Potentials of mean force and escape times of surfactants from micelles and hydrophobic surfaces using molecular dynamics simulations

Experimental and simulation-based characterization of surfactant adsorption layers at fluid interfaces

Adsorption of surfactants to fluid interfaces occurs in numerous technological and daily-life contexts. The coverage at the interface and other properties of the formed adsorption layers determine the performance of a surfactant with regard to the desired application. Given the importance of these applications, there is a great demand for the comprehensive characterization and understanding of surfactant adsorption layers. In this review, we provide an overview of suitable experimental and simulation-based techniques and review the literature in which they were used for the investigation of surfactant adsorption layers. We come to the conclusion that, while these techniques have been successfully applied to investigate Langmuir monolayers of water-insoluble surfactants, their application to the study of Gibbs adsorption layers of water-soluble surfactants has not been fully exploited. Finally, we emphasize the great potential of these methods in providing a deeper understanding of the behavior of soluble surfactants at interfaces, which is crucial for optimizing their performance in various applications.

Interface Adsorption versus Bulk Micellization of Surfactants: Insights from Molecular Simulations

Surfactants play essential roles in many commonplace applications and industrial processes. Although significant progress has been made over the past decades with regard to model-based predictions of the behavior of surfactants, important challenges have remained. Notably, the characteristic time scales of surfactant exchange among micelles, interfaces, and the bulk solution typically exceed the time scales currently accessible with atomistic molecular dynamics (MD) simulations. Here, we circumvent this problem by introducing a framework that combines the general thermodynamic principles of self-assembly and interfacial adsorption with atomistic MD simulations. This approach provides a full thermodynamic description based on equal chemical potentials and connects the surfactant bulk concentration, the experimental control parameter, with the surfactant surface density, the suitable control parameter in MD simulations. Self-consistency is demonstrated for the nonionic surfactant C12EO6 (hexaethylene glycol monododecyl ether) at an alkane/water interface, for which the adsorption and pressure isotherms are computed. The agreement between the simulation results and experiments is semiquantitative. A detailed analysis reveals that the used atomistic model captures well the interactions between surfactants at the interface but less so their adsorption affinities to the interface and incorporation into micelles. Based on a comparison with other recent studies that pursued similar modeling challenges, we conclude that the current atomistic models systematically overestimate the surfactant affinities to aggregates, which calls for improved models in the future.

Molecular dynamics study on micelle-small molecule interactions: developing a strategy for an extensive comparison

Theoretical predictions of the solubilizing capacity of micelles and vesicles present in intestinal fluid are important for the development of new delivery techniques and bioavailability improvement. A balance between accuracy and computational cost is a key factor for an extensive study of numerous compounds in diverse environments. In this study, we aimed to determine an optimal molecular dynamics (MD) protocol to evaluate small-molecule interactions with micelles composed of bile salts and phospholipids. MD simulations were used to produce free energy profiles for three drug molecules (danazol, probucol, and prednisolone) and one surfactant molecule (sodium caprate) as a function of the distance from the colloid center of mass. To address the challenges associated with such tasks, we compared different simulation setups, including freely assembled colloids versus pre-organized spherical micelles, full free energy profiles versus only a few points of interest, and a coarse-grained model versus an all-atom model. Our findings demonstrate that combining these techniques is advantageous for achieving optimal performance and accuracy when evaluating the solubilization capacity of micelles. All-atom (AA) and coarse-grained (CG) umbrella sampling (US) simulations and point-wise free energy (FE) calculations were compared to their efficiency to computationally analyze the solubilization of active pharmaceutical ingredients in intestinal fluid colloids.

Revealing the Formation Dynamics of Janus Polymer Particles: Insights from Experiments and Molecular Dynamics

Seeded emulsion polymerization is one of the best-known methods for preparing polymer particles with a controlled size, composition, and shape. It first requires the preparation of seed particles, which are then swollen with additional monomer (the same as the one used for the seed or a different one), to either increase the seed's size or change its morphology. The use of surfactants plays a central role in guaranteeing the required colloidal stability and contributing to the final shape and structure of the particles by lowering the interfacial energy between the polymer of the seed and the added monomer. We here study the polymerization of methyl methacrylate in the presence of polystyrene seed particles at various surfactant concentrations in the presence and absence of a surfactant (sodium dodecyl sulfate). We first show experimentally that the morphology of the colloidal particles can be tuned from Janus to core-shell, depending on the presence or absence of surfactant on the seeds particles' surface. Furthermore, using classical molecular dynamics simulations, we investigate the mechanism and behavior of the surfactants during the first stages of the polymerization process. We use a newly developed approach based on contact statistical analysis to confirm the critical role played by the organization of surfactant molecules on the surface of the seed particles in dictating the final particle morphology.

