• 전기화학회지
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• 제7권4호
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• pp.194-200
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• 2004

The constant correlation factors between the Temkin and the Langmuir or the Frumkin adsorption isotherms of over-potentially deposited hydrogen (OPD H) for the cathodic H2 evolution reaction (HER) at poly-Pt and Re/0.5M $H_2SO_4$ and poly-Ni/0.05 M KOH aqueous electrolyte interfaces have been experimentally and consistently found using the phase-shift method. At intermediate values of the fractional surface coverage $(\theta),\;i.e.,\;02<{\theta}<0.8$, the Langmuir and Temkin adsorption isotherms of OPD H for the cathodic HER are correlated to each other even though the adsorption conditions or processes are different from each other. At the same range of $\theta$, correspondingly, the Frumkin and Temkin adsorption isotherms of OPD H for the cathodic HER are correlated to each other. The equilibrium constants $(K_o)$ for the Temkin adsorption isotherms $({\theta}\;vs.\; E)$ are consistently ca. 10 times greater than those (K, Ko) for the corresponding Langmuir or Frumkin adsorption isotherms ($({\theta}\;vs.\; E)$. The interaction parameters (g) for the Temkin adsorption isotherms $({\theta}\;vs.\; E)$ are consistently ra. 4.6 greater than those (g) for the corresponding Langmuir or Frumkin adsorption isotherms $({\theta}\;vs.\; E)$. These numbers (10 times and 4.6) can be taken as constant correlation factors between the corresponding adsolftion isotherms (Temkin, Langmuir, Frumkin) at the interfaces. The Temkin adsorption isotherm corresponding to the Langmuir or the Frumkin adsorption isotherm, and vice versa, can be effectively verified or confirmed using the constant correlation factors. Both the phase-shift methodand constant correlation factors are useful and effective for determining or confirming the suitable adsorption isotherms (Temkin, Langmuir, Frumkin) of intermediates for sequential reactions in electrochemical systems.

• 전기화학회지
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• 제9권1호
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• pp.19-28
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• 2006

The phase-shift method for determining the Langmuir, Frumkin, and Temkin adsorption isotherms ($\theta_H\;vs.\;E$) of H for the cathodic $H_2$ evolution reaction (HER) at a Pt/0.1 M KOH solution interface has been proposed and verified using cyclic voltammetric, differential pulse voltammetric, and electrochemical impedance techniques. At the Pt/0.1 M KOH solution interface, the Langmuir and Temkin adsorption isotherms ($\theta_H\;vs.\;E$), the equilibrium constants ($K_H=2.9X10^{-4}mol^{-1}$ for the Langmuir and $K_H=2.9X10^{-3}\exp(-4.6\theta_H)mol^{-1}$ for the Temkin adsorption isotherm), the interaction parameters (g=0 far the Langmuir and g=4.6 for the Temkin adsorption isotherm), the rate of change of the standard free energy of $\theta_H\;with\;\theta_H$ (r=11.4 kJ $mol^{-1}$ for g=4.6), and the standard free energies (${\Delta}G_{ads}^{\circ}=20.2kJ\;mol^{-1}$ for $k_H=2.9\times10^{-4}mol^{-1}$, i.e., the Langmuir adsorption isotherm, and $16.7<{\Delta}G_\theta^{\circ}<23.6kJ\;mol^{-1}$ for $K_H=2.9\times10^{-3}\exp(-4.6\theta_H)mol^{-1}$ and $0.2<\theta_H<0.8$, i.e., the Temkin adsorption isotherm) of H for the cathodic HER are determined using the phase-shift method. At intermediate values of $\theta_H$, i.e., $0.2<\theta_H<0.8$, the Temkin adsorption isotherm ($\theta_H\;vs.\;E$) corresponding to the Langmuir adsorption isotherm ($\theta_H\;vs.\;E$), and vice versa, is readily determined using the constant conversion factors. The phase-shift method and constant conversion factors are useful and effective for determining the Langmuir, Frumkin, and Temkin adsorption isotherms of intermediates for sequential reactions and related electrode kinetic and thermodynamic data at electrode catalyst interfaces.

