New methodology to determine the rate-limiting adsorption kinetics mechanism from experimental dynamic surface tension data

We present a new methodology to determine the rate-limiting adsorption kinetics mechanism (diffusion-controlled vs mixed diffusion-barrier controlled), including deducing the kinetics parameters (the diffusion coefficient, D, and the energy-barrier parameter, beta), from the experimental short-time dynamic surface tension (DST) data. The new methodology has the following advantages over the existing procedure used to analyze the experimental DST data: (a) it does not require using a model for the equilibrium adsorption isotherm, and (b) it only requires using the experimental short-time DST data measured at two initial surfactant bulk solution concentrations. We apply the new methodology to analyze the experimental short-time DST data of the following alkyl poly(ethylene oxide), CiEj, nonionic surfactants: C12E4, C12E6, C12E8, and C10E8 measured using the pendant-bubble apparatus. We find that for C12E4 and C12E6, the effect of the energy barrier on the overall rate of surfactant adsorption can be neglected for surfactant bulk solution concentrations below their respective critical micelle concentrations (CMCs), and therefore, that the rate-limiting adsorption kinetics mechanism for C12E4 and C12E6 is diffusion-controlled at any of their premicellar surfactant bulk solution concentrations. On the other hand, for C12E8 and C10E8, we find that their respective CMC values are large enough to observe a significant effect of the energy barrier on the overall rate of surfactant adsorption. In other words, for C12E8 and C10E8, the rate-limiting adsorption kinetics mechanism shifts from diffusion-controlled to mixed diffusion-barrier controlled as their premicellar surfactant bulk solution concentrations increase. We test the new methodology by predicting the short-time DST profiles at other initial surfactant bulk solution concentrations, and then comparing the predicted DST profiles with those measured experimentally. Very good agreement is obtained for the four CiEj nonionic surfactants considered. We also compare the results of implementing the new methodology with those of implementing the existing procedure, and conclude that using a model for the equilibrium adsorption isotherm can lead not only to different values of D and beta, but it can also lead to a completely different determination of the rate-limiting adsorption kinetics mechanism. Since the new methodology proposed here does not require using a model for the equilibrium adsorption isotherm, we conclude that it should provide a more reliable determination of the rate-limiting adsorption kinetics mechanism, including the deduced kinetics parameters, D and beta.     

Adsorption relaxation for nonionic surfactants under mixed barrier-diffusion and micellization-diffusion control

Relaxation processes of surfactant adsorption and surface tension, which are characterized by two specific relaxation times, are theoretically investigated. We are dealing with fluid interfaces and small initial deviations from equilibrium. For surfactant concentrations below the critical micellization concentration (CMC), we consider adsorption under mixed barrier-diffusion control. General analytical expressions are derived, which are convenient for both numerical computations and asymptotic analysis. Series expansions for the short- and long-time limit are derived. The results imply that the short-time asymptotics is controlled by the adsorption barrier, whereas the long-time asymptotics is always dominated by diffusion. Furthermore, for surfactant concentrations above the CMC, adsorption under mixed micellization-diffusion control is considered. Again, a general analytical expression is derived for the relaxation of surfactant adsorption and surface tension, whose long- and short-time asymptotics are deduced. The derived equations show that at the short times the relaxation is completely controlled by the diffusion, whereas the long-time asymptotics is affected by both demicellization and diffusion. The micellar effect is manifested as an exponential (rather than square-root) decay of the perturbation. The derived expressions are applied to process available experimental data for the nonionic surfactant Triton X-100 and to determine the respective demicellization rate constant.     

