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We simultaneously designed the porosity and plane symmetry of self-assembling colloidal films by using isohedral tiles to determine the location and shape of enthalpically interacting surface patches on motifs being functionalized. The symmetries of both the tile and motif determine the plane symmetry group of the final assembly. Previous work has either ignored symmetry considerations altogether or accounted for only the tile's properties, applicable only when the motif is asymmetric; this approach provides a complete account and enables the design of symmetric colloids using this tile-based approach, which are often more practical to manufacture. We present the methodology, based on the type of the tile, and provide computational tools that enable the automatic classification of all tiles for a given motif and the optimization of the tile to fit the motif, sometimes referred to as "Escherization".

Marine environmental monitoring efforts often rely on the bioaccumulation of persistent anthropogenic contaminants in organisms to create a spatiotemporal record of the ecosystem. Intercorrelation results from the origin, uptake, and transport of these contaminants throughout the ecosystem and may be affected by organism-specific processes such as biotransformation. Here, we explore trends that machine learning tools reveal about a large, recently released environmental chemistry data set of common anthropogenic pollutants measured in the eggs of five seabird species from the North Pacific Ocean. We modeled these data with a variety of machine learning approaches and found models that could accurately determine a range of taxonomic and spatiotemporal trends. We illustrate a general workflow and set of analysis tools that can be used to identify interpretable models which perform nearly as well as state-of-the-art "black boxes." For example, we found shallow decision trees that could resolve genus with greater than 96% accuracy using as few as two analytes and a k -nearest neighbor classifier that could resolve species differences with more than 94% accuracy using only five analytes. The benefits of interpretability outweighed the marginally improved accuracy of more complex models. This demonstrates how machine learning may be used to discover rational, quantitative trends in these systems.

We describe a method for deriving surface functionalization patterns for colloidal systems that can induce self-assembly into any chosen periodic symmetry at a planar interface. The result is a sequence of letters, s ∈ {A,T,C,G}, or a gene, that describes the perimeter of the colloidal object and programs its self-assembly. This represents a genome that is finite and can be exhaustively enumerated. These genes derive from symmetry, which may be topologically represented by two-dimensional parabolic orbifolds; since these orbifolds are surfaces that may be derived from first principles, this represents an ab initio route to colloid functionality. The genes are human readable and can be employed to easily design colloidal units. We employ a biological (genetic) analogy to demonstrate this and illustrate their connection to the designs of Maurits Cornelis (M. C.) Escher.

We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.

Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density.

The accurate prediction of stable crystalline phases is a long-standing problem encountered in the study of conventional atomic and molecular solids as well as soft materials. One possible solution involves enumerating a reasonable set of candidate structures and then screening them to identify the one(s) with the lowest (free) energy. Candidate structures in this set can also serve as starting points for other routines, such as genetic algorithms, which search via optimization. Here, we present a framework for crystal structure enumeration of two-dimensional systems that utilizes a combination of symmetry- and stoichiometry-imposed constraints to compute valid configurations of particles that tile Euclidean space. With mild assumptions, this produces a computationally tractable total number of proposed candidates, enabling multicomponent systems to be screened by direct enumeration of possible crystalline ground states. The python code that enables these calculations is available at https://github.com/usnistgov/PACCS.

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.

The phenomenon of dynamic arrest, more commonly referred to as gel and glass formation, originates as particle motion slows significantly. Current understanding of gels and glasses stems primarily from dispersions of spherical particles, but much less is known about how particle shape affects dynamic arrest transitions. To better understand the effects of particle shape anisotropy on gel and glass formation, we systematically measure the rheology, particle dynamics, and static microstructure of thermoreversible colloidal dispersions of adhesive hard rods (AHR). First, the dynamic arrest transitions are mapped as a function of temperature T, aspect ratio L/D≈ 3 to 7, and volume fraction φ≈ 0.1 to 0.5. The critical gel temperature T gel and glass volume fraction φ g are determined from the particle dynamics and rheology. Second, an effective orientation-averaged, short-range attraction between rods is quantified from small-angle scattering measurements and characterized by a reduced temperature τ. Similar τ is found at low rod concentrations, indicating that rod gelation occurs at similar effective attraction strength independent of L/D. Monte Carlo simulations reveal a similar convergence in τ when rods cluster and percolate with an average bond coordination number 〈n c 〉≈ 2.4, supporting the link between physical gelation and rigidity percolation. Lastly, AHR results are mapped onto a dimensionless state diagram to compare with previous predictions of attraction-driven gels, repulsion-driven glasses, and liquid crystal phases.

