3.052 Nanomechanics of

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3.052 Nanomechanics of Materials and
Biomaterials
LECTURE 13 ELECTROSTATIC FORCES
BETWEENCHARGED SURFACES IN LIQUIDS
Prof. Christine Ortiz DMSE, RM 13-4022 Phone
[phone] Email cortiz_at_mit.edu WWW
http//web.mit.edu/cortiz/www
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The Double Electric Layer
water
solvated counterion
Diffuse Layer
Stern or Helmholtz layer
bound ions
negatively charged solid surface
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Interaction Between Two Similarly Charged Surfaces
D1
D1 gtD2
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Interaction Between Two Similarly Charged Surfaces
D2 ltD1
D1
s
s
rs
e
rx
rs
rs
rs
ro
rx
r? ro0
x
x0
x-D/2
xD/2
x-D/2
xD/2
x0
midplane
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Pressure Between Two Similarly Charged Surfaces
D2 ltD1
D1
s
s
rs
e
rx
rs
rs
rs
ro
rx
r? ro0
x
x0
x-D/2
xD/2
x-D/2
xD/2
x0
midplane
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Interaction Between Two Similarly Charged
Surfaces In the Presence of an Electrolyte
D2 ltD1
D1
s
s
rs
rs
e
rs
(rx)
rs
ro
r? ro
counterions(rx)
x
coions(rx-)
x0
x-D/2
xD/2
x-D/2
xD/2
x0
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Electric Potential of a Charged Surfaces In the
Presence of an Electrolyte
s
yoys
yx
c3
yo/e
c2
c1
x
x0
1/k1
1/k2
1/k3
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Interaction Between Two Similarly Charged
Surfaces In the Presence of an Electrolyte
increased electrolyte concentration
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The DLVO Theory (Derjaguin-Landau-Verwey-Overbe
ek)