Topology, length scales, and energetics of surfactant micelles

Topological Analysis of Molecular Dynamics Simulations using the Euler Characteristic

Molecular dynamics (MD) simulations are used in diverse scientific and engineering fields such as drug discovery, materials design, separations, biological systems, and reaction engineering. These simulations generate highly complex data sets that capture the 3D spatial positions, dynamics, and interactions of thousands of molecules. Analyzing MD data sets is key for understanding and predicting emergent phenomena and in identifying key drivers and tuning design knobs of such phenomena. In this work, we show that the Euler characteristic (EC) provides an effective topological descriptor that facilitates MD analysis. The EC is a versatile, low-dimensional, and easy-to-interpret descriptor that can be used to reduce, analyze, and quantify complex data objects that are represented as graphs/networks, manifolds/functions, and point clouds. Specifically, we show that the EC is an informative descriptor that can be used for machine learning and data analysis tasks such as classification, visualization, and regression. We demonstrate the benefits of the proposed approach through case studies that aim to understand and predict the hydrophobicity of self-assembled monolayers and the reactivity of complex solvent environments.

Flow-induced scission of wormlike micelles in nonionic surfactant solutions under shear flow

We investigate flow-induced scission of wormlike micelles with dissipative particle dynamics simulations of nonionic surfactant solutions under shear flow. To understand flow-induced scission in terms of micellar timescales, we propose a method to evaluate the longest relaxation time of unentangled surfactant micelles from the rotational relaxation time and the average lifetime at equilibrium. The mean squared displacement of surfactant molecules provides evidence that the longest relaxation time estimated by the proposed method serves as the characteristic timescale at equilibrium. We also demonstrate that the longest relaxation time plays an essential role in flow-induced scission. Using conditional statistics based on the aggregation number of micelles, we examine the statistical properties of the lifetime of wormlike micelles. We then conclude that flow-induced scission occurs when the Weissenberg number defined as the product of the longest relaxation time and the shear rate is larger than a threshold value.

Coarse-Grained Model Incorporating Short- and Long-Range Effective Potentials for the Fast Simulation of Micelle Formation in Solutions of Ionic Surfactants

A coarse-grained model comprising short- and long-range effective potentials, parametrized with the iterative Boltzmann inversion (IBI) method, is presented for capturing micelle formation in aqueous solutions of ionic surfactants using as a model system sodium dodecyl sulfate (SDS). In the coarse-grained (CG) model, each SDS molecule is represented as a sequence of four beads while each water molecule is modeled as a single bead. The proposed CG scheme involves ten potential energy functions: four of them describe bonded interactions and control the distribution functions of intramolecular degrees of freedom (bond lengths, valence angles, and dihedrals) along an SDS molecule while the other six account for intermolecular interactions between pairs of SDS and water beads and control the radial distribution functions. The nonbonded effective potentials between coarse-grained SDS molecules extend up to about 12 nm and capture structural and morphological features of the micellar solution both at short and long distances. The long-range component of these potentials, in particular, captures correlations between surfactant molecules belonging to different micelles and is essential to describe ordering associated with micelle formation. A new strategy is introduced for determining the effective potentials through IBI by using information (target distribution functions) extracted from independent atomistic simulations of a micellar reference system (a salt-free SDS solution at total surfactant concentration c_T equal to 103 mM, temperature T equal to 300 K, and pressure P equal to 1 atm) obtained through a multiscale approach described in an earlier study. It employs several optimization steps for bonded and nonbonded interactions and a gradual parametrization of the short- and long-range components of the latter, followed by reparametrization of the bonded ones. The proposed CG model can reproduce remarkably accurately the microstructure and morphology of the reference system within only a few hours of computational time. It is therefore very promising for future studies of structural and morphological behavior of various liquid surfactant formulations.

