3.052 Nanomechanics of Materials and Biomaterials

Prof. Christine OrtizDMSE, RM 13-4022

Phone : (617) 452-3084Email : cortiz@mit.edu

WWW : http://web.mit.edu/cortiz/www

LECTURE #9 : QUANTITATIVE TREATMENT OF

INTRA- AND INTERMOLECULAR FORCES

Review : Lecture #4Experimental Aspects of Force Spectroscopy III :

I. Comparison of high-resolution force spectroscopy techniques :• atomic force microscopy (AFM), surface forces apparatus (SFA), optical tweezers (OT), biomembrane surface probe (BSP)

II. Conversion of raw data in a high-resolution force spectroscopy experiment :

• sensor output, s transducer displacement, force, F

• z-piezo deflection, z tip-sample separation distance, DIII. Typical force spectroscopy data for a weak cantilever on stiff substrate (ksample>>kcantilever) :APPROACH : (*sample and tip come together)• A: tip and sample out of contact, no interaction, cantilever undeflected, zero force (set F=0)• B/C: attractive interaction pulls tip down tosurface and tip jumps to contact, cantilever exhibits mechanical instability• D: contact, constant compliance regime,no sample indentation, tip and sample move in unison (s/z=1)RETRACT :(*sample and tip move apart)• D: repulsive contact, constant compliance Regime, tip deflected up • E: attractive force (adhesion) keep tip attached to surface, tip deflected down• F: tip pulls off from surface, cantilever instability • G: same as region A

s/m F=k

D=z

RAW DATA

Tip-Sample Separation Distance, D (nm)

For

ce, F

(nN

)

adhesion

0

repulsiveregime

attractive regime

z-PiezoDeflection, z (nm)

Pho

todi

ode

Sens

or O

utpu

t, s (V

)CONVERTED DATA

jump-to-contact

substrate compression no interaction

0 0

kc

RAW DATA

Tip-Sample Separation Distance, D (nm)

For

ce, F

(nN

)

adhesion

0

repulsiveregime

attractive regime

z-PiezoDeflection, z (nm)

Pho

todi

ode

Sens

or O

utpu

t, s (V

)CONVERTED DATA

jump-to-contact

substrate compression no interaction

0 0

kc

AB/C

D

D

EF G

AB/C

DD

EF

G

Adhesive Interaction

Types of Intra- and Intermolecular Interactions in Different Materials

Material Interactionmetals metallic

ceramics and glasses covalent / ionicsemiconductors covalent / ionic

diamond covalentwater covalent, H-bonding

inert gases dispersionsolid salt crystals ionic

alkanes, hydrocarbons,flourocarbons, amphiphiles

in water

hydrophobic

polymers covalent, dispersion + H-bonding,dipole-dipole, ionic depending on

chemical structure

Biomolecular Adhesion• controlled by bonds between molecular

“ligands” and cell surface “receptors” which exhibit the “lock-n-key principle”

(e.g. biotin-streptavidin)

• complex, multiatomic, relatively weak• formed by an assembly of multiple, weak non-covalent interactions

(e.g. H-bonding, coulombic, van der Waals, hydrophilic / hydrophobic, electrostatic)• complementary, sterically-contrained geometric considerations

• specificity

• Grubmüller, et al, Science 1996

(*http://www.mpibpc.gwdg

.de/abteilungen/071/strept.html)

(*http://www.amber.u

csf.edu/amber/tutorial/

streptavidin/index.html)

BRIDGING THE GAP BETWEEN LENGTH SCALES

r(nm)-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0 0.2 0.4 0.6 0.8 1

F(r)(nN

)

Tip-Sample Separation Distance, D (nm)

Forc

e,

F (

nN

)

0

kc

Characterizing an Individual Intra- and Intermolecular Interaction

interaction force (electromagnetic

in origin) (nN)

interaction distance

(nm)interaction

energy(kJ/mol)

Characterizing an Individual Intra- and Intermolecular Interaction

interaction force (electromagnetic

in origin) (nN)

interaction distance

(nm)interaction

energy(kJ/mol)

0

0.5

1

1.5

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

r(nm)

w(r

)(k B

T)

Steric Repulsion Interaction Potentials

Soft RepulsionHard-Core Repulsion

n=

0

0.5

1

1.5

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7r(nm)

w(r

)(k B

T)

Soft RepulsionB=10-134Jm12

n=12

• Due to overlap of negatively charged electron clouds (e.g. PauliExclusion principle) and (+) charged nuclei, quantum mechanical in origin; “short-range”, i.e. takes place over the order of distances ofbond lengths ~0.1 nm

n

n

= hard sphere diameter = 2R

n hard

BU (r) =

rr

s

(

phere poten l

nm)

tia

repulsive

Attractive Interaction Potentials

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.2 0.4 0.6 0.8 1

r(nm)

w(r

) (k B

T)

A=10-77Jm6

m=6

Londondispersion interaction

m (m ~ 1 6)A

U (r) = -r

attractive

• longer range > ~1 nm

• A is a constant determined by the

polarizability or ease of distortion of electron

cloud

Net or Complete Interaction Potential : The Lennard-Jones or “6-12” Potential

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1w(r

) (k B

T)

A=10-77Jm6

B=10-134Jm12

n=12, m=6

r(nm)

BLJ

LJ 7

B

s s

12 6

6 12

13

m = 6, n = 12

m = 6, n = 12

r r

-A BU ( ) = = 4E

r r

-6A 12BF ( ) =

r rE = "binding energy,"

"bond dissociation energy,"

or depth of potential well

r = distance at which U(r )

exhibits

s RUPTURE

e

e e

o o o

and inflection point,

F(r ) min imum F

r = equilibrium bond length,

distance at which U(r ) = minimum, F(r ) = 0

r = = distance at which U(r ) 0, F(r )

Interaction Strength

EB

Interaction Strength,kJ/ mol(HOH)

Strength,kBT

(HOH)dispersion 0.05-40 0.02-16

hydrophobic 0.4 0.17dipole-induced dipole 2-10 0.8-4

THERMAL ENERGY 2.5 1dipole-dipole : H-bonding 5 2

ion-ion 13 5lipid in bilayer(hydrophobic)

25 10

carbohydrate-L-selection 62 25biotin-avidin 125 50

single covalent, C-C 380 150double covalent, C=C 630 250triple covalent, CC 840 340

Equilibrium Interaction Distance, re

re

Bond Type InteractionDistance (nm)

dispersion 0.35hydrophobic 0.35H-bonding 0.3

ion-ion 0.25covalent 0.1-0.2

-0.7

-0.5

-0.3

-0.1

0.1

0.3

0.5

0 0.2 0.4 0.6 0.8 1

wLJ(r

) (k B

T)

A=10-77Jm6

B=10-134Jm12

n=12, m=6

r (nm)

re

re’>re

Force Profile for The Lennard-Jones or “6-12” Potential

r(nm)

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 0.2 0.4 0.6 0.8 1

w(r) (k

BT)

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0 0.2 0.4 0.6 0.8 1

F(r)(nN

)

rorers

Fruptu

re

LJ 7 13m = 6, n = 12-6A 12B

F ( ) = r r

s s

e e

o o

When :

U(r ) F(r ) min imum

U(r ) min imum, F(r ) 0

U(r ) 0, F(r )

inflection point,

More Complicated Interaction Potentials

• Grubmüller, et al, Science 1996(*http://www.mpibpc.gwdg.de/abteilungen/071/

strept.html)

R. MERKEL*†, P. NASSOY*‡, A. LEUNG*, K. RITCHIE* & E. EVANS*§, Nature 397, 50 - 53 (1999)