REVIEW : LECTURE 15 THE ELECTRICAL DOUBLE LAYER BETWEEN TWO CHARGED SURFACES Explored the solution for for two interacting charged surfaces ELECTRICAL DOUBLE LAYER POTENTIALS FOR DIFFERENT GEOMETRIES / DLVOCARTILAGE TISSUE INTRODUCTIONCARTILAGE TISSUE STRUCTURE3.052 Nanomechanics of Materials and Biomaterials Thursday 04/12/07 Prof. C. Ortiz, MIT-DMSE I LECTURE 16: NANOMECHANICS OF CARTILAGE Outline : REVIEW LECTURE #15 : EDL BETWEEN TWO CHARGED SURFACES............................................... 2THE ELECTRICAL DOUBLE LAYER IN DIFFERENT GEOMETRIES/ DLVO POTENTIALS .................. 3CARTILAGE TISSUE .............................................................................................................................4-5 Introduction ............................................................................................................................. 4 Structure.................................................................................................................................. 5 CARTILAGE NANOMECHANICS...........................................................................................................6-8 Nanomechanics of Opposing Aggrecan................................................................................. 6 Nanoscale Stiffness versus Strain of Aggrecan..................................................................... 7 Effect of Age on Aggrecan Nanoscale Interactions................................................................ 8 Objectives: To understand the molecular origins of the biomechanical properties of cartilage tissue Readings: Course Reader Documents 26, 27, Supplements Multimedia : Cartilage Podcast 2, Ng, et al. J. Biomech. 2007 40, 05 1011 (contained within folder linked under "Podcast Papers" on stellar. 13.052 Nanomechanics of Materials and Biomaterials Thursday 04/12/07 Prof. C. Ortiz, MIT-DMSE REVIEW : LECTURE 15 THE ELECTRICAL DOUBLE LAYER BETWEEN TWO CHARGED SURFACES 22=ψεo2Fcd(z) Fψ(z)sinhdz RT 1D P-B Equation,1:1 monovalent electrolyte Apply appropriate boundary conditions to solve the P-B equation for ψ(z); constant surface charge or constant surface potential Linearized approximation; 1o()−−==κψψ κz2oεRTzewhere : 2F c"salt screening" Explored the solution forψ(z) for two interacting charged surfaces σz=0Ψ(z)ψο=ψszψο/e1/κ11/κ21/κ3c1c2c3 Calculate pressure (Force/Area) between two charged surfaces : ∞jP(z = z ) - P( ) = "electrical" + "osmotic" ⎛⎞⎛⎞⎜⎟⎜⎟⎝⎠⎝⎠ψm0FP=2RTc cosh -1RT →solve for ψm PB equation →linearized approximation D−=κELECTROSTATIC ESP(D) C e σ + + +++++++++ + + + + + + + + + ψ(x) ()Reference position in the bulk where: ψ(z) = 0 E = dψ/d z = 0 ci(z) = cio (z→∞) z = -D/2 z = D/2 control box z z = zj z =0 ψm 23.052 Nanomechanics of Materials and Biomaterials Thursday 04/12/07 Prof. C. Ortiz, MIT-DMSE ELECTRICAL DOUBLE LAYER POTENTIALS FOR DIFFERENT GEOMETRIES / DLVO (From Leckband, Israelachvili, Quarterly Reviews of Biophysics, 34, 2, 2001) -Monovalent Electrolyte, Linearized P-B formulation, Similarly charged surfaces, Temperature = 37°C Constant Potential Prefactor: ()()-1 -11 2οοZJ m =9.38×10 tanh(ψ /107) ;ψ [mV] - CR 25, 12.16 Conversion to Constant Charge: ()-2ο ooσ Cm = 0.116sinh(ψ /53.4) c ;c [M] = mole/L - CR 25, 12.12 33.052 Nanomechanics of Materials and Biomaterials Thursday 04/12/07 Prof. C. Ortiz, MIT-DMSE CARTILAGE TISSUE INTRODUCTION -Cartilage tissue load bearing tissue in joints that cushions the ends of bones. -Osteoarthritis (OA) is a degenerative chronic joint disease characterized by breakdown of the joint's cartilage. Cartilage breakdown causes bones to rub against each other, causing pain and loss of movement. -OA affects 20 - 40 million Americans; 80% of > age 65, 100% of > age 80 - ~80% of torn anterior cruciate ligament (ACL) progress to OA in 14 years (average age 38 years old) Ann. Rheum. Dis. 2004; 63:269-73. 1 mmE. Hunziker1 mmE. Hunziker1 mmE. Hunziker Stefan LohmanderStefan Lohmander 43.052 Nanomechanics of Materials and Biomaterials Thursday 04/12/07 Prof. C. Ortiz, MIT-DMSE CARTILAGE TISSUE STRUCTURE 82)82)0.5 nmOCOOHHHOHOHHHOOCH2OHHOHNHCOCH3HHHOSO3n=10---n=10-50-GAG contourlength~ 45 nm●covalent attachment of ~100 glycosaminoglycans(GAGs) to protein core separated by ~ 2-4 nm50 nm50 nmfetal epiphysealmature nasalaggrecancontourlength ~ 400 nmhyaluronan(pKa COO-= 3.5-4, pKa SO3-=2-2.5(Ng+ J. Struct. Bio. 143(3), 242, 2003) 0.5 nmOCOOHHHOHOHHHOOCH2OHHOHNHCOCH3HHHOSO3n=10---n=10-50-GAG contourlength~ 45 nm●covalent attachment of ~100 glycosaminoglycans(GAGs) to protein core separated by ~ 2-4 nm50 nm50 nm50 nm50 nmfetal epiphysealmature nasalaggrecancontourlength ~ 400 nm(pKa COO-= 3.5-4, pKa SO3-=2-2.5(Ng+ J. Struct. Bio. 143(3), 242, 2003) hyaluronan - ● load bearing tissue in joints withstands ~3 MPa compressive stress and 50% compressive strain (static conditions), equilibrium compressive moduli ~0.1-1MPa ● ~80% HOH, collagen (50-60% solid content, mostly type II), aggrecan (30-35% solid content), hyaluronan, ~3-5% cartilage cells (chondrocytes) 53.052 Nanomechanics of Materials and Biomaterials Thursday 04/12/07 Prof. C. Ortiz, MIT-DMSE NANOMECHANICS OF OPPOSING AGGRECAN 0 400 800 12000246810Distance (nm)Force (nN)0400 800 12000246810Distance (nm)Force (nN)1M0.1M0.01M0.001MOH-SAM Tip vs. Aggrecan Substrate Aggrecan Tip vs. Aggrecan Substrate0.01M0.001M0.1M1M0 400 800 12000246810Distance (nm)Force (nN)0400 800 12000246810Distance (nm)Force (nN)1M0.1M0.01M0.001MOH-SAM Tip vs. Aggrecan Substrate Aggrecan Tip vs. Aggrecan Substrate0.01M0.001M0.1M1M 63.052 Nanomechanics of Materials and Biomaterials Thursday 04/12/07 Prof. C. Ortiz, MIT-DMSE NANOSCALE STIFFNESS VERSUS STRAIN OF CARTILAGE AGGRECAN 00.511.500.20.40.60.81StrainStiffness (MPa)M(Seog+ J. Biomech 2005 in press, online &Dean, Han+ unpublished data 2005)● stiffens nonlinearly with increasing strain at the molecular level→mechanism to prevent large strains that could result in permanent deformation, fracture, or tearing.(Macro)compressive