Investigation of supramolecular structures in various aqueous solutions of an amyloid forming peptide using small-angle X-ray scattering.

Aggregation of peptide molecules into amyloid fibrils is a characteristic feature of several degenerative diseases. However, the details behind amyloid-formation, and other self-assembled peptide aggregates, remain poorly understood. In this study, we have used small-angle X-ray scattering (SAXS), static and dynamic light scattering (SLS and DLS) as well as cryogenic transmission electron microscopy (cryo-TEM) to determine the structural geometry of self-assembled peptide aggregates in various dilute aqueous solutions. Pramlintide was used as a model peptide to assess the aggregation behaviour of an amyloid-forming peptide. The effects of adding sodium chloride (NaCl), sodium thiocyanate (NaSCN), and sodium fluoride (NaF) and the co-solvent dimethyl sulfoxide (DMSO) on the aggregation behaviour were studied. Our scattering data analysis demonstrates that small oligomeric fibrils aggregate to form networks of supramolecular assemblies with fractal dimensions. The choice of anion in small amounts of added salt has a significant impact on the size of the fibrils as well as on the fractal dimensions of supramolecular clusters. In DMSO the fractal dimension decreased with increasing DMSO concentration, indicating the formation of a less compact structure of the supramolecular assemblies.

Spontaneous Formation of Ultrasmall Unilamellar Vesicles in Mixtures of an Amphiphilic Drug and a Phospholipid.

We have observed ultrasmall unilamellar vesicles, with diameters of less than 20 nm, in mixtures of the tricyclic antidepressant drug amitriptyline hydrochloride (AMT) and the unsaturated zwitterionic phospholipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) in physiological saline solution. The size and shape of spontaneously formed self-assembled aggregates have been characterized using complementary techniques, i.e., small-angle neutron and X-ray scattering (SANS and SAXS) and cryo-transmission electron microscopy (cryo-TEM). We observe rodlike mixed micelles in more concentrated samples that grow considerably in length upon dilution, and a transition from micelles to vesicles is observed as the concentration approaches the critical micelle concentration of AMT. Unlike the micelles, the spontaneously formed vesicles decrease in size with each step of dilution, and ultrasmall unilamellar vesicles, with diameters as small as about 15 nm, were observed at the lowest concentrations. The spontaneously formed ultrasmall unilamellar vesicles maintain their size for as long we have investigated them (i.e., several months). To the best of our knowledge, such small vesicles have never before been reported to form spontaneously in a biocompatible phospholipid-based system. Most interestingly, the size of the vesicles was observed to be strongly dependent on the chemical structure of the phospholipid, and in mixtures of AMT and the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), the vesicles were observed to be considerably larger in size. The self-assembly behavior in the phospholipid-drug surfactant system in many ways resembles the formation of equilibrium micelles and vesicles in mixed anionic/cationic surfactant systems.

Investigation of the enhanced ability of bile salt surfactants to solubilize phospholipid bilayers and form mixed micelles.

The self-assembly in mixtures of the anionic bile salt surfactant sodium deoxycholate (NaDC) and the zwitterionic phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) in physiological saline solution has been investigated using light scattering, small-angle X-ray scattering and cryo-transmission electron microscopy. Rather small tri-axial ellipsoidal NaDC-DMPC mixed micelles form at a high content of bile salt in the mixture, which increase in size as an increasing amount of DMPC is incorporated into the micelles. Eventually, the micelles begin to grow substantially in length to form long wormlike micelles. At higher mole fractions of DMPC, the samples become turbid and cryo-TEM measurements reveal the existence of large perforated vesicles (stomatosomes), coexisting with geometrically open disks. To our knowledge, stomatosomes have not been observed before for any bile salt-phospholipid system. Mixed micelles are found to be the sole aggregate structure in a very wide regime of bile salt-phospholipid compositions, i.e. up to about 77 mol% phospholipid in the micelles. This is much higher than the corresponding value of 25 mol% observed for the conventional surfactant hexadecyltrimethylammonium bromide (CTAB) mixed with DMPC in the same solvent. The enhanced ability of bile salt surfactants to solubilize phospholipid bilayers and form mixed micelles is rationalized using bending elasticity theory. From our theoretical analysis, we are able to conclude that amphiphilic molecules rank in the following order of increasing spontaneous curvature: phospholipids < conventional surfactants < bile salts. The bending rigidity of the different amphiphilic molecules increases according to the following sequence: bile salts < conventional surfactants < phospholipids.