Synergism of Surfactant Mixture in Lowering Vapor-Liquid Interfacial Tension

Through employing molecular dynamics, in this work, we study how a two-component surfactant mixture cooperatively reduces the interfacial tension of a flat vapor-liquid interface. Our simulation results show that in the presence of a given insoluble surfactant, adding a secondary surfactant would either further reduce interfacial tension, indicating a positive synergistic effect, or increase the interfacial tension instead, indicating a negative synergistic effect. The synergism of the surfactant mixture in lowering surface tension is found to depend strongly on the structure complementary effect between different surfactant components. The synergistic mechanisms are then interpreted with minimization of the bending free energy of the composite surfactant monolayer via cooperatively changing the monolayer spontaneous curvature. By roughly describing the monolayer spontaneous curvature with the balanced distribution of surfactant heads and tails, we confirm that the positive synergistic effect in lowering surface tension is featured with the increasingly symmetric head-tail distributions, while the negative synergistic effect is featured with the increasingly asymmetric head-tail distributions. Furthermore, our simulation results indicate that minimal interfacial tension can only be observed when the spontaneous curvature is nearly zero.

Micelle kinetics of photoswitchable surfactants: Self-assembly pathways and relaxation mechanisms

HYPOTHESIS

A key question in the kinetics of surfactant self-assembly is whether exchange of unimers or fusion/fission of entire micelles is the dominant pathway. In this study, an isomerizable surfactant is used to explore fundamental out-of-equilibrium kinetics and mechanisms for growth and dissolution of micelles.

EXPERIMENTS

The kinetics of cationic surfactant 4-butyl-4'-(3-trimethylammoniumpropoxy)-phenylazobenzene was studied using molecular dynamics simulations. The fusion and exchange processes were investigated using umbrella sampling. Equilibrium states were validated by comparison with small-angle X-ray scattering data. The photo-isomerization event was simulated by modifying the torsion potential of the photo-responsive group to emulate the trans-to-cis transition.

FINDINGS

Micelle growth is dominated by unimer exchange processes, whereas, depending on the conditions, dissolution can occur both through fission and unimer expulsion. Fusion barriers increase steeply with the aggregation number making this an unlikely pathway to equilibrium for micelles of sizes that fit with the experimental data. The barriers for unimer expulsion remain constant and are much lower for unimer insertion, making exchange more likely at high aggregation. When simulating photo-conversion events, both fission and a large degree of unimer expulsion can occur depending on the extent of the out-of-equilibrium stress that is put on the system.

Molecular Insights on Morphology, Composition, and Stability of Mixed Micelles Formed by Ionic Surfactant and Nonionic Block Copolymer in Water Using Coarse-Grained Molecular Dynamics Simulations

The nanoscale association domains are the ultimate determinants of the macroscopic properties of complex fluids involving amphiphilic polymers and surfactants, and hence, it is foremost important to understand the role of polymer/surfactant concentration on these domains. We have used coarse-grained molecular dynamics simulations to investigate the effect of polymer/surfactant concentration on the morphology of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO, i.e., pluronics or poloxamers) block copolymer, and ionic surfactants sodium dodecyl sulfate (SDS), mixed micelles in aqueous solution. The proclivity of the surfactant to form the mixed micelles is also probed using umbrella sampling simulations. In this study, we observed that the core of the pluronic + SDS formed mixed micelles consists of PPO, the alkyl tail of SDS, and some water molecules, whereas the PEO, water, and sulfate headgroups of SDS form a shell, consistent with experimental observations. The micelles are spherical at high-pluronic/low-SDS compositions, ellipsoidal at high-SDS/low-pluronic compositions, and wormlike-cylindrical at high-pluronic/high-SDS compositions. The transitions in micelle morphology are governed by the solvent accessible surface area of mixed aggregates, electrostatic repulsion between SDS-headgroups, and dehydration of PEO and PPO segments. The free energy barrier for SDS escape is much higher in mixed micelles than in pure SDS micelles, indicating a stronger tendency for SDS to form pluronic-SDS mixed micelles.

