Micelle Aggregation Research Articles

Excipient-free lyophilization of block copolymer micelles for potential lung surfactant therapy applications

Polymer lung surfactant (PLS) is a polyethylene glycol (PEG)-brushed block copolymer micelle designed for pulmonary surfactant replacement therapy. Saccharides (e.g., sucrose and (2-hydroxypropyl)-β-cyclodextrin) and water-soluble polymers (e.g., PEG), common excipients for lyophilization, were found to severely impair the surface activity of lyophilized PLS. To investigate the feasibility of excipient-free lyophilization of PLS, we studied the effects of both PLS material parameters and lyophilization operating parameters on the redispersibility and surface availability of reconstituted PLS, all without relying on excipients. We found that the redispersibility was improved by three factors; a faster cooling rate during the freezing stage reduced freezing stress; a higher PEG grafting density enhanced dissipating effects; and the absence of hydrophobic endgroups in the PEG block further prevented micelle aggregation. Consequently, the surface availability of PLS increased, enabling the micelle monolayer at the air/water interface to achieve a surface tension below 10 mN/m, which is a key pharmaceutical function of PLS. Moreover, the lyophilized micelles in powder form could be easily dispersed on water surfaces without the need for reconstitution, which opens up the possibility of inhalation delivery, a more patient-friendly administration method compared to instillation. The successful excipient-free lyophilization unlocks the potential of PLS for addressing acute respiratory distress syndrome (ARDS) and other pulmonary dysfunctions.

Biocompatible, 3D Printable Magnetic Soft Actuators – Ink Formulation, Rheological Characterization and Hydrogel Actuator Prototypes

Abstract3D printable inks for the preparation of magnetic hydrogel actuators are difficult to formulate because magnetic nanoparticles tend to aggregate without stabilization through other ink components. At the same time, such inks need to be shear‐thinning and recover their high viscosity state sufficiently fast to be suitable for the printing process. Here, the use of chitosan as dispersing agent for Fe2O3 nanoparticles is reported. Combined with Pluronic F127 as a rheology modifier and acrylamide as the base monomer, thermoresponsive and shear‐thinning magnetic inks containing well‐dispersed particles are obtained. The ink viscosity is tuned over two orders of magnitude by varying the chitosan and Pluronics F127 content. 3D‐printed shapes with good shape fidelity are obtained at a print bed temperature of 50 °C, where aggregation of the Pluoronics F127 micelles occurs. This leads to a fast recovery of the high viscosity state of the material, so that the printed shape can then be locked in by UV cross‐linking. This treatment yielded magneto‐responsive prototypes which are promising for soft robotics applications. Thanks to the simplicity of the ink formulation, it is easily transferable also to nonspecialist laboratories, and the concept is potentially applicable also to other types of nanoparticles.

A comprehensive assessment of interfacial and bulk properties of sodium dodecylsulfate via addition of competitive Hofmeister ions in presence of Cosolvent: A combined experimental and theoretical study

The synergistic interaction of sodium dodecyl sulphate (SDS) and added electrolyte in presence of cosolvent is investigated by determining the critical micelle concentration of SDS. The present system is carried out with two different types of counterions from Hofmeister series where Hofmeister chaotropic ion i.e. NH4+ is attracted more towards the negatively charged chaotropic dodecyl sulphate headgroup of SDS than the kosmotropic ion. To understand the thermodynamic behavior of SDS micelle, counterion binding constant values are measured using the well-established Corrin-Harkins or modified Corrin-Harkins equations. Various assessments of aggregation and adsorption phenomena of SDS micelle are established from both experimental and theoretical concepts. The exchange of counterion i.e. Na+ ion by NH4+ ions can occur at a particular electrolyte concentration where SDS micelle leads to the formation of ammonium dodecyl sulphate (AmDS) in the present cosolvent media. Therefore, the Hofmeister chaotropic ion (NH4+) is found to be a competitive ion. In addition to that, solvophobicity of the cosolvent mixture is another important parameter which could influence SDS micellization differently.

Active Micelle Pumping Channel Triggers Nonequilibrium Surface Excess Aggregation.