We demonstrate a method based on symmetry to predict the structure of self-assembling, multicomponent colloidal mixtures. This method allows us to feasibly enumerate candidate structures from all symmetry groups and is many orders of magnitude more computationally efficient than combinatorial enumeration of these candidates. In turn, this permits us to compute ground-state phase diagrams for multicomponent systems. While tuning the interparticle potentials to produce potentially complex interactions represents the conventional route to designing exotic lattices, we use this scheme to demonstrate that simple potentials can also give rise to such structures which are thermodynamically stable at moderate to low temperatures. Furthermore, for a model two-dimensional colloidal system, we illustrate that lattices forming a complete set of 2-, 3-, 4-, and 6-fold rotational symmetries can be rationally designed from certain systems by tuning the mixture composition alone, demonstrating that stoichiometric control can be a tool as powerful as directly tuning the interparticle potentials themselves.

We present analytic expressions for the second virial coefficient of hard particles in slit and cylindrical pores with arbitrary square-well fluid-fluid and fluid-solid interactions, number of fluid components, and pore sizes. We derive multiple methods to predict the isotherms in confined materials based on the virial expansion and find that the thermodynamic and structural properties calculated from the virial expansion to second order in the dilute limit display excellent qualitative agreement with previous simulation results.

Monte Carlo simulations are the foundational technique for predicting thermodynamic properties of open systems where the process of interest involves the exchange of particles. Thus, they have been used extensively to computationally evaluate the adsorption properties of nanoporous materials and are critical for the in silico identification of promising materials for a variety of gas storage and chemical separation applications. In this work we demonstrate that a well-known biasing technique, known as "flat-histogram" sampling, can be combined with temperature extrapolation of the free energy landscape to efficiently provide significantly more useful thermodynamic information than standard open ensemble MC simulations. Namely, we can accurately compute the isosteric heat of adsorption and number of particles adsorbed for various adsorbates over an extremely wide range of temperatures and pressures from a set of simulations at just one temperature. We extend this derivation of the temperature extrapolation to adsorbates with intramolecular degrees of freedom when Rosenbluth sampling is employed. Consequently, the working capacity and isosteric heat can be computed for any given combined temperature/pressure swing adsorption process for a large range of operating conditions with both rigid and deformable adsorbates. Continuous thermodynamic properties can be computed with this technique at very moderate computational cost, thereby providing a strong case for its application to the in silico identification of promising nanoporous adsorbents.

Cylindrical or rod-like particles are promising materials for the applications of fillers in nanocomposite materials and additives to control rheological properties of colloidal suspensions. Recent advances in particle synthesis allows for cylinders to be manufactured with short-ranged attractions to study the gelation as a function of packing fraction, aspect ratio and attraction strength. In order to aid in the analysis of small-angle scattering experiments of rod-like particles, computer simulation methods were used to model these particles with specialized Monte Carlo algorithms and tabular superquadric potentials. The attractive interaction between neighboring rods increases with the amount of locally-accessible surface area, thus leading to patchy-like interactions. We characterize the clustering and percolation of cylinders as the attractive interaction increases from the homogenous fluid at relatively low attraction strength, for a variety of aspect ratios and packing fractions. Comparisons with the experimental scattering results are also presented, which are in agreement.

