We present a new approach to the design and optimization of colloidal and nanoparticle assemblies that is generalizable to many types of materials problems. We present a rigorous statistical thermodynamic framework underlying "digital alchemy," in which material features are optimized computationally for target structures and function in an automated fashion. We demonstrate the usefulness of this approach for the self assembly of hard polyhedra, as well as colloidal spheres interacting via oscillating pair potentials, into complex crystals. We discuss extensions of digital alchemy to other materials design problems.
*in collaboration with G. van Anders, D. Klotsa and P. Dodd

Crystalline nanoparticles (CNPs) covered by ligands can self-organize into highly periodic supercrystals (SCs), which possess a range of crystal symmetries (e.g., face-centered cubic FCC, body centered cubic BCC, simple hexagonal SH etc.). These SCs exhibit a variety of exotic properties (e.g, reversible metal-to-insulator transitions, enhanced conductivity), which make them suitable for various energy, technology and device applications. Despite the widespread efforts in synthesis of SCs, a fundamental understanding of the physical forces underlying the self-assembly process is still in its infancy. In particular, the key role played by ligands in driving the self-organization of CNPs into SCs with a particular crystal symmetry, and the influence of their nano-scale dynamics on the physical properties of SCs are still unclear. Here, using coarse grained molecular dynamics (CGMD) based on the well-known MARTINI force field, we demonstrate that the self-assembly of CNPs is critically controlled by the decorating ligands via their (a) self-interaction, (b) mobility on the CNP surface, (c) re-organization/inter-digitation, and associated dynamics. Our quasi-hydrostatic high-pressure small-angle X-ray scattering (SAXS) and X-ray diffraction (XRD) studies showed that the size of CNP building blocks control the symmetry of self assembled SC. Smaller (~4.7) nm PbS particles decorated by oleic acid ligands organize into BCC SC, while at larger sizes (~7 nm) they assemble into FCC SC. Furthermore, the BCC SCs show near-perfect elastic behavior under applied pressures ~55 GPa, while FCC SC show some hysteresis during the loading-unloading cycles without losing its structural integrity. Our CGMD simulations predict pressure behavior during the loading-unloading cycles consistent with our experiments. In addition, these simulations indicate the ligands strongly govern the pressure behavior of SCs via (a) re-arranging on the CNP surface, and (b) inter-digitating with neighboring CNPs without being locked in permanently. These enable the SCs to retain their structural organization even at extremely high pressures by merely reducing the distance between neighboring CNPs. We will discuss these results in the context of engineering novel ordered CNP architectures with prescribed mechanical, electronic, and physical properties.

The thiolate group (SR) protected gold nanoclusters (AuNCs) have attracted intense concerns due to the potential applications in catalysis, sensor and biomedicine. A series of Au_n(SR)_m nanoclusters were synthesized in experiment with size-dependent physical and chemical properties. The chemical formula of Au_n(SR)_m can be identified by mass spectrum analysis into matched n and m. For example, n = 18 is corresponding to m = 14 as Au₁₈(SR)₁₄. However, determination of the atomic structure of Au_n(SR)_m is still a challenge in experiments largely because most single crystals of which are difficult to be obtained. To identify the exact structure of Au_n(SR)_m, the theoretical scientists want to make contributions from the numerical study together with the experimental characterization. Till now, there are some independent predicted or theoretical and experimental consistent structure of Au_n(SR)_m have been achieved, including Au₁₈(SR)₁₄, Au₂₀(SR)₁₆, Au₂₄(SR)₂₀, [Au₂₅(SR)₁₈]^-, and Au₃₈(SR)₂₄. In the theoretical prediction of Au_n(SR)_m, the density functional theory (DFT) calculations are important tools to give a deep insight into the molecular structure of Au_n(SR)_m. The general structure of these nanoclusters includes a high-symmetric Au-core and a series of semiring staple motifs. The super atom model is utilized to identify the high stable structure of Au_n(SR)_m by calculating the total number of free valence electron.
Recently, we successfully synthesize the stable Au₂₄Peptide₈ complex (Peptide = CysCys-6peptides). As a biomedical probe, Au₂₄Peptide₈ is utilized to achieve the quantitation of membrane protein integrin for cancer early diagnosis. However, the atomic structure of Au₂₄Peptide₈ is unknown. Especially, it is critical to identify the dominant coupling structure Au₂₄(SCys-CysS)₈ for the probe characteristics. Although there are 24 Au atoms in both Au₂₄(SCys-CysS)₈ and Au₂₄(SR)₂₀, the ratio of Au:S in amino acid coated Au₂₄(SCys-CysS)₈ is unmatched to that in SR coated Au₂₄(SR)₂₀ with the known molecular structure. In this work, we focus on identifying the atomic structure of Au₂₄(SCys-CysS)₈. According to the super atom model, the total number of Au₂₄(SCys-CysS)₈ is 8e, which satisfies the number of electrons to fill closed electron shell within the framework of spherical jellium model. The atomic structure of Au₂₄(SCys-CysS)₈ is resolved by the numerical calculations into Au₁₃ cubocatahedral core and protected -Au-SCys- motifs. For the lowest-energy isomer, we both theoretically compute and experimentally measure its UV-vis absorption spectrum, which is in the good agreement to each other. It is the new knowledge for the atomic structure of amino acid coated AuNCs. Meanwhile, the atomic details of amino acid coated AuNCs support us to applicate the biocompatibility more effectively in biomedicine.