Adsorbate transport during the electrochemical process mostly follows the electric-field direction or the high-to-low direction along the concentration gradient and thus often limits the reactant concentration at the adsorption site and requires specific mechanical or chemical bonds of adsorbates to trigger local excess aggregation for advanced framework structure assembly. Herein, we have discovered an active pumping channel during electrochemical adsorption of a manganese colloid, which follows a low-to-high direction inverse concentration gradient. It triggers surface excess micelle aggregation with even over 16-folds higher concentration than that in bulk owing to hydrogen-bonding difference of the micelle surface between in bulk and at the water surface. Micelles in the channel exhibit unique polymerization behaviors by directly polymerizing monomer micelles to form highly catalytic MnO2 of dendritic frameworks, which can serve as a scalable thin-layer aqueous-phase reactor. It increases the understanding of the interface-dependent dynamic nature of micelle or more adsorbates and inspires transformative synthesizing approaches for advanced oxide materials.

Self-aggregation of cationic gemini surfactants with amide groups in the spacer and variable alkyl chain length

AbstractSynthesis, aggregation parameters and antimicrobial activity of novel cationic gemini surfactants with two amide groups in gemini spacer structure and a variable number of carbon atoms in alkyl tails ranging from 12 to 15 are reported. The critical micelle concentration of gemini surfactants was determined using surface tension and electrical conductivity methods. The cmc values were found in the range 0.83 to 0.06 mM. The interfacial area, micelle ionisation degree and the Gibbs free energy per molecule and alkyl chain were calculated from the surface tension and conductivity curves. Particle size analysis using the dynamic light scattering method confirmed the formation of small spherical micelles 6–7 nm large in size for gemini surfactants with 12 and 13 carbon atoms in the alkyl chain. A large size above 50 nm was found for the aggregates composed of long-chain gemini molecules with 14 and 15 carbon atoms. The zeta potential of gemini surfactants shows a continuous increase with the increasing alkyl chain length. Micelle aggregation number of gemini surfactants correlates well with the hydrodynamic size data. Small aggregation number values were found for short-chain gemini molecules with 12 and 13 carbon atoms in the alkyl chain. Long-chain gemini molecules with 14 and 15 carbon atoms exhibit aggregate growth represented by an increase in the aggregation number values while maintaining the spherical or spheroidal shape of micelles. The investigations of antimicrobial activity against Gram-positive bacteria, Gram-negative bacteria and yeast indicate the increasing antimicrobial efficiency towards the short-chain surfactant with 12 carbon atoms in the alkyl chain. A possible cut-off effect presence is proposed to explain the dependence of antimicrobial activity on the surfactant alkyl tail length.

Identification of the coagulation properties of Chinese Holstein bovine milk: Effects of milk compositions, milk protein polymorphism, and phosphorylation levels on milk coagulation ability

Milk coagulation ability plays critical roles in cheese production. To assess the effects of milk composition, protein polymorphisms, and phosphorylation levels on milk coagulation properties, milk samples were collected from 3625 Chinese Holstein cows and milk was pooled based on their coagulation properties. The results showed that good coagulating milk had shorter rennet coagulation time and higher gel firmness with tighter connections within the formed gel. Multiple factors were observed to differ among milk with different coagulation ability. For example, lower milk pH, higher amounts of proteins and casein, were related to good coagulation properties. The salt distributions also influenced milk coagulation ability. Especially the calcium content has a large influence on milk coagulation. This may be due to its influence on the aggregation of paracasein micelles in the secondary phase of rennet coagulation. Protein polymorphisms and phosphorylation degrees were found being higher in non-coagulating milk. The proteomics results showed that lower amounts of αS1-casein may result in non-coagulation. Differences of milk fat globule membrane proteins were also observed among milk samples with different coagulation ability, possibly being related to milk protein and fat synthesis, in turn influencing the coagulation process. In addition, Ser76 of αS2-CN was found being highly phosphorylated in non-coagulating milk which may be related to its binding with other caseins during the second phase of rennet coagulation. Of these factors, salt distribution, mainly calcium and magnesium, may be the most important factor affecting casein structures and thereby milk coagulation. Importantly, these factors can affect each other while forming the cheese matrix, resulting in a complex relation with milk coagulation.

