 = RT ln a 1 ? ?v m,1 RT ∑ c j j all?ions * Eqn 15 (?μ 1 ) ion ? (?μ 1 ) ion =?v m,1 RT ∑ (c j ? c * j ) j o The electrolyte dissolved in water provides mobile cations and anions in the solution and in the gel: o E.g. NaCl: Na + ν+ Cl - ν+ (s) → ν + Na + (aq) + ν - Cl - (aq) o ν + = ν - = 1 stoichiometric coefficients Eqn 16 C ν + z?z + A ν ? →ν + C z + +ν ? A z? ? e.g. CaCl 2 : ν + = 1, ν - = 2, z + = 2, z - = 1 Eqn 17 ν + +ν ? =ν ? …for a 1:1 electrolyte ? Eqn 18 ν + =ν ? = ν …for a 1:1 electrolyte 2 * * * ? * Eqn 19 c + + c ? = (ν + +ν ? )c s =νc s …total concentration of ions o We will derive equations for an anionic network o Assuming activities ~ concentrations o Inside gel: Eqn 20 c + = ν + c s Eqn 21 c - = ν - c s + ic 2 /z - o c 2 is the moles of ionizable repeat groups on gel chains per volume o First term comes from electrolyte anions in gel, second term from counter-ions associated with ionized groups on the polymer chains o The degree of ionization i can be related to the pH of the environment and the pKa of the network groups: [] Eqn 22 K a = [ RCOO ? ] H + [ RCOOH ] Lecture 9 – polyelectrolyte hydrogels 13 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Eqn 23 [ RCOO ? ] K a H + i = [ RCOO ? ] [RCOOH] [] K a K a 10 ? pK a = = = = = H + [ RCOOH ] + [ RCOO ? ] [ RCOO ? ] 1+ K a [] + K a 10 ? pH + K a 10 ? pH + 10 ? pK a H +1+ [ RCOOH ] [] o Outside gel: Eqn 24 c + * = ν + c s * Eqn 25 c - * = ν - c s * o Our relationship for the ionic chemical potentials is now: all?ions () * () * Eqn 26 ?μ 1 ion = v m,1 RT ∑( c j ? c * j ) =v m,1 RT ( c + + c ? ? c + ? c ? * ) 1 ion ??μ j o Using Eqn 20, Eqn 21, Eqn 24, and Eqn 25, Eqn 26 becomes: ? ? ? ? * Eqn 27 () ?μ * () 1 ion = v m,1 RT ? ? ν + c s +ν ? c ? + ic 2 ? ? c s ? ? = v m,1 RT ? ? ν c s + ic 2 ? ? c s ? ? 1 ion ??μ ν ? ν * z ? z ? ? ? ν(c s ? c s = v m,1 RT ? ? ic 2 ? ? * ) ? ? z ? o How can we relate c s and c s *? o We can make simplifications for a 1:1 cation:anion electrolyte: o The chemical potentials of the mobile ions must also be equilibrated inside/outside the gel: Eqn 28 μ + = μ + * Eqn 29 μ - = μ - * o Add Eqn 29 to Eqn 28: Eqn 30 μ + + μ - = μ + * + μ - * ν + Eqn 31 RT ln a + + RT ln a ? ν ? = RT ln a + *ν + + RT ln a ? *ν ? o Therefore we can write: ν+ a ? ν? = a + Eqn 32 a + *ν+ a ? *ν? ? Assuming dilute solutions where the activities are approximately equal to the concentrations: ν+ ν? ? c + ? ? c ? * ? Eqn 33 ? ? c + = * ? ? ? ? c ? ? ? Lecture 9 – polyelectrolyte hydrogels 14 of 17 ? ? ? ? ? ? BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 ? ? ν? ? ν + c s ? ν+ ? * ? ? Eqn 34 ? ? ν + c * s ? ? = ? ν ? c s ? ? ν ? c s + ic 2 ? ? ? ν ? z ? ? ν? ? ? ν+ ? * ? ? c ? c Eqn 35 ? ? c * s ? ? = ? ? s ic 2 ? ? ? s ? ? c s + ν ? z ? ? ? ? ν? ? ?ν+ * ? * ? 1 ? ? ?? ic * 2 ? ? ? 2 Eqn 36 c * s c ? * s c s = 1? ? ? ? ? c s + c s ic 2 ? ? ? = 1 ? c s + c s ic 2 = ν ic 2 * ? ? ? 2z + z ? ν 2 ? ? c s ? z ? c s ? ? ν ? z ? ? ν ? z ? o Derivation of this equation in appendix o Now Eqn 27 becomes: ? i 2 c 2 2 ? () * Eqn 37 ?μ () 1 ion = v m,1 RT ? ? 2z + z ? ν * ? ? 1 ion ??μ ? c s o But definition of ionic strength I is: all _ ions ? c s * Eqn 38 I = 1 ∑ z i 2 c i = z + z ? ν …for a 1:1 electrolyte 2 i 2 null Where z i is the charge on ion i o Therefore: ? i 2 φ 2 ? () * 2,s Eqn 39 ?μ () 1 ion = v m,1 RT ? ? ? i 2 c 2 2 ? ? ? = v m,1 RT ? ? 4Iv sp,2 M 0 2 ? ? 1 ion ??μ 4I 2 φ 2,s o (Using relation c 2 = v sp,2 M 0 =moles ionizable groups/volume) o Eqn 39 can be re-cast in terms of the solution pH: 2 ? () 1 * ion ?? () μ = v m,1 RT ? K a ? 2 ? φ 2,s ? 2 ? K a ? 2 ? φ 2,s 2 Eqn 40 ?μ 1 ion 4I ? ? 10 ? pH + K a ? ? ? ? z ? v sp,2 M 0 ? ? = v m,1 RT ? ? 