Drying polymer–polymer and colloid–polymer mixtures were studied using Langevin dynamics computer simulations. Polymer–polymer mixtures vertically stratified into layers, with the shorter polymers enriched near the drying interface and the longer polymers pushed down toward the substrate. Colloid–polymer mixtures stratified into a polymer-on-top structure when the polymer radius of gyration was comparable to or smaller than the colloid diameter, and a colloid-on-top structure otherwise. We also developed a theoretical model for the drying mixtures based on dynamical density functional theory, which gave excellent quantitative agreement with the simulations for the polymer–polymer mixtures and qualitatively predicted the observed polymer-on-top or colloid-on-top structures for the colloid–polymer mixtures.

The structures formed by mixtures of dissimilarly shaped nanoscale objects can significantly enhance our ability to produce nanoscale architectures. However, understanding their formation is a complex problem due to the interplay of geometric effects (entropy) and energetic interactions at the nanoscale. Spheres and rods are perhaps the most basic geometrical shapes and serve as convenient models of such dissimilar objects. The ordered phases formed by each of these individual shapes have already been explored, however, when mixed, spheres and rods have demonstrated only limited structural organization to date. Here, we show using experiments and theory that the introduction of directional attractions between rod ends and isotropically interacting spherical nanoparticles (NPs) through DNA base pairing leads to the formation of ordered three-dimensional lattices. The spheres and rods arrange themselves in a complex alternating manner, where the spheres can form either a face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice, or a disordered phase, as observed by in situ X-ray scattering. Increasing NP diameter at fixed rod length yields an initial transition from a disordered phase to the HCP crystal, energetically stabilized by rod-rod attraction across alternating crystal layers, as revealed by theory. In the limit of large NPs, the FCC structure is instead stabilized over the HCP by rod entropy. We, therefore, propose that directionally specific attractions in mixtures of anisotropic and isotropic objects offer insight into unexplored self-assembly behavior of noncomplementary shaped particles.Keywords: anisotropic colloids; colloidal crystals; DNA nanotechnology; nanoparticles; polymorphism; self-assembly;

Stratification in binary colloidal mixtures was investigated using implicit-solvent molecular dynamics simulations. For large particle size ratios and film Péclet numbers greater than unity, smaller colloids migrated to the top of the film, while big colloids were pushed to the bottom, creating an “inverted” stratification. This peculiar behavior was observed in recent simulations and experiments conducted by Fortini et al. [ Phys. Rev. Lett. 2016, 116, 118301]. To rationalize this behavior, particle size ratios and drying rates spanning qualitatively different Péclet number regimes were systematically studied, and the dynamics of the inverted stratification were quantified in detail. The stratified layer of small colloids was found to grow faster and to larger thicknesses for larger size ratios. Interestingly, inverted stratification was observed even at moderate drying rates where the film Péclet numbers were comparable to unity, but the thickness of the stratified layer decreased. A model based on dynamical density functional theory is proposed to explain the observed phenomena.

ConspectusMolecular simulation techniques using classical force-fields occupy the space between ab initio quantum mechanical methods and phenomenological correlations. In particular, Monte Carlo and molecular dynamics algorithms can be used to provide quantitative predictions of thermodynamic and transport properties of fluids relevant for geologic carbon sequestration at conditions for which experimental data are uncertain or not available. These methods can cover time and length scales far exceeding those of quantum chemical methods, while maintaining transferability and predictive power lacking from phenomenological correlations. The accuracy of predictions depends sensitively on the quality of the molecular models used. Many existing fixed-point-charge models for water and aqueous mixtures fail to represent accurately these fluid properties, especially when descriptions covering broad ranges of thermodynamic conditions are needed. Recent work on development of accurate models for water, CO2, and dissolved salts, as well as their mixtures, is summarized in this Account. Polarizable models that can respond to the different dielectric environments in aqueous versus nonaqueous phases are necessary for predictions of properties over extended ranges of temperatures and pressures. Phase compositions and densities, activity coefficients of the dissolved salts, interfacial tensions, viscosities and diffusivities can be obtained in near-quantitative agreement to available experimental data, using relatively modest computational resources. In some cases, for example, for the composition of the CO2-rich phase in coexistence with an aqueous phase, recent results from molecular simulations have helped discriminate among conflicting experimental data sets. The sensitivity of properties on the quality of the intermolecular interaction model varies significantly. Properties such as the phase compositions or electrolyte activity coefficients are much more sensitive than phase densities, viscosities, or component diffusivities. Strong confinement effects on physical properties in nanoscale media can also be directly obtained from molecular simulations. Future work on molecular modeling for CO2 and aqueous brines is likely to be focused on more systematic generation of interaction models by utilizing quantum chemical as well as direct experimental measurements. New ion models need to be developed for use with the current generation of polarizable water models, including ion–ion interactions that will allow for accurate description of dense, mixed brines. Methods will need to be devised that go beyond the use of effective potentials for incorporation of quantum effects known to be important for water, and reactive force fields developed that can handle bond creation and breaking in systems with carbonate and silicate minerals. Another area of potential future work is the integration of molecular simulation methods in multiscale models for the chemical reactions leading to mineral dissolution and flow within the porous media in underground formations.