• Korean Chemical Engineering Research
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• 제54권6호
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• pp.734-745
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• 2016

This review article described the electrochemical Frumkin, Langmuir, and Temkin adsorption isotherms of over-potentially deposited hydrogen (OPD H) and deuterium (OPD D) for the cathodic $H_2$ and $D_2$ evolution reactions (HER, DER) at Pt, Ir, Pt-Ir alloy, Pd, Au, and Re/normal ($H_2O$) and heavy water ($D_2O$) solution interfaces. The Frumkin, Langmuir, and Temkin adsorption isotherms of intermediates (OPD H, OPD D, etc.) for sequential reactions (HER, DER, etc.) at electrode/solution interfaces are determined using the phase-shift method and correlation constants, which have been suggested and developed by Chun et al. The basic procedure of the phase-shift method, the Frumkin, Langmuir, and Temkin adsorption isotherms of OPD H and OPD D and related electrode kinetic and thermodynamic parameters, i.e., the fractional surface coverage ($0{\leq}{\theta}{\leq}1$) vs. potential (E) behavior (${\theta}$ vs. E), equilibrium constant (K), interaction parameter (g), standard Gibbs energy (${\Delta}G_{\theta}{^{\circ}}$) of adsorption, and rate (r) of change of ${\Delta}G_{\theta}{^{\circ}}$ with ${\theta}$ ($0{\leq}{\theta}{\leq}1$), at the interfaces are briefly interpreted and summarized. The phase-shift method and correlation constants are useful and effective techniques to determine the Frumkin, Langmuir, and Temkin adsorption isotherms and related electrode kinetic and thermodynamic parameters (${\theta}$ vs. E, K, g, ${\Delta}G_{\theta}{^{\circ}}$, r) at electrode/solution interfaces.

• 전기화학회지
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• 제15권1호
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• pp.54-66
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• 2012

The phase-shift method and correlation constants, which are unique electrochemical impedance spectroscopy techniques for studying the linear relationship between the phase shift ($90^{\circ}{\geq}-{\varphi}{\geq}0^{\circ}$) vs. potential (E) behavior for the optimum intermediate frequency ($f_o$) and the fractional surface coverage ($0{\leq}{\theta}{\leq}1$) vs. E behavior, are proposed and verified to determine the Frumkin, Langmuir, and Temkin adsorption isotherms and the related electrode kinetic and thermodynamic parameters. At Ni/0.5 M $H_2SO_4$ and 0.1M LiOH aqueous solution interfaces, the Frumkin and Temkin adsorption isotherms (${\theta}$ vs. E) of H for the cathodic hydrogen ($H_2$) evolution, interaction parameters (g), equilibrium constants (K), standard Gibbs energies (${\Delta}G^0_{\theta}$) of H adsorption, and rates of change (r) of ${\Delta}G^0_{\theta}$ with ${\theta}$ have been determined using the phase-shift method and correlation constants. A lateral repulsive interaction (g>0) between the adsorbed H species appears. The value of K in the alkaline aqueous solution is much greater than that in the acidic aqueous solution.

• 전기화학회지
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• 제16권4호
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• pp.211-216
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• 2013

At Pt(111), Pt(100), Pt, and Rh interfaces, the Frumkin adsorption isotherm of underpotentially deposited hydrogen (UPD H) and related electrode kinetic data are determined using the standard Gibbs energy of adsorption. The Temkin adsorption isotherm of UPD H correlating with the Frumkin adsorption isotherm of UPD H is readily determined using the correlation constants between the Temkin and Frumkin or Langmuir adsorption isotherms. At the Pt(111), Pt(100), Pt, and Rh interfaces, the lateral repulsive interaction between the UPD H species is interpreted using the interaction parameter for the Frumkin adsorption isotherm. The lateral repulsive interaction between the UPD H species at the Pt(111), Pt(100), Pt, and Rh interfaces is significantly different from the lateral attractive interaction between the overpotentially deposited hydrogen (OPD H) species at Pt, Ir, and Pt-Ir alloy interfaces.

