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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers
A Discrete and Discontinuous Increase in Micellar Aggregation Number: Effects of Alkyl Chain Length on Platonic Micelles Shota Fujii, Shimpei Yamada, Masataka Araki, Ji Ha Lee, Rintaro Takahashi, and Kazuo Sakurai Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b04204 • Publication Date (Web): 30 Jan 2019 Downloaded from http://pubs.acs.org on February 3, 2019
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Langmuir
A Discrete and Discontinuous Increase in Micellar Aggregation Number: Effects of Alkyl Chain Length on Platonic Micelles Shota Fujii†, Shimpei Yamada†, Masataka Araki, Ji Ha Lee, Rintaro Takahashi, and Kazuo Sakurai*
Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan
KEYWORDS Platonic micelle, micellar aggregation number, small-angle X-ray scattering, Tammes problem, calix[4]arene, alkyl chain length
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ABSTRACT Micelles with perfect monodispersity in terms of the aggregation number (Nagg) have recently been discovered, whose values of Nagg interestingly always coincide with the vertex or face number of regular polyhedral structures (i.e., Platonic solids). Owing to the monodispersity of the micelles, named Platonic micelles, we could expect them to exhibit unprecedented aggregation behavior. In this study, the effects of alkyl chain length on micellar aggregation behavior were characterized using small-angle scattering techniques such as small-angle X-ray scattering and asymmetrical flow field-flow fractionation coupled with multi-angle light scattering, as well as analytical ultracentrifugation measurements. The Nagg of Platonic micelles discretely and discontinuously increased when increasing the alkyl chain length, which differs markedly from the findings for conventional micelles. This aggregation behavior could be reasonably explained by the relationship between the thermodynamic stability of the micelles and the coverage density defined by one of the unsolved mathematical problems: the Tammes problem.
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INTRODUCTION
Micelles are soft materials that have attracted attention in both academia and industry as typical supramolecular self-assembled particles that are useful for a range of applications, especially as drug carriers for therapeutic use.1-2 Since MacBain’s proposal of the word of micelles 100 years ago3, in which the hydrophilic headgroup is externally exposed at the interface with water while the hydrophobic tail is hidden in the particle core4, intensive theoretical and experimental studies on micelles, particularly spherical ones, have been performed. Micelles’ structure can basically be predicted using the principle of the packing parameter: V/aeh, where ae, V, and h are the equilibrium interfacial area between hydrophilic domain and hydrophobic domain, and the volume and length of surfactant tails, respectively.5 This is the very simple thermodynamic model proposed by Tanford.6 This principle works well for predicting and understanding micellar morphology, and its use has been reported for many micellar systems composed of small and macromolecular surfactants.7-13 The micellar aggregation number (Nagg) is also an important parameter relating to the thermodynamic stability of micelles, which has been experimentally and theoretically established and confirmed.