New theoretical framework for designing nonionic surfactant mixtures that exhibit a desired adsorption kinetics behavior

How does one design a surfactant mixture using a set of available surfactants such that it exhibits a desired adsorption kinetics behavior? The traditional approach used to address this design problem involves conducting trial-and-error experiments with specific surfactant mixtures. This approach is typically time-consuming and resource-intensive and becomes increasingly challenging when the number of surfactants that can be mixed increases. In this article, we propose a new theoretical framework to identify a surfactant mixture that most closely meets a desired adsorption kinetics behavior. Specifically, the new theoretical framework involves (a) formulating the surfactant mixture design problem as an optimization problem using an adsorption kinetics model and (b) solving the optimization problem using a commercial optimization package. The proposed framework aims to identify the surfactant mixture that most closely satisfies the desired adsorption kinetics behavior subject to the predictive capabilities of the chosen adsorption kinetics model. Experiments can then be conducted at the identified surfactant mixture condition to validate the predictions. We demonstrate the reliability and effectiveness of the proposed theoretical framework through a realistic case study by identifying a nonionic surfactant mixture consisting of up to four alkyl poly(ethylene oxide) surfactants (C(10)E(4), C(12)E(5), C(12)E(6), and C(10)E(8)) such that it most closely exhibits a desired dynamic surface tension (DST) profile. Specifically, we use the Mulqueen-Stebe-Blankschtein (MSB) adsorption kinetics model (Mulqueen, M.; Stebe, K. J.; Blankschtein, D. Langmuir 2001, 17, 5196-5207) to formulate the optimization problem as well as the SNOPT commercial optimization solver to identify a surfactant mixture consisting of these four surfactants that most closely exhibits the desired DST profile. Finally, we compare the experimental DST profile measured at the surfactant mixture condition identified by the new theoretical framework with the desired DST profile and find good agreement between the two profiles.     

Surface properties of mixtures of surface-active sugar derivatives with ionic surfactants: theoretical and experimental investigations

Surface properties of systems that are mixtures of ionic surfactants and sugar derivatives-anionic surfactant sodium dodecyl sulfate and n-dodecyl-beta-D-maltoside (SDS/DM) and cationic surfactant dodecyltrimethylammonium bromide and n-dodecyl-beta-D-glucoside (DTABr/DG)-were investigated. The experimental results obtained from measurements of surface tension of mixtures with various ratio of ionic to nonionic components were analyzed by two independent theories. First is Motomura theory, derived from the Gibbs-Duhem equation, allowing for indirect evaluation of the composition of mixed monolayers and the Gibbs energies of adsorption, corresponding to mutual interaction between surfactants in mixed adsorbed film. As second theory we used our newly developed theoretical model of adsorption of ionic-nonionic surfactant mixtures. Using this approach, we were able to describe the experimental surface tension isotherms for mixtures of surface-active sugar derivatives and ionic surfactants. We obtained a good agreement with experimental data using the same set of model parameters for a whole range of studied compositions of a given surfactant mixture. The values of surface excess calculated from both theories agreed with each other with a reasonable accuracy. However, the newly developed model of adsorption of ionic-nonionic surfactant mixtures has the advantage of straightforward determination of surface layer composition. By the solution of equations of adsorption, one can obtain directly the values of surface excess of all components (surfactant ions, counterions, and nonionic surfactants molecules), which are present in the investigated system.     

Heterogemini Surfactants Based on Fatty Acid Synthesis and Interfacial Properties

A series of novel nonionic surfactants based on fatty acids, each with two hydrophilic and two hydrophobic groups in the molecule (so-called Gemini surfactants), have been synthesized. The hydrophobic part of the surfactant, made from oleylnitrile, has a double bond in the middle of the chain to which the hydrophilic part is attached. One of the hydrophilic groups is a methyl-capped polyoxyethylene chain with 11 or 16 oxyethylene units, whereas the other is a secondary hydroxyl group. The reason for using the nitrile derivative of the fatty acid instead of a more conventional derivative such as an ester or amide is to achieve good hydrolytic stability, which is often demanded for cleaning applications. The cmc values of the surfactants were determined to be 0.2 and 0.4 mM for NIHG550 and NIHG750, respectively, using tensiometry and fluorescence. Pulsed-field gradient spin-echo NMR measurements gave similar but slightly higher values. The micelle size of NIHG750 was estimated to be on the order of 40 ?, as calculated from the self-diffusion coefficient. The dynamic surface tension, gamma(t), was measured in the range 1 ms-1 s using a maximum bubble pressure instrument and analyzed in terms of asymptotic solutions to the Ward and Tordai equation. The results suggest that at the beginning the adsorption is essentially diffusion-controlled. However, close to equilibrium, the DST decays are not consistent with a diffusion-controlled adsorption mechanism. One important result from the present work is that the heterogeminis seem to align better than conventional surfactants at the air-liquid and solid-liquid interfaces. Copyright 2001 Academic Press.     

