Lecture 9: Polyelectrolyte Hydrogels - Dspace.mit.edu
BEH.462/3.962J Molecular Principles of BiomaterialsSpring 2003Lecture 9: Polyelectrolyte HydrogelsLast Day:Physical hydrogelsStructure and chemistryToday:polyelectrolyte hydrogels, complexes, and coacervatesPolyelectrolyte multilayerstheory of swelling in ionic hydrogelsReading: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-sensitivehydrogels,’ Chem. Eng. Sci. 46(3) 715-722 (1991).USE DEMO OF AMINOETHYL METHACRYLATE HYDROGEL TO SHOW PH-DEPENDENT SWELLING?Covalent polyelectrolyte hydrogelsResponse of polyelectrolyte gels to pH of environmentoReminder of the response of ionizable groups to pH changes:ionization of charged groups1.210.80.60.40.20012345678910 11 12 13 14pHoPresence of ionizable groups makes polyelectrolyte hydrogels sensitive to:o pHo Ionic strengtho Electric fieldso (T)Lecture 9 – polyelectrolyte hydrogels1 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsoSpring 2003Observed swelling as a function of pH:o Data1 for poly(2-hydroxyethyl methacrylate-co-acrylic acid) gels cross-linked with ethylene glycoldimethacrylateoPhysical chemistry of swelling at high pH (example for anionic gels):o Stepwise process in basic solutions:11. Ionization of carboxyl groups, releasing H a. At high ionic group density, carboxylate anions repel one another, drivingswelling- but this is not the main driving force for swelling in typical conditionsi. Electrostatic force decays as 1/r2, too weak at typical charged groupseparation to have a significant effectii. In water: F q1q2/4πεr2 -e2/4τεr2 2.04x10-39/r2 (r in m)1. ε 80 in water2. e 1.602x10-19 Ciii. F1 nm/F0.2 nm 0.04!2. H recombines with OH- to give water3. Charge is compensated by diffusion of cations (e.g. Na ) and OH- into gel4. Influx of new ions creates osmotic pressure that drives swelling2Lecture 9 – polyelectrolyte hydrogels2 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsoSpring 2003Kinetics: 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 observedswelling behavioro Implies that response time of gels will scale inversely with the size of the gelo Swelling rate inversely proportional to square of gel size3o Swelling rate can also be increased by creating greater porosity in gel- increasesurface/volume ratio allows solute to diffuse into gel more rapidlyRapid swelling/deswelling of superporous gels:Low pHoHigh pH(Zhao and Moore, 2001)hydrogels containing basic groups show opposite pH sensitivityo swelling in acidic solutionso e.g. Peppas papersLecture 9 – polyelectrolyte hydrogels3 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsSpring 2003Polyion complex hydrogels4Coacervatesocomplexation between two oppositely charged polyelectrolytes can lead to:1. precipitation (insoluble solid phase) driven by charge neutralization on hydrophobic polymers driven by macro-aggregate formation2. coacervate formation (dense liquid phase)3. soluble complexesomechanisms of formationoo1. initial rapid Coulombic bonding2. formation of new bonds/restructuring of chain distortions3. aggregation of secondary complexesmixing of two polyions can lead to 90% complex formationPolyelectrolytes studied as coacervates for biomaterials:4o Polyanionso Carboxymethylcelluloseo Alginateo Dextran sulfateo Carboxymethyl dextrano Heparino Carrageenano Pectino xanthano Polycationso Chitosan (derived from crab shells)o Polyethyleneimineo Poly(4-vinyl-N-butylpyridinium) bromideo Quarternized polycationso Poly(vinylbenzyltrimethyl)ammonium