Binary superlattices constructed from nano- or micron-sized colloidal particles have a wide variety of applications, including the design of advanced materials. Self-assembly of such crystals from their constituent colloids can be achieved in practice by, among other means, the functionalization of colloid surfaces with single-stranded DNA sequences. However, when driven by DNA, this assembly is traditionally premised on the pairwise interaction between a single DNA sequence and its complement, and often relies on particle size asymmetry to entropically control the crystalline arrangement of its constituents. The recently proposed "multi-flavoring" motif for DNA functionalization, wherein multiple distinct strands of DNA are grafted in different ratios to different colloids, can be used to experimentally realize a binary mixture in which all pairwise interactions are independently controllable. In this work, we use various computational methods, including molecular dynamics and Wang-Landau Monte Carlo simulations, to study a multi-flavored binary system of micron-sized DNA-functionalized particles modeled implicitly by Fermi-Jagla pairwise interactions. We show how self-assembly of such systems can be controlled in a purely enthalpic manner, and by tuning only the interactions between like particles, demonstrate assembly into various morphologies. Although polymorphism is present over a wide range of pairwise interaction strengths, we show that careful selection of interactions can lead to the generation of pure compositionally ordered crystals. Additionally, we show how the crystal composition changes with the like-pair interaction strengths, and how the solution stoichiometry affects the assembled structures.

We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer's radius of gyration. This approach is based on the principle of using fluctuations in a system's extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations.

We used flat-histogram sampling Monte Carlo to study capillary phase transitions in deformable adsorbent materials. Specifically, we considered a pure adsorbate fluid below its bulk critical temperature within a slit pore of variable pore width. The instantaneous pore width is dictated by a number of factors, such as adsorbate loading, reservoir pressure, fluid-wall interaction, and bare adsorbent properties. In the slit pores studied here, the bare adsorbent free energy was assumed to be biparabolic, consisting of two preferential pore configurations, namely, the narrow pore and the large pore configurations. Four distinct phases could be found in the adsorption isotherms. We found a low-pressure phase transition, driven primarily by capillary condensation/evaporation and accompanied by adsorbent deformation in response. The deformation can be a relatively small contraction/expansion as seen in elastic materials, or a large-scale structural transformation of the adsorbent. We also found a high-pressure transition driven by excluded volume effects, which tends to expand the material and thus results in a large-scale structural transformation of the adsorbent. The adsorption isotherms and osmotic free energies can be rationalized by considering the relative free energy differences between the basins of the bare adsorbent free energy.

We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy.

Virial coefficients are predicted over a large range of both temperatures and model parameter values (i.e., alchemical transformation) from an individual Mayer-sampling Monte Carlo simulation by statistical mechanical extrapolation with minimal increase in computational cost. With this extrapolation method, a Mayer-sampling Monte Carlo simulation of the SPC/E (extended simple point charge) water model quantitatively predicted the second virial coefficient as a continuous function spanning over four orders of magnitude in value and over three orders of magnitude in temperature with less than a 2% deviation. In addition, the same simulation predicted the second virial coefficient if the site charges were scaled by a constant factor, from an increase of 40% down to zero charge. This method is also shown to perform well for the third virial coefficient and the exponential parameter for a Lennard-Jones fluid.

We systematically investigate the assembly of binary multi-flavored colloidal mixtures in two dimensions. In these mixtures all pairwise interactions between species may be tuned independently. This introduces an additional degree of freedom over more traditional binary mixtures with fixed mixing rules, which is anticipated to open new avenues for directed self-assembly. At present, colloidal self-assembly into non-trivial lattices tends to require either high pressures for isotropically interacting particles, or the introduction of directionally anisotropic interactions. Here we demonstrate tunable assembly into a plethora of structures which requires neither of these conditions. We develop a minimal model that defines a three-dimensional phase space containing one dimension for each pairwise interaction, then employ various computational techniques to map out regions of this phase space in which the system self-assembles into these different morphologies. We then present a mean-field model that is capable of reproducing these results for size-symmetric mixtures, which reveals how to target different structures by tuning pairwise interactions, solution stoichiometry, or both. Concerning particle size asymmetry, we find that domains in this model's phase space, corresponding to different morphologies, tend to undergo a continuous "rotation" whose magnitude is proportional to the size asymmetry. Such continuity enables one to estimate the relative stability of different lattices for arbitrary size asymmetries. Owing to its simplicity and accuracy, we expect this model to serve as a valuable design tool for engineering binary colloidal crystals from multi-flavored components.

