Kinetics of Surfactant Micellization: A Free Energy Approach

Dynamics and Equilibration Mechanisms in Block Copolymer Particles

Self-assembly of block copolymers into interesting and useful nanostructures, in both solution and bulk, is a vibrant research arena. While much attention has been paid to characterization and prediction of equilibrium phases, the associated dynamic processes are far from fully understood. Here, we explore what is known and not known about the equilibration of particle phases in the bulk, and spherical micelles in solution. The presumed primary equilibration mechanisms are chain exchange, fusion, and fragmentation. These processes have been extensively studied in surfactants and lipids, where they occur on subsecond time scales. In contrast, increased chain lengths in block copolymers create much larger barriers, and time scales can become prohibitively slow. In practice, equilibration of block copolymers is achievable only in proximity to the critical micelle temperature (in solution) or the order-disorder transition (in the bulk). Detailed theories for these processes in block copolymers are few. In the bulk, the rate of chain exchange can be quantified by tracer diffusion measurements. Often the rate of equilibration, in terms of number density and aggregation number of particles, is much slower than chain exchange, and consequently observed particle phases are often metastable. This is particularly true in regions of the phase diagram where Frank-Kasper phases occur. Chain exchange in solution has been explored quantitatively by time-resolved SANS, but the results are not well captured by theory. Computer simulations, particularly via dissipative particle dynamics, are beginning to shed light on the chain escape mechanism at the molecular level. The rate of fragmentation has been quantified in a few experimental systems, and TEM images support a mechanism akin to the anaphase stage of mitosis in cells, via a thin neck that pinches off to produce two smaller micelles. Direct measurements of micelle fusion are quite rare. Suggestions for future theoretical, computational, and experimental efforts are offered.

Triblock copolymer micelle model of spherical paraspeckles

Paraspeckles are nuclear bodies scaffolded by RNP complexes of NEAT1_2 RNA transcripts and multiple RNA-binding proteins. The assembly of paraspeckles is coupled with the transcription of NEAT1_2. Paraspeckles form the core-shell structure, where the two terminal regions of NEAT1_2 RNP complexes compose the shell of the paraspeckle and the middle regions of these complexes compose the core. We here construct a theoretical model of paraspeckles by taking into account the transcription of NEAT1_2 in an extension of the theory of block copolymer micelles. This theory predicts that the core-shell structure of a paraspeckle is assembled by the association of the middle region of NEAT1_2 RNP complexes due to the multivalent interactions between RBPs bound to these regions and by the relative affinity of the terminal regions of the complexes to the nucleoplasm. The latter affinity results in the effective repulsive interactions between terminal regions of the RNA complexes and limits the number of complexes composing the paraspeckle. In the wild type, the repulsive interaction between the middle and terminal block dominates the thermal fluctuation. However, the thermal fluctuation can be significant in a mutant, where a part of the terminal regions of NEAT1_2 is deleted, and distributes the shortened terminal regions randomly between the shell and the core, consistent with our recent experiments. With the upregulated transcription, the shortened terminal regions of NEAT1_2 in a deletion mutant is localized to the core to decrease the repulsive interaction between the terminal regions, while the structure does not change with the upregulation in the wild type. The robustness of the structure of paraspeckles in the wild type results from the polymeric nature of NEAT1_2 complexes.

Nanomicellar Extraction of Polyphenols-Methodology and Applications Review

The selection of the appropriate extraction method is crucial, especially for the receiving of active substances from plant material. The extraction using supercritical liquids and micellar-mediated extraction (MME) is the most advantageous among the alternative methods to classical solid-liquid extraction. However, the latter seems to be the best solution when the desired actives are polar. The following article presents a comprehensive review of the micellar-mediated extraction method in the last decade. The theoretical principle of the process was also refreshed and the current state of knowledge on the applications for analytical and manufacturing purposes was summarized.

In situ quantitative study of the phase transition in surfactant adsorption layers at the silica-water interface using total internal reflection Raman spectroscopy

Dimethyldodecylamine N-oxide (DDAO), a unique type of surfactant, shows high surface activity with two distinct energy states at the buried hydrophilic silica/aqueous solution interface studied by total internal reflection (TIR) Raman spectroscopy combined with ratiometric and kinetic analysis. Different from other types of surfactant, i.e., ionic and nonionic, the adsorption of DDAO demonstrates a specific critical surface aggregation concentration (csac) at 0.15 mM gives a complete surface coverage of 6.6 ± 0.3 μmol m^-2, much lower than the bulk critical micellization concentration (cmc) at the same conditions (csac ≈ 0.072 cmc). A phase transition of adsorbed layers from liquid crystalline as the intermediate state to the disordered liquid phase is spectroscopically and energetically analyzed. The adsorption of DDAO on silica surfaces is described quantitatively in a potential energy curve.

