Dissertation originale pr´esent´ee par Alexandre Chauen vue de l’obtention du grade de docteur en sciences de l’ing´enieur
Promoteur : Prof. Alain Delchambre Co-promoteur : Prof. Pierre Lambert
Ann´ee acad´emique 2007-2008 Recherche financ´ee par le F.R.I.A.
Theoretical and experimental study of capillary condensation and of
its possible application in micro-assembly
Etude th´eorique et exp´erimentale de la condensation capillaire
en vue de son application au micro-assemblage
Universit´e Libre de Bruxelles Facult´e des Sciences Appliqu´ees Syst`emes bio, ´electrom´ecaniques / Bio, electro and mechanical systems Groupe microtechnologies / Microtechnologies group
Theoretical and experimental study of capillary condensation and of
its possible application in micro-assembly
Abstract
Nowadays, the assembly of small (<1mm) components has become an industrial reality.
Many domains like MEMS, surgery, telecommunications, car industry, etc. now have large use of micro-parts. At this scale, predominant forces are different than inmacroworld (for a presentation of the microworld, see [Lambert07]). The pieces often undergo adhesion problems. The adhesion forces can be splitted in different components : van der Waals, electrostatics and capillary condensation. This work focuses on capillary condensation as it often can be the major component of the adhesion force.
The first part of this work details a review of literature of different fields involved in capillary condensation. A simulation tool is then implemented and theoretically validated in the second part of the work. Finally, a test bed is presented; this bed is then used to experimentally validate the simulation results.
Experiments and simulation results are shown to concord. Therefore, the simulation tool can be used to model the force due to capillary condensation.
R´esum´e
L’assemblage de composants de petite taille (<1mm) est devenu une r´ealit´e indus- trielle. De nombreux domaines comme les MEMS, la chirurgie, les t´el´ecommunications ou l’industrie automobile utilisent maintenant de nombreux micro-composants. A cette
´echelle, les forces pr´edominnates ne sont plus les mˆemes que dans lemacromonde (pour une pr´esentation du micromonde, voir [Lambert07]). Les pi`eces sont soumises `a des probl`emes d’adh´esion. L’adh´esion est s´epar´ee en plusieurs composantes, van der Waals, les forces
´electrostatiques et la condensation capillaire. Ce travail se concentre sur l’´etude de la condensation capillaire.
Le travail est structur´e en 3 parties : la premi`ere partie reprend une revue de la litt´erature pour diff´erents domaines utiles dans l’´etude de la condensation capillaire. La seconde partie d´etaille l’outil de simulation r´ealis´e ainsi que sa validation th´eorique. La troisi`eme partie reprend la description du banc de mesure r´ealis´e. Ce banc a ´et´e utilis´e pour valider les r´esultats de simulation.
L’exp´erience montre ainsi que les r´esultats th´eoriques correspondent `a ceux mesur´es et que l’outil de simulation peut donc ˆetre utilis´e pour mod´eliser la force due `a la condensation capillaire.
Contact details Alexandre Chau, alexandre@chau.be
Prof. Pierre Lambert, plambert@ulb.ac.be Prof. Alain Delchambre, adelch@ulb.ac.be
Bio, electro and mechanical systems - beams@ulb.ac.be http://beams.ulb.ac.be
Universit´e libre de Bruxelles CP 165/14 1050 Bruxelles
Belgium
To obtain a copy of this thesis, please contact Pierre Lambert.
Related publications
Alexandre Chau, Pierre Lambert and Alain Delchambre. Mod´elisation de la condensation capillaire pour le micro-assemblage. in Actes de la premi`ere journ´ee sur la mod´elisation et l’anayse dimensionnelle - organized by EPFL, Lausanne, Suisse (2005)
Alexandre Chau, Pierre Lambert and Alain Delchambre. A general 3D model to compute capillary force. in Proc. Of MicroMechanics Europe 2005, G¨oteborg, Sweden, pp. 156-9 (2005)
Alexandre Chau, Alain Delchambre, St´ephane R´egnier and Pierre Lambert. Towards a general three dimensional model for capillary nanobridges and capillary forces. in Proc.
of the 5th International Workshop on Microfactories (IWMF), Besan¸con, France (2006) Alexandre Chau, St´ephane R´egnier, Alain Delchambre and Pierre Lambert. Three di- mensional model for capillary nanobridges an capillary forces. Modelling and simulation in materials science and engineering 15: 305-317 (2007)
Alexandre Chau, St´ephane R´egnier, Alain Delchambre and Pierre Lambert. Influence of geometrical parameters on capillary forces. in Proceedings of IEEE International Sympo- sium on Assembly and Manufacturing (2007)
Pierre Lambert, Marion Sausse Lhernould, Alexandre Chau, Vincent Vandaele, Jean- Baptiste Valsamis and Alain Delchambre. Surface Forces Modelling: Application to Mi- croassembly. in Proceedings of IARP, Paris, pp. 13 (2006)
Julien Vitard, Pierre Lambert, Alexandre Chau and St´ephane R´egnier. Capillary Forces Models for the Interaction Between a Cylinder and a Plane. in Proc. of the 5th Interna- tional Workshop on Microfactories (4 pages), Besan¸con (2006)
Remerciements
Encore un peu de fran¸cais en plus du titre...