We present a machine learning technique to discover and distinguish relevant ordered structures from molecular simulation snapshots or particle tracking data. Unlike other popular methods for structural identification, our technique requires no a priori description of the target structures. Instead, we use nonlinear manifold learning to infer structural relationships between particles according to the topology of their local environment. This graph-based approach yields unbiased structural information which allows us to quantify the crystalline character of particles near defects, grain boundaries, and interfaces. We demonstrate the method by classifying particles in a simulation of colloidal crystallization, and show that our method identifies structural features that are missed by standard techniques.

Using molecular dynamics simulations, we study a simple and scalable method for fabricating patchy nanoparticles via the assembly of binary polymer blends under a rapid solvent exchange. Patchiness can be achieved by incorporating a glassy component, which kinetically traps the particle morphology along the path to the equilibrium configuration. Our simulations reveal that the number of surface patches increases for larger nanoparticles and for more asymmetric blend ratios, while the size distribution of the patches remains rather uniform. Other than multi-patch nanoparticles, Janus structures have been obtained for small nanoparticles. Further, ribbon structures with elongated surface domains have also been observed for more symmetric blend ratios. Our simulations demonstrate that the nanoprecipitation technique allows for independent control over nanoparticle size, patchiness and composition. This work gives microscopic insights on the static and dynamic properties of the self-assembled particles, and provides useful guidelines for fabricating tailored patchy nanoparticles for applications in various areas.

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.

We present a method for the template-free characterization of binary superlattices. This is an extension of the Neighborhood Graph Analysis method, a technique which evaluates relationships between observed structures based on the topology of their first coordination shell [W. F. Reinhart, et al., Soft Matter, 2017, 13, 4733]. In the present work, we develop a framework for the analysis of multi-atom patterns, which incorporate structural information from the second coordination shell while providing a unified signature for all constituent particles in the superlattice. We construct an efficient metric for making quantitative comparisons between these patterns, making our algorithm the first capable of characterizing partial or defective superlattice structures. As in our previous work, we leverage machine learning techniques to characterize a range of self-assembled crystal structures, discovering a set of emergent collective variables which map each observed pattern into an intuitive global phase space. We demonstrate the method by performing classification of configurations from simulations of binary colloidal self-assembly in two dimensions.

Phase equilibria of water/CO2 and water/n-alkane mixtures over a range of temperatures and pressures were obtained from Monte Carlo simulations in the Gibbs ensemble. Three sets of Drude-type polarizable models for water, namely the BK3, GCP, and HBP models, were combined with a polarizable Gaussian charge CO2 (PGC) model to represent the water/CO2 mixture. The HBP water model describes hydrogen bonds between water and CO2 explicitly. All models underestimate CO2 solubility in water if standard combining rules are used for the dispersion interactions between water and CO2. With the dispersion parameters optimized to phase compositions, the BK3 and GCP models were able to represent the CO2 solubility in water, however, the water composition in CO2-rich phase is systematically underestimated. Accurate representation of compositions for both water- and CO2-rich phases cannot be achieved even after optimizing the cross interaction parameters. By contrast, accurate compositions for both water- and CO2-rich phases were obtained with hydrogen bonding parameters determined from the second virial coefficient for water/CO2. Phase equilibria of water/n-alkane mixtures were also studied using the HBP water and an exponenial-6 united-atom n-alkanes model. The dispersion interactions between water and n-alkanes were optimized to Henry’s constants of methane and ethane in water. The HBP water and united-atom n-alkane models underestimate water content in the n-alkane-rich phase; this underestimation is likely due to the neglect of electrostatic and induction energies in the united-atom model.

We present an algorithm based on linear bounding volume hierarchies (LBVHs) for computing neighbor (Verlet) lists using graphics processing units (GPUs) for colloidal systems characterized by large size disparities. We compare this to a GPU implementation of the current state-of-the-art CPU algorithm based on stenciled cell lists. We report benchmarks for both neighbor list algorithms in a Lennard-Jones binary mixture with synthetic interaction range disparity and a realistic colloid solution. LBVHs outperformed the stenciled cell lists for systems with moderate or large size disparity and dilute or semidilute fractions of large particles, conditions typical of colloidal systems.

Monte Carlo simulations were performed to obtain the phase behavior of binary H2O–CaCl2 and ternary H2O–CaCl2–CO2 mixtures over a range of conditions. The solubility of CO2 in brines plays a key role in determining the amount that can be trapped via geological carbon storage. Isobaric-isothermal and Gibbs ensemble Monte Carlo simulations with several fixed-point charge force field models were used for the calculations of liquid densities and vapor pressures for the binary, and compositions of both phases for the ternary system. We used the SPC and SPC/E models for water; the Åqvist, Deublein et al., and Smith–Dang parameterizations for CaCl2; and the EPM2, Murthy et al., and TraPPE models for CO2. While none of the model combinations were able to reproduce all the properties of interest, we found that some combinations produce accurate descriptions of individual properties. For the binary system, liquid densities are well represented by the SPC/E and Åqvist model combination, and vapor pressures are best described by the SPC and Åqvist model combination. For CO2 solubility in aqueous CaCl2, the combination of SPC, Smith–Dang, and TraPPE models gives the best predictions, but all the models studied show good predictive capabilities, given that no intermolecular potential parameters were optimized in the present study. These results are broadly consistent with previous calculations for the H2O–NaCl–CO2 system; CaCl2 is found to have a stronger salting-out effect than NaCl at the same molality.