Architectural Change of the Shell-Forming Block from Linear to V-Shaped Accelerates Micellar Disassembly, but Slows the Complete Enzymatic Degradation of the Amphiphiles

Tuning the enzymatic degradation and disassembly rates of polymeric amphiphiles and their assemblies is crucial for designing enzyme-responsive nanocarriers for controlled drug delivery applications. The common methods to control the enzymatic degradation of amphiphilic polymers are to tune the molecular weights and ratios of the hydrophilic and hydrophobic blocks. In addition to these approaches, the architecture of the hydrophilic block can also serve as a tool to tune enzymatic degradation and disassembly. To gain a deeper understanding of the effect of the molecular architecture of the hydrophilic block, we prepared two types of well-defined PEG-dendron amphiphiles bearing linear or V-shaped PEG chains as the hydrophilic blocks. The high molecular precision of these amphiphiles, which emerges from the utilization of dendrons as the hydrophobic blocks, allowed us to study the self-assembly and enzymatic degradation and disassembly of the two types of amphiphiles with high resolution. Interestingly, the micelles of the V-shaped amphiphiles were significantly smaller and disassembled faster than those of the amphiphiles based on linear PEG. However, the complete enzymatic cleavage of the hydrophobic end groups was significantly slower for the V-shaped amphiphiles. Our results show that the V-shaped architecture can stabilize the unimer state and, hence, plays a double role in the enzymatic degradation and the induced disassembly and how it can be utilized to control the release of encapsulated or bound molecular cargo.

Molecular Semiconductor Surfactants with Fullerenol Heads and Colored Tails for Carbon Dioxide Photoconversion

The leaf is a prime example of a material converting waste (CO2 ) into value with maximum sustainability. As the most important constituent, it contains the coupled photosystems II and I, which are imbedded in the cellular membrane of the chloroplasts. Can key functions of the leaf be packed into soap? We present next-generation surfactants that self-assemble into bilayer vesicles (similar to the cellular membrane), are able to absorb photons of two different visible wavelengths, and exchange excited charge carriers (similar to the photosystems), followed by conversion of CO2 (in analogy to the leaf). The amphiphiles contain five dye molecules as the hydrophobic entity attached exclusively to one hemisphere of a polyhydroxylated fullerene (Janus-type). We herein report on their surfactant, optical, electronic, and catalytic properties. Photons absorbed by the dyes are transferred to the fullerenol head, where they can react with different species such as CO2 to give formic acid.

Enzyme-Induced Kinetic Control of Peptide-Polymer Micelle Morphology

In this paper, experiment and simulation were combined to provide a view of the molecular rearrangements underlying the equilibrium and nonequilibrium transitions occurring in stimuli-responsive block copolymer amphiphile self-assemblies. Three block copolymer amphiphiles were prepared, each consisting of a hydrophilic peptide brush, responsive to proteolytic enzymes, and containing one of three possible hydrophobic blocks: (1) poly(ethyl acrylate), (2) poly(styrene), or (3) poly(lauryl acrylate). When assembled, they generate three spherical micelles each responsive to the addition of the bacterial protease, thermolysin. We found core-block-dependent phase transitions in response to the hydrophilic block being truncated by the stimulus. In one example, we found an unexpected, well-defined, pathway-dependent spherical micelle to vesicle phase transition induced by enzymatic stimulus.

Origins of low-symmetry phases in asymmetric diblock copolymer melts

Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order-disorder transition temperature (TODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank-Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the TODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEXC) upon heating and cooling. The process-path-dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank-Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

Blending block copolymer micelles in solution; Obstacles of blending

Amphiphilic block copolymers can assemble into a variety of structures on the nanoscale in selective solvent. The micelle blending protocol offers a simple unique route to reproducibly produce polymer nanostructures. Here we expand this blending protocol to a range of polymer micelle systems and self-assembly routes. We found by exploring a range of variables that the systems must be able to reach global equilibrium at some point for the blending protocol to be successful. Our results demonstrate the kinetics requirements, specifically core block glass transition temperature, Tg, and length of the block limiting the exchange rates, for the blending protocol which can then be applied to a wide range of polymer systems to access this simple protocol for polymer self-assembly.