Hierarchical supramolecular self-assembly of Bi-Valine-Containing Poly(phenylacetylene) and tunable chirality

A challenging aim is the precisely controlled construction of hierarchical chiral self-assembly in synthetic polymers both from the fundamental and advanced technological development perspectives. Amphiphilic polymers can be assembled into well-organized aggregates with morphological varieties, and external stimuli remarkably affect their self-assembly behavior. We designed and synthesized an amphiphilic helical poly(phenylacetylene) homopolymer containing bi-valine pendants. The hierarchical chiral self-assembly behavior of the homopolymer was realized and investigated by adding a polar solvent into the poly (L-1) solution. Furthermore, the influences of the solvent components and temperature on the supramolecular chirality and morphologies of the ordered nanostructures were studied via circular dichroism (CD), transmission electron microscopy (TEM), and dynamic light scattering (DLS). Various morphologies such as spheres, beads-string micelles, vesicles, nanorods, flower-like, and blocky nanostructures were obtained. The polyphenylacetylene backbone was successfully endowed with chirality from L-Boc-valine pendants, and this property was further transferred and enhanced in high-ordered supramolecular self-assemblies. With the increase of polar solvent fraction, the enhanced driving force of solvophobic interaction and π-π stacking might significantly promote the aggregation of multi micelles.

Metamorphosis of Topical Semisolid Products-Understanding the Role of Rheological Properties in Drug Permeation under the "in Use" Condition.

When developing topical semisolid products, it is crucial to consider the metamorphosis of the formulation under the "in use" condition. Numerous critical quality characteristics, including rheological properties, thermodynamic activity, particle size, globule size, and the rate/extent of drug release/permeation, can be altered during this process. This study aimed to use lidocaine as a model drug to establish a connection between the evaporation and change of rheological properties and the permeation of active pharmaceutical ingredients (APIs) in topical semisolid products under the "in use" condition. The evaporation rate of the lidocaine cream formulation was calculated by measuring the weight loss and heat flow of the sample using DSC/TGA. Changes in rheological properties due to metamorphosis were assessed and predicted using the Carreau-Yasuda model. The impact of solvent evaporation on a drug's permeability was studied by in vitro permeation testing (IVPT) using occluded and unconcluded cells. Overall, it was found that the viscosity and elastic modulus of prepared lidocaine cream gradually increased with the time of evaporation as a result of the aggregation of carbopol micelles and the crystallization of API after application. Compared to occluded cells, the permeability of lidocaine for formulation F1 (2.5% lidocaine) in unoccluded cells decreased by 32.4%. This was believed to be the result of increasing viscosity and crystallization of lidocaine instead of depletion of API from the applied dose, which was confirmed by formulation F2 with a higher content of API (5% lidocaine) showing a similar pattern, i.e., a 49.7% reduction of permeability after 4 h of study. To the best of our knowledge, this is the first study to simultaneously demonstrate the rheological change of a topical semisolid formulation during volatile solvent evaporation, resulting in a concurrent decrease in the permeability of API, which provides mathematical modelers with the necessary background to build complex models that incorporate evaporation, viscosity, and drug permeation in the simulation once at a time.

An injectable thermo-sensitive hydrogel of PNICL-PEG-PNICL block copolymer as a sustained release carrier of EGCG

Biodegradable in situ thermo-sensitive hydrogels have potential applications in ophthalmic pharmaceutical preparations. Herein, a thermo-gel of PNICL-PEG-PNICL loaded with the natural compound epigallocatechin gallate (EGCG) used as a drug sustained release carrier was prepared by block bending strategy. Compared to mono polymers that cannot form a gel, mixing two block copolymers through a block blending strategy allows for the preparation of thermo-sensitive hydrogels. The temperature sensitive behavior of the system can be easily regulated by varying the blending ratios of the two polymers. Furthermore, the internal structure of the gel was investigated that indicated the system formed a permeable network through micelle aggregation. The biosafety of the system and its ability to sustainably release EGCG at 37 °C for 240 h were preliminarily demonstrated in vitro. This study has revealed the internal structural changes of block blending thermo-gels and tentatively justified their potential as drug carriers.

Temperature-Induced Nanostructure Transition for Supramolecular Gelation in Water.

