A Generalized Theoretical Model for the Relationship Between Critical Micelle Concentrations, Pressure, and Temperature for Surfactants,Journal of Surfactants and Detergents

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A Generalized Theoretical Model for the Relationship Between Critical Micelle Concentrations, Pressure, and Temperature for Surfactants
Journal of Surfactants and Detergents ( IF 1.6 ) Pub Date : 2019-11-28 , DOI: 10.1002/jsde.12360
Sudharsan Thiruvengadam _{1,

2} , Matthew Murphy ₂ , Jei Shian Tan ₂ , Karol Miller ₁

Affiliation

Directional solvent extraction (DSE) has been gaining interest as a water treatment technology in recent years. DSE utilizes the process of micellization for the purposes of species separation between water and complex chemical systems. In this article, we develop a conformal geometric algebra‐based formulation that models surfactants, their solubilities, and critical micelle concentration (CMC), with relation to temperature and pressure. Molecules are represented as spatially distributed networks embedded in R^4,1 space, and the mathematical characterizations of these molecules are shown to be effective in modelling CMC as a function of temperature and pressure. One of the contributions of this work is the utilization of this formulation to develop a governing expression, in the form of a three‐dimensional relationship, between CMC, pressure, and temperature for a general surfactant. In prior works, the CMC–temperature plane and CMC–pressure plane expressions have been extensively documented for sodium alkyl sulfates. In this work, we extend the formulation to model the CMC of decanoic acid, sodium octyl sulfate, sodium decyl sulfate, sodium dodecyl sulfate, and sodium tetradecyl sulfate. Using this theoretical model, a relationship between CMC and the directional solubility of water in a surfactant is determined. Directional solubility is related to temperature and pressure, and on this basis, we devise a directional solubility–pressure–temperature expression for an arbitrary surfactant to improve the state of the art for DSE. From this expression, we propose a novel isothermal DSE process for water treatment.

中文翻译：

表面活性剂临界胶束浓度，压力和温度之间关系的广义理论模型

近年来，定向溶剂萃取（DSE）作为水处理技术已引起人们的兴趣。DSE利用胶束化过程来实现水与复杂化学系统之间的物种分离。在本文中，我们开发了一种基于保形几何代数的公式，该公式可对表面活性剂，其溶解度和临界胶束浓度（CMC）随温度和压力进行建模。分子表示为嵌入在R ^4,1中的空间分布网络空间，以及这些分子的数学特征在根据温度和压力对CMC进行建模方面显示出了有效的作用。这项工作的贡献之一是利用该配方开发了一种通用表面活性剂的CMC，压力和温度之间的三维关系形式的主导表达。在以前的工作中，对于烷基硫酸钠，已经广泛记录了CMC温度平面和CMC压力平面的表达式。在这项工作中，我们扩展了公式以模拟癸酸，辛基硫酸钠，癸基硫酸钠，十二烷基硫酸钠和十四烷基硫酸钠的CMC。使用该理论模型，可以确定CMC与水在表面活性剂中的定向溶解度之间的关系。定向溶解度与温度和压力有关，在此基础上，我们设计了任意表面活性剂的定向溶解度-压力-温度表达式，以改善DSE的技术水平。根据该表达式，我们提出了一种新颖的等温DSE工艺用于水处理。

更新日期：2019-11-28

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