A novel explanation for the enhanced colloidal stability of silver nanoparticles in the presence of an oppositely charged surfactant.

The structural behavior in aqueous mixtures of negatively charged silver nanoparticles (Ag NPs) together with the cationic surfactants cetyltrimethylammonium bromide (CTAB) and dodecyltrimethylammonium chloride (DTAC), respectively, has been investigated using SANS and SAXS. From our SANS data analysis we are able to conclude that the surfactants self-assemble into micellar clusters surrounding the Ag NPs. We are able to quantify our results by means of fitting experimental SANS data with a model based on cluster formation of micelles with very good agreement. Based on our experimental results, we propose a novel mechanism for the stabilization of negatively charged Ag NPs in a solution of positively charged surfactants in which cluster formation of micelles in the vicinity of the particles prevents the particles from aggregating. Complementary SAXS and DLS measurements further support this novel way of explaining stabilization of small hydrophilic nanoparticles in surfactant-containing solutions.

Growth Behavior, Geometrical Shape, and Second CMC of Micelles Formed by Cationic Gemini Esterquat Surfactants.

Micelles formed by novel gemini esterquat surfactants have been investigated with small-angle neutron scattering (SANS). The growth behavior of the micelles is found to differ conspicuously depending on the length of the gemini surfactant spacer group. The gemini surfactant with a long spacer form rather small triaxial ellipsoidal tablet-shaped micelles that grow weakly with surfactant concentration in the entire range of measured concentrations. Geminis with a short spacer, on the other hand, form weakly growing oblates or tablets at low concentrations that start to grow much more strongly into polydisperse rodlike or wormlike micelles at higher concentrations. The latter behavior is consistent with the presence of a second CMC that marks the transition from the weakly to the strongly growing regime. It is found that the growth behavior in terms of aggregation number as a function of surfactant concentration always appear concave in weakly growing regimes, while switching to convex behavior in strongly growing regimes. As a result, we are able to determine the second CMC of the geminis with short spacer by means of suggesting a rather precise definition of it, located at the point of inflection of the growth curve that corresponds to the transition from concave to convex growth behavior. Our SANS results are rationalized by comparison with the recently developed general micelle model. In particular, this theory is able to explain and reproduce the characteristic appearances of the experimental growth curves, including the presence of a second CMC and the convex strongly growing regime beyond. By means of optimizing the agreement between predictions from the general micelle model and results from SANS experiments, we are able to determine the three bending elasticity constants spontaneous curvature, bending rigidity, and saddle-splay constant for each surfactant.

Spontaneous transformations between surfactant bilayers of different topologies observed in mixtures of sodium octyl sulfate and hexadecyltrimethylammonium bromide.

The influence of adding salt on the self-assembly in sodium octyl sulfate (SOS)-rich mixtures of the anionic surfactant SOS and the cationic surfactant hexadecyltrimethylammonium bromide (CTAB) have been investigated with the two complementary techniques, small-angle neutron scattering (SANS) and cryo-transmission electron microscopy. We are able to conclude that addition of a substantial amount of inert salt, NaBr, mainly has three effects on the structural behaviors: (i) the micelles become much larger at the transition from micelles to bilayers, (ii) the fraction of bilayer disks increases at the expense of vesicles, and (iii) bilayer aggregates perforated with holes are formed in the most diluted samples. A novel form factor valid for perforated bilayer vesicles and disks is introduced for the first time and, as a result, we are able to directly observe the presence of perforated bilayers by means of fitting SANS data with an appropriate model. Moreover, we are able to conclude that the morphology of bilayer aggregates changes according to the following sequence of different bilayer topologies, vesicles → disks → perforated bilayers, as the electrolyte concentration is increased and surfactant mole fraction in the bilayer aggregates approaches equimolarity. We are able to rationalize this sequence of transitions as a result of a monotonous increase of the bilayer saddle-splay constant (k(c)(bi)) with decreasing influence from electrostatics, in agreement with theoretical predictions as deduced from the Poisson-Boltzmann theory.