Hierarchical Aggregation in a Complex Fluid─The Role of Isomeric Interconversion

There is an ever-increasing body of evidence that metallic complexes involving amphiliphic ligands do not form normal solutions in organic solvents. Instead, they form complex fluids with intricate structures. For example, the metallic complexes may aggregate into clusters, and these clusters themselves may aggregate into superclusters. To gain a deeper insight into the mechanisms at play, we have used an improved force field to conduct extensive molecular dynamics simulations of a system composed of zirconium nitrate, water, nitric acid, tri-n-butyl phosphate, and n-octane. The important new finding is that a dynamic equilibrium between the cis and trans isomers of the metal complex is likely to play a key role in the aggregation behavior. The isolated cis and trans isomers have similar energies, but simulation indicates that the clusters consist predominantly of cis isomers. With increasing metal concentration, we hypothesize that more clustering occurs and the chemical equilibrium shifts toward the cis isomer. It is possible that such isomeric effects play a role in the liquid-liquid extraction of other species and the inclusion of such effects in flow sheet modeling may lead to a better description of the process.

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.

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.

Molecular Driving Force for Facet Selectivity of Sequence-Defined Amphiphilic Peptoids at Au-Water Interfaces

Shape-controlled colloidal nanocrystal syntheses often require facet-selective solution-phase chemical additives to regulate surface free energy, atom addition/migration fluxes, or particle attachment rates. Because of their highly tunable properties and robustness to a wide range of experimental conditions, peptoids represent a very promising class of next-generation functional additives for control over nanocrystal growth. However, understanding the origin of facet selectivity at the molecular level is critical to generalizing their design. Herein we employ molecular dynamics simulations and biased sampling methods and report stronger selectivity to Au(111) than to Au(100) for Nce3Ncp6, a peptoid that has been shown to assist the formation of 5-fold twinned Au nanostars. We find that facet selectivity is achieved through synergistic effects of both peptoid-surface and solvent-surface interactions. Moreover, the amphiphilic nature of Nce3Ncp6 together with the order of peptoid-peptoid and peptoid-surface binding energies, that is, peptoid-Au(100) < peptoid-peptoid < peptoid-Au(111), further amplifies its distinct collective behavior on different Au surfaces. Our studies provide a fundamental understanding of the molecular origin of facet-selective adsorption and highlight the possibility of future designs and uses of sequence-defined peptoids for predictive syntheses of nanocrystals with designed shapes and properties.

Micellar Composition Affects Lipid Accretion Kinetics in Molecular Dynamics Simulations: Support for Lipid Network Reproduction

Mixed lipid micelles were proposed to facilitate life through their documented growth dynamics and catalytic properties. Our previous research predicted that micellar self-reproduction involves catalyzed accretion of lipid molecules by the residing lipids, leading to compositional homeostasis. Here, we employ atomistic Molecular Dynamics simulations, beginning with 54 lipid monomers, tracking an entire course of micellar accretion. This was done to examine the self-assembly of variegated lipid clusters, allowing us to measure entry and exit rates of monomeric lipids into pre-micelles with different compositions and sizes. We observe considerable rate-modifications that depend on the assembly composition and scrutinize the underlying mechanisms as well as the energy contributions. Lastly, we describe the measured potential for compositional homeostasis in our simulated mixed micelles. This affirms the basis for micellar self-reproduction, with implications for the study of the origin of life.

Interactions of Crosslinked Polyacrylic Acid Polyelectrolyte Gels with Nonionic and Ionic Surfactants

The morphology and stability of surfactant-loaded polyelectrolyte gels are of great interest for a variety of personal care, cosmetic, and pharmaceutical products. However, the mechanisms of surfactant interactions with gel-forming polymers are poorly understood and experimentally challenging. The aim of this work is to explore in silico the specifics of surfactant absorption within polyelectrolyte gels drawing on the examples of typical non-ionic octaethylene glycol monooctyl ether (C₈E₈) and anionic sodium dodecyl sulfate (SDS) surfactants and polyacrylic acid modified with hydrophobic sidechains mimicking the practically important Carbopol polymer. Using the systematically parameterized coarse-grained dissipative particle dynamics models, we generate and characterize the equilibrium conformations and swelling of the polymer films in aqueous solutions with the surfactant concentrations varied up to the critical micelle concentration (cmc). We discover the striking difference in interactions of Carbopol-like polymers with nonionic and ionic surfactants under mildly acidic conditions. The sorption of C₈E₈ within the polymer film is found substantial. As the surfactant concentration increases, the polymer film swells and, close to cmc, becomes unstable due to the formation and growth of water pockets filled with surfactant micelles. Sorption of SDS at the same bulk concentrations is found much lower, with only about 1% of surfactant mass fraction achieved at cmc. As the SDS concentration increases further, a lamellae structure is formed within the film, which remains stable. Reduced swelling and higher stability indicate better prospects of using SDS-type surfactants with Carbopol-based gels in formulations for detergents and personal care products.

