Markov chain model for the critical micelle concentration of surfactant mixtures

An extension of the Markov chain model (MC) for micellization is proposed, which allows the distribution of the surfactants between the monomer solution and the micelles in a mixed surfactant system to be predicted. The dependence of the critical micelle concentration (cmc) on the composition of the solution is investigated. The equilibrium thermodynamic relation between cmc and micelle composition is discussed. The case of ternary mixtures is analyzed, and theoretical triangular diagram is constructed according to MC. Available experimental data for binary and ternary mixtures agree well with the new MC theory. The dependence of MC parameters on the structure of the surfactants is discussed. Comparison of MC with the simple mixture (“regular solution”) model is presented. The parameters of the MC theory are related to the interaction parameter β _SM of the simple mixture model.     

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.     

甲酰胺与正负离子表面活性剂有序溶液的研究

对羧酸钠与烷基三甲基溴化铵1：1混合体系的研究表明：常温下各体系在不同比例甲酰胺（FA）／水混合溶剂中，表面张力随浓度变化均有明显的转折点，显示了混合体系中胶团的存在．实验中发现随混合溶剂中FA比例增加，各体系的临界胶团浓度（cmc）增大．在较高温度下发现在甲酰胺中亦存在着因胶团形成而产生的表面张力-浓度对数（γ－logc）曲线的转折点，利用相分离模型对体系胶团热力学参数进行了计算．并探讨了FA对正负离子表面活性剂囊泡的影响．     

Quantifying the hydrophobic effect. 2. A computer simulation-molecular-thermodynamic model for the micellization of nonionic surfactants in aqueous solution

In this article, the validity and accuracy of the CS-MT model is evaluated by using it to model the micellization behavior of seven nonionic surfactants in aqueous solution. Detailed information about the changes in hydration that occur upon the self-assembly of the surfactants into micelles was obtained through molecular dynamics simulation and subsequently used to compute the hydrophobic driving force for micelle formation. This information has also been used to test, for the first time, approximations made in traditional molecular-thermodynamic modeling. In the CS-MT model, two separate free-energy contributions to the hydrophobic driving force are computed. The first contribution, gdehydr, is the free-energy change associated with the dehydration of each surfactant group upon micelle formation. The second contribution, ghydr, is the change in the hydration free energy of each surfactant group upon micelle formation. To enable the straightforward estimation of gdehydr and ghydr in the case of nonionic surfactants, a number of simplifying approximations were made. Although the CS-MT model can be used to predict a variety of micellar solution properties including the micelle shape, size, and composition, the critical micelle concentration (CMC) was selected for prediction and comparison with experimental CMC data because it depends exponentially on the free energy of micelle formation, and as such, it provides a stringent quantitative test with which to evaluate the predictive accuracy of the CS-MT model. Reasonable agreement between the CMCs predicted by the CS-MT model and the experimental CMCs was obtained for octyl glucoside (OG), dodecyl maltoside (DM), octyl sulfinyl ethanol (OSE), decyl methyl sulfoxide (C10SO), decyl dimethyl phosphine oxide (C10PO), and decanoyl-n-methylglucamide (MEGA-10). For five of these surfactants, the CMCs predicted using the CS-MT model were closer to the experimental CMCs than the CMCs predicted using the traditional molecular-thermodynamic (MT) model. In addition, CMCs predicted for mixtures of C10PO and C10SO using the CS-MT model were significantly closer to the experimental CMCs than those predicted using the traditional MT model. For dodecyl octa(ethylene oxide) (C12E8), the CMC predicted by the CS-MT model was not in good agreement with the experimental CMC and with the CMC predicted by the traditional MT model, because the simplifying approximations made to estimate gdehydr and ghydr in this case were not sufficiently accurate. Consequently, we recommend that these simplifying approximations only be used for nonionic surfactants possessing relatively small, non-polymeric heads. For MEGA-10, which is the most structurally complex of the seven nonionic surfactants modeled, the CMC predicted by the CS-MT model (6.55 mM) was found to be in much closer agreement with the experimental CMC (5 mM) than the CMC predicted by the traditional MT model (43.3 mM). Our results suggest that, for complex, small-head nonionic surfactants where it is difficult to accurately quantify the hydrophobic driving force for micelle formation using the traditional MT modeling approach, the CS-MT model is capable of making reasonable predictions of aqueous micellization behavior.     

