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The Kiselev isotherm for adsorption at the liquid-solid interface: Solving the mystery of negative equilibrium constants
Journal of Molecular Liquids ( IF 6 ) Pub Date : 2021-09-25 , DOI: 10.1016/j.molliq.2021.117674
Khim Hoong Chu 1
Affiliation  

Equilibrium data for aqueous adsorption systems are often correlated using isotherm models originally developed for adsorption at the gas-solid interface. A prominent example is the Langmuir isotherm which has been used in thousands of investigations to describe adsorption of dissolved substances at the liquid-solid interface. Another example is the Kiselev isotherm, which was proposed to account for adsorption at the gas-solid interface when adsorbate-adsorbate interactions are significant. Researchers who applied the Kiselev isotherm to adsorption data for liquid-solid systems were puzzled by the fact that data fittings in most cases returned negative numerical values for the adsorbate-adsorbate association equilibrium constant. It is shown in the present study that the problem of obtaining a negative equilibrium constant is a direct consequence of misapplications of the Kiselev isotherm. In all previous studies, the Kiselev isotherm was used to describe type I isotherms which are always convex upward. Because the concept of adsorbate-adsorbate interactions is incompatible with a type I isotherm, using the Kiselev isotherm to fit data of type I will return a negative association equilibrium constant which is physically nonsensical. The Kiselev isotherm was devised to account for type V isotherms exhibiting a sigmoid or S-shaped data trend. It will return a positive association equilibrium constant if it is applied to a type V isotherm.



中文翻译:

液固界面吸附的基谢列夫等温线:解开负平衡常数之谜

水性吸附系统的平衡数据通常使用最初为气固界面吸附而开发的等温线模型相关联。一个突出的例子是朗缪尔等温线,该等温线已在数以千计的研究中用于描述溶解物质在液固界面的吸附。另一个例子是 Kiselev 等温线,当吸附质 - 被吸附质相互作用显着时,它被提议用于解释气固界面处的吸附。将 Kiselev 等温线应用于液-固系统吸附数据的研究人员对大多数情况下数据拟合返回吸附质-吸附质缔合平衡常数的负数值这一事实感到困惑。本研究表明,获得负平衡常数的问题是误用 Kiselev 等温线的直接后果。在之前的所有研究中,Kiselev 等温线用于描述始终向上凸出的 I 型等温线。由于吸附质-吸附质相互作用的概念与 I 型等温线不相容,因此使用 Kiselev 等温线拟合 I 型数据将返回负关联平衡常数,这在物理上是无意义的。设计 Kiselev 等温线是为了说明 V 型等温线表现出 sigmoid 或 S 形数据趋势。如果将其应用于 V 型等温线,它将返回正关联平衡常数。Kiselev 等温线用于描述始终向上凸出的 I 型等温线。由于吸附质-吸附质相互作用的概念与 I 型等温线不相容,因此使用 Kiselev 等温线拟合 I 型数据将返回负关联平衡常数,这在物理上是无意义的。设计 Kiselev 等温线是为了说明 V 型等温线表现出 sigmoid 或 S 形数据趋势。如果将其应用于 V 型等温线,它将返回正关联平衡常数。Kiselev 等温线用于描述始终向上凸出的 I 型等温线。由于吸附质-吸附质相互作用的概念与 I 型等温线不相容,因此使用 Kiselev 等温线拟合 I 型数据将返回负关联平衡常数,这在物理上是无意义的。设计 Kiselev 等温线是为了说明 V 型等温线表现出 sigmoid 或 S 形数据趋势。如果将其应用于 V 型等温线,它将返回正关联平衡常数。设计 Kiselev 等温线是为了说明 V 型等温线表现出 sigmoid 或 S 形数据趋势。如果将其应用于 V 型等温线,它将返回正关联平衡常数。设计 Kiselev 等温线是为了说明 V 型等温线表现出 sigmoid 或 S 形数据趋势。如果将其应用于 V 型等温线,它将返回正关联平衡常数。

更新日期:2021-09-27
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