Inorganic-organic hybrid vesicles with counterion- and pH-controlled fluorescent properties

Two inorganic-organic hybrid clusters with one or two covalently linked pyrene fluorescent probes, [(n-C(4)H(9))(4)N](2)[V(6)O(13){(OCH(2))(3)C(NH(CO)CH(2)CH(2)CH(2)C(16)H(9))}{(OCH(2))(3)C-(NH(2))}] ((TBA(+))(2)1) and [(n-C(4)H(9))(4)N](2)[V(6)O(13){(OCH(2))(3)C(NH(CO)CH(2)CH(2)CH(2)C(16)H(9))}(2)] ((TBA(+))(2)2), respectively, are synthesized from Lindqvist type polyoxometalates (POMs). The incorporation of pyrene into POMs results in amphiphilic hybrid molecules and simultaneously offers a great opportunity to study the interaction between hybrid clusters and their counterions. 2D-NOESY NMR and fluorescence techniques have been used to study the role of counterions such as tetrabutyl ammonium (TBA) in the vesicle formation of the hybrid clusters. The TBA(+) ions not only screen the electrostatic repulsions between the POM head groups but also are involved in the hydrophobic region of the vesicular structure where they interrupt the formation of pyrene excimers that greatly perturbs the luminescence signal from the vesicle solution. By replacing the TBA(+) counterions with protons, the new vesicles demonstrate interesting pH-dependent fluorescence properties.     

Influence of the block hydrophilicity of AB2 miktoarm star copolymers on cluster formation in solutions

We investigated the formation of various micelle shapes of lipid-like amphiphilic AB(2) miktoarm star copolymers in a solution, by performing dissipative particle dynamics simulations. AB(2) miktoarm star copolymer molecules are modeled with coarse-grained structures that consist of a relatively hydrophilic head (A) group with a single arm and a hydrophobic tail (B) group with double arms. A decrease in the hydrophilicity of the head group leads to a reduction of the polymer-solvent contact area, causing cluster structure changes from spherical micelles to vesicles. Consequently, a spherical exterior with multi-lamellar or cylindrical phase interior structures forms under poor solvent conditions without the introduction of spherical hard-wall containers. Furthermore we observed that, for small head group lengths, vesicles were formed in much wider range of solvent-head interaction strength than for long head groups, indicating that molecules with short head group offer a superior vesicle forming property. A phase diagram, the structure and kinetics of the cluster formation, a density profile, and a detailed shape analysis are presented to discuss the molecular characteristics of potential candidates for drug carriers that require superior and versatile vesicle forming properties. We also show that, under certain solvent-hydrophilic head group interaction conditions, initially formed cylindrical micelles transform to bilayer fragments through redistribution of copolymers within the cluster.     

Design of hydrophobic polyoxometalate hybrid assemblies beyond surfactant encapsulation

Grafting of C-6, C-16 and C-18 alkyl chains onto the hydrophilic Mn-Anderson clusters (compounds 2-4) has been achieved. Exchange of the tetrabutyl ammonium (TBA) with dimethyldioctadecyl ammonium (DMDOA) results in the formation of new polyoxometalate (POM) assemblies (compounds 5-6), in which the POM cores are covalently functionalized by hydrophilic alkyl-chains and enclosed by surfactant of DMDOABr. As a result, we have been able to design and synthesize POM-containing hydrophobic materials beyond surfactant encapsulation. In solid state, scanning electron and transmission electron microscopy (SEM and TEM) studies of the TBA salts of compounds 3 and 4 show highly ordered, uniform, reproducible assemblies with unique segmented rodlike morphology. SEM and TEM studies of the DMDOA salts of compounds 5 and 6 show that they form spherical and sea urchin 3D objects in different solvent systems. In solution, the physical properties of compound 5 and 6 (combination of surfactant-encapsulated cluster (SEC) and surface-grafted cluster (SGC)) show a liquid-to-gel phase transition in pure chloroform below 0 degrees C, which are much lower than other reported SECs. By utilizing light scattering measurements, the nanoparticle size for compounds 5 and 6 were measured at 5 degrees C and 30 degrees C, respectively. Other physical properties including differential scanning calorimetry have been reported.     

