Electrostatic interactions in micellar solutions of sodium <Emphasis Type="Italic">n</Emphasis>-alkyl sulfates and applicability of the poisson-boltzmann equation for their calculation

By the example of four even members in a homologous series of sodium n-alkyl sulfates (decyl-, dodecyl-, tetradecyl-, and hexadecyl sulfate) and with the use of the Debye-Hueckel theory of strong electrolytes the parameters are calculated that determine electrostatic interactions in micellar solutions of surfactants. Calculation results for the Gibbs electrostatic energy of micellization are compared to those obtained from one of the approximate solutions of the Poisson-Boltzmann equation and also to the results of its numerical integration for spherical micelles. Applicability conditions of the Debye-Hueckel theory are determined with respect to the micelle concentration and size and the number of carbon atoms in a surfactant molecule. It is shown that the Debye-Hueckel theory in the proposed version enables an efficient and quite accurate calculation of all electrostatic properties of micelles and ionic micellar solutions for surfactants with a number of carbon atoms in a molecule starting from 10 and more and at concentrations up to 0.15 mol/dm³.     

Molecular thermodynamics for micellar branching in solutions of ionic surfactants

We develop an analytical molecular-thermodynamic model for the aggregation free energy of branching portions of wormlike ionic micelles in 1:1 salt solution. The junction of three cylindrical aggregates is represented by a combination of pieces of the torus and bilayer. A geometry-dependent analytical solution is obtained for the linearized Poisson-Boltzmann equation. This analytical solution is applicable to saddle-like structures and reduces to the solutions known previously for planar, cylindrical, and spherical aggregates. For micellar junctions, our new analytical solution is in excellent agreement with numerical results over the range of parameters typical of ionic surfactant systems with branching micelles. Our model correctly predicts the sequence of stable aggregate morphologies, including a narrow bicontinuous zone, in dependence of hydrocarbon tail length, head size, and solution salinity. For predicting properties of a spatial network of wormlike micelles, our aggregation free energy is used in the Zilman-Safran theory. Our predictions are compared with experimental data for branching micelles of ionic surfactants.     

Estimation of micellization parameters of sodium dodecyl sulfate in water+1-butanol using the mixed electrolyte model for molar conductance

The mixed electrolyte model of Shanks and Franses has been applied to estimate the critical micelle concentration, aggregation number, and counterion binding constant of sodium dodecyl sulfate in a water + 1-butanol medium from its measured conductivity data at 25 degrees C. The surface potential of the ionic micelle in this mixed solvent medium was computed by solving the nonlinear Poisson-Boltzmann equation. The standard free energy terms of micellization were also calculated. The present study confirms further the observation made in the previous studies that ionic micelles do not contribute to the ionic strength of a surfactant solution, an inference originally made by McBain and coworkers.     

离子液体1-烷基-3-甲基咪唑四氟硼酸盐在水溶液中的聚集行为

采用等温滴定量热法、静态荧光猝灭法和电导法系统研究了典型离子液体1-烷基-3-甲基咪唑四氟硼酸盐([Cnmim][BF₄])在水溶液中的聚集行为, 获得了胶束形成的临界胶束浓度(cmc), 摩尔焓变(ΔH_mic), 摩尔吉布斯自由能变(ΔG_mic), 摩尔熵变(ΔS_mic)以及不同浓度时[Cnmim][BF₄]胶束的平均聚集数等基本参数. 发现这类离子液体的聚集为熵驱动, 阳离子的烷基链越长, ΔG_mic越负, 聚集更容易发生. 此外, 结合[C_nmim]X (X=Cl^-, Br^-)的相关研究发现, 阳离子相同时, 体积越大和疏水性越强的阴离子与头基的结合能力越强, 能有效地降低头基之间的静电排斥, 降低cmc, 利于胶束的形成. 对于[C₁₂mim][BF₄], 添加剂β-环糊精(β-CD)的加入可使cmc增大, ΔH_mic和ΔS_mic减小, 而KBF₄则可使cmc和ΔH_mic减小, ΔS_mic增大.     

Electrostatic interaction between two parallel cylinders

Explicit exact analytic expressions are obtained for the electric potential distribution and for the electrostatic interaction energy for the system of two parallel dissimilar cylinders in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation.     

