Research Note pubs.acs.org/IECR
Evaluation of Ion Effects on Surfactant Aggregation from Improved Molecular Thermodynamic Modeling Yakun Zhu* and Michael L. Free Department of Metallurgical Engineering, University of Utah, 135 S 1460 E, Room 412, Salt Lake City, Utah 84112, United States S Supporting Information *
ABSTRACT: An improved molecular thermodynamic model has been developed and applied to various pure, binary, and ternary mixed surfactants in aqueous solution containing salt (0−3 M). The effect of counterion activity and surfactant activity on surfactant aggregation is considered. The effect of counterion and co-ion specificity on aggregation properties is successfully evaluated. The predicted aggregation properties, including critical micelle concentration (cmc), micelle shape, micelle size, and sphere-to-rod transition, agree well with experimental data. The developed model provides a potential method to evaluate ion effects on aggregation properties of various surfactants in salt solution at various concentration levels, and thus will be of great value to guide the application of surfactants in industrial products and processes, such as corrosion prevention, oil recovery, and pharmaceuticals.
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INTRODUCTION Surfactants have been widely used in many industrial products and processes, such as corrosion prevention, oil recovery, pharmaceuticals, food industries, cosmetics, biological fields, mineral flotation, and other areas.1−4 Particularly, surfactant mixtures are well-known because of the superior physicochemical properties and capabilities in efficient solubilization, dispersion, suspension, and transportation, when compared to the production and use of pure surfactants.1−4 Despite extensive progress in theoretical and experimental work that has been made in the study of aggregation properties of ionic surfactants5−8 the effects of added salt and specific ions (dissociated from surfactants and salts) are not well understood. The ions usually shift the critical micelle concentration (cmc), micelle size (aggregation number), sphere-to-rod transition, and counterion binding coefficient.9,10 The micelle shape, micelle composition (for mixed surfactants), and micelle distribution are also affected.9,10 It is reported that the major effect of specific ions arises from the counterion at relatively low to immediate salt concentration.11 The counterion usually depresses the cmc and the degree of depression follows the Hofmeister series: Li+ < Na+ < K+ < Cs+ for anionic surfactants; OH− < F− < Cl− < Br− < NO3− < ClO3− < I− < benzoate− < salicylate− for cationic surfactants.9,12 For micelle size and sphere-to-rod transition the effect of counterion is generally in the same order as for cmc.9 At low salt concentration the co-ion effect on cmc, micelle size, and sphere-to-rod transition is negligible.8,13,14 However, as salt concentration increases the co-ion effect becomes increasingly noticeable.8,13 Particularly at relatively high salt concentration the co-ion effect on micelle size becomes dramatic as discussed in the text below. In the present work an improved model based on existing molecular thermodynamic theory2,5,8,15,16 has been applied to various pure and mixed surfactants. Activities of monomeric surfactant and counterion, which are evaluated from the Setchenov equation17 and Pitzer’s method18 or the Davies19 © 2015 American Chemical Society
equation, respectively, are incorporated in the model. The specific headgroup-counterion pair is introduced to model counterion specificity. The counterion binding coefficient is initially set as a variable and its optimal value is found by minimizing micellization free energy. The effect of co-ion is reflected from salt-dependent factors, including the Setchenov coefficient ks, the dielectric decrement of salt δs, and the correlation between the change of surface tension and the change of salt concentration of aqueous solution, dσo/dCs (σo is surface tension and Cs is salt concentration), as listed in Table 1. The radius of hydrated ion is summarized in Table 2. The Table 1. Model Parameters of Specific Salt salt
ks (L/mol)20
dσo/dCs (mN/(m M))21
δs22
LiCl NaCl KCl CsCl NaBr
0.11 0.05 0.04 0.03 0.03
2.2 2.1 1.84 1.6 1.89
−13.07 −11.27 −9.67 −7.87 −11.87
Table 2. Radius of Hydrated Ions23 ions
Li+
Na+
K+
Cs+
Cl−
Br−
radius (nm)
0.238
0.184
0.125
0.119
0.121
0.118
developed model has been applied to pure (anionic/cationic), binary (anionic/nonionic), and ternary (anionic/nonionic/ nonionic, and cationic/cationic/cationic) mixed surfactants in aqueous solution containing various salt concentrations. The predicted cmc, micelle size, counterion binding coefficient, and Received: Revised: Accepted: Published: 9052
June 10, 2015 August 26, 2015 August 27, 2015 August 27, 2015 DOI: 10.1021/acs.iecr.5b02103 Ind. Eng. Chem. Res. 2015, 54, 9052−9056
Research Note
Industrial & Engineering Chemistry Research
Figure 1. (a) cmc and (b) weight-based aggregation number nw of alkyl sulfate XDS vs salt XCl concentration. X = Li+, Na+, K+, and Cs+. Solid and dashed lines represent model prediction; symbols represent experimental data cited from references.24−29 Model inputs based on experimental conditions: 25−45 °C, and total solution concentration of surfactant set at 10−100 mM depending on specific surfactant. The experimental cmc data of LiDS, KDS, and CsDS at salt concentration ≥1 M is reported from the present research.
and Stern layer thickness dst), and associated calculation are provided by Supporting Information. The cmc (in mole fraction basis Xcmc) is estimated using the optimized free energy Δμom* based on the equation below
sphere-to-rod transitions are in good agreement with reported values.