Free energy of micellization of dodecyl phosphocholine (DPC) from molecular simulation: Hybrid PEACH-BAR method

A new method to extract the free energy of aggregation versus aggregate size from molecular simulation data is proposed and applied to a united atom model of the zwitterionic surfactant dodecyl phosphocholine in water. This system's slow dissociation rate and low critical micelle concentration (CMC of approximately 1-2 mM) make extraction of cluster free energies directly from simulation results using the "partition-enabled analysis of cluster histogram" (PEACH) method impractical. The new approach applies PEACH to a model with weakened attractions between aggregants, which allows sampling of a continuous range of cluster sizes, then recovers the free energy of aggregation under the original fully-attractive force field using the BAR free energy difference method. PEACH-BAR results are compared with free energy differences calculated via umbrella sampling, and are used to make predictions of CMC, average cluster size, and SAXS scattering profiles that are in fair agreement with experiment.

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.

Influence of Bile Composition on Membrane Incorporation of Transient Permeability Enhancers

Transient permeability enhancers (PEs), such as caprylate, caprate, and salcaprozate sodium (SNAC), improve the bioavailability of poorly permeable macromolecular drugs. However, the effects are variable across individuals and classes of macromolecular drugs and biologics. Here, we examined the influence of bile compositions on the ability of membrane incorporation of three transient PEs—caprylate, caprate, and SNAC—using coarse-grained molecular dynamics (CG-MD). The availability of free PE monomers, which are important near the absorption site, to become incorporated into the membrane was higher in fasted-state fluids than that in fed-state fluids. The simulations also showed that transmembrane perturbation, i.e., insertion of PEs into the membrane, is a key mechanism by which caprylate and caprate increase permeability. In contrast, SNAC was mainly adsorbed onto the membrane surface, indicating a different mode of action. Membrane incorporation of caprylate and caprate was also influenced by bile composition, with more incorporation into fasted- than fed-state fluids. The simulations of transient PE interaction with membranes were further evaluated using two experimental techniques: the quartz crystal microbalance with dissipation technique and total internal reflection fluorescence microscopy. The experimental results were in good agreement with the computational simulations. Finally, the kinetics of membrane insertion was studied with CG-MD. Variation in micelle composition affected the insertion rates of caprate monomer insertion and expulsion from the micelle surface. In conclusion, this study suggests that the bile composition and the luminal composition of the intestinal fluid are important factors contributing to the interindividual variability in the absorption of macromolecular drugs administered with transient PEs.

Molecular Dynamics Simulations of Micelle Properties and Behaviors of Sodium Lauryl Ether Sulfate Penetrating Ceramide and Phospholipid Bilayers

Molecular dynamics (MD) simulations with the umbrella sampling (US) method were used to investigate the properties of micelles formed by sodium lauryl ether sulfate with two ether groups (SLE2S) and behaviors of corresponding surfactants transferring from micelles to ceramide and DMPC bilayer surfaces. Average micelle radii based on the Einstein-Smoluchowski and Stokes-Einstein relations showed excellent agreement with those measured by dynamic light scattering, while those obtained by evaluating the gyration radius or calculating the distance between the micelle sulfur atoms and center of mass overestimate the radii. As an SLE2S micelle was pulled down to the ceramide bilayer surface in a 400 ns constant-force steered MD (cf-SMD) simulation, the micelle was partially deformed on the bilayer surface, and several SLE2S surfactants easily were partitioned from the micelle into the ceramide bilayer. In contrast, a micelle was not deformed on the DMPC bilayer surface, and SLE2S surfactants were not transferred from the micelle to the DMPC bilayer. Potential of mean force (PMF) calculations revealed that the Gibbs free energy required for an SLE2S surfactant monomer to transfer from a micelle to bulk water can be compensated by decreased Gibbs free energy when an SLE2S monomer transfers into the ceramide bilayer from bulk water. In addition, micelle deformation on the ceramide bilayer surface can reduce the Gibbs free energy barrier required for a surfactant to escape the micelle and help the surfactant partition from the micelle into the ceramide bilayer. An SLE2S surfactant partitioning into the ceramide bilayer is attributed to hydrogen bonding and favorable interactions between the hydrophilic surfactant head and ceramide molecules, which are more dominant than the dehydration penalty during bilayer insertion. Such interactions between surfactant and lipid molecule heads are considerably reduced in DMPC bilayers owing to dielectric screening by water molecules deep inside the head/tail boundary between the DMPC bilayer. This computational work demonstrates the distinct behavior of SLE2S surfactant micelles on ceramide and DMPC bilayer surfaces in terms of variation in Gibbs free energy, which offers insight into designing surfactants used in transdermal drug delivery systems and cosmetics.