Thermogel is an injectable biomaterial that functions at body temperatures due to the ease of the sol-to-gel transition. However, most conventional physically cross-linked thermogels generally have relatively low stiffness, which limits various biomedical applications, particularly for stem-cell-based studies. While chemical cross-linking through double-network (DN) structures can increase the stiffness of the hydrogel, they generally lack injectable and thermoresponsive properties due to strong covalent bonds between molecules. To address this challenge, we have developed a temperature-induced nanostructure transition (TINT) system for preparing physical DN supramolecular hydrogels. These hydrogels possess injectable, thermoreversible characteristics and relatively high storage modulus (G'), which increases ∼14-fold from 20 to 37 °C (body temperature). Our bottom-up strategy is based on the co-assembly of aromatic peptide (Ben-FF) and poly(ethylene glycol) (PEG) to form a thermogel at 37 °C through a nanofiber dissociation pathway that differs from the well-known micelle aggregation or polymer shrinkage mechanisms. Peptide molecules form helical packing and weak, noncovalent interactions with PEG, resulting in co-assembled metastable nanofibers. Thermal perturbation initiates lateral dissociation of nanofibers into extensively cross-linked DN nanostructures and subsequent hydrogelation (ΔG = -13.32 kJ/mol). The TINT hydrogel is nontoxic to human mesenchymal stem cells and supports enhanced cell adhesion, suggesting the potential of this strategy in the applications of tissue engineering and regenerative medicine.

Investigating the Acid- and Enzyme-Induced Coagulation of Raw Milk Using Dielectric and Rheological Measurements

In this study, the enzyme-induced and acid coagulation of raw milk samples were investigated, and these two processes were monitored by determining the changes in dielectric and rheological behavior to see if any correlations could be found between these two properties. For the enzyme-induced experiments, 250 cm3 of raw milk sample and industrial chymosin were used, and during the acid coagulation, industrial thermophile yogurt culture was added to the same amount of milk. The apparent viscosity was monitored with a vibro viscometer, and the dielectric constant was measured in a frequency range of 200–2400 MHz with an open-ended dielectric assessment kit (DAK) connected to a vector network analyzer (VNA). Our experimental findings revealed that during both enzyme-induced and acid coagulation, two distinct phases could be found in terms of dielectric and rheological properties, and regardless of the molecular mechanisms behind the aggregation of casein micelles, a strong correlation (with R2-values ranging between 0.967 and 0.992) can be found between the extent of the apparent viscosity and dielectric constant, suggesting that dielectric measurements might be adequately used in these dairy processing technologies. These results verified the applicability of the non-destructive dielectric measurements in dairy technologies.

A kinetic approach to the mechanism of formation of mesoporous silica nanoparticles

The synthesis of mesoporous silica nanoparticles (MSNs), widely investigated for application in nanomedicine, depends on many experimental factors and lacks reproducibility. Furthermore, its mechanism is not fully understood, in particular for the chemistry of the hydrolysis and condensation of tetraethoxysilane (TEOS). We coupled simple pH measurements with light diffusion monitoring directly within the reaction vessel in order to understand the early stages of the synthesis until the formation of nanoparticles. We found that two regimes of hydrolysis can be detected before the nanoparticles are formed. At the turning point, only 28% of the TEOS molecules are singly hydrolyzed and the condensation reaction only starts after the aggregation of the silicate-surfactant micelles. Experimental factors such as stirring strength or presence of carbonates of sodium hydroxide exert a strong influence on the kinetics of MSNs formation and on their size, and must be carefully controlled for reproducibility. Based on all our experimental evidence and on previous literature reports, a formation mechanism was proposed in order to highlight the importance of the interplay between chemical and physicochemical processes in such a complex system.

Surfactant-based enrichment of rare earth elements from NdFeB magnet e-waste: Optimisation of cloud formation and rare earths extraction

Appropriate waste and resource management are essential for a sustainable circular economy with reduced environmental impact. With critical resources, e-waste may serve as indirect raw material. For example, with NdFeB permanent magnets, Neodymium (Nd) and the co-present Dysprosium (Dy) are critical rare earth elements (REEs). However, there exists no economically viable technology for recycling them from electronic waste (e-waste). Here, a method is presented based on cloud point extraction (CPE). The work involves basic complexation chemistry in a cloud medium with pure REE salts, as well as, with real NdFeB-magnets (nearly 28% REE content by weight) from an old hard disk drive (5.2 g magnet in a 375 g HDD). High extraction efficiency (>95%) was achieved for each REE targeted (Nd, Dy, Praseodymium (Pr)). With the magnet waste, the cloud phase did hardly contain any Nickel (Ni), Cobalt (Co), or Boron (B), but some Aluminium (Al) and Iron (Fe). Dynamic light scattering results indicated aggregation of ligand-surfactant micelles with the cloud phase. The preconcentrated products can be used for new Nd magnet manufacturing or further enriched using established transition metal removal techniques. Reuse of solvent, low chemical inventory demand, and using non-inflammable, non-volatile organic extractants promise safe large-scale operation, low process costs, and less environmental impact than using hydrometallurgical methods used with urban or primary mining.

