Regarding the Young equation

Regarding the Young equationMiguel A. Rodrguez Valverde

Aula C11, Aulario Mecenas

Lunes 19 Noviembre, 12:30 p.m.

2In memory to Pierre Gilles De Gennesprix Nobel de physique en 1991

3Motivation

to avoid misdleading interpretations of the Young equation

StarovPlatikanovRusanov

4The Solid Surfaces evilInterfacial tension or interfacial energy?

5Outline

Historical overview

Revised Surface Thermodynamics

The Solid Surfaces evil

Other controversial issues

References

6Outline

Historical overview




References

7E. A. Vogler, On the Origins of Water Wetting Terminology, in Water in Biomaterials Science, M. Morra (ed.), John Wiley, pp. 149-182 (2001).

TimelineHistorical overview

8Thomas Young (1773-1829) "An Essay on the Cohesion of Fluids",

Philosophical Transactions of the Royal Society of London, 95, 65-87, (1805).

Historical overview

http://gallica.bnf.fr/ark:/12148/bpt6k55900p

9 "Principia Generalia Theoriae Figurae Fluidorum"Comment. Soc. Regiae Scient. Gottingensis Rec. 7 (1830).

Johann Carl Friedrich Gauss (1777-1855)

Gauss used the Principle of Virtual Work to unify the achievements of Young and Laplace

"Thorie mcanique de la chaleur. Paris, Gauthier-Villars, 1869

( )1 cosadh LVw = +L'angle de raccordement

Athanase Dupr (1808-1869)

Historical overview

http://gallica.bnf.fr/ark:/12148/bpt6k99405t

10

Controversy about the Young equation

1. Experimental verification

2. Mechanistic derivation/interpretation

3. Restrictive concept of ideal solid surface

4. Influence of external field, contact angle hysteresis, effect of drop size

Historical overview

11

As resultthe delirious renaming of the Young equation

VOLPE C D SIBONI S MANIGLIA D, About the Validity of the So-calledDupre-Gamo Equation, Journal of the Adhesion Society of Japan (2003), 39(2) 64-66

TOMINAGA HIROSHI, SAKATA GORO, ISHIBUCHI TOMOMI, OUMIMASAHARU, "Gamo Triangles of Wetting" (Provisional Name) and Re-verification of Dupre-Gamo Equation, Journal of the Adhesion Society of Japan (2000), 36(5) 176-178

Historical overview

Reply:

12

cosSV SL LV Y =Experimental verification of the Young equation

cosSV SL LV Y =Experimentally accessible quantitiesNo readily measurable quantities

Erik Johnson, The Elusive Liquid-solid Interface, Science 19 April 2002: Vol. 296. no. 5567, pp. 477 - 478

212Ad

=d A typical Zisman plot:n- alkanes on teflon

extrapolation to cos Y= 1=> C = 18 ergs/cm2

cos Y1

0.9

0.8

20 30 LVc SV SL =

-Hertz and JKR theories (Contact Mechanics: adhesion, friction, and fracture)-Adhesion (pull-off) forces by SFA-Elastomeric solids

Pull-offEquilibrium

1

2

Historical overview

13

A.I. Bailey, S.M. Kay, A Direct Measurement of the Influence of Vapour, of Liquid and of Oriented Monolayers on the Interfacial Energy of Mica Proc. Roy. Soc. A301 (1967), p. 47

Johnson, K. L.; Kendall, K.; Roberts, A. D. Surface Energy and the Contact of Elastic Solid Proc. R. Soc. London, A 1971, A324, 301.

R. M. Pashley, J. N. Israelachvili, "A Comparison of Surface Forces andInterfacial Properties of Mica in Purified Surfactant Solutions" Colloids& Surfaces 2 (1981) 169-187

Manoj K. Chaudhury, George M. Whitesides, "Direct Measurement of Interfacial Interactions between Semispherical Lenses and Flat Sheets of Poly(dimethyl siloxane) and Their Chemical Derivatives," Langmuir 7 (1991):1013-1025

After ~ 200 years

Historical overview

14

Outline

Historical overview




References

15

Concept of interface

-phase-phase

One-component system(substance j)

-phase

InterfaceInterphase

-phase

-phase -phase

0r

Josiah Willard Gibbs, On the Equilibrium of Heterogeneous Substances, The American Journal of Science and Arts Third Series, Vol. XVI, No. 96, December 1878, pp. 441-58


Stretching: work against the forces of surface tension

Cutting-off:work against the cohesional forces

dA dA

How can we form a new interface ?1 2

dW dA = dW dA =Intensive scalar quantity

(=surface grand thermodynamic potential)Intensive tensorial quantity

( ), 0jT >http://www.iupac.org/reports/2001/colloid_2001/manual_of_s_and_t/node23.html

