ADHESIVE FORCES ON HELIUM IN NONTRIVIAL ...congress.cimne.upc.es/rpmbt14/frontal/talks/L5_3...ADHESIVE FORCES ON HELIUM IN NONTRIVIAL GEOMETRIES E. S. H. , A. Hernando , R. Mayol and

ADHESIVE FORCES ON HELIUM INNONTRIVIAL GEOMETRIES

E. S. H.

, A. Hernando

, R. Mayol

and M. Pi

[email protected]

University of Buenos Aires, Argentina

University of Barcelona, Spain

RPMBT14, July 2007 – p.1

Vapor particle + matter






A popular choice

! "


A popular choice

! "

$# %'& & ( # *) *+ ,


A popular choice

! "

$# %'& & ( # *) *+ ,

# .- / # 01 2 2 / 3 2 2 - "


Geometries with high symmetry

The LJ potential is analytically integrable (or quasiintegrable)


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))


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).)


Open questions

4

4 How legitimate is the continuum hypothesis?

How accurate is a LJ potential?



(1998).)


Open questions

4


4 How accurate is a LJ potential?



(1998).)


Open questions

4


4 How accurate is a LJ potential?

4 For metallic planar half-solids, an ab-initio

#

is

65 5 7 $# 8 :9;


(1998).)


New question

Is the inverse problem solvable?, i.e., given < = $#

, can wefind sources

?

< = # & ( # *) *+

If so, then for almost any geometry,


New question

Is the inverse problem solvable?, i.e., given < = $#

, can wefind sources

?

< = # & ( # *) *+

If so, then for almost any geometry,


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


It is solvable!


# > ? ?@A B C 2 DFE GH 2 true for the LJ family

. $I J ? ?LKNM O C D E GH



It is solvable!


# > ? ?@A B C 2 DFE GH 2 true for the LJ family

. $I J ? ?LKNM O C D E GH


> ? ?@ A B CPRQ Q ? P D

E GH PRQ Q ? P


A friendly unit cell


Six half-solids make an hexagonal pore


with strong overlap at the vertices


so, we recommend SIX CUSPS INSTEAD


with potential landscape


The wedge


The wedge was (ESH et al in PRB 73, 245406 (2006))


while it may be


with potential


A striped substrate


A sawtooth substrate


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


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


Metallic hexagonal pores

0 5 10d (Å)

-40

-20

0

20

40

Cs

Integrated elementary vCCZ six planes with VCCZ

Potential along diagonal



0 5 10d (Å)

-40

-20

0

20

40

CsK





0 5 10d (Å)

-80

-60

-40

-20

0

20

40

CsKCs

Mg

Cs





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




Standard DF theory at zero temperature

S T U V

gives



S T U V

T W *) # X % )ZY # [

gives



S T U V

T W *) # X % )ZY # [ V W *) # % )ZY #

gives



S T U V

T W *) # X % )ZY # [ V W *) # % )ZY #

\ S\ % ]

gives



S T U V

T W *) # X % )ZY # [ V W *) # % )ZY #

\ S\ % ]

gives

^ !`_ a cb % b ed )ZY # " % )ZY # U % )ZY #


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


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)


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)


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.


Why Cesium?


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))



Why Cesium?


4


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))



Why Cesium?


4


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.


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


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.


Some summary



4 if one knows the planar field #

.

The numerical algorithm is fast and precise.





Some summary




.

4 The numerical algorithm is fast and precise.





Some summary




.


4 No sound qualitative differences are to be found ineither calculation,




Some summary




.



4 but substantial quantitative ones may show up.



Some summary




.



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.


Documents

ADHESIVE FORCES ON HELIUM IN NONTRIVIAL ...congress.cimne.upc.es/rpmbt14/frontal/talks/L5_3...ADHESIVE FORCES ON HELIUM IN NONTRIVIAL GEOMETRIES E. S. H. , A. Hernando , R. Mayol and