• 대한수학회보
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• 제57권4호
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• pp.909-919
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• 2020

The 4-dimensional solvable Lie group Sol₀⁴ does not admit a lattice. The purpose of this paper is two-fold. We study poly-crystallographic groups of Sol₀⁴, and then we study Nielsen fixed point theory on the spaces modeled on Sol₀⁴.

• Macromolecular Research
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• 제11권1호
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• pp.14-18
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• 2003

Grafting of glycidyl methacrylate (GMA) upon coralline hydroxyapatite in conjugation with demineralized bone matrix (CHA-DBM) using equal molar ratio of potassium persulfate/sodium metabisulfite redox initiating system was investigated in aqueous medium. The optimum reaction condition was standardized by varying the concentrations of backbone, monomer, initiator, temperature and time. The results obtained imply that the percent grafting was found to increase initially and then decrease in most of the cases. The optimum temperature and time were found to be 50 $^{\circ}C$ and 180 min, respectively, to obtain higher grafting yield. Fourier transform infrared (FT-IR) spectroscopy and X-ray powder diffraction (XRD) method were employed for the proof of grafting. The FT-IR spectrum of grafted CHA-DBM showed epoxy groups at 905 and 853 $cm^{-1}$ / and ester carbonyl group at 1731 $cm^{-1}$ / of poly(glycidyl methacrylate) (PGMA) in addition to the characteristic absorptions of CHA-DBM, which provides evidence of the grafting. The XRD results clearly indicated that the crystallographic structure of the grafted CHA-DBM has not changed due to the grafting reaction. Further, no phase transformation was detected by the XRD analysis, which suggests that the PGMA is grafted only on the surface of CHA-DBM backbone. The grafted CHA-DBM will have better functionality because of their surface modification and hence they may be more useful in coupling of therapeutic agents through epoxy groups apart from being used as osteogenic material.

• Macromolecular Research
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• 제14권4호
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• pp.408-415
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• 2006

Temperature-dependent, wide-angle, x-ray diffraction (WAXD) patterns and infrared (IR) spectra were measured for biodegradable poly(3-hydroxybutyrate) (PHB) and its copolymers, poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) P(HB-co-HHx) (HHx=2.5, 3.4, 10.5, and 12 mol%), in order to explore their crystal and lamellar structure and their pattern of C-H...O=C hydrogen bonding. The WAXD patterns showed that the P(HB-co-HHx) copolymers have the same orthorhombic system as PHB. It was found from the temperature-dependent WAXD measurements of PHB and P(HB-co-HHx) that the a lattice parameter is more enlarged than the b lattice parameter during heating and that only the a lattice parameter shows reversibility during both heating and cooling processes. These observations suggest that an interaction occurs along the a axis in PHB and P(HB-co-HHx). This interaction seems to be due to an intermolecular C-H...O=C hydrogen bonding between the C=O group in one helical structure and the $CH_3$ group in the other helical structure. The x-ray crystallographic data of PHB showed that the distance between the O atom of the C=O group in one helical structure and the H atom of one of the three C-H bonds of the $CH_3$ group in the other helix structure is $2.63{\AA}$, which is significantly shorter than the sum of the van der Waals separation ($2.72{\AA}$). This result and the appearance of the $CH_3$ asymmetric stretching band at $3009 cm^{-1}$ suggest that there is a C-H...O=C hydrogen bond between the C=O group and the $CH_3$ group in PHB and P(HB-co-HHx). The temperature-dependent WAXD and IR measurements revealed that the crystallinity of P(HB-co-HHx) (HHx =10.5 and 12 mol%) decreases gradually from a fairly low temperature, while that of PHB and P(HB-co-HHx) (HHx = 2.5 and 3.5 mol%) remains almost unchanged until just below their melting temperatures. It was also shown from our studies that the weakening of the C-H...O = C interaction starts from just above room temperature and proceeds gradually increasing temperature. It seems that the C-H...O=C hydrogen bonding stabilizes the chain holding in the lamellar structure and affects the thermal behaviour of PHB and its copolymers.

• 한국결정학회지
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• 제2권2호
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• pp.13-21
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• 1991

50% terephthaloyl chloride(TPA)와 50%(1-phenylethyl) hydroquinone(PEHQ)으로부터 합성된 열 액정폴리에스터 poly(1-phenylethyl-p-phenylene-terephthalate)의 chalk conformation 및 packing 상태를 X-선 회절법을 이용하여 해석하였다. 단위세포상수는 a=12.77 A, b=10.17 A(unlque axis), c=12.58 A (fiber axis), β=90.1°, 그리고 공간군은 P2l 이고 단사정계이며 Z:4 이었다. 미세구조는 주쇄상의 Phenyl-COO 그리고 COO-Phenyl 평면간의 그리고 주축과 측쇄간의 torsion angle 들을 중심으로 37개의 회절반점에 대해 Linked Atom Least Square(LALS) 방법을 이용하여 해석하였으며, 1-phenylethyl 치환체는 ortho-와 met a위치에 각각 확률적으로 0.5의 가중치를 부여함에 의해 구조적으로 모델링 되었다. 주쇄상의 Phenyl-COO그리고 Phenyl-COO평면간의 torsion angle은 각각 -6.1°와 65.6°로 주어졌으며 결국 주축상의 Phenol 평면들은 서로 59.5°로 엇갈려 주축을 형성하고 있음을 알 수 있었다. (단 ester, COO-, 기는 평면으로 가정되었다.)