Specific excess interfacial free energyInterfacial tension


17

11

22

0 1 0 1 00 0 1 0 1

sh

= = +

t

Interfacial stress tensor (principal directions)

( )1 :12 = tt

+11

22

sh

sh=

Anisotropic interfaces

( ):dW de A = t t

Isotropic stress Shear stress

Surface strain tensor


18

-In crystalline solids, the surface tension depends on the crystal plane and its direction

http://www.virginia.edu/ep/SurfaceScience/Thermodynamics.html

Wulff construction: the shape of things

-The equilibrium shape of a crystal is obtained by minimizing the integral :

S

W A de = t t


19

:C S

W F dr A de = = r tr t

[ ]0ij

= rr

mdFdl

=r

r t

Nm t = Mechanical equilibrium condition (fluid interfaces)

t

Nm-phase

-phase

-phase

m m =t

EigenvectormEigenvalue


conormal unit vector

20

Franz Ernst Neumann (1798 -1895)

1-phase

2-phase

3-phase

12 12m

32 32m 31 31m1

2

3

Neumanns Triangle equation (no generalized Young equation!)

Neumann, F. ,Vorlesungen ber die Theorie der Capillaritt, 152 (Teubner, Leipzig, 1894).

12 12 31 31 32 32 0m m m + + =r

3 2 1

12 31 32

sin sin sin = =

3 1 0 !!!or = =


21

Relation between ty

( )( ) ( ) ( )( ) ( )00

1z

j j j j j jz

z c z dz z c z dz

= + + t t t t t t

( )j j = t t( )j j = t tLocal concentration of the substance j( )jc z

Chemical potential tensor of the substance j( )j zt in the bulk of -phase in the bulk of -phase

( )( ) ( )( )00

1 1z

z

P P z dz P P z dz

= + t tt tt

Local stress tensor

Normal coordinate to the interface

-phase

-phase

z

0z Dividing plane


22

( ) ( )1 11 1V V

P P dV P P dVA A

= + t tt tt

( ) ( )1 11 j j j j j jV V

c dV c dVA A

= + + t t t t t t

3D tensors

=j j j

= =t t tChemical equilibrium

( )1 :13 = ttRevised Surface Thermodynamics

23

( ) ( ),sll lv

SL SVALVA VdE g dx y A Af dVf = +

.; .l v sl svV V A A

dV const dA const = = Closure conds.

Thermodynamic equilibrium condition (solid-liquid-fluid interfaces)

Energy functional of a solid-liquid-vapor (SLV) system (ideal solid surface)

( ),f x y

Energy functional minimization

( )( )2, 0

, 0

E f x y

E f x y

= > local minimum condition:

z


24

1. The Young equation is necessary condition for the global equilibrium, but it is not sufficient condition. The Young equation is associated to whatever metastate of a real SLV system (local minima), instead of to the global equilibrium state (global minimum)

2. The Young equation is independent of the interfacial geometry and the gravitational field

Young Eq.Young-Laplace Eq.

( ) ( ) ( ) ( ), , , ,ext ext ext extlSL SV

f x y f x y f x y f x yLV LV LV

lLV

l lv V sf AVA dg V

= +

( ) ( ), , lf x y E f x Vy Grand canonical potential ( ), ,lT V

http://www.iupac.org/publications/pac/2001/pdf/7308x1349.pdf0P = Pressure difference at

lV const=Conditioned minimization

0f =


25

cosSV SL LV Y =Young equation: (local) thermodynamic equilibrium condition(NOT force balance!)

3. Boundary condition of the Young-Laplace equation, derived by thermodynamic arguments

4. Young contact angle is a thermodynamic quantity, a conceptual, unlocated angle


26

Outline

Historical overview




References

27

Air Liquid vapour(unsaturated atmosphere)

Liquid vapour(saturated atmosphere)

L Vj j

reservoirsIn practice

although

=j j j

= =t t tChemical equilibrium


Liquid vapour(oversaturated atmosphere)

L Vj j =2ln LV LV plane

VH

RTvP

P

J. Phys. Chem. B, Vol. 111, No. 19, 2007

28

Non-uniformity of chemical potentials near the solid surface:

Absence of diffusion equilibrium

-Diffusion in real solids proceeds slowly(diffusion time >> experiment time)

SF SF The Solid Surfaces evil

God made solids, but surfaces were the work of the devil------Wolfgang Pauli

-Ill-defined thermodynamic states


29

Liquid-Fluid interface: Variable number of interfacial molecules

Solid-Fluid interface:Constant number of interfacial molecules

Plastic deformation

hole

Elastic deformation

Stretching of interfaces

LF LF = SF SF


30

( ) ( ) ( )1 11F L

F LSF SL j j j j j jSF L

VS

V

c dV c dVA A

= + t t t t t t t

L Fj j j t t t

( )1 SF SLSF SL t t t


But if

SF SL SF SL Equal principal directions

31

Young modulus

Ridge height


L-phase

V-phase

S-phase

32 31 m m= LV

SVSL

cosSV SL LV =

Mechanical equilibrium condition (solid-liquid-fluid interfaces)

Reaction force (passive)

Gravity force (active)

sin 0LV w r + =

R rw E= Elastic restoring force (passive)

32

How minimize the solid stresses along the contact line?