6, 14-15
The relationship between micellar Nagg and ae can be explained by the following equation: Nagg ~ (4πh2)/ae
(1)
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The Nagg of micelles such as sodium dodecyl sulfate (SDS) is normally large (e.g., >60) with a narrow distribution, although the Nagg always tends to be distributed over a certain range, rather than being monodisperse.16 However, a recent discovery revealed the existence of special micelles that deviate considerably from conventional ones. These micelles consist of calix[4]arene-based amphiphiles, whose Naggs are always less than 20 and interestingly demonstrate perfect monodispersity.17-19 Notably, their Naggs are consistent with the vertex or face number of regular polyhedral structures: Platonic solids (Figure 1a). It has been proposed that the Tammes problem, an unsolved mathematical problem describing the packing of a given number (N) of identical spherical caps on a spherical surface such that the distance among the caps is maximized, explains the anomalous aggregation behavior of the micelles. The coverage density [D(N)] in the Tammes problem correlates with the efficiency with which identical spherical caps cover the spherical surface,20-21 which could be regarded as the interface between the hydrophobic core and the hydrophilic shell in micellar systems. When D(N) is high, the interfacial free energy would be low, resulting in the formation of thermodynamically stable micelles. Figure S1 shows the relationship between D(N) and the number of spherical caps (N), that is, the Nagg in a micellar system. When the Nagg is small, the profile presents certain local maxima at certain values that coincide with the vertex or face number of Platonic solids. It is reasonable to assume that there is a relationship between the Tammes problem and the thermodynamic stability of micelles with small Nagg regarding the formation of monodisperse micelles; these are named Platonic micelles, considering their characteristic Nagg values. Both micellar size and Nagg are basically proportional to the carbon number in alkyl chains of surfactants.22-23 As described in this paper, we found an unusual dependence of alkyl chain
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length on the Nagg of calix[4]arene-based Platonic micelles, which appeared to be related to the Tammes problem. Herein, we describe the preparation of quaternary amines bearing calix[4]arene-based amphiphiles with different alkyl chain lengths, referred to as QACaLn, where n represents the number of carbons in each alkyl chain, as shown in Figure 1b. The micellar aggregation behavior was characterized by three independent methods: small-angle Xray scattering (SAXS), asymmetrical flow field-flow fractionation coupled with multi-angle light scattering (AF4-MALS), and analytical ultracentrifugation (AUC). (a)
(b)
4Br N
N N
N N
Cone-shaped amphiphile
N NN N N
N
O OO R RR
Platonic micelles
N
N N N N
O R
R: Alkyl chains
Figure 1. (a) Schematic illustration of the formation of Platonic micelles composed of coneshaped amphiphiles. (b) The chemical structure of calix[4]arene-based amphiphiles bearing quaternary amines (QACaLn). R represents alkyl chains including propyl (C3), butyl (C4), heptyl (C5), hexyl (C6), heptyl (C7), octyl (C8), and nonyl (C9) tails.
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RESULTS and DISCUSSION
The calix[4]arene-based amphiphiles were synthesized via Scheme S1. The azidefunctionalized calix[4]arene derivative was synthesized by a previously reported procedure.24 The final product, QACaLn, was prepared using azide-alkyne click chemistry. All chemical structures were confirmed by 1H-NMR spectra, and the molecular weight of the final products was confirmed by ESI-mass spectral analysis (see Supplementary Information). Since the calix[4]arene-based micellar structure is stabilized under conditions with excess NaCl, probably because the calix[4]arene structure is stabilized by trapping the sodium ions in the calix[4]arene cavity,17 all measurements were conducted in 50 mM NaCl aqueous solutions. Figure 2 shows the SAXS profiles of QACaLn micelles in 50 mM NaCl aqueous solutions. For the SAXS profiles of the micelles bearing propyl (C3), butyl (C4), pentyl (C5), hexyl (C6), heptyl (C7), and octyl (C8) tails, the scattering intensity in the low-q region satisfies the relationship of I(q) ∝ q0, indicating the formation of isolated particles, namely, spherical micelles. In contrast, the SAXS profile of QACaL9, bearing nonyl (C9) tails, displays different behavior in the low-q region, satisfying the relationship I(q) ∝ q−1, which suggests the presence of cylindrical objects. The morphological transition for longer alkyl chains is attributed to the increase of the packing parameter. For reproducing the SAXS profile of QACaL9, however, the mixture model including cylindrical and spherical core-shell structures was required, which suggests that the spherical micelles coexist with cylindrical micelles.