A polarizable intermolecular potential model with short-range directional hydrogen-bonding interactions was developed for water. The model has a rigid geometry, with bond lengths and angles set to experimental gas-phase values. Dispersion interactions are represented by the Buckingham potential assigned to the oxygen atom, whereas electrostatic interactions are modeled by Gaussian charges. Polarization is handled by a Drude oscillator site, using a negative Gaussian charge attached to the oxygen atom by a harmonic spring. An explicit hydrogen-bonding term is included in the model to account for the effects of charge transfer. The model parameters were optimized to density, configurational energy, pair correlation function, and the dielectric constant of water under ambient conditions, as well as the minimum gas-phase dimer energy. Molecular dynamics and Gibbs ensemble Monte Carlo simulations were performed to evaluate the new model with respect to the thermodynamic and transport properties over a wide range of temperature and pressure conditions. Good agreement between model predictions and experimental data was found for most of the properties studied. The new model yields better performance relative to the majority of existing models and outperforms the BK3 model, which is one of the best polarizable models, for vapor–liquid equilibrium properties, whereas the new model is not better than the BK3 model for representation of other properties. The model can be efficiently simulated with the thermalized Drude oscillator algorithm, resulting in computational costs only 3 times higher than those of the nonpolarizable TIP4P/2005 model, whereas having significantly improved properties. Because it involves only a single Drude oscillator site, the new model is significantly faster than polarizable models with multiple sites. With the explicit inclusion of hydrogen-bond interactions, the model may provide a better description of the phase behavior of aqueous mixtures.

We studied the directed assembly of soft nanoparticles through rapid micromixing of polymers in solution with a nonsolvent. Both experiments and computer simulations were performed to elucidate the underlying physics and to investigate the role of various process parameters. In particular, we discovered that no external stabilizing agents or charged end groups are required to keep the colloids separated from each other when water is used as the nonsolvent. Furthermore, the size of the nanoparticles can be reliably tuned through the mixing rate and the ratio between polymer solution and nonsolvent. Our results demonstrate that this mechanism is highly promising for the mass fabrication of uniformly sized colloidal particles, using a wide variety of polymeric feed materials.Keywords: colloids; experiments; flash nanoprecipitation; self-assembly; simulation;

A polarizable intermolecular potential model using three classical Drude oscillators on the atomic sites has been developed for CO2. The model is rigid with bond lengths and molecular geometries set to their experimental values. Electrostatic interactions are represented by three Gaussian charges connected to the molecular frame by harmonic springs. Nonelectrostatic interactions are represented by the Buckingham exponential-6 potential, with potential parameters optimized to vapor–liquid equilibria (VLE) data. A nonpolarizable CO2 model that shares the other ingredients of the polarizable model was also developed and optimized to VLE data. Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to evaluate the two models with respect to a variety of thermodynamic and transport properties, including the enthalpy of vaporization, second virial coefficient, density in the one-phase fluid region, isobaric and isochoric heat capacities, radial distribution functions, self-diffusion coefficient, and shear viscosity. Excellent agreement between model predictions and experimental data was found for all properties studied. The polarizable and nonpolarizable models provide a similar representation of CO2 properties, which indicates that the properties of pure CO2 fluid are not strongly affected by polarization. The polarizable model, which has an order of magnitude higher computational cost than the nonpolarizable model, will likely be useful for the study of a mixture of CO2 and polar components for which polarization is important.

Molecular dynamics and Monte Carlo simulations were performed to obtain thermodynamic and transport properties of the binary H2O + NaCl system using the polarizable force fields of Kiss and Baranyai ( J. Chem. Phys. 2013, 138, 204507 and 2014, 141, 114501). In particular, liquid densities, electrolyte and crystal chemical potentials of NaCl, salt solubilities, mean ionic activity coefficients, vapor pressures, vapor–liquid interfacial tensions, and viscosities were obtained as functions of temperature, pressure, and salt concentration. We compared the performance of the polarizable force fields against fixed-point-charge (nonpolarizable) models. Most of the properties of interest are better represented by the polarizable models, which also remain physically realistic at elevated temperatures.

Polymers dilutely adsorbed in colloidal crystals play an underappreciated role in determining the stability of the crystal phase. Recent work has shown that tailoring the size and shape of the adsorbing polymer can help tune the relative thermodynamic stability of the face-centered cubic (FCC) and hexagonal close-packed (HCP) polymorphs [N. A. Mahynski, A. Z. Panagiotopoulos, D. Meng, and S. K. Kumar, Nat. Commun., 2014, 5, 4472]. This is a consequence of how different polymorphs uniquely distribute their interstitial voids. By engineering an adsorbent's morphology to be complementary to the interstices in a desired crystal form, other competing forms may be thermodynamically suppressed. Previous investigations into this effect focused solely on linear polymers, while here we investigate the effects of more complex polymer architectures, namely that of star polymers. We find that even small perturbations to an adsorbing polymer's architecture lead to significant, qualitative changes in the relative stability of close-packed colloidal crystal polymorphs. In contrast to the linear homopolymer case, the FCC phase may be re-stabilized over the HCP with sufficiently large star polymers, and as a result, solvent quality may be used as a polymorphic “switch” between the two forms. This suggests that star polymers can be engineered to stabilize certain crystal phases at will using experimentally accessible parameters such as temperature.