Although the advent of modern theoretical techniques and high performance computing have provided us with a range of sophisticated tools for simulating nanoscale materials, modeling realistic systems to reproduce real experiments remains challenging. Each of the applications for nanoparticles, such as energy conversion and storage, communications, electronics or medicine, all have different material needs; but share one thing in common. All involve large collections of small particles, the properties and stability of which will depend on how and where they are used. Consider for example the case of a non-toxic nanoparticle, such as nanodiamond, being used in nanomedicine the treatment of cancer. Individual particles using for this purpose need to be mechanically stable, able to adsorb and desorb drugs in a controlled fashion, capable of forming porous meso-structures to moderate doses and dose rates, and able operate reliably under relevant thermochemical conditions (not “clean”, and in a vacuum). This means that simulating this application transcends length scales, from molecular, to nanoscale and even micron scale; must capture the complexity of the individual particles and their interactions; and must include the influence of the relevant environments and the proximity of large numbers of particles. In this presentation we will see how quantum mechanical simulations can be used to underpin higher level models that enable the direct simulation of distributions and mixtures of hundreds of thousands of faceted colloidal particles.

Globally ordered colloidal lattices have broad utility in a wide range of novel optical and catalytic devices, for example, as photonic bandgap materials. However, the self-assembly of stereospecific structures is often confounded by defects. Small free energy differences different crystal polymorphs, making it difficult to produce a single morphology at will. Current techniques to handle this problem usually rely on energy minimization; many colloids have been computationally engineered with anisotropic pairwise interactions to achieve morphological control. However, the complexity of these designs often makes experimental realization difficult. In this presentation, recent computer simulation and theoretical work [1-3] on the effects of polymeric co-solutes on crystallizing colloidal suspensions is summarized. These can be used to direct colloidal structures by relying upon the polymer's entropic interactions resulting from the interplay between the polymer's internal degrees of freedom and the void structure of a material. This represents a novel design paradigm that has the potential to significantly simplify control over colloidal polymorphism. I will elaborate on how to rationally design the co-solute structure to thermodynamically stabilize a single desired polymorph in a binary mixture, and the consequences that thermal perturbations have on this effect [2]. I will then offer insights into how to design temperature-dependent co-solute “switches” that allow the stability of a polymorph to be controlled via experimentally accessible parameters [3].
[1] N. A. Mahynski, A. Z. Panagiotopoulos, D. Meng, and S. K. Kumar; Nature Comm., 5: 4472, 8 pp (2014).
[2] N. A. Mahynski, S. K. Kumar, and A. Z. Panagiotopoulos; Soft Matter, 11: 280-9(2015).
[3] N. A. Mahynski, S. K. Kumar, and A. Z. Panagiotopoulos; Soft Matter, DOI: 10.1039/c5sm00631g(2015).