Scission energy and topology of micelles controlled by the molecular structure of additives

We employ coarse-grained (CG) molecular dynamics simulations (MD) to investigate the effects of the molecular structure of additives on the scission energy and morphology of charged micelles. Considering sodium dodecyl sulfate (SDS) as a representative charged surfactant and taking trimethylphenylammonium chloride (TMPAC) and octyltrimethylammonium bromide (OTAB) as oppositely charged additives, we show that the scission energy and topology of micelles vary significantly depending on the molecular structure of the hydrophobic part of the additives. The cyclic aromatic tail of the TMPAC disrupts the core structure of the SDS micelle and hence decreases the micelle scission energy, whereas the linear alkyl tail of the OTAB packs very well with the micelle core and increases the scission energy. Although both the additives have similar head structures, they lead to very different micelle morphologies because of the difference in the shape of their tail structures; ring-like or toroidal shaped micelles are formed in SDS/TMPAC solution whereas bicelle-like structures are formed in SDS/OTAB solution when the additive to surfactant ratio is higher than a certain value.

The rise and fall of branching: A slowing down mechanism in relaxing wormlike micellar networks

A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached with both thermal quenches and small perturbations of the system. The scaling of this relaxation time is exponential with the free energy of an end cap and with the branching free energy. We argue that the subtle end-recombination dynamics might yield effects that are difficult to detect in rheology experiments, with possible underestimates of the typical time scales of viscoelastic fluids.

Surfactant desorption and scission free energies for cylindrical and spherical micelles from umbrella-sampling molecular dynamics simulations

HYPOTHESIS

The free energies associated with adsorption/desorption of individual surfactants from micelles and the fusion/scission of long micelles can be used to estimate the rate constants for micellar kinetics as functions of surfactant and salt concentration.

EXPERIMENTS

We compute the escape free energies △G_esc of surfactant from micelles and the scission free energies △G_sciss of long micelles from coarse-grained molecular dynamics simulations coupled with umbrella sampling, for micelles of both sodium dodecylsulfate (SDS) in sodium chloride (NaCl) and cetyltrimethylammonium chloride (CTAC) in sodium salicylate (NaSal).

FINDINGS

For spherical micelles, △G_esc values have maxima at certain aggregation numbers, and at salt-to-surfactant molar concentration ratios R near unity, consistent with experiments. For cylindrical micelles, SDS/NaCl shows a minimum, and CTAC/NaSal a maximum in △G_esc, both at R ~ 0.7, while △G_sciss of CTAC micelles also peaks at around R ~ 0.7 and that of SDS micelles increases monotonically with R. We explain the non-monotonic dependence of escape and scission free energies on R by a combination of electrostatic screening and the decrease of micelle radius with increasing R. Transitions from predominantly spherical to cylindrical micelles, and between adsorption/desorption and fusion/scission kinetics with changing salt concentration can be inferred from the free energies for CTAC/NaSal.

Additives-directed lyotropic liquid crystals architecture: Simulations and experiments

In this study, alkanes and sucrose esters are employed to investigate the influence of additives on lyotropic liquid crystal architecture. After molecular dynamic simulations and experiment characterization, we showed how the additives control the structure of LLCs. By controlling the polarity of additives, the phase behavior of LLCs can be engineered to form the required structure. Dissipative particle dynamics (DPD) is introduced for simulating the self-assembly of phytantriol (PT), providing intuitionistic images and structure information, which shows that additives with low-polarity complicate the internal structure of liquid crystal systems. Then the ternary phase diagrams of additives, PT, and water are constructed to systematically study the effects of additives on the phase behavior of LLCs. Consistent with DPD simulation results, there is a certain regularity in the effects of additives on the structure of liquid crystals. The difference in the structure of LLCs is due to the variability in the critical packing parameter (CPP) obtained by changing the polarity of additives. Our findings demonstrate that additives polarity is a key factor in LLCs structure, and may pave a promising avenue for novel LLCs development and translation, determining the self-assembly process and the resulting phase of LLCs.

