ADHESIVE FORCES ON HELIUM INNONTRIVIAL GEOMETRIES
E. S. H.
, A. Hernando
, R. Mayol
and M. Pi
University of Buenos Aires, Argentina
University of Barcelona, Spain
RPMBT14, July 2007 – p.1
Vapor particle + matter
RPMBT14, July 2007 – p.2
Vapor particle + matter
RPMBT14, July 2007 – p.2
Vapor particle + matter
RPMBT14, July 2007 – p.2
A popular choice
! "
RPMBT14, July 2007 – p.3
A popular choice
! "
$# %'& & ( # *) *+ ,
RPMBT14, July 2007 – p.3
A popular choice
! "
$# %'& & ( # *) *+ ,
# .- / # 01 2 2 / 3 2 2 - "
RPMBT14, July 2007 – p.3
Geometries with high symmetry
The LJ potential is analytically integrable (or quasiintegrable)
RPMBT14, July 2007 – p.4
FSM-16 hexagonal pores with six 3-9’s
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14d (Å)
-280-260-240-220-200-180-160-140-120-100
-80-60-40-20
02040
A, D
A, M
B, M
B, DA, D
B, M
B, D
Summation of six 3-9 potentials
(from M. Rossi, D. E. Galli and L. Reatto, JLTP 146, 98 (2006))
RPMBT14, July 2007 – p.5
Open questions
4
How legitimate is the continuum hypothesis?
How accurate is a LJ potential?
For metallic planar half-solids, an ab-initio is
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
Open questions
4
4 How legitimate is the continuum hypothesis?
How accurate is a LJ potential?
For metallic planar half-solids, an ab-initio is
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
Open questions
4
4 How legitimate is the continuum hypothesis?
4 How accurate is a LJ potential?
For metallic planar half-solids, an ab-initio is
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
Open questions
4
4 How legitimate is the continuum hypothesis?
4 How accurate is a LJ potential?
4 For metallic planar half-solids, an ab-initio
#
is
65 5 7 $# 8 :9;
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
New question
Is the inverse problem solvable?, i.e., given < = $#
, can wefind sources
?
< = # & ( # *) *+
If so, then for almost any geometry,
RPMBT14, July 2007 – p.7
New question
Is the inverse problem solvable?, i.e., given < = $#
, can wefind sources
?
< = # & ( # *) *+
If so, then for almost any geometry,
RPMBT14, July 2007 – p.7
It is solvable!
For a half-solid with bulk density % & ,
# > ? ?@A B C 2 DFE GH 2
true for the LJ family
so that for other matter distributions
RPMBT14, July 2007 – p.8
It is solvable!
For a half-solid with bulk density % & ,
# > ? ?@A B C 2 DFE GH 2 true for the LJ family
. $I J ? ?LKNM O C D E GH
so that for other matter distributions
RPMBT14, July 2007 – p.8
It is solvable!
