Thermodynamic and Kinetic Foundations of the Micellization Theory: 5. Hierarchy of Kinetic Times

The characteristic kinetic times of micellization in the solution of a nonionic surfactant: the times of establishment of quasi-equilibrium concentrations of molecular aggregates in micellar, subcritical, and overcritical regions, times of establishment of quasi-equilibrium concentrations of molecular aggregates in the near-critical region of their sizes, the average time between two successive acts of emission of surfactant monomers by a micelle, the average value of micelle lifetime, the time of establishment of quasi-stationary mode of matter exchange between the solution and molecular aggregate, as well as the times of fast and slow relaxation in a solution were analyzed. The hierarchy of these times disclosing complex multistage kinetic process of micelle formation and decomposition and the establishment of equilibrium in the micellar solution was revealed. It was shown that this hierarchy is provided by the small parameters of the kinetic theory. The inverse problem of micellization kinetics was discussed; this problem allows us to find the characteristics of the formation work for micellar aggregate from the experimental data on the relaxation time of micellar solution.     

On the Theory of Micellization Kinetics

Summary: We consider certain general features of aggre‐ gation (micellization) processes in solutions of amphiphilic molecules, in particular, block‐copolymers. We demonstrate that non‐equilibrium effects can be very important for micellization. In particular, we show that micelle formation at the conventional (equilibrium) critical micelle concentration (CMC, ) can be inhibited by high activation energy barriers. This is likely to be the case when the micelles are large. In this case an aggregation actually occurs at higher concentrations, above an apparent CMC, . The concentration can be much higher than the equilibrium CMC. Hence significant hysteresis effects are inherent in amphiphilic systems since micelle formation and dissociation are activation processes. To further clarify this idea we consider relaxation of a micellar system after a temperature jump (or a jump of another essential parameter) and discuss qualitatively different relaxation times corresponding to the relaxations of the micellar sizes and of the total number of micelles. We also discuss different kinetic pathways of micelle formation and relaxation and show that in certain cases the ideal‐gas (combinatorial) contribution to the micelle free energy is significant for the kinetics.

Micelle association and dissociation times vs. reduced concentration.     

Adsorption of Methylene Blue from Aqueous Solution on High Lime Fly Ash: Kinetic,Equilibrium, and Thermodynamic Studies

Kinetic, equilibrium, and thermodynamic studies were performed for the batch adsorption of methylene blue (MB) on the high lime fly ash as a low cost adsorbent material. The studied operating variables were adsorbent amount, contact time, dye concentration, and temperature. The kinetic data were analyzed using the pseudo-first order and pseudo-second order kinetic models and the adsorption kinetic was followed well by the pseudo-second order kinetic model. The equilibrium data were fitted with the Freundlich, Langmuir, and Dubinin Radushkevich (D–R) isotherms and the equilibrium data were found to be well represented by the Freundlich and D–R isotherms. Based on these two isotherms MB is taken by chemical ion exchange and active sites on the high lime fly ash have different affinities to MB molecules. Various thermodynamic parameters such as enthalpy of adsorption (ΔH°), free energy change (ΔG°), and entropy change (ΔS°) were investigated. The positive value of ΔH° and negative value of ΔG° indicate that the adsorption is endothermic and spontaneous. The positive value of ΔS° shows the increased randomness at the solid–liquid interface during the adsorption. A single-stage batch adsorber was also designed based on the Freundlich isotherm for the removal of MB by the high lime fly ash.     

On So-Called Concentration and True Thermodynamic Equilibrium Constants in Solution

Advantages and disadvantages of the concentration and thermodynamic constants of equilibria in solution were compared. The standard state of a solute in solution with a finite ionic strength was shown to have practical advantages (as in biochemical thermodynamics where a solution with an ionic strength of 0.25 is referred to as a standard). It was suggested that a solution with a certain finite ionic strength can be used more widely as an informally (or even formally) adopted second standard state in solution thermodynamics.     