J’aimerais remercier toutes les personnes qui m’ont aid´e ou soutenu, participant ainsi `a la r´ealisation de ce travail : Prof. Pierre Lambert, pour ses discussions constructives et ses innombrables conseils Prof. Alain Delchambre, pour l’accueil dans le service Prof. Marie-Paule Delplancke & Prof. Frank Ogletree pour le savoir qu’ils m’ont fait partager Bruno Tartini et Nicolas Bastin, pour la r´ealisation deSmurf, mon banc de mesure St´ephane R´egnier, Mehdi Boukallel & Maxime Girot, pour leur accueil et leur aide au LRP Tout le service Beams, Parce qu’on y est quand mˆeme mieux que chez les autres Le service Mati`eres & Mat´eriaux, Parce que chez nous on est bien, mais que eux ont des instruments tr`es utiles Mmes Carolyn Straehle et Monique Wurm, Pour la correction de mon anglais, Mes parents, sans qui je n’aurais d’ailleurs pas ´et´e l`a pour les remercier Et Laurence, pour sa pr´esence et son support Enfin, je verse une petite larme, parce qu’apr`es plusieurs ann´ees devie commune, Vincent & moi allons nous s´eparer
Ce travail a pu ˆetre r´ealis´e grˆace au soutien financier des organismes suivants :
Le Fonds pour la formation `a la Recherche dans l’Industrie et dans l’Agriculture – FRIA, Le Fonds Emile Defay, Le Fonds d’Encouragement `a la Recherche de l’ULB, La Communaut´e Franc¸aise de Belgique, via le projet ARC Mµn et via le Commissariat g´en´eral aux relations internationales
Contents
Nomenclature xvii
1 Context 1
1.1 Context of the research . . . . 1
1.2 Intuitive approach . . . . 1
1.3 Size definitions . . . . 3
1.3.1 Size effects . . . . 3
1.4 Outline . . . . 4
1.5 Contribution . . . . 5
1.6 Quick reading outline . . . . 5
I State-of-the-art 7 2 Introduction 9 3 Applicative context 11 3.1 Manipulation . . . . 11
3.2 MEMS . . . . 12
3.3 Nanostructured surfaces . . . . 13
3.4 Carbon nanotubes . . . . 13
3.5 Porous media . . . . 14
3.6 Other demonstration systems . . . . 14
3.7 Metrology . . . . 15
3.8 Colloids . . . . 15
3.9 Natural examples . . . . 16
4 Vocabulary & concepts 19 4.1 Introduction . . . . 19
4.2 Definition . . . . 20
4.3 Historical background . . . . 20
4.4 Wetting . . . . 20
4.5 Surface tension . . . . 22
4.6 Adsorption - Desorption . . . . 22
4.6.1 Adsorption isotherm . . . . 23
4.6.2 Desorption . . . . 24
4.7 Nucleation . . . . 24
4.8 Thermodynamics . . . . 24
4.9 Phase transitions . . . . 25
v
CONTENTS
4.10 Meniscus nomenclature . . . . 26
4.11 Conclusion . . . . 27
4.A Nomenclature of phase transitions . . . . 29
4.A.1 Bridging - Capillary condensation . . . . 29
4.A.2 Wetting - Layering . . . . 29
5 Condensation Models 31 5.1 Macroscopic models . . . . 31
5.1.1 Young-Laplace equation . . . . 32
5.1.2 Kelvin Equation . . . . 32
5.1.3 Other forms of the Kelvin equation . . . . 32
5.1.4 Validity limits of the Kelvin equation . . . . 33
5.1.5 Corrections to the Kelvin equation . . . . 33
5.1.6 Dependence of surface tension on curvature . . . . 36
5.1.7 Other macroscopic models . . . . 36
5.2 Molecular scale models . . . . 38
5.2.1 Molecular Dynamics . . . . 38
5.2.2 Monte Carlo Simulations . . . . 40
5.2.3 Lattice models . . . . 43
5.3 Mixed models . . . . 43
5.3.1 Interfacial models . . . . 44
5.3.2 Density functional theory . . . . 44
5.3.3 Integral equation approach . . . . 47
5.4 Comments on models . . . . 47
5.4.1 MC-MD comparison . . . . 47
5.4.2 Limitations of GCMC . . . . 48
5.4.3 MC-DFT comparison . . . . 48
5.4.4 Combination of methods . . . . 48
5.4.5 Dynamics of meniscus . . . . 49
5.4.6 Summary . . . . 49
5.5 Fluid-fluid interactions . . . . 49
5.5.1 Lennard-Jones . . . . 49
5.5.2 Weeks-Chandler-Andersen (WCA) model . . . . 50
5.5.3 Hard sphere . . . . 50
5.5.4 Associating fluids . . . . 50
5.5.5 Other models . . . . 52
5.6 Fluid-Solid interactions . . . . 52
5.6.1 Disjoining pressure . . . . 52
5.6.2 Interaction potential . . . . 53
5.7 Wetting films . . . . 54
5.7.1 Mica . . . . 54