Effect of hydrophilic groups of Ca surfactants and hydrophobic chains of C(n)DMAO on coordinated vesicle formation

The effects of hydrophilic headgroups of Ca surfactants, calcium dodecylsulfate (Ca(DS)(2)), calcium dodecylsulfonate (Ca(DSA)(2)), and calcium laurate (CaL(2)) and hydrophobic chains of alkyldimethylamine oxide (C(n)DMAO, n = 12, 14, 16) on the formation of Ca(2+)-ligand coordinated vesicles was investigated in detail. On the basis of phase behavior studies, rheological properties and freeze-fracture transmission electron microscope (FF-TEM) images were measured. Quite different phase behaviors were observed in different surfactant systems. For a Ca surfactant with a highly polar group, Ca(DS)(2), vesicles were observed in all Ca(DS)(2)/C(n)DMAO (n = 12, 14, and 16) systems, whereas for Ca surfactant with lower polar group, Ca(DSA)(2), vesicles can form in Ca(DSA)(2)/C(n)DMAO systems of n = 14 and 16 but not for n = 12. For CaL(2), the surfactant with the least polar group, vesicles form only in the CaL(2)/C(16)DMAO system. The results demonstrate that in the systems formed by Ca surfactants and C(n)DMAO, the formation of vesicles is driven not only by interaction between Ca(2+) and the N → O groups of C(n)DMAO but also by electrostatic and hydrophobic interactions. Vesicles prefer to form in Ca surfactants with highly polar headgroups and C(n)DMAO with long chain length.     

Fabrication of positively charged catanionic vesicles from ion pair amphiphile with double-chained cationic surfactant

In this study, a pseudodouble-chained ion pair amphiphile, hexadecyltrimethylammonium-dodecylsulfate (HTMA-DS), was prepared from a mixture of cationic surfactant, hexadecyltrimethylammonium bromide, and anionic surfactant, sodium dodecylsulfate. Positively charged catanionic vesicles were then successfully fabricated from HTMA-DS with the addition of cationic surfactants, dialkyldimethylammonium bromide (DXDAB), including ditetradecyldimethylammonium bromide (DTDAB), dihexadecyldimethylammonium bromide, and dioctadecyldimethylammonium bromide (DODAB), with a mechanical disruption approach. The control of charge characteristic and physical stability of the catanionic vesicles through the variations of DXDAB molar fraction and alkyl chain length was then explored by size, zeta potential, and Fourier transform infrared analyses. It was found that the molecular packing and/or molecular interaction of HTMA-DS with DXDAB rather than the electrostatic repulsion between the charged vesicles dominated the physical stability of the mixed HTMA-DS/DXDAB vesicles. The presence of DTDAB, which possesses short alkyl chains, could adjust the packing of the unmatched chains of HTMA⁺ and DS^? and promote the vesicle formation. However, the weak molecular interaction due to the short chains of DTDA⁺ could not maintain the vesicle structures in long-term storage. With increasing the alkyl chain length of DXDAB, it was possible to improve the vesicle physical stability through the enhanced molecular interaction in the vesicular bilayer. However, the long alkyl chains of DODAB unmatched with those of HTMA-DS, resulting in the vesicle disintegration in long-term storage. For the formation of stable charged catanionic vesicles of HTMA-DS/DXDAB, a good match in hydrophobic chains and strong molecular interaction were preferred for the vesicle-forming molecules.     

Controllable self-assembly of organic-inorganic amphiphiles containing Dawson polyoxometalate clusters

An organic-inorganic molecular hybrid containing the Dawson polyoxometalate, ((C(4)H(9))(4)N)(5)H[P(2)V(3)W(15)O(59)(OCH(2))(3)CNHCOC(15)H(31)], was synthesized and its surfactant-like amphiphilic properties, represented by the formation of bilayer vesicles, were studied in polar solvents. The vesicle size decreases with both decreasing hybrid concentration and with increasing polarity of the solvent, independently. The self-assembly behavior of this hybrid can be controlled by introducing different counterions into the acetonitrile solutions. The addition of ZnCl(2) and NaI can cause a gradual decrease and increase of vesicular sizes, respectively. Tetraalkylammonium bromide is found to disassemble the vesicle assemblies. Moreover, the original counterions of the hybrid can be replaced with protons, resulting in pH-dependent formation of vesicles in aqueous solutions. The hybrid surfactant can further form micro-needle structures in aqueous solutions upon addition of Ca(2+) ions.     

