pH- and cinnamic acid-triggerable dioleoylphophatidylethanolamine liposome bearing polyethyleneimine/palmitic acid mixture

pH and cinnamic acid (CA)-triggerable liposome was prepared by stabilizing dioleoylphosphatidylethanolamine (DOPE) bilayer with polyethyleneimine (PEI)/palmitic acid (PA) mixture. PEI/PA mixture was air/water interface-active, possibly due to the formation of PEI/PA salt conjugate. When the weight ratio of DOPE to PEI/PA mixture was 200:1, 100:1, 50:1, and 20:1, the fluorescence quenching degree of calcein loaded in the DOPE/PEI/PA assembly prepared using PBS (10 mM, pH 7.4) was 70.7%, 68.7%, 35.3%, and 14%, respectively, indicating that DOPE could be assembled into liposome at the physiological pH value with the aid of the PEI/PA mixture. The hydrodynamic mean diameter of liposome increased from 289 nm to 702 nm on increasing the weight ratio of the DOPE to PEI/PA mixture, possibly because of the bulky PEI chains. The release degree in 120 seconds at pH 4.5, pH 6.0, pH 7.4, and pH 9.0 was about 85%, 24.1%, 10.1%, and 62.0%, respectively, when the suspension of liposome of which the DOPE to PEI/PA mixture weight ratio was 50:1 (pH 7.4) was injected into the release medium of different pH values. The triggered release upon the acidification (i.e., pH 7.4–4.5) and the alkalization (i.e., pH 7.4–9.0) was possibly because PA and PEI were deionized under acidic and alkali conditions, respectively; thus the salt bridge of PEI/PA conjugate could break down. The DOPE liposome also exhibited CA-triggered release. The release degree in 120 seconds at 25°C was 23.1% and it was higher than the release degree at 50°C, 10.9%, possibly because CA could render PEI chains condensed and assembled under upper the critical solution temperature.     

Effect of tris(hydroxymethyl) aminomethane on the phase behavior of poly(ethylene imine)/cinnamic acid conjugate and the release property of cubic phase containing the conjugate

The upper critical solution temperature (UCST) of poly(ethylene imine)/cinnamic acid (PEI/CA) conjugate decreased as the tris(hydroxymethyl) aminomethane (THMAM) concentration increased. On the optical micrographs of PEI/CA mixture solutions at 25°C, the microspheres were found when the THMAM concentration was 0?mM and 100?mM, but hardly found at 200?mM. Monoolein (MO) cubic phase containing PEI, CA, and THMAM exhibited a bilayer structure on the TEM micrograph. The release degree of methylene blue loaded in the cubic phase was not strongly dependent on THMAM concentration at 25°C and 37°C, but strongly dependent on the concentration at 50°C.     

Effect of temperature on the organized self-assembly of SDS/β-Cyclodextrin aqueous solution by dielectric relaxation behavior

The temperature dependence of microstructures of SDS/β-cyclodextrin aqueous solution was investigated by impedance analyzer at the temperature range of 15°C to 55°C. The dielectric relaxation behaviors were observed from 15°C to 35°C, which was attributed to the Maxwell-Wagner interfacial polarization. The microstructure transition of the SDS/β-cyclodextrin aqueous solution from micro-tube to vesicle and then to monomer with increasing temperature was confirmed by conjointly analyzing dielectric parameters, confocal laser scanning microscopy, and infrared spectra. Furthermore, the dielectric analysis was proved to be useful to study surfactant-based organized self-assembly.     

Thermo- and UV Photo-Triggerable Monoolein Cubic Phase Bearing Poly(Hydroxyethyl Acrylate-co-Coumaryl Acrylate-co-Octadecyl Acrylate)