Mesoscale models of dispersions stabilized by surfactants and colloids

In this paper we discuss and give an outlook on numerical models describing dispersions, stabilized by surfactants and colloidal particles. Examples of these dispersions are foams and emulsions. In particular, we focus on the potential of the diffuse interface models based on a free energy approach, which describe dispersions with the surface-active agent soluble in one of the bulk phases. The free energy approach renders thermodynamic consistent models with realistic sorption isotherms and adsorption kinetics. The free energy approach is attractive because of its ability to describe highly complex dispersions, such as emulsions stabilized by ionic surfactants, or surfactant mixtures and dispersions with surfactant micelles. We have classified existing numerical methods into classes, using either a Eulerian or a Lagrangian representation for fluid and for the surfactant/colloid. A Eulerian representation gives a more coarse-grained, mean field description of the surface-active agent, while a Lagrangian representation can deal with steric effects and larger complexity concerning geometry and (amphiphilic) wetting properties of colloids and surfactants. However, the similarity between the description of wetting properties of both Eulerian and Lagrangian models allows for the development of hybrid Eulerian/Lagrangian models having advantages of both representations.

Multi-scale times and modes of fast and slow relaxation in solutions with coexisting spherical and cylindrical micelles according to the difference Becker-Döring kinetic equations

The eigenvalues and eigenvectors of the matrix of coefficients of the linearized kinetic equations applied to aggregation in surfactant solution determine the full spectrum of characteristic times and specific modes of micellar relaxation. The dependence of these relaxation times and modes on the total surfactant concentration has been analyzed for concentrations in the vicinity and well above the second critical micelle concentration (cmc2) for systems with coexisting spherical and cylindrical micelles. The analysis has been done on the basis of a discrete form of the Becker-Döring kinetic equations employing the Smoluchowsky diffusion model for the attachment rates of surfactant monomers to surfactant aggregates with matching the rates for spherical aggregates and the rates for large cylindrical micelles. The equilibrium distribution of surfactant aggregates in solution has been modeled as having one maximum for monomers, another maximum for spherical micelles and wide slowly descending branch for cylindrical micelles. The results of computations have been compared with the analytical ones known in the limiting cases from solutions of the continuous Becker-Döring kinetic equation. They demonstrated a fair agreement even in the vicinity of the cmc2 where the analytical theory looses formally its applicability.

Formation of large micellar aggregates before equilibrium in diluted solutions

We study the formation of premicelles for different values of the concentration of amphiphile molecules in water. Our model consists of a square lattice with water molecules occupying one cell of the lattice while the amphiphilic molecules, represented by chains of five interconnected sites, occupy five cells of the lattice. We perform Monte Carlo simulations in the NVT ensemble, for a fixed temperature and different concentration of amphiphiles, ranging from below to above the critical micelle concentration. We start our simulations from a monomeric state and follow in time all the aggregates sizes until the equilibrium state is reached. We pay particular attention to two aggregate sizes, one related to the minimum and the other to the maximum of the aggregate-size distribution curve obtained at equilibrium. We show that these aggregates evolve in time exhibiting a maximum concentration well before the equilibrium state, revealing the formation of premicelles. The times to reach these maximum concentrations decrease exponentially with the total concentration of the system.

Direct observation of the formation of surfactant micelles under nonisothermal conditions by synchrotron SAXS

Self-assembly of amphiphilic molecules into micelles occurs on very short times scales of typically some milliseconds, and the structural evolution is therefore very challenging to observe experimentally. While rate constants of surfactant micelle kinetics have been accessed by spectroscopic techniques for decades, so far no experiments providing detailed information on the structural evolution of surfactant micelles during their formation process have been reported. In this work we show that by applying synchrotron small-angle X-ray scattering (SAXS) in combination with the stopped-flow mixing technique, the entire micelle formation process from single surfactants to equilibrium micelles can be followed in situ. Using a sugar-based surfactant system of dodecyl maltoside (DDM) in dimethylformamide (DMF), micelle formation can be induced simply by adding water, and this can be followed in situ by SAXS. Mixing of water and DMF is an exothermic process where the micelle formation process occurs under nonisothermal conditions with a temperature gradient relaxing from about 40 to 20 °C. A kinetic nucleation and growth mechanism model describing micelle formation by insertion/expulsion of single molecules under nonisothermal conditions was developed and shown to describe the data very well.