Monte Carlo simulations of amphiphilic nanoparticle self-assembly

Role of Entropy in Colloidal Self-Assembly

Entropy plays a key role in the self-assembly of colloidal particles. Specifically, in the case of hard particles, which do not interact or overlap with each other during the process of self-assembly, the free energy is minimized due to an increase in the entropy of the system. Understanding the contribution of entropy and engineering it is increasingly becoming central to modern colloidal self-assembly research, because the entropy serves as a guide to design a wide variety of self-assembled structures for many technological and biomedical applications. In this work, we highlight the importance of entropy in different theoretical and experimental self-assembly studies. We discuss the role of shape entropy and depletion interactions in colloidal self-assembly. We also highlight the effect of entropy in the formation of open and closed crystalline structures, as well as describe recent advances in engineering entropy to achieve targeted self-assembled structures.

Entropic colloidal crystallization pathways via fluid-fluid transitions and multidimensional prenucleation motifs

Complex crystallization pathways are common in protein crystallization, tetrahedrally coordinated systems, and biomineralization, where single or multiple precursors temporarily appear before the formation of the crystal. The emergence of precursors is often explained by a unique property of the system, such as short-range attraction, directional bonding, or ion association. But, structural characteristics of the prenucleation phases found in multistep crystallization remain unclear, and models are needed for testing and expanding the understanding of fluid-to-solid ordering pathways. Here, we report 3 instances of 2-step crystallization of hard-particle fluids. Crystallization in these systems proceeds via a high-density precursor fluid phase with prenucleation motifs in the form of clusters, fibers and layers, and networks, respectively. The density and diffusivity change across the fluid-fluid phase transition increases with motif dimension. We observe crystal nucleation to be catalyzed by the interface between the 2 fluid phases. The crystals that form are complex, including, notably, a crystal with 432 particles in the cubic unit cell. Our results establish the existence of complex crystallization pathways in entropic systems and reveal prenucleation motifs of various dimensions.

Predicting low-temperature free energy landscapes with flat-histogram Monte Carlo methods

We present a method for predicting the free energy landscape of fluids at low temperatures from flat-histogram grand canonical Monte Carlo simulations performed at higher ones. We illustrate our approach for both pure and multicomponent systems using two different sampling methods as a demonstration. This allows us to predict the thermodynamic behavior of systems which undergo both first order and continuous phase transitions upon cooling using simulations performed only at higher temperatures. After surveying a variety of different systems, we identify a range of temperature differences over which the extrapolation of high temperature simulations tends to quantitatively predict the thermodynamic properties of fluids at lower ones. Beyond this range, extrapolation still provides a reasonably well-informed estimate of the free energy landscape; this prediction then requires less computational effort to refine with an additional simulation at the desired temperature than reconstruction of the surface without any initial estimate. In either case, this method significantly increases the computational efficiency of these flat-histogram methods when investigating thermodynamic properties of fluids over a wide range of temperatures. For example, we demonstrate how a binary fluid phase diagram may be quantitatively predicted for many temperatures using only information obtained from a single supercritical state.

Polymer directed aggregation and dispersion of anisotropic nanoparticles

The aggregation and dispersion of two anisotropic nanoparticles (NPs), cubes and tetrahedrons, in a polymer matrix are studied in this work using coarse-grained molecular dynamics simulations. We present the phase diagrams of NP-polymer composites, depicting microscopically phase-separated, dispersed, and bridged cubes and tetrahedrons in a polymer matrix, which depend on the interaction between the NPs and polymer (εnp), along with the NPs' volume fraction (ϕ). The microscopic phase separation occurs at very low εnp, where NPs self-organize into multidimensional structures, depending on ϕ. In particular, for tetrahedrons, a cross-over from an ordered spherical aggregate to a disordered sheet-like aggregate is observed with increasing ϕ. In the case of cubes, a transition from cubic array → square column → square array (sheet) is identified with increasing ϕ. The clusters of NPs are characterized by their asphericity and principal radii of gyration. The free energy profile for a structured assembly is estimated, which clearly shows that the successful assembly of NPs is energetically favorable at a lower temperature. However, there exists an energy barrier for the successful assembly of all the NPs in the system. At intermediate εnp, a transition from a clustered state to a state comprising dispersed cubes and tetrahedrons in a polymer matrix is observed. At higher εnp, a further transition takes place, where gas-like dispersed NPs form a liquid-like aggregate via polymer layers. Therefore, the findings in this work illustrate that the effective interaction between anisotropic NPs in a polymer matrix is very diverse, which can generate multidimensional structured assemblies, with the disordered clustering, dispersion, and bridging-induced aggregation of NPs.