hydroxideLecture 9 – polyelectrolyte hydrogels4 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsoSpring 2003Microstructure of coacervate hydrogelsoExample structures: xanthan/chitosan coacervates (Dumitriu et al. 1998)oPore sizes formed 0.1-1 µm; fiber diameters 100 nmPolyelectrolyte multilayers (PEMs)Structure of PEMsAssembly Layer-by-layer depositiono How is it doneo Surface properties change in digital fashion with adsorption of sequential layers5Lecture 9 – polyelectrolyte hydrogels5 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsSpring 2003Surface properties dominated by lastlayer deposited:θ Assembly figure source: http://www.chem.fsu.edu/multilayers/Assembly on complex surfaceso Polyelectrolytes will adsorb to surfaces with complex topographyo Polyelectrolytes themselves may have complex geometries (e.g. particles or dendrimers)6Generation 7 poly(amidoamine) dendrimer:(Khopade and Caruso, 2002) Dendrimer image source: agin3/Lecture 9 – polyelectrolyte hydrogels6 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsoSpring 2003Assembly on protein crystals to encapsulate proteins:7 Blah blah(Caruso et al., 2000) Cells as living PEM assembly substrates:SEM micrograph ofmultilayer-coatedechinocyte blood cell(F. Caruso)o(Source: http://www.chem.fsu.edu/multilayers/)What elseBuilding PEMs on biomaterials8 Assembly of PEMs on amino-modified poly(lactide)5o Alternating adsorption of sulfonated polystyrene and chitosan (polycation)Lecture 9 – polyelectrolyte hydrogels7 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsH2 N-Spring 2003CH2 CH2 -NH2CH3 O-(CH -C-O)n-CH3 O H-CH -C-N-CH2CH2-NH2 HO-PEM-modified polylactideLecture 9 – polyelectrolyte hydrogels8 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsSpring 2003Utility of polyeletrolyte gels in biomaterials/bioengineeringooCell encapsulation: In situ formation with no ‘additives’, no change in pH, no change in temperature, in physiologicalsolutionso Useful for safe encapsulation of cellsDrug delivery: Ionic interactions for protein-polymer complexes prior to gel formation allow high protein entrapmentefficiencieso PEMs can form hollow capsulesDrug release from PSS/PAMAM PEM capsules:Fluorescent drug-loaded PEM capsulesooEnzyme immobilization: binding to ionic groups for biosensors or active biomaterialsProtein separations/recovery:9 some binding specificity can be achieved in certain situations to allow for selectivesorption of a target proteino Addition of polycation or polyanion to solution of protein leads to protein-polyelectrolyte coacervate formationo Bound proteins released by adjustment of pH/ionic strengthLecture 9 – polyelectrolyte hydrogels9 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsoSpring 2003Microvalves for bioMEMS and lab-on-a-chip applications:10,11 Utilize fast response of swelling in microsized gelsto control flow through microfluidicso Example: PHEMA-co-AA networks patterned in microfluidic channels: Schematic shows an example lab-on-a-chip analysis approachLecture 9 – polyelectrolyte hydrogels10 of 17
