Crystal and Liquid Crystal Phase Transitions in Colloidal Suspensions of Spheres, Rods, and Plates H.N.W.
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Crystal and Liquid Crystal Phase Transitions in Colloidal Suspensions of Spheres, Rods, and Plates H.N.W. Lekkerkerker Van ’t Hoff Laboratorium voor Fysische en Colloidchemie Debye Instituut Universiteit Utrecht Peter Debye 1884 - 1966 Punkt und Linie zu Fläche & Entropy Wassily Kandinsky (1866-1944) Bauhaus 1926 Photo Kandinsky examen Oskar Schlemmer Entropie und Wahrscheinlichkeit S = k ln W Ludwig Boltzmann, 1844 – 1906 Professor Theoretische Physik, München, 1889 - 1893 Entropy of mixing Outline A brief introduction to colloids Hard problems with hard spheres Shape matters Entropy engineering Concluding remarks Ein Kolloid: was ist das eigentlich? quarks protonen, neutronen 10-15 1fm atomen & moleculen 10-12 1pm 10-9 1nm COLLOIDS International Union of Pure and Applied Chemistry “The term colloidal refers to a state of subdivision, implying that the molecules or polymolecular particles dispersed in a medium have at least in one direction a dimension roughly between 1 nm and 1 mm.” 10-6 1mm 10-3 1mm 1 1m 103 1km 106 Wolfgang Ostwald 1883-1943 Die Welt der vernachlässigten Dimensionen Colloids in nature: milk Colloids in nature: blood 7 mm Rode bloedcellen in ‘gezond’ bloed Rode bloedcellen in ‘ziek’ bloed Colloids in nature: clay 1 mm Natural and synthetic colloids: Latex • Paint • Condom Synthetic magnetic colloids Magnetic colloids in magnetotactic bacteria A. Philipse, D. Maas, Langmuir 2002. Ann. d. Physik, 17, 549 (1905) Albert Einstein (1879-1955) Colloids as atoms Jean Perrin (1870-1942) Nobel prize Physics 1926 “For his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium.” 10 mm “The same equations have the same solutions.” Richard Feynman (1918-1988) …so what is new? • Colloìds: variable shape • Colloids: variable interactions energie W W repulsie W repulsie repulsie 0 0 attractie R afstand attractie R 0 R new and fascinating behaviour! Die Geschichte vom hässlichen Entlein Die Kolloidforschung ist aus dem vernachlässigsten Tummelplatz einiger Chemiker und Ingenieure ein blühendes und faszinierendes interdiszplinares Forschungsgebiet geworden Peter Schurtenberger Physik in unserer Zeit 34, 3 (2003) Outline A brief introduction to colloids Hard problems with hard spheres Shape matters Entropy engineering Concluding remarks Packing of spheres Grocers the world over know the most efficient way to pack spheres. Packing efficiency straal R roosterconstante a2 2 R 4 volumefractie 4 3 3 a R 3 3 2 0.74048... “Kepler’s conjecture” 1611 Johannes Kepler “De Nive sexangula” Geen stapeling kan dichter zijn dan een vlakgecentreerd kubisch rooster 1900 David Hilbert: 23 Mathematische Probleme. Vortrag gehalten auf dem internationalen Mathematiker-Kongress zu Paris Problem 18: Bolstapelingsprobleem 1997 Kepler’s conjecture finally confirmed!? Thomas Hales Johannes Kepler Hard spheres with thermal motion Computer simulations: Alder & Wainwright (1957) Wood & Jacobson (1957) F + K Fluïdum 0.494 Kristal 0.545 volumefractie 0.740 No attraction yet phase transition!? “...the transition goes a little