Defect Patterns Programing Self-Assembled By Block Copolymers Under Polygonal Confinements

Soft crystals are usually formed by the self-assembly of various molecular groups via rather weak inter-actions which are termed as nanocrystal or mesocrystal.In contrast to hard crystals,a notable feature of soft crystals is their softness.Therefore,the entropic contribution becomes non-ignorable,comparable to or even more important than the enthalpic contribution,in the free energy of soft crystals.As consequence,soft crystals are sensitively responsive to thermal fluctuations as well as external fields.On one hand,the responsiveness to thermal fluctuations increases the occurring probability of crystallographic defects.On the other hand,the re-sponsiveness to external fields offers opportunities for one to control the fabrication of soft crystals.It has been demonstrated that defects are not always harmful although they destroy the perfection of crystals by breaking the translational or rotational order.In fact,both defect-free patterns and defective structures are potentially applicable in semiconductor industry.Here we focus on the fabrication of defect patterns via the heterogeneous nucleations occurred in the two-dimensional diblock copolymer/homopolymer(AB/C)system simulated by the cell dynamics simulation(CDS)based on the time-dependent Ginzburg-Landau(TDGL)theory.An brief introduction to block copolymers(BCPs)is given in chapter one.In chapter two,we introduce two frequently-used theoretical methods on BCPs researching,i.e.self-consistent field theory(SCFT)and TDGL theory.In chapter three,we propose a simple method of fabricating defect patterns in crystalline structures,which are composed of regularly distributed defects,via heterogeneous nucleation process.The validity of this method is demonstrated by means of the nucleations of the hexagonal ordered phase from the disordered state in AB/C model system,which are induced by various regular polygonal confinements.Simulation results suggest that the defect-free hexagonal patterns are obtained in the polygons whose vertex angle is matched with the hexagonal lattice including the regular triangle and hexagon,while a variety of defect patterns are generated in the polygons with mismatched vertex angles such as square,regular pentagon and octagon.In general,the boundary of the polygons with mismatched vertex angles is able to trigger two kinds of heterogeneous nucleations,comer-and side-induced nucleations,which often result in different defect patterns.For the side-induced nucleations by a strong surface field,where each side induces a nucleation domain grain independently,regular radial defect patterns are formed with the number of radial lines equal to the number of sides and each radial line pointing to the vertex.In contrast,the defect patterns from the corner-induced nucleations by a weak surface field are more changeable because the number and orientation of the nucleated domain grains at each corner depend on the vertex angle.For the square confinement,a single crystalline grain is formed at each corner with the highest density of domains(HDD,e.g.the<10>)plane randomly aligned along one side of the corner but normal to the other side.This implies that the different combinations of orientations of the domain grains at the four corners would lead to different defect patterns including"+","?","?" and”(?)”.Interestingly,in the pentagonal confinement,the domain lattice is deformed to fit into the mismatched comer,thus leading to a single crystalline domain grain with one HDD plane at every side of the comer.As a result,the radial defect pattern with each radial line normal to the side is formed as these domain grains at the five corners meeting with each other.In contrast,in the octagonal confinement,a larger angle deviation may cause a higher energy penalty associated with the deformation of the single crystalline domain lattice.So,the single crystalline grain is split into double crystalline grains at each corner.Thus defects are enriched on the radial boundary of the twin grains.,resulting in the radial defect pattern with each radial line pointing to the vertex,which is similar to that formed by the side-induced nucleations.In chapter four,the distance between 5-7 defect pairs(or dislocations)enriched on the boundary in various defect patterns is studied.By examining the distance of defect dislocations occurred in square and regular pentagon confinements,we found that the relation between the distance of defect dislocations and the mismatched angle is in good agreement with the theoretical formula in hard materials.To confirm this relationship,we build a test model system which consists of only two domain grains with a controllable mismatched angle.The statistical results obtained in the test model system still satisfy the theoretical relation well.In summary,the theoretical relation between the distance of defect dislocations and the mismatched angle between two neighboring grains is robust for either hard or soft crystalline systems.This thesis demonstrates an efficient method of tailoring the defect distribution via the controlled heteroge-neous nucleations by the polygonal confinement,leading to the formation of interesting defect patterns.On one hand,this concept can be expanded further to program the locations of nucleation agents for more desired defect patterns that may have potential applications in many fields such as phonotic crystals and nanotechnology.On the other hand,the conclusions from this model system should hold for other crystalline systems.