5.7.2 Sodium chloride (salt) - NaCl . . . . 55
5.7.3 Other results . . . . 55
5.8 Conclusions . . . . 55
5.A Peterson-Gubbins method . . . . 57
5.B Density functional theories . . . . 57
vi
CONTENTS
6 Surfaces modelling 59
6.1 Introduction . . . . 59
6.2 Influence of roughness . . . . 59
6.3 Ideal surfaces . . . . 60
6.4 Classical geometric roughness representation . . . . 61
6.4.1 Statistical descriptions . . . . 61
6.4.2 Extreme-value height descriptions . . . . 63
6.4.3 Spatial parameters . . . . 64
6.4.4 Spatial functions . . . . 64
6.4.5 Wenzel roughness factor . . . . 64
6.4.6 Applications . . . . 65
6.4.7 Limitations . . . . 65
6.5 Fractal descriptions . . . . 66
6.5.1 Weierstrass-Mandelbrot function . . . . 66
6.5.2 Univariate Weierstrass-Mandelbrot function . . . . 66
6.5.3 Multiariate Weierstrass-Mandelbrot function . . . . 66
6.5.4 Spatial functions . . . . 67
6.5.5 Capillary condensation and fractal surfaces . . . . 68
6.6 Conclusions . . . . 68
6.A Fractals . . . . 69
6.A.1 Hausdorff-Besicovitch dimension . . . . 69
6.A.2 Box dimension . . . . 69
6.A.3 Geometrical properties of fractals . . . . 70
6.A.4 Weierstrass function . . . . 71
7 Conclusions 73 II Model 75 8 Choice of the model 77 8.1 Introduction . . . . 77
8.2 Capillary condensation . . . . 77
8.3 Surfaces . . . . 78
8.4 Force . . . . 78
8.5 Contact and deformation . . . . 78
8.6 Softwares . . . . 78
9 Developed model 81 9.1 Introduction . . . . 81
9.2 Surface Evolver . . . . 81
9.2.1 Surface Evolver principle . . . . 81
9.2.2 Surface Evolver description . . . . 82
9.3 More complex geometries . . . . 84
9.3.1 Series development . . . . 84
9.4 Variable separation . . . . 86
9.5 Convergence improvement . . . . 87
9.5.1 Facets removal . . . . 87
vii
CONTENTS
9.5.2 Sharp angles . . . . 87
9.6 Additional degrees of freedom . . . . 89
9.6.1 Translational degrees of freedom . . . . 89
9.6.2 Rotational degrees of freedom . . . . 89
9.7 Force computation . . . . 90
9.7.1 Computation of the derivative . . . . 91
9.8 Conclusions . . . . 91
9.A Meshing problems . . . . 93
9.B Integrals transformations . . . . 93
9.B.1 Volume integrals . . . . 94
9.B.2 Energy integrals . . . . 94
9.B.3 Examples . . . . 95
9.C Tilt induced modifications . . . . 96
9.C.1 Volume integrals . . . . 97
9.C.2 Surface integrals . . . . 98
9.C.3 Examples . . . . 98
10 Theoretical validation 103 10.1 Comparison with literature . . . . 103
10.1.1 Sphere-plane . . . . 104
10.1.2 Paraboloid-plane . . . . 105
10.1.3 Cone-plane . . . . 107
10.2 Accuracy of results . . . . 108
10.3 Note on the derivative . . . . 108
10.4 Note on the Kelvin radius . . . . 108
10.5 Conclusions . . . . 109
10.A Curvature estimation . . . . 111
10.A.1 vectors used . . . . 111
10.A.2 Normals computation . . . . 112
10.B Computations for theoretical comparisons . . . . 113
10.B.1 plane-plane . . . . 114
10.B.2 cone-plane . . . . 114
11 Theoretical results 115 11.1 Influence of the distance/indentation . . . . 115
11.2 Influence of the tilt angle . . . . 117
11.2.1 Sphere . . . . 117
11.2.2 Cone . . . . 117
11.2.3 Paraboloidal tip . . . . 117
11.2.4 Rounded pyramidal tip . . . . 118
11.3 Centering influence . . . . 120
11.3.1 sphere-sphere . . . . 120
11.3.2 Cone - cone . . . . 121
11.4 Tip-object rotation . . . . 123
11.4.1 2 pyramidal tips . . . . 123
11.5 Humidity control . . . 124
11.5.1 sphere-plane . . . . 124
11.5.2 cone-plane . . . . 125
viii
CONTENTS
11.5.3 paraboloidal tip - plane . . . 125
11.5.4 rounded pyramidal tip . . . . 125
11.5.5 note . . . . 129
11.6 Temperature control . . . . 129
11.6.1 sphere . . . . 129
11.6.2 cone, paraboloidal tip, rounded pyramidal tip . . . . 131
11.7 Conclusions . . . . 131
11.A Computation procedure . . . . 133
11.A.1 Hydra . . . . 133
11.A.2 evolver file generation . . . . 133
11.A.3 shell script . . . . 133
11.A.4 data treatment . . . . 133
11.B Tilt angle . . . . 134
11.B.1 paraboloid . . . . 134
