Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes's free energy that reduces a strong first order transition, and...Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes's free energy that reduces a strong first order transition, and set up adata base of free energy calculated by means of Tao-Sheng Lin's extended molecular field theory that can explain theexperiments of the equilibrium properties of nematic liquid crystal very well. Then we use the free energy method oflattice Boltzmann developed by Oxford group to study the phase decomposition, pattern formation in the flow of theliquid crystal near transition temperature.展开更多
For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C...For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0,T),W1,n). For the hydrodynamic flow (u,d) of nematic liquid crystals in dimensions n = 2 or 3, it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2, u ∈ Lt∞ L2x∩L2tHx1, ▽P∈ Lt4/3 Lx4/3 , and ▽d∈ L∞t Lx2∩Lt2Hx2; or (ii) for n = 3, u ∈ Lt∞ Lx2∩L2tHx1∩ C([0,T),Ln), P ∈ Ltn/2 Lxn/2 , and ▽d∈ L2tLx2 ∩ C([0,T),Ln). This answers affirmatively the uniqueness question posed by Lin-Lin-Wang. The proofs are very elementary.展开更多
Poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) (PBDT), a kind of liquid-crystalline (LC) molecule, has high molecular weight, negative charge and a semi-rigid structure. The aqueous solution of PBDT show...Poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) (PBDT), a kind of liquid-crystalline (LC) molecule, has high molecular weight, negative charge and a semi-rigid structure. The aqueous solution of PBDT shows nematic liquid crystalline state above a critical PBDT concentration, CLC*, of 2 wt%-3wt%. Different from the flexible polyelectrolyte, PBDT shows a variety of self-assembling structures in aqueous solution with and without salt due to the semi-rigid nature and highly charged property. In addition, the hydrogels with ordered structure are developed by polymerizing a cationic monomer N-[3-(N,N-dimethylamino) propyl] acrylamide methyl chloride quarternary (DMAPAA-Q) in the presence of a small amount of PBDT below the CLC*. During the polymerization of cationic monomer, the polycations form a complex with semi-rigid PBDT through electrostatic interaction; these complexes self-assemble into ordered structures that are frozen in the hydrogel. Several different structures, including the anisotropic, dual network-like structure, and cylindrically symmetric structure, with various length scales from micrometer to millimeter, are observed. The hydrogels with ordered liquid crystalline assemblies and particular optical properties should promise applications in many fields, such as in bionics, tissue engineering, and mechano-optical sensors.展开更多
文摘Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes's free energy that reduces a strong first order transition, and set up adata base of free energy calculated by means of Tao-Sheng Lin's extended molecular field theory that can explain theexperiments of the equilibrium properties of nematic liquid crystal very well. Then we use the free energy method oflattice Boltzmann developed by Oxford group to study the phase decomposition, pattern formation in the flow of theliquid crystal near transition temperature.
基金supported by the National Science Foundations (Nos. 0700517, 1001115)
文摘For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0,T),W1,n). For the hydrodynamic flow (u,d) of nematic liquid crystals in dimensions n = 2 or 3, it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2, u ∈ Lt∞ L2x∩L2tHx1, ▽P∈ Lt4/3 Lx4/3 , and ▽d∈ L∞t Lx2∩Lt2Hx2; or (ii) for n = 3, u ∈ Lt∞ Lx2∩L2tHx1∩ C([0,T),Ln), P ∈ Ltn/2 Lxn/2 , and ▽d∈ L2tLx2 ∩ C([0,T),Ln). This answers affirmatively the uniqueness question posed by Lin-Lin-Wang. The proofs are very elementary.
基金supported by a Grant-in-Aid for the Specially Promoted Research (18002002) from the Ministry of Education, Science, Sports and Culture of Japan
文摘Poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) (PBDT), a kind of liquid-crystalline (LC) molecule, has high molecular weight, negative charge and a semi-rigid structure. The aqueous solution of PBDT shows nematic liquid crystalline state above a critical PBDT concentration, CLC*, of 2 wt%-3wt%. Different from the flexible polyelectrolyte, PBDT shows a variety of self-assembling structures in aqueous solution with and without salt due to the semi-rigid nature and highly charged property. In addition, the hydrogels with ordered structure are developed by polymerizing a cationic monomer N-[3-(N,N-dimethylamino) propyl] acrylamide methyl chloride quarternary (DMAPAA-Q) in the presence of a small amount of PBDT below the CLC*. During the polymerization of cationic monomer, the polycations form a complex with semi-rigid PBDT through electrostatic interaction; these complexes self-assemble into ordered structures that are frozen in the hydrogel. Several different structures, including the anisotropic, dual network-like structure, and cylindrically symmetric structure, with various length scales from micrometer to millimeter, are observed. The hydrogels with ordered liquid crystalline assemblies and particular optical properties should promise applications in many fields, such as in bionics, tissue engineering, and mechano-optical sensors.