Thermo- and UV photo-triggerable monoolein (MO) cubic phases were developed by incorporating poly(hydroxyethyl acrylate-co-coumaryl acrylate-co-octadecyl acrylate) (P(HEA-CA-ODA)) in the cubic phases. P(HEA-CA-ODA)s, for which the HEA/CA/ODA molar ratio was 98.6:0:1.4, 96.7:2.0:1.3, 96.2:2.6:1.2, 95:3.8:1.2, and 92.8:6.1:1.1, calculated on the ¹H NMR spectra, were prepared by a free radical reaction. The air–water interfacial tension was inversely proportional to the CA content of the copolymer. The copolymers for which the CA content was 2.6%, 3.8%, and 6.1% exhibited their phase transition temperature in an aqueous solution in the temperature range from 25°C to 40°C. As the CA content was more, the temperature sensitivity was higher and the phase transition temperature was lower. The UV light (254 nm, 6 W)-induced dimerization degree of CA was proportional to its content in the copolymers. The release of fluorescein isothiocyanate-dextran from cubic phases containing P(HEA/CA/ODA)s was promoted by UV light irradiation, possibly due to the photo-induced collapse of the copolymer chains. The release from cubic phases incorporating copolymers, for which the CA content was 3.8% and 6.1%, was enhanced by increasing the releasing medium temperature from 23°C to 37°C, possibly due to the thermal collapse of the copolymer chains.     

Comparative Analysis of the Properties of Tween‐20, Tween‐60, Tween‐80, Arlacel‐60, and Arlacel‐80

Foamability and foam stability, emulsifying power, surface tension, and interfacial tension were investigated for Tween‐20 (polyoxyethylene sorbitan monolaurate), Tween‐60 (polyoxyethylene sorbitan monostearate), Tween‐80 (polyoxyethylene sorbitan monooleate), Arlacel‐60 (Sorbitan stearate), and Arlacel‐80 (Sorbitan oleate). Among all the surfactants tested for their foaming power and foamabilty, Arlacel‐60 and Arlacel‐80 showed the best results; the foaming power and foamability was found to be 100%. The surfactants having foam stability more than 50% can be considered as metastable and those less than 50% are considered as low‐stability foams. In case of surface tension and interfacial tension property measurements, Arlacel‐80 showed the best results. At 1% surfactant concentration, the surface tension and interfacial tension of Arlacel‐80 was found to be 29.9 dynes/cm and 1.1 dynes/cm at 30°C ambient temperature. Also, Arlacel‐60 was found to exhibit the best emulsifying power among all the surfactants tested. At 30°C, the emulsifying property of Arlacel‐60 was 6 hours.     

THE EFFECTS OF MIXED MICELLES OF SURFACTANTS ON POLYMERIZATION OF ACRYLAMIDE

The polymerization of acrylamide in mixed micellar solutions of surfactants, initiated by NaHSO₃ has been studied at 20 and 3Q° C with time variable method of thermokinetics for 1. 5-order reaction. The results indicate that the mixed micellar systems of cationic or anionic with zwitterionic surfactants (SLS/ CTAB, SLS/ TTAB, SLS/ SDS) and cationic with nonionic surfactants (Brij 357sol; CTAB, Bri-J35/TTAB, Brij35/ DTAB) have catalytic effect on the polymerization in the order, at 20° C. SLS/ SDS SLS/ TTAB SLS/ CTAB Brij35/ CTAB at 30° C SLS/ SDS SLS/ TTAB≈ / CTAB Bri-j35/ DTAB= sBrij35/ TTAB as Brij35/ CTAB, while Brij35/ SDS mixed micellar system has inhibition. These effects are attributed to the effect of the Stern layer of mixed micelles on the step of initiator (HSOT) to form free radical.     

Silica thin-layer chromatographic studies of surfactants with mixed aqueous-organic eluents containing thiourea: simultaneous separation of co-existing cetyltrimethylammonium bromide, dodecyltrimethylammonium bromide, and polyoxyethylene (20) sorbitan monolaurate

Silica thin-layer chromatography of three surfactants using various solvent systems is described. The mutual separation of coexisting cetyltrimethylammonium bromide (CTAB), dodecyltrimethyl-ammonium bromide (DTAB), and polyoxyethylene (20) sorbitan monolaurate (Tween 20) is achieved on silica layer using 5% aqueous thiourea-acetone-methanol (60:20:20,v/v/v) as the mobile phase. The effect of the carbon chain length of alcohols (methanol, ethanol, n-propanol, and n-butanol) on the mobility of these surfactants is examined on silica layers. The comparative study is performed with sulfur- (thiourea) and oxygen- (urea) containing compounds in the eluent on the mobility as well as on the separation of co-existing CTAB, DTAB, and Tween 20. The interference on the resolution of the mixture of CTAB, DTAB, and Tween 20, due to presence of metal cations as impurities, is also examined. The limits of detection of CTAB, DTAB, and Tween 20 are estimated.     