We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.

We use Monte Carlo simulations to investigate the thermodynamic behavior of soft porous crystal (SPC) adsorbents under the influence of an external barostat. We consider SPCs that naturally exhibit polymorphism between crystal forms of two distinct pore sizes. In the absence of barostatting, these crystals may be naturally divided into two categories depending on their response to stress applied by the adsorbate fluid: those which macroscopically deform and change the volume of their unit cell ("breathing") and those which instead undergo internal rearrangements that change the adsorbate-accessible volume without modifying the unit cell volume ("gate-opening"). When breathing SPCs have a constant external pressure applied, in addition to the thermodynamic pressure of the adsorbate fluid, we find that the free energy difference between the crystal polymorphs is shifted by a constant amount over the entire course of adsorption. Thus, their relative stability may be easily controlled by the barostat. However, when the crystal is held at a fixed overall pressure, changes to the relative stability of the polymorphs tend to be more complex. We demonstrate a thermodynamic analogy between breathing SPCs held at a fixed pressure and macroscopically rigid gate-opening ones which explains this behavior. Furthermore, we illustrate how this implies that external mechanical forces may be employed to tune the effective free energy profile of an empty SPC, which may open new avenues to engineer the thermodynamic properties of these polymorphic adsorbents, such as selectivity.

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.

Measurement of the pore-size distribution (PSD) via gas adsorption and the so-called "kernel method" is a widely used characterization technique for rigid adsorbents. Yet, standard techniques and analytical equipment are not appropriate to characterize the emerging class of flexible adsorbents that deform in response to the stress imparted by an adsorbate gas, as the PSD is a characteristic of the material that varies with the gas pressure and any other external stresses. Here, we derive the PSD for a flexible adsorbent using statistical mechanics in the osmotic ensemble to draw analogy to the kernel method for rigid materials. The resultant PSD is a function of the ensemble constraints including all imposed stresses and, most importantly, the deformation free energy of the adsorbent material. Consequently, a pressure-dependent PSD is a descriptor of the deformation characteristics of an adsorbent and may be the basis of future material characterization techniques. We discuss how, given a technique for resolving pressure-dependent PSDs, the present statistical mechanical theory could enable a new generation of analytical tools that measure and characterize certain intrinsic material properties of flexible adsorbents via otherwise simple adsorption experiments.

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.

We use flat-histogram Monte Carlo simulations to study how changing the flexibility of soft porous crystals (SPCs) affects their selective adsorption of a binary, size-asymmetric supercritical fluid. Specifically, we consider mesoporous SPCs which have multiple minima in their free energy profiles as a function of pore size such that they are capable of exhibiting polymorphism between a narrow and large pore phase. While specific fluid-pore interactions determine the shape of both pores' selectivity curve as a function of adsorbate pressure, an individual pore tends to selectively adsorb a species based on the size of the adsorbate molecule relative to itself, thereby shifting the pore's selectivity curve relative to its polymorph. By controlling the flexibility of a SPC, the relative thermodynamic stability of the two pore phases may be varied, thereby changing the overall selectivity of the SPC during adsorbate loading. We investigate this for two classes of SPCs: one representative of "gate-opening" materials and another of "breathing" materials. For gate-opening materials, this control is much more salient than in breathing ones. However, for the latter, we illustrate how to tune the free energy profile to create materials which breathe multiple times during adsorption/desorption.

We demonstrate an extensible flat-histogram Monte Carlo simulation methodology for studying the adsorption of multicomponent fluids in flexible porous solids. This methodology allows us to easily obtain the complete free energy landscape for the confined fluid-solid system in equilibrium with a bulk fluid of any arbitrary composition. We use this approach to study the adsorption of a prototypical coarse-grained binary fluid in "Hookean" solids, where the free energy of the solid may be described as a simple spring. However, our approach is fully extensible to solids with arbitrarily complex free energy profiles. We demonstrate that by tuning the fluid-solid interaction ranges, the inhomogeneous fluid structure inside the pore can give rise to enhanced selective capture of a larger species through cooperative adsorption with a smaller one. The maximum enhancement in selectivity is observed at low to intermediate pressures and is especially pronounced when the larger species is very dilute in the bulk. This suggest a mechanism by which the selective capture of a minor component from a bulk fluid may be enhanced.