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003Second figure on right depicts a sorting valve that can determine whether fluid flow goes left or rightbased on pH of solutiono Composed of one polybase gel (poly(dimethylaminoethyl methacrylate-co-hydroxyethylmethacrylate) 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 pHSurface modification agents: as described above for polylactide and other biomaterialsBrannon-Peppas theory of swelling in ionic hydrogels Original theory for elastic networks developed by Flory and Mehrer12-14, refined for treatment of ionic hydrogels byBrannon-Peppas and Peppas15,16Other theoretical treatments17Derivation of ionic hydrogel swelling Model structure of the system:Model of system:Inorganic anion, e.g. Cl Inorganic cation, e.g. Na water(-)(-)(-)(-)(-)(-)(-)(-)(-)a a *aa-*c c *cc-*csc2µ1*µ10µ1MMcn1χ System is composed of permanently cross-linked polymer chains, water, and saltWe will derive the thermodynamic behavior of the ionic hydrogel using the model we previously developed forneutral hydrogels swelling in good solvent Model parameters:activity of cations in gelactivity of cations in solutionactivity of anions in gelactivity of anions in solutionconcentration of cations in gel (moles/volume)concentration of cations in solution (moles/volume)concentration of anions in solution (moles/volume)concentration of anions in solution (moles/volume)concentration of electrolyteconcentration of ionizable repeat units in gel(moles/volume)chemical potential of water in solutionchemical potential of water in the hydrogelchemical potential of pure water in standard stateMolecular weight of polymer chains before cross-linkingMolecular weight of cross-linked subchainsnumber of water molecules in swollen gelpolymer-solvent interaction parameterLecture 9 – polyelectrolyte hydrogelskBTvm , 1vm,2vsp,1vsp,2V2VsVrννeν ν φ1,sφ2,sφ2,rx1x1*Boltzman constantabsolute temperature (Kelvin)molar volume of solvent (water, volume/mole)molar volume of polymer (volume/mole)specific volume of solvent (water, volume/mass)specific volume of polymer (volume/mass)total volume of polymertotal volume of swollen hydrogeltotal volume of relaxed hydrogelnumber of subchains in networknumber of ‘effective’ subchains in networkstoichiometric coefficient for eletrolyte cationstoichiometric coefficient for eletrolyte anionvolume fraction of water in swollen gelvolume fraction of polymer in swollen gelvolume fraction of polymer in relaxed gelmole fraction of water in swollen gelmole fraction of water in solution11 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsSpring 2003oAsterisks denote parameters in solutionoFree energy has 3 components: free energy of mixing, elastic free energy, and ionic free energy Gtotal Gmix Gel GionEqn 1oAt equilibrium, the chemical potential of water inside and outside the gel are equal:Eqn 2µ1* µ1Eqn 3µ1* - µ10 µ1 – µ10oSolution contains ions so µ1* is not equal to µ10Eqn 4( µ1*) TOTAL ( µ1)TOTALEqn 5( µ1*) ion ( µ1)mix ( µ1)el ( µ1)ionoThe equation we’ll try to solve is a rearrangement of this:Eqn 6o( µ1*) ion - ( µ1)ion ( µ1)mix ( µ1)elContributions to the free energy:o Free energy of mixing: Gmix Hmix – T SmixEqn 7oWe previously derived the contribution from mixing using the Flory-Rehner lattice model:Eqn 8 Gmix kBT[n1ln (1-φ2,s) χn1φ2,s]Eqn 9( µ1)mix ( Gmix ) 22 k B T[ln(1 φ 2,s ) φ 2,s χφ 2,s ] RT[ln(1 φ 2,s ) φ 2,s χφ 2,s ] n T ,P1ooSecond expression puts us on a molar basis instead of per moleculeElastic free energy: Gel (3/2)kBTνe(α2 – 1 – ln α)Eqn 10( µ1)elEqn 111/ 3 ( Gel ) ( Gel ) α 2 M c v m,1 φ 2,s 1 φ 2,s RTν 1 M Vr 2 φ 2rs n1 T ,P α T ,P n1 T ,P φ 2rs v 2M φ 1/ 3 1 φ m,1c RT 1 φ 2,r 2,s 2,s vMM2 φ 2rs sp,2 c φ 2rs oLast equality uses:o ν V2/vsp,2Mc(on handout)(on handout)o Vr V2/φ2,ro Thus ν/Vr φ2,r/vsp,2McIonic free energy:o Term driving dilution of ions diffusing into