Effects of Charged Surfactants on Interfacial Water Structure and Macroscopic Properties of the Air-Water Interface

Surfactants are used to control the macroscopic properties of the air-water interface. However, the link between the surfactant molecular structure and the macroscopic properties remains unclear. Using sum-frequency generation spectroscopy and molecular dynamics simulations, two ionic surfactants (dodecyl trimethylammonium bromide, DTAB, and sodium dodecyl sulphate, SDS) with the same carbon chain lengths and charge magnitude (but different signs) of head groups interact and reorient interfacial water molecules differently. DTAB forms a thicker but sparser interfacial layer than SDS. It is due to the deep penetration into the adsorption zone of Br⁻ counterions compared to smaller Na⁺ ones, and also due to the flip-flop orientation of water molecules. SDS alters two distinctive interfacial water layers into a layer where H⁺ points to the air, forming strong hydrogen bonding with the sulphate headgroup. In contrast, only weaker dipole-dipole interactions with the DTAB headgroup are formed as they reorient water molecules with H⁺ point down to the aqueous phase. Hence, with more molecules adsorbed at the interface, SDS builds up a higher interfacial pressure than DTAB, producing lower surface tension and higher foam stability at a similar bulk concentration. Our findings offer improved knowledge for understanding various processes in the industry and nature.     

Characterization of Cinnamic Acid-Attached Nonionic Amphiphiles in UV Extinction,Emulsification, and In Vitro Toxicity

Cinnamic acid (CA) was covalently attached to nonionic surfactants by condensation reaction. The mass and the molar extinction coefficient of CA residue of each conjugate did not markedly deviate from those of free CA, indicating CA could absorb the UV light after being conjugated to the surfactants. When the concentration of the conjugates in aqueous phase was 0.1% and 1.0%, mineral oil could readily be emulsified by polyoxyehtylene(20) cetyl ether–CA conjugate (CE20–CA), polyoxyethylene(20) oleyl ether–CA conjugate (OE20–CA), and polyoxyehtylene(20) sorbitan monolaurate–CA conjugate (Tween 20–CA). The extinction coefficients of the surfactant–CA conjugates contained in O/W emulsion did not markedly deviate from those of the conjugates dissolved in water, suggesting that the conjugate could maintain their extinction coefficients when they coexisted with oil droplets. According to the result of 3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyltetrazolium bromide (MTT) assay, the viability of cell (BALB/c 3T3 clone A31) was greater than 80% for all the surfactant–CA conjugates tested when the conjugate concentration was 0.2%. It is believed that CE20–CA, OE20–CA, and Tween 20–CA could be used as an emulsifier which absorbs UV light effectively.     

Interaction of Sodium Dodecyl Sulfate with Poly(ethyleneimine) in Bulk Solution and at the Air-Solution Interface

Interaction of sodium dodecyl sulfate (SDS) with the cationic polyelectrolyte poly(ethyleneimine) (PEI) was investigated in this study. Turbidity measurements were performed in order to analyze the interaction and complex formation in bulk solution as a function of polymer concentration and pH. Surface tension measurements were made to investigate the properties of SDS/PEI/water mixtures at air/solution interface. Results revealed that SDS/PEI complexes form in solution depending on the surfactant and polymer concentration. A decrease was observed in surface tension values in the presence of SDS/PEI mixtures compared to the values of pure SDS solutions. Both solution and interfacial properties exhibited pH dependent behavior. A shift was seen in the critical micelle concentration of SDS solutions as a function of PEI concentration and solution pH. Monovalent and divalent salt additions showed some influence on the interfacial properties of SDS solutions in the presence of PEI.     

The effect of UV irradiation on air/water interfacial activity of Tween 20–coumarin conjugates

In order to obtain photo-sensitive surfactants, coumarin derivatives were covalently attached, through either ester bond or ether bond, to hydroxyl groups located at the ends of PEO segments of Tween 20. The molar ratios of Tween 20 to coumarin residues in both Tween 20–coumarin conjugate having ester bond (TCES) and ether bond (TCET) were about 1:1 despite the excess coumarin in the reaction mixture. The photo-dimerization degree was in the order of TCET?>?TCES?>?a free coumarin derivative. And the air/water interfacial activity was in the order of TCET?>?Tween 20?>?TCES. The interfacial activities of TCES and TCET increased with the UV irradiation time. This is possibly because the coumarin residues of TCES and TCET are photo-dimerized to produce Gemini surfactant-like dimeric surfactants. The photo-induced change in the interfacial activity of TCES was slightly greater than that of TCET, probably due to the difference in the length, the polarity, and the flexibility of the linker between two monomeric conjugates of Gemini-like dimeric surfactants.     