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.

Self-assembly and viscosity changes of binary surfactant solutions: A molecular dynamics study

HYPOTHESIS

Structure and self-assembly of surfactants in the solution shows a fundamental influence on its viscosity. Through molecular simulations using Martini force field, synergistic effects in aggregation as well as the viscosity changes of a binary ionic surfactant system can be modelled. Simulations: Coarse-grained molecular dynamics simulations are performed to model the SDS/CAPB binary surfactant solution, and both equilibrium and non-equilibrium methods are used to calculate the viscosity of the equilibrated micellar systems.

FINDINGS

Our simulation results indicate that the new version of the Martini force field can provide more reasonable self-assembly of surfactant, both single and binary system. Synergistic effects in micelle formation for SDS/CAPB have been successfully reproduced, that is, the formation of cylindrical micelles or even wormlike micelles at a lower concentration when compared with the pure system. Meanwhile, both equilibrium and non-equilibrium methods provide quantitatively comparable viscosity for each system. For pure micellar system, the viscosity linearly increases with the total concentration. Nevertheless, our simulation fails to capture the viscosity enhancement of the solution in corresponding with the formation of rodlike or wormlike micelles, and a full parameter optimization of force field is still necessary.

Aging of living polymer networks: a model with patchy particles

Microrheology experiments show that viscoelastic media composed by wormlike micellar networks display complex relaxations lasting seconds even at the scale of micrometers. By mapping a model of patchy colloids with suitable mesoscopic elementary motifs to a system of worm-like micelles, we are able to simulate its relaxation dynamics, upon a thermal quench, spanning many decades, from microseconds up to tens of seconds. After mapping the model to real units and to experimental scission energies, we show that the relaxation process develops through a sequence of non-local and energetically challenging arrangements. These adjustments remove undesired structures formed as a temporary energetic solution for stabilizing the thermodynamically unstable free caps of the network. We claim that the observed scale-free nature of this stagnant process may complicate the correct quantification of experimentally relevant time scales as the Weissenberg number.

Different strategies of foam stabilization in the use of foam as a fracturing fluid

An attractive alternative to mitigate the adverse effects of conventional water-based fluids on the efficiency of hydraulic fracturing is to inject foam-based fracking fluids into reservoirs. The efficiency of foaming fluids in subsurface applications largely depends on the stability and transportation of foam bubbles in harsh environments with high temperature, pressure and salinity, all of which inevitably lead to poor foam properties and thus limit fracturing efficiency. The aim of this paper is to elaborate popular strategies of foam stabilization under reservoir conditions. Specifically, this review first discusses three major mechanisms governing foam decay and summarizes recent progress in research on these phenomena. Since surfactants, polymers, nanoparticles and their composites are popular options for foam stabilization, their stabilizing effects, especially the synergies in composites, are also reviewed. In addition to reporting experimental results, the paper also reports recent advances in interfacial properties via molecular dynamical simulation, which provide new insights into gas/liquid interfacial properties under the influence of surfactants at molecular scale. The results of both experiments and simulations indicate that foam additives play an essential role in foam stability and the synergic effects of surfactants and nanoparticles exhibit more favorable performance.

Interfacial Interaction Enhanced Rheological Behavior in PAM/CTAC/Salt Aqueous Solution-A Coarse-Grained Molecular Dynamics Study

Interfacial interactions within a multi-phase polymer solution play critical roles in processing control and mass transportation in chemical engineering. However, the understandings of these roles remain unexplored due to the complexity of the system. In this study, we used an efficient analytical method-a nonequilibrium molecular dynamics (NEMD) simulation-to unveil the molecular interactions and rheology of a multiphase solution containing cetyltrimethyl ammonium chloride (CTAC), polyacrylamide (PAM), and sodium salicylate (NaSal). The associated macroscopic rheological characteristics and shear viscosity of the polymer/surfactant solution were investigated, where the computational results agreed well with the experimental data. The relation between the characteristic time and shear rate was consistent with the power law. By simulating the shear viscosity of the polymer/surfactant solution, we found that the phase transition of micelles within the mixture led to a non-monotonic increase in the viscosity of the mixed solution with the increase in concentration of CTAC or PAM. We expect this optimized molecular dynamic approach to advance the current understanding on chemical-physical interactions within polymer/surfactant mixtures at the molecular level and enable emerging engineering solutions.