Facilitation effect of oligonucleotide on vesicle formation from single‐chained cationic surfactant—Dependences of oligonucleotide sequence and size and surfactant structure

The interaction between DNA and surfactant has both biological and technological significances. Recently, we reported for the first time that oligo d(C)₂₅ can induce single‐chained cationic surfactant molecules to aggregate into vesicles. In this article, we studied systematically the formation of vesicles from traditional single‐chained cationic surfactant molecules in the presence of a series of oligonucleotides and found that the facilitation efficiency of oligonucleotide on vesicle formation depends on its size and base composition. Oligo d(T)_n cannot induce vesicle formation, whereas the other oligonucleotides can. Moreover, the oligonucleotide with a bigger size or with a hairpin structure favors vesicle formation more, and the increases in the size of the head group and/or the length of the alkyl group of surfactant decrease the facilitation efficiency of oligonucleotide. Since so far, there is very limited report about the vesicle formation in DNA/single‐chained cationic surfactant solution, this study could be expected to increase the efficiency and applicability for DNA/amphiphile system. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 434–449, 2009     

Preparation and properties of vesicles made of nonpolar/polar/nonpolar fullerene amphiphiles

Twenty potassium complexes of penta-[(4-substituted)phenyl][60]fullerene anions were synthesized and examined for their ability to form bilayer vesicles in water. The 4-substituents include alkyl groups ranging from methyl to icosanyl groups and perfluoromethyl, perfluorobutyl, and perfluorooctyl groups. The overall structure of the amphiphiles can be described as a nonpolar/polar/nonpolar (n-p-n') motif as opposed to the usual polar/nonpolar motif of lipid amphiphiles. Despite the hydrophobicity of the fullerene moiety (n-part) and alkyl/perfluoroalkyl chains (n'-part), all compounds except for the one with perfluoromethyl groups were soluble in water because of the centrally located fullerene cyclopentadienide (p-part) and spontaneously formed a vesicle of 25- to 60-nm diameter with a narrow unimodal size distribution. The vesicles are stable upon heating to 90 °C or standing over one year in air, as well as on a solid substrate in air or in vacuum, maintaining their spherical form. The vesicle membrane consists of an interdigitated bilayer of the amphiphile molecules, in which the fullerene n-part is inside and the n'-side is exposed to water. These vesicles, in particular the one bearing icosanyl chains, exhibit the smallest water permeability coefficient ever found for a self-assembled membrane in water.     

Light‐ and Solvent‐Controlled Self‐Assembly Behavior of Spiropyran–Polyoxometalate–Alkyl Hybrid Molecules

A molecular photochromic spiropyran–polyoxometalate–alkyl organic–inorganic hybrid has been synthesized and fully characterized. The reversible switching of the hydrophobic spiropyran fragment to the hydrophilic merocyanine one can be easily achieved under light irradiation at different wavelengths. This switch changes the amphiphilic feature of the hybrid, leading to a light‐controlled self‐assembly behavior in solution. It has been shown that the hybrid can reversibly self‐assemble into vesicles in polar solvents and irreversibly into reverse vesicles in non‐polar solvents. The sizes of the vesicles and the reverse vesicles are both tunable by the polarity of the solvent, with the hydrophobic interactions being the main driving force.     

Amphiphilic properties of dumbbell-shaped inorganic-organic-inorganic molecular hybrid materials in solution and at an interface

Five novel dumbbell-shaped polyoxometalate (POM)-based inorganic-organic-inorganic molecular hybrids are investigated both in polar solvents and at interfaces for potential amphiphilic properties, which are compared with those of conventional surfactants. These hybrids with the general formula {P(2)V(3)W(15)}(2)-bis(TRIS)-linker are formed by linking two Wells-Dawson-type clusters, [P(2)V(3)W(15)O(62)](9-), with different linear bis(TRIS) linker ligands between the two TRIS moieties. Laser light scattering (LLS) studies reveal the presence of self-assembled vesicular structures in water/acetone mixed solvents, and the vesicle size increases with increasing acetone content, suggesting a charge-regulated process. The elastic constants, which are used to calculate the bending energy during vesicle formation, reveal that the organic ligands play an important role in determining the self-assembly process and that the hybrids do demonstrate amphiphilic behavior at the water/air interface. Furthermore, it is shown that some of the hybrids form monolayers at the interface, with an average molecular area that can be correlated with their organic linkers, as determined from their π-A isotherms. Finally, the hybrids not only display amphiphilic behavior akin to that of a surfactant but also exhibit an unusually high entropy contribution to vesicle formation as a result of their unique large, polar head groups, complex organic linkers, and their special molecular architectures as well as because of the involvement of the amphiphilic tetrabutylammonium (TBA) counterions.     