Thermodynamics of micellization of multiheaded single-chain cationic surfactants

The energetics of micelle formation of three single-chain cationic surfactants bearing single (h = 1), double (h = 2), and triple (h = 3) trimethylammonium [(+)N(CH(3))(3)] headgroups have been investigated by microcalorimetry. The results were compared with the microcalorimetric data obtained from well-known cationic surfactant, cetyl trimethylammonium bromide (CTAB), bearing a single chain and single headgroup. The critical micellar concentrations (cmc's) and the degrees of counterion dissociation (alpha) of micelles of these surfactants were also determined by conductometry. The cmc and the alpha values increased with the increase in the number of headgroups of the surfactant. The relationship between the cmc of the surfactant in solution and its free energy of micellization (DeltaG(m)) was derived for each surfactant. Exothermic enthalpies of micellization (DeltaH(m)) and positive entropies of micellization (DeltaS(m)) were observed for all the surfactants. Negative DeltaH(m) values increased from CTAB to h = 1 to h = 2 and decreased for h = 3 whereas DeltaS(m) values decreased with increase in the number of headgroups. The DeltaG(m) values progressively became less negative with the increase in the number of headgroups. This implies that micelle formation becomes progressively less favorable as more headgroups are incorporated in the surfactant. From the steady-state fluorescence measurements using pyrene as a probe, the micropolarities sensed by the probe inside various micelles were determined. These studies suggest that the micelles are more hydrated with multiheaded surfactants and the micropolarity of micelles increases with the increase in the number of headgroups.     

Microcalorimetric and conductivity studies with micelles prepared from multi-headed pyridinium surfactants

A set of novel single-chain surfactants bearing one (P1), two (P2), and three (P3) pyridinium headgroups have been synthesized in an attempt to achieve control over the aggregate properties. The critical micellar concentrations (cmc's) and the degrees of counterion dissociation (alpha) of micelles of these surfactants were determined by conductometry. The cmc and the alpha values increased with increase in the number of headgroups of the surfactant. The thermodynamics of micellization of these surfactants were investigated by microcalorimetry, and the results were compared with that of well-known single-chain/single-headgroup surfactant, cetylpyridinium bromide (CPB). The relationship between the cmc of surfactant in solution and its free energy of micellization (deltaG(o)m) was derived for each surfactant. Exothermic enthalpies of micellization (deltaH(o)m) and positive entropies of micellization (deltaS(o)m) were observed for all the surfactants. deltaH(o)m values were found to be more negative for CPB than P1, and it increased with a negative sign from P1 to P2 and decreased for P3. In contrast the deltaS(o)m values decreased with increase in the number of headgroups. The deltaG(o)m values progressively became less negative with increase in the number of headgroups. This implies that micelle formation becomes less favorable as more headgroups are incorporated in the surfactant.     

Mechanism of surfactant micelle formation

The mechanism of micelle formation of surfactants sodium dodecyl sulfate (SDS), n-hexyldecyltrimethylammonium bromide (CTAB) and Triton X-100 (TX-100) in heavy water solutions was studied by 1H NMR (chemical shift and line shape) and NMR self-diffusion experiments. 1H NMR and self-diffusion experiments of these three surfactants show that their chemical shifts (delta) begin to change and resonance peaks begins to broaden with the increase in concentration significantly below their critical micelle concentrations (cmc's). At the same time, self-diffusion coefficients ( D) of the surfactant molecules decrease simultaneously as their concentrations increase. These indicate that when the concentrations are near and lower than their cmc's, there are oligomers (premicelles) formed in these three surfactant systems. Carefully examining the dependence of chemical shift and self-diffusion coefficient on concentration in the region just slightly above their cmc's, one finds that the pseudophase transition model is not applicable to the variation of physical properties (chemical shift and self-diffusion coefficient) with concentration of these systems. This indicates that premicelles still exist in this concentration region along with the formation of micelles. The curved dependence of chemical shift and self-diffusion coefficient on the increase in concentration suggests that the premicelles grow as the concentration increases until a definite value when the size of the premicelle reaches that of the micelle, i.e., the system is likely dominated by the monomers and micelles. Additionally, the approximate values of premicelle coming forth concentration (pmc) and cmc were obtained by again fitting chemical shifts to reciprocals of concentrations at a different perspective, and are in good accordant with experimental results and literature values and prove the former conclusion.     