Water-in-CO2 Microemulsions Stabilized by Fluorinated Cation-Anion Surfactant Pairs

High-water-content water-in-supercritical CO₂ (W/CO₂) microemulsions are considered to be green, universal solvents, having both polar and nonpolar domains. Unfortunately, these systems generally require environmentally unacceptable stabilizers like long and/or multifluorocarbon-tail surfactants. Here, a series of catanionic surfactants having more environmentally friendly fluorinated C₄-C₆ tails have been studied in terms of interfacial properties, aggregation behavior, and solubilizing power in water and/or CO₂. Surface tensions and critical micelle concentrations of these catanionic surfactants are, respectively, lowered by ∼9 mN/m and 100 times than those of the constituent single fluorocarbon-tail surfactants. Disklike micelles in water were observed above the respective critical micelle concentrations, implying the catanionic surfactants have a high critical packing parameter, which should be suitable for the formation of reverse micelles. Based on visual observation of phase behavior and Fourier transform infrared spectroscopic and small-angle neutron scattering studies, one of the three catanionic surfactants tested was found to form transparent single-phase W/CO₂ microemulsions with a water-to-surfactant molar ratio of up to ∼50. This is the first successful demonstration of the formation of W/CO₂ microemulsions by synergistic ion-pairing of anionic and cationic single-tail surfactants. This indicates that catanionic surfactants offer a promising approach to generate high-water-content W/CO₂ microemulsions.

Stretch and Breakage of Wormlike Micelles under Uniaxial Strain: A Simulation Study and Comparison with Experimental Results

We use coarse-grained (CG) molecular dynamics simulations to determine the effect of uniaxial strain on the stress, scission stress, and scission energy of solutions of wormlike micelles of cetyltrimethylammonium chloride/sodium salicylate (NaSal). We find that the breaking stress, stretch modulus, and scission energy of the charged micelles are nonmonotonic functions of oppositely charged hydrotrope (NaSal) concentration. While the stretch modulus shows a peak at a value of surfactant-to-hydrotrope concentration ratio ( R) close to unity as expected due to neutralization of head-group charge at R = 1, the breaking stress and scission energy produce a peak at R < 1.0 because of thinning of the micelle diameter with increased R. The breaking stress from the simulations depends on the rate of deformation and roughly agrees with the experimental values of Rothstein ( J. Rheol. 2003 , 47 , 1227 ) after extrapolation to the much lower experimental rates. The method and results can be used to predict the effects of flow and mechanical stress on rates of micellar breakage, which is important in the rheology of wormlike micellar solutions.

How Hydrophobic Hydration Destabilizes Surfactant Micelles at Low Temperature: A Coarse-Grained Simulation Study

Micelles are self-assembled aggregates of amphiphilic surfactant molecules that are important in a variety of applications, including drug delivery, detergency, and catalysis. It is known that the micellization process is driven by the same physiochemical forces that drive protein folding, aggregation, and biological membrane self-assembly. Nevertheless, the molecular details of how micelle stability changes in water at low temperature are not fully clear. We develop and use a coarse-grained model to investigate how the interplay between nonionic surfactants and the surrounding water at the nanoscale affects the stability of micelles at high and low temperatures. Simulations of preformed C₁₂E₅ micelles in explicit water at a range of temperatures reveal the existence of two distinct surfactant conformations within the micelle, a bent structure and an extended structure, the latter being more prevalent at low temperature. Favorable interactions of the surfactant with more ordered solvation water stabilizes the extended configuration, allowing nanoscale wetting of the dry, hydrophobic core of the micelle, leading to the micelle breaking. Taken together, our coarse-grained simulations unravel how energetic and structural changes of the surfactant and the surrounding water destabilize micelles at low temperature, which is a direct consequence of the weakened hydrophobicity. Our approach thus provides an effective mean for extracting the molecular-level changes during hydrophobicity-driven destabilization of molecular self-assembly, which is important in a wide range of fields, including biology, polymer science, and nanotechnology.