Formation of vesicular structures by a mono-tethered polyhedral oligomeric silsesquioxane amphiphilic diacid derivative in a solvent mixture

Polyhedral oligomeric silsesquioxane (POSS) molecules contain a silicon/oxygen nano-size cage substituted with organic groups. 2-(Propylcarbamoyl)terephthalic acid heptaisobutyl polyhedral oligomeric silsesquioxane (POSS DCA) is a novel mono-tethered POSS compound which is not commercially available yet and can be regarded as a single-tail surfactant. In contrast to theoretically possible micellization of amphiphilic POSS compounds very rare interest is paid by scientific community to this issue. POSS DCA vesiculation occurred at a very low concentration (0.09 mM) in a mixture of acetone, ethanol and 1-propanol according to the experiments. Critical packing parameter of POSS DCA is bigger than one and it must self-assemble into inverted-micelle morphology in a non-polar solvent. The vesicle formation for POSS DCA in a relatively polar solvent system was mainly attributed to formation of stable various-size intermolecular bridges of ethanol or 1-propanol. Also, π–π interaction between aromatic rings is another driving force. Vesicles can trap both hydrophilic and hydrophobic solvents and change composition of a solvent mixture. For the first time, we studied this property for POSS DCA vesicles in different concentrations by a gas chromatographic method. Significant increase in surface tension was attributed to the changes in solvent system composition due to vesicle formation and variation in vesicles morphology.     

Characterization of the aggregates of N-alkyl-N-methylpyrrolidinium bromide surfactants in aqueous solution

We have characterized a new class of surfactant molecules using fluorescence spectroscopic and light-scattering techniques. Our results suggest that this homologous series of N-alkyl-N-methlypyrrolidinium bromide (CnMPB) surfactants with n = 10, 12, 14, 16, and 18 represents a bridge between the well-characterized alkyltrimethylammonium bromide (CnTAB) and dialkyldimethylammonium bromide (di-CnDAB) surfactant series. For the smaller members of the CnMPB series with n = 10, 12, and 14, our results are consistent with the formation of spherical micelles as the surfactant concentration is increased. With increasing alkyl chain length, we observe that the critical micelle concentration decreases and the aggregation number increases, typical of single-tail surfactants. For C16MPB, the formation of micelles at dilute concentrations (0.10 mM) is likely, followed by the coexistence of micelles and small unilamellar vesicles at higher concentrations up to 0.82 mM where only vesicles are present. For C18MPB, our data are consistent with the formation of vesicles only. We demonstrate in this study that the combination of spectroscopic and light-scattering methods is a powerful approach to reveal aspects of aggregate structure and morphology in aqueous CnMPB surfactant systems. In particular, the sensitivity of the fluorescence probe prodan to the polarity of its microenvironment enables the rich complexity of surfactant aggregates exhibited by this series of amphiphilic molecules to be detected.     

Macromolecule-to-Amphiphile Conversion Process of a Polyoxometalate-Polymer Hybrid and Assembled Hybrid Vesicles

We report our findings on the macromolecule-to-amphiphile conversion process of a polyoxometalate-polymer hybrid and the assembled hybrid vesicles formed by aggregation of the hybrid amphiphile. The polyoxometalate-polymer hybrid is composed of a polyoxometalate (POM) cluster, which is covered by five tetrabutylammonium (Bu(4) N(+) ) countercations, and a polystyrene (PS) chain. Through a cation-exchange process the Bu(4) N(+) countercations can be replaced by protons to form a hybrid amphiphile composed of a hydrophilic, protonated POM cluster and a hydrophobic PS chain. By implementing a directed one-dimensional diffusion and analyzing the diffusion data, we confirmed that the diffusion of solvated protons rather than macromolecules or aggregates is the key factor controlling the conversion process. Once the giant hybrid amphiphiles were formed, they immediately assembled into kinetically favored vesicular aggregates. During subsequent annealing these vesicular aggregates were transformed into thermodynamically stable vesicular aggregates with a perfect vesicle structure. The success in the preparation of the POM-containing hybrid vesicles provides us with an opportunity of preparing POM-functionalized vesicles.     