Structure and Dynamics of Spherical and Rodlike Alkyl Ethoxylate Surfactant Micelles Investigated Using NMR Relaxation and Atomistic Molecular Dynamics Simulations

Predicting and controlling the properties of amphiphile aggregate mixtures require understanding the arrangements and dynamics of the constituent molecules. To explore these topics, we study molecular arrangements and dynamics in alkyl ethoxylate nonionic surfactant micelles by combining NMR relaxation measurements with large-scale atomistic molecular dynamics simulations. We calculate parameters that determine relaxation rates directly from simulated trajectories, without introducing specific functional forms to describe the dynamics. NMR relaxation rates, which depend on relative motions of interacting atom pairs, are influenced by wide distributions of dynamic time scales. We find that relative motions of neighboring atom pairs are rapid and liquidlike but are subject to structural constraints imposed by micelle morphology. Relative motions of distant atom pairs are slower than nearby atom pairs because changes in distances and angles are smaller when the moving atoms are further apart. Large numbers of atom pairs undergoing these slow relative motions contribute to predominantly negative cross-relaxation rates. For spherical micelles, but not for cylindrical micelles, cross-relaxation rates are positive only for surfactant tail atoms connected to the hydrophilic headgroup. This effect is related to the lower packing density of these atoms at the hydrophilic-hydrophobic boundary in spherical vs cylindrical arrangements, with correspondingly rapid and less constrained motion of atoms at the boundary.

Protobiotic Systems Chemistry Analyzed by Molecular Dynamics

Systems chemistry has been a key component of origin of life research, invoking models of life's inception based on evolving molecular networks. One such model is the graded autocatalysis replication domain (GARD) formalism embodied in a lipid world scenario, which offers rigorous computer simulation based on defined chemical kinetics equations. GARD suggests that the first pre-RNA life-like entities could have been homeostatically-growing assemblies of amphiphiles, undergoing compositional replication and mutations, as well as rudimentary selection and evolution. Recent progress in molecular dynamics has provided an experimental tool to study complex biological phenomena such as protein folding, ligand-receptor interactions, and micellar formation, growth, and fission. The detailed molecular definition of GARD and its inter-molecular catalytic interactions make it highly compatible with molecular dynamics analyses. We present a roadmap for simulating GARD's kinetic and thermodynamic behavior using various molecular dynamics methodologies. We review different approaches for testing the validity of the GARD model by following micellar accretion and fission events and examining compositional changes over time. Near-future computational advances could provide empirical delineation for further system complexification, from simple compositional non-covalent assemblies towards more life-like protocellular entities with covalent chemistry that underlies metabolism and genetic encoding.

Search for the Source of an Apparent Interfacial Resistance To Mass Transfer of CnEm Surfactants To the Water/Oil Interface

Experiments have shown that relaxation of oil/water interfacial tension by adsorption of alkyl ethoxylate surfactants from water onto an oil droplet is delayed relative to diffusion-controlled adsorption. We examine possible causes of this delay, and we show that several are implausible. We find that redissolution of the surfactant in the oil droplet cannot explain the apparent interfacial resistance at short times because the interface will preferentially fill before any such redissolution occurs. We also perform umbrella sampling with molecular dynamics simulation and do not find any evidence of a free-energy barrier or low-diffusivity zone near the interface. Nor do we find evidence from the simulation that premicellar aggregation slows diffusion enough to cause the observed resistance to interfacial adsorption. We are therefore unable to pinpoint the cause of the resistance, but we suggest that "dead time" associated with the experimental method could be responsible-specifically a local depletion of surfactant by the ejected droplet when creating the fresh interface between the oil and water.

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.

