RESUMEN
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.
RESUMEN
Thermodynamic integration is one of the most established methods to quantify excess free energies between different metastable states. Excess intermolecular interactions in surfactant assemblies are on the scale of the energy of thermal fluctuations. Therefore, these materials can be deformed and topologically altered via relatively small mechanical stresses. It is thus intuitive to design reaction paths and associated order parameters that exploit the "soft" nature of these materials to mechanically rather than alchemically morph surfactant assemblies from state to state. Here, we propose a novel method coined "density field thermodynamic integration" (DFTI) that adopts the universality and transferability of alchemical methods while simultaneously exploiting the soft excess interactions between surfactant molecules. DFTI was designed for a rapid quantification of the free energy differences between different metastable structures in soft fluid materials. The DFTI method uses an external field coupled to the local density to mechanically morph the system between metastable states of interest. Here, we explored the capability of the DFTI method to swiftly and accurately calculate free energy differences between states. To this aim, we studied two different coarse-grained lipidic surfactant systems: (i) a fusion stalk and (ii) a worm-like micelle. Our results illustrate that DFTI can provide an efficient, versatile, and rather reliable method to calculate the free energy differences between surfactant assemblies.