For a half-solid with bulk density % & ,
# > ? ?@A B C 2 DFE GH 2 true for the LJ family
. $I J ? ?LKNM O C D E GH
so that for other matter distributions
> ? ?@ A B CPRQ Q ? P D
E GH PRQ Q ? P
RPMBT14, July 2007 – p.8
A friendly unit cell
RPMBT14, July 2007 – p.9
Six half-solids make an hexagonal pore
RPMBT14, July 2007 – p.10
with strong overlap at the vertices
RPMBT14, July 2007 – p.11
so, we recommend SIX CUSPS INSTEAD
RPMBT14, July 2007 – p.12
with potential landscape
RPMBT14, July 2007 – p.13
The wedge
RPMBT14, July 2007 – p.14
The wedge was (ESH et al in PRB 73, 245406 (2006))
RPMBT14, July 2007 – p.15
while it may be
RPMBT14, July 2007 – p.16
with potential
RPMBT14, July 2007 – p.17
A striped substrate
RPMBT14, July 2007 – p.18
A sawtooth substrate
RPMBT14, July 2007 – p.19
FSM-16 hexagonal pores
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14d (Å)
-280-260-240-220-200-180-160-140-120-100
-80-60-40-20
02040
A, D
A, M
B, M
B, DA, D
B, M
B, D
Summation of six 3-9 potentials
RPMBT14, July 2007 – p.20
FSM-16 hexagonal pores
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14d (Å)
-280-260-240-220-200-180-160-140-120-100
-80-60-40-20
02040
A, D
A, M
B, M
B, DA, D
B, M
B, D
Summation of 3-9 potentialsvs. integration of the LJ field
RPMBT14, July 2007 – p.20
Metallic hexagonal pores
0 5 10d (Å)
-40
-20
0
20
40
Cs
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Metallic hexagonal pores
0 5 10d (Å)
-40
-20
0
20
40
CsK
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Metallic hexagonal pores
0 5 10d (Å)
-80
-60
-40
-20
0
20
40
CsKCs
Mg
Cs
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Metallic hexagonal pores
0 5 10d (Å)
-280
-240
-200
-160
-120
-80
-40
0
40
CsKMgFSM-16 Potential B
CsKMgFSM-16 Potential BFSM-16 Potential A
CsKMg
CsKMg
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Standard DF theory at zero temperature
S T U V
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [ V W *) # % )ZY #
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [ V W *) # % )ZY #
\ S\ % ]
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [ V W *) # % )ZY #
\ S\ % ]
gives
^ !`_ a cb % b ed )ZY # " % )ZY # U % )ZY #
RPMBT14, July 2007 – p.22
Some density profiles obtained with DFT
-10 -5 0 5 10x (Å)
-10
-5
0
5
10
z (Å
)
4He in FSM-16 poreN/L = 0.8 Å-1
-10 -5 0 5 10x (Å)
-10
-5
0
5
10
z (Å
)
4He in Cs poreN/L = 2 Å-1
RPMBT14, July 2007 – p.23
Some EOS computed with DFT
-6
-4
-2
0
2
Ω /
N (
K)
Six planar V3-9 potentialsIntegrated VLJ
EOS for 4He in FSM-16 hexagonal porePotential B
0 0.2 0.4 0.6 0.8 1N / L (Å-1)
-150
-140
-130
-120
-110
E / N (K)µ (K)
RPMBT14, July 2007 – p.24
Some EOS computed with DFT
-4
-3
-2
-1
0Ω
/ N
(K
)Six VCCZ potentialsIntegrated vCCZ
EOS for 4He in Mg hexagonal poreCCZ potential
0 0.2 0.4 0.6 0.8 1N / L (Å-1)
-60-55-50-45-40-35
E / N (K)µ (K)
RPMBT14, July 2007 – p.24
Some energetics
f g fh i jh T lk m ln m opoLo qr qsq sopoLo
t f uv Y j
-178.36 -135.98 0.31t f u v Y g
-140.77 -105.36 0.34
w -51.04 -37.62 0.36Wx
-23.98 -17.22 0.39Vzy -16.35 -11.58 0.41m
-10.41 -7.24 0.44i
-9.45 -6.54 0.44|~ -9.01 -6.22 0.45RPMBT14, July 2007 – p.25
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
4
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
4
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
4 Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
4
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
4 Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
4 the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Some comparison among methods
-10 -5 0 5 10x (Å)
-10
-5
0
5
10
z (Å
)
He on Cs Hexagonal pore
0 5 10d (Å)
0
0.01
0.02
0.03
0.04
0.05
x-axis
integrationsummation
at N / L = 7 Å-1
z-axis
RPMBT14, July 2007 – p.27
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
if one knows the planar field .
The numerical algorithm is fast and precise.
No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
The numerical algorithm is fast and precise.
No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
4 No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
4 No sound qualitative differences are to be found ineither calculation,
4 but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
4 No sound qualitative differences are to be found ineither calculation,
4 but substantial quantitative ones may show up.
4 Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of
He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28