Oscillatory and Steady Shear Rheology of Model Hydrophobically Modified Ethoxylated Urethane-Thickened Waterborne Paints

Hydrophobically modified ethoxylated urethane (HEUR) thickeners are widely used as rheology modifiers for waterborne paints. Although the rheology of HEUR solutions in water is fairly well-understood, their impact on the rheology of waterborne latex/pigment suspensions (formulated paints) is more complicated. We study the shear rheology of model HEUR/latex/TiO₂ suspensions in water and investigate the dependence of both oscillatory and steady shear behaviors on the strength of the HEUR hydrophobes. We observe that in both oscillatory and steady shear experiments, rheological curves could be shifted onto a single master curve, demonstrating a "time-hydrophobe superposition". We also note that the oscillatory shear behavior exhibits a power-law spectrum of relaxation times, unlike the single-Maxwellian behavior of pure HEUR solutions. On the basis of these results and earlier experimental and theoretical findings, we propose that the rheology of the HEUR-thickened latex/TiO₂ suspensions is mainly determined by the transient network of HEUR-bridged latex particles, with a broad distribution of the characteristic lifetimes of the bridge. The model is found to be in good qualitative and semiquantitative agreement with the experiments for both steady shear and oscillatory shear.

Molecular-Scale Description of SPAN80 Desorption from a Squalane-Water Interface

Extensive all-atom molecular dynamics calculations on the water-squalane interface for nine different loadings with sorbitan monooleate (SPAN80), at T = 300 K, are analyzed for the surface tension equation of state, desorption free-energy profiles as they depend on loading, and to evaluate escape times for adsorbed SPAN80 into the bulk phases. These results suggest that loading only weakly affects accommodation of a SPAN80 molecule by this squalane-water interface. Specifically, the surface tension equation of state is simple through the range of high tension to high loading studied, and the desorption free-energy profiles are weakly dependent on loading here. The perpendicular motion of the centroid of the SPAN80 headgroup ring is well-described by a diffusional model near the minimum of the desorption free-energy profile. Lateral diffusional motion is weakly dependent on loading. Escape times evaluated on the basis of a diffusional model and the desorption free energies are 7 × 10^-2 s (into the squalane) and 3 × 10² h (into the water). The latter value is consistent with desorption times of related lab-scale experimental work.

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.

ChannelsDB: database of biomacromolecular tunnels and pores

ChannelsDB (http://ncbr.muni.cz/ChannelsDB) is a database providing information about the positions, geometry and physicochemical properties of channels (pores and tunnels) found within biomacromolecular structures deposited in the Protein Data Bank. Channels were deposited from two sources; from literature using manual deposition and from a software tool automatically detecting tunnels leading to the enzymatic active sites and selected cofactors, and transmembrane pores. The database stores information about geometrical features (e.g. length and radius profile along a channel) and physicochemical properties involving polarity, hydrophobicity, hydropathy, charge and mutability. The stored data are interlinked with available UniProt annotation data mapping known mutation effects to channel-lining residues. All structures with channels are displayed in a clear interactive manner, further facilitating data manipulation and interpretation. As such, ChannelsDB provides an invaluable resource for research related to deciphering the biological function of biomacromolecular channels.

Extracting Aggregation Free Energies of Mixed Clusters from Simulations of Small Systems: Application to Ionic Surfactant Micelles

Micelle cluster distributions from molecular dynamics simulations of a solvent-free coarse-grained model of sodium octyl sulfate (SOS) were analyzed using an improved method to extract equilibrium association constants from small-system simulations containing one or two micelle clusters at equilibrium with free surfactants and counterions. The statistical-thermodynamic and mathematical foundations of this partition-enabled analysis of cluster histograms (PEACH) approach are presented. A dramatic reduction in computational time for analysis was achieved through a strategy similar to the selector variable method to circumvent the need for exhaustive enumeration of the possible partitions of surfactants and counterions into clusters. Using statistics from a set of small-system (up to 60 SOS molecules) simulations as input, equilibrium association constants for micelle clusters were obtained as a function of both number of surfactants and number of associated counterions through a global fitting procedure. The resulting free energies were able to accurately predict micelle size and charge distributions in a large (560 molecule) system. The evolution of micelle size and charge with SOS concentration as predicted by the PEACH-derived free energies and by a phenomenological four-parameter model fit, along with the sensitivity of these predictions to variations in cluster definitions, are analyzed and discussed.

