Download Casimir and Critical Casimir effects An overview Sergio Ciliberto

Casimir and Critical Casimir effects
An overview
Sergio Ciliberto
Laboratoire de Physique, ENS de Lyon, UMR5672 CNRS, Lyon, France
lundi 2 novembre 2015
Casimir and Critical Casimir effects
An overview
Outline
(1) Introduction to Casimir effect
(2) Experiments on electromagnetic Casimir effect
(3) Introduction to critical Casimir effect
(4) Experiments in wetting films and binary mixtures
(5) Casimir effects and colloids
(7) Conclusons and perspectives
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
In 1930 London showed how the leading behavior of the Van de Waals force between
neutral molecules could be understood from quantum mechanics, using an effective
interaction potential between the dipoles
M2
M1
VLondon
hν α1 α2
∝
R6
R
where ν the frequency, α the electronic polarisability
and R the distance bewteen de molecules
In 1948 Casimir and Polder introduced retardation, resulting in a potential
which for large distances falls off faster,
VCasimir−P older
hc α1 α2
∝
R R6
M2
M1
R
tdelay = R/C
Both results can be understood by dimensional considerations.
In 1948 Casimir showed that zero-point energy was responsible for the intermolecular force.
He used this idea to compute the force between two parallel perfectly conducting plates
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
Two parallel, perfectly conducting and uncharged metallic plates
in vacuum attract each other due to the quantum fluctuations of
the electromagnetic fields,
S >>
L
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
Two parallel, perfectly conducting and uncharged metallic plates
in vacuum attract each other due to the quantum fluctuations of
the electromagnetic fields,
S >>
L
lundi 2 novembre 2015
Boundary conditions on the
components of electromagnetic fields
EII , B⊥ = 0
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
Two parallel, perfectly conducting and uncharged metallic plates
in vacuum attract each other due to the quantum fluctuations of
the electromagnetic fields,
S >>
L
Boundary conditions on the
components of electromagnetic fields
EII , B⊥ = 0
The fluctuation modes of the fields in the space within the two plates
can only have a specific set of L-dependent allowed wave-vectors:
k⊥ = π n/L with n = 1, 2, . . ..
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
Two parallel, perfectly conducting and uncharged metallic plates
in vacuum attract each other due to the quantum fluctuations of
the electromagnetic fields,
S >>
L
Boundary conditions on the
components of electromagnetic fields
EII , B⊥ = 0
The fluctuation modes of the fields in the space within the two plates
can only have a specific set of L-dependent allowed wave-vectors:
k⊥ = π n/L with n = 1, 2, . . ..
The “unbalance” between the pressure exerted by the allowed modes within the plates
and the one exerted by the modes outside them is at the origin of the Casimir effect
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
Two parallel, perfectly conducting and uncharged metallic plates
in vacuum attract each other due to the quantum fluctuations of
the electromagnetic fields,
S >>
L
Boundary conditions on the
components of electromagnetic fields
EII , B⊥ = 0
The fluctuation modes of the fields in the space within the two plates
can only have a specific set of L-dependent allowed wave-vectors:
k⊥ = π n/L with n = 1, 2, . . ..
The “unbalance” between the pressure exerted by the allowed modes within the plates
and the one exerted by the modes outside them is at the origin of the Casimir effect
This statement can be made quantitative by calculating the size-dependent energy E(L)
of the electromagnetic fields in the vacuum within the plates
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
The size-dependent energy
S >>
L
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
The size-dependent energy
S >>
L
lundi 2 novembre 2015
In the vacuum this quantity is divergent and meaningless.
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
The size-dependent energy
S >>
L
In the vacuum this quantity is divergent and meaningless.
What is observable is the change in the zero-point energy when matter is introduced
In this way we can calculate the Casimir forces.
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
The size-dependent energy
S >>
The expansion in decreasing powers of L takes the form :
L
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
The size-dependent energy
S >>
The expansion in decreasing powers of L takes the form :
L
is the energy associated to the
electromagnetic field of the vacuum
in the absence of the plates within
the volume of space V = SL
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
The size-dependent energy
S >>
The expansion in decreasing powers of L takes the form :
L
is the energy associated to the
electromagnetic field of the vacuum
in the absence of the plates within
the volume of space V = SL
is the sum of the energies
associated to the introduction of
each single plate in the vacuum
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
The size-dependent energy
S >>
The expansion in decreasing powers of L takes the form :
L
is the energy associated to the
electromagnetic field of the vacuum
in the absence of the plates within
the volume of space V = SL
This is the Casimir term which
represents the interaction energy
between the two plates, due to their
simultaneous presence in space.
is the sum of the energies
associated to the introduction of
each single plate in the vacuum
lundi 2 novembre 2015
Electromagnetic Casimir and van der Waals force
Casimir H B 1948 Proc. K. Ned. Akad. Wet. 51 793
S >>
The expansion in decreasing powers of L takes the form :
This is the Casimir term which
represents the interaction energy
between the two plates, due to their
simultaneous presence in space.