Sugar-derived tricatenar catanionic surfactant: synthesis, self-assembly properties, and hydrophilic probe encapsulation by vesicles

A new sugar-derived tricatenar catanionic surfactant (TriCat) was developed to obtain stable vesicles that could be exploited for drug encapsulation. The presence of the sugar moiety led to the formation of highly hydrophilic stoichiometric catanionic surfactant systems. The three hydrophobic chains permitted vesicles to form spontaneously. The self-assembly properties (morphology, size, and stability) of TriCat were examined in water and in buffer solution. Encapsulation studies of a hydrophilic probe, arbutin, commonly used in cosmetics for its whitening properties, were performed to check the impermeability of the vesicle bilayer. The enhancement of hydrophobic forces by the three chains of TriCat prevented surfactant equilibrium between the bilayer and the solution and enabled the probe to be retained in the aqueous cavity of the vesicles for at least 30 h. Thus, the present study suggests that this tricatenar catanionic surfactant could be a promising delivery system for hydrophilic drugs.     

Macromolecule-to-Amphiphile Conversion Process of a Polyoxometalate–Polymer Hybrid and Assembled Hybrid Vesicles

We report our findings on the macromolecule-to-amphiphile conversion process of a polyoxometalate–polymer hybrid and the assembled hybrid vesicles formed by aggregation of the hybrid amphiphile. The polyoxometalate–polymer hybrid is composed of a polyoxometalate (POM) cluster, which is covered by five tetrabutylammonium (Bu₄N⁺) countercations, and a polystyrene (PS) chain. Through a cation-exchange process the Bu₄N⁺ countercations can be replaced by protons to form a hybrid amphiphile composed of a hydrophilic, protonated POM cluster and a hydrophobic PS chain. By implementing a directed one-dimensional diffusion and analyzing the diffusion data, we confirmed that the diffusion of solvated protons rather than macromolecules or aggregates is the key factor controlling the conversion process. Once the giant hybrid amphiphiles were formed, they immediately assembled into kinetically favored vesicular aggregates. During subsequent annealing these vesicular aggregates were transformed into thermodynamically stable vesicular aggregates with a perfect vesicle structure. The success in the preparation of the POM-containing hybrid vesicles provides us with an opportunity of preparing POM-functionalized vesicles.     

Microstructure and lateral diffusion in monolayers of polymerizable amphiphiles

Lipid analogue amphiphilic molecules containing polymerizable units were investigated in monolayers at the air/water interface by using film balance measurements, fluorescence microscopy, and photobleaching techniques. The polymerizable groups (diene-, diyne-, and methacrylate units) were introduced into the hydrophobic alkyl chains or into the polar head of the amphiphilic molecules.In the case of the diene- and diyne-containing compounds the polymerizable units are incorporated into the hydrophobic alkyl chains, enabling them to form a two-dimensional network. Due to the free chain flexibility of the monomers the lateral mobility was comparable to that of saturated lipid analogues and decreases upon polymerization proportionally to the dose of UV irradiation. In addition, fluid/solid phase transitions of compounds with polymerizable groups in the hydrophobic part tend to vanish during the formation of the polymers. However, the direct observation of the growth of polymeric crystalline domains can be followed by using diacetylene lipid analogues.In the case of the methacrylate derivatives the polymerizable unit was coupled to the polar part via a flexible spacer. For these systems the characteristics of the monomeric phase transition are retained after polymerization. However, it shows a significant, strong decrease of the in-plane mobility already in the fluid-expanded phase of the polymer. The quantitative measurements of the lateral diffusion in the monolayers can be correlated with fluorescence microscopic images of their structure.     