Heat stability of sheep's skim milk: Aggregation and interaction of proteins

Sheep's milk proteins are susceptible to heat-induced coagulation, but the protein interactions under high heat treatment have not been determined. Heat stability and protein interactions of sheep's skim milk (SSM) at pH 6.2–7.2 were examined at 140 °C. SSM had the longest heat coagulation time at pH 6.9, but became very unstable at higher or lower pH. Protein aggregates formed consisted mainly of whey proteins and κ-casein (κ-CN)-depleted casein micelles. Modification of SSM pH alters ionic calcium concentration, dissociation of caseins and electrostatic interactions, resulting in different extents of protein interactions. The extent of dissociation of κ-CN from casein micelles increased with increasing pH (from ∼6.6 to 7.0) before and after heat treatment, contributing to κ-CN-depleted casein micelle aggregation. High ionic calcium concentrations, low levels of κ-CN on casein micelles and ready dissociation of κ-CN from casein micelles may be responsible for the low heat stability of sheep's milk.

Effect of CSN3 Gene Polymorphism on the Formation of Milk Gels Induced by Physical, Chemical, and Biotechnological Factors.

During the last decade, research into genetic markers in the casein gene cluster has been actively introduced in cattle breeding programs. A special interest has been paid to the polymorphism of the CSN3 gene, responsible for the expression of the k-casein, playing a key role in protein coagulation, interaction with whey proteins, stabilization, and aggregation of casein micelles. This paper aimed to determine the effect of CSN3 genetic polymorphism on acid; rennet; acid-rennet; heat- and acid-induced as well as heat- and calcium-induced coagulation in skimmed milk; and protein-standardized milk systems (UF, NF, RO, VE). The influence of polymorphic variants of the CSN3 gene on the coagulation ability of milk proteins was assessed by the particle size of casein micelles, protein retention factor in the clot, and coagulation ability (duration of induction period, mass coagulation period, dynamic viscosity in gel point). The correlation between CSN3 gene polymorphism and protein coagulation was revealed. Milk systems obtained from CSN3 BB milk were found to have the shortest duration of coagulation, formation of better gel strength values, and increased yield compared to CSN3 AA. This study will improve the efficiency of milk processing and optimize the technology of dairy product production.

Topical Cream Carrying Drug-Loaded Nanogels for Melanoma Treatment.

In this study, nanogel creams carrying paclitaxel (PTX) and temozolomide (TMZ) were prepared for thetopical treatment of melanoma. PTX and TMZ were first loaded in poly-(D,L-lactide-co-glycolide)-block-poly(ethylene glycol)-block-poly-(D,L-lactide-co-glycolide) (PLAG-b-PEG-b-PLGA)thermosensitive nanogels, which made a transition from a free-flowing sol (formation of micellar network) at 25°C with the z-average particle size of c.a. 96nm to a gel (aggregation of micelles) at 33°C with the z-average particle size of c.a. 427nm. An anhydrous absorption ointment base, aquaphor, was then added to drug-loaded nanogels to form nanogel creams carrying PTX and TMZ. Nanogel creams permitted controlled release of the payloads and improved the penetration of the payloads through the rodent skin compared to drug(s)-loaded nanogels. PTX and TMZ in a combination were synergistically effective in inhibiting SK-MEL28, A375, and B16-F10 melanoma cancer cells in vitro. Topically applied nanogel creams carrying TMZ/PTX (4mg/1.5mg/dose) showed a trend of tumor volume inhibition on B16-F10-bearing xenograft mice in vivo.

Mesoscopic Characterization of the Early Stage of the Glucono-δ-Lactone-Induced Gelation of Milk via Image Analysis Techniques.

We provide a method for quantifying the kinetics of gelation in milk acidified with glucono-δ-lactone (GDL) using image analysis techniques, particle image velocimetry (PIV), differential variance analysis (DVA) and differential dynamic microscopy (DDM). The gelation of the milk acidified with GDL occurs through the aggregation and subsequent coagulation of the casein micelles as the pH approaches the isoelectric point of the caseins. The gelation of the acidified milk with GDL is an important step in the production of fermented dairy products. PIV qualitatively monitors the average mobility of fat globules during gelation. The gel point estimated by PIV is in good agreement with that obtained by rheological measurement. DVA and DDM methods reveal the relaxation behavior of fat globules during gelation. These two methods make it possible to calculate microscopic viscosity. We also extracted the mean square displacement (MSD) of the fat globules, without following their movement, using the DDM method. The MSD of fat globules shifts to sub-diffusive behavior as gelation progresses. The fat globules used as probes show the change in matrix viscoelasticity caused by the gelling of the casein micelles. Image analysis and rheology can be used complementarily to study the mesoscale dynamics of the milk gel.

