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. 2018 Sep 10;3(9):10907–10911. doi: 10.1021/acsomega.8b01667

Micelle and Surface Tension of Double-Chain Cationic Surfactants

Chi Minh Phan †,*, Shin-ichi Yusa ‡, Tomoko Honda ‡, Komol Kanta Sharker ‡, Anita Evelyn Hyde †, Cuong Van Nguyen †,§
PMCID: PMC6645429  PMID: 31459201

Abstract

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Since the early 20th century, the slightly disparate measurements of a surfactant’s critical micelle concentration, via either surface tension or electrical conductivity, have been assumed one and the same. As a consequence, the possibility that micelles can adsorb at the air/water surface has been disregarded and has led to some abnormalities in the literature that remain as yet unresolved. In this paper, we closely examined the two critical concentrations for a double-chain cationic surfactant. We confirmed that the two concentrations represent two different physical phenomena. Furthermore, the results verified the existence of surface micelles, which are different from the bulk micelles. The formation of the surface micelles can be explained by the structural changes of the adsorption layer, which was also corroborated by molecular simulations. The findings open new challenges to examine the surface adsorption, which  offers new insights into the molecular levels.

Introduction

In surfactant studies, the critical micellization concentration (cmc) is an important measure for surfactant characterization. The cmc is often used as the effective concentration threshold for practical applications.1 In the literature, the cmc is often measured via either surface tension or electrical conductivity, these being the two oldest and simplest methods. Furthermore, these two methods can be done without additional chemical probes, which can interfere with the micellization process.2

The first method (surface tension) is based on the surface properties of the sample, whereas the second method (conductivity) is based on the properties in the bulk. The two values, denoted here as ccs and ccc, respectively, are demonstrated in Figure 1. In both cases, the cmc is defined as the breakpoint in the measured variable with respect to concentration.

Figure 1.

Figure 1

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Critical concentrations of surfactant via surface tension and electrical conductivity (a) typical data (b) dodecyltrimethylammonium bromide mixture with a trianion, where the conductivity-determined cmc was much higher than the tension-determined cmc. [“Reprinted with permission from ref (18). Copyright (2009) American Chemical Society”.]

Changes in conductivity provided the first evidence of aggregate existence, which were originally thought of as the associated form of the surfactant.3 Subsequently, it was argued that the aggregates consist of multiple molecules and counterions and are referred to as “micelles”.4 It should be noted that there is a wide transition region between the two linear trends in the conductivity data. Consequently, complicated mathematical treatments can be applied instead of linear regression5 to improve the precision in identifying the breakpoint. With surface tension data, determination of the breakpoint remains almost the same as it was a century ago.1

After earlier reports with anionic surfactants,6 most studies in the literature assumed that the two measurements of the critical micelle concentration held the same physical meaning, attributing the variance in the values to artifacts of the measurement method. This assumption allowed surfactant studies to be significantly simplified. The main consequences can be found in the hypotheses in now-common texts:

  • (1)

    Surface activity (or surface tension reduction) is governed by the monomer only, not aggregates/micelles.1

  • (2)

    The saturation of the surface layer corresponds to interfacial saturation of the monomer. All excessive surfactant molecules form micelles and do not affect the surface layer.7

  • (3)

    These same arguments apply equally to oil/water and solid/water interfaces.

In summary, if the two concentrations (ccs and ccc) are the same, it follows that micelles have no impact on the surface layer. Yet, this assumption has not been verified. Seven decades ago, Lottermoser and Stoll proposed that micelles can quantitatively interact with the adsorbed monomer and affect the surface tension.8 Subsequently, Powney and Addison6 argued that micelles may indirectly affect surface tension by increasing the concentration of the free counterions (as micelles are not neutrally charged and their balancing counterions remains dissociated in the bulk). Later on, Israelachvili has showed theoretically that “hemimicelles” can exist at the air/water interface.9 Recent studies on adsorbed surfactants at the air/water surface have indicated that micelles can cause a deviation between the obtained adsorption and the theoretical prediction from the Gibbs adsorption equation, occurring at as low as 80% of cmc.10 Our previous tension model also demonstrated the failure of the conventional model near the cmc.11 More recently, Rusanov looked closely at the surface tension near cmc of cationic and nonionic surfactants and concluded that the micelles can slightly reduce surface tension above cmc.12 Collectively, the available reports suggested that micelles have a certain impact on the surface tension above cmc. Yet, under what conditions will micelles start interacting with surface tension? Furthermore, is there any quantitative evidence of such an impact?