Self-assembly in mixtures of an anionic and a cationic surfactant: a comparison between small-angle neutron scattering and cryo-transmission electron microscopy.

The self-assembly in SOS-rich mixtures of the anionic surfactant sodium octyl sulfate (SOS) and the cationic surfactant hexadecyltrimethylammonium bromide (CTAB) has been investigated with the complementary techniques small-angle neutron scattering (SANS) and cryo-transmission electron microscopy (cryo-TEM). Both techniques confirm the simultaneous presence of open and closed bilayer structures in highly diluted samples as well as the existence of small globular and large elongated micelles at higher concentrations. However, the two techniques sometimes differ with respect to which type of aggregates is present in a particular sample. In particular, globular or wormlike micelles are sometimes observed with cryo-TEM in the vicinity of the micelle-to-bilayer transition, although only bilayers are present according to SANS and the samples appear bluish to the eye. A similar discrepancy has previously been reported but could not be satisfactorily rationalized. On the basis of our comparison between in situ (SANS) and ex situ (cryo-TEM) experimental techniques, we suggest that this discrepancy appears mainly as a result of the non-negligible amount of surfactant adsorbed at interfaces of the thin sample film created during the cryo-TEM specimen preparation. Moreover, from our detailed SANS data analysis, we are able to observe the unusually high amount of free surfactant monomers present in SOS-rich mixtures of SOS and CTAB, and the experimental results give excellent agreement with model calculations based on the Poisson-Boltzmann mean field theory. Our careful comparison between model calculations and experiments has enabled us to rationalize the dramatic microstructural transformations frequently observed upon simply diluting mixtures of an anionic and a cationic surfactant.

Geometrical shape of micelles formed by cationic dimeric surfactants determined with small-angle neutron scattering.

The influence of spacer group on the geometrical shape of micelles formed by quaternary-bis dimeric (Gemini) surfactants C(12)H(25)N(CH(3))(2)(CH(2))(s)N(CH(3))(2)C(12)H(25) (12-s-12) has been investigated with small-angle neutron scattering (SANS). Dimeric surfactants with a short spacer unit (12-3-12 and 12-4-12) are observed to form elongated general ellipsoidal micelles with half axes a < b < c, whereas SANS data demonstrate that 12-s-12 surfactants with 6 ≤ s ≤ 12 form rather small spheroidal micelles rather than strictly spherical micelles. By means of comparing our present SANS results with previously determined growth rates using time-resolved fluorescence quenching, we are able to conclude that micelles formed by 12-6-12, 12-8-12, 12-10-12, and 12-12-12 are shaped as oblate rather than prolate spheroids. As a result, our present investigation suggests a never before reported structural behavior of Gemini surfactant micelles, according to which micelles transform from elongated ellipsoids to nonelongated oblate spheroids as the length of the spacer group is increased. The aggregation number of oblate micelles is observed to monotonously decrease with an increasing length of the surfactant spacer group, mainly as a result of a decreasing minor half axis (a), whereas the major half axis (b) is rather constant with respect to s. We argue that geometrically heterogeneous elongated micelles are formed by dimeric surfactants with a short spacer group mainly as a result of the surface charges becoming less uniformly distributed over the micelle interface. As the length of the spacer group increases, the distance between intramolecular charges become approximately equal to the average distance between charges on the micelle interface, and as a result, rather small oblate spheroidal micelles with a more uniform distribution of surface charges are formed by dimeric 12-s-12 surfactants with 6 ≤ s ≤ 12.