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METHODS AND EXPERIMENTS Assuming the monomeric surfactant mi (i = 1, 2, or 3, ...) is completely dissociated in aqueous solution containing counterion mj (j = 1, 2, or 3, ...) but in the micelle form the surfactant is associated with some extent with counterions, the surfactant micellization is described by the following process
⎛ Δμo * ⎞ Xcmc = exp⎜⎜ m ⎟⎟ ⎝ kT ⎠
where k is Boltzmann constant. The homologous cationic surfactants benzalkonium chlorides (BAC), including benzyl dimethyl dodecyl ammonium chloride (C12BzCl), benzyl dimethyl tetradecyl ammonium chloride (C14BzCl), and benzyl dimethyl hexadecyl ammonium chloride (C16BzCl), and alkali metal dodecyl sulfate were supplied by Sigma-Aldrich Co. LLC with assay values higher than 99%. The cmc of surfactants was calculated from the plots of surface tension vs surfactant concentration in solution. The experimental data of other surfactants are cited from literature. The surface tension of test solutions was measured within a precision of 0.1 mN/m by the platinum ring method using a Krüss K10 ST digital tensiometer, equipped with an isothermal vessel holder. All the measurements were performed at a constant temperature of 40 ± 0.2 °C, which has been shown to be higher than the Krafft point of the surfactants and their mixtures in aqueous media containing various concentrations of salt. The constant temperature was maintained through a water circulation bath using a Polystat temperature controller, purchased from Cole-Parmer. The platinum ring was rinsed with water and heated to an orange color using a Bunsen burner between tests to ensure the complete removal of contaminants. Triplicate measurements were used to confirm reproducibility.
n(∑ αizi +∑j δjzj)
n ∑ αimi zi + n ∑ δjmj zj ↔ Mnαiδj i
(1)
j
i
where αi is the composition of surfactant i in the micelle, Mnαiδj, which has an micelle size n, micelle composition αi, and a counterion binding coefficient δj. For micelles of pure surfactant, αi = 1; for mixed micelles, 0 < αi < 1. zi and zj are the valences of ionic surfactant i in dissociated form and counterion j. For nonionic surfactant i, zi = 0 and δj = 0. The micellization free energy Δμom is estimated from several contributing terms as described below: o o o o o Δμmo = Δμtrto + Δμint + Δμpack + Δμsto + Δμent + Δμelec + Δμact
(2)
Δμotrt,
Δμoint,
Δμopack,
Δμost,
Δμoent,
(3)
Δμoelec
where and are the free energy contributions from hydrocarbon transfer from water into micelle, formation of micellar core−water interface, hydrocarbon tail packing in the micelle, surfactant headgroup steric interaction, headgroup−counterion mixing, and electroo static interaction, respectively.2,8,15 Δμact comes from the 2 activity contribution. Free energy micellization as a function of variables, including on micelle shape S, micelle composition αi (i represents surfactant), micellar core minor radius lc, and counterion binding coefficient δj (j represents ion), at given solution conditions is minimized using a home-designed MATLAB code. The minimized micellization free energy is then used for the evaluation of cmc, micelle size, counterion binding coefficient, and sphere-to-rod transition. Descriptions of model derivation, model parameters (area per surfactant molecule at micellar core-water interface a, distance from the surface of micellar core to the center of charged headgroup dch,
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RESULTS AND DISCUSSION The model is applied to pure anionic surfactants, alkali metal dodecyl sulfate XDS, in aqueous solution with various added salts XCl (X = Li+, Na+, K+, and Cs+) to examine the counterion effect, as shown in Figure 1 which presents the model prediction (various lines) and experimental data (various symbols) of cmc and weight-based micelle size nw. The predicted cmc agrees well with experimental data at low to 9053
DOI: 10.1021/acs.iecr.5b02103 Ind. Eng. Chem. Res. 2015, 54, 9052−9056
Research Note
Industrial & Engineering Chemistry Research
Figure 2. (a) cmc and (b) weight-based aggregation number nw of alkyltrimethylammonium bromide/chloride CnTAX (X = Br−, Cl−) vs salt concentration. The salt type is specified as it is in the legend; if not specified the salt is NaBr. Solid and dashed lines represent model prediction; symbols represent experimental data cited from references.30−35 Model inputs based on experimental conditions: 35 °C, and total solution concentration of surfactant set at 10 mM for C14TABr and C16TABr/Cl, and at 30 mM for C12TABr.
Figure 3. (a) cmc, (b) weight-based aggregation number nw, and (c) counterion binding coefficient of binary mixed surfactants SDS and OG vs solution composition or micelle composition of OG. Solid and dashed lines represent model prediction; symbols represent experimental data cited from references.37,38 Model inputs based on experimental conditions: 20 mM NaCl, 25 °C, various mixed molar ratios, and total solution concentration of mixed surfactants set at 25 mM.
C12TABr with added NaBr above 1 M. An excellent agreement is observed between predicted and experimental nw. The transition threshold of salt concentration is well predicted as indicated by the change of nw. For C16TABr with KBr for example, the predicted threshold is 0.08 M and the experimental threshold is 0.1 M.34 The Hofmeister series, which indicates Cl− < Br− for cationic surfactant aggregation, is reflected by the effect of counterion on the depression of cmc, and on the increment of nw by comparing C16TABr and C16TACl (see Figure 2). The effect of co-ion is examined by adding different salts (NaBr and KBr) to the aqueous solutions containing C16TABr: the co-ion effect on cmc and on nw is minor at low salt concentration, whereas with increasing salt concentration the co-ion effect becomes increasingly noticeable as shown in Figure 2. It has been reported that upon varying the concentration of KBr the micelle size nw of C16TABr from experimental measurement goes through a maximum value around the concentration of 1.5 M for KBr, which corresponds to the maximum viscosity or the biggest cylindrical micelle.35,36 However, the micelle continues to grow according the model prediction. The model is applied to anionic/nonionic surfactant mixture dodecyl sulfate (SDS) and octylglucoside (OG) with NaCl in
medium salt concentrations (