Effect of Aqueous Phase pH on the Dynamic Interfacial Tension of Acidic Crude Oils and Myristic Acid in Dodecane

The time dependence of the interfacial tension between water–acidic crude oil and water–synthetic oil was investigated for aqueous phase pHs ranging from 2 to 9 using the du Noüy ring method at 20°C. Myristic acid in dodecane was selected as a model (synthetic oil) for acidic crude oil containing indigenous surfactants, and the similarities and differences between the dynamic interfacial tension behaviours of the natural and synthetic crude oil systems were compared. The initial interfacial tension and the relaxation of the interfacial tension are sensitive to the aqueous phase pH for both systems. The adsorption kinetics of the indigenous surfactants and myristic acid could be well fitted with the monoexponential model, and the time constants obtained in this manner indicates that reorganization of the indigenous surfactants and myristic acid at the w/o interface are pH dependent. The experimental results also indicate that indigenous surfactants in acidic crude oil and myristic acid in dodecane have similar film formation behaviours at the w/o interface for the range of pHs investigated.     

Miscibility of sodium dodecyl sulfate and sodium decyl sulfate in the adsorbed film and micelle

The interfacial tension of the aqueous solution of sodium dodecyl sulfate (SDS) and sodium decyl sulfate (SDeS) mixture against hexane was measured as a function of the total molality and composition of the surfactant mixture at 298.15 K under atmospheric pressure. The compositions of adsorbed film and micelle were evaluated numerically by applying the thermodynamic relations to the experimental results. These results were shown in the form of the phase diagrams of adsorption and micelle formation and compared with those of the aqueous solution of sodium perfluorooctanoate (SPFO) and SDeS mixture. It was found that the diagrams of SDS and SDeS system have swollen cigar shapes and are quite different from those of SPFO and SDeS system which show non-ideal mixing both in the adsorbed film and micelle. This finding was attributed to the fact that the interaction between fluorocarbon and hydrocarbon chains is weaker than that between hydrocarbon chains.     

Novel phase behavior in adsorbed film of fluoroalkanol and cationic surfactant mixture

The surface tension of the aqueous solution of the binary mixture of 1H,1H-heptafluoro-1-butanol (FC4OH) and dodecyltrimethylammonium bromide (DTAB) was measured as a function of the total molality of the mixture and the composition (mole fraction in the surfactant mixture) of DTAB at 298.15 K under atmospheric pressure to examine the phase behavior in the adsorbed film. The results of the surface tension measurement were analyzed by the thermodynamic procedure proposed by us and the composition of the mixed adsorbed film in equilibrium with their bulk solution was calculated. Three different phases of the adsorbed film appeared by a subtle balance between the attractive interaction of the polar head groups and weak dispersion interaction of the hydrophobic chains. In the low-concentration regime, FC4OH molecules and DTAB molecules form a gaseous film and mix attractively in the whole composition by the long-range ion–dipole attraction between hydrophilic groups. The effect of the attractive dispersion interaction between CH and CF chains became more influential in the expanded film within a restricted composition region, where it should be noted that the interaction between CH and CF is weaker than that between CH chains or between CF chains alone. Furthermore, the adsorbed films at two specific compositions are stabilized by the stoichiometric arrangements of the molecules, which help ion–dipole attraction, in them.     