Self-aggregation of binary mixtures of alkyltriphenylphosphonium bromides: a critical assessment in favor of more than one kind of micelle formation

The micellization behavior of binary combinations of alkyltriphenylphosphonium bromides (ATPBs) with alkyl chain carbons 10, 12, 14, and 16 has been studied by conductometry and calorimetry. The combinations C(10)-C(12), C(10)-C(14), C(10)-C(16), C(12)-C(14), C(12)-C(16), and C(14)-C(16) were found to form two cmc's by both the methods, with good agreement, except C(14)-C(16)TPB, which has evidenced only a single cmc by calorimetry for all combinations. The combinations C(10)-C(12) (for both cmc(1) and cmc(2)) and C(10)-C(14)TPB (for cmc(2)) formed ideal mixtures, whereas the rest were nonideal. In the nonideal binary mixtures, the ATPB components showed antagonistic interaction with each other. The cmc, interaction parameter (beta), mixed micellar composition, extent of counterion binding, and thermodynamic parameters for the micellization process have been reported and discussed. The enthalpy of mixed micelle formation has been found to have a fair correlation with a Clint-type relation applicable to ideal binary mixtures of surfactants.     

Mixed micelle formation among anionic gemini surfactant (212) and its monomer (SDMA) with conventional surfactants (C12E5 and C12E8) in brine solution at pH 11

The micellization of anionic gemini surfactant, N,N'-ethylene(bis(sodium N-dodecanoyl-beta-alaninate)) (212), and its monomer, N-dodecanoyl-N-methyl alaninate (SDMA), and polyethoxylated nonionic surfactants, C(12)E(5) and C(12)E(8), has been studied tensiometrically in pure and mixed states in an aqueous solution of 0.1 M NaCl at pH 11 to determine physicochemical properties such as critical micellar concentration (cmc), surface tension at the cmc (gamma(cmc)), maximum surface excess (Gamma(max)) and minimum area per surfactant molecule at the air/water interface (A(min)). The theories of Rosen, Rubingh, Motomura, Maeda, and Nagarajan have been applied to investigate the interaction between those surfactants at the interface and in the micellar solution, the composition of the aggregates formed, the theoretical cmc in pure and mixed states, and the structural parameters as proposed by Tanford and Israelachvili. Various thermodynamic parameters (free energy of micellization and interfacial adsorption) have been calculated with the help of regular solution theory and the pseudophase model for micellization.     

Micelle–monomer equilibria in solutions of ionic surfactants and in ionic–nonionic mixtures: A generalized phase separation model

On the basis of a detailed physicochemical model, a complete system of equations is formulated that describes the equilibrium between micelles and monomers in solutions of ionic surfactants and their mixtures with nonionic surfactants. The equations of the system express mass balances, chemical and mechanical equilibria. Each nonionic surfactant is characterized by a single thermodynamic parameter — its micellization constant. Each ionic surfactant is characterized by three parameters, including the Stern constant that quantifies the counterion binding. In the case of mixed micelles, each pair of surfactants is characterized with an interaction parameter, β, in terms of the regular solution theory. The comparison of the model with experimental data for surfactant binary mixtures shows that β is constant — independent of the micelle composition and electrolyte concentration. The solution of the system of equations gives the concentrations of all monomeric species, the micelle composition, ionization degree, surface potential and mean area per head group. Upon additional assumptions for the micelle shape, the mean aggregation number can be also estimated. The model gives quantitative theoretical interpretation of the dependence of the critical micellization concentration (CMC) of ionic surfactants on the ionic strength; of the CMC of mixed surfactant solutions, and of the electrolytic conductivity of micellar solutions. It turns out, that in the absence of added salt the conductivity is completely dominated by the contribution of the small ions: monomers and counterions. The theoretical predictions are in good agreement with experimental data.     