Micellar solutions of ionic surfactants and their mixtures with nonionic surfactants: Theoretical modeling vs. Experiment

Here, we review two recent theoretical models in the field of ionic surfactant micelles and discuss the comparison of their predictions with experimental data. The first approach is based on the analysis of the stepwise thinning (stratification) of liquid films formed from micellar solutions. From the experimental step-wise dependence of the film thickness on time, it is possible to determine the micelle aggregation number and charge. The second approach is based on a complete system of equations (a generalized phase separation model), which describes the chemical and mechanical equilibrium of ionic micelles, including the effects of electrostatic and non-electrostatic interactions, and counterion binding. The parameters of this model can be determined by fitting a given set of experimental data, for example, the dependence of the critical micellization concentration on the salt concentration. The model is generalized to mixed solutions of ionic and nonionic surfactants. It quantitatively describes the dependencies of the critical micellization concentration on the composition of the surfactant mixture and on the electrolyte concentration, and predicts the concentrations of the monomers that are in equilibrium with the micelles, as well as the solution’s electrolytic conductivity; the micelle composition, aggregation number, ionization degree and surface electric potential. These predictions are in very good agreement with experimental data, including data from stratifying films. The model can find applications for the analysis and quantitative interpretation of the properties of various micellar solutions of ionic surfactants and mixed solutions of ionic and nonionic surfactants.     

Prediction of conformational characteristics and micellar solution properties of fluorocarbon surfactants

A molecular-thermodynamic theory is developed to model the micellization of fluorocarbon surfactants in aqueous solutions, by combining a molecular model that evaluates the free energy of micellization of fluorocarbon surfactant micelles with a previously developed thermodynamic framework describing the free energy of the micellar solution. In the molecular model of micellization developed, a single-chain mean-field theory is combined with an appropriate rotational isomeric state model of fluorocarbon chains to describe the packing of the fluorocarbon surfactant tails inside the micelle core. Utilizing this single-chain mean-field theory, the packing free energies of fluorocarbon surfactants are evaluated and compared with those of their hydrocarbon analogues. We find that the greater rigidity of the fluorocarbon chain promotes its packing in micellar aggregates of low curvatures, such as bilayers. In addition, the mean-field approach is utilized to predict the average conformational characteristics (specifically, the bond order parameters) of fluorocarbon and hydrocarbon surfactant tails within the micelle core, and the predictions are found to agree well with the available experimental results. The electrostatic effects in fluorocarbon ionic surfactant micelles are modeled by allowing for counterion binding onto the charged micelle surface, which accounts explicitly for the effect of the counterion type on the micellar solution properties. In addition, a theoretical formulation is developed to evaluate the free energy of micellization and the size distribution of finite disklike micelles, which often form in the case of fluorocarbon surfactants. We find that, compared to their hydrocarbon analogues, fluorocarbon surfactants exhibit a greater tendency to form cylindrical or disklike micelles, as a result of their larger molecular volume as well as due to the greater conformational rigidity of the fluorocarbon tails. The molecular-thermodynamic theory developed is then applied to several ionic fluorocarbon surfactant-electrolyte systems, including perfluoroalkanoates and perfluorosulfonates with added LiCl or NH(4)Cl, and various micellar solution properties, including critical micelle concentrations (cmc's), optimal micelle shapes, and average micelle aggregation numbers, are predicted. The predicted micellar solution properties agree reasonably well with the available experimental results.     

Structural thermodynamics of lamellar cationic lipid-DNA complex: DNA compressibility modulus

We have studied theoretically the compressibility modulus B of DNA and complexation adsorption isotherms of DNA and lipids, as a function of DNA spacing d(DNA) and NaCl electrolyte concentration, respectively, in isoelectric states of lamellar DNA/cationic lipid (CL) self-assemblies. The electrostatic free energy derived from the Poisson-Boltzmann theory predicts partial agreement with measured B values for interhelical separations d(DNA)>33 A when use is made of a fit of hydration repulsion from bulk DNA hexagonal phases in solution. For lower interchain separations the prediction worsens due to the hydration interaction that overcomes the electrostatic contribution. An exact match of the system's counterion electrochemical potentials and the coions of salt in aqueous phase leads to the electrostatic part of the free energy that renders isotherms of d(DNA) versus ionic strength in qualitative consistency with general trends of available experimental data of CL-DNA complexes.     