Recent work [Mahynski et al., Nat. Commun., 2014, 5, 4472] has demonstrated that the addition of long linear homopolymers thermodynamically biases crystallizing hard-sphere colloids to produce the hexagonal close-packed (HCP) polymorph over the closely related face-centered cubic (FCC) structure when the polymers and colloids are purely repulsive. In this report, we investigate the effects of thermal interactions on each crystal polymorph to explore the possibility of stabilizing the FCC crystal structure over the HCP. We find that the HCP polymorph remains at least as stable as its FCC counterpart across the entire range of interactions we explored, where interactions were quantified by the reduced second virial coefficient, −1.50 < B*2 < 1.01. This metric conveniently characterizes the crossover from entropically to energetically dominated systems at B*2 ≈ 0. While the HCP relies on its octahedral void arrangement for enhanced stability when B*2 > 0, its tetrahedral voids produce a similar effect when B*2 < 0 (i.e. when energetics dominate). Starting from this, we derive a mean-field expression for the free energy of an infinitely-dilute polymer adsorbed in the crystal phase for nonzero B*2. Our results reveal that co-solute biasing of a single polymorph can still be observed in experimentally realizable scenarios when the colloids and polymers have attractive interactions, and provide a possible explanation for the experimental finding that pure FCC crystals are elusive in these binary mixtures.

In this article, we focus on simulation methodologies to obtain the critical micelle concentration (cmc) and equilibrium distribution of aggregate sizes in dilute surfactant solutions. Even though it is now relatively easy to obtain micellar aggregates in simulations starting from a fully dispersed state, several major challenges remain. In particular, the characteristic times of micelle reorganization and transfer of monomers from micelles to free solution for most systems of practical interest exceed currently accessible molecular dynamics time scales for atomistic surfactant models in explicit solvent. In addition, it is impractical to simulate highly dilute systems near the cmc. We have demonstrated a strong dependence of the free surfactant concentration (frequently, but incorrectly, taken to represent the cmc in simulations) on the overall concentration for ionic surfactants. We have presented a theoretical framework for making the necessary extrapolations to the cmc. We find that currently available atomistic force fields systematically underpredict experimental cmc’s, pointing to the need for the development of improved models. For strongly micellizing systems that exhibit strong hysteresis, implicit-solvent grand canonical Monte Carlo simulations represent an appealing alternative to atomistic or coarse-grained, explicit-solvent simulations. We summarize an approach that can be used to obtain quantitative, transferrable effective interactions and illustrate how this grand canonical approach can be used to interpret experimental scattering results.

We use large-scale molecular dynamics simulations with a coarse-grained model to investigate the self-assembly of solvent-free grafted nanoparticles into thin free-standing films. Two important findings are highlighted. First, for appropriately chosen values of system parameters the nanoparticles spontaneously assemble into monolayer thick films. Further, the nanoparticles self-assemble into a variety of morphologies ranging from dispersed particles, finite stripes, long strings, to percolating networks. The main driving force for these morphologies is the competition between strong short-range attractions of the particle cores and long-range entropic repulsions of the grafted chains. The grafted nanoparticle systems provide practical means to realize two-length-scale systems that have been previously seen, using a simple two-dimensional model [G. Malescio and G. Pellicane, Nat. Mater., 2003, 2, 97], to generate a variety of morphologies. However, there are only relatively narrow ranges of interaction strengths and chain lengths for which anisotropic self-assembly is possible.

In this contribution, we use dissipative particle dynamics simulations to investigate the orientations of lamella-forming copolymers with two blocks of equal molecular weight confined in thin films. We employ neutral and symmetric interactions between the copolymer blocks and the walls, a situation for which contradicting observations have been made in experiments and previous theoretical studies. Our model takes into account a realistic degree of conformational asymmetry between the blocks, which stems from unequal Kuhn lengths of the constituent monomers. We perform a thorough scaling analysis to exclude finite size effects, and find, in agreement with experiments, a remarkable cascade of morphological transitions from parallel to perpendicular orientations when the film height is varied. We demonstrate that the emergence of a stable parallel configuration stems from entropic effects due to the conformational asymmetry and the confinement of the system.

Monte Carlo simulations in the Gibbs ensemble were used to obtain optimized intermolecular potential parameters to describe the phase behavior of the mixture CO2/H2O, over a range of temperatures and pressures relevant for carbon capture and sequestration processes. Commonly used fixed-point-charge force fields that include Lennard-Jones 12–6 (LJ) or exponential-6 (Exp-6) terms were used to describe CO2 and H2O intermolecular interactions. For force fields based on the LJ functional form, changes of the unlike interactions produced higher variations in the H2O-rich phase than in the CO2-rich phase. A major finding of the present study is that for these potentials, no combination of unlike interaction parameters is able to adequately represent properties of both phases. Changes to the partial charges of H2O were found to produce significant variations in both phases and are able to fit experimental data in both phases, at the cost of inaccuracies for the pure H2O properties. By contrast, for the Exp-6 case, optimization of a single parameter, the oxygen–oxygen unlike-pair interaction, was found sufficient to give accurate predictions of the solubilities in both phases while preserving accuracy in the pure component properties. These models are thus recommended for future molecular simulation studies of CO2/H2O mixtures.