Aggregation of polymer-grafted nanoparticles in good solvents: a hierarchical modeling method

Brownian dynamics simulations are carried out to study the aggregation behavior of polymer-grafted nanoparticles (NPs) in good solvents by using the coarse-grained model derived from the all-atom force field, according to the hierarchical modeling strategy, and here PEG-grafted gold nanoparticles (GNPs) were taken as an example. Generally, grafting PEG to the surface of GNPs is to protect them from aggregation in the solution. However, our results reveal that PEG-grafted GNPs may also aggregate when concentration increases. Our simulations indicate that there exists a critical aggregating concentration (CAC), beyond which the PEG-grafted GNPs will aggregate. We further check the effects of grafting density and the length of grafted chains on the aggregation behavior of the grafted GNPs, and find that there exists an optimized length of grafted chain, at which the system has the maximal CAC. Furthermore, the aggregate size of self-assembled mesostructures formed by the grafted GNPs increases with the concentration. Interestingly, it is observed that the aggregation favors to form linear gold nanowires rather than compact gold nanoclusters, and the corresponding mechanism is also addressed. It is expected that this work would provide useful information for the fabrication of metal nanowires and the surface modification of metal nanoparticles.

Block copolymer mimetic self-assembly of inorganic nanoparticles

Emerging strategies for assembling inorganic nanoparticles into ensembles with multiscale organization are establishing a new paradigm for the synthesis of devices and functional materials with applications ranging from drug delivery to photonics. In this work, the solution self-assembly of amphiphilic ionic block copolymers into morphologically tunable aggregates provides the inspiration and design strategy for nanoparticle building blocks with the essential chemical and conformational features of ionic block copolymer chains in aqueous media. We produce inorganic nanoparticles with surface-tethered mixed brushes of hydrophobic and chargeable hydrophilic chains which self-assemble in polar solvent mixtures into unprecedented hierarchical superstructures analogous to known ionic block copolymer aggregates but with complex organizations of nanoparticles in three dimensions. Electrostatic repulsion between hydrophilic chains forces nonequilibrium pathways to variable kinetic structures with internal lamellar organization of nanoparticles; however, decreasing electrostatic interactions through salt or acid addition allows tunable equilibrium assemblies, including supermicelles and bilayer vesicles of nanoparticles, to be formed. The application of ionic block copolymer assembly principles and mechanisms opens a new chemical toolbox for the organization of nanoparticles into functional assemblies.

An artificial intelligence approach for modeling molecular self-assembly: agent-based simulations of rigid molecules

Agent-based simulations are rule-based models traditionally used for the simulations of complex systems. In this paper, an algorithm based on the concept of agent-based simulations is developed to predict the lowest energy packing of a set of identical rigid molecules. The agents are identified with rigid portions of the system under investigation, and they evolve following a set of rules designed to drive the system toward the lowest energy minimum. The algorithm is compared with a conventional Metropolis Monte Carlo algorithm, and it is applied on a large set of representative models of molecules. For all the systems studied, the agent-based method consistently finds a significantly lower energy minima than the Monte Carlo algorithm because the system evolution includes elements of adaptation (new configurations induce new types of moves) and learning (past successful choices are repeated).

Statistical thermodynamics of biomembranes

An overview of the major issues involved in the statistical thermodynamic treatment of phospholipid membranes at the atomistic level is summarized: thermodynamic ensembles, initial configuration (or the physical system being modeled), force field representation as well as the representation of long-range interactions. This is followed by a description of the various ways that the simulated ensembles can be analyzed: area of the lipid, mass density profiles, radial distribution functions (RDFs), water orientation profile, deuterium order parameter, free energy profiles and void (pore) formation; with particular focus on the results obtained from our recent molecular dynamic (MD) simulations of phospholipids interacting with dimethylsulfoxide (Me(2)SO), a commonly used cryoprotective agent (CPA).