Discrete and Discontinuous Increase in the Micellar Aggregation Number: Effects of the Alkyl Chain Length on Platonic Micelles

Abstract

Micelles with perfect monodispersity in terms of the aggregation number (N agg) have recently been discovered, whose values of N agg 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 N agg 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.

Asymmetric flow field-flow fractionation as a multifunctional technique for the characterization of polymeric nanocarriers

“…In addition, measuring the molar mass can prove particularly meaningful for materials with a precisely defined structure, where it can provide information about the number of subunits or the stoichiometry of a complex. For example, AF4-MALS can ascertain how chemical functionalization affects the aggregation number of nanogels [78] or polymeric micelles [79], or assess the stoichiometry of polymeric carriers/ nanocomplexes [80,81]. On the downside, MALS needs purely monodisperse samples, making the coupling to a fractionation technique necessary.…”

Structural Polymorphism of Resorcinarene Assemblies

“…Φ­( x ) ≡ 3­(sin x – x cos x )/ x 3 . The SANS profiles in the low q region follow the Guinier relation where I (0) is the forward scattering intensity and the molar mass M is determined by .…”

“…The detailed experimental procedures are reported elsewhere. 23 The absolute SAXS intensities were recorded using the absolute scattering intensities of water. 24 AUC Measurements.…”

Monodisperse Micelles with Aggregation Numbers Related to Platonic Solids

“…In recent years, we designed various calix [4]arene-based surfactants to make micelles (Figure 1). [17][18][19][20][21][22][23][24][25][26][27][28] Various calix [4]arenebased surfactants were self-assembled to micelle structures, which showed monodisperses in aqueous solutions. Interestingly, the aggregation numbers were 4, 6, 8, 12, or 20.…”