• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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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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• v.11 no.1
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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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• v.14 no.4
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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.

• Korean Journal of Crystallography
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• v.2 no.2
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• pp.13-21
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• 1991

X-ray methods have been used to determine the chain conformation and packing of the thermotropic liquid crystalline copolyester prepared from 50% tarephthaloyl chloride(TPA) and 50% (1-phenylethyl) hydroquinone(PEHQ). The x-ray patterns of annealed melt-spun fibers contain a series of annealed melt-Pointing to a well ordered crystalline structure, despite the random sense(2 or 3-) of the 1-phenylethyl substiuttion on the TPA-hydroquinone backbone. The crystalline fiber is monoclinic with space group P2l and the unit cell has dimensions 11=12.77 A, b=10.17 A (upique axis), c=12.58 h (fiber axis). and β=90.1° and contains TPA-PEHO units of to or chains. The random substitution of 1-phenylethyl groups was modelled by placing these groups at both the 2and 3 positions and giving each a weight of one-hal(. T he structure has been refined by linked a rom least square methods(LALS) against 16 observed and 21 unobserved reflections. and had a final R value of 0.20. Packing of the side chains is effected by staggering adjacent chains along the b axis by approximately c/2, so that the side chains are interleaved. The phenyl-COO and COO-phenyl torsion angles are -6.1 and 65.6, respectively, such that the main chain phenyls are mutually inclined at 59.5 (the ester groups are assumed to be planar). These torsion angles compare very well with those for the model compounds, notably phenylbenzoate, and can be used in future analyses of the structures of more complex random sequence copolyesters.