Adsorption and Micellization in Solutions of Dodecylpyridinium Bromide–Nonionic Surfactant Mixtures

Dependences of the surface tension of aqueous solutions of cationic (dodecylpyridinium bromide) and nonionic (Tween 80, Triton X-100) surfactants and their mixtures on total surfactant concentration and solution composition were studied. The values of critical micellization concentration (CMC) and excess free energy of adsorption were determined from tensiometric measurements. Based on Rubingh–Rosen model (approximation of the theory of regular solutions), the compositions of micelles and adsorption layers at the solution–air interface as well as parameters of interaction between the molecules of cationic and nonionic surfactants were calculated for the systems indicated above. It was established that, in the case of surfactant mixtures with considerable difference in the CMCs, the micelles of individual surfactant with lower CMC value are formed. The effect of negative deviation from the ideality during the adsorption of surfactants from mixed solutions at the solution–air interface was disclosed. It was shown that the interaction energy depends significantly on the composition of mixed systems.     

十八烷基二甲基氯化铵水溶液动态表面张力及吸附动力学研究

使用最大气泡法测定了十八烷基二甲基氯化铵（C_(18)DAC）水溶液的动态表 面张力,考察了浓度、温度等对其DST的影响,详细表征了DST随时间的变化过程, 计算了动态表面张力的各种参数（n,t_i,t~*,t_m,R_(1/2)）。结合Word- Tordai方程计算了表观扩散系数（D_a）和吸附势垒（E_a）,对其吸附动力学模式 进行了研究,探讨了DST参数的物理意义。结果表明,t~*值越小,吸附势垒E_a越 大,宏观扩散系数D_a越小,表面活性剂分子越不易吸附在溶液表面;C_(18)DAC低 浓度时吸附属于扩散控制模式,高浓度时属于混合控制模式;高浓度时,在吸附初 期（t → 0）为扩散控制模式,吸附后期（t → ∞）为混合控制模式。     

Interaction behavior in ultrafiltration of nonionic surfactant micelles by adsorption

Adsorption of nonionic surfactant micelles onto ultrafiltration (UF), membranes was studied. Two homologous series of nonionic surfactants, namely, Tritons (alkylphenol ethoxylates) and Neodols (alcohol ethoxylates), were used to characterize surface properties of two polymeric ultrafiltration membranes with 20,000 nominal cutoff. Particularly, a cellulose acetate and a polysulfone membrane were investigated. Static adsorption experiments were carried out using surfactant solutions at concentrations above their critical micelle concentration. The characterization of surface properties of UF membranes was based on the adsorption behavior of surfactant species. The adsorption extent on UF membranes was affected by the hydrophobicity-to-hydrophilicity ratio mainly determining the interactions developed at the membrane-surfactant species interface. Adsorption experimental data seem generally to fit the Langmuir isotherm model. Atomic force microscopy was used to examine the alteration of the top membrane surface morphology.     