We study thin films of homopolymers (PS) and monolayers of cylinder-forming diblock copolymers (PS–PHMA) under shear. To this end, we employed both experiments and computer simulations that correctly take into account hydrodynamic interactions and chain entanglements. Excellent quantitative agreement for static as well as dynamic properties in both the homopolymer and diblock copolymer cases was achieved. In particular, we found that the homopolymer thin films exhibit a distinct shear thinning behavior, which is strongly correlated with the disentanglement and shear alignment of the constituent polymer chains. For the PS–PHMA films, we show that shear can be employed to induce long-range ordering to the spontaneously self-assembled microdomains, which is required for many applications such as the fabrication of nanowire arrays. We found that the impact of chemical incompatibility on the viscosity is only minor in shear-aligned films. Once the domains were aligned, the films exhibited an almost Newtonian response to shear because the cylindrical microdomains acted as guide rails, along which the constituent copolymer chains could simply slide. Furthermore, we developed a model for predicting the onset of shear alignment based on equilibrium dynamics data, and found good agreement with our shear simulations. The employed computational method holds promise for a faster and more cost-effective route for developing custom tailored materials.Keywords: cylinder-forming diblock copolymers; homopolymers; shear; thin films

In this review, we focus on simulation studies performed to provide a molecular-level understanding of shear-induced morphological transitions and domain alignment of block copolymers in the bulk and in thin films. Block copolymers are highly relevant for many scientific and industrial applications due to their ability to form uniform domains of controllable shape at nanometer length scales. In the bulk, morphologies depend on the constituent block interactions and their volume fractions, while for thin films the surface properties and film thickness also play important roles. Spontaneously formed samples do not usually have the long-range order required in many applications. Long-range order can be induced by external guidance, for example using electric fields, surface patterns, or shear forces. In particular, shearing of both bulk systems and thin films is an excellent method for achieving long-range order, and remarkable progress has been made in experimental techniques for controlling pattern formation and transferring them to materials of interest, e.g., metal nanowires. Many simulation studies of pattern formation in copolymer systems have been performed, but simulations using explicit representations of the chains and incorporating shear have only been attempted in recent years. Because of length- and time-scale limitations, most simulations of shear alignment are performed on coarse-grained models. We survey the methods used for obtaining parameters for coarse-grained models to represent specific block copolymer systems, and the simulation algorithms utilized to impose shear. The simulations are in general agreement with experiments on the relative ease of alignment of lamellar, cylinder-forming, and sphere-forming systems, and provide insights into alignment mechanisms. Both simulations and experiments display a strong dependence of alignment quality on film thickness and substrate–polymer interactions. The review closes with a summary of unresolved questions for future research.

A new class of conductive composite materials, solvent-free ionically grafted nanoparticles, were modeled by coarse-grained molecular dynamics methods. The grafted oligomeric counterions were observed to migrate between different cores, contributing to the unique properties of the materials. We investigated the dynamics by analyzing the dependence on temperature and structural parameters of the transport properties (self-diffusion coefficients, viscosities and conductivities) and counterion migration kinetics. Temperature dependence of all properties follows the Arrhenius equation, but chain length and grafting density have distinct effects on different properties. In particular, structural effects on the diffusion coefficients are described by the Rouse model and the theory of nanoparticles diffusing in polymer solutions, viscosities are strongly influenced by clustering of cores, and conductivities are dominated by the motions of oligomeric counterions. We analyzed the migration kinetics of oligomeric counterions in a manner analogous to unimer exchange between micellar aggregates. The counterion migrations follow the “double-core” mechanism and are kinetically controlled by neighboring-core collisions.

Atomistic molecular dynamics simulations are reported over a wide range of water contents and temperatures to obtain a better understanding of the structural and transport aspects of water sorption in Nafion, a perfluorosulfonic acid membrane, under equilibrium conditions. For the short Nafion chains studied, good agreement is found between the water sorption isotherms from simulations and experiments at intermediate hydration (2 ≲ λ ≲ 7, where λ is the number of water molecules per sulfonate group), suggesting that, in that range, the isotherm is insensitive to effects of polymer chain relaxation. If polymer chain relaxation were important for water sorption at these conditions, then the water uptake of experimental membranes, which contain very long chains, might be far from equilibrium, making it difficult to obtain agreement with equilibrated, short-chain simulations. At λ ≲ 7, strong water–sulfonate interactions, rather than chain relaxation, may control water sorption, despite the fact that chain relaxation time increases dramatically with decreasing hydration. Evidence for strong water–sulfonate interactions is found in the observation that sulfonate groups share water molecules in their first coordination shells at λ ≲ 7. Strong water–sulfonate interactions are also observed to influence transport properties like water diffusivity, and are as important for understanding these transport properties as larger-scale phenomena like morphology and percolation transitions. Finally, at low humidity (λ ≈ 1–2), rod-like hydrophilic clusters are observed, as well as a mechanism of water diffusion that differs qualitatively from that of water at high hydration (λ ≳ 7) and in the bulk, pure-component phase.