Activity Coefficients of Aqueous Mixed Ionic Surfactant Solutions from Osmometry

Osmotic techniques for measuring thermodynamic activities, such as isopiestic equilibration, are well established for multicomponent solutions, especially mixed salt solutions. Surprisingly, these techniques have not yet been applied to mixed ionic surfactants, despite the numerous practical applications of these systems and the importance of the Gibbs free energy for micelle stability. In this study, mass-action equations are developed for the osmotic coefficients of solutions of ionic surfactant CA + ionic surfactant CB, with common counterion C. Extended Debye–Hückel equations are used for the ionic activity coefficients. The equilibrium constants for mixed micelle formation are evaluated by Gibbs–Duhem integration of critical micelle concentrations. Fitting the derived equations to the osmotic coefficients of aqueous sodium decanoate + sodium dodecylsulfate solutions measured by freezing-point osmometry is used to evaluate the activities of the total surfactant components. Very large departures from ideal solution behavior are indicated, including stoichiometric surfactant activity coefficients and micelle activity coefficients that drop below 0.05 and 10^?8, respectively, relative to unity for ideal solutions. Osmometry offers many interesting and unexplored possibilities for studies of mixed surfactant thermodynamics.     

Composition of Surface Layer at the Water–Air Interface and Micelles of Triton X-100 + Rhamnolipid Mixtures

Measurements of the surface tensions, densities and viscosities of aqueous solutions of Triton X-100 (TX-100) and rhamnolipid (RL) mixtures, at constant concentration of RL or TX-100, were carried out. The measured values of the surface tension were compared to those determined using different theoretical models and on the basis of the surface tension of aqueous solutions of individual surfactants. From the surface tension isotherms, the Gibbs surface excess concentration of TX-100 and RL, the composition of surface layer and the standard Gibbs free energy of adsorption at the water–air interface were determined. Moreover, on the basis of surface tension, density and viscosity isotherms, the CMC of surfactants mixtures were evaluated. From the density isotherms, apparent and partial molar volumes of TX-100 and RL were also determined. These volumes were compared to those calculated from the sizes of TX-100 and RL molecules. There was observed a synergetic effect in the reduction of water surface tension and micelle formation, which was confirmed by the intermolecular interactions parameter. In the case of micelle formation, this effect was discussed based on the standard Gibbs free energy of micellization as well as of TX-100 and RL mixing in the micelles. The synergism of TX-100 and RL mixtures in the reduction of water surface tension and micelle formation was explained on the basis of electrostatic interactions between the hydrophilic part of TX-100 and RL molecules; this was supported by pH measurements.     

Structural,electrostatic, and thermodynamic properties of the surface of spherical micelles in solutions of sodium <Emphasis Type="Italic">n</Emphasis>-alkyl sulfate homologues. II. Electrostatic and thermodynamic characteristics

The structural characteristics of micelles from our previous work (Part I) are used to calculate the electrostatic energy of ions in the electric double layer on the surface of spherical ionic micelles in solutions of sodium n-alkyl sulfate homologues with the following number of carbon atoms in the molecule: n _C = 8, 10, 12, and 14. This energy is found to depend on the thickness of the electric double layer and its average radius on the surface of a micelle, the aggregation number, the degree of binding of counterions, and the dielectric constant. The developed semi-empirical method is used to calculate interfacial tensions in spherical micelles for the said homologues in solutions at their critical micellar concentrations and T = 303 K. These values are split into the contributions from the hydrophobic and electrostatic components. The electrostatic component of the interfacial tension in spherical micelles is compared with the expression for the ion–ion repulsion energy to obtain the values of static permittivity (dielectric constant) in the surface layer of micelles.     

Structure and interactions of charged triblock copolymers studied by small-angle X-ray scattering: dependence on temperature and charge screening

