Thermodynamics and bending energetics of toruslike micelles

Where are those lipid nano rings?

Highly curved toroidal micelles with diameters as small as 100 nm have been successfully constructed by self-assembly of amphiphilic block copolymers. These structures may have potential applications in gene or drug delivery. Experimental observations suggest that toroidal micelles likely originate from spherical or disc-like micelles which are tricked into forming toroidal micelles upon external stimuli ('smart' materials). Since self-assembly of polymeric and lipid surfactants is guided by the same physical principles, we hypothesize that 'smart' lipid surfactants can be equivalently tricked into forming highly curved toroidal micelles that are tenfold smaller (≃10 nm diameter). Paradoxically, these 'nano rings' have never been observed. Using coarse-grained molecular dynamics (MD) simulations in conjunction with a state-of-the-art free energy calculation method (a string method), we illustrate how a thermo-responsive lipid surfactant is able to form toroidal micelles. These micelles originate from disc-like micelles that are spontaneously perforated upon heat shocking, thereby supporting a longstanding hypothesis on the possible origin of polymeric toroidal micelle phases observed in experiments. We illustrate that kinetically stable 'nano rings' are substantially shorter lived than their tenfold larger polymeric analogs. The estimated life-time (milliseconds) is in fact similar to the characteristic breaking time of the corresponding worm-like micelle. Finally, we resolve the characteristic finger print which 'nano rings' leave in time-resolved X-ray spectra and illustrate how the uptake of small DNA fragments may enhance their stability. Despite a shared kinetics of self-assembly, length scale dependent differences in the life-time of surfactant phases can occur when phases are kinetically rather than thermodynamically stable. This results in the apparent absence or presence of toroidal micelle phases on different length scales. Our theoretical work precisely illustrates that the universality of surfactants nevertheless remains conserved even at different length scales.

A molecular model for the free energy, bending elasticity, and persistence length of wormlike micelles

An expression for the elastic free-energy density of a wormlike micelle is derived taking into account interactions between its constituent molecules. The resulting expression is quadratic in the curvature and torsion of the centerline of micelle and thus resembles free-energy density functions for polymer chains and helical filaments such as DNA. The model is applied on a wormlike micelle in the shape of a circular arc, open or closed. Conditions under which linear chains in dilute systems transform into toroidal rings are analyzed. Two concrete anisotropic soft-core interaction potentials are used to calculate the elastic moduli present in the derived model, in terms of the density of the molecules and their dimensions. Expressions for the persistence length of the wormlike micelle are found based on the flexural rigidities so obtained. Similar to previous observations, our results indicate that the persistence length of a wormlike micelle increases as the aspect ratio of its constituent molecules increases. A detailed application of the model on wormlike micelles of toroidal geometry, along with employing statistical-thermodynamical concepts of self-assembly is performed, and the results are found to be well consistent with the literature. Steps to obtain the material parameters through possible experiments are discussed.

Determining scaling in known phase diagrams of nonionic microemulsions to aid constructing unknown

Microemulsions based on nonionic surfactants of the ethylene oxide alkyl ether type C(m)E(n), have been studied thoroughly for around 30 years. Thanks to the considerable amount of published data available on these systems, it is possible to observe trends to make predictions of phase diagrams not yet determined. Strey and Kahlweit, and subsequently Sottmann and Strey, with coworkers have studied and published phase diagrams for systems with a fixed ratio of oil to water, varying the surfactant, the so-called Kahlweit fish-cut diagrams. Some properties of the phase diagrams can be scaled to become general and not system dependent. Here are shown two examples of scaling data from phase diagrams and the use of trends to determine phase diagrams, both inside and outside a dataset. The trends of microemulsions with fixed ratio of surfactant to oil, the so-called Lund-cut diagrams, are also investigated. The trends are used to determine a new phase diagram and this is compared with previously unpublished experimental data on C(12)E(5)-Octadecane-Water system. The scalings and trends make it possible to get good estimations of many of the important properties of the phase diagrams, both temperatures and surfactant concentrations of interest, by investigating one sample in the 3-phase region of the balanced fish-cut diagram.

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.