The shear alignment of lamellae-forming diblock copolymers in thin films is examined using coarse-grained Langevin dynamics simulations. We investigate how lamellar orientation is affected by the shear rate, and interactions between polymer segments and the confining surfaces. For neutral confining surfaces, we find that above a critical stress, lamellae melt and reform in the direction of the shear (perpendicular to the walls), irrespective of their initial orientation. The time needed for reorientation was four times longer when the initial configuration was parallel to the walls, relative to lamellae initially oriented perpendicular to both the walls and the shear direction. When the surface–block interactions become non-neutral, there is critical interaction strength above which the perpendicular orientation is no longer favored, because of enthalpic contributions of one block preferentially wetting the non-neutral surface. The formation of parallel lamellae in films under shear requires a smaller degree of preferential interfacial interactions if both confining surfaces are non-neutral. The film thickness affects the rate of lamellar reorientation as well as the lamellar periodicity. Overall, our results are in good agreement with experimental findings and provide insights into how to use shear to control alignment of lamellar structures in thin films.

Due to the relatively long time scales inherent to ionic surfactant self-assembly (>μs), an aggressive computational approach is needed to obtain converged data on micellar solutions. This work presents a study of micellization using a coarse-grained (CG) model of aqueous ionic surfactants in replicated molecular dynamics (MD) simulations run on graphics processing unit hardware. The performance of our implementation of the CG model with electrostatics into the HOOMD-Blue GPU-accelerated MD software package is comparable to that of a modest sized cluster running a highly optimized parallel CPU code. From 0.36 ms of cumulative trajectory data, we are able to predict equilibrium thermodynamic and morphological properties of ionic surfactant micellar solutions. Estimating the critical micelle concentrations (CMC) from the free monomer (ρ1) and premicellar concentrations obtained from simulations of sodium hexyl sulfate (S6S, CMC of 460 ± 6 mM) at high (1 M) concentration, a value in good agreement with experimental results is obtained; however, the same method applied to simulations of sodium nonyl sulfate (S9S, ρ1 of 2.4 ± 0.01 mM) and sodium dodecyl sulfate (SDS, ρ1 of 0.02 ± 0.01 mM) at the same total concentration systematically underestimates the CMCs. An alternative method for calculating the CMC is presented, where the free monomer concentration computed from high concentration CG-MD data is used as the input to a simple theoretical model which can be used to extrapolate to a more accurate prediction of the CMC. Better agreement between the empirical and predicted CMC is obtained from this theory for S9S (28.7 ± 0.3 mM) and SDS (3.32 ± 0.04 mM), though the CMC for S6S is slightly underestimated (304 ± 3 mM). We also present statistically converged morphological data, including aggregation number distributions and the principal components of the gyration tensor. This data suggest a transition from spherical micelles to rod-like at a specific aggregation number, which increases with increasing hydrocarbon length.

Molecular dynamics simulations have been used to study the micellization behavior of atomistic models for sodium alkyl sulfates in explicit water. A major finding of the present work is the observation of a strong dependence of free surfactant concentration on overall surfactant concentration, that has not been reported previously and that is key to comparing simulation results for the critical micelle concentration (CMC) to experimental data. The CMC and aggregate size distributions were obtained for alkyl tail lengths from six to nine at temperatures from 268 to 363 K, from 400 ns simulations covering a number of surfactant and water model combinations. The free surfactant concentration is much lower than the critical micelle concentration for strongly micellizing systems at the relatively high concentrations accessible by simulations. Thus, counterion association must be accounted for in determining the CMC from the raw simulation data. Simulation results are in qualitative agreement with experimental trends for aggregate size and CMC as functions of alkyl tail length and temperature.

A molecular model of silica nanoparticles grafted with poly(ethylene oxide) oligomers has been developed for predicting the transport properties of nanoparticle organic-hybrid materials (NOHMs). Ungrafted silica nanoparticles in a medium of poly(ethylene oxide) oligomers were also simulated to clarify the effect of grafting on the dynamics of nanoparticles and chains. The model approximates nanoparticles as solid spheres and uses a united-atom representation for chains, including torsional and bond-bending interactions. The calculated viscosities from Green–Kubo relationships and temperature extrapolation are of the same order of magnitude as experimental data but show a smaller activation energy relative to real NOHMs systems. Grafted systems have higher viscosities, smaller diffusion coefficients, and slower chain dynamics than the ungrafted ones at high temperatures. At lower temperatures, grafted systems exhibit faster dynamics for both nanoparticles and chains relative to ungrafted systems, because of lower aggregation of particles and enhanced correlations between nanoparticles and chains. This agrees with the experimental observation that NOHMs have liquidlike behavior in the absence of a solvent. For both grafted and ungrafted systems at low temperatures, increasing chain length reduces the volume fraction of nanoparticles and accelerates the dynamics. However, at high temperatures, longer chains slow down nanoparticle diffusion. From the Stokes–Einstein relationship, it was determined that the coarse-grained treatment of nanoparticles leads to slip on the nanoparticle surfaces. Grafted systems obey the Stokes–Einstein relationship over the temperature range simulated, but ungrafted systems display deviations from it.