• 전기화학회지
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• 제10권2호
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• pp.132-140
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• 2007

백금족/수용액 계면에서 Langmuir, Frumkin, Temkin 흡착등온식(${\theta}\;vs.\;E$)을 결정하기 위해 최적중간주파수 일 때 위상이동($0^{\circ}{\leq}-{\varphi}{\leq}90^{\circ}$) 거동($-{\varphi}\;vs.\;E$)과 표면피복율($1{\geq}{\theta}{\geq}0$) 거동(${\theta}\;vs.\;E$) 사이의 선형 관계식 연구에 관한 위상이동 방법 및 상관계수를 제안하고 증명하였다. Ir/0.1 M KOH수용액 계면에서 음극 $H_2$ 발생 반응에 관한 수소의 Langmuir 및 Temkin 흡착등온식(${\theta}\;vs.\;E$), 평형상수(Langmuir 흡착등온식: $K=3.3{\times}10^{-4}mol^{-1}$, Temkin 흡착등온식: $K=3.3{\times}10^{-3}{\exp}(-4.6{\theta})\;mol^{-1}$), 상호작용 파라미터(Temkin 흡착등온식: g=4.6), 표준자유에너지($K=3.3{\times}10^{-4}mol^{-1}$ 일 때 ${\Delta}G_{ads}^0=19.9kJ\;mol^{-1},\;K=3.3{\times}10^{-3}{\exp}(-4.6{\theta})\;mol^{-1}$ 및 $0.2<{\theta}<0.8$일 때 $16.5<{\Delta}G_{\theta}^0<23.3kJ\;mol^{-1}$)를 결정한다. 수소 흡착부위의 비균일 및 측 방향 상호작용 효과는 무시할 수 있다. ${\theta}$의 중간값 즉, $0.2<{\theta}<0.8$일 때 Langmuir 또는 Frumkin 흡착등온식과 상관관계에 있는 Temkin 흡착등온식은 상관계수를 이용하여 쉽게 결정할 수 있다. 위상이동 방법 및 상관계수는 흡착동온식(${\theta}\;vs.\;E$) 및 연관된 전극속도론과 열역학 파라미터(K, g, ${\Delta}G_{ads}^0, {\Delta}G_{\theta}^0$)를 결정하기 위한 정확하고 확실한 기술 및 방법이다.

• 청정기술
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• 제26권1호
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• pp.30-38
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• 2020

입상 활성탄에 대한 Acid Red 66의 흡착 등온선과 동력학적, 열역학적 파라미터에 대해 염료의 초기농도, 접촉시간, 온도를 흡착변수로 하여 조사하였다. 흡착평형자료는 Langmuir, Freundlich, Temkin, Redlich-Peterson 및 Temkin 등온흡착식에 적용하였다. Freundlich 등온흡착식이 가장 잘 맞았으며, 계산된 Freundlich 분리계수 값(1/n = 0.125 ~ 0.232)으로부터 입상 활성탄이 Acid Red 66을 효과적으로 처리할 수 있다는 것을 알 수 있었다. Temkin의 흡착열관련상수(B_T = 2.147 ~ 2.562 J mol^-1)는 이 공정이 물리흡착임을 나타냈다. 동력학적 실험으로부터 흡착공정은 유사 이차 반응속도식에 잘 맞았다. 입자 내 확산식에 대한 결과는 경계층 확산을 나타내는 첫 번째 직선의 기울기보다 입자내 확산을 나타내는 두 번째 직선의 기울기가 작게 나타나서 입자 내 확산이 율속단계인 것을 확인하였다. 열역학 실험으로부터 활성화 에너지는 35.23 kJ mol^-1로 흡착공정이 물리흡착공임을 확인하였다. Gibbs 자유에너지 변화(ΔG = -0.548 ~ -7.802 kJ mol^-1)와 엔탈피 변화(ΔH = +109.112 kJ mol^-1)은 각각 흡착공정이 자발적 공정 및 흡열과정임을 나타내었다. 등량흡착열은 흡착된 염료분자들의 측면상호작용을 나타내는 표면부하량이 증가함에 따라 증가하였다.

