Mean-field Description of the Structure and Tension of Curved Fluid Interfaces. Joris Kuipers

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1 Mean-field Description of the Structure and Tension of Curved Fluid Interfaces Joris Kuipers

2 Mean-field description of the structure and tension of curved fluid interfaces / J. Kuipers Copyright c 2009, by J. Kuipers. All rights reserved. ISBN Typeset in L A TEX Coverdesign by C. van der Kamp Printed by Ipskamp Drukkers, Enschede, The Netherlands

3 Mean-field Description of the Structure and Tension of Curved Fluid Interfaces Proefschrift ter verkrijging van de graad van Doctor aan de Universiteit Leiden, op gezag van Rector Magnificus prof.mr. P.F. van der Heijden, volgens besluit van het College voor Promoties te verdedigen op woensdag 16 december 2009 klokke uur door Joris Kuipers geboren te Roosendaal en Nispen in 1982

4 iv Promotiecommissie promotor co-promotor : Prof.dr. D. Bedeaux : Dr. E.M. Blokhuis Overige Leden : Prof.dr.ir. J.G.E.M. Fraaije Universiteit Leiden Prof.dr. W.K. Kegel Universiteit Utrecht Prof.dr.ir. F.A.M. Leermakers Universiteit Wageningen Dr. D.G.A.L. Aarts Oxford University, UK

5 v Science is what we have learned about how not to fool ourselves about the way the world is. - R.P. Feynman Even a stopped clock gives the right time twice a day

6 List of Publications E. M. Blokhuis and J. Kuipers, Thermodynamic expressions for the Tolman length J. Chem. Phys. 124, (2006) (Chapter 2) E. M. Blokhuis and J. Kuipers, On the determination of the structure and tension of the interface between a fluid and curved hard wall J. Chem. Phys. 126, (2007) (Chapter 3) J. Kuipers and E. M. Blokhuis, Interfacial properties of colloid-polymer mixtures J. Coll. Interface Sci. 315, 270 (2007) (chapter 5) E. M. Blokhuis, J. Kuipers and R. L. C. Vink, Description of the fluctuating colloid-polymer interface Phys. Rev. Lett. 101, (2008) J. Kuipers and E. M. Blokhuis, Wetting and drying transitions in mean-field theory: Describing the surface parameters for the theory of Nakanishi and Fisher in terms of a microscopic model J. Chem. Phys. 131, (2009) (chapter 4) J. Kuipers and E. M. Blokhuis, Wetting to drying reversal in colloid-polymer systems (Chapter 6, to be submitted) J. Kuipers, J. Groenewold and W. K. Kegel, The Pickering Interface (chapter 7 and appendix E, to be submitted) vi

7 Contents List of Publications Table of Contents vi vii 1 Introduction Historical Background Interfaces Curved Interfaces Helfrich free energy Mean Field theory van der Waals theory: square-gradient approach Outline of this Thesis Thermodynamic Expressions for the Tolman length Introduction Thermodynamics Relation with the isothermal compressibility of the liquid The Tolman length using the van der Waals equation of state Discussion The Interfacial structure and tension between a fluid and a curved hard wall Introduction Mechanical equilibrium and the wall theorem Square-gradient Theory Planar hard wall Spherically shaped hard wall Density functional theory Planar hard wall Spherically shaped hard wall Summary vii

8 CONTENTS viii 4 Wetting and Drying transitions in mean-field theory Introduction The model of Nakanishi and Fisher Landau mean-field lattice model Density functional theory Square-gradient fluid in a square-well potential Simulation results by van Swol and Henderson Discussion Interfacial properties of colloid-polymer mixtures Introduction Perturbation theory Calculation of interfacial properties Surface tension Bending rigidity Discussion Wetting in colloid-polymer systems Introduction Second order free volume theory Nakanishi-Fisher model approximation Direct comparison with the results by Aarts et al Numerical solution for the contact angle Discussion Pickering Stabilisation Introduction Thermodynamics Calculating the Interfacial Tension Testing the model on the work of Sacanna et al Close Packing Discussion Bibliography 104 A Alternative thermodynamic derivation of the Tolman length in terms of the free energy density 113 B Verification of mechanical equilibrium 115 C Virial expressions for the surface tension and Tolman length 118 D Full α(ρ) and excluded volume interactions 122

9 CONTENTS ix E A detailed description of the interface in Pickering Emulsions 125 E.1 2 D description E.2 3 D description Summary 131 Algemene Samenvatting 134 Curriculum Vitae 137 Dankwoord 138

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