Anisotropic reversed micelles with fluorocarbon-hydrocarbon hybrid surfactants in supercritical CO2

Previous work (M. Sagisaka, et al. Langmuir 31 (2015) 7479-7487), showed the most effective fluorocarbon (FC) and hydrocarbon (HC) chain lengths in the hybrid surfactants FCm-HCn (sodium 1-oxo-1-[4-(perfluoroalkyl)phenyl]alkane-2-sulfonates, where m = FC length and n = HC length) were m and n = 6 and 4 for water solubilization, whereas m 6 and n 6, or m 6 and n 5, were optimal chain lengths for reversed micelle elongation in supercritical CO₂. To clarify why this difference of only a few methylene chain units is so effective at tuning the solubilizing power and reversed micelle morphology, nanostructures of water-in-CO₂ (W/CO₂) microemulsions were investigated by high-pressure small-angle neutron scattering (SANS) measurements at different water-to-surfactant molar ratios (W₀) and surfactant concentrations. By modelling SANS profiles with cylindrical and ellipsoidal form factors, the FC6-HCn/W/CO₂ microemulsions were found to increase in size with increasing W₀ and surfactant concentration. Ellipsoidal cross-sectional radii of the FC6-HC4/W/CO₂ microemulsion droplets increased linearly with W₀, and finally reached ∼39 Å and ∼78 Å at W₀ = 85 (close to the upper limit of solubilizing power). These systems appear to be the largest W/CO₂ microemulsion droplets ever reported. The aqueous domains of FC6-HC6 rod-like reversed micelles increased in size by 3.5 times on increasing surfactant concentration from 35 mM to 50 mM: at 35 mM, FC6-HC5 formed rod-like reversed micelles 5.3 times larger than FC6-HC6. Interestingly, these results suggest that hybrid HC-chains partition into the microemulsion aqueous cores with the sulfonate headgroups, or at the W/CO₂ interfaces, and so play important roles for tuning the W/CO₂ interfacial curvature. The super-efficient W/CO₂-type solubilizer FC6-HC4, and the rod-like reversed micelle forming surfactant FC6-HC5, represent the most successful cases of low fluorine content additives. These surfactants facilitate VOC-free, effective and energy-saving CO₂ solvent systems for applications such as extraction, dyeing, dry cleaning, metal-plating, enhanced oil recovery and organic/inorganic or nanomaterial synthesis.

Nonmonotonic Scission and Branching Free Energies as Functions of Hydrotrope Concentration for Charged Micelles

Using coarse-grained molecular dynamics simulations and an umbrella sampling method that uses local surfactant density as a reaction coordinate, we directly calculate, for the first time, both the scission and branching free energies of a model charged micelle [cationic cetyltrimethylammonium chloride (CTAC)] in the presence of inorganic and organic salts (hydrotropes). We find that while inorganic salt only weakly affects the micelle scission energy, organic hydrotropes produce a strong, nonmonotonic dependence of both scission energy and branching on salt concentration. The nonmonotonicity in scission energy is traced to a competition between electrostatic screening of the repulsions among the surfactant head groups and thinning of the micellar core, which result from attachment of the hydrotropes to the micelle surface. We are able to correlate the nonmonotonicity in the scission energy of CTAC micelles with the peak observed experimentally in viscosity versus hydrotrope concentration and the location of this peak in CTAC solutions.

