1. 3.052 Nanomechanics of Materials and Biomaterials
LECTURE # 15 : • MOLECULAR MECHANICS OF CARTILAGE
Prof. Christine Ortiz
DMSE, RM
Phone : (617)
WWW :

2. Interactions Between Charged Surfaces in Liquids
Review : Lecture #13,14
Interactions Between Charged Surfaces in Liquids
I. Charged Surfaces : formation mechanisms : (1) ionization or dissociation of surface chemical groups and
(2) adsorption (or physical binding, VDW) of ions from solution onto a neutral surface
II. Qualitative Aspects of the Counterion Electrical Double Layer :
translational / rotational entropy which drives counterions away from the surface 
electrostatic attraction to fixed surface charge which drives counterions to the surface
• repulsive force with decreasing D between charged surfaces comes from :
overlap of counterion electrical double layers
III. Quantitative Aspects of the Counterion Electrical Double Layer :
• PARAMETERS :
s= uniformly distributed surface charge density (C/m2)
rx=counterion density or concentration at any point x
within the gap between two surfaces (# counterions/m3)
ro=r=ionic concentration in midplane (x=0)
rs=ionic concentration at surfaces (x=±D/2)
yx=electrical potential at any point x within the gap between
two surfaces, yx=yoexp[-kx] where :k-1= DEBYE LENGTH
P=P(D)planes=F(D)/unit area (N/m2)
= mean osmotic pressure between two charged planes
(no added electrolyte)

3. Interactions Between Charged Surfaces in Liquids
Review : Lecture #13,14
Interactions Between Charged Surfaces in Liquids
P(D)=kBTro(D)
P(D)=kBT[rs(D)-rs()]
IV. The Electric Double Layer in the Presence
of an Electrolyte (Dissociated Salt) :
P(D)=kBT[ro(D)-ro()]
F(D)PLANES=2eeok2yo2exp[-kD]=[2s2/eeo]exp[-kD]
W(D)PLANES=2eeokyo2exp[-kD]=[2s2/keeo]exp[-kD]
(per unit area)
V. The DLVO Theory :
P(D)=electrostatic + VDW

4. Structural Hierarchy and Function of
the Components of Articular Cartilage
(*Buckwalter, et al., J. Bio. Chem.,1982)

5. Structure of Aggrecan HA
(Rotary Shadowing EM : Hardingham, et al. FASEB J Mörgelin, et al. Biophys. Chem ) HA - b
n=25.5

6. TMAFM Images of Sparse Monolayer of Fetal Bovine Articular Cartilage Aggrecan Monomers (A1A1D1D1) in Air on APS-Mica
(Ng, et al. Polym. Prepr. 2003)
amplitude
height

7. TMAFM Images of Sparse Monolayer of Cartilage Aggrecan Monomers (A1A1D1D1) in Air on APS-Mica
(Ng, et al. Polym. Prepr. 2003)
1.1 nm
50 nm
50 nm
0.6 nm
FETAL
MATURE
0 nm

8. TMAFM Amplitude Images of Dense Monolayer of Fetal Bovine Articular Cartilage Aggrecan Monomers (A1A1D1D1) in Air on APS-Mica
(Ng, et al. Polym. Prepr. 2003)

9. (Seog, et al. Macromolecules 2002)
Nanomechanics.....
(Seog, et al. Macromolecules 2002)
~32 nm

10. FTOTAL = F D FELECTROSTATIC + FSTERIC + FVDW + FHYDRATION
microfabricated cantilever
(Seog, et al. Macromolecules 2002)
Chemical HRFS :
Sulfate-Functionalized
Probe Tip versus GAG
Brush Surface -
Rtip~25 nm - - - + - - + - - + - - - - + - - - - + + - - - - + + - - - - - - - + + + - + + + +
s1(-) + + + - + - + + +
tip diffuse
counterion
double layer - + + - + + + +
Si3N4 probe tip : Au-coated + + + + + + + + + + + + + + + - + + - + - + + + + + + D + - + - +
bulk
concentration
of electrolyte ions + - - + - + - - - + - + + + - +
FTOTAL =
FELECTROSTATIC
+ FSTERIC
+ FVDW
+ FHYDRATION + - + - + + + +
surface diffuse
counterion double layer + + + - + + + + + - + - + + + + + + + + + + + + + + + + - - - - + - - - + + - + - - + - - + + + - + - - - - + - - + - - - - - + - - - - -
end-grafted CS-GAG brush on a planar surface + - - - - +
s2(-) + - - + - + - - - + + - + + + - + - + - + - - + + + - - - - + - - + - + - - - - - - + - + - + - - + - + - - - + + - - + - - + + - + - - - + + - + - - - + - + - - - - - - Si + + + - + - +
CH3 SAM
Au-coated silicon chip
s~6.5 nm

