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
F A
The energy per unit area is γ It can often be thought of as a force
http://www.funsci.com/fun3_en/exper2/exper2.htm 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
Jozef Stefan 1835-1893
From K.S. Birdi, Surface and Colloid Chemistry, Principles and Applications 2010, CRC Press Effect of surfactants on surface tension
Critical micellar concentration Surfactants
Surfactant classification according to the composition of their head: nonionic, anionic, cationic, amphoteric. Pierre-Simon de Laplace Laplace (1749-1827)
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) 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
Pext
Pin R The mechanical equilibrium of a half-droplet requires
γ γ
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
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
http://iopscience.iop.org/1367-2630/7/1/040/media/movie1_SD.mpg 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
PMMA in pores Cu nanowires
Nano Lett., 2007, 7 (1), pp 183–187
Appl. Phys. Lett. 85, 5337 (2004) Joseph Plateau
Doctoral thesis at the University of Liège (1829) Professor of experimental physics in Ghent Joseph Plateau University (1835) 1801-1883
Plateau’s laws The phenakistiscope (“phenakizein” means “to deceive”) 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. http://people.rit.edu/andpph/exhibit-bubbles.html
What can you tell about the pressure in a liquid from the shape of a rising bubble?