Van Waals force - uni-muenchen.de...Electrostatic interaction in water the electricdouble layer...

Caddie 30.04.2019

Van der Waals forceorigin dipol dipol interaction Edipoen

Yaw ß VAWinteraction energy ß J.nl

repulsion In

SLI attraction 6

Macroscopic implicationsPt V b RT seal gas equation

b excluded volume b ER N R Radius

a2T Na ß interactionparameter

I neg pressureVdweofl

Types of VAW contributions

1 Kasan interaction two permanent dipoles

In NIELIFE AT VG

2 London dispersion interaction QM

V frequency do polarizability

Von der Waals Forces between macroscopic bodies

Integration Uth 4 h.dk dk

example h atom densityIndensity

hatiiiD

UM III energyperana

Bittet p Hunsaker constantly

For two curved surfaces

µFYI 2T Nd bergagnin approximation

Force IN energyfanalhit

DW Force between two spheres of radius K

Frau sphere sphere Yt

Force apparatus two crossed cylinders mica

1z

U atinnadins

11 Welt 4i

er

Er Coulomb law in dielectric

eg ions in oil Z valency of ion

Field energy of an iv im a continuum Bonn energy

wy.ua ED E Er E energy density

Wee Es.su Edv kEoEif.uf s.E 4iTv'der

Ii8ts.GR electrostatic selfenergy

contributes to the chemicalpotential of the ionMin µ

t AT lm X t Wee

A molar fraction

Nat El Cattexample0.1 0.138 0.1 umRim

µ evWIEWIE 801 0,088 0,05 0,36 e

Electrostatic interaction in water the electric double layert free ions of valuing Zi

I.tn i im speciest

ZteManion conoid Ziel mit 0 Efteae.ly

Problem Find electrostatic potential 4G14h Poisson Eg

r ziem charge densityzieh

ne r lol exp Boltzmann

1414 Z.ziemilolexp.EEPoisson Boltzmann Ey

43 approximation exp x 1 txt

for zielt AT

1414 44 2 ziemi

linear PoissonBoltzmann

Ü egmation

with ui 1 ziemE Er AT i

Vi Debey screening length

Solution ofPB Eg for a pointlike manion

Ii riceansatz yay p II g ö

KV

4h e4T E Er

Solution for mano ion of finite size RtURI Kv

4ms 4he

4T E Er 1 t KR

löws

414 TE.E fitktz.kz surface potential

Solution of PB Eg for a flat surface

4 xnix

eF 4T E Er