Detecting Branching in Wormlike Micelles via Dynamic Scattering Methods

Topological differences in a model series of wormlike micelles (WLMs) with varying degrees of branching are investigated via neutron spin echo (NSE) and dynamic light scattering (DLS). Branching was previously verified via microscopy, scattering methods, and rheology. NSE measurements reveal that on the shortest length scales, where WLMs are topologically similar, the dynamic behavior is independent of branching level. However, branching leads to deviations from wormlike chain behavior on length scales relevant to branching. These differences continue into the DLS regime, where two relaxation modes are observed. While measuring micellar branching is challenging, our measurements of segmental dynamics provide a direct dynamic measurement of WLM branching and demonstrate promise for future identification of topological changes in self-assembled materials.

Growth of wormlike micelles in nonionic surfactant solutions: Quantitative theory vs. experiment

Despite the considerable advances of molecular-thermodynamic theory of micelle growth, agreement between theory and experiment has been achieved only in isolated cases. A general theory that can provide self-consistent quantitative description of the growth of wormlike micelles in mixed surfactant solutions, including the experimentally observed high peaks in viscosity and aggregation number, is still missing. As a step toward the creation of such theory, here we consider the simplest system - nonionic wormlike surfactant micelles from polyoxyethylene alkyl ethers, C_iE_j. Our goal is to construct a molecular-thermodynamic model that is in agreement with the available experimental data. For this goal, we systematized data for the micelle mean mass aggregation number, from which the micelle growth parameter was determined at various temperatures. None of the available models can give a quantitative description of these data. We constructed a new model, which is based on theoretical expressions for the interfacial-tension, headgroup-steric and chain-conformation components of micelle free energy, along with appropriate expressions for the parameters of the model, including their temperature and curvature dependencies. Special attention was paid to the surfactant chain-conformation free energy, for which a new more general formula was derived. As a result, relatively simple theoretical expressions are obtained. All parameters that enter these expressions are known, which facilitates the theoretical modeling of micelle growth for various nonionic surfactants in excellent agreement with the experiment. The constructed model can serve as a basis that can be further upgraded to obtain quantitative description of micelle growth in more complicated systems, including binary and ternary mixtures of nonionic, ionic and zwitterionic surfactants, which determines the viscosity and stability of various formulations in personal-care and house-hold detergency.

Prediction of striped cylindrical micelles (SCMs) formed by dodecyl-β-d-maltoside (DDM) surfactants

Using fully atomistic and coarse-grained (CG) molecular dynamics (MD) simulations, we report, for the first time, the self-assembly of initially randomly dispersed dodecyl-β-d-maltoside (DDM) surfactants into a striped cylindrical micelle (SCM) with lamellae of surfactant heads and tails alternating along the cylindrical axis, with both heads and tails in contact with the water. By changing the interaction strength of the head group with water relative to itself, we find that such micelles are most likely for head groups with marginal solubility in the water solvent. Unlike the surfactants in a regular cylindrical micelle, whose tails are in the fluid micelle interior, the diffusion of DDM surfactants along the micelle body is blocked by the lamellar patterning. As a consequence, branches cannot slide along the micelle body and surfactant molecules cannot exchange between the micelle body and the branch, which should have a significant impact on the rheological properties of these micelles.

Scission Free Energies for Wormlike Surfactant Micelles: Development of a Simulation Protocol, Application, and Validation for Personal Care Formulations

We present a scheme to calculate wormlike micelle scission free energies from a potential of mean force (PMF) derived from a weighted histogram analysis method (WHAM) applied to coarse grained dissipative particle dynamics (DPD) simulations. In contrast to previous related work, we use a specially chosen external potential based on a reaction coordinate that reversibly drives surfactants out of the nascent scission location. For the application to a model body wash formulation, we predict how addition of NaCl and small molecules such as perfume raw materials (PRMs) affect scission energies. The results show qualitative agreement and correct trends compared to recently determined scission energies for the same system; however, a more rigorous parametrization of the underlying DPD potential is required for quantitative agreement.