L
is universal. and does not depend on the specific
material of the plates, but only on geometrical
properties (S and L) and on fundamental constants
The higher order term in the expansion:
is a material-dependent parameter which describes the
deviations of the plates from the perfectly conducting behaviour
Finite temperature corrections can be usually neglected
lundi 2 novembre 2015
First experimental verification of the Casimir force
The amplitude of the force : S=100X100 μm2
S �c
−11
F �
� 6 10 N
4
L
and
L= 1 μm
It can be measured using :
a torsion pendulum : S. K. Lamoreaux, Phys. Rev. Lett. 78, 5 (1997).
an AFM
lundi 2 novembre 2015
:
U. Mohideen and Anushree Roy Phys. Rev. Lett. 81, 4549 (1998) ;
Phys. Rev. D 60 ,111101 (1999)
First experimental verification of the Casimir force
Corrections for real measurements
•
Sphere-plane instead of plane-plane interactions
3
π
R�c
o
Fc (d) = −
360 d3
• Finite conductivity of the plates
p
Fc (d)
=
o
Fc (d)
�
1+f
For metals
Plasma Frequency : ωp � 1016 rad/s
and λp = 2πc/ωp � 100 nm
lundi 2 novembre 2015
�
λp
d2π
�
��
�
λp
−1
f
� 10
at d = 10 nm
2π d
�
�
λp
f
� 0.7 at d = 100 nm
2π d
First experimental verification of the Casimir force
Corrections for real measurements
•
Sphere-plane instead of plane-plane interactions
3
π
R�c
o
Fc (d) = −
360 d3
plates
• Finite conductivity of the
�
�
Fcp (d)
•
=
Fco (d)
1+f
�
λp
� 10−1 at d = 10 nm
2π d
�
�
λp
f
� 0.7 at d = 100 nm
2π d
��
f
2
The roughness of the surfaces with variance σr
Fcr (d) = Fcp (d)
•
λp
d2π
�
�
1+O
�
σr2
d2
��
Finite temperature corrections are negligible
lundi 2 novembre 2015
� 3�
2 kB T d
O g where g(T, d) �
� 2 ∗ 10−4 nm−1 d
�c
First experimental verification of the Casimir force
After that all these corrections are taken into account
Phys. Rev. D 60 ,111101 (1999)
lundi 2 novembre 2015
Other
experiments on electromagnetic Casimir
Bressi et al. PRL 88, 041804-1(2002)
R. Decca et al.
Phys. Rev. D, 75 :077101,2007.
S. de Manet al., PRL 103, 040402 (2009)
J. N. Munday et al, Nature 457, 170 (2009)
attractive
repulsive
Rico F. Tabor et al., PRL 106, 064501 (2011)
lundi 2 novembre 2015
Correction of finite conductivity and temperature
J. Laurent et al. Phys. Rev. B 85, 035426 (2012)
lundi 2 novembre 2015
Experimental verifications of the Casimir force
lundi 2 novembre 2015
The critical Casimir effect
Thirty years after the seminal paper by Casimir,
M. E. Fisher and P. -G. de Gennes published a note :
”On the phenomena at the walls in a critical binary mixture”
R. Acad. Sci. Paris,Ser. B 287, 20 (1978)
in which it was shown that
Casimir-like effects (i.e., fluctuation-induced forces) arise also
in statistical physics when a medium in which fluctuations of a
certain nature take place is spatially confined
Let us consider a mixture of two fluids A and B of concentration CA and CB
lundi 2 novembre 2015
The critical Casimir effect
Phase Diagram
The binary mixture
of two fluids
Homogenous phase at low temperature
Increasing the temperature the liquid demixes into an A- and a B-rich solution and
becomes inhomogeneous in the test tube where the two solutions are typically
separated by an interface.
The transition between the mixed and the demixed phases occurs at the solid first-order
transition line. The lower point is the critical point and the transiion becomes second
order
lundi 2 novembre 2015
The critical Casimir effect
Phase Diagram
The relevant observable is the
local concentration
mean concentraction
< cA (x) >= cA
The order parameter of the
transition can be identified with
The correlation
defines the spatial correlation length
The correlation length is fixed by the fluctuations of the order parameter
lundi 2 novembre 2015
The critical Casimir effect
Phase Diagram
local concentration
mean
< cA (x) >= cA
order parameter
The spatial correlation length
what are the consequences of confinement ?