• 전기화학회지
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• 제12권1호
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• pp.26-33
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• 2009

The phase-shift method and correlation constants, i.e., the unique electrochemical impedance spectroscopy (EIS) techniques for studying the linear relationship between the behavior ($-{\varphi}$ vs. E) of the phase shift ($90^{\circ}{\geq}-{\varphi}{\geq}0^{\circ}$) for the optimum intermediate frequency and that ($\theta$ vs. E) of the fractional surface coverage ($0{\leq}{\theta}{\leq}1$), have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms of H and related electrode kinetic and thermodynamic parameters at noble metal (alloy)/aqueous solution interfaces. At a Zr/0.2 M ${H_2}{SO_4}$ aqueous solution interface, the Frumkin and Temkin adsorption isotherms ($\theta$ vs. E), equilibrium constants (K = $1.401{\times}10^{-17}\exp(-3.5{\theta})mol^{-1}$ for the Frumkin and K = $1.401{\times}10^{-16}\exp(8.1{\theta})mol^{-1}$ for the Temkin adsorption isotherm), interaction parameters (g = 3.5 for the Frumkin and g = 8.1 for the Temkin adsorption isotherm), rates of change of the standard free energy (r = $8.7\;kJ\;mol^{-1}$ for g = 3.5 and r = $20\;kJ\;mol^{-1}$ for g = 8.1) of H with $\theta$, and standard free energies ($96.13{\leq}{\Delta}G^0_{\theta}{\leq}104.8\;kJ\;mol^{-1}$ for K = $1.401{\times}10^{-17}\exp(-3.5{\theta})mol^{-1}$ and $0{\leq}{\theta}{\leq}1$ and ($94.44<{\Delta}G^0_{\theta}<106.5\;kJ\;mol^{-1}$ for K = $1.401{\times}10^{-16}\exp(-8.1{\theta})mol^{-1}$ and $0.2<{\theta}<0.8$) of H are determined using the phase-shift method and correlation constants. At 0.2 < $\theta$ < 0.8, the Temkin adsorption isotherm correlating with the Frumkin adsorption isotherm, and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are probably the most accurate, useful, and effective ways to determine the adsorption isotherms of H and related electrode kinetic and thermodynamic parameters at highly corrosion-resistant metal/aqueous solution interfaces.

• Korean Chemical Engineering Research
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• 제53권1호
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• pp.64-70
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• 2015

본 연구는 활성탄에 의한 congo red의 흡착 거동에 대해 회분식 실험을 통해 알아보았다. 흡착변수로 흡착제의 양, pH, 초기농도와 접촉시간과 온도를 사용하였다. 흡착평형자료는 Langmuir, Freundlich, Temkin 및 Dubin-Radushkevich 식에 적용하여 보았다. 평가된 Freundlich 분리계수(1/n)로부터 활성탄에 의한 congo red의 흡착공정이 적절한 처리방법이 될 수 있음을 알았고, Temkin 상수(B)와 Dubinin-Radushkevich 상수(E)로부터 물리흡착공정임을 알았다. 동력학적 실험을 통해 흡착공정이 유사이차반응속도식에 잘 일치함을 알았다. 입상활성탄에 대한 congo red의 흡착공정은 발열반응(${\Delta}H$=42.036 kJ/mol)이었고, Gibbs 자유에너지값(${\Delta}G$=-2.414~-4.596 kJ/mol)은 온도가 증가할수록 감소하였다.

• Korean Chemical Engineering Research
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• 제54권2호
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• pp.255-261
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• 2016

활성탄을 사용한 Acid Yellow 14 염료의 흡착 실험은 흡착제의 양, pH, 초기농도, 접촉시간과 온도를 흡착변수로 사용하여 수행하였다. 흡착평형자료는 Langmuir, Freundlich 및 Temkin 등온식을 사용하여 해석하였는데, Freundlich 식이 가장 좋은 일치도를 나타냈다. 평가된 Freundlich 상수(1/n=0.129~0.212)와 Langmuir 분리계수($R_L=0.202{\sim}0.243$)로부터 활성탄에 의한 Acid Yellow 14의 흡착조작은 적절한 처리방법이 될 수 있음을 알았다. Temkin의 흡착열관련상수(B)는 5.101~9.164 J/mol로 평가되어, 흡착공정이 물리흡착임을 알았다. 흡착속도실험자료를 유사일차반응속도식과 유사이차반응속도식에 적용해 본 결과, 흡착동력학은 유사이차반응속도식에 잘 맞는 것으로 나타났다. Gibbs 자유에너지(-4.81~-10.33 kJ/mol)와 엔탈피(+78.59 kJ/mol)는 흡착이 자발적이고 흡열공정으로 진행된다는 것을 나타낸다.