智能軟材料水凝膠

1、1 1Soft Active Materials Zhigang SuoHarvard UniversityIII. Polyelectrolytes2Polyelectrolyte: polymer with electrolyte groupIn a solvent, the electrolyte dissociates.solventfixed chargecounterionCaClco-ioncounterion covalent bondionic bondpolymer chain3Polyelectrolyte gel-+-GelExternal solutionFixed

2、chargesCounterionsCo-ions-+-A network of polymersSolvent (e.g., water)Crosslinks4Many tissues are polyelectrolyte gelsStructure and function:Cartilage is polyelectrolyte. Does this fact have anything to do with low friction of a joint?5Plant cell walls are polyelectrolytesPectin6Gels regulate flow i

3、n plantsZwieniecki, Melcher, Holbrook,Hydrogel control of xylem hydraulic resistance in plants Science 291, 1095 (2001)Missy Holbrook7Osmosis in a polyelectrolyte gelmembranesolutionsolventOsmosis balanced by gravityNetwork tatters fixed charges.To maintain electroneutrality, fixed charges are balan

4、ced by counterions. Counterions cause osmosiscrosslink-+fixed chargecounterionwaternetworkOsmosis balanced by elasticity8Super absorbent diaperSodium polyacrylate: polyelectrolyteMasuda, Trends in the development of superabsorbent polymers for diapers, pp. 88-89, Superabsorbent polymers: science and

5、 technology (1994). 9Ion exchanger2NaXCaCaXNa210pH-sensitive gel HRCOORCOOHfixedmobileKRCOOHHRCOO11pH-sensitive hydrogelHlogpH1012pH-sensitive valves in microfluidics Beebe, Moore, Bauer, Yu, Liu, Devadoss, Jo, Nature 404, 588 (2000)Deformation and force regulated by physiological variables (pH, sal

6、t, temperature)Mechanics and chemistryDavid Beebe13Adaptive optics with soft materialsDong, Agarwal, Beebe, Jiang, Nature 442, 551 (2006)14Electric potential Electrochemical potentialGibbs (1878)electrodebattery, Fpump, melectrons, dqIons, dMMqFmdddF0MezqddMezFdmdFMFezFmelectroneutralityequilibriumM

7、aterial AMaterial BelectrodeBattery does work on electrons, FdqPump does work on ions, mdMHelmholtz free energy of system, F15Lithium-ion batteryElectrolyteLi-ionLoadNegativeelectrodePositive electrodeWang, Wu, Wang, Chen, 2005. Journal of Power Sources 140, 125Chan et al., 2008. Nature Nanotechnolo

8、gy 3, 31electronLiFePO4SiliconJohn B. Goodenough163 ways of doing work to a gelFFaaaiiiidVCdAqdVdAxTdVxBdmddddstate reference in volume species of ions of#,atCaXgelmapumpPweightxMaa) reference stateb) current statedry polymerX = (X1, X2, X3)x(X, t)batteryQqdamHong, Zhao, Suo. J. Mech. Phys. Solids 5

9、8 (2010) 558-577.17A field theory of thermodynamic equilibriumDeformation gradientKiiKXtxtF,XXKKXttEF,XX0,tBXtsiKiKXXtQXtDKK,XXEquivalent conditions of equilibriumiKiKFWsKKDWEGausss lawaaaCWezFm,21CCWWDFtCa,XfixfixaaCezCezqQConcentrationsMaterial model:constantamFFaaaiiiidVCdAqdVdAxTdVxBWdVdmdddddEq

10、uilibrium:Hong, Zhao, Suo. J. Mech. Phys. Solids 58 (2010) 558-577.18microscopic processesSwelling increases entropy by mixing solvent and polymers.Swelling decreases entropy by straightening the polymers.Redistributing mobile ions increases entropy by mixing.Neutrality reduces electrostatic energy.

11、-M-XXM gel external solution19Free-energy function DFFDF,21pmsaWCCWWCW FFdetlog2321iKiKsFFNkTWFlory, Rehner, J. Chem. Phys., 11, 521 (1943)sbbsbbssssamcvCCCkTvCvvCvCCkTCW1log11log0n Free energy of mixingFree-energy functionn Free energy of polarizationLKiLiKpDDFFWdet21,FDFn Free energy of stretching

12、Zhao, Hong, Suo, Physical Review B 76, 134113 (2007)20Swelling regulated by concentration of ions10-610-510-410-310-235404550556065700.005vc0vCs + 1Nv = 0.001 = 0.10.002vC0 = 0.01vC*s + 1nonionic gelSwelling ratioConcentration of ions in external solutionConcentration of fixed ions21Constrained swel

13、lingConcentration of ions in external solution10-610-510-410-310-2303234363840420.005vc0vCs + 1Nv = 0.001 = 0.10.002vC0 = 0.01vC*s + 1Concentration of fixed ionsSwelling ratiogelExternal solution5 . 1022Debye lengthx0-+022cekTLD0F gel external solution23-5-4-3-2-10-2-1.5-1-0.50 x/LDeF/kTvc0 = 10-510

14、-410-3-5-4-3-2-1002468x 10-5x/LDvs22/kTvc0 = 10-510-410-3-5-4-3-2-10-1-0.50 x 10-3x/LDvQ/e10-510-4vc0 = 10-3Nv = 0.001 = 0.1vC0 = 0.002-5-4-3-2-1039404142x/LDvCsvc0 = 10-510-410-3In gel, near interfacex0-+00ccinfinity10cv22s22sliquidgel24pH-sensitive hydrogelHRCOORCOOHfixedmobileaKRCOOHHRCOO25ionsol

15、NkT1132112321321321111logSsolvkTHH/cccc1HH/cccccccccckTionHHAccccHKNcccAAHAH321vfccAAHDonnan equilibriumElectroneutralityConstant of acidic dissociationConservation of particles111123Marcombe, Cai, Hong, Zhao, Lapusta, Suo, Soft Matter 6, 784 (2010)Ricka, Tanaka,Macromolecules17, 2916 (1984).Osmosis

16、 is balanced by elasticity26Free swelling27Constrained swelling28Finite element methodSSCCCWWmmmmm)()(HHccWW,HFdAxTdVxBdVWiiiiddddAxTdVxBnnnnWdViiiiSSdddmdmdmdmdHHH,CCCWWFHH/cccc1HH/ccccaAKNcccvfccccH1HHdet/FCondition of equilibriumLegendre transformationShengqiang CaiMarcombe, Cai, Hong, Zhao, Lapusta, Suo, Soft Matter 6, 784 (2010)ABAQUS UMAT posted online.29pH-