The false equilibrium of a sessile drop(the Solid Surfaces evil contd)


33

Deformation of the solid surface: Everything flows, nothing stands still

Hard matter versus Soft matter: timescales

after millions of years or minutes

Non-equilibrium (but stable) configurationInitial configuration

Local equilibriumconfiguration

Both local and total equilibrium configuration


34http://www.sg.geophys.ethz.ch/geodynamics/klaus/hands-on/deborah.pdf

Deborah Number ~ 1: viscoelastic

Silly putty

Bitumen film

rel

obs

tDht


35

Pitch drop experiment

http://www.physics.uq.edu.au/pitchdrop/pitchdrop.shtml

Date Event

1927 Experiment set up

1930 The stem was cut

December 1938 1st drop fell

February 1947 2nd drop fell

April 1954 3rd drop fell

May 1962 4th drop fell

August 1970 5th drop fell

April 1979 6th drop fell

July 1988 7th drop fell

November 28, 2000 8th drop fell

Deborah Number >> 1: solid-like


36

October 12, 2007

This morning an overshadowing landslide collapsed from the Cima Una peak (2.598 meters) of the Dolomites in Southern Tyrol, which is situated in Northern Italy.

Teams of the Italian Civil Defense, of the Fire Department and of the Police Department are already working since a few moments after the fact, they affirmed that 60.000 cubic meters fell, obscurating the sky and complicating their work, but fortunately nothing makes think that there are injured people or victims.

Huge landslide at the Dolomites in Italy

Deborah Number >>> 1: solid-like


37

History of solid surfaces (the Solid Surfaces evil contd)

Formative and environmental history of the sample

Cleaving, Grinding, Polishing, Etching, Sandblasting

Presence (or absence) of adsorbed species and surface contamination


38

Kinetic hysteresis (swelling)


39

Outline

Historical overview




References

40

Contact angle hysteresis(history of the system)


41

Scales of contact angle

extrap

Optically or atomically ideal surface?


42

Drop Size on contact angle: line tension, long-range forces


43

sl

lvredistribution of liquidRinteraction

xd x

l(x)

sv

Schematic drop profile. In the vicinity of the three-phase contact line there is a redistribution of liquid from the spherical cap profile observable, which is caused by the effective interface potential.

cos cosint Yl

v

c

l

v

s

r

= Line TensionOther controversial issues

44

Precursor film: surface pressure

Formation of a precursor film with an apparent contact angle app

app

cosSV SL LV Y = cosS SL LV Y =Young-Bangham equation


45

Drying, Soldering, Polymerization

Surface oxidation

Polymerization shrinkage

Dental resinOxidized solder

Unoxidized solder

Shape of desiccated, solder, polymerized drops may not represent neither their surface tension nor their contact angle

0 s 19 min 1 s

3 h 49 min 28 s 6 h 42 min 40 s

Bitumen emulsion

Desiccation


46

Outline

Historical overview




References

47

Robert Finn, The contact angle in capillarity, Physics of fluids 18, 047102, 2006

P.-G. de Gennes, F. Brochard-Wyart, and D. Qur, Capillarity and WettingPhenomena Springer, Berlin, 2004, p. 18

P. Roura and Joaquim Fort, Local thermodynamic derivation of Young'sequation, Journal of Colloid and Interface Science Volume 272, Issue 2, 15 April 2004, Pages 420-429

Borislav V. Toshev and Dimo Platikanov, Wetting: Gibbs superficial tensionrevisited, Colloids and Surfaces A: Physicochemical and Engineering AspectsVolume 291, Issues 1-3, 15 December 2006, Pages 177-180

A.I. Rusanov Problems of surface thermodynamics, Pure &App. Chem., Vol. 64, No. 1, pp. 111-124, 1992

C. Della Volpe, S. Siboni, and M. Morra, Comments on Some Recent Papers on Interfacial Tension and Contact Angles, Langmuir, 18 (4), 1441 -1444, 2002

References

48

Coming Soon Forever Young

?Result MeasureQuantity

?

Regarding the Young equation

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Regarding the Young equation