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Figure 2. (a) SAXS profiles of QACaLn micelles (gray circles) in 50 mM aqueous NaCl. The red curves are calculated using theoretical models of a sphere and a cylinder. (b) The Guinier plots (i.e., ln I(q)Ke−1c−1/Munimer versus q2, where Ke is an optical constant in SAXS) derived from the spherical micelles of QACaLn. (orange: QACaL3, green: QACaL4, red: QACaL5, yellow: QACaL6, blue: QACaL7, gray: QACaL8)
The first sharp minimum on the oscillation of the SAXS curves shifted to the low-q region with increasing alkyl chain length, meaning that the micelles became larger for longer alkyl tails. Note that the sharpness of the first minimum in the SAXS oscillation indicates the monodispersity of the Nagg as well as the micellar size.25-26 The gyration radii (Rg) for QACaLn micelles were determined by Guinier plots shown in Figure 2B; their size is summarized in Table 1. The Rg clearly increased with increasing alkyl chain length. All SAXS profiles of QACaL3, 4, 5, 6, 7, and 8 were reproduced with the theoretical curves calculated using a core-shell spherical model; the fitting parameters are also summarized in Table 1. For the calculation, the electron densities of the micellar shell (𝜌s) and core (𝜌c) were almost constant in the QACaLn-based
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spherical micelles, while the adjustable parameters were only the radii of micellar core (Rc) and shell (Rs). According to the fitting, the micellar size increased with increasing alkyl chain length, as with the case for Rg. The intercept value of the Guinier plot in Figure 2B corresponds to the inverse of the micellar Nagg. The molar mass of QACaLn micelles was also calculated, as summarized in Table 2. Their Naggs determined from the micellar molar mass were 8, 12, 12, 20, 20, and 45 for QACaL3, 4, 5, 6, 7, and 8, respectively. Table 1. SAXS Fitting Parameters and Gyration Radius (Rg) for QACaLn Micelles in 50 mM Aqueous NaCl 𝜌c 𝜌s 𝑅g 𝑅c, sphere 𝑅s, sphere 𝑅c, cylinder 𝑅s, cylinder Sample −3 −3 [nm] [nm] [nm] [nm] [e nm ] [e nm ] [nm] QACaL3 0.790 1.80 − − 270 400 1.63 QACaL4 1.10 2.10 − − 270 410 1.82 QACaL5 1.20 2.25 − − 270 408 1.91 QACaL6 1.40 2.50 − − 270 410 2.06 QACaL7 1.78 2.80 − − 270 410 2.51 QACaL8 2.10 3.15 − − 270 408 3.03 QACaL9 2,30 3.22 1.35 2.38 270 430 − 𝑅𝑐, sphere and 𝑅𝑠, sphere are the radii of the core and shell of the spherical model, respectively. 𝑅𝑐, cylinder and 𝑅𝑠, cylinder are the cross-sectional radii of the core and shell of the cylindrical model, respectively. 𝜌𝑐 and 𝜌𝑠 are the electron densities of the core and shell, respectively.
Figure 3A shows a fractogram of AF4-MALS for QACaLn micelles. For the micelles of QACaL3, 4, 5, 6, 7, and 8, we applied constant cross flow at 3.0 mL min−1 as the elution mode, while exponentially decreasing the flow rate over time for the measurement of QACaL9 micelles to detect particles of large size, including cylindrical micelles as well as spherical ones. Both light scattering and UV profiles overlapped with each other in the fractograms of QACaL3, 4, 5, 6, and 7, meaning that their micelles were completely monodisperse because the light scattering (LS) intensity is proportional to both the molar mass and the concentration of micelles, while the UV absorbance is just dependent on the concentration. The fractogram of QACaL8 also probably indicates monodispersity, but the LS and UV profiles slightly diverge from those of the others.
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Figure 3. (a) AF4-MALS fractograms of QACaLn micelles in 50 mM NaCl aqueous solutions. (b) The Zimm plots [i.e., KcMuminer/Rθ (1/Nagg) versus q2] at the peak top in the AF4-MALS fractogram corresponding to the spherical micelles of QACaLn. (orange: QACaL3, green: QACaL4, red: QACaL5, yellow: QACaL6, blue: QACaL7, gray: QACaL8, purple: QACaL9)
The peak position in this fractogram gradually shifted to a longer elution time with increasing alkyl chain length. In the AF4 system, smaller particles were detected earlier than larger ones, which means that the micellar size gradually increased with increasing alkyl chain length, which is consistent with the SAXS results. QACaL9 micelles exhibited two peaks in the AF4 fractogram, as shown in Figure 3A. The Zimm plot at the first peak top did not show any angular dependence (Figure 3B), indicating that the scattering object detected in the first peak corresponds to small particles (