12 Conclusions 135 12.1 Application to micro-assembly . . . . 135
12.2 Design ideas . . . . 136
12.2.1 Tilting . . . . 136
12.2.2 Environment control . . . . 136
12.2.3 Rotation . . . . 136
12.2.4 Multiple tip actuation . . . 137
12.2.5 Graphical summary . . . . 137
12.3 Perspectives and possible future work . . . . 137
12.3.1 Experiments . . . . 137
12.3.2 Additional object . . . . 137
12.3.3 Shapes . . . . 137
12.3.4 External actuation . . . . 138
12.3.5 Coupling with other models . . . . 138
III Experiments 139 13 Introduction 141 14 Specifications 143 14.1 Introduction . . . 143
14.2 Requirements . . . . 143
14.3 Detailed specifications : parameters measurement . . . . 143
14.3.1 Force measurement . . . . 143
14.3.2 Humidity measure . . . . 143
14.3.3 Temperature measurement . . . . 145
14.3.4 Tip characterization . . . . 145
14.4 Detail specifications : parameters control . . . . 145
14.4.1 Humidity control . . . . 145
14.4.2 Temperature control . . . . 147
14.4.3 Position control . . . . 147
14.5 Tip choice . . . . 150
ix
CONTENTS
14.A Humidities and temperatures . . . . 151
14.B Water vapor saturating pressure . . . . 151
14.B.1 Reference formula . . . . 151
14.B.2 Values . . . . 153
14.C Bubbler design . . . . 153
14.D Tip comparison . . . . 154
14.E Tip materials . . . . 154
14.F Microscopy techniques and limits . . . . 154
15 Test bed 159 15.1 Introduction . . . 159
15.2 Existing beds . . . . 159
15.2.1 Scanning probe microscopy principle . . . . 159
15.2.2 Microforce Beams bed . . . . 159
15.2.3 LRP bed . . . . 160
15.2.4 commercial AFM . . . . 161
15.3 AFM . . . . 161
15.3.1 AFM force measurement . . . . 161
15.3.2 AFM limitations . . . . 163
15.4 Developed test bed . . . . 163
15.4.1 Material . . . . 163
15.4.2 Software . . . . 165
15.4.3 Force measurement principle, resolution and limits . . . . 165
15.5 Design notes . . . . 167
15.5.1 Flexibility . . . . 167
15.5.2 Adjustments . . . . 168
15.5.3 Humidity sensibility . . . . 168
15.6 Validation . . . . 169
15.7 Conclusion . . . . 169
15.A Datasheets . . . . 171
15.A.1 PI-P528.ZCD datasheets . . . . 171
15.A.2 PI-M126 datasheets . . . . 171
15.A.3 Tilt actuation . . . . 171
15.A.4 laser . . . . 171
15.A.5 photodiode . . . . 171
15.A.6 Isolation workstation . . . . 171
15.B Setup . . . . 184
15.B.1 Tip placement . . . . 184
15.B.2 Laser setup . . . . 184
15.B.3 Photodiode focussing . . . . 186
15.C Software . . . . 186
15.C.1 Safety notes . . . . 187
15.C.2 Description . . . . 187
15.D Laser resolution calculation . . . . 188
15.D.1 Laser path . . . . 189
15.D.2 Spot size . . . . 189
15.D.3 Physical limitations . . . . 189
15.D.4 Resolution . . . . 189
x
CONTENTS
15.D.5 Influence of spot centering . . . . 190
16 Experimental results 191 16.1 Introduction . . . 191
16.2 Procedure . . . . 191
16.3 Tips . . . . 192
16.4 Results . . . . 192
16.4.1 Dependence on tilt angle . . . . 193
16.5 Sources of experimental errors . . . . 194
16.5.1 Quality of the substrate surfaces . . . . 194
16.5.2 Quality of the tip surface . . . . 194
16.5.3 Temperature . . . . 194
16.5.4 Cantilever stiffness variability . . . . 195
16.5.5 “Other forces” . . . . 196
16.5.6 50 Hz perturbations . . . . 196
16.5.7 Sensor-tip distance . . . . 196
16.5.8 Contact detection variability . . . . 197
16.5.9 Dependence on environmental parameters . . . . 197
16.5.10 Summary . . . . 198
16.6 Data fitting . . . . 198
16.7 Model comparison . . . . 199
16.8 Model fitting . . . . 201
16.9 Discussion . . . . 202
16.A Definitions . . . . 205
16.A.1 Graphical representation . . . . 205
16.B Measurement procedure . . . . 205
16.C Tips . . . . 205
16.C.1 batch 1 . . . . 207
16.C.2 batch 2 . . . . 207
16.C.3 Tolerances . . . . 207
17 Conclusions 209 IV Conclusions & perspectives 211 18 Conclusions 213 19 Further work 215 19.1 Noise reduction . . . . 215
19.2 Other liquids . . . . 215
