Adsorption phenomena and anchoring energy in nematic liquid crystals

Giovanni Barbero, Luiz Roberto Evangelista0849335841, 9780849335846

Despite the large quantity of phenomenological information concerning the bulk properties of nematic phase liquid crystals, little is understood about the origin of the surface energy, particularly the surface, interfacial, and anchoring properties of liquid crystals that affect the performance of liquid crystal devices. Self-contained and unique, Adsorption Phenomena and Anchoring Energy in Nematic Liquid Crystals provides an account of new and established results spanning three decades of research into the problems of anchoring energy and adsorption phenomena in liquid crystals. The book contains a detailed discussion of the origin and possible sources of anchoring energy in nematic liquid crystals, emphasizing the dielectric contribution to the anchoring energy in particular. Beginning with fundamental surface and anchoring properties of liquid crystals and the definition of the nematic phase, the authors explain how selective ion adsorption, dielectric energy density, thickness dependence, and bias voltage dependence influence the uniform alignment of liquid crystals and affect the performance of liquid crystal devices. They also discuss fundamental equations regulating the adsorption phenomenon and the dynamic aspects of ion adsorption phenomenon in liquid crystalline systems. Adsorption Phenomena and Anchoring Energy in Nematic Liquid Crystals serves as an excellent source of reference for graduates and researchers working in liquid crystals, complex fluids, condensed matter physics, statistical physics, chemical engineering, and electronic engineering, as well as providing a useful general introduction to and background information on the nematic liquid crystal phase.