10 ? pH + K a ? ? ? ? 4Iv sp,2 M 0 2 ? ? o Returning to the equilibrium criterion: Lecture 9 – polyelectrolyte hydrogels 15 of 17 ? ? ? ? ? ? BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Eqn 41 2 ? ? 10 ? pK a ? 2 ? φ 2,s 2 ? v m,1 ? ? ? ? 1? 2 M c ? ? ? ? ? ? ? φ 2,s ? ? 1/3 ? 1 ? ? φ 2,s ? ? ? ? 2 v m,1 ? ? 10 ? pH + 10 ? pK a ? ? ? ? 4Iv sp,2 M 0 2 ? ? = ln(1 ?φ 2,s ) +φ 2,s +χφ 2,s +φ 2,r ? ? v sp,2 M c ? ? M ? ? φ 2,r ? 2 ? φ 2,r ? ? o Brannon-Peppas paper analyzes Polyacrylates/polymethacrylates: o In water pH 7.0 with I = 0.35 o χ = 0.8 o pK a = 6.0 o v sp,2 = 0.8 cm 3 /g o M = 75,000 g/mole o M c = 12,000 g/mole o M 0 = 90 g/mole o φ 2,r = 0.5 Lecture 9 – polyelectrolyte hydrogels 16 of 17 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 References 1. De, S. K. et al. Equilibrium swelling and kinetics of pH-responsive hydrogels: Models, experiments, and simulations. Journal of Microelectromechanical Systems 11, 544-555 (2002). 2. Tanaka, T. & Fillmore, D. J. Kinetics of Swelling of Gels. Journal of Chemical Physics 70, 1214-1218 (1979). 3. Zhao, B. & Moore, J. S. Fast pH- and ionic strength-responsive hydrogels in microchannels. Langmuir 17, 4758- 4763 (2001). 4. Chornet, E. & Dumitriu, S. Inclusion and release of proteins from polysaccharide-based polyion complexes. Adv Drug Deliv Rev 31, 223-246. (1998). 5. Zhu, Y., Gao, C., He, T., Liu, X. & Shen, J. Layer-by-Layer assembly to modify poly(L-lactic acid) surface toward improving its cytocompatibility to human endothelial cells. Biomacromol. 4, 446-452 (2003). 6. Khopade, A. J. & Caruso, F. Stepwise self-assembled poly(amidoamine) dendrimer and poly(styrenesulfonate) microcapsules as sustained delivery vehicles. Biomacromolecules 3, 1154-1162 (2002). 7. Caruso, F., Trau, D., Mohwald, H. & Renneberg, R. Enzyme encapsulation in layer-by-layer engineered polymer multilayer capsules. Langmuir 16, 1485-1488 (2000). 8. Elbert, D. L., Herbert, C. B. & Hubbell, J. A. Thin polymer layers formed by polyelectrolyte multilayer techniques on biological surfaces. Langmuir 15, 5355-5362 (1999). 9. Wang, Y. F., Gao, J. Y. & Dubin, P. L. Protein separation via polyelectrolyte coacervation: Selectivity and efficiency. Biotechnology Progress 12, 356-362 (1996). 10. Beebe, D. J. et al. Functional hydrogel structures for autonomous flow control inside microfluidic channels. Nature 404, 588-+ (2000). 11. Beebe, D. J., Mensing, G. A. & Walker, G. M. Physics and applications of microfluidics in biology. Annual Review of Biomedical Engineering 4, 261-286 (2002). 12. James, H. M. & Guth, E. Simple presentation of network theory of rubber, with a discussion of other theories. J. Polym. Sci. 4, 153-182 (1949). 13. Flory, P. J. & Rehner Jr., J. Statistical mechanics of cross-linked polymer networks. I. Rubberlike elasticity. J. Chem. Phys. 11, 512-520 (1943). 14. Flory, P. J. & Rehner Jr., J. Statistical mechanics of cross-linked polymer networks. II. Swelling. J. Chem. Phys. 11, 521-526 (1943). 15. Brannonpeppas, L. & Peppas, N. A. Equilibrium Swelling Behavior of Ph-Sensitive Hydrogels. Chemical Engineering Science 46, 715-722 (1991). 16. Peppas, N. A. & Merrill, E. W. Polyvinyl-Alcohol) Hydrogels - Reinforcement of Radiation-Crosslinked Networks by Crystallization. Journal of Polymer Science Part a-Polymer Chemistry 14, 441-457 (1976). 17. Ozyurek, C., Caykara, T., Kantoglu, O. & Guven, O. Characterization of network structure of poly(N-vinyl 2- pyrrolidone/acrylic acid) polyelectrolyte hydrogels by swelling measurements. Journal of Polymer Science Part B- Polymer Physics 38, 3309-3317 (2000). Lecture 9 – polyelectrolyte hydrogels 17 of 17