Shear-induced sphere-to-cylinder transitions in diblock copolymer thin films have been studied using coarse-grained Langevin dynamics simulations. Parameters of the coarse-grained model were chosen to represent a polystyrene–polyisoprene copolymer with molecular weights of the blocks equal to 68 and 12 kg/mol, respectively, matching the system studied experimentally by Hong et al. [Soft Matter2009, 5, 1687]. At zero-shear conditions and below the order–disorder transition temperature, thin films form a monolayer or bilayer of spheres. The minority block has higher affinity for the confining surfaces, thus forming wetting layers whose chains interpenetrate those forming the microdomain layer(s). Once a shear field is applied and above a critical shear rate, the spheres elongate and merge with their neighbors to form cylinders. We find that shear-induced cylinder formation is closely related to stretching of individual diblock chains. Our simulations suggest that a higher stress is required to achieve the sphere-to-cylinder transition in monolayer versus bilayer thin films because the wetting layers transfer momentum into the film by stretching the chains, which in turn causes higher shear stress for a given surface velocity. This observation is in agreement with experimental findings. In addition to the effects of shear, the impact of temperature was investigated with respect to chain stretching and the formation of cylinders under shear.

We have examined the influence of coarse-graining polymer chains in dissipative particle dynamics simulations on both phase behavior and aggregation dynamics. Our coarse-graining approach involves replacing several beads of a chain with a single bead of larger size and mass, and extends a framework recently developed by Backer et al. [J. Chem. Phys. 2005, 123, 114905]. The parameters governing the interactions between particles are determined on the basis of conserving the number of interactions per particle, mass density, pressure, and shear viscosity of the original reference system. Phase diagrams of coarse-grained polymer/solvent systems are conserved, aside from a simple vertical shift in the direction of a12, the repulsion parameter between solvent and polymer particles. The dynamics of the aggregation process are well conserved upon coarse-graining in a diblock copolymer/solvent system. We find that the invariance of the phase diagrams and aggregation dynamics occurs when the molecular volume of each species is conserved upon coarse-graining. However, this suggests that our coarse-graining approach cannot be applied to a monomeric solvent, in which case each solvent molecule already has the minimum number of degrees of freedom. Our results suggest that considerable freedom exists for selection of mapping ratios from real monomer units to model beads in dissipative particle dynamics simulations of chains in a solvent.

We have investigated micellization properties of surfactants using a recently developed implicit-solvent model and grand canonical Monte Carlo simulations. The original model had been parametrized for ionic surfactants at a single temperature; it is extended here to aqueous solutions of nonionic surfactants and given an explicit temperature dependence. Specifically, we have developed an implicit-solvent model of polyethylene glycol (PEG) surfactants and obtained the critical micelle concentrations (cmc’s) and micellar aggregation numbers at low surfactant loadings. Various combinations of ethoxy and hydrocarbon tail segments were investigated in order to explore the predictive capabilities of the model. For the temperature dependence of the micellization properties, we have utilized thermodynamic approaches to quantify the hydrophobic attraction at temperatures ranging from 280 to 365 K. The temperature dependence of the cmc and the aggregate sizes were obtained for various ionic and nonionic surfactants, specifically sodium dodecyl sulfate, dodecyltrimethylammonium bromide and chloride, and PEG surfactants. For all systems studied, the model yields cmc and aggregation sizes that are in near-quantitative agreement with experimental results.

The behavior of thin films of diblock copolymers under shear has been studied using coarse-grained Langevin dynamics simulations. The morphologies the film exhibits are examined as functions of composition, segregation strength, and the strength of the shear field. Below the order-disorder transition (ODT) the film generates a rich variety of structures corresponding to a monolayer of compressed micelles. Once a shear field is applied and above a critical shear rate, the system self-assembles into cylindrical micelles with orientation parallel to the shear direction, in agreement to experimental observations. In addition to formation of cylinders parallel to the sheared direction, we have identified the conditions under which cylinders under the influence of shear flow adopt an orientation perpendicular to the shear flow. The segregation strength is the main parameter that triggers the order-order steady state orientation transition.

Diffusivities and viscosities of poly(ethylene oxide) (PEO) oligomer melts with 1 to 12 repeat units have been obtained from equilibrium molecular dynamics simulations using the TraPPE-UA force field. The simulations generated diffusion coefficients with high accuracy for all of the molar masses studied, but the statistical uncertainties in the viscosity calculations were significantly larger for longer chains. There is good agreement of the calculated viscosities and densities with available experimental data, and thus, the simulations can be used to bridge gaps in the data and for extrapolations with respect to chain length, temperature, and pressure. We explored the convergence characteristics of the Green−Kubo formulas for different chain lengths and propose minimal production times required for convergence of the transport properties. The chain-length dependence of the transport properties suggests that neither Rouse nor reptation models are applicable in the short-chain regime investigated.