We have used computer simulations to reveal how colloidal crystals may be assembled by engineering the shape and charge of polymeric additives, which act as structure-directing agents (SDAs). Using these agents, only a single desired polymorph may be obtained from a crystallizing mixture of colloids and polymers, which would otherwise result in a defective crystal in the absence of these agents. Building on previous work, which demonstrated this principle in the limiting case of high-density, close-packed crystals, we have now achieved this control over low-density, open crystals, which have broad utility especially in optical applications. These results reveal the general utility of the SDA paradigm in assembling tailored colloidal crystals, which represents a new design method that does not rely on any modification of the colloids themselves.

Globally ordered colloidal crystal lattices have broad utility in a wide range of optical and catalytic devices, for example, as photonic band gap materials. However, the self-assembly of stereospecific structures is often confounded by polymorphism. Small free-energy differences often characterize ensembles of different structures, making it difficult to produce a single morphology at will. Current techniques to handle this problem adopt one of two approaches: that of the "top-down" or "bottom-up" methodology, whereby structures are engineered starting from the largest or smallest relevant length scales, respectively. However, recently, a third approach for directing high fidelity assembly of colloidal crystals has been suggested which relies on the introduction of polymer cosolutes into the crystal phase [Mahynski, N.; Panagiotopoulos, A. Z.; Meng, D.; Kumar, S. K. Nat. Commun. 2014, 5, 4472]. By tuning the polymer's morphology to interact uniquely with the void symmetry of a single desired crystal, the entropy loss associated with polymer confinement has been shown to strongly bias the formation of that phase. However, previously, this approach has only been demonstrated in the limiting case of close-packed crystals. Here, we show how this approach may be generalized and extended to complex open crystals, illustrating the utility of this "structure-directing agent" paradigm in engineering the nanoscale structure of ordered colloidal materials. The high degree of transferability of this paradigm's basic principles between relatively simple crystals and more complex ones suggests that this represents a valuable addition to presently known self-assembly techniques.

We study the effective interactions and phase behavior of star polymer-colloid mixtures through theory and Monte Carlo simulations. We extend previous theoretical approaches for calculating the effective star-colloid pair potential to take into account attractive contributions, which become significant at worsening solvent conditions. In order to assess the validity of our simulation and theory, we compute the effective interactions via virtual move parallel tempering Monte Carlo simulations using a microscopic bead-spring model for the star polymer and achieve excellent agreement. Finally, we perform grand canonical Monte Carlo simulations of the coarse-grained systems to study the effect of solvent quality on the phase behavior.

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.

We investigate the thermodynamic behavior of a model polymer-grafted nanoparticle (GNP) system on a fine lattice, using grand canonical Monte Carlo simulations, to compare and contrast the validity of two different models for GNPs: "nanoparticle amphiphiles" versus "patchy particles." In the former model, continuous self-assembly processes are expected to dominate the system, whereas the latter are characterized by first-order phase separation into novel equilibrium phases such as "empty liquids." We find that, in general, considering GNPs as amphiphiles within the framework of a recent mean-field theory [Pryamtisyn et al., J. Chem. Phys. 131, 221102 (2009)] provides a qualitatively accurate description of the thermodynamics of GNP systems, revealing either first-order phase separation into two isotropic phases or continuous self-assembly. Our model GNPs display no signs of empty liquid formation, suggesting that these nanoparticles do not provide a route to such phases.

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 < 1.01. This metric conveniently characterizes the crossover from entropically to energetically dominated systems at B ≈ 0. While the HCP relies on its octahedral void arrangement for enhanced stability when B > 0, its tetrahedral voids produce a similar effect when B < 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. 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.

