Viscoelastic properties of bis(phenyl)fluorene‐based cardo polymers with different chemical structure

Viscoelastic properties of urethane and ester conjugation cardo polymers that contain fluorene group, 9,9‐bis(4‐(2‐hydroxyethoxy)phenyl)fluorene (BPEF), were investigated. As for the urethane‐type cardo polymers containing BPEF in the main chain, it had a high glass‐transition temperature (T_g), which was observed as the α dispersion on viscoelastic measurement, and its temperature depended on the chemical structure of the spacing unit, such as toluene diisocyanate (TDI), 4,4′‐methylene diphenyl diisocyanate (MDI), methylene dicycloexyl diisocyanate (CMDI), and hexamethylene diisocyanate (HDI). Moreover, the T_g of urethane‐type cardo copolymers with various cardo contents increased with an increase of cardo content. Owing to the increase of T_g of cardo polymers, another molecular motion can be measured at the temperature between the α and β dispersion that was assigned to the molecular motion of urethane conjugation unit around 200 K, and it was referred to as the α_sub dispersion. The peak temperature of the α_sub dispersion was influenced by the chemical structure of the spacing unit, but it did not change for the cardo polymer containing the same spacing unit. Consequently, it was deduced that the α_sub dispersion was originated in the subsegmental molecular motions of the cardo polymers. Ester‐type cardo polymer had higher T_g in comparison with noncardo polymer that consisted of dimethyl groups (BPEP) instead of BPEF as well. The α_sub dispersion was also measured at the temperature between the α and β dispersion, which was assigned to the molecular motion of ester conjugation unit, around 220 K. For ester cardo polymer, the γ dispersion was measured in a low‐temperature region around 140 K, and it was due to a small unit motion in the ester‐type cardo polymers, such as ethoxyl unit, ? C₂H₄O? . Moreover, the intensity of the γ dispersion of noncardo polymer was higher than that of cardo polymer, which means the molecular motion was much restricted by the cardo structure of BPEF. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2259–2268, 2005     

A Coset-Type Construction for the Deformed Virasoro Algebra

An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra U_q(sl₂). A similar construction is proposed for the elliptic algebra A_q,p(sl₂).     

Solvable lattice models related to the vector representation of classical simple Lie algebras

A series of solvable lattice models with face interaction are introduced on the basis of the affine Lie algebraX _n ⁽¹⁾ =A _n ⁽¹⁾ ,B _n ⁽¹⁾ ,C _n ⁽¹⁾ ,D _n ⁽¹⁾ . The local states taken on by the fluctuation variables are the dominant integral weights ofX _n ⁽¹⁾ of a fixed level. Adjacent local states are subject to a condition related to the vector representation ofX _n . The Boltzmann weights are parametrized by elliptic theta functions and solve the star-triangle relation.     

TheA n /(1) face models

Presented here is the construction of solvable two-dimensional lattice models associated with the affine Lie algebraA _n ^/(1) and an arbitrary pair of Young diagrams. The models comprise two kinds of fluctuation variables; one lives on the sites and takes on dominant integral weights of a fixed level, the other lives on edges and assumes the weights of the representations ofsl(n+1, C) specified by Young diagrams. The Boltzmann weights are elliptic solutions of the Yang-Baxter equation. Some conjectures on the one point functions are put forth.     

Constraints in the variational principle for stationary states

Constraints in the variational principle for stationary states (VPSS) are classified in accordance with Dirac’s constrained classical mechanics and the time-dependent variational principle (TDVP). All of the VPSS constraints are required to belong to the first-class TDVP as constants of motion to ensure the real-valuedness of the Lagrange multipliers. The VPSS constraints are further classified as either first-class or second-class. The first-class VPSS constraints are constants of variation with symmetry-adapted wave functions. If the representation basis for the constraint operators is incomplete, however, the first-class VPSS constraints lead to broken-symmetry solutions. The nondegenerate energies of \({}^2E'\) at the \(D_{3h}\) geometry in the Jahn–Teller distortion of H\(_3\) are presented as an example of a problem with broken-symmetry. An ad hoc adjustment is suggested by considering the second-class pseudo-VPSS constraints with new adiabatic parameters.     

Enhancement of optical birefringence in tellurite glasses containing silver nanoparticles induced via thermal poling

Wavelength-selective enhancement of optical birefringence has been observed in a tellurite glass containing silver nanoparticles (Ag NPs) induced via thermal poling. The birefringence appears as an optical rotation of linearly polarized light; a large optical rotation is observed at around the wavelength of localized surface plasmon resonance (LSPR) of Ag NPs. The optic axis is oriented along the electric field applied during the thermal poling, suggesting that birefringence induced in the glass matrix through the thermal poling is drastically enhanced by the NPs at around the LSPR. Because of the birefringence of the matrix, the wavelength of LSPR shifts depending on the polarization state of the incident light, which in turn induces the polarization dependence of the real part of the refractive index via the Kramers–Kronig relation.     

Second-harmonic generation in thermally poled chalcohalide glass

Second-harmonic generation in 60GeS(2)-20Ga(2)S(3)-20KBr chalcohalide glass was investigated by the thermal poling method. A large second-order nonlinear susceptibility, as high as 7.0 pm/V, was obtained in a poled sample by Maker fringe analysis. We believe this to be the first time that a clear second-harmonic wave was observed in chalcohalide glasses containing large amount of alkali ions (6.25 at. %). Such observation is of great potential use in all optical waveguide devices.