Regulating phase behavior of nanoparticle assemblies through engineering of DNA-mediated isotropic interactions.

Self-assembly of isotropically interacting particles into desired crystal structures could allow for creating designed functional materials via simple synthetic means. However, the ability to use isotropic particles to assemble different crystal types remains challenging, especially for generating low-coordinated crystal structures. Here, we demonstrate that isotropic pairwise interparticle interactions can be rationally tuned through the design of DNA shells in a range that allows transition from common, high-coordinated FCC-CuAu and BCC-CsCl lattices, to more exotic symmetries for spherical particles such as the SC-NaCl lattice and to low-coordinated crystal structures (i.e., cubic diamond, open honeycomb). The combination of computational and experimental approaches reveals such a design strategy using DNA-functionalized nanoparticles and successfully demonstrates the realization of BCC-CsCl, SC-NaCl, and a weakly ordered cubic diamond phase. The study reveals the phase behavior of isotropic nanoparticles for DNA-shell tunable interaction, which, due to the ease of synthesis is promising for the practical realization of non-close-packed lattices.

Diffusion of knots in nanochannel-confined DNA molecules.

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an "opening up process," wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.

Deep learning for characterizing the self-assembly of three-dimensional colloidal systems.

Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems' stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. We first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.

Grand canonical inverse design of multicomponent colloidal crystals.

Inverse design methods are powerful computational approaches for creating colloidal systems which self-assemble into a target morphology by reverse engineering the Hamiltonian of the system. Despite this, these optimization procedures tend to yield Hamiltonians which are too complex to be experimentally realized. An alternative route to complex structures involves the use of several different components, however, conventional inverse design methods do not explicitly account for the possibility of phase separation into compositionally distinct structures. Here, we present an inverse design scheme for multicomponent colloidal systems by combining active learning with a method to directly compute their ground state phase diagrams. This explicitly accounts for phase separation and can locate stable regions of Hamiltonian parameter space which grid-based surveys are prone to miss. Using this we design low-density, binary structures with Lennard-Jones-like pairwise interactions that are simpler than in the single component case and potentially realizable in an experimental setting. This reinforces the concept that ground states of simple, multicomponent systems might be rich with previously unappreciated diversity, enabling the assembly of non-trivial structures with only few simple components instead of a single complex one.

Coarse-grained model of nanoscale segregation, water diffusion, and proton transport in Nafion membranes.

We present a coarse-grained model of the acid form of Nafion membrane that explicitly includes proton transport. This model is based on a soft-core bead representation of the polymer implemented into the dissipative particle dynamics (DPD) simulation framework. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with water beads. Morse bond formation and breakup artificially mimics the Grotthuss hopping mechanism of proton transport. The proposed DPD model is parameterized to account for the specifics of the conformations and flexibility of the Nafion backbone and sidechains; it treats electrostatic interactions in the smeared charge approximation. The simulation results qualitatively, and in many respects quantitatively, predict the specifics of nanoscale segregation in the hydrated Nafion membrane into hydrophobic and hydrophilic subphases, water diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from a collection of isolated water clusters to a 3D network of pores filled with water embedded in the hydrophobic matrix. The segregated morphology is characterized in terms of the pore size distribution with the average size growing with hydration from ∼1 to ∼4 nm. Comparison of the predicted water diffusivity with the experimental data taken from different sources shows good agreement at high and moderate hydration and substantial deviation at low hydration, around and below the percolation threshold. This discrepancy is attributed to the dynamic percolation effects of formation and rupture of merging bridges between the water clusters, which become progressively important at low hydration, when the coarse-grained model is unable to mimic the fine structure of water network that includes singe molecule bridges. Selected simulations of water diffusion are performed for the alkali metal substituted membrane which demonstrate the effects of the counter-ions on membrane self-assembly and transport. The hydration dependence of the proton diffusivity reproduces semi-qualitatively the trend of the diverse experimental data, showing a sharp decrease around the percolation threshold. Overall, the proposed model opens up an opportunity to study self-assembly and water and proton transport in polyelectrolytes using computationally efficient DPD simulations, and, with further refinement, it may become a practical tool for theory informed design and optimization of perm-selective and ion-conducting membranes with improved properties.

A Deep Learning Framework Discovers Compositional Order and Self-Assembly Pathways in Binary Colloidal Mixtures.

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of r A/r B = 0.8 to r A/r B = 0.95) can promote the self-assembly of defect-free BSLs much more effectively than systems of identically sized particles, as nearly defect-free BCC-CsCl, FCC-CuAu, and IrV crystals are observed in the former case. The framework additionally reveals that size-disparate colloidal mixtures can undergo nonclassical nucleation pathways where BSLs evolve from dense amorphous precursors, instead of directly nucleating from dilute solution. These findings illustrate that the presented characterization framework can assist in enhancing mechanistic understanding of the self-assembly of binary colloidal mixtures, which in turn can pave the way for engineering the growth of defect-free BSLs.

Temperature-Controlled Reconfigurable Nanoparticle Binary Superlattices.