• We intoduce a plate into de mixture
• The plate shows preferential adsorption for one of the two components, say, A.
• The presence of the plate in the mixture induces a local increase of < δcA (x) >
The plate imposes boundary conditions on the order parameter
lundi 2 novembre 2015
The critical Casimir effect
Phase Diagram
glass plate
L<ξ
what are the consequences of confinement ?
• We intoduce a plate into de mixture
• The plate shows preferential adsorption for one of the two components, say, A.
• The presence of the plate in the mixture induces a local increase of < δcA (x) >
The plate imposes boundary conditions on the order parameter
lundi 2 novembre 2015
Analogies and differences between electromagnetic and
critical Casimir effects.
lundi 2 novembre 2015
Analogies and differences between electromagnetic and
critical Casimir effects.
glass plate
bulk energy
L
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surface energy
The wall interact only if L < ξ
Casimir energy
Analogies and differences between electromagnetic and
critical Casimir effects.
glass plate
bulk energy
surface energy
Casimir energy
The wall interact only if L < ξ
L
The scaling function ΘII depends only on some gross features of:
(a) the bulk, e.g. symmetries of the interaction, kind of order parameter
(b) the surfaces of the wall, e.g. the symmetries of the bulk which they break
(c) The shape of the walls
(a) and (b) define the bulk and surface universality classes of the confined system
lundi 2 novembre 2015
Analogies and differences between electromagnetic and
critical Casimir effects.
glass plate
bulk energy
L
surface energy
Casimir energy
The wall interact only if L < ξ
The scaling function ΘII depends only on the features of the universality classes of the
confined system and on the confining geometry
The scaling function can be computed by means of suitable representative
models belonging to the same bulk and surface universality classes of the system
lundi 2 novembre 2015
Analogies and differences between electromagnetic and
critical Casimir effects.
glass plate
L
The critical Casimir Force
The amplitude of the force : S=100X100 μm2 , T=300K and
Critical
Electromagnetic
lundi 2 novembre 2015
L= 1 μm
F � S kB T /L3 � 4 10−11 N
F � S � c/L4 � 6 10−11N
Experiments on critical Casimir
The first experimental tests have been performed around 2000
(1) Thin wetting films close to critical point in binary mixtures and in 4He
(2)
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
Experiments on critical Casimir
The first experimental tests have been performed around 2000
(1) Thin wetting films close to critical point in binary mixtures and in 4He
liquid-gas phase transition
vapour
condensation
liquid film
formation
on a substrate
L diverges at Po
The liquid is confined between the solid substrate and the liquid-vapour interface
L is determined by the van der Waals interactions
Close to the end point the Casimir force adds up to the van-der-Waals forces
in determining the equilibrium distance L
lundi 2 novembre 2015
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
Two different critical binary liquid mixtures have been used
methanol + hexane (MH) and
2-methoxy-ethanol + methylcyclohexane (MM),
onto the Si wafer
lundi 2 novembre 2015
Experimental details
Liquid mixtures properties
methanol + hexane (MH) and
2-methoxy-ethanol + methylcyclohexane (MM),
Upper critical point (MH)
correlation
length versus
temperature
ν � 0.6
which is the correct
3D Ising model exponent
lundi 2 novembre 2015
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
Two different critical binary liquid mixtures have been used
methanol + hexane (MH) and
2-methoxy-ethanol + methylcyclohexane (MM),
onto the Si wafer
lundi 2 novembre 2015
Experimental details
Measure of the film thickness
Phase-modulated ellipsometer
o
Incident angle near the Brewster angle � 76
Ellipticity ρ = [Im(rp /rs )]θB
where rp and rs are the complex reflection amplitudes
for p (in plane) and s (out of plane) polarizations
rp � 0 at θB
extremely good film thickness resolution of 0.02nm
averaged over the focused laser beam diameter of 0.25mm
lundi 2 novembre 2015
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
Two different critical binary liquid mixtures have been used
methanol + hexane (MH) and
2-methoxy-ethanol + methylcyclohexane (MM),
onto the Si wafer
lundi 2 novembre 2015
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
