Can purely repulsive soft potentials predict micelle formation correctly?

Dissipative particle dynamics simulations in colloid and Interface science: a review

Dissipative particle dynamics (DPD) is one of the most efficient mesoscale coarse-grained methodologies for modeling soft matter systems. Here, we comprehensively review the progress in theoretical formulations, parametrization strategies, and applications of DPD over the last two decades. DPD bridges the gap between the microscopic atomistic and macroscopic continuum length and time scales. Numerous efforts have been performed to improve the computational efficiency and to develop advanced versions and modifications of the original DPD framework. The progress in the parametrization techniques that can reproduce the engineering properties of experimental systems attracted a lot of interest from the industrial community longing to use DPD to characterize, help design and optimize the practical products. While there are still areas for improvements, DPD has been efficiently applied to numerous colloidal and interfacial phenomena involving phase separations, self-assembly, and transport in polymeric, surfactant, nanoparticle, and biomolecules systems.

Thermodynamic signatures and cluster properties of self-assembly in systems with competing interactions

Colloidal particles, amphiphiles and functionalized nanoparticles are examples of systems that frequently exhibit short-range attraction coupled with long-range repulsion. We vary the ratio of attraction and repulsion in a simple isotropic model with competing interactions, using molecular simulations, and observe significant differences in the properties of the self-assembled clusters that form. We report conditions that lead to the self-assembly of clusters of a preferred size, accompanied by a change in the slope of the pressure with respect to density, similar to micelles formed by amphiphilic molecules. We also report conditions where repulsion dominates, clusters of a preferred size form and the pressure vs. density slope is unaffected by self-assembly. We investigate cluster structure by calculating the size distributions, free colloid density, cluster shape and density profiles. The system dynamics are characterized by cluster life-times. We do not find qualitative differences in structure or dynamics of the clusters, regardless the pressure behavior. Therefore, thermodynamic and structural quantities are required to classify the different clustering characteristics that are observable in systems with competing interactions. Our results have implications in terms of development of design principles for stable cluster self-assembly.

Adsorption and Depletion Regimes of a Nonionic Surfactant in Hydrophilic Mesopores: An Experimental and Simulation Study

Adsorption and aggregation of nonionic surfactants at oxide surfaces has been studied extensively in the past, but only for concentrations below and near the critical micelle concentration. Here we report an adsorption study of a short-chain surfactant (C₆E₃) in porous silica glass of different pore sizes (7.5 to 50 nm), covering a wide composition range up to 50 wt % in a temperature range from 20 °C to the LCST. Aggregative adsorption is observed at low concentrations, but the excess concentration of C₆E₃ in the pores decreases and approaches zero at higher bulk concentrations. Strong depletion of surfactant (corresponding to enrichment of water in the pores) is observed in materials with wide pores at high bulk concentrations. We propose an explanation for the observed pore-size dependence of the azeotropic point. Mesoscale simulations based on dissipative particle dynamics (DPD) were performed to reveal the structural origin of this transition from the adsorption to the depletion regime. The simulated adsorption isotherms reproduce the behavior found in the 7.5 nm pores. The calculated bead density profiles indicate that the repulsive interaction of surfactant head groups causes a depletion of surfactant in the region around the corona of the surface micelles.

Surfactant chain length and concentration influence on the interfacial tension of two immiscible model liquids: a coarse-grained approach

The interfacial tension between immiscible liquids is studied as a function of a model linear surfactant length and concentration using coarse-grained, dissipative particle dynamics numerical simulations. The adsorption isotherms obtained from the simulations are found to be in agreement with Langmuir's model. The reduction of the interfacial tension with increasing surfactant concentration is found to display some common characteristics for all the values of chain length modeled, with our predictions being in agreement with Szyszkowski's equation. Lastly, the critical micelle concentration is predicted for all surfactant lengths, finding exponentially decaying behavior, in agreement with Kleven's model. It is argued that these findings can be helpful guiding tools in the interpretation of available experiments and in the design of new ones with new surfactants and polymers.

Hierarchical multi-scale simulations of adhesion at polymer–metal interfaces: dry and wet conditions

Multi-scale simulations are performed to study the adhesion properties of different polymer–metal interfaces in the absence and presence of water.

Prediction of the Critical Micelle Concentration of Nonionic Surfactants by Dissipative Particle Dynamics Simulations

Micellization of surfactant solutions is a ubiquitous phenomenon in natural systems and technological processes, and its theoretical description represents one of the cornerstone problems in the physical chemistry of colloidal systems. However, successful attempts of quantitative modeling confirmed by experimental data remains limited. We show, for the first time, that the dissipative particle dynamics with rigorously defined soft repulsion interaction and rigidity parameters is capable of predicting micellar self-assembly of nonionic surfactants. This is achieved due to a novel approach suggested for defining the interaction parameters by fitting to the infinite dilution activity coefficients of binary solutions formed by reference compounds that represent coarse-grained fragments of surfactant molecules. Using this new parametrization scheme, we obtained quantitative agreement with the experimental critical micelle concentration and aggregation number for several typical surfactants of different chemical structures. The proposed approach can be extended to various colloidal and polymeric systems beyond nonionic surfactant solutions.