19.3 Workstation development/Applicative demonstrator . . . . 215
19.4 Integration with other models . . . . 216
19.5 Additional control parameters . . . . 216
Bibliography 217
Index 225
xi
CONTENTS
xii
List of Figures
1.1 Strategies to handle adhesion forces . . . . 2
1.2 Forces scale effects . . . . 4
3.1 Manipulation of microspheres . . . . 11
3.2 Schematic description of surface micromachining . . . . 12
3.3 Schematic of cantilever beam adhering to substrate . . . . 12
3.4 SEM image of a stiction failure of a RF MEMS switch . . . . 13
3.5 Columnar 2D lattice . . . . 13
3.6 AFM image for two overlapping multi-wall nanotubes . . . . 14
3.7 Polysilicon cantilever beams . . . . 14
3.8 Polymer beams . . . . 15
3.9 Novascan ultrasharp AFM tip . . . . 15
3.10 Structure of a gecko seta . . . . 16
3.11 Adhesion of geckos to highly hydrophobic substrate . . . . 17
4.1 Formation and growth of a meniscus . . . . 19
4.2 Surface wetting (1) . . . . 21
4.3 Surface wetting (2) . . . . 21
4.4 Phase diagram : wetting transition . . . . 21
4.5 Adsorption-desorption isotherms and classification . . . . 23
4.6 Free energy plots for a pore . . . . 24
4.7 Everett-Haynes nucleation scenario . . . . 24
4.8 Liquid bridge hysteresis between two wetted objects . . . . 25
4.9 Schematic adsorption isotherms for a slit . . . . 26
4.10 Nomenclature . . . . 26
5.1 Ideal geometries . . . . 34
5.2 Slit model . . . . 34
5.3 Phase diagram for Ar . . . . 37
5.4 Wedge shapewrt γ . . . . 37
5.5 Geometrical model of condensation . . . . 37
5.6 Phase diagram for macroscopic adsoprtion . . . . 38
5.7 MD results from [Miyahara00] . . . . 39
5.8 Isotherms computed by [Neimark00b] . . . . 41
5.9 Condensation between nanowires . . . . 41
5.10 Results from [Celestini97] . . . . 42
5.11 Lattice simulation results . . . . 43
5.12 Chemical potential and pressurewrt density . . . . 46
5.13 Examples of density profiles . . . . 46
xiii
LIST OF FIGURES
5.14 Global hysteresis loop and subloops . . . . 47
5.15 Fluid-fluid interaction potentials . . . . 50
5.16 Classification of fluids . . . . 51
5.17 Water model . . . . 52
5.18 Water adsorption isotherm on NaCl(1 0 0) . . . . 55
6.1 Basic lattices . . . . 60
6.2 Example of reticulation plane . . . . 60
6.3 crystal imperfections . . . . 61
6.4 Surface profiles having the sameRa value . . . . 62
6.5 Kurtosis and skewness . . . . 63
6.6 Machining influence on skewness and kurtosis . . . . 63
6.7 Wetting on a rough surface . . . . 65
6.8 Examples of fractal surfaces . . . . 67
6.9 Hausdorff dimension . . . . 70
6.10 Ways of defining boxes . . . . 71
9.1 Evolution from a cube to a sphere . . . . 82
9.2 liquid meniscus between two planes . . . . 84
9.3 Meniscus between a plane and a three-faces pyramid . . . . 84
9.4 View of the “development planes” . . . . 85
9.5 Evolution of series-developed tip . . . . 86
9.6 Meniscus between a plane and a three-faces rounded pyramid . . . . 87
9.7 Sharp angles . . . . 88
9.8 Gibbs phenomenon . . . . 89
9.9 Tip degrees of freedom . . . . 90
9.10 “Complete” tip . . . . 90
9.11 Tilted disk and its projection on thez= 0 plane . . . . 99
9.12 Tilted sphere parameters . . . . 100
9.13 Sphere and tilted sphere . . . . 100
9.14 Tilt limitations . . . . 101
10.1 Comparison cith [Orr75] and [Israelachvili92] . . . . 104
10.2 RH /ψ relationship . . . . 105
10.3 Introduction of the sphere-plane distance D . . . . 105
10.4 Separated spheres. Comparison with [Israelachvili92] and [Rabinovich05] for different sphere raddi, contact angles and surface tensions. . . . 106
10.5 Comparison with [Stifter00] . . . . 106
10.6 Determination of critical distance (see text for its definition) . . . . 107
10.7 A posteriori computation of the curvature . . . . 108
10.8 Illustration of the different arrays involved . . . . 112
10.9 definition of the geometry . . . . 114
11.1 Indentation . . . . 115
11.2 Indentation . . . . 116
11.3 Tilted cone . . . . 117