Effect of equimolar salt to decyltrimethylammonium decyl sulfate on vesicle formation and surface adsorption

The aqueous solution of mixture of sodium decyl sulfate (SDeS) and decyltrimethylammonium bromide (DeTAB) has been found to form equilibrium multilamellar vesicles (MLV) spontaneously. We measured the surface tension of the aqueous solution of 1:1 mixture of SDeS and DeTAB as a function of temperature T at various molalities m under atmospheric pressure. The surface density, the entropy of adsorption and the entropy of vesicle formation are evaluated and compared with those of the decyltrimethylammonium decyl sulfate (DeTADeS) aqueous solution system to investigate the role of small counterions in the mechanism of equilibrium vesicle formation. The saturated surface density Gamma (H,C ) vs T curve of the SDeS/DeTAB system sits below that of the DeTADeS system. Therefore, sodium and bromide ions are negatively adsorbed and nevertheless, they neutralize the electric charge of the decyl sulfate ion DeS(-) and the decyltrimethylammonium ion DeTA(+) to some extent to weaken the electrostatic attraction between the polar head groups in the adsorbed film. The net surfactant concentration required for vesicle formation was larger in the SDeS/DeTAB system. Hence, the electrostatic attraction between the polar head groups of the surfactant ions which is one of the major driving forces for vesicle formation is weakened by the presence of the counterions Na(+) and Br(-). Small but distinct changes in the surface density and the entropies of MLV formation of the SDeS/DeTAB system from those of the DeTADeS system were also found.     

A series of long-chain lamellar hydrated copper(II) alkylsulfonates with different chain molecular assemblies

Reaction of copper(II) salts with n-alkylsulfonate anions yields light blue lamellar Cu(C(n)H(2n + 1)SO3)2 x zH2O displaying distinct (mono/bi-layer) chain packing with increasing alkyl chain lengths. This may be attributed to the amphiphilic nature of the surfactants, i.e., the hydrophilic sulfonate head groups, mediating the coordination, and H-bonding interactions, and the hydrophobic alkyl chains.     

嵌段序列对聚合物囊泡形成过程影响的Monte Carlo模拟

采用Monte Carlo模拟方法研究了具有相同链长和组分比的不同嵌段序列的AB两嵌段共聚物与ABA三嵌段共聚物在选择性溶剂中形成囊泡的动力学过程. 模拟结果表明, AB两嵌段共聚物囊泡的形成与ABA三嵌段共聚物囊泡的形成的动力学过程不同. 在慢速退火条件下, ABA三嵌段共聚物囊泡是通过亲水链段向胶束的表面和中心扩散而形成的, 而AB两嵌段共聚物囊泡则由片层弯曲闭合而形成. 相对而言, 退火速度对AB两嵌段共聚物囊泡形成的动力学过程没有显著影响, 其改变仅影响亲水链段与疏水链段发生相分离的难易程度. 当退火速度较快时, 亲水链段和疏水链段发生相分离的速度较快且相分离发生在囊泡形成之前; 而当退火速度较慢时亲水链段和疏水链段之间的相分离在囊泡形成之后仍在进行.     

Spider-web amphiphiles as artificial lipid clusters: design, synthesis, and accommodation of lipid components at the air-water interface

As a novel category of two-dimensional lipid clusters, dendrimers having an amphiphilic structure in every unit were synthesized and labeled "spider-web amphiphiles". Amphiphilic units based on a Lys-Lys-Glu tripeptide with hydrophobic tails at the C-terminal and a polar head at the N-terminal are dendrically connected through stepwise peptide coupling. This structural design allowed us to separately introduce the polar head and hydrophobic tails. Accordingly, we demonstrated the synthesis of the spider-web amphiphile series in three combinations: acetyl head/C16 chain, acetyl head/C18 chain, and ammonium head/C16 chain. All the spider-web amphiphiles were synthesized in satisfactory yields, and characterized by 1H NMR, MALDI-TOFMS, GPC, and elemental analyses. Surface pressure (pi)-molecular area (A) isotherms showed the formation of expanded monolayers except for the C18-chain amphiphile at 10 degrees C, for which the molecular area in the condensed phase is consistent with the cross-sectional area assigned for all the alkyl chains. In all the spider-web amphiphiles, the molecular areas at a given pressure in the expanded phase increased in proportion to the number of units, indicating that alkyl chains freely fill the inner space of the dendritic core. The mixing of octadecanoic acid with the spider-web amphiphiles at the air-water interface induced condensation of the molecular area. From the molecular area analysis, the inclusion of the octadecanoic acid bears a stoichiometric characteristic; i.e., the number of captured octadecanoic acids in the spider-web amphiphile roughly agrees with the number of branching points in the spider-web amphiphile.