This short paper addresses the above two questions. First, we re-examine the reported data for cmc measurement of common cationic surfactants. Subsequently, we present evidence that the two values are not the same. More importantly, we confirm the measurable impact of micelles on surface tension. Finally, the consequences, in both fundamental knowledge and practical application, are discussed.

Analysis

While the last century has seen many reports in the literature of discrepancies in the cmc measured by different methods, the difference could be caused by impurities or measurement errors. Hence, we only list the studies in which both reported values were obtained from the same sample (Table 1). The two values are denoted as ccs (from surface tension measurement) and ccc (from conductivity measurement). Because the reported cmc for all ionic surfactant are enormous (Rosen has compiled a long table of 16 pages),1 we will restrict ourselves to the cationic surfactants with trimethyl ammonium as the head group. It should be noted that the results in Table 1 were obtained within the last 20 years and employed the latest apparatuses.

Table 1. Reported Critical Concentration for Alkyl Trimethyl Ammonium Bromide (in mM).

surfactants reference ccs ccc
C18H37(CH3)3N Br (13) 0.35 0.33
C16H33(CH3)3N Br (14) 0.91 1.0
  (13) 1.00 0.98
  (15) 0.80 0.90
C14H29(CH3)3N Br (14) 3.9 3.2
  (13) 3.98 3.90
  (15) 2.34 3.60
C12H25(CH3)3N Br (14) 15.3 14.3
  (16) 15.0 15.5
  (13) 15.20 15.10
  (15) 14.45 15.8
C10H21(CH3)3N Br (14) 66.9 58.8
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Statistically, the reported values cannot confirm the hypothesis that ccc = ccs. The most profound difference was reported by Menger and Shi, in which ccc was 10 times higher than ccs.17 The result subsequently led to the debate on the applications of the Gibbs excess adsorption and surface tension.18 It is noteworthy that this large deviation (Figure 1b) was obtained for the mixture of C12H25(CH3)3NBr and a trianionic compound, rather than a single surfactant.

In this paper, we confirm the difference with another cationic surfactant, a double-chain surfactant with dimethylammonium as the head group. This class of surfactants has two distinct breakpoints in surface tension.16,19 The synthesis and measurement of the surfactant hexadecyldimethyldodecyl ammonium bromide, C16H33C12H25(CH3)2NBr, are described in the Supporting Information. In addition to the surface tension and conductivity measurements, a simulation of the surfactant at the air/water interface was also carried out. The results (Figure 2a) clearly show two critical concentrations from surface tension, consistent with previous reports.19 With conductivity results (Figure 2b), it is clear that ccs1 < ccc < ccs2. The relative differences between these critical concentrations were more than three times. An analysis with symmetric double-chain surfactant, C12H25C12H25(CH3)2NCl,20 also indicated that ccc was ∼3ccs1 (whereas ccs2 was non-detectable).

Figure 2.

Figure 2

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Surface tension (a) and conductivity (b) of hexadecyldimethyldodecyl ammonium bromide. Critical concentrations: ccs1 = 3.1 × 10–6 M, ccs2 = 1.1 × 10–4 M and ccc = 3.9 × 10–5 M.

The reduction of surface tension between ccs1 and ccs2 indicates that the aggregate(s) have a quantifiable effect on the surface tension. Here, we propose a possible mechanism, as illustrated in Figure 3: the formation of surface micellization. In this instance, surface micelles are formed when monomers from the bulk aggregate together with surfactant molecules on the surface. The micelles should have an asymmetric shape, such as a “hemisphere”, as predicted theoretically by Israelachvili.9 The existence of “hemimicelles” on solid surfaces has been well-accepted21 and directly observed well below the ccc.22 At the air/water surface, the surface micelles reduce surface tension by re-arranging the surfactant monolayer. Because of the steric repulsion between the two tails, adsorbed monolayer of the surfactants have a looser packing, in comparison with single-chain surfactants. The notion that both tails of the surfactant are pointing to air phase was originated from the molecular simulation (Figure 4). It can be seen that the ends of both (CH3– group) are clearly in the air/phase, ∼0.5 nm from the Gibbs dividing plane. As a result of the looser packing, the surface tension of double-tailed surfactant is higher than that of the single-tailed surfactant. Experimentally, the surface tension of C16H33C12H25(CH3)2NBr at cs1 (Figure 2a) was 40 mN/m, which is ∼7 mN/m higher than the surface tension at the cmc of C16TAB. Unfortunately, we cannot simulate the surface micelle formation because of the limited computing capacity. It has been verified that the simulation of bulk aggregates would require a timescale of 50 ns and simulation cell of more than 5 nm.21 For the surface micelles, the simulation box and time would be much larger to correctly simulate the unfolding of the carbon chains and fluctuation of the surface.23

Figure 3.