L*
lundi 2 novembre 2015
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
Free Energy per unit area
substrate
liquid
lundi 2 novembre 2015
liquid
vapor
gravity
non
critical
critical
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
Free Energy per unit area
substrate
liquid
liquid
vapor
gravity
Van der Waals interaction between the
substrate and the vapor phase
for sufficiently thin films (L < 10–20 nm)
in the nonretarded regime
W is the Hamaker constant
lundi 2 novembre 2015
non
critical
critical
Repulsive structural interaction due to the
presence of the solid wall
δ is of the order of the molecular diameter
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
Free Energy per unit area
substrate
liquid
liquid
vapor
Critical
ωc
lundi 2 novembre 2015
�
L
ξ±
gravity
�
=
kB T θ
non
critical
+,−
L2
�
critical
L
ξ±
�
Wetting film in binary mixtures
substrate
liquid
liquid
vapor
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
non
critical
gravity
ωc
The minimum of F gives:
�
L
ξ±
�
critical
=
kB T θ+,−
L2
�
L
ξ±
�
At T far from Tc
θ+,− (L/ξ) � 0
this equation can be used for
calibration
For small H , L is large :
lundi 2 novembre 2015
At large H , L ≈ L*
gravity is negligible
the only free parameter is now
δ which is determined by the
crossover
Wetting film in binary mixtures
lundi 2 novembre 2015
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
Wetting film in binary mixtures
Ashis Mukhopadhyay and Bruce M. Law
PRL 82, 772 (1999) and PRE 62, 5201 (2000)
y = L/ξ
ν � 0.6
which is the correct
3D Ising model exponent
lundi 2 novembre 2015
Wetting film in binary mixtures
lundi 2 novembre 2015
Experiments in He
PRL 83, 1187 (1999)
lundi 2 novembre 2015
Experiments in He
h
CF
liquid films
G
CV
vapor
d
liquid film
1
1
1
=
+
C
CV
CF
lundi 2 novembre 2015
CF
Experiments in He
Effective dielectric constant for capacitor 1 as a function of temperature.
Inset (a) shows the film thickness calculated using Eq. (3), where a dip
is found 2.6 mK below Tλ
lundi 2 novembre 2015
Experiments in He
t = (T − Tλ )/Tλ
ν = 0.66
is the exponent
of the XY model
for 4 He film on Cu,
γ0 � 2.6 K nm3
and
d1/2 � 20nm
lundi 2 novembre 2015
Experiments in He
comparison with theory
The data points are
obtained
by Monte Carlo simulation
of the XY model on the
lattice
(Vasilyev O, Gambassi A, Maciolek
A, and Dietrich S 2007 EPL 80
60009)
The solid red line
represents the
experimental
results
(Garcia R and Chan M H W 1999
Phys. Rev. Lett. 83, 1187)
lundi 2 novembre 2015
Experiments on critical Casimir
The first experimental tests have been performed around 2000
(1) Thin wetting films close to critical point in binary mixtures and in 4He
(2)
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
Direct measure on a collidal bead inside a binary mixture
Hertlein C, Helden L, Gambassi A, Dietrich S and Bechinger C 2008 Nature 451 172
Bulk phase diagram of the binary liquid
mixture of water and 2,6-lutidine (dimethylpyridine C7H9N)
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
Hertlein C, Helden L, Gambassi A, Dietrich S and Bechinger C 2008 Nature 451 172
R � 1µm
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
�
�
Φ(z)
P (z) = Po exp −
kB T
Φ(z) = −kB T log(P (Z)/Po )
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
Hertlein C, Helden L, Gambassi A, Dietrich S and Bechinger C 2008 Nature 451 172
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
Hertlein C, Helden L, Gambassi A, Dietrich S and Bechinger C 2008 Nature 451 172
electrostatic interaction
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
Hertlein C, Helden L, Gambassi A, Dietrich S and Bechinger C 2008 Nature 451 172
gravity
electrostatic interaction
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
Surface treatement of the cell:
1) rinsed by NaOH :
hydrophilic (-)
2) Hexamethyldisilizane vapors : hyfrophobic (+)
Two kind of polystyrene beads : hydrophilic (-) and hyfrophobic (+)
(-)(-)
L
kB T
Φ(z) = A exp(−kz) + S 2 ϑ|| ( )
L
ξ
lundi 2 novembre 2015
(-)(+)
Direct measure on a collidal bead inside a binary mixture
Surface treatement of the cell:
1) rinsed by NaOH :
hydrophilic (-)
2) Hexamethyldisilizane vapors : hyfrophobic (+)
Two kind of polystyrene beads : hydrophilic (-) and hyfrophobic (+)
(-)(-)
(-)(+)
Theoretical curves are obtained by Monte Carlo simulation of 3D Ising model which
belongs to the same universality class of binary mixtures.