Self-assembling properties of ionisable amphiphilic drugs in aqueous solution.

HYPOTHESIS: Common amphiphilic drug molecules often have a more rigid nonpolar part than conventional surfactants. The rigidity is expected to influence the self-assembling properties and possibly give rise to aggregation patterns different from that of regular surfactants. EXPERIMENTS: We have investigated self-assembling properties of the hydrochloride salts of adiphenine (ADP), pavatrine (PVT), and amitriptyline (AMT) at concentrations up to 50 wt% using small-angle x-ray scattering, dynamic light scattering, cryo-transmission electron microscopy, and surface tension measurements. FINDINGS: All drugs form small micelles of oblate spheroidal shape at concentrations above the critical micelle concentrations (CMC). The micelles grow weakly in size up to about 20 wt%, where the aggregation number reaches a maximum followed by a slight decrease in size at higher drug concentrations. We observe a correlation between the decrease in micelle size at high concentrations and an increasing charge of the micelles, as the degree of ionization increases with increasing drug concentration and decreasing pH. In contrast to what has previously been reported, the aggregation behavior of all studied drugs resembles the closed association behavior of conventional surfactants with a short aliphatic chain as hydrophobic tail group i.e. the micelles are always small in size and lack a second CMC. CMC values were determined with surface tension measurements, including also lidocaine hydrochloride (LDC) and chlorpromazine hydrochloride (CHL).

Synergistic effects in mixtures of oppositely charged surfactants as calculated from the Poisson-Boltzmann theory: a comparison between theoretical predictions and experiments.

Critical micelle concentrations in mixtures of an anionic surfactant and a cationic amphiphilic drug have been investigated using a model-independent procedure to quantify observed synergistic effects. Experimental results were compared with a theory based on the Poisson-Boltzmann mean field approximation of a charged interface with a diffuse layer of counterions. Explicit expressions for the activity coefficients from which the critical micelle concentration can be calculated and quantitatively predicted have been derived and excellent agreement between experimental data and theory was obtained. As a result, we demonstrate that it is possible to rationalize and predict the magnitude of synergism in mixtures of oppositely charged surfactants in the presence of added salt.

Model calculations of the spontaneous curvature, mean and Gaussian bending constants for a thermodynamically open surfactant film.

The spontaneous curvature (H(0)), mean and Gaussian bending constants (k(c) and k (c)), as defined in the well-known Helfrich expression, have been calculated from a detailed model for a thermodynamically open surfactant layer. The effect of head group cross-section area, surfactant tail length and electrolyte concentration for monovalent ionic surfactants have been investigated. Geometrical packing constraints subjected to the aggregated hydrocarbon tails and electrostatics are found to be the dominant contributions to H(0), k(c) and k (c). In addition, the transition from spherocylindrical micelles to vesicles were investigated in terms of the three parameters and the following simple expressions were derived as criteria for coexistence between micelles and vesicles H(0)=1/4 xi and N(ves)/N(mic)=exp[4 pi(k(c)+k (c))/kT], where xi is the thickness of the hydrocarbon part of the film and N(mic) and N(ves) the average aggregation numbers of micelles and vesicles, respectively. However, it is found that the ratio N(ves)/N(mic) is order of magnitudes too large for vesicles to form at all in charged single-surfactant systems where the surfactant head is of moderate size.

A small-angle neutron and static light scattering study of micelles formed in aqueous mixtures of a nonionic alkylglucoside and an anionic surfactant.