Colloids often crystallize into polymorphic structures, which are only separated by marginal differences in free energy. Due to this fact, the face-centred cubic and hexagonal close-packed hard-sphere morphologies, for example, usually crystallize simultaneously from a supersaturated solution. The resulting lack of long-range order in these polymorphic structures has been a significant barrier to the widespread application of these crystals in, for instance, photonic bandgap materials. Here, we report a simple method to stabilize one out of two competing polymorphs by exploiting the fact that they have significantly different spatial distributions of voids. We use a variety of polymeric additives whose geometries can be tuned such that their entropy loss, which is related to crystal void symmetries, is different in the two competing polymorphs. This, in turn, controls which polymorph is most thermodynamically stable, providing a generalizable means to stabilize a selected crystal polymorph from a suite of competing structures.

We employ extensive computer simulations to study the flow behavior of spherical, nanoscale colloids in a viscoelastic solvent under Poiseuille flow. The systems are confined in a slit-like microfluidic channel, and viscoelasticity is introduced explicitly through the inclusion of polymer chains on the same length scale as the dispersed solute particles. We systematically study the effects of flow strength and polymer concentration, and identify a regime in which the colloids migrate to the centerline of the microchannel, expelling the polymer chains to the sides. This behavior was recently identified in experiments, but a detailed understanding of the underlying physics was lacking. To this end, we provide a detailed analysis of this phenomenon and discuss ways to maximize its effectiveness. The focusing mechanism can be exploited to separate and capture particles at the sub-micrometer scale using simple microfluidic devices, which is a crucial task for many biomedical applications, such as cell counting and genomic mapping.

We investigate the depletion-induced phase behavior of athermal colloid-star polymer mixtures on a fine lattice using grand canonical Monte Carlo simulations in the "protein limit," that is, where polymer dimensions exceed those of the colloid. We consider the influence of the star's functionality, f, the macroscopic size ratio, qr = 2Rg, s∕σc, where Rg, s is the radius of gyration of the star and σc is the colloid diameter, and the microscopic size ratio, d = σm∕σc, where σm is the diameter of a Kuhn segment. Recent theoretical predictions concerning the qualitative interplay of qr and f in determining the phase stability of these mixtures [D. Marzi, C. N. Likos, and B. Capone, J. Chem. Phys. 137, 014902 (2012)] in the limit of large f are mostly corroborated by our results which span a much lower range of functionalities. Our results suggest a direct connection between the phase behavior and the scaling regimes of single star structure in the classical Daoud-Cotton (DC) description [M. Daoud and J. P. Cotton, J. Phys. 43, 531-538 (1982)]. Using this formalism, we define a "low" functionality limit through scaling arguments, for which our model provides a mapping of the phase behavior of colloidal mixtures with star polymers (f > 2) to linear chains (f = 2). Furthermore, our simulations suggest that as qr increases, both the critical monomer and colloid densities tend to a constant, finite value for all f; thus, we do not find the prediction by Marzi and co-workers of an upper limit to immiscibility (infinite critical densities) in terms of qr to be accurate for the stars we have investigated.

Structural features of phase-separated athermal colloid-polymer mixtures in the so-called "protein limit," where polymer chain dimensions exceed those of the colloid, are investigated using grand canonical Monte Carlo simulations on a fine lattice. Previous work [N. A. Mahynski et al., Phys. Rev. E 85, 051402 (2012)] has shown that this model accurately captures the phase behavior of experimental systems, and that colloids with sufficiently small diameters, σ(c), relative to that of the monomeric segments, σ(s), phase separate more readily than their large-diameter counterparts. In the present study, we directly connect colloid and polymer structure with their phase behavior by investigating these solutions along their binodal curves; we also explore the role of colloid surface curvature in destabilizing such solutions. Our findings suggest that simple consideration of an additional depletion radius, on the order of the σ(s), leads to a quantitatively accurate prediction of the division between stable and unstable ranges of d=σ(s)/σ(c). We compare these results to continuum models with different bonding potentials between monomer segments in order to elucidate the significance of the lattice model's bond fluctuations and inherently coarse colloid surface. In a number of cases, the continuum models deviate both qualitatively and quantitatively from the lattice results, but the binodals of the continuum models are presently not known, making a strong conclusion about these differences impossible.