合成氨反应动力学平衡常数与热力学平衡常数的关系

根据当前普遍被接受的氨合成和氨分解机理,明确了氨合成及分解反应的速度控制步骤,确定了氨合成和氨分解反应的动力学方程,进而导出合成氨反应的动力学平衡常数表达式,与热力学平衡常数进行了比较,明确了2者之间的关系。有助于理解合成氨热力学平衡常数与反应速率的关系。     

HCl-CoSO4水溶液热力学性质

在HCl-COSO4-H2O体系中,恒定溶液总离子强度I分别为0．2、0．4、0．6、0．8、1．0、1．5mol/kg．CoSO4在溶液中的离子强度分数yB分别恒定为0．00、0．10、0．20、0．30、0．50和0．70条件下,应用经典的电动势方法测定无液体接界电池(A)在278．15—323．15K温度范围内的电动势为：Pt,H2(10^5Pa)|HCl(cA),COSO4(cB),H2O|AgCl-Ag(A) 根据测得电池(A)的电动势数据,考虑到该体系存在硫酸的二级解离,应用数学迭代方法确定平衡体系氢离子的浓度,进而确定了混合溶液中HCl的活度系数γA。结果表明,在溶液中总离子强度保持恒定时,HCl的活度系数服从Hamed规则。在溶液组成恒定时,log γA对热力学温度1／T作图,是一条直线。     

平衡法对理想稀溶液的讨论

利用平衡法讨论理想稀溶液,并通过亨利定律讨论获得溶剂分子与溶质分子之间作用力的基本方法和基本原理。     

Thermodynamic and Kinetic Study of the Interaction between Alkylpyridinium Ions and Pyrene Derivatives in Aqueous Solution

Abstract— The kinetics of fluorescence quenching of pyrene and three of its derivatives by a series of n -alkylpyridinium ions has been studied. The quenching process is diffusion controlled for all the systems studied, independent of the charge in the aromatic molecule and the size of the alkyl chain in the pyridinium ions. Pyrensulfonate, PS, and pyranine form ground-state complexes with these quenchers. The association constants were determined by using a kinetic scheme where both dynamic and static quenching were included. A linear relationship between the free energy change and number of carbon atoms was found for PS, and a methylene contribution equal to -1.1 kJ/mol was determined from the slope. A similar correlation was established for pyranine, but a slope change was observed when the alkyl chain has more than 10 carbon atoms. From the initial slope, an incremental free energy of -0.35 kJ/mol was obtained. The ground-state complex formation is determined mainly by an electrostatic interaction, but there is a hydrophobic effect on the value of the measured association constants.     

Thermodynamic Characteristics of the Micellization in Droplet and Quasi-Droplet Models of Surfactant Molecular Aggregates with Account of Experimental Data on Equilibrium Micelle Distribution

Formuals for the thermodynamic characteristics of micellization in the droplet and quasi-droplet models of surfactant molecular aggregates are derived. These formulas account for the experimental data on the mean size of micelles and average statistical scatter of their sizes in the equilibrium state. These formulas cover critical micellization concentration corresponded to the onset of surfactant accumulation in micelles and higher (than CMC) concentrations at which micelles incorporate noticeable or even the largest portion of surfactant in micellar solution. Analytical dependence of thermodynamic characteristics of micellization on the initial parameters of droplet and quasi-droplet models of molecular aggregates at critical micellization concentration is disclosed.     

Thermodynamic Equilibrium between an Ionite's Gel Part and a Simple-Salt Solution with Allowance for Water Dissociation

When solving an ion-exchange equilibrium problem it is usually taken into account that the ionite, according to a two-phased model, comprises microphases of a gel and an equilibrium solution. The question of equilibrium in this case involves the necessity to take into account not only ions of salt contained in an aqueous solution, but ions of hydrogen and hydroxyl, which emerge in the water dissociation process, as well. Setting up such a problem is dictated, for example, by the application of electrodialysis for the production of deeply-desalinated water. In the work, for a solution of a simple salt, relations are established, which allow one to compute complete ionic composition of phases of solution and gel on the basis of specified values of concentrations of cations and anions of salt in solution.     