Experimental observations on the scaling of adsorption isotherms for nonionic surfactants at a hydrophobic solid-water interface

The self-assembly of nonionic surfactants in bulk solution and on hydrophobic surfaces is driven by the same intermolecular interactions, yet their relationship is not clear. While there are abundant experimental and theoretical studies for self-assembly in bulk solution and at the air-water interface, there are only few systematic studies for hydrophobic solid-water interfaces. In this work, we have used optical reflectometry to measure adsorption isotherms of seven different nonionic alkyl polyethoxylate surfactants (CH3(CH2)I-1(OCH2CH2)JOH, referred to as CIEJ surfactants, with I = 10-14 and J = 3-8), on hydrophobic, chemically homogeneous self-assembled monolayers of octadecyltrichlorosilane. Systematic changes in the adsorption isotherms are observed for variations in the surfactant molecular structure. The maximum surface excess concentration decreases (and minimum area/molecule increases) with the square root of the number of ethoxylate units in the surfactant (J). The adsorption isotherms of all surfactants collapse onto the same curve when the bulk and surface excess concentrations are rescaled by the bulk critical aggregation concentration (CAC) and the maximum surface excess concentration. In an accompanying paper we compare these experimental results with the predictions of a unified model developed for self-assembly of nonionic surfactants in bulk solution and on interfaces.     

Dynamic surface tension and adsorption mechanisms of surfactants at the air-water interface

Recent advances in understanding dynamic surface tensions (DSTs) of surfactant solutions are discussed. For pre-CMC solutions of non-ionic surfactants, theoretical models and experimental evidence for a mixed diffusion-kinetic adsorption mechanism are covered. For micellar solutions of non-ionics, up to approximately 100 x CMC, the DST behaviour can also be accounted for using a mixed mechanism model. Finally, the first reported measurements of the dynamic surface excess Gamma(t), using the overflowing cylinder in conjunction with neutron reflection, are described.     

Effect of interactions between the adsorbed species on the properties of single and mixed-surfactant monolayers at the air/water interface

Experimental data on surface tension available from the literature and generated in the present study are analyzed to estimate the applicability of adsorption models, based on the Frumkin equation, to nonionic and ionic surfactants and their mixtures. Optimization programs based on the least-squares method in media of Delphi V and Pascal VII are used. The effect of interactions between the adsorbed species on surface tension is considered in all cases. The results are compared to those obtained with the simpler Szyszkowski equation, employed in numerous studies of nonionic surfactants, when interactions are neglected. Cases where the Frumkin model can be successfully employed with ionic surfactants and mixtures are presented and the conditions of its applicability are analyzed. Related characteristic quantities (maximum adsorption, standard free energy of surfactant adsorption, energy of interaction between adsorbed species, standard free energy of counterion adsorption, degree of coverage by surfactant/counterion associates) are established as a function of: The properties of an adsorption layer from a mixture of nonionic and ionic surface-active species are compared to those of the single surfactants.     

短碳链醇/水混合溶剂中表面活性剂的表面性质

对不同类型表面活性剂(阳离子型、阴离子型、非离子型、正负混合型)在短碳链醇/水混合溶剂中的表面物化性质进行了较为系统的研究,探讨了短碳链醇加入对体系Υcmc值和cmc值的影响。发现各类体系的Υcmc随短碳链醇加入的变化规律并非决定于表面活性剂类型而取决于该表面活性剂在水溶液中的饱和吸附量和Υcmc值的大小。     

Nonionic surfactants and the wool fibre surface

Nonionic surfactants are found in many wool processing operations. This study shows that X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectrometry (SIMS) are useful tools in the investigation of the interaction of nonionic surfactants and the wool fibre surface. Results confirm that nonionic surfactants such as TN450 and Teric N4 will adsorb onto the fibre surface with the bound lipid intact. Even after extensive rinsing, surfactant molecules are present suggesting that these molecules bind strongly to the fibre surface. In addition, the nature of the fibre surface is shown to influence the adsorption of nonionic surfactant. The removal of the bound lipid from the fibre surface facilitates the adsorption process and the subsequent surfactant treatment enhances the fibre’s wettability. These results have important practical implications. Also it is shown that the surfactant is not removed by extensive rinsing.     