Micro-mechanical, continuum-mechanical, and AFM-based descriptions of elasticity in open cylindrical micellar filaments

We present theoretical and experimental descriptions of the elasticity of cylindrical micellar filaments using micro-mechanical and continuum theories, and atomic force microscopy. Following our micro-mechanical elasticity model for micellar filaments [M. Asgari, Eur. Phys. J. E: Soft Matter Biol. Phys., 2015, 38(9), 1-16], the elastic bending energy of hemispherical end caps is found. The continuum description of the elastic bending energy of a cylindrical micellar filament is also derived using constrained Cosserat rod theory. While the continuum approach provides macroscopic description of the strain energy of the micellar filament, the micro-mechanical approach has a microscopic view of the filament, and provides expressions for kinetic variables based on a selected interaction potential between the molecules comprising the filament. Our model predicts the dependence of the elastic modulus of the micellar filaments on their diameter, which agrees with previous experimental observations. Atomic force microscopy is applied to estimate the elastic modulus of the filaments using force volume analysis. The obtained values of elastic modulus yield the persistence length of micellar filaments on the same order of the previously reported values. Consistent with previous studies, our results indicate that semi-flexible linear micelles have a relatively large local strain energy at their end points, which explains their tendency to fuse to minimize the number of end caps at relatively low total surfactant volume fractions. Also, the elastic modulus of micellar filaments was found to increase when the indentation frequency increases, a finding which agrees with previous rheological observations on the bulk shear modulus of micellar solutions.

Anomalous diffusion and stress relaxation in surfactant micelles

We investigate the mechanisms of anomalous diffusion in cationic surfactant micelles using molecular dynamics simulations in the presence of explicit salt and solvent-mediated interactions. Simulations show that when the counterion density increases, saddle-shaped branched interfaces manifest. In experiments, branched structures exhibit lower viscosity as compared to linear and wormlike micelles. This has long been attributed to stress relaxation arising from the sliding motion of branches along the main chain. Our simulations reveal a mechanism of branch motion resulting from an enhanced counterion condensation at the branched interfaces and provide quantitative evidence of stress relaxation facilitated by branched sliding. Furthermore, depending on the surfactant and salt concentrations, which in turn determine the microstructure, we observe normal, subdiffusive, and superdiffusive motions of surfactants. Specifically, superdiffusive behavior is associated with branch sliding, breakage and recombination of micelle fragments, as well as constraint release in entangled systems.

Molecular-Scale Design of Hydrocarbon Surfactant Self-Assembly in Supercritical CO2

Forming wormlike reverse micelles (RMs) by hydrocarbon surfactant self-assembly is an economic and environmental strategy to improve the physicochemical properties of supercritical carbon dioxide (scCO₂), but it remains challenging. Introducing cosurfactant in hydrocarbon surfactant self-assembly system is a potential method to generate wormlike RMs. Here, adopting molecular dynamics simulations, we performed hydrocarbon surfactant (TC14) self-assembly with introducing cosurfactants (C₈Benz). It is found that adding the C₈Benz molecules will induce the spherical RMs to a short rodlike form. In this case, the microstructure of the short rodlike RMs shows a dumbbell-like form that is composed by three parts including a middle part of C₈Benz and two parts of TC14 aggregation at both ends of rodlike RMs, which is regarded as the origin of RMs shape transition. Further, the analysis of free energy for RMs fusion indicates that the high fusion ability of C₈Benz aggregation drives the formation of the dumbbell-like RMs. Accordingly, enhancing the affinity of the C₈Benz is found to be effective strategy to further fusion of rodlike RMs in end-to-end manner, yielding a wormlike RMs with a beads-on-a-string structure. It is expected that this work will provide a valuable information for design the hydrocarbon wormlike RMs and facilitate the potential application of scCO₂.