gel to maintain charge neutralityLecture 9 – polyelectrolyte hydrogels12 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsoChemical potential change in solution:( µ1)ion µ µ*Eqn 12*1o01 RT ln a RT ln x RT ln(1 *1*1all ionsv RT n vm,1 nm,1jRT RT x nj( µ1)ionall solutes*jj x)approximation in third equality is used for dilute solutionsall ions*Eqn 13Spring 2003*j*jall ions nall ions*j v m,1RTj c*jjThe first approximation holds if Σxj* is smallFourth equality holds because we assume in the liquid lattice model that the molar volume ofall species is the same, thus vm,1n V, the total volume of the systemChemical potential change in gel:ooo( µ1 )ion µ1 µ10 RT ln a1Eqn 14 vm,1 RTall ions cjj( µ1 )*ion ( µ1 )ion vm,1 RT (c j c*j )all ionsEqn 15joThe 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 coefficientsCνz Aνz ν C z ν A z Eqn 16 e.g. CaCl2: ν 1, ν- 2, z 2, z- 1Eqn 18ν ν ν̂νˆν ν for a 1:1 electrolyteEqn 19c * c * (ν ν )c s* νˆc *s total concentration of ionsEqn 17 for a 1:1 electrolyte2oWe will derive equations for an anionic networko Assuming activities concentrationso Inside gel:Eqn 20c ν csEqn 21c- ν-cs ic2/zoooc2 is the moles of ionizable repeat groups on gel chains per volumeFirst term comes from electrolyte anions in gel, second term from counter-ions associatedwith ionized groups on the polymer chainsThe degree of ionization i can be related to the pH of the environment and the pKa of thenetwork groups:[RCOO ][H ] Eqn 22Ka [RCOOH ]Lecture 9 – polyelectrolyte hydrogels13 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsEqn 23Spring 2003[RCOO ] Ka [RCOO ]10 pK a[RCOOH ] [H ] K a K ai H ] K a 10 pH K a 10 pH 10 pK aRCOO ] 1 K a[RCOOH ] [RCOO ][[1 [H ][RCOOH ] oOutside gel:Eqn 24c * ν cs*Eqn 25c-* ν-cs*oOur relationship for the ionic chemical potentials is now:( µ1)ion ( µ1)ion v m,1RT*Eqn 26all ions (cj c *j ) v m,1RT (c c c * c * )joUsing Eqn 20, Eqn 21, Eqn 24, and Eqn 25, Eqn 26 becomes: ( µ1)ion ( µ1)ion v m,1RT ν c s ν c *Eqn 27 ic 2ic νˆc *s v m,1RT νˆ c s 2 νˆc *s z z ic v m,1RT 2 νˆ (c s c *s ) z oHow can we relate cs and cs*?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 28µ µ *Eqn 29µ- µ-*oAdd Eqn 29 to Eqn 28:Eqn 30µ µ- µ * µ-*Eqn 31RT ln aν RT ln a ν RT ln a* ν RT ln a *ν oEqn 32Therefore we can write:aν a ν a* ν a *ν Assuming dilute solutions where the activities are approximately equal to the concentrations:ν Eqn 33 c * c ν c* c Lecture 9 – polyelectrolyte hydrogels14 of 17
BEH.462/3.962J Molecular Principles of Biomaterials ν c s ν * ν c s Eqn 34ν Spring 2003 ν ν c* s ν c ic 2 sν z cs* ic2 cs ν z ν Eqn 35 c s* cs Eqn 36 ν **csc *sic 2cs cs 1 1 *icicˆcsνz c *s2 c 2 c s sν z ν z ν o( µ1)ion ( µ1)ion*I 12all ions z c2i iiTherefore:( µ1)ion ( µ1)ionooz z νˆc *s2*Eqn 39Eqn 40 for a 1:1 electrolyteWhere zi is the charge on ion i o i 2c 22 v m,1RT * 2z z νˆc s But definition of ionic strength I is:Eqn 38o2o Derivation of this equation in appendixNow Eqn 27 becomes:Eqn 37o 1 ic 2 2 * 2z z νˆ c s (Using relation i 2φ 2 i 2c 22 2, s v m,1RT v m ,1RT 22 4I 4 Iv sp ,2 M 0 c2 φ 2,sv sp ,2 M 0 moles ionizable groups/volume)Eqn 39 can be re-cast in terms of the solution pH:( µ1)ion ( µ1)ion* v RT K m,1 pH a 4I 10 K a 22 φ 2 2 φ 2,s Ka2,s v m,1RT pH 22 10 K a 4Iv sp,2 M 0 z v sp,2 M 0 Returning to the equilibrium criterion:Lecture 9 – polyelectrolyte hydrogels15 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsEqn 41oSpring 20032 v 2 M φ 1/ 3 1 φ 2 φ 2,s10 pK a2m,1c v m,1 pH ln(1 φ 2,s ) φ 2,s χφ 2,s φ 2,r 1 2,s 2,s 22 pK a M φ 2,r 2 φ 2,r 10 10 4Iv sp,2 M 0 v sp,2 M c Brannon-Peppas paper analyzes Polyacrylates/polymethacrylates:o In water pH 7.0 with I 0.35o χ 0.8o pKa 6.0o vsp,2 0.8 cm3/go M 75,000 g/moleo Mc 12,000 g/moleo M0 90 g/moleo φ2,r 0.5Lecture 9 – polyelectrolyte hydrogels16 of 17