The size and shape of micelles formed in aqueous mixtures of the anionic surfactant sodium dodecyl sulfate (SDS) and the nonionic sugar-based surfactant n-decyl beta-D-glucopyranoside (C(10)G) at different concentrations of added salt have been investigated with small-angle neutron and static light scattering. Rather small prolate ellipsoidal micelles form in the absence of added salt and at [NaCl] = 10 mM in D(2)O. The micelles grow considerably in length to large rods as the electrolyte concentration is raised to [NaCl] = 0.1 M. In excess of nonionic surfactant ([SDS]/[C(10)G] = 1:3) at [NaCl] = 0.1 M in D(2)O, several thousands of Angstroms long wormlike micelles are observed. Most interestingly, a conspicuously large isotope solvent effect was observed from static light scattering data according to which micelles formed at [SDS]/[C(10)G] = 1:3 and [NaCl] = 0.1 M in H(2)O are at least five times smaller than micelles formed in the corresponding samples in D(2)O.

Explaining the growth behavior of surfactant micelles.

The growth behavior of surfactant micelles has been investigated from a theoretical point of view. It is demonstrated that predictions deduced from the spherocylindrical micelle model, which considers micelles that are only able to grow in the length direction, are inconsistent with experimental measurements. Accordingly, the rise in aggregation numbers above a certain concentration, roughly corresponding to the second critical micelle concentration, appears to be much stronger than predicted by the spherocylindrical micelle model. On the other hand, predictions deduced from the general micelle model, which considers micelles that are able to grow with respect to both width and length, show excellent agreement with experimental observations. The latter theory is based on bending elasticity and it is demonstrated that the associated three parameters spontaneous curvature, bending rigidity and saddle-splay constant may all be determined for a micellar system from experimental measurements of the aggregation number as a function of surfactant concentration. The three parameters turn out to influence the appearance of a micellar growth curve rather differently. In accordance, the location of the second cmc is mainly determined by the saddle-splay constant and the bending rigidity. The shape of the growth curve, when going from the region of weakly growing micelles at low surfactant concentrations to strongly growing micelles above the second cmc, is mainly influenced by the bending rigidity.

Structural behaviour of mixed cationic surfactant micelles: a small-angle neutron scattering study.

Self-assembly in mixtures of two single-chain cationic surfactants, with different tail lengths (CTAB and DTAB) as well as of a single-chain (DTAB) and a double-chain (DDAB) cationic surfactant, with identical tail lengths, have been investigated with small-angle neutron scattering (SANS) and rationalised in terms of bending elasticity properties. The growth behaviour of micelles with respect to surfactant composition appears completely different in the two surfactant mixtures. DTAB form small oblate spheroidal micelles in presence of [NaBr]=0.1 M that transform into prolate spheroidal mixed CTAB/DTAB micelles upon adding moderate amounts of CTAB, so as to give a mole fraction y=0.20 in solution. Most unexpectedly, upon further addition of CTAB the mixed CTAB/DTAB micelles grow with an almost equal rate in both length and width directions to form tablets. In contrast to this behaviour, mixed DDAB/DTAB micelles grow virtually exclusively in the length direction, in presence of [NaBr]=0.1 M, to form elongated ellipsoidal (tablet-shaped) and subsequently long wormlike micelles as the fraction of DDAB in the micelles increases. Mixed DDAB/DTAB micelles grow to become as long as 2000Å before an abrupt transition to large bilayer structures occurs. This means that the micelles are much longer at the micelle-to-bilayer transition as compared to the same mixture in absence of added salt. It is found that the point of transition from micelles to bilayers is significantly shifted towards higher fractions of aggregated DTAB as an appreciable amount of salt is added to DDAB/DTAB mixtures, indicating a considerable reduction of the spontaneous curvature with an increasing [NaBr]. By means of deducing the various bending elasticity constants from our experimental results, according to a novel approach by ours, we are able to conclude that the different growth behaviours appear as a consequence of a considerably lower bending rigidity, as well as higher saddle-splay constant, for DDAB/DTAB surfactant mixtures in presence of [NaBr]=0.1 M, as compared to mixtures of CTAB/DTAB in [NaBr]=0.1 M and DDAB/DTAB in absence of added salt.

