• Journal of the Korean Electrochemical Society
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• v.7 no.4
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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.

• Journal of the Korean Electrochemical Society
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• v.9 no.1
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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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• v.54 no.6
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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.

• Journal of the Korean Electrochemical Society
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• v.15 no.1
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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.

• Journal of the Korean Electrochemical Society
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• v.16 no.4
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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.

• Journal of the Korean Electrochemical Society
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• v.10 no.2
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• pp.132-140
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• 2007

The phase-shift method and correlation constants for studying a linear relationship between the behavior ($-{\varphi}\;vs.\;E$) of the phase shift ($0^{\circ}{\leq}-{\varphi}{\leq}90^{\circ}$) for the optimum intermediate frequency and that (${\theta}\;vs.\;E$) of the fractional surface coverage ($1{\geq}\theta{\geq}0$) have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms (${\theta}\;vs.\;E$) at noble metal/aqueous electrolyte interfaces. At an Ir/0.1 M KOH aqueous electrolyte interface, the Langmuir and Temkin adsorption isotherms (${\theta}\;vs.\;E$), equilibrium constants ($K=3.3{\times}10^{-4}\;mol^{-1}$ for the Langmuir and $K=3.3{\times}10^{-3}{\exp}(-4.6{\theta})\;mol^{-1}$ for the Temkin adsorption isotherm), interaction parameter (g = 4.6 for the Temkin adsorption isotherm), and standard free energies (${\Delta}G_{ads}^0=19.9kJ\;mol^{-1}\;for\;K=3.3{\times}10^{-4}\;mol^{-1}$ and $16.5<{\Delta}G_{\theta}^0<23.3\;kJ\;mol^{-1}\;for\;K=3.3{\times}10^{-3}{\exp}(-4.6{\theta})\;mol^{-1}\;and\;0.2<\theta<0.8$) of H for the cathodic $H_2$ evolution reaction are determined using the phase-shift method and correlation constants. The inhomogeneous and lateral interaction effects on the adsorption of H are negligible. At the intermediate values of ${\theta},\;i.e,\;0.2<{\theta}<0.8$, the Temkin adsorption isotherm (${\theta}\;vs.\;E$) correlating with the Langmuir or the Frumkin adsorption isotherm (${\theta}\;vs.\;E$), and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are accurate and reliable techniques to determine the adsorption isotherms (${\theta}\;vs.\;E$) and related electrode kinetic and thermodynamic parameters(K, g, ${\Delta}G_{ads}^0, {\Delta}G_{\theta}^0$).

• Clean Technology
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• v.26 no.1
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• pp.30-38
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• 2020

The kinetic and thermodynamic parameters of Acid Red 66, adsorbed by granular activated carbon, were investigated on areas of initial concentration, contact time, and temperature. The adsorption equilibrium data were applied to Langmuir, Freundlich, Temkin, Redlich-Peterson, and Temkin isotherms. The agreement was found to be the highest in the Freundlich model. From the determined Freundlich separation factor (1/n = 0.125 ~ 0.232), the adsorption of Acid Red 66 by granular activated carbon could be employed as an effective treatment method. Temkin's constant related to adsorption heat (B_T = 2.147 ~ 2.562 J mol^-1) showed that this process was physical adsorption. From kinetic experiments, the adsorption process followed the pseudo-second order model with good agreement. The results of the intraparticle diffusion equation showed that the inclination of the second straight line representing the intraparticle diffusion was smaller than that of the first straight line representing the boundary layer diffusion. Therefore, it was confirmed that intraparticle diffusion was the rate-controlling step. From thermodynamic experiments, the activation energy was determined as 35.23 kJ mol^-1, indicating that the adsorption of Acid Red 66 was physical adsorption. The negative Gibbs free energy change (ΔG = -0.548 ~ -7.802 kJ mol^-1) and the positive enthalpy change (ΔH = +109.112 kJ mol^-1) indicated the spontaneous and endothermic nature of the adsorption process, respectively. The isosteric heat of adsorption increased with the increase of surface loading, indicating lateral interactions between the adsorbed dye molecules.

• Journal of the Korean Electrochemical Society
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• v.12 no.1
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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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• v.53 no.1
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• pp.64-70
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• 2015

Batch experiment studies were carried out for adsorption of congo red using granular activated carbon with various parameters such as activated carbon dose, pH, initial dye concentration, temperature and contact time. Equilibrium experimental data are fitted to the Langmuir, Freundlich, Temkin and Dubin-Radushkevich isotherm equations. From Freundlich's separation factor (1/n) estimated, adsorption could be employed as effective treatment method for adsorption of congo red from aqueous solution. Base on Temkin constant (B) and Dubinin-Radushkevich constant (E), this adsorption process is physical adsorption. Adsorption kinetics has been tested using pseudo-first order and pseudo second order models. The results followed pseudo second order model with good correlation. Adsorption process of congo red on granular activated carbon was endothermic (${\Delta}H$=42.036 kJ/mol) and was accompanied by decrease in Gibbs free energy (${\Delta}G$=-2.414 to -4.596 kJ/mol) with increasing adsorption temperature.

• Korean Chemical Engineering Research
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• v.54 no.2
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• pp.255-261
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• 2016

Adsorption experiments of Acid Yellow 14 dye using activated carbon were carried out as function of adsorbent dose, pH, initial concentration, contact time and temperature. The equilibrium adsorption data were analyzed by Langmuir, Freundlich and Temkin isotherm model. The experimental data were best represented by Freundlich isotherm model. Base on the estimated Freundlich constant (1/n=0.129~0.212) and Langmuir separation factor ($R_L=0.202{\sim}0.243$), this process could be employed as effective treatment method. The heat of adsorption of Temkin isotherm model was 5.101~9.164 J/mol indicated that the adsorption process followed a physical adsorption. Adsorption kinetics experimental data were modeled using the pseudo-first-order and pseudo-second-order kinetic equation. It was shown that pseudo-second-order kinetic equation could best describe the adsorption kinetics. Base on the negative Gibbs free energy (-4.81~-10.33 kJ/mol) and positive enthalpy (+78.59 kJ/mol) indicate that the adsorption is spontaneous and endothermic process.