11.4 Tilted paraboloid (1) . . . . 118
11.5 Tilted paraboloid (2) . . . . 119
11.6 Tilted pyramid . . . . 119
xiv
LIST OF FIGURES
11.7 Sphere sphere centering sketch . . . . 120
11.8 Sphere sphere centering effect . . . . 120
11.9 Cone centering effect . . . . 121
11.10Cone centering effect Y . . . . 122
11.11Pyramid-pyramid rotation effect . . . . 123
11.12RH effect : sphere/plane . . . . 124
11.13RH effect : sphere/plane . . . . 125
11.14RH effect : cone/plane . . . . 126
11.15RH effect : cone/plane . . . . 126
11.16RH effect : paraboloid/plane . . . . 127
11.17RH effect : paraboloid/plane . . . . 127
11.18RH effect : Rounded pyramid/plane . . . . 128
11.19RH effect : Rounded pyramid/plane . . . . 128
11.20Temperature effect : Sphere/plane . . . . 130
11.21Temperature effect : Sphere/plane . . . . 130
11.22Effect of the tilt angle on the contact point . . . . 134
12.1 Manipulation . . . . 135
12.2 Efficiency ratio . . . . 137
14.1 TEM example image . . . . 145
14.2 TEM image . . . . 146
14.3 Bubbling system . . . . 146
14.4 Tip degrees of freedom . . . . 149
14.5 Conversion graph : Dew point ↔ relative humidity . . . . 152
14.6 Different tips available . . . . 155
14.7 Microscopy techniques . . . . 156
14.8 nanometrology techniques . . . . 157
15.1 Scanning probe microscopy principle . . . . 160
15.2 Microforce Beamsbed . . . . 160
15.3 AFM principle . . . . 161
15.4 AFM force measurement cycle (1) . . . . 162
15.5 AFM force measurement cycle (2) . . . . 162
15.6 Developed test bed sketch . . . . 164
15.7 Test bed picture . . . . 165
15.8 Software interface . . . . 166
15.9 AFM resolution calculation : the blue paths are the mirrored red paths. 166 15.10Degrees of freedom of the test bed (1) . . . . 168
15.11Degrees of freedom of the test bed (1) . . . . 169
15.12Pull off curve obtained with the test bed . . . . 170
15.13Nanopositioning stage datasheet . . . . 172
15.14Nanopositioning stage datasheet (continued) . . . . 173
15.15Micropositioning stage datasheet . . . . 174
15.16Micropositioning stage datasheet(continued) . . . . 175
15.17Laser datasheet . . . . 176
15.18Laser datasheet (continued) . . . . 177
15.19Photodiode datasheet . . . . 178
xv
LIST OF FIGURES
15.20Photodiode datasheet (continued) . . . . 179
15.21isolation workstation datasheet . . . . 181
15.22Breadboard datasheet . . . . 182
15.23Breadboard datasheet (continued) . . . . 183
15.24Tip (re)placement . . . . 184
15.25Laser path . . . . 185
15.26Tip focussing d-o-f . . . . 186
15.27Photodiode focussing d-o-f . . . . 187
15.28Software interface . . . . 187
15.29Laser path . . . . 189
16.1 TEM pictures of tips . . . . 192
16.2 Force plotted with respect to relative humidity . . . . 193
16.3 Tip holder picture . . . 193
16.4 Influence of mica cleavage . . . . 195
16.5 Blank test . . . . 196
16.6 Effect of the relative humidity on the translator . . . . 198
16.7 Force with respect to humidity : simulation results . . . . 200
16.8 Comparison between model and experiment . . . . 201
16.9 Force dependence on humidity : experimental results. . . . 202
16.10Comparison between model and experiment (2) . . . . 203
16.11Precision, resolution, etc. . . . 205
16.12Algorithm used for measurement . . . . 206
xvi
Nomenclature
α aperture angle of a cone or a pyramid γ Surface tension
µ Chemical potential ψ Filling angle τ tilt angle of a tip θ Contact angle
AFM Atomic force microscope DP Dew point
ew Water vapor saturating pressure
F Force
k stiffness
MEMS Micro electro mechanical systems RH Relative humidity
RT Room temperature
SEM scanning electron microscope T Temperature
TEM transmission emission microscope
V Volume
W Surface energy rK Kelvin radius Vm Molar volume
xvii
LIST OF FIGURES
xviii
1
Context
1.1 Context of the research
The Beams1 department of the Universit´e libre de Bruxelles comprises different research groups, one of them being the microtechnologies group. Historically, the group focused