BEH.462/3.962J Molecular Principles of BiomaterialsSpring 16.17.De, S. K. et al. Equilibrium swelling and kinetics of pH-responsive hydrogels: Models, experiments, andsimulations. Journal of Microelectromechanical Systems 11, 544-555 (2002).Tanaka, T. & Fillmore, D. J. Kinetics of Swelling of Gels. Journal of Chemical Physics 70, 1214-1218 (1979).Zhao, B. & Moore, J. S. Fast pH- and ionic strength-responsive hydrogels in microchannels. Langmuir 17, 47584763 (2001).Chornet, E. & Dumitriu, S. Inclusion and release of proteins from polysaccharide-based polyion complexes. AdvDrug Deliv Rev 31, 223-246. (1998).Zhu, Y., Gao, C., He, T., Liu, X. & Shen, J. Layer-by-Layer assembly to modify poly(L-lactic acid) surface towardimproving its cytocompatibility to human endothelial cells. Biomacromol. 4, 446-452 (2003).Khopade, A. J. & Caruso, F. Stepwise self-assembled poly(amidoamine) dendrimer and poly(styrenesulfonate)microcapsules as sustained delivery vehicles. Biomacromolecules 3, 1154-1162 (2002).Caruso, F., Trau, D., Mohwald, H. & Renneberg, R. Enzyme encapsulation in layer-by-layer engineered polymermultilayer capsules. Langmuir 16, 1485-1488 (2000).Elbert, D. L., Herbert, C. B. & Hubbell, J. A. Thin polymer layers formed by polyelectrolyte multilayer techniqueson biological surfaces. Langmuir 15, 5355-5362 (1999).Wang, Y. F., Gao, J. Y. & Dubin, P. L. Protein separation via polyelectrolyte coacervation: Selectivity andefficiency. Biotechnology Progress 12, 356-362 (1996).Beebe, D. J. et al. Functional hydrogel structures for autonomous flow control inside microfluidic channels. Nature404, 588- (2000).Beebe, D. J., Mensing, G. A. & Walker, G. M. Physics and applications of microfluidics in biology. Annual Reviewof Biomedical Engineering 4, 261-286 (2002).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).Flory, P. J. & Rehner Jr., J. Statistical mechanics of cross-linked polymer networks. I. Rubberlike elasticity. J.Chem. Phys. 11, 512-520 (1943).Flory, P. J. & Rehner Jr., J. Statistical mechanics of cross-linked polymer networks. II. Swelling. J. Chem. Phys.11, 521-526 (1943).Brannonpeppas, L. & Peppas, N. A. Equilibrium Swelling Behavior of Ph-Sensitive Hydrogels. ChemicalEngineering Science 46, 715-722 (1991).Peppas, N. A. & Merrill, E. W. Polyvinyl-Alcohol) Hydrogels - Reinforcement of Radiation-Crosslinked Networksby Crystallization. Journal of Polymer Science Part a-Polymer Chemistry 14, 441-457 (1976).Ozyurek, C., Caykara, T., Kantoglu, O. & Guven, O. Characterization of network structure of poly(N-vinyl 2pyrrolidone/acrylic acid) polyelectrolyte hydrogels by swelling measurements. Journal of Polymer Science Part BPolymer Physics 38, 3309-3317 (2000).Lecture 9 – polyelectrolyte hydrogels17 of 17
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Observed swelling as a function of pH: o Data1 for poly . 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 2 N-C H CH 3 O
Introduction of Chemical Reaction Engineering Introduction about Chemical Engineering 0:31:15 0:31:09. Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26 Lecture 27 Lecture 28 Lecture
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