• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.215-223
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• 2009

The helicoidal surfaces with pointwise 1-type or harmonic gauss map in Euclidean 3-space are studied. The notion of pointwise 1-type Gauss map is a generalization of usual sense of 1-type Gauss map. In particular, we prove that an ordinary helicoid is the only genuine helicoidal surface of polynomial kind with pointwise 1-type Gauss map of the first kind and a right cone is the only rational helicoidal surface with pointwise 1-type Gauss map of the second kind. Also, we give a characterization of rational helicoidal surface with harmonic or pointwise 1-type Gauss map.

• Polymer(Korea)
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• v.30 no.4
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• pp.338-349
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• 2006

Fully or nearly fully(8-cholesteryloxycarbonyl)heptanoated polysaccharide derivatives were synthesized by reacting cellulose, amylose, chitosan, chitin, alginic acid, pullulan or amylopectin with (8-cholesteryloxycarbonyl)heptanoyl chloride (CH8C), and their thermotropic liquid crystalline behaviors were investigated. Like in the case of CH8C, all the polysaccharide derivatives formed monotropic cholesteric phases with left-handed helicoidal structures whose optical pitches $({\lambda_m}'s)$ decrease with increasing temperature. Amylopectin derivative also formed a monotropic cholesteric phase with lefthanded helicoidal structures but, in contrast with the other derivatives, did not display reflection colors over the full cholesteric range, suggesting that the helicoidal twisting power of the cholesteryl group highly depends on the branched structure in amylopectin. The thermal stability and degree of order in the mesophase, the magnitude of ${\lambda}_m$ at the same temperature, and the temperature dependence of the ${\lambda}_m$ observed for polysaccharide derivatives were entirely different from those reported for the polymers in which the cholesteryl groups are attached to flexible or semiflexible backbones through flexible spacers. The results were discussed in terms of the difference in the chemical structures of the main and side chains and flexibility of the main chain.

• Polymer(Korea)
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• v.31 no.1
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• pp.58-67
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• 2007

Fully cholesteryloxycarbonated and (8-cholesteryloxycarbonyl) heptanoated disaccharide derivatives were synthesized by reacting cellobiose, maltose, and lactose with cholesteryl chloroformate or 8- cholesteryloxycarbonylheptanoyl chloride, and their thermotropic liquid crystalline properties were investigated. All the cholesteryloxycarbonated derivatives (CH1DSs) formed enantiotropic cholesteric phases, whereas all the (8-cholesteryloxycarbonyl) heptanoated derivatives (CH8DSs) exhibited monotropic cholesteric phases with left-handed helicoidal structures whose optical pitches (${\lambda}m's$) decrease with increasing temperature. All the CH1DSs, contrast with the CH8DSs, did not display reflection colors over the full cholesteric range, suggesting that the helicoidal twisting power of the cholesteryl group highly depends on the length of the spacer joining the cholesteryl group to the disaccharide chain. The thermal stability and degree of order in the mesophase and the temperature dependence of the ${\lambda}m$ observed for EH8DSs were entirely different from those reported for the cholesterol-bearing dimers and triplet and the (8-cholesteryloxycarbonyl) heptanoated polysaccharide derivatives. The results were discussed in terms of the difference in the number of the mesogenic units per mole of repeating unit and the flexibility of the main chain.

• Polymer(Korea)
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• v.28 no.1
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• pp.41-50
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• 2004

A new hydroxypropyl chitosan capable of forming a thermotropic liquid crystalline phase and two kinds of derivatives based on the hydroxypropyl chitosan (6-cholesteryloxycarbonylpentoxypropyl) chitosans (CHPCTs) and acrylic acid esters of CHPCT (CHPCTEs) were synthesized. The crosslinked films with liquid crystalline order were also prepared by photocrosslinking CHPCTE in mesophase. The liquid crystalline properties for all the samples and the swelling behavior of the crosslinked samples in acetone were investigated. In contrast with the hydroxypropyl chitosan, all the uncrosslinked cholesteryl-bearing samples farmed monotropic cholesteric phases with left-handed helicoidal structures and exhibited reflection colors over the full cholesteric range. This is the first report of a thermotropic cholesteric liquid crystalline chitosan derivative with reflection bands in the visible region. Both the optical pitches (λ$\_$m/'S) of CHPCT and CHPCTE decrease with temperature or with cholesteryl content at a given temperature. However, the λ$\_$m/ of CHPCT was larger than that of CHPCTE at the same temperature and at the same cholesteryl content. All the crosslinked samples did not display reflection colors, indicating that the cholesteric structure of CHPCTE significantly changes upon crosslinking. The two-dimentional anisotropic swelling characteristic of liquid crystalline networks was observed for all the crosslinked samples.