LSmn系列表面化学性质与胶束化作用

通过表面张力的测定, 研究了十二烷基聚氧乙烯聚氧丙烯醚(LSmn)系列表面活性剂LS36、LS45、LS54在溶液表面吸附和形成胶束的热力学函数随温度的变化. 给出了它们在水溶液中的二组分相图.结果表明, LS36、LS45、LS54的表面活性都较高. 在25～50 ℃范围内, 临界胶束浓度(cmc)和平衡表面张力分别在4.44×10－6～17.3×10－6 mol•L－1和30.1～33.5 mN•m－1之间, 表面吸附和形成胶束的自由能分别在－40.0～－49.5 kJ•mol－1和－27.2～－33.1 kJ•mol－1之间.不论是在溶液表面吸附还是形成胶束均为熵驱动过程.其中LS36由于含具有亲水能力较强的聚氧乙烯基团(EO)成分较低, 因此不论其浊点还是其表面吸附和形成胶束的热力学函数均与LS45、LS54具有较大差异.     

Nonionic Micellar Catalyzed Oxidation of Vitamins by Chloramine-T in HClO4 Medium: A Kinetic Study

The kinetics of oxidation of vitamin B₁ (thiamine hydrochloride) and vitamin B₆ (pyridoxine hydrochloride) by chloramine-T (CAT) in perchloric acid medium and in presence of a non ionic surfactant (Triton x-100) have been investigated. A catalytic effect of the nonionic micelle on the rate of oxidation has been observed and rate is found to be proportional to 7lcub;k′ + k″ [Triton x-100]}, where k′ and k″ are the rate constants in absence and presence of surfactant, respectively. The rate shows a first-order, a fractional order and a zero order dependence on [Chloramine-T]_o, [Vitamin]_o and [H⁺]₀, respectively in absence as well as in presence of surfactant. A mechanism involving association/binding between the oxidant and the surfactant micelle, which is supported by spectrophotometric evidence has been proposed. The binding parameters have also been evaluated using a pseudo-phase kinetic model.     

Theoretical,Equilibrium, Kinetics and Thermodynamic Investigations of Methylene Blue Adsorption onto Lignite Coal

The interaction of methylene blue (MB) dye with natural coal (collected from coal landfills of the Kosovo Energy Corporation) in aqueous solutions was studied using adsorption, kinetics, and thermodynamic data, and Monte Carlo (MC) calculations. In a batch procedure, the effects of contact duration, initial MB concentration, pH, and solution temperature on the adsorption process were examined. The Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich (D–R) isotherms were used to examine the equilibrium adsorption data. The equilibrium data fit well to the Freundlich and Langmuir adsorption isotherm models; however, the Freundlich model suited the adsorption data to a slightly better extent than the Langmuir model. The kinetics experimental data was fitted using pseudo-first-order, first-order, pseudo-second-order, second-order, Elvoich equation, and diffusion models. The pseudo-second-order rate model manifested a superlative fit to the experimental data, while the adsorption of MB onto coal is regulated by both liquid film and intraparticle diffusions at the same time. Thermodynamic parameters, such as Gibbs free energy (ΔG⁰), enthalpy (ΔH⁰), and entropy (ΔS⁰) were calculated. The adsorption of MB was confirmed to be spontaneous and endothermic. The theoretical results were in agreement with the experimental ones.     

溶液反应机理与动力学-2：影响因素与动力学方程的一般形式

对引起溶液反应与气相反应速率差异的因素进行了分析。指出大量溶剂分子的存在,并不会导致反应物分子之间的碰撞频率大幅度降低。除影响反应物活度和起催化作用之外,溶剂化和微观粘度是影响溶液反应速率的主要因素。微观粘度的影响可正可负,可能存在"负粘度"效应。基于简单碰撞理论和过渡态理论,给出了溶液反应速率公式的一般形式,可以综合活化能和微观粘度的影响。该方法可以比较合理地解释一些实验现象。     