A series of thermo-responsive cationic triblock copolymers composed of methoxy-poly(ethylene glycol) (MPEG, hydrophilic), poly(N-isopropylacrylamide) (PNIPAAM, temperature sensitive), and poly((3-acrylamidopropyl) trimethyl ammonium chloride) (PN(+), cationic) has been investigated as a function of temperature and ionic strength. In the MPEG-b-PNIPAAM-b-PN(+) copolymers, the MPEG block length is constant, and the lengths of the PNIPAAM and PN(+) blocks are varied. The solubility of the PNIPAAM block decreases with increasing temperature, and the triblock copolymer thus provides the possibilities of studying micelles with both neutral and charged blocks in the micelle corona as well as the interplay between these two blocks as the electrostatic interactions are varied by addition of salt. Investigation of the systems by densitometry and small-angle X-ray scattering (SAXS) in a temperature range from 20 to 70 °C gave detailed information on the behavior both below and above the critical micelle temperature (CMT). A clear effect of the addition of salt is observed in both the apparent partial specific volume, obtained from the densitometry measurements, and the SAXS data. Below the CMT, the single polymers can be described as Gaussian chains, for which the repulsive interchain interactions, originating from the charged PN(+) block, have to be taken into account in salt-free aqueous solution. Increasing the salt concentration of the solution to 30 mM NaCl leads to an increase in the apparent partial specific volume, and the electrostatic repulsive interchain interactions between the single polymers vanish. Raising the temperature results in micelle formation, except for the copolymer with only 20 NIPAAM units. The SAXS data show that the polymer with the medium PNIPAAM block length forms spherical micelles, whereas the polymer with the longest PNIPAAM block forms cylindrical micelles. Increasing the temperature further above the CMT results in an increase in the micellar aggregation number for both of the polymers forming spherical and cylindrical micelles. The addition of salt to the solution also influences the aggregates formed above the CMT. Overall, the micelles formed in the salt solution have a smaller cross-section radius than those in aqueous solution without added salt.     

醋酸离子液体[C2mim][OAc]水溶液的摩尔表面Gibbs自由能

在288.15-318.15 K温度范围内测定了不同浓度离子液体1-乙基-3-甲基咪唑醋酸盐([C₂mim][OAc])水溶液的表面张力和密度;在改进李以圭等人的溶液表面张力模型基础上,提出摩尔表面Gibbs自由能新概念,建立了摩尔表面Gibbs自由能随溶液浓度变化的线性经验方程,利用这个经验方程估算了[C₂mim][OAc]水溶液的摩尔表面Gibbs自由能,并进一步预测了该溶液的表面张力,其预测值与相应的表面张力实验值高度相关并非常相似。由此可见,摩尔表面Gibbs自由能与等张比容极其类似,可能成为预测离子液体及其溶液性质的一种新的半经验方法。在指定溶液浓度下,根据溶液的摩尔表面Gibbs自由能随温度呈线性变化的规律,得到了新的Eötvös方程,与传统的Eötvös方程相比,新Eötvös方程的每一个参数都有明确的物理意义:斜率的负值是摩尔表面熵,截距是摩尔表面焓,在指定浓度的溶液中摩尔表面焓几乎不随温度变化。     

The gibbs energy,chemical potential,and state parameters of the surface of an ionic micelle in the form of an ellipsoid of revolution

A molecular-thermodynamic model of an ionic micelle in the form of an ellipsoid of revolution was suggested. Equations for the chemical potential of an ellipsoidal micelle, the work of transfer of ions from solution volume into the micelle, and the state parameters of the surface of the micelle (fraction of free hydrophobic surface, surface tension coefficient, and surface charge density) were obtained. The Gibbs energy, chemical potential, work of transfer, and state parameters of an ellipsoidal micelle were determined as depending on the form factor of the corresponding ellipsoid. The model was verified for the example of sodium decyl sulfate micelles. The calculated parameters were close to the thermochemical data on the asymmetrization of spherical micelles in a solution of sodium decyl sulfate. The equilibrium ion-micellar solution composition was estimated.     

The unusual importance of activity coefficients for micelle solutions illustrated by an osmometry study of aqueous sodium decanoate and aqueous sodium decanoate + sodium chloride solutions

Freezing-point and vapor-pressure osmometry data are reported for aqueous sodium decanoate (NaD) solutions and aqueous NaD + NaCl solutions. The derived osmotic coefficients are analyzed with a mass-action model based on the micelle formation reaction qNa(+) + nD(-) = (Na(q)D(n))(q-n) and Guggenheim equations for the micelle and ionic activity coefficients. Stoichiometric activity coefficients of the NaD and NaCl components and the equilibrium constant for micelle formation are evaluated. Illustrating the remarkable but not widely appreciated nonideal behavior of ionic surfactant solutions, the micelle activity coefficient drops to astonishingly low values, below 10(-7) (relative to unity for ideal solutions). The activity coefficients of the Na(+) and D(-) ions, raised to large powers of q and n, reduce calculated extents of micelle formation by up to 15 orders of magnitude. Activity coefficients, frequently omitted from the Gibbs equation, are found to increase the calculated surface excess concentration of NaD by up to an order of magnitude. Inflection points in the extent of micelle formation, used to calculate critical micelle concentration (cmc) lowering caused by added salt, provide unexpected thermodynamic evidence for the elusive second cmc.     

