CHIM0698 Surface tension

2014-2015

Surface tension

On Youtube http://www.youtube.com/watch?v=E6_vXVd_0O4

The surface tension can be thought of as a force

http://www.funsci.com/fun3_en/exper2/exper2.htm

F A

The energy per unit area is γ It can often be thought of as a force

Wilhelmy’s ring (and plate)

http://www.funsci.com/fun3_en/exper2/exper2.htm

Values of γ for some usual liquids

Substance Surface tension (mN/m) Water (10°C) 74.2 Water (25°C) 72.0 Water (50°C) 67.9 Mercury (25°C) 485.5 Acetone (25°C) 23.5 Ethanol (25°C) 23.2 Formamide (25°C) 57.0 Nitrogen (77°K) 8.85

Values from Butt, Graf & Kappl, Physics and Chemistry of Interfaces, Wiley, 2006

There is an extra energy associated with a surface

Molecules on the surface are less bounded than molecules in the bulk.

There is therefore an energy associated with a free surface.

More rigorously: there is a free energy

associated with an interface. This energy is the surface tension γ

A rough estimation of γ from the energy of vaporization

Cyclohexane @ 25°C Uevap = 30.5 kJ/mol ρ=773 kg/m³ M=84.16 g/mol

Assuming a cubic structure (6-coordinated), Uevap converts to 5.08 kJ/mol for each bond. Each molecule on the surface has one missing bond. All is left to determine is the area of each molecule on the surface. This can be estimated as a² with NA a³ ρ = M, i.e. a = 0.565 nm The final estimate is about 26 mJ/m² (the experimental value is ~ 25 mJ/m²)

Stefan’s law

From K.S. Birdi, Surface and Colloid Chemistry, Principles and Applications

2010, CRC Press

Jozef Stefan 1835-1893

Effect of surfactants on surface tension

Critical micellar concentration

Surfactants

Surfactant classification according to the composition of their head: nonionic, anionic,

cationic, amphoteric.

Laplace

Nous devons donc envisager l’état présent de l’univers comme l’effet de son état antérieur et comme la cause de celui qui va suivre. Une intelligence qui, pour un instant donné, connaîtrait toutes les forces dont la nature est animée, et la situation respective des êtres qui la composent, si d’ailleurs elle était assez vaste pour soumettre ces données à l’Analyse, embrasserait dans la même formule les mouvements des plus grands corps de l’univers et ceux du plus léger atome : rien ne serait incertain pour elle et l’avenir, comme le passé serait présent à ses yeux. (Laplace, Essai philosophique sur les probabilités, 1795)

Géomètre de première catégorie, Laplace n’a pas tardé à se montrer un administrateur plus que médiocre ; de son premier travail nous avons immédiatement compris que nous nous étions trompés. Laplace ne traitait aucune question d’un bon point de vue : il cherchait des subtilités de partout, il avait seulement des idées problématiques et enfin il portait l’esprit de l’infiniment petit jusque dans l’administration. (Napoléon Bonaparte, à propos du passage de Laplace au ministère de l’intérieur)

Pierre-Simon de Laplace (1749-1827)

Thomas Young

Thomas Young 1773-1829

•  Optics: the double-slit interference experiments •  Mechanics: Young’s modulus •  Wetting phenomena: Young-Laplace & Young-Dupré relations •  Vision and color theory: Young-Helmholtz, 3-dimensional color space •  Physiology: pulse speed •  Linguistics: he introduced the idea of « Indo-European languages » •  Egyptology: he decyphered the hieroglyphs (before Champollion) •  Music: Young temperament

Young-Laplace equation

R

Pext

Pin

γ γ

The mechanical equilibrium of a half-droplet requires

For a more complex interface, the relation is

with R1 & R2 being the principal radii of curvature

What is the pressure in a soap bubble ?

« Amusons nous sur la terre comme sur l'onde, Malheureux celui qui se fait un nom

Richesses, Honneurs, Faux éclat de ce monde Tout n’est que boules de savon. »

Taken from the Nobel lecture of P.-G. de Gennes Rev. Modern Phys. 64 (1992) 645

And in an anti-bubble?

http://www.youtube.com/watch?v=6r_8Pp9WkF0

Laplace equation applies to solid particles as well

Lattice Contraction and Surface Stress of fcc Nanocrystals J. Phys. Chem. B, 2001, 105 (27), pp 6275–6277

What happens now?

A small and a large droplets lie on a fiber wetted by a thin liquid film.

How does the system evolve?

Some menisci configurations

Ostwald ripening

Wilhelm Ostwald 1853-1932

http://iopscience.iop.org/1367-2630/7/1/040/media/movie1_SD.mpg

New Journal of Physics Volume 7 2005 D G A L Aarts et al 2005 New J. Phys. 7 40 doi:10.1088/1367-2630/7/1/040

Interfacial dynamics in demixing systems with ultralow interfacial tension

Minimal surfaces

Costa’s minimal surface (1982)

Minimal surfaces in materials sciences

Micron, Volume 38, July 2007, Pages 478–485

Plateau-Rayleigh instability

1 2

Think about the pressure difference between 1 and 2

Plateau-Rayleigh instabilities in materials science

Appl. Phys. Lett. 85, 5337 (2004)

Nano Lett., 2007, 7 (1), pp 183–187

Cu nanowires PMMA in pores

Joseph Plateau

Joseph Plateau 1801-1883

Doctoral thesis at the University of Liège (1829) Professor of experimental physics in Ghent University (1835)

The phenakistiscope (“phenakizein” means “to deceive”)

Plateau’s laws

John Strutt (1842-1919) 3rd baron Rayleigh

Second Cavendish professor of physics at Cambridge (following Maxwell)

•  Dynamic soaring (flying of birds) •  Rayleigh scattering (why is the sky blue) •  Rayleigh waves (acoustics and mechanics) •  Rayleigh-Jeans law (blackbody radiation) •  Discovery of Argon with Ramsay (Nobel Prize for physics 1904) •  Etc.

What can you tell about the pressure in a liquid from the shape of a rising bubble?

http://people.rit.edu/andpph/exhibit-bubbles.html