Measurements of Forces at the Nanoscalesome ideas for measurements at LEPES in 2005

J. Chevrier

18 November 2004

we consider three different forces:

- Casimir: hc [J.m]

- Electrostatic: e2/40 [J.m]

-Gravity: Gm2 [J.m]

-electrostatic: Charles A. Coulomb 1736-1806 - strong force- long range

today “Easily” measured

-gravity: Henry CavendishNice 1731 - Londres 1810

- weaker force: (e2/40) / Gm2 1040

- long range

a bit more difficult…but still a student training

- Casimir/van der Waals versus electrostatic:

hc / (e2/40) 137

fine structure constant

However unless at very short distances (< 1nm)(if static charges present …not neutral)

electrostatic >> Casimir

Casimir… short rangecharacteristic distance at the nanoscale

Nanosciences

Sphere diameter 50 msphere/surface: 10nm -1 m

origin of van der waals/casimir interaction between two neutral systems in their fundamental state:

electron-photon coupling by dipolar interaction -d.E

-d.E

-d.E

-d.E

Fundamental state

Fundamental state

Fundamental state

Fundamental state

temps

-d.E

Electronic excitations(q,)

Characteristic length for two metallic surfaces(jellium model)

defined by electronic excitations coupled to photons:

surface plasmons

characteristic length:

p= 2 c/ p

Aluminium h p= 14eV

p 100nm

Surface Surface plasmonsplasmons

metal (1<0)

Hy

ExEz

+++ --- +++ --- +++ ---

Surface Surface plasmonsplasmons

x

Hy

EEz+++ --- +++ --- +++ ---

metal (1<0)+++ --- +++ --- +++ --- metal (2<0)

d<< p

Coupling ofCoupling of

F<0 répulsif

F>0 attractif

d=10nm

Al

SiCPlasmon polariton

Phononpolariton

Plasmon polaritond<< p

Surface Surface plasmonsplasmons

metal (1<0)

Hy

ExEz

+++ --- +++ --- +++ ---

Changing coupling of plasmons with extended photon modes ???

kph

a

ksp

1

2 kx

xck

12

Zn ,2 a

nkx

21

21spk

2,...1,0,n ,2sin

c

ka

nk spph

kx

xck

/a

1

The way the plasmon-photon coupling is changed

Experiment:Force measurement at distances

close to 10nm below the plasma lengthto be sensitive to surface electronic excitations

Using a resonating oscillatorperturbed by the van der Waals/Casimir interaction.

kFdf res

2

sample

Interaction F

k,

sample

10 100 10000,1

1

10

100

1000

Freq

uenc

y sh

ift H

z

Distance (nm)

Electrostatic calibration

Dispersion forcein the non retarded régime

Home made force machine built within the X tip european project at the ESRF in 2004

Pour le LEPES en 2005:

extension to measurement at short distances d<< punder vacuum and at low T (4K)

…...

hope we shall avoid such a hard collision next timehope we shall avoid such a hard collision next time

good point however: good point however: parallelparallel surfaces well prepared…. surfaces well prepared….

Very very large roughness...

Experimental objective:

Combination of sphere on cantilever or on tuning fork

+

measurement of frequency shift with resolution close to 1mHz

Mario Rodriguezstage de Master 2ESRF

Gauthier TorricelliThèse LEPES/ESRF

Guillaume JourdanThèse LEPES/Lab. Kastler BrosselDirection: J. Chevrier/ A. Lambrecht