Simulating Bilayers of Nonionic Surfactants with the GROMOS-Compatible 2016H66 Force Field

Polyoxyethylene glycol alkyl ether amphiphiles (C_iE_j) are important nonionic surfactants, often used for biophysical and membrane protein studies. In this work, we extensively test the GROMOS-compatible 2016H66 force field in molecular dynamics simulations involving the lamellar phase of a series of C_iE_j surfactants, namely C₁₂E₂, C₁₂E₃, C₁₂E₄, C₁₂E₅, and C₁₄E₄. The simulations reproduce qualitatively well the monitored structural properties and their experimental trends along the surfactant series, although some discrepancies remain, in particular in terms of the area per surfactant, the equilibrium phase of C₁₂E₅, and the order parameters of C₁₂E₃, C₁₂E₄, and C₁₂E₅. The polar head of the C_iE_j surfactants is highly hydrated, almost like a single polyethyleneoxide (PEO) molecule at full hydration, resulting in very compact conformations. Within the bilayer, all C_iE_j surfactants flip-flop spontaneously within tens of nanoseconds. Water-permeation is facilitated, and the bending rigidity is 4 to 5 times lower than that of typical phospholipid bilayers. In line with another recent theoretical study, the simulations show that the lamellar phase of C_iE_j contains large hydrophilic pores. These pores should be abundant in order to reproduce the comparatively low NMR order parameters. We show that their contour length is directly correlated to the order parameters, and we estimate that they should occupy approximately 7-10% of the total membrane area. Due to their highly dynamic nature (rapid flip-flops, high water permeability, observed pore formation), C_iE_j surfactant bilayers are found to represent surprisingly challenging systems in terms of modeling. Given this difficulty, the results presented here show that the 2016H66 parameters, optimized independently considering pure-liquid as well as polar and nonpolar solvation properties of small organic molecules, represent a good starting point for simulating these systems.

Surfactant Assemblies on Selected Nanostructured Surfaces: Evidence, Driving Forces, and Applications

Surfactant adsorption at solid-liquid interfaces is critical for a number of applications of vast industrial interest and can also be used to seed surface-modification processes. Many of the surfaces of interest are nanostructured, as they might present surface roughness at the molecular scale, chemical heterogeneity, as well as a combination of both surface roughness and chemical heterogeneity. These effects provide lateral confinement on the surfactant aggregates. It is of interest to quantify how much surfactant adsorbs on such nanostructured surfaces and how the surfactant aggregates vary as the degree of lateral confinement changes. This review focuses on experimental evidence on selected substrates, including gold- and carbon-based substrates, suggesting that lateral confinement can have pronounced effects both on the amount adsorbed and on the morphology of the aggregates as well as on a systematic study, via diverse simulation approaches, on the effect of lateral confinement on the structure of the surfactant aggregates. Atomistic and coarse-grained simulations conducted for surfactants on graphene sheets and carbon nanotubes are reviewed, as well as coarse-grained simulations for surfactant adsorption on nanostructured surfaces. Finally, we suggest a few possible extensions of these studies that could positively impact a few practical applications. In particular, the simultaneous effect of lateral confinement and of the coadsorption of molecular compounds within the surface aggregates is expected to yield interesting fundamental results with long-lasting consequences in applications ranging from drug delivery to the design of advanced materials.

Formulation-Controlled Positive and Negative First Normal Stress Differences in Waterborne Hydrophobically Modified Ethylene Oxide Urethane (HEUR)-Latex Suspensions

Hydrophobically modified ethylene oxide urethane (HEUR) associative thickeners are widely used to modify the rheology of waterborne paints. Understanding the normal stress behavior of the HEUR-based paints under high shear is critical for many applications such as brush drag and spreading. We observed that the first normal stress difference, N₁, at high shear (large Weissenberg number) can be positive or negative depending on the HEUR hydrophobe strength and concentration. We propose that the algebraic sign of the N₁ is primarily controlled by two factors: (a) adsorption of HEURs on the latex surface and (b) the ability of HEURs to form transient molecular bridges between latex particles. Such transient bridges are favored for dispersions with small interparticle distances and dense surface coverages; in these systems; HEUR-bridged latex microstructures flow-align in high shear and exhibit positive N₁. In the absence of transient bridges (large interparticle distances, low surface coverage), the dispersion rheology is similar to that of weakly interacting spheres, exhibiting negative N₁. The results are summarized in a simplified phase diagram connecting formulation, microstructure, and the N₁ behavior.