A Viscometric and Conductometric Investigation of the Micellar and Solution Properties of Two-Headed Surfactant Systems, the Disodium 4-Alkyl-3-sulfonatosuccinates

A family of two-headed surfactants, the disodium 4-alkyl-3-sulfonatosuccinates, has been prepared by reacting maleic anhydride with the appropriate chain-length alcohol and subsequent addition of sodium bisulfite to the corresponding monoester. The properties of the micelles formed by these compounds in aqueous solution (aggregation numbers, degrees of counterion binding, and the cmc values) have been investigated as a function of temperature and surfactant chain length using viscosity, density, and conductance measurements. The critical micelle concentrations (cmc's) and the aggregation numbers appear to indicate that, in agreement with the earlier literature on other two-headed surfactants systems, these amphiphiles have higher cmc and lower aggregation numbers when compared to single-headed surfactants of comparable chain length. In addition, viscosity B coefficients and the thermodynamic parameters of activation of viscous flow have been determined. These results are interpreted in terms of the structure-making or -breaking properties of the surfactant amphiphiles below the cmc region. Finally, the thermodynamic properties of micelle formation have been estimated from the dependence of the cmc on the absolute temperature according to the charged pseudo-phase separation model of micelle formation. All these results are discussed in terms of how the addition of the second charged surfactant headgroup alters the micellar and solution properties of two-headed surfactants vs. their single-headed counterparts.     

Thermodynamic characterization of 3-[(3-cholamidopropyl)-dimethylammonium]-1-propanesulfonate (CHAPS) micellization using isothermal titration calorimetry: temperature, salt, and pH dependence

A systematic investigation of the micellization process of a biocompatible zwitterionic surfactant 3-[(3-cholamidopropyl)-dimethylammonium]-1-propanesulfonate (CHAPS) has been carried out by isothermal titration calorimetry (ITC) at temperatures between 278.15 K and 328.15 K in water, aqueous NaCl (0.1, 0.5, and 1 M), and buffer solutions (pH = 3.0, 6.8, and 7.8). The effect of different cations and anions on the micellization of CHAPS surfactant has been also examined in LiCl, CsCl, NaBr, and NaI solutions at 308.15 K. It turned out that the critical micelle concentration, cmc, is only slightly shifted toward lower values in salt solutions, whereas in buffer media it remains similar to its value in water. From the results obtained, it could be assumed that CHAPS behaves as a weakly charged cationic surfactant in salt solutions and as a nonionic surfactant in water and buffer medium. Conventional surfactants alike, CHAPS micellization is endothermic at low and exothermic at high temperatures, but the estimated enthalpy of micellization, ΔHM0, is considerably lower in comparison with that obtained for ionic surfactants in water and NaCl solutions. The standard Gibbs free energy, ΔGM0, and entropy, ΔSM0, of micellization were estimated by fitting the model equation based on the mass action model to the experimental data. The aggregation numbers of CHAPS surfactant around cmc, obtained by the fitting procedure also, are considerably low (nagg ≈ 5 ± 1). Furthermore, some predictions about the hydration of the micelle interior based on the correlation between heat capacity change, Δcp,M0, and changes in solvent-accessible surface upon micelle formation were made. CHAPS molecules are believed to stay in contact with water upon aggregation, which is somehow similar to the micellization process of short alkyl chain cationic surfactants.     

Gemini阳离子表面活性剂在水溶液中胶团化行为的温度效 应与焓、熵补偿

测定了Cemini阳离子表面活性剂C~m-----s-----C~m·2Br(m=8,10,12,;s=2,6及m=12;s=3,4)水溶液的电导,从电导(k)～表面活性剂浓度(c)曲线的转折点可求得临界胶团浓度cmc.实验发现,Gemini阳离子表面活性剂的胶团化倾向明显强于其“单体分子”)即单离子头基单烷烃链表面活性剂)。根据质量作用模型计算了胶经过程的吉布氏能、焓和熵的改变。结果表明Gemini表面活性剂聚集机理和其对应的“单体分子”类似,主要来自熵驱动。所有的焓/熵补偿图均呈现良好的线性关系,补偿直线在γ轴的截距随s减小而变小,这意味着具有较小s的Gemini表面活性剂倾向于生成稳定的胶团。     