• Polymer(Korea)
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• v.31 no.4
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• pp.356-367
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• 2007

Three kinds of amylose derivatives such as: cholesteryloxycarbonated amyloses(CAMs) with degree of esterification(DE) ranging from 1.8 to 3, (6-cholesteryloxycarbonyl)pentanoated amyloses(PAMs) with DE ranging from 0.3 to 3, and fully cholesteryloxycarbonated PAMs(CPAMs) were synthesized, and their thermotropic liquid crystalline properties were investigated. CAMs with $DE{\geq}2.6$, PAM with DE=1.6 and all the CPAMs formed enantiotropic cholesteric phases, whereas PAM with $DE{\geq}2.2$ exhibited monotropic cholesteric phases. PAM with $DE{\geq}2.2$ and CPAMs with (6-cholesteryloxycarbonyl)pentanoyl DE (DS) more than 1.0 formed cholesteric phases with left-handed helical structures whose optical pitches (${\lambda}_{m'}s$) decrease with increasing temperature. However, the ${\lambda}_{m'}s$ of these samples decreased with increasing DS at the same temperature. On the other hand, CAMs, PAM with DE=1.6, and CPAM with DS=0.3 did not display reflection colors over the full cholesteric range, suggesting that the helicoidal twisting power of the cholesteryl group highly depends on the length of the spacer joining the cholesteryl group to the main chain and DS. The thermal stability and degree of order in the mesophase observed for the amylose derivatives highly depended on DE or DS. The results were discussed in terms of the difference ul the hydrogen bond, the internal plasticization, and the decoupling of the motion of side group with the main chain.

• Polymer(Korea)
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• v.28 no.1
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• pp.92-102
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• 2004

(6-Cholesteryloxycarbonylpentoxypropyl)celluloses (CHPCs) with degree of esterification (DE) ranging from 2.25 to 2.91 were synthesized by reacting hydroxypropyl cellulose with 6-cholesteryloxycarbonylpentanoyl chloride. The acrylic esters of CHPCs (CHPCEs) and their photocrosslinked films with liquidcrystalline order were also synthesized. The thermotropic properties of mesophase for both uncrosslinked and crosslinked samples and the swelling behavior of the crosslinked samples in acetone were investigated. The hydroxypropyl cellulose exhibited an enantiotropic cholesteric phas, while all the uncrosslinked cholesterylbearing samples exhibited a monotropic cholesteric phases; the 6-cholesteryloxycarbonylpentanoyl chloride also showed a monotropic smectic phase. The hydroxypropyl cellulose formed a right-handed helix whose optical pitch (λ$\sub$m/) increases with temperature, whereas all the uncrosslinked derivatives farmed left-handed helices whose λ$\sub$m/'s decreased with temperature. The thermal stability of the mesophase and the magnitude of λ$\sub$m/ at the same temperature for both CHPCs and CHPCEs decreased with increasing DE. All the crosslinked samples, in constrast with CHPCEs, did not display reflection colors but exhibited an anisotropic swelling characteristic of crosslinked gel retaining liquid-crystalline order.

• Polymer(Korea)
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• v.25 no.2
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• pp.279-292
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• 2001

Two kinds of (hydroxypropyl)cellulose(HPCs) with different molar substitution (MS) and three types of derivatives based on the HPCs: (acetoxypropyl)celluloses, (ethoxypropyl)celluloses, and (cyanoethoxyprofyl)celluloses were synthesized, and their thermal and mesomorphic properties were investigated. All samples, which exhibit cholesteric reflection colours at room temperature, formed right-handed helicoidal structures whose optical pitches (λ$_{ms}$ ) increase with temperature. However, the isotropization ($T_{i}$) and glass temperatures, the magnitude of λ$_{m}$ of the mesophase at the same temperature, and the temperature dependence of λ$_{m}$ of the investigated derivatives highly depended on MS and the length and structure of the side chain introduced in HPC. The results were discussed in terms of the difference in the polarity and flexibility of the substituents and the distance between the main chains. For all derivatives, Am values approached infinity at temperatures above the $T_{i}$, of the mesophase, and no reversal in the sense of the pitch with temperature was detected.