Effect of the salt-induced micellar microstructure on the nonlinear shear flow behavior of ionic cetylpyridinium chloride surfactant solutions

The shear flow dynamics of linear and branched wormlike micellar systems based on cetylpyridinium chloride and sodium salicylate in brine solution is investigated through rheometric and scattering techniques. In particular, the flow and the structural flow response are explored via velocimetry measurements and rheological and rheometric small-angle neutron scattering (SANS) experiments, respectively. Although all micellar solutions display a similar shear thinning behavior in the nonlinear regime, the experimental results show that shear banding sets in only when the micelle contour length L[over ¯] is sufficiently long, independent of the nature of the micellar connections (either linear or branched micelles). Using rheometric SANS, we observe that the shear banding systems both show very similar orientational ordering as a function of Weissenberg number, while the short branched micelles manifest an unexpected increase of ordering at very low Weissenberg numbers. This suggests the presence of an additional flow-induced relaxation process that is peculiar for branched systems.

The role of the binding salt sodium salicylate in semidilute ionic cetylpyridinium chloride micellar solutions: a rheological and scattering study

The viscosity varies as a consequence of binding, first, and screening, later, action of the penetrating salt.

Coarse-grained molecular dynamics study on the self-assembly of Gemini surfactants: the effect of spacer length

This work provides a molecular-level understanding of the underlying mechanism of the self-assembly of Gemini surfactants.

Effect of long-range interactions on nanoparticle-induced aggregation

The process of attaching liquid media molecules to dispersed nanoparticles is studied by numerically investigating the time evolution of the size distribution of the emerging aggregates. Within the considered mechanism of aggregation, both the primary particles and the resulting aggregates are assumed to connect freely dispersing molecules, but the particles and aggregates are not allowed to self-link or self-assemble at each evolution stage of the system, due to, e.g., repulsive interactions. The process of random attachment of dispersing molecules to immersed nanoparticles and aggregates is considered to be driven by attractive long-range interactions of the van der Waals type. The molecule binding rate is, in consequence, modeled as being dependent not only on the size and surface morphology of the existing aggregates, but also on the van der Waals forces, whose strength is itself treated as dependent on the aggregate size. It is demonstrated that these forces diminish, in general, the inhomogeneity of aggregate size. Such an effect is shown to be especially distinct when the interaction strength is relatively large but does not increase as aggregates increase in size, i.e., when strongly attracted media molecules functionalize the resultant aggregates to prevent the increase of the interaction strength. This result can be helpful to construct stable complex substances containing aggregates with low size dispersion. Surprisingly, the evolution of aggregating systems toward more significant inhomogeneity takes place when the interaction strength is initially large and increases fast enough with the size of aggregates.

Self-Assembly of Nanoparticle-Surfactant Complexes with Rodlike Micelles: A Molecular Dynamics Study

The self-assembly of nanoparticles (NPs) with cationic micelles of cetyltrimethylammonium chloride (CTAC) is known to produce stable nanogels with rich rheological and optical properties. Coarse-grained molecular dynamics (MD) simulations are performed to explore the molecular mechanisms underlying this self-assembly process. In an aqueous solution of CTAC surfactants, a negatively charged NP with a zeta potential of less than -45 mV is observed to form a stable vesicular structure in which the particle surface is almost entirely covered with a double layer of surfactants. In comparison, surfactants form a monolayer, or a corona, around an uncharged hydrophobic NP with the tailgroups physically adsorbed onto the particle. In the presence of sodium salicylate salt, such NP-surfactant complexes (NPSCs) interact with rodlike CTAC micelles, resulting in the formation of stable junctions through the opening up of the micelle end-cap followed by surfactant exchange, which is diffusion-limited. The diffusive regime spans several hundred nanoseconds, thereby necessitating MD simulations over microsecond time scales. The energetics of NPSC-micelle complexation is analyzed from the variation in the total pair-potential energy of the structures.