十二烷基硫酸钠水溶液的动态表面吸附性质

利用MPTC型气泡压力张仪研究了十二烷基硫酸钠(SDS)溶液在不同NaCl 浓度下的动态表面吸附性质, 分析了离子型表面活性剂在表面吸附层和胶束中形成双电层结构产生表面电荷对动态表面扩散过程和胶束性质的影响. 结果表明, SDS在表面吸附过程中, 表面电荷的存在会产生5.5 kJ·mol^-1的吸附势垒(E_a), 显著降低十二烷基硫酸根离子(DS^-)的有效扩散系数(D_eff). 十二烷基硫酸根离子的有效扩散系数与自扩散系数(D)的比值(D_eff/D)仅为0.013, 这表明SDS与非离子型表面活性剂不同, 在吸附初期为混合动力控制吸附机制. 加入NaCl可以降低吸附势垒. 当加入不小于80 mmol·L^-1 NaCl后, E_a小于0.3 kJ·mol^-1, D_eff/D在0.8-1.2之间, 表现出与非离子型表面活性剂相同的扩散控制吸附机制. 同时, 通过分析SDS胶束溶液的动态表面张力获得了表征胶束解体速度的常数(k₂). 发现随着NaCl 浓度的增大, k₂减小, 表明SDS胶束表面电荷的存在会增加十二烷基硫酸根离子间的排斥力, 促进胶束解体.     

Study on the Surface Property of Surfactant Ionic Liquids Solutions

The surfactant TX-100 can be dissolved in ionic liquid bmimPF6 and decrease the surface tension of 1-buty1-3-methylimidazolium hexafluorophosphate (bmimPF6) solutions. Here, we confirmed that in this new system, the pure solvents need rearrangement at the air-wate rinterface at the initial stage. The dynamic surface tension (DST) study shows that at the initial adsorption stage, the adsorption model of surfactant accords with the diffusion-controlled adsorption mechanism, and the dilute ionic liquids solutions is further close to the diffusion-controlled adsorption.     

Electrophoretic behaviour and viscosities of metal oxides in mixed surfactant systems

 The electrokinetic behavior and viscosity of anatase and alumina in mixed-surfactant solutions were investigated. Sodium dodecylsulfate and nonionic polyoxyethylene ethers were investigated as model surfactants. Pure nonionic surfactants adsorbed on anatase and coated the particles, so that the zeta potential was nearly zero near the critical micelle concentration of surfactant. At higher surfactant concentrations, an increase in the zeta potentials was observed, suggesting a change in the microstructure of the adsorbed layer. Addition of nonionic surfactant to positively charged anatase and alumina with some preadsorbed sodium dodecylsulfate reversed the surface charge of the oxide to negative, indicating enhanced coadsorption of the anionic surfactant. At higher concentrations of the nonionic surfactant, the charge reversed back to positive. Nonionic surfactants did not reverse the surface charge of these oxides in the absence of the anionic surfactant. Coenhanced adsorption of nonionic and anionic surfactants was used to stabilize alumina at the isoelectric point, where neither surfactant adsorbed appreciably on its own. These results suggest a dramatic change in conformation of the surfactant chains in mixed systems. Further explanation and justification of the proposed changes in adsorbed surfactant conformation require spectroscopic evidence. Received: 12 March 1997 Accepted: 22 July 1997     