Bending elasticity of nonionic surfactant layers.

A novel approach to evaluate the bending elasticity of monolayers formed by nonionic surfactants with a rigid head group is introduced by means of considering head group repulsion as derived from the free energy of mixing rigid hydrophilic head groups with surrounding solvent molecules as well as contributions related to the hydrophobic tails. Explicit expressions for the spontaneous curvature (H0), bending rigidity (kc) and saddle-splay constant (kc) have been derived for the constraint of constant chemical potential of free surfactant (thermodynamically open layers) as well as the constraint of constant aggregation number (thermodynamically closed layers). Most interestingly, it is demonstrated that kc for thermodynamically open layers formed by a nonionic surfactant with rigid tail and head group always must be zero. However, kc for surfactants with a flexible tail as a function of the head group-to-tail volume ratio is found to go through a maximum at some large, positive value of kc and H0 approximately 0. Eventually, kc falls below zero as the head group volume increases above a certain value. Hence, we may conclude that nonionic surfactants with a rigid head group may form thermodynamically stable fluid layers or aggregates only insofar the hydrophobic part is flexible with respect to chain conformational degrees of freedom and the head group is not too voluminous. It is found that the head group repulsion contribution to kcH0 is always positive whereas the corresponding contribution to kc may be positive or negative depending on whether the hydrophobic layer of the film is thicker or thinner than the hydrophilic layer.

Thermodynamics and bending energetics of toruslike micelles.

The self-assembly of surfactants forming toruslike or toroidal micelles has been investigated from a theoretical point of view, in particular the structural behaviour and stability of tori in terms of the three bending elasticity constants spontaneous curvature (H(0)), bending rigidity (k(c)) and saddle-splay constant (k(c)). It is demonstrated that the size of toruslike micelles increases with an increasing bending rigidity, but is independent of both spontaneous curvature and saddle-splay constant. Similar to conventional micelles, toruslike micelles are found to be stable over bilayers as the spontaneous curvature times the surfactant layer thickness exceeds 1/4. Moreover, it is shown that toruslike micelles, in general, are favoured at the expense of long spherocylindrical micelles as a result of elimination of the unfavourable end-caps. However, conventional micelles that are able to grow with respect to both width and length (tablets) may be stable over tori as well as spheres in much wider regimes of different bending elasticity constants. As a result, toruslike micelles are predicted to be stable over conventional micelles, including rods, at large values of the effective bending constant k(eff) identical with 2k(c)+k(c), i.e. in the same region where infinite cylinders are expected to be observed. This result is consistent with the fact that toruslike micelles have usually been observed to coexist with large networks of branched cylinders.

Bending energetics of tablet-shaped micelles: a novel approach to rationalize micellar systems.

A novel approach to rationalize micellar systems is expounded in which the structural behavior of tablet-shaped micelles is theoretically investigated as a function of the three bending elasticity constants: spontaneous curvature (H0), bending rigidity (k(c)), and saddle-splay constant (k(c)). As a result, experimentally accessible micellar properties, such as aggregation number, length-to-width ratio, and polydispersity, may be related to the different bending elasticity constants. It is demonstrated that discrete micelles or connected cylinders form when H0 > 1/4xi, where xi is the thickness of a surfactant monolayer, whereas various bilayer structures are expected to predominate when H0 < 1/4xi. Our theory predicts, in agreement with experiments, a transition from discrete globular (tablet-shaped) micelles to a phase of ordered, or disordered, connected cylinders above a critical surfactant concentration. Moreover, a novel explanation for the mechanism of growth, from small globular to long rodlike or wormlike micelles, follows as a consequence from the theory. In accordance, polydisperse elongated micelles (large length-to-width ratio) form as the bending rigidity is lowered, approaching the critical point at k(c) = 0, whereas monodisperse globular micelles (small length-to-width ratio) are expected to be present at large k(c) values. The spontaneous curvature mainly determines the width of tablet-shaped or ribbonlike micelles, or the radius of disklike micelles, whereas the saddle-splay constant primarily influences the size but not the shape of the micelles.

