• Korean Journal of Mathematics
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• 제19권2호
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• pp.129-147
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• 2011

In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.

• 상하수도학회지
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• 제14권4호
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• pp.343-349
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• 2000

Techniques such as dissolved air flotation and electroflotation, which utilize micro bubbles, are increasingly used for water and wastewater treatment. Most studies have concentrated on particle characteristics. Pretreatments that manipulate particle size and zeta potential were considered important. A recent study, which modeled the collision mechanism between micro bubbles and particles in dissolved air flotation, suggested bubble characteristics should also be important. Hydrogen micro bubbles were generated electrolytically and their zeta potentials measured under various conditions using a novel electrophoresis method. Effects of several parameters were investigated. Bubble zeta potentials were found to be pH dependent, and to have a negative value around neutral pH, becoming zero or positive at lower pH. The pH at zero zeta potential was 5.0 under study conditions. Using artificial solution and tap water, at fixed pH, bubble zeta potentials varied with solution composition. Zeta potentia]s of bubbles were affected by the types of cations and anions in solution but not by the voltage applied. These findings will help improve efficiencies of particle removal processes that utilize micro bubbles. As bubble zeta potential varies with solution composition, it needs to be measured for each composition to understand those effects, which increase removal efficiency.

• 대한전자공학회논문지
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• 제24권2호
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• pp.242-247
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• 1987

Electrophysical phenomena at the silicon semiconductor-electrolyte solution interfaces were analyzed based on the zeta potential of the electrical double layer and microelectrophoresis. The suspensions were composed of the p or n-type silicon particles suspended in the KCI or pH buffer solutions. The approximate diameter of the prepared and sampled sioicon semiconductor pardticles was 1.5\ulcorner. The sign of the zeta poetntials of the p and n-type silicon particles in the KCl and pH buffer solution was positive. A range of electrophoretic mobilities of the p and n-type silicons in the KCl solutions was 5.5-8.9x10**-4 cm\ulcornerV-sec and 4.2-7.9x10**-4cm\ulcornerV-sec, respectively. The range of zeta potentials corresponding to the electrophoretic mobilities is 70.4-114.0mV nad 53.9-101.2mV, respectively. On the other hand, a range of electrophoretic mobilities of the p and n-type silicons in the pH buffer solutions was 1.1x10**-4-2.2x10**-3cm\ulcornerV-sec and 0-2.1x10**-3cm\ulcornerV-sec, respectively. The range of zeta potentials corresponding to the electrophoretic mobilities is 14.1-281.6mV and 0-268.8mV, respectively. The zeta potentials and electrical double layers of the doped silicon semiconductors are decisively influenced by the positively charged ions in the solutions. The maximum values of the zeta potentials in the KCl solutions appeared at a concentration of about 10-\ulcorner. The isoelectric point of the n-type silicon semiconductors appeared at about a pH 7. The effect of the space charge of the doped silicon semiconductors can be neglected compare with the effect of the surface charge.

• Carbon letters
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• 제8권4호
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• pp.321-325
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• 2007

The oxygen and nitrogen enriched activated carbons were obtained from modification of commercial activated carbon by using nitric acid, sodium hydroxide and urea. Zeta-potentials of modified activated carbons were investigated in relation to copper ion adsorption. The structural properties of modified activated carbons were not so much changed, but the zeta-potentials and isoelectric points were considerably changed. The zeta-potential of nitric acid modified activated carbon was the most negative than other activated carbons in the entire pH region, and the $pH_{IEP}$ was shifted from pH 4.8 to 2.6, resulted in the largest copper ion adsorption capacities compare with other activated carbons in the range of pH 3~6.5. In case of urea modified activated carbon, copper ion adsorption was larger than that of the as-received activated carbon from pH 2 to pH 6.5 even though the $pH_{IEP}$ was shifted to pH 6.0, it was due to the coordination process operated between nitrogen functional groups and copper ion. The adsorption capacity of copper ion was much influenced by zeta-potential and $pH_{IEP}$ of carbon adsorbent.

• 대한전자공학회논문지
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• 제24권4호
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• pp.640-645
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• 1987

Surface states and interfacial phenomena at the undoped polycrystalline semiconductor particale-electrolyte interfaces were qualitatively analyzed based on the zeta potentials which were measured with microelectrophoresis measurements. The suspensions were composed of the undoped polycrystaline silicon(Si) or gallium arsenide (GaAs) semiconductor particles stalline Si and GaAs particles in the KCl electrolytes was 3.73~6.2x10**-4 cm\ulcornerV.sec and -2.3~1.4x10**-4cm\ulcornerV.sec at the same conditions, respectively. The range of zeta potentials corresponding to the electrophoretic mobilities is 47.8~80.1mV and -30.1~17.9mV, respectively. The variation of the zeta potentials of the undoped polycrystalline Si was similar to the doped crystalline Si. On the other hand, two points of zeta potential reversal occurred at the undoped polycrystalline GaAs-KCl electrolyte interfaces. The surface states of the undoped polycrystalline Si and GaAs were dominated by positively charged donor surface states. These surface states are attributed to adsorbed ion surface states (slow states) at the semiconductor oxide layer-electrolyte interfaces.

• Bulletin of the Korean Chemical Society
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• 제26권1호
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• pp.107-114
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• 2005

Molecular aggregates of surfactant molecules consisting of one or more bilayers arranged in a hollow, closed, usually spherical geometry are termed “esicles”or “iposomes” In recent years it has been found that in certain systems the vesicular structure forms spontaneously and is long lived, and it has been suggested that these structures may in fact constitute the equilibrium state in these cases (as is true of micelles) This paper deals with the mixed CMC, vesicles, phase behavior, phase transition, geometrical structure, their formation and characterization in the aqueous solutions of mixed cationic/anionic surfactants systems. TEM micrographs revealed that the vesicles were of spherical shape and that their size was of around 180 nm. The zeta potentials are positive at CGS1-rich regions and negative at SLES-rich regions. In the region where SLES/CGS1 (6/4), the zeta potentials are very small, implying that the vesicles at this surfactant ratio may be less stable. At other surfactant ratios, the vesicles are thought to be stable, supported by large absolute values of zeta potentials and little change in UV absorbance for several months.

