Mean-field description of the structure and tension of curved fluid interfaces
Kuipers, J.
Citation
Kuipers, J. (2009, December 16). Mean-field description of the structure and tension of curved fluid interfaces. Retrieved from https://hdl.handle.net/1887/14517
Version: Corrected Publisher’s Version
License: Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden
Downloaded from: https://hdl.handle.net/1887/14517
Note: To cite this publication please use the final published version (if applicable).
Mean-field Description of the Structure and Tension of Curved Fluid Interfaces
Joris Kuipers
Mean-field description of the structure and tension of curved fluid interfaces / J. Kuipers
Copyright c 2009, by J. Kuipers. All rights reserved.
ISBN 978-90-9024828-8
Typeset in LATEX
Coverdesign by C. van der Kamp
Printed by Ipskamp Drukkers, Enschede, The Netherlands
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 15.00 uur
door
Joris Kuipers
geboren te Roosendaal en Nispen
in 1982
iv
Promotiecommissie
promotor : Prof.dr. D. Bedeaux co-promotor : 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
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
List of Publications
• E. M. Blokhuis and J. Kuipers, “Thermodynamic expressions for the Tolman length” J. Chem. Phys. 124, 074701 (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, 054702 (2007) (Chapter 3)
• J. Kuipers and E. M. Blokhuis, “Interfacial properties of colloid-polymer mix- tures” 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, 086101 (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, 044702 (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
Contents
List of Publications vi
Table of Contents vii
1 Introduction 1
1.1 Historical Background . . . 4
1.2 Interfaces . . . 6
1.2.1 Curved Interfaces . . . 6
1.2.2 Helfrich free energy . . . 7
1.3 Mean Field theory . . . 8
1.3.1 van der Waals theory: square-gradient approach . . . 9
1.4 Outline of this Thesis . . . 11
2 Thermodynamic Expressions for the Tolman length 13 2.1 Introduction . . . 14
2.2 Thermodynamics . . . 17
2.3 Relation with the isothermal compressibility of the liquid . . . 20
2.4 The Tolman length using the van der Waals equation of state . . . . 22
2.5 Discussion . . . 24
3 The Interfacial structure and tension between a fluid and a curved hard wall 27 3.1 Introduction . . . 28
3.2 Mechanical equilibrium and the wall theorem . . . 29
3.3 Square-gradient Theory . . . 32
3.3.1 Planar hard wall . . . 33
3.3.2 Spherically shaped hard wall . . . 35
3.4 Density functional theory . . . 36
3.4.1 Planar hard wall . . . 37
3.4.2 Spherically shaped hard wall . . . 38
3.5 Summary . . . 41
vii
CONTENTS viii
4 Wetting and Drying transitions in mean-field theory 43
4.1 Introduction . . . 44
4.1.1 The model of Nakanishi and Fisher . . . 44
4.2 Landau mean-field lattice model . . . 46
4.3 Density functional theory . . . 48
4.4 Square-gradient fluid in a square-well potential . . . 53
4.4.1 Simulation results by van Swol and Henderson . . . 56
4.5 Discussion . . . 58
5 Interfacial properties of colloid-polymer mixtures 61 5.1 Introduction . . . 62
5.2 Perturbation theory . . . 62
5.3 Calculation of interfacial properties . . . 65
5.3.1 Surface tension . . . 66
5.3.2 Bending rigidity . . . 69
5.4 Discussion . . . 73
6 Wetting in colloid-polymer systems 77 6.1 Introduction . . . 78
6.2 Second order free volume theory . . . 79
6.3 Nakanishi-Fisher model approximation . . . 82
6.3.1 Direct comparison with the results by Aarts et al. . . . 86
6.3.2 Numerical solution for the contact angle . . . 87
6.4 Discussion . . . 91
7 Pickering Stabilisation 93 7.1 Introduction . . . 94
7.2 Thermodynamics . . . 95
7.2.1 Calculating the Interfacial Tension . . . 96
7.3 Testing the model on the work of Sacanna et al. . . . 99
7.3.1 Close Packing . . . 100
7.4 Discussion . . . 100
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
CONTENTS ix
E A detailed description of the interface in Pickering Emulsions 125 E.1 2 D description . . . 125 E.2 3 D description . . . 128
Summary 131
Algemene Samenvatting 134
Curriculum Vitae 137
Dankwoord 138