The presence of diffusionless transformations during the assembly of DNA-functionalized particles (DFPs) is highly significant in designing reconfigurable materials whose structure and functional properties are tunable with controllable variables. In this paper, we first use a variety of computational models and techniques (including free energy methods) to address the nature of such transformations between face-centered cubic (FCC) and body-centered cubic (BCC) structures in a three-dimensional binary system of multiflavored DFPs. We find that the structural rearrangements between BCC and FCC structures are thermodynamically reversible and dependent on crystallite size. Smaller nuclei favor nonclose-packed BCC structures, whereas close-packed FCC structures are observed during the growth stage once the crystallite size exceeds a threshold value. Importantly, we show that a similar reversible transformation between BCC/FCC structures can be driven by changing temperature without introducing additional solution components, highlighting the feasibility of creating reconfigurable crystalline materials. Lastly, we validate this thermally responsive switching behavior in a DFP system with explicit DNA (un)hybridization, demonstrating our findings' applicability to experimentally realizable systems.

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.

Self-Assembly of DNA-Functionalized Nanoparticles Guided by Binding Kinetics.

We use a coarse-grained model of DNA-functionalized particles (DFPs) to understand the role of DNA strand length on their self-assembly. We find that the increasing strand length for a given particle size decreases the propensity to form ordered crystalline assemblies within the simulation time. Instead, disordered structures form when the strand length exceeds a certain threshold, consistent with the previous experiments. Analysis of the simulation data based on a pair of DFPs suggests weakening interparticle interactions with increasing strand length, thereby shifting the suitable assembly conditions to lower temperatures. We find that DNA (un)hybridization kinetics at these lower temperatures becomes significantly slower, preventing systems with longer DNA strands from crystallizing successfully. We suggest that a suitable strategy to overcome this kinetic barrier is to enhance interparticle interactions for DFPs with longer DNA strands, which is achieved by increasing the DNA grafting density. We directly test this hypothesis and show successful crystallization within the simulation time for DFPs with longer strands with higher grafting densities. Our results highlight the power of computational modeling in elucidating the fundamental design principles and guiding the assembly of nanoparticles to form complex nanostructures in cases where experiments alone have not been able to do so.

Size-dependent thermodynamic structural selection in colloidal crystallization.

Nucleation and growth of crystalline phases play an important role in a variety of physical phenomena, ranging from freezing of liquids to assembly of colloidal particles. Understanding these processes in the context of colloidal crystallization is of great importance for predicting and controlling the structures produced. In many systems, crystallites that nucleate have structures differing from those expected from bulk equilibrium thermodynamic considerations, and this is often attributed to kinetic effects. In this work, we consider the self-assembly of a binary mixture of colloids in two dimensions, which exhibits a structural transformation from a non-close-packed to a close-packed lattice during crystal growth. We show that this transformation is thermodynamically driven, resulting from size dependence of the relative free energy between the two structures. We demonstrate that structural selection can be entirely thermodynamic, in contrast to previously considered effects involving growth kinetics or interaction with the surrounding fluid phase.

Parametrization of Chain Molecules in Dissipative Particle Dynamics.

This paper presents a consistent strategy for parametrization of coarse-grained models of chain molecules in dissipative particle dynamics (DPD), where the soft-core DPD interaction parameters are fitted to the activities in solutions of reference compounds that represent different fragments of target molecules. The intercomponent parameters are matched either to the infinite dilution activity coefficients in binary solutions or to the solvent activity in polymer solutions. The respective calibration relationships between activity and intercomponent interaction parameter are constructed from the results of Monte Carlo simulation of the coarse-grained solutions of reference compounds. The chain conformation is controlled by the near neighbor and second neighbor bond potentials, which are parametrized by fitting the intramolecular radial distribution functions of the coarse-grained chains to the respective atomistic molecular dynamics simulations. The consistency, accuracy, and transferability of the proposed parametrization strategy is demonstrated drawing on the example of nonionic surfactants of the poly(ethylene oxide) alkyl ether (CnEm) family. The lengths of tail and head sequences are varied (n = 8-12 and m = 3-9), so that the critical micelle concentration ranges from 10 to 0.1 mM. The surfactants are modeled at different coarse-graining levels using DPD beads of different diameters. We found consistent agreement with experimental data for the critical micelle concentration and aggregation number, especially for surfactants with relatively long hydrophilic segments. Depending on the system, we observed surfactant aggregation into spheroidal, elongated, or core-shell micelles, as well as into irregular agglomerates. Using the models at different coarse-graining levels for the same molecules, we found that the smaller the bead size the better is agreement with experimental data.

Modeling Aggregation of Ionic Surfactants Using a Smeared Charge Approximation in Dissipative Particle Dynamics Simulations.

Using dissipative particle dynamics (DPD) simulations, we explore the specifics of micellization in the solutions of anionic and cationic surfactants and their mixtures. Anionic surfactant sodium dodecyl sulfate (SDS) and cationic surfactant cetyltrimethylammonium bromide (CTAB) are chosen as characteristic examples. Coarse-grained models of the surfactants are constructed and parameterized using a combination of atomistic molecular simulation and infinite dilution activity coefficient calibration. Electrostatic interactions of charged beads are treated using a smeared charge approximation: the surfactant heads and dissociated counterions are modeled as beads with charges distributed around the bead center in an implicit dielectric medium. The proposed models semiquantitatively describe self-assembly in solutions of SDS and CTAB at various surfactant concentrations and molarities of added electrolyte. In particular, the model predicts a decline in the free surfactant concentration with the increase of the total surfactant loading, as well as characteristic aggregation transitions in single-component surfactant solutions caused by the addition of salt. The calculated values of the critical micelle concentration reasonably agree with experimental observations. Modeling of catanionic SDS-CTAB mixtures show consecutive transitions to worm-like micelles and then to vesicles caused by the addition of CTAB to micellar solution of SDS.