We employ molecular dynamics simulations to study the solubility and molecular conformations of n-alkane chains in water. We find nearly exponential decrease in solubility with carbon number up to n-eicosane (C20), and excellent agreement with experiment up to n-dodecane (C12). We detect no sharp break in the dependence of the solubility upon carbon number. A free energy landscape analysis of the chain conformations reveals remarkable similarities between the ideal gas and solvated phase landscapes, suggesting that solvated chain conformations are driven primarily by ideal gas statistics. We find no evidence for hydrophobic collapse of n-alkane chains shorter than n-eicosane (C20). The primary effect of the solvent is the appearance of a barrier on the order kBT, not present in the ideal gas, between the free energy basins corresponding to compact and extended chain conformations, and destabilization of the most extended conformations. Our findings are robust to nontrivial modification of the potential model, suggesting that the absence of strong solvent effects on the free energy landscapes is fundamental to relatively short (≤20-mer) chains composed of small hydrophobic monomers, and does not depend on the precise nature of the chain interactions.

We have used atomistic simulations to study the role of electrostatic screening and charge correlation effects in self-assembly processes of ionic surfactants into micelles. Specifically, we employed grand canonical Monte Carlo simulations to investigate the critical micelle concentration (cmc), aggregation number, and micellar shape in the presence of explicit sodium chloride (NaCl). The two systems investigated are cationic dodecyltrimethylammonium chloride (DTAC) and anionic sodium dodecyl sulfate (SDS) surfactants. Our explicit-salt results, obtained from a previously developed potential model with no further adjustment of its parameters, are in good agreement with experimental data for structural and thermodynamic micellar properties. We illustrate the importance of ion correlation effects by comparing these results with a Yukawa-type surfactant model that incorporates electrostatic screening implicitly. While the effect of salt on the cmc is well-reproduced even with the implicit Yukawa model, the aggregate size predictions deviate significantly from experimental observations at low salt concentrations. We attribute this discrepancy to the neglect of ion correlations in the implicit-salt model. At higher salt concentrations, we find reasonable agreement of the Yukawa model with experimental data. The crossover from low to high salt concentrations is reached when the electrostatic screening length becomes comparable to the headgroup size.

We propose a method for parametrization of implicit solvent models for the simulation of the self-assembly of ionic surfactants into micelles. The parametrization is carried out in two steps. The first step involves atomistic molecular dynamics simulations of headgroups and counterions with explicit solvent to determine structural properties. An implicit solvent model of the headgroup/counterion system is obtained by matching structural quantities between explicit solvent and implicit solvent systems. In the second step, we identify the solvophobic attractions between the tail beads. We determine the solvophobic parameters using grand canonical Monte Carlo simulations with histogram reweighting techniques. The matching objective for the identification of solvophobic attractions is the critical micelle concentration (cmc). We choose sodium dodecyl sulfate as the reference system. On the basis of hydrophobic parameters obtained from this particular model, we study specific ion effects (lithium and potassium instead of sodium) as well as the effect of cationic headgroups (dodecyltrimethylammonium bromide/chloride). Furthermore, the chain length dependence of micellization properties is investigated for sodium alkyl sulfate, with alkyl lengths between 6 and 14. All cases considered give results in broad agreement with experimental data, confirming the transferability of parameters and the generality of the approach.

We present a coarse-grained, implicit solvent model for polystyrene-b-poly(ethylene oxide) in aqueous solution and study its assembly kinetics using Brownian dynamics simulations. The polymer is modeled as a chain of freely jointed beads interacting through effective potentials. Coarse-grained force field parameters are determined by matching experimental thermodynamic quantities including radius of gyration, second virial coefficient, aggregation number, and critical micelle concentration. We investigate the influence of cooling rate (analogous to the rate of solvent quality change in rapid precipitations), polymer concentration, and friction coefficient on the assembly kinetics and compare simulation results to flash nanoprecipitation experiments. We find that assembly kinetics show a linear scaling relation with inverse friction coefficient when the friction coefficient is larger than 1. When the cooling time is less than the characteristic micellization time, stable kinetically arrested clusters are obtained; otherwise, close-to-equilibrium micelles are formed. The characteristic micellization time is estimated to be only 3−6 ms, in contrast to 30−40 ms previously determined in experiments. We suggest that previous experiments probed the formation of micellar clusters while simulations in this work studied the kinetics of a single micelle assembled from free polymer chains.

In this communication, we investigate the use of grand canonical Monte Carlo simulations to estimate the second virial coefficient. Histogram reweighting calculations were performed to collect two-dimensional histogram for the number of particles and the energy to evaluate the density and pressure at low density. The histogram collected is reweighted for a series of chemical potentials to accumulate pressure, density, and temperature data along the isotherm to obtain the second virial coefficient. While exact calculation of second virial coefficients for arbitrary systems (e.g. mixtures and polyatomic molecules) involves multidimensional integrals, grand canonical simulations can, in principle, provide equation of state information from simulations at appropriately low densities. Our results indicate that the methodology yields reasonable estimates of the second virial coefficient. Agreement to analytical and experimental values is within a few percent for a variety of model and real fluids. There are however practical accuracy issues associated with this method. We discuss why this approach fails to find more precise values of the second virial coefficient even when long runs are used.