11. A UNIVERSAL SCIENTIFIC PROBLEM :
Deconvoluting the Total Intersurface Interaction Si Au F
chemically
functionalized
probe tip Lo Lo

12. SULFATE-Functionalized Probe Tip versus GAG Surface
at pH=5.6 as a Function of NaCl Ionic Strength
AVERAGED CURVES ON APPROACH
(Seog, et al. Macromolecules 2002)
Lcontour(GAG)
A M
B 0.001M
C 0.01M
D 0.1M
E 1M A B C D E

13. 3 Theoretical Models of Electrostatic Double Layer Forces
SURFACE CHARGE
(Parsegian, et al. J. Theor. Bio. 1971
Butt, et al. Biophys. J. 1991)
VOLUME CHARGE
(Ohshima, et al.
Coll. Polym. Sci. 1999)
ROD LIKE CHARGE
(Dean, et al. Langmuir 2003)
Fixed :
eW,, k-1, s1, s2 , RHEMI
Fixed :
eW,, k-1, s1, rVOLUME , RHEMI
Fit : h
Fixed :
eW,, k-1, s1, rROD, s, RHEMI
Fit : h,w
● How do molecular level changes in charge distribution inside polyelectrolyte brushes affect electrostatic double layer forces ?

14. Comparison of Electrostatic Models to HRFS Data: Sulfate Probe Tip vs
Comparison of Electrostatic Models to HRFS Data: Sulfate Probe Tip vs. CS-GAG Brush (0.1M NaCl) (Dean and Seog, et al. Langmuir 2003)
0.5
HRFS Data
stip 20
RHEMI
0.6
rROD
0.4 D
0.5 w s
0.4
0.3 h
Force/Radius (mN/m)
Stress (MPa)
Force (nN)
0.3
0.2
Surface Charge
Model
Charged Rod Model
Best-fit h=25nm
Best-fit w= 2nm
0.2
0.1
Volume Charge Model
Best-fit h=20nm
0.1
0.0
0.0 10 20 30
Distance (nm)

15. GAG VERSUS GAG : FTOTAL = F D FELECTROSTATIC + FSTERIC + FVDW
(Seog, et al. Physics Today 2002) F
microfabricated cantilever
GAG
VERSUS
GAG :
Si3N4 probe tip
+ Au-coated
+ end-grafted
CS-GAG brush
+ methyl SAM : C12H25-SH -
Rtip <150 nm - + + + - - + - + - + - + - - + - - - - + + - - - - - - - + - - - - - - - - + - + + + - - - - + - + + +
s(-) + - + - - + - + + - - + + - - - + - - - - + - - - - - - + + - + - + - - + + -
tip diffuse
counterion
double layer - - - - + + + + + + + + + + + + + - + + + + + - - + + + + + + + D + - + - +
bulk
concentration
of electrolyte ions + - - + - + - - - + - + + + -
FTOTAL =
FELECTROSTATIC
+ FSTERIC
+ FVDW
+ FHYDRATION + + - + - + + + +
surface diffuse
counterion double layer + + + - + + + + + + + + - - + + + + + + + + + + + + + + - - + - - + + - - - - + - + - - - + - + - + + - - - - + - + - - - - + - - - - -
end-grafted CS-GAG brush on a planar surface - + + - - - + - - - + +
s(-) - - + - + - + + - - + - + - - + + - - + + + - - + - + - - - - - - - + - + + - - - + - - + - - - + + - + - + - - + - + - - - - + + - + - + - + + - - - - - - - - + + + - + - +
methyl SAM :
C12H25-SH
Au-coated
silicon chip Si
s~6.5 nm

16. GAG-Modified Probe Tip versus GAG-Modified Surface
at pH=5.6 , IS=0.0001M
(Seog, et al. Physics Today 2002)
A GAG vs GAG
B Sulfate vs. GAG
C Hydroxy vs. GAG A B
Electrically coated tip: immerse tip into GAG solution; 0.15 V DC applied to tip w.r.t platinum electrode for 9 hrs. The current was maintained below 50 nA to prevent electrolysis, which would change bath pH and prevent binding C

17. Effect of Molecular Deformation Mechanism on Opposing Polyelectrolyte Brushes, 0.1 M NaCl (Dean, et al. Langmuir 2003)
GAG
0.5 D
0.6 h
0.4
Both
Collapse to Volume Charge Model at Small D
0.5
Interdigitated Rod Model
GAG
0.3
0.4
Force (nN)
Stress (MPa) D
0.3
0.2 h h’
0.2
0.1
Compressed / Excluded Rod Model
0.1
0.0
0.0 10 20 30 40 50 60 70 80
Distance (nm)
STERIC FORCES : configurational, mixing, and translational entropies
DEHYDRATION FORCES : enthalpic disruption of supramolecular structure (e.g., due to GAG-water hydrogen bonding). HYDRODYNAMICS.