—among other subjects— on the management of assembly lines. With technological advances, specifically with the miniaturization of systems and components, a problem arose that was almost inexistant in the “usual” world; it became much more difficult to pick and place objects that were too “small” 2.
1.2 Intuitive approach
The problem arises from the size dependence of different forces. When picking up an object in the “usual” world, for instance picking up an apple, the force that must be overcome is gravity. If an object is not correctly picked up, it simply falls.
When objects become “smaller”, gravity becomes less important : if an apple is dropped, it falls. If a postage stamp if dropped, it falls, but air resistance will limit the speed of the stamp. If a speck of dust is put in the air, it will almost not fall at all.
The same effect can be observed with pick and place operations : with a wet finger, it is impossible to pick up an apple, while it is possible to pick up a postage stamp; it is possible to release the stamp simply by shaking the hand vigorously. But if a speck of dust is picked up with a wet finger, it is almost impossible to release it by shaking the hand.
The conclusion of these examples and the motto of this research is :
“small sticks”
1Beamsstands for Bio, Electro And Mechanical Systems;Beamsis a department that is part of the Faculty of Engineering of the Universit´e libre de Bruxelles. The department is the result of a recent fusion of three former departments : CAD/CAM, MicroElectronics and Electrical Engineering - website : http://beams.ulb.ac.be
2Definition of “small” and size considerations will come later.
1
CHAPTER 1. CONTEXT
In the race towards smaller, cheaper, more reliable, and more functional equipment, the assembly of small parts has become a crucial problem for enterprises. Such diversified domains as automotive engineering, medicine, IT or domestic appliances tend to manufac- ture smaller components every day. Parallel to downscaling, adhesion forces have become increasingl important, notably in assembly.
The importance of the adhesion forces has led to the development of new strategies to pick and place small objects. These strategies can be separated into four types, illustrated in figure 1.1 : reduction, overcoming, exploitation and avoidance.
Figure 1.1 Strategies to take adhesion forces into consideration [Vandaele07]
Nowadays, techniques used for the assembly of small components remain rather empir- ical. The grippers are at present designed with the costly so-called trial-and-error method due to the lack of models of forces. At these small scales, surface forces become predom- inant. The gripper and the piece can thus undergo adhesion and the release of the piece often becomes difficult.
One of the long-term goals of this work is to provide designers with models that permit them to predict the behaviour of pieces when they are caught and released, avoiding the realization of many expensive non functional prototypes.
A general review of the manipulation strategies has already been realized in the de- partment [Lambert07]. This work will focus on adhesion, as it will be explained later.
Even if it is not the specific domain of theBeamsdepartment, it must be noted that, obviously, adhesion problems, hence adhesion force, occur not only in assembly but in every process where very small distances between small objects are involved, for instance in atomic force microscopy, AFM.
Adhesion forces are usually separated into 3 components :
electrostatic force
van der Waals force
capillary force
The former two forces arise from the associated electromagnetic phenomena while the latter is associated with the presence of a medium between the bodies. This medium is different —in nature and/or in thermodynamic properties— from the surrounding envi- ronment of the bodies.