Figure 3

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Proposed mechanisms of micelles/surface tension interaction: “surface micelle” and “adsorbed micelle”. The shaded areas represent the “hydrophobic core” of the micelles.

Figure 4.

Figure 4

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Density distribution of double-tailed surfactant at air/water interface, the Gibbs dividing plane was determined from water profile.

Previously, it has been proposed that the bulk micelles of double-tailed surfactants could consist of a combination of different size, from dimers and trimers to large bilayer vesicles.24 Hence, one might expect that the surface micelles can exist in a range of different size as well. Qualitatively, there is a key difference between the surface and bulk micelles. The bulk micelles of double-chains surfactants can contain both tails, especially when the second tail is longer than six carbons.25 The proposed surface micelles, in contrast, should contain a single chain only. The surface micelles are formed at much lower concentration (cs1) than the bulk micelle. In this case, the adsorbed monolayer acts as “seeds” to lower the required entropy for aggregation. The relative ease between surface/bulk micelle formation is similar to heterogeneous/homogeneous nucleation. The surface micelles reach saturation at cs2, above which all excessive surfactants form bulk micelles.

Discussion and Conclusion

The critical insight from this double-tailed surfactant is that the impact of micelles on surface tension can be significant enough to be measurable. The tension difference between ccs1 and ccs2 was more than 15 mN/m. On the other hand, the reduction of single-chain C12TAB micelles was about 0.5 mN/m,26 which is in same order of the measurement errors. The difference was systematically observed for a large number double-chain surfactants with long hydrophobic tails.19 The second tail of the surfactant clearly plays a critical role in the surface aggregation and surface tension reduction. As this branch gets shortened, the tension difference between ccs1 and ccs2 is gradually diminished.19 Eventually, the surfactant is reduced to C16TAB and the impact of micelles on surface tension becomes unobservable. Nevertheless, the micelles of C16TAB can still affect the adsorbed surfactants at the surface, as reported via neutron reflectometry.10 The reduction was also smaller when the longer chain was reduced from 16 to 1419 or 12 carbons.16 For these double-chain surfactants, ccs2 is the true threshold for surface saturation, which comprises a multilayer arrangement. While the available experimental techniques might not be able to distinguish the surface micelles,9 one might rely on the theoretical model or simulation. There are a number of mathematical formulae to model the gradual tension reduction by the surface micelles. For example, one of the possibilities is the theoretical combination of mass action law and Gibbs adsorption equation.12 Furthermore, the formation/adsorption of the surface micelles can be further examined by extending the molecular simulations.

The observation can be expected with other surfactant types of double-chain surfactants, either anionic or nonionic ones. Furthermore, the phenomena can be applicable to the famous double-chain structure, gemini surfactants.27 For these surfactants, the two tails are attached to two separate heads, which are distanced by a short alkanediyl spacer, CsH2s. The geminis can be synthesized with many different head-groups and have many advantages over the single-chain surfactants.28 For the gemini structure, however, the spacer between head-groups plays a crucial role. Available reports with the dimethylammonium bromides29 showed that the conductivity-based cmc increased with the spacer length initially and then decreased once the spacer is greater than 5 carbons. Hence, it can be expected that the short-spaced geminis behave as the double-chain surfactant in this study, that is, forming distinct surface micelles. The long-spaced geminis, in contrast, should behave as single-chain surfactants.

In conclusion, the results showed that micelles can be formed at the surface surfactant layer, independently from the bulk micelles. Most importantly, the two measured critical concentrations correspond explicitly to different physical phenomena. To account for the differences, the surface tension should be modeled by considering a real interfacial zone with multiple molecular arrangements between different species. The value of ccs2 should be referred to as the “critical surface concentration”, at which point the air/water surface is truly saturated. As micelles can interfere with the surfactant monolayer, the saturation concentration might be different from corresponding oil/water and solid/water surfaces. Hence, the saturation thresholds of surfactants should be evaluated against the specific surface, rather than using the conductivity data.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b01667.

  • Synthesis, characterization, and measurement procedure are included in the Supporting Information (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao8b01667_si_001.pdf (204.6KB, pdf)

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Associated Data

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Supplementary Materials

ao8b01667_si_001.pdf (204.6KB, pdf)

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