Bending elasticity of charged surfactant layers: the effect of mixing.

Expressions have been derived from which the spontaneous curvature (H(0)), bending rigidity (k(c)), and saddle-splay constant (k(c)) of mixed monolayers and bilayers may be calculated from molecular and solution properties as well as experimentally available quantities such as the macroscopic hydrophobic-hydrophilic interfacial tension. Three different cases of binary surfactant mixtures have been treated in detail: (i) mixtures of an ionic and a nonionic surfactant, (ii) mixtures of two oppositely charged surfactants, and (iii) mixtures of two ionic surfactants with identical headgroups but different tail volumes. It is demonstrated that k(c)H(0), k(c), and k(c) for mixtures of surfactants with flexible tails may be subdivided into one contribution that is due to bending properties of an infinitely thin surface as calculated from the Poisson-Boltzmann mean field theory and one contribution appearing as a result of the surfactant film having a finite thickness with the surface of charge located somewhat outside the hydrophobic-hydrophilic interface. As a matter of fact, the picture becomes completely different as finite layer thickness effects are taken into account, and as a result, the spontaneous curvature is extensively lowered whereas the bending rigidity is raised. Furthermore, an additional contribution to k(c) is present for surfactant mixtures but is absent for k(c)H(0) and k(c). This contribution appears as a consequence of the minimization of the free energy with respect to the composition of a surfactant layer that is open in the thermodynamic sense and must always be negative (i.e., k(c) is generally found to be brought down by the process of mixing two or more surfactants). The magnitude of the reduction of k(c) increases with increasing asymmetry between two surfactants with respect to headgroup charge number and tail volume. As a consequence, the bending rigidity assumes the lowest values for layers formed in mixtures of two oppositely charged surfactants, and k(c) is further reduced in anionic/cationic surfactant mixtures where the surfactant in excess has the smaller tail volume. Likewise, the reduction of k(c) is enhanced in mixtures of an ionic and a nonionic surfactant where the ionic surfactant has the smaller tail. The effective bilayer bending constant (k(bi)) is also found to be reduced by mixing, and as a result, k(bi) is seen to go through a minimum at some intermediate composition. The reduction of k(bi) is expected to be most pronounced in mixtures of two oppositely charged surfactants where the surfactant in excess has the smaller tail in agreement with experimental observations.

Bending elasticity of charged surfactant layers: the effect of layer thickness.

The bending properties of charged one-component surfactant films of finite thickness have been theoretically investigated. It is demonstrated that finite thickness effects are of crucial importance for layers formed by an ionic surfactant with a flexible hydrophobic tail, whereas the influence on layers formed by a surfactant with a rigid tail is less pronounced. As a matter of fact, in the former case, the spontaneous curvature and mean and Gaussian bending constants all become significantly modified as compared to an infinitely thin surface and assume identical values as if the surfactant layer were bent at constant layer thickness. As a result, the spontaneous curvature is found to decrease, whereas the magnitudes of the mean and Gaussian bending constants both increase with increasing layer thickness as well as with increasing hydrophobic-hydrophilic interfacial tension. All of these trends are consistent with experimental observations. In addition, it is demonstrated that separating the hydrophilic-hydrophobic interface and the surface of charge a certain distance from each other tends to increase the spontaneous curvature and the mean bending constant, whereas the Gaussian bending constant becomes increasingly negative. It is also found that the work of bending a bilayer into a geometrically closed vesicle is substantially raised to large positive values for surfactants with flexible aliphatic chains, whereas the corresponding quantity is negative for surfactants with rigid tails, indicating that stable bilayer structures may only be formed by the former surfactant. Furthermore, each of the bending elasticity constants for monolayers formed by a double-chain ionic surfactant are found to assume lower values as compared with layers formed by the corresponding single-chain surfactant.