The influence of micelle formation on the stability of colloid surfactant mixtures

The stability of colloidal dispersions can be severely affected by the presence of surfactants. Because surfactants can adsorb at colloidal surfaces as well as form micelles, one can expect an interplay between both phenomena. Using grand-canonical coarse-grained Monte Carlo simulations on surfactant solutions confined between two surfaces, we investigate how adsorption and micelle formation affects the effective interaction between two colloidal particles, and hence, the stability of the colloidal dispersion. For solvophilic colloidal surfaces, we observe a short-ranged oscillatory solvation pressure that is hardly affected by the presence of surfactants in the system. The effective surface-surface interaction, however, reveals a decrease in solvophilic stabilization as a function of surfactant chemical potential. For solvophobic surfaces, we find that the capillary evaporation observed in a confined pure solvent, is counteracted by the addition of surfactants. Around the critical micelle concentration (CMC), the surface-surface interaction even becomes repulsive, enhancing stabilization of the colloidal dispersion. In contrast, the formation of micelles at concentrations above the CMC causes an additional depletion effect, resulting in an effective attraction, which in turn can destabilize a colloidal dispersion.

Alcohol solubility in a lipid bilayer: Efficient grand-canonical simulation of an interfacially active molecule

We derive a new density-biased Monte Carlo technique which preserves detailed balance and improves the convergence of grand-canonical simulations of a species with a strong preference for an interfacial region as compared to the bulk. This density-biasing technique is applied to the solubility of "alcohol" molecules in a mesoscopic model of the lipid bilayer, a system which has anesthetic implications but is poorly understood.

Molecular simulations of droplet coalescence in oil/water/surfactant systems

We report a molecular simulation study of the mechanism by which droplets covered with a surfactant monolayer coalesce. We study a model system where the rate-limiting step in coalescence is the rupture of the surfactant film. Our simulations allow us to focus on the stages at the core of the coalescence process: the initial rupture of the two surfactant monolayers, the rearrangement of the surfactant molecules to form a channel connecting the two droplets, and the expansion of the radius of the resulting channel. For our numerical study, we made use of the dissipative particle dynamics method. We used a coarse-grained description of the oil, water, and surfactant molecules. The rupture of the surfactant film is a rare event on the molecular time scale. To enhance the sampling of the rupture of the surfactant film, we used forward flux sampling (FFS). FFS not only allows us to estimate coalescence rates, it also provides insight into the molecular structure and free energy of the "transition" state. For an oil-water-oil film without surfactant, the rupture rate decreases exponentially with increasing film thickness. The critical state is different in thin and thick films: Thin films break following a large enough thickness fluctuation. Thicker films break only after a sufficiently large hole fluctuation-they can heal. Next, we designed surfactant molecules with positive, zero, and negative natural curvatures. For a water film between two surfactant-covered oil droplets, the rupture rate is highest when the surfactant has a negative natural curvature, lowest when it has zero natural curvature, and lying in between when it has a positive natural curvature. This nonmonotonic variation with curvature stems from two effects: First, the surfactants with a large absolute value of the natural curvature have lower interfacial tension and bending rigidity. This promotes the interfacial fluctuations required to nucleate a channel. Second, the sign of the natural curvature determines whether there is a critical channel radius at which the channel free energy has a maximum. The latter is in agreement with the hole-nucleation theory of Kabalnov and Wennerstrom [Langmuir 12, 276 (1996)]. Our simulations seriously overestimate the relative stability of surfactant free emulsions. We argue that this is due to the fact that our model does not allow for nanobubble formation and capillary evaporation-processes that are presumably of key importance in the coalescence of surfactant-free emulsions.

Sampling the kinetic pathways of a micelle fusion and fission transition

The mechanism and kinetics of micellar breakup and fusion in a dilute solution of a model surfactant are investigated by path sampling techniques. Analysis of the path ensemble gives insight in the mechanism of the transition. For larger, less stable micelles the fission/fusion occurs via a clear neck formation, while for smaller micelles the mechanism is more direct. In addition, path analysis yields an appropriate order parameter to evaluate the fusion and fission rate constants using stochastic transition interface sampling. For the small, stable micelle (50 surfactants) the computed fission rate constant is a factor of 10 lower than the fusion rate constant. The procedure opens the way for accurate calculation of free energy and kinetics for, e.g., membrane fusion, and wormlike micelle endcap formation.

The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations

We present an improved and extended version of our coarse grained lipid model. The new version, coined the MARTINI force field, is parametrized in a systematic way, based on the reproduction of partitioning free energies between polar and apolar phases of a large number of chemical compounds. To reproduce the free energies of these chemical building blocks, the number of possible interaction levels of the coarse-grained sites has increased compared to those of the previous model. Application of the new model to lipid bilayers shows an improved behavior in terms of the stress profile across the bilayer and the tendency to form pores. An extension of the force field now also allows the simulation of planar (ring) compounds, including sterols. Application to a bilayer/cholesterol system at various concentrations shows the typical cholesterol condensation effect similar to that observed in all atom representations.

Equation of motion for coarse-grained simulation based on microscopic description

We have derived an equation of motion for coarse-grained particles by using a projection operator. Because the derived coarse-grained equation is based on microscopic description, it can be the basis for models of various coarse-grained simulations. We show that by substitution of random forces into fluctuating forces in the coarse-grained equation, the equations for Brownian dynamics and dissipative particle dynamics are reproduced.

Prediction of an autocatalytic replication mechanism for micelle formation

We report molecular simulations suggesting that the kinetics of surfactant micelle formation can be sped up significantly by a replication mechanism, in which growing micelles become unstable and split into two similar sized micelles. We argue that for certain surfactants types around the critical micelle concentration, such a mechanism becomes more dominant than the commonly accepted nucleation pathway.