Spectral studies of safranin-O in different surfactant solutions

The interaction of Safranin-O (SO), a cationic dye, with various surfactants viz., anionics; Sodiumdodecylsulfate (SDS) and Sodiumdodecylsulfonate (SDSo), nonionics; polyoxyethylenesorbitanmonolaurate (Tween 20) and polyoxyethylenedodecylether (Brij 35), cationic; Dodecyltrimethylammoniumbromide (DTAB) and zwitterionic; Laurylsulfobetaine (LSB) was studied spectrophotometrically as a function of surfactant concentration ranging from premicellar to postmicellar region in aqueous media in the absence and presence of cosolvents. The binding constants (K(b)) and fraction of bound SO to micelles (f), were calculated by means of Benesi-Hildebrand Equation. The binding tendency of SO to micelles followed the order as; Tween 20>Brij 35>SDS>SDSo>LSB. The presence of cosolvents, such as Methanol, Dimethylformamide (DMFA) and 1,4 Dioxan (DX) at various volume percentages, increased the CMC of both SDS and Tween 20 and at a certain concentration totally inhibited the micellization. The binding of SO to micelles decreased as the concentration of the cosolvents increased. This inhibitory effect of cosolvents on binding of SO to micelles followed the order as; Methanol>DMFA>DX.     

The effects of the addition of the polyelectrolyte, poly(ethyleneimine), on the adsorption of mixed surfactants of sodium dodecylsulfate and dodecyldimethylaminoacetate at the air-water interface

The effects of the addition of the polyelectrolyte, poly(ethyleneimine), PEI, on the adsorption of the mixed surfactants of sodium dodecylsulfate, SDS, and dodecyldimethylaminoacetate, dodecyl betaine, at the air-water interface have been investigated using neutron reflectivity and surface tension. In the absence of PEI the SDS and dodecyl betaine surfactants strongly interact and exhibit synergistic adsorption at the air-water interface. The addition of PEI, at pH 7 and 10, results in a significant modification of the surface partitioning of the SDS/dodecyl betaine mixture. The strong surface interaction at high pH (pH 7 and 10) between the PEI and SDS dominates the surface behavior. For solution compositions in the range 20/80-80/20 mol ratio dodecyl betaine/SDS at pH 7 the surface composition is strongly biased towards the SDS. At pH 10 a similar behavior is observed for a solution composition of 50/50 mol ratio dodecyl betaine/SDS. This strong partitioning in favor of the SDS at high pH is attributed to the strong ion-dipole attraction between the SDS sulfate and the PEI imine groups. At pH 3, where the electrostatic interactions between the surfactant and the PEI are dominant, the dodecyl betaine more effectively competes with the SDS for the interface, and the surface composition is much closer to the solution composition.     

Acrylamide as cosurfactant and hydrotrope in the pseudoternary Span 80-Tween 85/isopar M/water emulsion/microemulsion forming system

The aim of this study was to investigate the effects of acrylamide on emulsification of the pseudoternary Span 80-Tween 85/isopar M/water system at 40 °C. It was revealed that acrylamide could act as a surface-active agent to decrease the isopar M/water interfacial tension, and as a hydrotrope to increase the aqueous solubility of Tween 85, and further remarkably influence the emulsification of the investigated pseudoternary Span 80-Tween 85/isopar M/water system. The surface-active role of acrylamide could reduce the minimal weight fraction of the mixture of Span 80 and Tween 85 in pseudoternary systems (X_ST) to form stable water-in-oil (W/O) emulsions when the weight fraction of acrylamide in the aqueous domain (X_AM) is below 0.1; while its hydrotropic role at high X_AM levels (>0.1) could drive more Tween 85 molecules to transfer into aqueous phase and slightly improved the minimal X_ST to form stable W/O emulsions, as compared to that of X_AM at 0.1. Moreover, under a given X_ST, the mean diameter of the droplet size distribution of the W/O emulsion remarkably decreased with the increase in X_AM; while the smaller droplets in the W/O emulsion systems at higher level of X_AM still coalesced rapidly when the compositions of the emulsion was slightly above the visually determined boundary between non-emulsion and stable emulsion regions.     

Experimental and theoretical investigation of the micellar-assisted solubilization of ibuprofen in aqueous media