• 대한화장품학회지
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• 제33권2호
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• pp.105-110
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• 2007

제타전위를 이용하여 이산화티탄의 분산 안정성을 평가하고 이를 통하여 분산안정도 향상에 응용하고자 하였다. 본 연구에서는 제타전위와 관련된 전기이중층, 전기영동, 등전점 및 전기 침투에 대하여 설명하였으며 측정이론을 기술하였다. H-S equation을 이용하여 수계에 분산된 미립자 이산화티탄의 pH변화에 따른 제타전위 변화를 측정하였으며 제타전위는 pH $3.0{\sim}9.0$에서 음의 값으로 측정되었다. 제타전위 값은 pH값 상승에 따라 절대값이 증가하였으며 분산액의 pH 8.0과 9.0에서는 지속적으로 분산이 유지되었다. 이를 통하여 제타전위가 이산화티탄의 분산에 영향을 미치며 제타전위의 절대값 크기가 수계에서 이산화티탄의 분산안정도에 중요한 역할을 하는 것으로 생각된다.

• 한국생물공학회:학술대회논문집
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• 한국생물공학회 2001년도 추계학술발표대회
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• pp.890-893
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• 2001

Zeta potential measurement not only can provide surface information on colloidal biomaterials but more importantly can be used in bioprocess control and products quality control. In this study, zeta potentials for intracrystalline proteins of each layers from oyster shell prepared in 1mM NaCl at different pH were measured. Also, in forming calcite crystals with intracrystalline proteins as an additive extracted from oyster shell, the zeta potentials were measured. These studies were performed to verify the primary role of intracrystalline proteins in controlling the formation, morphological development and crystallography of the biocomposite.

• Bulletin of the Korean Chemical Society
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• 제26권7호
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• pp.1083-1089
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• 2005

Most experimental studies available in the literature on filtration are based on observed average zeta potential of particles (usually 10 measurements). However, analyses of data using the average zeta potential alone can lead to misleading and erroneous conclusions about the attachment behavior because of the variation of particle zeta potentials and the heterogeneous distribution of the collector surface charge. To study characteristics of zeta potential, zeta potential distributions (ZPDs) of silica particles under 9 different chemical conditions were investigated. Contrary to many researchers’ assumptions, most of the ZPDs of silica particles were broad. The solids concentration removal was better near the isoelectric point (IEP) as many researchers have noticed, thus proper destabilization of particles is very important to achieve better particle removal in particle separation processes. While, the mean zeta potential of silica particles at a given coagulant dose was a function of particle concentration; the amount of needed coagulant for particle destabilization was proportional to the total surface charge area of particles in the suspension.

• 대한환경공학회지
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• 제37권8호
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• pp.441-449
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• 2015

본 연구에서는 시아노박테리아 배양액을 대상으로 여러 종류의 금속이온의 첨가에 의한 응집 및 응결 효과를 흡광도 또는 제타포텐셜 측정을 통하여 조사하였다. 흡광도 측정으로부터 얻은 시아노박테리아의 응결효율은 $Al^{3+}$>$La^{3+}$>$Ho^{3+}$>$Fe^{2+}$>$Ca^{2+}$ 순으로 높았으며, 특히 동일한 전하량을 갖는 +3가 금속이온의 경우, 응결 시 수반되는 금속 제거율을 측정한 결과, $Al^{3+}$>$La^{3+}$>$Ho^{3+}$ 순으로 응결효율과 상응하는 결과를 얻었다. 시아노박테리아의 제타포텐셜은 음의 값을 나타냈으며, 그 농도가 증가할수록 제타포텐셜 값도 증가하였다. 또한, 시아노박테리아 용액의 pH를 증가시킬 때 pH < 5.5 이하에서는 빠르게 제타포텐셜 값이 감소하였으나, $5.5{\leq}pH{\leq}10$ 범위에서는 거의 일정한 제타포텐셜 값($-46{\pm}1mV$)을 보였다. 일정한 시아노박테리아의 농도($A_{730}=0.25$)에서 금속이온의 농도에 따른 제타포텐셜 증가 효과는 $Al^{3+}$>$Ho^{3+}$>$La^{3+}{\gg}Mg^{2+}{\geq}Ca^{2+}{\gg}K^+$ 순으로 나타났다. 일정한 금속이온 농도에서 시아노박테리아의 농도에 따른 제타포텐셜 변화를 측정한 결과, $K^+$, $Mg^{2+}$ 및 $Ca^{2+}$이온의 경우 시아노박테리아의 농도가 증가하더라도 제타포텐셜의 변화가 미미하였다. 반면에, +3가 이온 중 $Ho^{3+}$와 $La^{3+}$이온의 경우에 시아노박테리아의 농도가 증가할수록 제타포텐셜 값이 감소하였으며, 감소율 면에서 $Ho^{3+}$이온이 $La^{3+}$이온보다는 작게 얻어졌다. 이와는 달리, $Al^{3+}$이온의 경우에는 시아노박테리아의 농도가 증가함에 따라 제타포텐셜 값이 증가하다가 감소하였다. $Al^{3+}$이온은 가수분해 중합체 생성의 영향으로 제타포텐셜 측정만으로는 응집 내지 응결 효과를 해석하기가 어려웠다.