Self-consistent field modeling of adsorption from polymer/surfactant mixtures

We report on the development of a self-consistent field model that describes the competitive adsorption of nonionic alkyl-(ethylene oxide) surfactants and nonionic polymer poly(ethylene oxide) (PEO) from aqueous solutions onto silica. The model explicitly describes the response to the pH and the ionic strength. On an inorganic oxide surface such as silica, the dissociation of the surface depends on the pH. However, salt ions can screen charges on the surface, and hence, the number of dissociated groups also depends on the ionic strength. Furthermore, the solvent quality for the EO groups is a function of the ionic strength. Using our model, we can compute bulk parameters such as the average size of the polymer coil and the surfactant CMC. We can make predictions on the adsorption behavior of either polymers or surfactants, and we have made adsorption isotherms, i.e., calculated the relationship between the surface excess and its corresponding bulk concentration. When we add both polymer and surfactant to our mixture, we can find a surfactant concentration (or, more precisely, a surfactant chemical potential) below which only the polymer will adsorb and above which only the surfactant will adsorb. The corresponding surfactant concentration is called the CSAC. In a first-order approximation, the surfactant chemical potential has the CMC as its upper bound. We can find conditions for which CMC < CSAC . This implies that the chemical potential that the surfactant needs to adsorb is higher than its maximum chemical potential, and hence, the surfactant will not adsorb. One of the main goals of our model is to understand the experimental data from one of our previous articles. We managed to explain most, but unfortunately not all, of the experimental trends. At the end of the article we discuss the possibilities for improving the model.     

吸附与润湿II.Triton X-100和Triton x-305在炭黑/水和炭黑/环己烷界面上的吸附层结构

测定了15℃和30℃时炭黑自水和环己烷中吸附非离子型表面活性剂TritonX-100和Triton X-305的等温线;计算了吸附过程的标准热力学函数;测定了石墨/水/环己烷和石墨/水/空气的接触角与表面活性剂浓度的关系, 分析所得结果,可得结论:在炭黑/水或石墨/水界面上,Triton型表面活性分子形成单分子吸附层,分子以憎水的iso-C8H17C6H4基团附着在表面,而以亲水的聚氧乙烯链伸入水相的方式取向;在炭黑/环已烷或石墨/环己烷界面上,分子是通过聚氧乙烯链吸附到表面上的,当浓度增加时分子在表面可能通过聚氧乙烯链间的相互作用而发生聚集,即可能形成表面反式胶团。     

Adsorption of mixtures of nonionic sugar-based surfactants with other surfactants at solid/liquid interfaces II. Adsorption of n-dodecyl-beta-D-maltoside with a cationic surfactant and a nonionic ethoxylated surfactant on solids

Synergy and antagonism between sugar-based surfactants, a group of environmentally benign surfactants, and cationic surfactants and nonionic ethoxylated surfactants have been investigated in this study with solids which adsorbs only one or other when presented alone. Sugar-based n-dodecyl-beta-D-maltoside (DM) does not adsorb on silica by itself. However, in mixtures with cationic dodecyltrimethylammonium bromide (DTAB) and nonionic nonylphenol ethoxylated decyl ether (NP-10), DM adsorbs on silica through hydrophobic interactions. In contrast, although DM does adsorb on alumina, the presence of NP-10 reduces the adsorption of DM as well as that of the total surfactant adsorption. Such synergistic/antagonistic effects of sugar-based n-dodecyl-beta-D-maltoside (DM) in mixtures with other surfactants at solid/liquid interfaces were systematically investigated and some general rules on synergy/antagonism in mixed surfactant systems are identified. These results have implications for designing surfactant combinations for controlled adsorption or prevention of adsorption.     

Competitive adsorption of nonionic surfactant and nonionic polymer on silica

Competitive adsorption of the nonionic polymer poly(ethylene oxide) (PEO) and the nonionic surfactant of the type poly(ethylene oxide) alkyl ether from aqueous solutions on a silica surface is examined. From one-component solutions, both species readily adsorb onto silica and, in the bulk of mixed (two-component) solutions, polymer-surfactant complexes are not observed. Because both species bind by the same mechanism to silica, subtle differences in layer structure, or other species-specific parameters, determine whether one or both of the species will adsorb. It was found that various surfactants can displace PEO up to a certain critical molecular weight. Surfactants with a high aggregation number, in bulk and on the surface, can displace PEO with a higher molar mass than surfactants with a low aggregation number. As the molar mass of the polymer increases, the time a surfactant needs to completely displace the polymer increases. We can explain both the existence of the critical molar mass and the decrease in adsorption kinetics with a shift in the critical surface association concentration (CSAC).