Effect of sodium alginate on the yogurt stability was dependent on the thickening effect and interaction between casein micelles and sodium alginate

The effect of sodium alginate (SA) on the yogurt stability and the related mechanisms were investigated. It was found that low-concentration SA (≤0.2 %) increased the yogurt stability, while high-concentration SA (≥0.3 %) decreased the yogurt stability. Sodium alginate increased the viscosity and viscoelasticity of yogurt and this effect was positively correlated with its concentration, suggesting that SA worked as the thickening agent in yogurt. However, addition of ≥0.3 % SA damaged the yogurt gel. These results suggested that interaction between milk protein and SA might play an important role in the yogurt stability besides the thickening effect. Addition of ≤0.2 % SA did not change the particle size of casein micelles. However, addition of ≥0.3 % SA induced aggregation of casein micelles and increased the size. And the aggregated casein micelles precipitated after 3 h storage. Isothermal titration calorimetry analysis showed that casein micelles and SA were thermodynamically incompatible. These results suggested that the interaction between casein micelles and SA induced aggregation and precipitation of casein micelles, which was critical in the destabilization of yogurt. In conclusion, the effect of SA on the yogurt stability was dependent on the thickening effect and the interaction between casein micelles and SA.

Spatial distribution of αs1-caseins and β-caseins in milk gels acidified with glucono-δ-lactone

Acid-induced destabilization of casein micelles leads to coagulation of milk which plays an important role in the formation of yogurt. The resulting protein network is formed by aggregation and reconfiguration of casein micelles, including the release of a portion of caseins from these micelles. It is so far unknown how individual αs1-and β-caseins are organized within this complex network, and how their distribution depends on yogurt composition and processing. Here, we imaged the spatial distribution of caseins using stimulated emission depletion (STED) microscopy and single-molecule localization microscopy (SMLM). We used fluorescently tagged antibodies against αs1-and β-caseins to localize them inside glucono-δ-lactone (GDL)-acidified milk gels. We conducted quantitative skeleton analysis of STED images and showed that αs1-and β-caseins contribute with different levels of connectivity to the acid induced milk network.

Is Structural Precision of Platonic Micelles Controlled Solely by Close-Packed Head Groups or Also by Hydrophobic Tail Packing? A DFT Exploration

Platonic micelles have been defined as structurally precise amphiphilic aggregates with discrete aggregation numbers corresponding to the close packing of spherical caps (representing head groups) on a sphere (representing hydrophobic core), analogous to the Tammes problem in geometry. Here, we use DFT to explore how an actual molecule behaves compared to the idealized picture based on the Tammes problem by also considering the packing of the tails. We modeled micelles of aggregation numbers 4 to 8 generated from the calix[4]arene amphiphile, PACaL3, with the tails forming a close-packed configuration while the headgroups are arranged as in Platonic solids. The DFT calculations reveal that tail packing overwhelmingly influences the equilibrium aggregation number. While the DFT prediction of a PACaL3 micelle of aggregation number 6 agrees with the scattering experiments of the Sakurai group, DFT calculations also suggest small concentrations of micelles of aggregation number 7. More interestingly, DFT calculations reveal that PACaL3 micelle formation occurs even though less than 20% of the hydrophobic tail surface is removed from contact with water, in contrast to the roughly 80% removal observed for classical surfactant micelles. While the close-packed head groups model predicts higher coverage of the hydrophobic surface for aggregation numbers 4 and 6 compared to 5 and 7, the DFT calculations also accounting for tail packing show that the surface coverage for aggregation numbers 5 and 7 is practically no different than that for aggregation number 4. Finally, although both the close-packed head groups model and the DFT calculations agree that the exposed hydrophobic surface area controls the equilibrium micelle aggregation number, the DFT calculations demonstrate how this exposed hydrophobic area is overwhelmingly determined by the tail group packing and not just by the close packing of head groups.