Salt effects on solute exchange in sodium dodecyl sulfate micelles

We describe the influence of sodium chloride on the rate of solute exchange in aqueous SDS micelles for a water-insoluble solute, a pyrene-containing triglyceride 1. The initially prepared solutions contained a small fraction of micelles containing two molecules of 1 and a large excess of empty micelles. These solutions showed a measurable excimer emission (of intensity I(E)) that was stable for days to weeks in the absence of added salt. Following additions of salt, I(E) decayed exponentially (rate constant, k(obs)) accompanied by an increase in pyrene monomer emission. Values of k(obs) increased strongly with ionic strength (k(obs) similar [Na(+)](4)). There was no contribution of the empty micelle concentration beyond its contribution to the sodium ion concentration. We conclude that the solute exchange involves spontaneous fragmentation of the SDS micelles into two submicelles, each bearing a molecule of 1, which then grow back to normal micelles through condensation of SDS monomers. We propose a model for the fragmentation process in which large amplitude surface fluctuations "pinch off" a subunit that becomes a submicelle. These fluctuations bring sulfate headgroups into close proximity. Fluctuations leading to fission become important only in the presence of sufficient counterion concentration to reduce the electrostatic repulsion between neighboring headgroups.     

An analytical expression for the approximate dependence of the degree of counterion binding on the composition of ionic-nonionic mixed micelles

A simple analytical expression is presented to describe the dependence of the degree of counterion binding beta of ionic-nonionic mixed micelles on the composition x(I) (the micelle mole fraction of the ionic species): 1/(1-beta)=1-x(I)+x(I)/[1-beta(x(I)=1)]. In the application of the relation, the value of beta for the pure ionic micelle, beta(x(I)=1), should be known in advance. An equivalent expression was first proposed by Hall et al. on purely empirical grounds but in the present study the relation is derived on the basis of the Poisson-Boltzmann equation of the plate model of micelles in a salt-free medium. The insensitive nature of beta toward a change in micelle concentration as well as to the addition of a salt is also derived under reasonable approximations. When the relation was applied to 12 mixed micelles both with and without added salt, it described quite well the observed composition dependencies of all examples examined. Two other simple analytical expressions are also derived, but they are much less satisfactory in describing the experimental data.     

The Aggregation Work and Shape of Molecular Aggregates upon the Transition from Spherical to Globular and Cylindrical Micelles

The transition from spherical to globular and cylindrical equilibrium modifications of micelles in solutions of nonionic surfactants is numerically studied within the framework of the droplet model of molecular aggregates. Two branches of the curve of micelle aggregation work are plotted as a function of aggregation numbers. One of these curves corresponds to the globular micelles; the other, to spherocylindrical micelles. At aggregation numbers corresponding to the limiting spherical packing, both the globules and spherocylinders are transformed into the limiting sphere. It is shown that the ratio between the branches depends on the dimensionless parameter characterizing the ratio of electrostatic and surface contributions to the aggregation work. It is elucidated that, at certain values of this parameter and surfactant monomer concentration in solution, in addition to the maximum in the region of submicellar aggregates for spherical micelles, the second maximum arises on the curve of aggregation work as a function of aggregation numbers in the region of transition to spherocylindrical micelles. The appearance of an additional maximum is shown to be caused by the sum of surface, electrostatic, and concentration contributions to the aggregation work and is not directly related to the conformational contribution to the aggregation work.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 3, 2005, pp. 363–376.Original Russian Text Copyright © 2005 by Kshevetskiy, Shchekin.     

Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects

This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three-dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 571(3) can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono- and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.     

Role of the solvophobic effect on micellization

Experimental data of amphiphiles aggregation phenomena in water-organic solvent mixtures were considered with the idea of investigating the role of the solvophobic effect on micellization. Changes in the critical micelle concentration, in the micellar ionization degree (for ionic surfactants) and in the aggregation number accompanying variations in the composition of the bulk phase of the micellar solutions were examined with the scope of understanding which properties of the water-organic solvent mixtures are important in the micellization process. Results point out that the cohesive energy density, measured either through the Hildebrand-Hansen solubility parameter or the Gordon parameter, seems to play an important role in determining the contribution of the solvophobic effect on the Gibbs energy of micellization in water-organic solvents mixtures.