bit against intuition; that is why so many people have difficulty with it, and surely, I am one of those.” George E. Uhlenbeck (1900-1988) January 1957 “I think it is quite unnecessary to have an attractive force to achieve a crystalline phase and one can produce simple intuitive arguments for that.” (1907-1959) Over de continuiteit van den gas – en vloeistoftoestand. Proefschrift Leiden, 1873. Condensatie vereist attractie en repulsie (1837-1923) maar kristallisatie… Ordering by entropy Crystal: Ordered positions Fluid: Disordered positions Sconfigurations Fluid high Crystal low Sfree volume low high Opal: ordered silica spheres Bragg’s law (1912): 2 d cos Sanders (1968) Geochemical formation of opal O Si Al Fe Ca Na K 46.5 28.0 8.1 5.1 3.5 2.8 2.5 Mg Ti H C Cl P S 2.0 0.58 0.20 0.20 0.19 0.11 0.10 n Si(OH)4 (SiO2)n + 2n H2O Stöber synthesis R R ethanol + ammonia R R OH OH tetraethoxysilane HO Si HO OH Si OH + C18H37OH O O Si Si N: C ount 15 95 M ean: 246.0nm S t. dev.: 7.3nm P olydisp.: 2.9% 10 5 210 nm 0 220 230 240 250 260 R adius (nm ) 270 280 Si OH HO Si very monodisperse! C18H37 Si T Si C18H37 Crystals of colloidal spheres Microscopy forever! 1905 2005 Confocal fluorescence microscopy kristal fluïdum 5 mm kristal Verhaegh en Van Blaaderen (1994). fluïdum 5 mm Abb. 4. Versuchsanordnung, mit der Max Max von Laue 1879-1960 Privatdozent München 1909-1912 Nobel prize Physics 1914 von Laue, Walter Friedrich und Paul Knipping 1912 die Interferenz von Röntgenstrahlen bei der Beugung in Kristallen entdeckten. Synchrotron Röntgenverstrooiing European Synchrotron Radiation Facility, Grenoble (030) (220) (120) (210) (020) (110) (300) (010) (200) (100) X-ray beam Close-packed crystals: FCC: HCP: RHCP: …ABCABC… …ABABAB… …ABACBC… h k 3n h k 3n 1 1 1 0 0.25 00.25 • Petukhov, Aarts, Dolbnya, de Hoog, Kasapidou, Vroege, Bras, HNWL, Phys.Rev.Let., 88, 208301 (2002); • Petukhov, Dolbnya, Aarts, Vroege, HNWL, Phys.Rev.Let., 90, 028304 (2003). Outline A brief introduction to colloids Hard problems with hard spheres Shape matters Entropy engineering Concluding remarks Lars Onsager (1903-1976) Nobel prize Chemistry 1968 Physical Review (1942) Isotroop-Nematische fase-overgang Onsager (1942,1949): de Isotroop-Nematische fase-overgang in een suspensie van staven komt door verlies van oriëntatieentropie en winst van vrij volumeentropie Rods at the van ‘t Hoff laboratory Al-(OR)3 in acidic aqueous solution 150 0C, 1 day boehmite AlOOH Al Fe Ca Na K 46.5 28.0 8.1 5.1 3.5 2.8 2.5 Mg H C Cl P S 2.0 Coating PIB 150-300 nm P.A.Buining et al., 1992 O Si Ti 0.58 0.20 0.20 0.19 0.11 0.10 Isotropic-nematic phase equilibrium I N boehmiet (AlOOH) dikte = 9 nm lengte = 160 nm volumefractie = 10% Thermodynamic stability of a smectic phase in a system of hard rods D. Frenkel, HNWL, A. Stroobants, Nature, 1988 New rods at the van ‘t Hoff laboratory: FeOOH O Si Al Fe Ca Na K 46.5 28.0 8.1 5.1 3.5 2.8 2.5 Mg Ti H C Cl P S 2.0 0.58 0.20 0.20 0.19 0.11 0.10 D. Thies A. Petukhov G.J. Vroege Smectic A reflected light crossed polarizers Lars Onsager (1903-1976) Nobel prize Chemistry 1968 Physical Review (1942) Isotropic-Nematic Phase Transition of Colloidal Platelets Orientational entropy