O. Vasilyev, A. Gambassi, A. Maciołek, and S. Dietrich, Phys.Rev. E 79, 041142 (2009)
Phys. Rev. E 80, 039902 (2009).
lundi 2 novembre 2015
Direct measure on a collidal bead inside a binary mixture
(-)(-)
(+)(+)
lundi 2 novembre 2015
(-)(+)
Direct measure on a collidal bead inside a binary mixture
(+)(+)
Off-critical composition.
Lutidine mass fraction 0.2
Temperatures close to the
demixing line.
lundi 2 novembre 2015
Casimir Force in action
Temperature tuned force
Patterned surfaces
lundi 2 novembre 2015
Torque on
ellipsoidal
bead
Horizontal force
on a bead
Casimir force in action
Patterned surfaces
F. Soyka et al., PRL 101, 208301 (2008)
lundi 2 novembre 2015
Conclusions
•
We have discussed several experimental problems related to the measure of the
electromagnetic and critical Casimir
•
Concerning the critical Casimir. We have shown the importance that it has in films
and colloids close to the critical points.
•
The direct measure has been performed in a few experiment and always mediated
by the mesure of the potential.
•
Casimir forces is a temperature driven force. It can be useful to tune MEMS, to tune
interactions between colloids.
Future developments
•
•
•
•
What are the fluctuations of the Casimir force ?
What about the transient Casimir effect ?
The role of viscosity
The energetics
lundi 2 novembre 2015
Out of Equilibrium fluctuations in confined
phase transitions
Experiments:
Bellon Ludovic, Crauste Caroline, Anne Le Cunuder, Ignacio Martinez
Devailly Clémence, Laurent Justine, Petrosyan Artyom,
Theory:
Holdsworth Peter, Francesco Puosi
David Lopez
lundi 2 novembre 2015
Experimental set-up Optical trap
-
Camera rapide
AOD
75 MHz
lundi 2 novembre 2015
Experimental set-up Optical trap
silica bead
laser beam
-
Camera rapide
AOD
75 MHz
lundi 2 novembre 2015
k 2
U (x) = x
2
Examples of traps
lundi 2 novembre 2015
Two silica beads trapped
by two laser beams
in a critical mixture of
water/C12E5
ξo � 3nm
Distance
between
particles
∆x
Probability density
function of the particle
distance
60
lundi 2 novembre 2015
Two silica beads trapped by two laser beams
in a critical mixture of water/C12E5
Fit of the PDF with the Casimir Potential
∆X = 2R + ∆Xs and ∆Xo = 2R + ∆Xs
Fitting parameters
R=0.8mm
61
lundi 2 novembre 2015
Two silica beads trapped by two laser beams
in a critical mixture of water/C12E5 ξo � 3nm
Casimir induced synchronisation
Non synchronised T<Tc
62
lundi 2 novembre 2015
Two silica beads trapped by two laser beams
in a critical mixture of water/C12E5
ξo � 3nm
Temperature dependent
synchronisation
Non synchronised T<Tc
Synchronised T≅Tc
63
lundi 2 novembre 2015
Two silica beads trapped by two laser beams
in a critical mixture of water/C12E5
ξo � 3nm
T<Tc
Temperature dependent
synchronisation
Non synchronised T<Tc
Synchronised T≅Tc
T≅Tc
64
lundi 2 novembre 2015
Two silica beads trapped by two laser beams
in a critical mixture of water/C12E5
ξo � 3nm
T<Tc
Temperature dependent
synchronisation
Non synchronised T<Tc
Probability of not being
synchronized
Synchronised T≅Tc
T≅Tc
Probability of being
synchronisized
65
lundi 2 novembre 2015
Two silica beads trapped by two laser beams
in a critical mixture of water/C12E5
Measure of Casimir forces
and potentials
ξo � 3nm
Temperature dependent
synchronisation
Non synchronised T<Tc
Synchronised T≅Tc
66
lundi 2 novembre 2015
Two silica beads trapped by two laser beams
in a critical mixture of water/C12E5
The work performed by the trap
�τ
T
Wα = − 0 k(α − x2 (t)) ◦ dt
where α stands for either ϕ or r
and τ is the ramp duration
< Wϕ >
< Wr >
67
lundi 2 novembre 2015
Conclusions
•
We have discussed several experimental problems related to the measure of the
electromagnetic and critical Casimir
•
Concerning the critical Casimir. We have shown the importance that it has in films
and colloids close to the critical points.
•
The direct measure has been performed in a few experiment and always mediated
by the mesure of the potential.
•
Casimir forces is a temperature driven force. It can be useful to tune MEMS, to tune
interactions between colloids.
Future developments
•
•
•
What are the fluctuations of the Casimir force ?
What about the transient Casimir effect ?
The energetics
lundi 2 novembre 2015
69
lundi 2 novembre 2015