Kinetics of Aggregation and Relaxation in Micellar Surfactant Solutions

Theoretical results published in the last 17 years on the kinetics of aggregation and relaxation in micellar surfactant solutions have been reviewed. The results obtained by the analytical and direct numerical solution of the Becker–Döring kinetic equations and the Smoluchowski generalized equations, which describe different possible mechanisms of aggregation and relaxation on all time scales from ultrafast relaxation while reaching the quasi-equilibrium in the region of subcritical molecular aggregates to the last stage of slow relaxation of micelles to the final aggregated state, have been considered in detail. The droplet model and the model linear with respect to aggregation numbers have been used for the work of aggregation to describe the dynamics of the rearrangement of micellar systems consisting of only spherical, only cylindrical, and coexisting spherical and cylindrical aggregates, with the dynamics being both linear and nonlinear with respect to deviations from equilibrium. The results of molecular simulation of the rearrangement kinetics of micellar systems subjected to initial disturbance have been reviewed.     

Thermodynamic Characteristics of Micellization in the Droplet Model of Surfactant Spherical Molecular Aggregate

The dependence of the work of the molecular aggregate formation on the aggregation number and surfactant monomer concentration in solution that has the key role for the theory of micellization was studied on the basis of a simple realistic droplet model of spherical aggregate composed of surfactant molecules (the o/w micelle type). Analytical formulas were derived for the coordinates of maximum and minimum of aggregate formation work on the aggregation number axis arising with an increase in the concentration of micellar solution. Model calculations of the thermodynamic characteristics of the kinetics of micellization were performed for premicellar and micellar regions of aggregate sizes within a wide range of solution concentration including the critical micellization concentration.     

Fulfillment of the Conditions of Thermodynamic Equilibrium in an Ice/Electrolyte Solution System with Constrained Geometry

For small volumes of a NaCl solution (10^–6 cm³) with concentrations of 0.1 and 1 M, temperature dependences of the length lof solution columns frozen in thin quartz capillaries (5–10 m in radius) are obtained. At the temperatures t above –4 and –8°C (for 0.1 and 1 M solutions, respectively), the l(t) dependences are reversible, independent of the direction of changes in temperature, and, hence, correspond to the equilibrium conditions of ice/solution system. From the constant mass condition of the solute, an expression for l(t) is derived that includes only one thermodynamic characteristic, namely, the temperature dependence of the solution concentration in equilibrium with ice. Deviations from the calculated l(t) dependences are observed at a temperatures below –2 and –5°C (for 0.1 and 1 M solutions, respectively), which can be explained by the adhesion of frozen solution to the capillary walls. The arising internal stresses lead to the deviations from the thermodynamic equilibrium conditions known for the bulk systems. On approaching the melting zone, the adhesion is failed because of the formation of thin nonfreezing water interlayers on the quartz surface.     

Initiation Kinetics in Free‐Radical Polymerization: Prediction of Thermodynamic and Kinetic Parameters Based on ab initio Calculations

Initiation kinetics in free radical polymerization is investigated using density functional theory. Thermodynamic and kinetic parameters of the initiation reactions are predicted, and the role of the initiators in the polymerization process is evaluated. Methyl acrylate, methyl methacrylate, acrylonitrile, and styrene homo‐polymerizations with different initiators are studied. Reaction enthalpy and activation energy for each reaction between monomer and the radical fragments arising from the initiators have been determined. The initiation kinetic constants for all of these initiation reactions are evaluated and compared with both computational and experimental propagation kinetic constants of each monomer.

     

Kinetic and Thermodynamic Studies for the Removal of Nickel Ions from an Aqueous Solution by Adsorption Technique

The kinetics and dynamics of nickel ions adsorption on activated carbon and bentonite were studied. The influence of parameters (pH, amount of adsorbent, adsorbate concentration, solution volume, rotation speed, and temperature) were investigated. Kinetic models of pseudo-first, pseudo-second and Weber-Morris models were applied. The data was better reported by the pseudo-second order model. Freundlich, Langmuir, and D-R models were utilized for the analysis of adsorption equilibrium. Evaluation of thermodynamic parameters reveal that adsorption is spontaneous and endothermic in nature. From the experimental data, it was concluded that bentonite has more efficiency for the adsorption of nickel ions than activated carbon.