Surfactants can be used to increase the solubility of poorly soluble drugs in water and to increase drug bioavailability. In this article, the aqueous solubilization of the nonsteroidal, antiinflammatory drug ibuprofen is studied experimentally and theoretically in micellar solutions of anionic (sodium dodecyl sulfate, SDS), cationic (dodecyltrimethylammonium bromide, DTAB), and nonionic (dodecyl octa(ethylene oxide), C12E8) surfactants possessing the same hydrocarbon "tail" length but differing in their hydrophilic headgroups. We find that, for these three surfactants, the aqueous solubility of ibuprofen increases linearly with increasing surfactant concentration. In particular, we observed a 16-fold increase in the solubility of ibuprofen relative to that in the aqueous buffer upon the addition of 80 mM DTAB and 80 mM C12E8 but only a 5.5-fold solubility increase upon the addition of 80 mM SDS. The highest value of the molar solubilization capacity (chi) was obtained for DTAB (chi = 0.97), followed by C12E8 (chi = 0.72) and finally by SDS (chi = 0.23). A recently developed computer simulation/molecular-thermodynamic modeling approach was extended to predict theoretically the solubilization behavior of the three ibuprofen/surfactant mixtures considered. In this modeling approach, molecular-dynamics (MD) simulations were used to identify which portions of ibuprofen are exposed to water (hydrated) in a micellar environment by simulating a single ibuprofen molecule at an oil/water interface (modeling the micelle core/water interface). On the basis of this input, molecular-thermodynamic modeling was then implemented to predict (i) the micellar composition as a function of surfactant concentration, (ii) the aqueous solubility of ibuprofen as a function of surfactant concentration, and (iii) the molar solubilization capacity (chi). Our theoretical results on the solubility of ibuprofen in aqueous SDS and C12E8 surfactant solutions are in good agreement with the experimental data. The ibuprofen solubility in aqueous DTAB solutions was somewhat overpredicted because of challenges associated with accurately modeling the strong electrostatic interactions between the anionic ibuprofen and the cationic DTAB. Our results indicate that computer simulations of ibuprofen at a flat oil/water interface can be used to obtain accurate information about the hydrated and the unhydrated portions of ibuprofen in a micellar environment. This information can then be used as input to a molecular-thermodynamic model of self-assembly to successfully predict the aqueous solubilization behavior of ibuprofen in the three surfactant systems studied.     

Emulsions Stabilized with poly(Hydroxyethyl Acrylate-co-Coumaryl Acrylate-co-2-Ethylhexyl acrylate)

Thermo- and photo-responsive emulsions were prepared using mineral oil as an oil phase and a thermo- and-photo-sensitive polymer as an emulsifier. Hydroxyethyl acrylate (HEA) was copolymerized with Coumaryl acrylate (CA) and 2-Ethylhexyl acrylate (EHA) by a free radical reaction with the content of CA in the reaction mixture being varied (0, 0.5, 1, 2, 3 mol%) and the content of EHA being kept constant (2 mol%). CA was used as a photo-responsive comonomer and EHA was used as a hydrophobic comonomer to endow the copolymer with amphiphilicity. The copolymers prepared using the HEA/CA/EHA mixture where CA content was 1, 2, 3 mol% exhibited a phase transition in the range of 20°C– 45°C, and the phase transition temperature decreased with increasing the content. The CA of the copolymers was readily dimerized under the irradiation of UV (365 nm. 400 W) and the dimerization degree was 27%–47% in 60 min. The droplet size of emulsions significantly increased with increasing the temperature from 27°C- 50°C, possibly due to the thermal contraction of the copolymers. Also, the size markedly increased by 60 min-irradiation of the UV light, possibly because of the photo collapse of the copolymers.     

Effect of molecular packing on adsorption and micelle formation of a homologous cationic surfactant mixture of hexadecyltrimethylammonium bromide and dodecyltrimethylammonium bromide

The surface tension of an aqueous solution of a hexadecyltrimethylammonium bromide (HTAB) and dodecyltrimethylammonium bromide (DTAB) mixture was measured as a function of the total molality and the composition of DTAB at 298.15 K under atmospheric pressure. The phase diagrams of adsorption and micelle formation were constructed and the excess Gibbs energy was evaluated by analyzing the phase diagrams thermodynamically. Both the excess Gibbs energy in the adsorbed film and the excess surface area are negative; therefore the mutual interaction between HTAB and DTAB is said to be stronger than that between the same species and is enhanced with increasing adsorption. By combining the results with those obtained in previous studies, we claimed that DTAB molecules can use effectively the space among the hydrocarbon chains of HTAB molecules and their polar head groups take a staggered arrangement at the surface so as to reduce the electrostatic repulsion. Consequently the dispersion force between hydrophobic chains becomes stronger. Furthermore, the comparison of the excess Gibbs energy in the adsorbed film with that in the micelle shows that the staggered arrangement of molecules is not necessary in the spherical micelle.