decreases Free volume entropy increases Al-(OR)3 in acidic aqueous solution 85 0C, 3 days A.M. Wierenga, T.A.J. Lenstra, A.P. Philipse, 1998 gibbsite, Al(OH)3 Coating PIB F.M vd Kooij, HNWL, 1998 200 nm Isotropic-Nematic Phase Transition I N gibbsiet (Al(OH)3) diameter = 200 nm dikte = 6 nm volumefractie = 20% Isotroop Nemaat Columnair Kristal J.A.C. Veerman, D. Frenkel, Phys. Rev. A (1992) I N 19% N 28% N C 41% C 47% volumefractie F.M. van der Kooij, K. Kassapidou, HNWL, Nature (2000) Columnar phase of colloidal gibbsite plates with <D>=200 nm GREEN ~ 530 nm hexagonal lattice with spacing d white light RED ~ 650 nm Bragg condition: 2 n d sin = measure index of refraction = 1.5 2GREEN = 107° 2RED = 160° d = 220 nm Distance between the columns: a = 2d/3 = 254 nm D. van der Beek & HNWL, Langmuir (2004) SEM of dried columnar phase D. van der Beek, S. Sacanna (2004) Columnar crystal: Hexagonal arrangement of columns DUBBLE @ ESRF A.V. Petukhov, D. van der Beek, S.M. Oversteegen, G.J. Vroege, HNWL (030) (120) (020) (010) (110) (100) (210) (200) Outline A brief introduction to colloids Hard problems with hard spheres Shape matters Entropy engineering Concluding remarks Scientific American, 2001 latexbollen in lucht luchtbollen in titaandioxyde Imhof & Pine (1997) Wijnhoven & Vos (1998) “From Do-it-yourself organization to self organization” (A. van Blaaderen) Sea Mouse Aphrodita Natur wird zunehmend zum Vorbild für wissenschaftliche und technische Entwicklungen. Outline A brief introduction to colloids Hard problems with hard spheres Shape matters Entropy engineering Concluding remarks Ordering in colloidal suspensions Kristal Fluïdum Isotroop Isotroop Nemaat Nemaat Columnair Smectisch concentration Kristal Kristal Alder en Wainwright (1957) Veerman en Frenkel (1992) Frenkel, HNWL en Stroobants (1988) Fundamental Research Chemistry Colloids Geology Physics Biology Industrial Applications In onderzoek gaat het om vier G’s: Paul Ehrlich (1854-1915) Geduld, Geschick, Geld... und Glück! Robert Finsy, Philipe Coulon, René Luyckx, Rudy van der Haegen, Erik Moreels Theo Overbeek, Phil de Bruyn, Agienus Vrij, Kees de Kruif, Jan Dhont, Daan Frenkel, Albert Philipse, Gert Jan Vroege, Willem Kegel, Alfons van Blaaderen, Ben Erné Alain Stroobants, Stephen Picken, George van Aken, Carla Smits, Paul Buining, Johan Buitenhuis, Jeroen van Duijneveldt, Dominique Thies-Weesie, Arnout Imhof, Henk Verduin, Nynke Verhaegh, Anieke Wierenga, Igor Bodnar, Haran Pathmamanoharan, Michel van Bruggen, Bianca van der Zande, Gerrit Vliegenthart, Felix van der Kooij, Els de Hoog, Tjerk Lenstra, Rik Wensink, David van der Beek, Dirk Aarts, Nikoleta Simeonova, Roel Dullens Wim Briels, Bela Mulder, Hong Xu, Yaode Yan, Felicity Lodge, Daniela Asnaghi, Hans Tromp, Paul van der Schoot, Jan Groenewold, Mohamed Ramzi, Katarina Kassapidou, Remco Tuinier, Valerie Anderson, Andrei Petukhov, Martijn Oversteegen, Judith Wijnhoven, Marcel Vogel, Annemieke ten Brinke Marina Uit de Bulten, Mieke Lanen, Kees Rietveld, Chantal Vonk, Bonny Kuipers, Emile Bakelaar Marjolein Dijkstra, René van Roij Theo Odijk ...en vele anderen, waar ook ter wereld! 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