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Table of contents :
ADSORPTION PHENOMENA AND ANCHORING ENERGY IN NEMATIC LIQUID CRYSTALS……Page 1
Contents……Page 5
PREFACE……Page 10
1.1 Nematic order parameters……Page 13
Table of Contents……Page 0
1.2 Maier-Saupe model for the nematic-isotropic phase transition……Page 15
1.3 Extension of the Maier-Saupe theory: Influence of the dimerization process on the nematic ordering……Page 19
1.4 Continuum description of the nematic phase……Page 26
1.5.1 Flexoelectric and dielectric contributions……Page 29
1.5.2 Magnetic interaction……Page 31
1.6 Equilibrium configuration in strong and weak anchoring situations……Page 32
1.6.1 Example 1: Hybrid aligned nematic cell (HAN)……Page 34
1.6.2 Example 2: Freedericksz transition–strong anchoring……Page 36
2.1 Anchoring……Page 40
2.2 The anchoring energy function……Page 41
2.2.1 Example 1: Freedericksz transition–weak anchoring……Page 43
2.2.2 Example 2: Freedericksz transition–nonhomogeneous anchoring energy……Page 46
2.3 Sources for the surface free energy……Page 49
2.3.1 Stochastic contribution to the anchoring energy……Page 51
2.3.2 Validity of the elastic model for nematic surface anchoring energy……Page 58
2.3.3 Contribution of the smectic-nematic interface to the surface energy……Page 63
3.1 Introduction……Page 72
3.2 Quadrupolar interaction……Page 73
3.3 Quadrupolar energy density in the bulk: direct calculation……Page 77
3.4 Quadrupolar energy density in the bulk: electrostatics approach……Page 81
3.5 Non-local analysis……Page 86
3.6 Interfacial contributions to the surface free energy……Page 88
Conclusions……Page 91
4.1 A model for the thermal renormalization of the anchoring energy……Page 94
4.1.1 Symmetry considerations……Page 95
4.1.2 Mean field approach……Page 97
4.1.3 Comparison with Akulov-Zener law……Page 104
4.1.4 Averaging with continuous Hamiltonian……Page 106
4.2 Temperature dependence of the surface tension near the nematic-isotropic transition……Page 110
4.3 Surface director gliding in lyotropic liquid crystals……Page 116
4.3.1 Surface molecular energy model……Page 119
4.3.2 Master equation and Fokker-Planck approximation……Page 122
4.3.3 Analytical and numerical results……Page 125
4.3.4 Temperature behavior and comparison with the experimental data……Page 127
Conclusions……Page 131
5.1 Introduction……Page 137
5.2 Adsorption at interfaces……Page 138
5.2.1 Thickness dependence of the coverage……Page 142
5.2.2 Adsorption phenomena for two adsorbates……Page 147
5.2.3 Statistical approach to the problem: Adsorption energy……Page 148
5.2.4 Adsorption of magnetic grains in magnetic fluids……Page 150
5.2.5 Adsorption energy as a non-local quantity……Page 154
5.3 Surface adsorption and anchoring transition……Page 157
Conclusions……Page 162
6.1.1 Introduction……Page 165
6.1.2 The Poisson-Boltzmann equation: Exponential approximation for the electric field……Page 167
6.1.3 Thickness dependence of anchoring energy: Langmuir approximation……Page 169
Thickness dependence of Weff……Page 174
6.2 Analysis of the influence of the surface electric field on the nematic orientation……Page 176
6.2.1 Basic equations of the problem……Page 177
6.2.2 First approximation……Page 179
6.2.3 Half-space approximation……Page 182
6.2.4 Finite sample limited by two identical surfaces……Page 186
6.2.5 Influence of the dielectric anisotropy on the instability……Page 191
6.2.6 Spontaneous Freedericksz transition……Page 192
Conclusions……Page 195
CHAPTER 7: EXPONENTIAL APPROXIMATION FOR THE ELECTRIC FIELD OF IONIC ORIGIN……Page 198
7.1 Non-linear Poisson-Boltzmann equation……Page 199
7.1.1 Limits of weak and strong adsorption……Page 203
7.1.2 Charge distribution and thickness of the surface layer……Page 205
7.2.1 Poisson-Boltzmann theory for a liquid submitted to an external field……Page 207
7.2.2 Limiting cases of small and large bias voltage……Page 209
7.3 Contribution to the surface energy of dielectric origin……Page 216
Conclusions……Page 220
CHAPTER 8: ADSORPTION PHENOMENON AND EXTERNAL FIELD EFFECTS: GENERAL APPROACH……Page 223
8.1 Motivation……Page 224
8.2 The model……Page 225
8.2.1 Low-voltage region……Page 228
8.2.2 High-voltage region……Page 229
8.3 The charge and field distributions……Page 230
8.4 Ionic adsorption in the absence of external field: Equilibrium distribution of charges……Page 236
8.4.1 Limits of small and large thickness……Page 238
8.4.2 Arbitrary thickness……Page 239
8.6 Effect of the adsorption energy on the anchoring energy of dielectric origin……Page 242
8.6.2 Case II: A+ = A ->*, Σ……Page 243
8.7 Contribution of the ion adsorption phenomenon to the effective anchoring energy……Page 247
8.8 Destabilizing effect of a surface electric field generated by ion adsorption on the molecular orientation of nematic liquid crystals……Page 250
9.1 The Fermi-like model……Page 257
9.2 Application: Ion adsorption in isotropic fluids……Page 262
9.2.1 Limits……Page 266
9.2.2 Numerical results……Page 270
Conclusions……Page 271
10.1.1 Continuity equation……Page 274
10.1.2 Diffusion equation……Page 275
10.1.3 No adsorption from the surfaces……Page 276
10.1.4 Adsorption from the surfaces……Page 278
10.2 Time evolution of the bulk and surface densities……Page 279
10.3 Drift current……Page 284
10.4 Relaxation time……Page 286
10.5 Time evolution of the density of ions……Page 289
10.6 Drift-diffusion phenomenon in nematic liquid crystals……Page 290
10.6.1 Drift in the presence of a non-homogeneous field in the absence of adsorption……Page 293
10.6.2 Validity of the phenomenological model……Page 297
10.7 Molecular reorientation dynamics in a nematic cell……Page 298
10.7.1 Basic equations for the electrical variables……Page 299
10.7.2 Numerical solution of the electrical equations……Page 304
10.7.3 Deformations induced by the external field……Page 312
11.1 Introduction……Page 321
11.2 The physical system and basic hypotheses……Page 323
11.3 Simple case in which the ions have the same mobility……Page 325
11.4 Effect of different anionic and cationic mobilities on the impedance spectroscopy……Page 337
11.5 Influence of the ion adsorption phenomenon on the impedance spectroscopy measurements……Page 345