Structural Properties of Nonionic Monorhamnolipid Aggregates in Water Studied by Classical Molecular Dynamics Simulations

Molecular dynamics simulations were carried out to investigate the structure and stabilizing factors of aggregates of the nonionic form of the most common congener of monorhamnolipids, α-rhamnopyranosyl-β-hydroxydecanoyl-β-hydroxydecanoate (Rha-C10-C10), in water. Aggregates of size ranging from 5 to 810 monomers were observed in the simulation forming spherical and ellipsoidal structures, a torus-like structure, and a unilamellar vesicle. The effects of the hydrophobic chain conformation and alignment in the aggregate, role of monomer···monomer and monomer···water H-bonds, and conformations of monomers in the aggregate were studied in detail. The unilamellar vesicle is highly stable due to the presence of isolated water molecules inside the core adding to the binding energy. Dissociation of a monomer from a larger micellar aggregate is relatively easy compared to that from smaller aggregates as seen from potential of mean force calculations. This analysis also shows that monomers are held more strongly in aggregates of Rha-C10-C10 than the widely used surfactant sodium dodecyl sulfate. Comparisons between the aggregation behavior of nonionic and anionic forms of Rha-C10-C10 are presented.

Surfactant Binding to Polymer-Water Interfaces in Atomistic Simulations

Attractive interactions between additive molecules and particle surfaces are key parameters in the design of waterborne suspensions and coatings. We use atomistic molecular dynamics (MD) simulations to determine the potential of mean force for a commonly used industrial surfactant sodium dodecyl sulfate (SDS) interacting with acrylate latex particles. We investigate how the potential of mean force and binding free energy depend on the amount of SDS adsorbed, solution ionic strength, and presence of other charged groups on the particle surface. We show that the potential of mean force for SDS is a sum of two independent terms, from the hydrophobic surfactant tail and charged headgroup: dragging the surfactant tail into solution contributes a linear potential of about kT per CH2 group, while the headgroup is repelled by like charges on the surface with a potential of about the zeta potential. Commercial acrylate latex particles also bear multivalent charged "hairs" as a remnant of their synthesis. These charged hairs result in a heterogeneously charged surface, for which SDS binds more or less strongly depending on the local environment.

Multiscale Molecular Dynamics Simulations of Model Hydrophobically Modified Ethylene Oxide Urethane Micelles

The flower-like micelles of various aggregation numbers of a model hydrophobically modified ethylene oxide urethane (HEUR) molecule, C16E45C16, and their corresponding starlike micelles, containing the surfactants C16E22 and C16E23, were studied by atomistic and coarse-grained molecular dynamic (MD) simulations. We used free energies from umbrella sampling to calculate the size distribution of micelle sizes and the average time for escape of a hydrophobic group from the micelle. Using the coarse-grained MARTINI force field, the most probable size of the model HEUR molecule was thereby determined to be about 80 hydrophobes per micelle and the average hydrophobe escape time to be about 0.1 s, both of which are consistent with previous experimental studies. Atomistic simulations reveal that hydrogen bond formation and the mean lifetime of hydration waters of the poly(ethylene oxide) (or PEO) groups are location-dependent in the HEUR micelle, with PEO groups immediately adjacent to the C16 groups forming the fewest hydrogen bonds with water and having hydration waters with longer lifetimes than those of the PEO groups located further away from the C16 groups.

Coarse-grained molecular dynamics simulation of self-assembly and surface adsorption of ionic surfactants using an implicit water model

We perform coarse-grained molecular dynamics simulations for sodium dodecyl sulfate (SDS) surfactant using a modification of the Dry Martini force field (Arnarez et al. 2014) with implicit water. After inclusion of particle mesh Ewald (PME) electrostatics, an artificially high dielectric constant for water (ε(r) = 150), and reparameterization, we obtain structural and thermodynamic properties of SDS micelles that are close to those obtained from the standard Martini force field with explicit water, which in turn match those of atomistic simulations. The gains in computational efficiency obtained by removing explicit water allow direct simulations of the self-assembly of SDS in solution. We observe surfactant exchange among micelles and micelle fission and fusion and obtain realistic, equilibrated micelle size distributions at modest computational cost, as well as a transition to cylindrical micelles at high surfactant concentration or with added salt. We further apply this parametrized force field to study the adsorption of SDS onto hydrophobic surfaces and calculate the adsorption kinetics and equilibrium adsorption isotherm. The greatly increased speed of computation of surfactant self-assembly made possible by this Dry Martini method should allow future simulation of competitive adsorption of multiple surfactant species to surfaces, as well as simulation of micellar shape transitions.