A model poly(ethylene oxide) (PEO) brush system, prepared by spreading a poly(ethylene oxide)-poly(n-butyl acrylate) (PEO-PnBA) amphiphilic diblock copolymer onto an air-water interface, was investigated under various grafting density conditions by using the X-ray reflectivity (XR) technique. The overall electron density profiles of the PEO-PnBA monolayer in the direction normal to the air-water interface were determined from the XR data. From this analysis, it was found that inside of the PEO brush, the water density is significantly lower than that of bulk water, in particular, in the region close to the PnBA-water interface. Separate XR measurements with a PnBA homopolymer monolayer confirm that the reduced water density within the PEO-PnBA monolayer is not due to unfavorable contacts between the PnBA surface and water. The above result, therefore, lends support to the notion that PEO chains provide a hydrophobic environment for the surrounding water molecules when they exist as polymer brush chains.

Grand canonical Monte Carlo and histogram reweighting techniques are used to study the fluid-phase behavior of an athermal system of colloids and nonadsorbing polymers on a fine lattice in the "protein limit," where polymer dimensions exceed those of the colloids. The main parameters are the chains' radius of gyration, R&#95;{g}, the diameter of the colloids, σ&#95;{c}, and the monomer diameter, σ&#95;{s}. The phase behavior is controlled by the macroscopic size ratio, q&#95;{r}=2R&#95;{g}/σ&#95;{c}, and the microscopic size ratio, d=σ&#95;{s}/σ&#95;{c}. The latter ratio is found to play a significant role in determining the critical monomer concentration for q&#95;{r}≲4 and the critical colloid density for all chain lengths. However, the critical (osmotic) pressure is independent of the microscopic size ratio at all macroscopic size ratios studied. Quantitative agreement is observed between our simulation results and experimental data. We scale our results based on the polymer correlation length, which has previously been suggested to universally collapse these binodals [Bolhuis et al., Phys. Rev. Lett. 90, 068304 (2003); Fleer and Tuinier, Phys. Rev. E 76, 041802 (2007)]. While the density binodals exhibit universal characteristics along the low-colloid-density branch, such features are not present in the corresponding high-density phase. However, pressure binodals do collapse nicely under such a scaling, even far from the critical point, which allows us to produce a binodal curve whose shape is independent of either size ratio.

We report the structural behavior for mixtures of two differently sized ("bidisperse") silica microspheres at the air-water interface under three different size ratio conditions (alpha (identical with R(S)/R(L)) = 0.375, 0.500, and 0.579). These bidisperse silica monolayers were studied via measurement of the surface pressure-area isotherm and optical microscopy at various particle surface coverages (theta identical with theta(S) + theta(L)) during compression. The silica colloids used in these trials were found to possess purely repulsive pair interactions at the air-water interface, which was confirmed by the pair correlation function calculated from the analysis of many optical images of the particles taken at dilute concentrations. The results revealed that, at certain mixture compositions (beta identical with theta(L)/theta(S)), compression can lead to the formation of 2D binary crystal structures. Specifically, at a particle size ratio of alpha = 0.375, LS1 crystal domains were observed at a surface coverage of theta approximately 0.619 when beta = 7.00 and 3.50, although this LS1 structure was not observed at higher total particle densities (where the system became phase-separated). At a size ratio of alpha = 0.579, compression produced 2D LS2 binary crystals at particle surface coverages (theta) above 0.641 when beta = 3.00, 1.50, or 1.00. However, at a size ratio of alpha = 0.500, compression triggered macroscopic phase separation, leading to the formation of two separate hexagonal-close-packed domains consisting purely of either large or small particles. In general, when the mixture composition (beta) was too different from the stoichiometric ratio needed for the formation of LS1 or LS2 superlattices, the bidisperse monolayer was observed to remain in an amorphous state rather than evolving to an ordered phase under compression. These findings suggest that, in two dimensions, contrary to what has been speculated in the literature, (1) purely repulsive pair potentials can give rise to LS1 and LS2 binary crystals under compression and also (2) perfectly spherical particles can form LS2 crystals. This discrepancy between our results and the predictions of previous simulations might indicate that the capillary interaction and/or the many-body effects play a significant role in determining the structure of bidisperse colloids at the air-water interface.