Phase-field Simulations Of Topological Structures In Liquid Crystals

Liquid crystal is a kind of soft material.Its molecules are similar to liquid in position distribution and have fluidity.However,due to the anisotropy of its molecular shape,its orientation distribution is anisotropic,and its macroscopic properties can be controlled under the action of external field.With these changes in properties,liquid crystal has been applied in important fields since the middle of last century,and now it is the main technical scheme for flat panel display.Liquid crystal is a bridge between solid and liquid.With the in-depth study of liquid crystal,more and more novel phenomena have been discovered,such as martensitic transformation of liquid crystal system,and the use of nematic liquid crystal topological defects to control fibroblasts and neuron cells.With the in-depth study of liquid crystal,new phenomena will be discovered and new technologies will be developed.Therefore,the study of liquid crystal is still an important direction of the development of science and technology.Defects in liquid crystal are important factors affecting its quality,and have topological properties.The study of liquid crystal involves physics,polymer chemistry,topology and other disciplines.Up to now,the research on liquid crystal,especially on the action rule of defects,has not been perfected.In this dissertation,we will use the phase-field method to study the topological phenomena in liquid crystals in the nematic phase.Firstly,a phase-field mondel for simulations of liquid crystal systems was developed based on the Landau-de Gennes theory.And then the model was used to simulate the topological charge interactions in a thin film of a nematic phase liquid crystal,and the directed sagittal field distribution of the nematic phase liquid crystal continuum to study the interactions between the spontaneously generated topological charges in the disk-shaped liquid crystal films.The computational results verify that the two-dimensional topological charge interactions follow the inversely proportional law of distance,which is different from the distance squared inverse relationship of the three-dimensional topological charge interactions.In this part,the "Coulomb's law" for two-dimensional nematic liquid crystals was obtained.Secondly,the size effect of the optimal distance between topological charges was investigated using the phase-field model of nematic liquid crystal.The nonlinear relationship between optimal distance and diameter of the system was obtained from the simulation results of liquid crystal films with different disks diameters.The results show that due to the large ratio of boundary length and the area for small radius liquid crystal disks,the boundary anchoring energy dominates the total free energy,which can affect the optimal distance between topological charges.Finally,pairwise generation and annihilation of topological charge were observed during the dynamic process of the above two parts of simulations.The algebraic sum of all topological charges values remained constant-conserved-during generation and annihilation,and this conserved value was determined by the boundaries of the liquid crystal system.The integral pointing to the inner and outer boundaries of the sagittal system solely determines the conserved value of topological charges within the boundary loop in this relationship.In this part,the"Ampere's loop theorem" in two-dimensional nematic liquid crystals was obtained,in which the law of conservation is universal and applicable to other similar liquid crystal systems.To summarize,the "Coulomb's law" for the quasi-electric fields and the"Ampere's law" for the quasi-electric magnetic fields of two-dimensional liquid crystal systems were obtained through the simulation of the nematic liquid crystal systems.The interacting force field and magnetic field were unified in the oriented,fluid medium of the columnar liquid crystal,and the symmetry and continuity of the orientation of the medium can be obtained by the two "quasi-fields".Additional part,firstly,a model for random walk simulation based on the Langevin equation was developed to simulate the dynamic diffusion process of magnetic particles within soft matter materials.And this model was used to study the hybridization of magnetic nanoparticles in a functional gradient material,to find the method to separately regulate the concentration of magnetic particles at both ends inside the soft material gel matrix.Secondly,this model was used to simulate programmable arrays of hybrid magnetic microparticles and to calculate the volumetric force distribution of the three microparticles under different external fields.In collaboration with experiments,the preparation of programmable microcolumn arrays was simulated,and the stress distribution,shape variables,and deflections were solved based on MATLAB finite element method and compared with experimental values.Lastly,we introduce the superhydrophobic transport device and micro soft manipulator for the preparation of programmable micro-column arrays.In appendix,a collection of visualization tools for post-processing phase-field data-DomainPub-was developed,whose features include visualizations of domain structure,3D vector field,free energy surface,and simulations of liquid crystal polarizer display,Multi-CPU parallel computing,GPU accelerating,batch processing,and video producing are all supported.