Electrostatic and van der Waals forces will not be a focus in this work; this thesis will restrict its scope to the description of and the model-building related to the capillary component.
2
1.3. SIZE DEFINITIONS
There are two ways to obtain a capillary force between two bodies : the most obvious consists in placing a droplet on a first body and then approaching a second one. A so- called capillary bridge, or meniscus, will then form, as illustrated later. Note that this kind of bridge can be avoided, as the drop is voluntarily placed. In addition, this problem has already been reviewed, e.g. in [Lambert07].
In the other approach, capillary condensation, the bridge will form because of the interactions of the bodies with the intermediate medium. Some liquid —water in uncon- trolled environment— condenses between the bodies. As this type of bridge is caused by surface interactions, the bodies have to be relatively close to each other, the capillary condensed bridge is smaller (tens of nanometers are typical lengthscales). As those inter- actions cannot be avoided, the presence of the bridge will depend only on environmental and the objects’ properties, not on the designer’s wishes.
In this respect, the models will mainly try to simulate the formation and conditions of presence of capillary condensed bridges. Different competencies will be required, as described later.
It is important to note that a large body of knowledge about capillary condensation exists in the literature. Capillary condensation is an important phenomenon in the study of colloids and of porous media and has been investigated for decades. The originality of this work is to apply the results of chemical research with a macroscopic, “mechanical”
point of view.
1.3 Size definitions
In all works on assembly, one very important parameter is the size of the objects to manipulate. This section aims at defining conventions for the sizes considered further.
The scales are rigorously defined with the International system of units: nano stands for 10−9 and micro stands for 10−6. Used for lengths, the size references are then the nanometre and the micrometre.
However, in the literature, it appears that those references are very randomly re- spected. Fashionable research themes often take the priority over a standard nomencla- ture. This work attempts to base the scales designation on the following principles :
micro/nano-objects : objects with micrometre/nanometre size features,e.g., a 1mm diameter sphere will not constitute a micro object, but a 1mm diameter gear with 100 µm teeth will.
micro/nanoforce : for force, the classical prefixes will be used.
1.3.1 Size effects
It was shown intuitively in section 1.2 that dominant forces are different at different scales.
The reason for this is that forces depend on different physical quantities. The weight of objects are dependent on their volume,i.e. on a dimension raised to the power of 3, while contact forces mainly depend on the contact surface.
When the characteristic dimension of a system is reduced by a factor of 10, the volume forces are divided by 103, while surface forces are divided only by 102. This is illustrated in figure 1.2.
3
CHAPTER 1. CONTEXT
10-8 10-6 10-4 10-2 100
10-20 10-15 10-10 10-5 100 105 1010
Size of the component [m]
Forces exerted on the component [N] Capillary gripping
Vacuum gripping
Classical gripping
Vacuum force ~ L2 Weight ~ L3 Capillary force ~ L
C B
A
Figure 1.2 Forces scale effects
These size effects can be captured by adimensional numbers,e.g., the Bond number.
The Bond number expresses the ratio between gravitational forces and surface tension forces :
Bo= ρgL2 γ
where ρ is the density, g the gravitational acceleration, L a characteristic length scale, andγ the surface tension. Bo is very small if gravitational forces are negligible.
1.4 Outline
The work will be organised in three parts :
Part I : State-of-the-art presents different fields involved in capillary condensation study
Part II : Model introduces presents the model developed that will be used in the rest of the thesis
– model presents the the model, with a focus on its mathematical justification – validation describes the computations validating the model in comparison with
studies from the literature
– theoretical results presents the new theoretical results that can be achieved using the model developed
Part III : Experiments demonstrates the experiments used to confirm the model results
– specifications lists the requirements of the test bed – test bed describes the test bed as it has been realized
– measurements presents and discusses the experimental results
4
1.5. CONTRIBUTION
1.5 Contribution
This work pursued different scientific goals :
The first one is to study geometrical and environmental effects on capillary force to improve the available results such as the approximation found in literature (e.g., [Israelachvili92]).
Another goal of this work is to know whether capillary forces due to capillary con- densation can be used to manipulate objects.
After studying the capillary force theoretically, one should ensure that those theo- retical results are physically valid. This will be done by developing a test bed and by giving force dependence on different parameters such as humidity and tilt angle as seen in the chapters dedicated to measurements.
1.6 Quick reading outline
For a rapid reading of this work, the author would recommend to focus on the following chapters :
Part I : chapter 3
Part II : chapters 9 and 11
Part III : chapters 15 and 16
In addition, it would be recommended to read the introductions and conclusions of each of the three parts.
5
CHAPTER 1. CONTEXT
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