Thermodynamics of micellization of tetradecyltrimethylammonium bromide in ethylene glycol–water binary mixtures

The aggregation behaviour of tetradecyltrimethylammonium bromide in ethylene glycol–water mixtures across a range of temperatures has been investigated by electrical conductivity measurements. The critical micelle concentration (cmc) and the degree of counterion dissociation of micelles were obtained at each temperature from plots of differential conductivity, (κ/c) _{T , P} , versus the square root of the total concentration of the surfactant. This procedure not only enables us to determine the cmc values more precisely than the conventional method, based on plots of conductivity against total concentration of surfactant, but also allows straightforward determination of the limiting molar conductance and the molar conductance of micellar species. The equilibrium model of micelle formation was applied to obtain the thermodynamics parameters of micellization. Only small differences have been observed in the standard molar Gibbs free energies of micellization over the temperature range investigated. The enthalpy of micellization was found to be negative in all cases, and it showed a strong dependence on temperature in the ethylene glycol poor solvent system. An enthalpy–entropy compensation effect was observed for all the systems, but whereas the micellization of the surfactant in the solvent system with 20 wt% ethylene glycol seems to occur under the same structural conditions as in pure water, in ethylene glycol rich mixtures the results suggest that the lower aggregation of the surfactant is due to the minor cohesive energy of the solvent system in relation to water. Received: 13 December 1998 Accepted in revised form: 25 February 1999     

Micelle formation of nonionic surfactants in a room temperature ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroborate: surfactant chain length dependence of the critical micelle concentration

Micellization behavior was investigated for polyoxyethylene-type nonionic surfactants with varying chain length (C(n)E(m)) in a room temperature ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroborate (bmimBF(4)). Critical micelle concentration (cmc) was determined from the variation of (1)H NMR chemical shift with the surfactant concentration. The logarithmic value of cmc decreased linearly with the number of carbon atoms in the surfactant hydrocarbon chain, similarly to the case observed in aqueous surfactant solutions. However, the slope of the straight line is much smaller in bmimBF(4) than in aqueous solution. Thermodynamic parameters for micelle formation estimated from the temperature dependence of cmc showed that the micellization in bmimBF(4) is an entropy-driven process around room temperature. This behavior is also similar to the case in aqueous solution. However, the magnitude of the entropic contribution to the overall micellization free energy in bmimBF(4) is much smaller compared with that in aqueous solution. These results suggest that the micellization in bmimBF(4) proceeds through a mechanism similar to the hydrophobic interaction in aqueous surfactant solutions, although the solvophobic effect in bmimBF(4) is much weaker than the hydrophobic effect.     

Aggregation of sodium 1-(n-alkyl)naphthalene-4-sulfonates in aqueous solution: micellization and microenvironment characteristics

In aqueous solution, the micellization and microenvironment characteristics of the micelle assemblies of three anionic surfactants, sodium 1-(n-alkyl)naphthalene-4-sulfonates (SANS), have been investigated by steady-state fluorescence and time-resolved fluorescence decay techniques using pyrene, Ru(bpy)3(2+), and 1,6-diphenyl-1,3,5-hexatriene as fluorescence probes. The critical micelle concentrations (cmc's), effective carbon atom numbers (neff's), hydrophilic-lipophilic balances (HLBs), mean micelle aggregation numbers, micropolarities, and microviscosities of these surfactant micelles have been determined. The logarithmic cmc of the alkylnaphthalene sulfonates decreases linearly with an increase in the neff. The logarithmic aggregation number of the alkylnaphthalene sulfonates increases linearly with an increase in the neff. However, in contrast to the alkylsufonates and the alkylbenzene sulfonates, the aggregation for these alkylnaphthalene sulfonate molecules is less sensitive to the increase in the neff. The micropolarity of these alkylnaphthalene sulfonate micelles is less sensitive to the increase in the alkyl chain length and is lower than that of sodium dodecyl sulfate (SDS). The microviscosity of these alkylnaphthalene sulfonate micelles increases with an increase in the alkyl chain length and is lower than those of nonionic surfactants and zwitterionic surfactants. These results suggest that naphthyl rings have a notable effect on the micellization of SANS.