In the active field of colloidally self assembled materials, simulation of large systems can be necessary to understand phase coexistence and nucleation, or to observe certain novel behaviors such as hexatic phases. One of the basic tools to understanding the thermodynamics of any system is to measure the state functions, but there are computational challenges for the non-differentiable potentials of the simplest (hard) particle models, particularly as system size is increased.
Computing the pressure -- volume state function is historically expensive in hard particle Monte Carlo simulations and traditional methods are inadequate for studying large systems. NpT simulations are far more computationally expensive than simulations in the NVT ensemble and become impossible for large system sizes. Pressure measurement in NVT simulations is analytic for few particle shapes. Perturbative numerical techniques, historically underutilized, are unclear or insufficient as previously published for general application to large systems of arbitrary particle shapes.
We combine and extend previous methods of pressure calculation from a perturbative thermodynamics approach and present an efficient and highly scalable implementation. This has allowed us to extract previously elusive thermodynamic data with the same computational efficiency as the rest of our highly parallel hard particle Monte Carlo code in studies of unprecedentedly large systems.

The self-assembly of finite clusters of colloidal particles into crystalline objects is a topic of technological interest, as a route to produce photonic crystals and other meta-materials. Quantitatively accurate models of the thermodynamics and dynamics of these systems are essential to producing defect-free crystals. Robust methods for controlling the assembly of these crystals would require reduced dimension process-models that link the particle-level dynamics of the colloids to the actuator states. In this paper, we describe the building of such models for two systems comprising 10-100 micron sized silica particles in aqueous solution that employ either a temperature-tunable depletion interaction potential or externally applied electric field as a mechanism to promote the assembly process. We model the assembly process using coarse-grained representations, based on the Fokker-Planck equation, which can capture both the dynamics and the equilibrium properties of these small clusters. We use diffusion maps (DMaps), a machine learning technique to identify the slow, low-dimensional manifolds in these systems. The DMap coordinates are correlated against a set of candidate order parameters (OPs) to identify a suitable choice of observables. The DMap technique is sensitive to the nature of defects observed in these two systems and this is manifest in the correlations with OPs. We construct free energy and diffusivity landscapes in the chosen OPs that serve as reduced order models for process control policy maps providing an optimal route to defect-free crystals.
To quantify the phase behavior, we have also conducted Monte Carlo simulations of these small colloidal clusters and generated potential energy histograms for various levels of the osmotic pressure (for the depletion potential system) that controls the strength of the interactions. We have used potential energy as the histogram variable to identify the fluid-like and solid-like phases. By carefully tuning the osmotic pressure, we observed bimodal distributions in the potential energy space that is indicative of coexistence between fluid-like and solid-like configurations. We report comparisons of phase behavior for these colloidal clusters obtained from the thermodynamic approach outlined here with results from above mentioned Fokker-Planck order parameter approach.

Most colloidal interactions can be tuned by changing properties of the medium. Here we show that activating the colloidal particles with random self-propulsion can induce giant effective interactions between large objects immersed in such a suspension. By performing Brownian dynamics simulations, we systematically study the effective force between two hard walls in a 2D suspension of self-propelled (active)colloidal hard spheres [1]. We find that at relatively high densities, the active colloidal hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing the density of active colloids, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction starts dominating the effective interaction between the two walls. The two long range forces oppose each other, and the effective interaction can be tuned from a long range repulsion into a long range attraction by reducing the density of active particles. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.
[1] R. Ni et al, Phys. Rev. Lett., 114, 018302 (2015)

We investigate a class of “shape allophiles” that fit together like puzzle pieces as a method to access and stabilize desired structures by controlling directional entropic forces. Squares are cut into rectangular halves, which are shaped in an allophilic manner with the goal of re-assembling the squares while self-assembling the square lattice. We examine the assembly characteristics of this system via the potential of mean force and torque, and the fraction of particles that entropically bind. We generalize our findings and apply them to self-assemble triangles into a square lattice via allophilic shaping. Through these studies we show how shape allophiles can be useful in assembling and stabilizing desired phases with appropriate allophilic design.
*This work currently in press in Soft Matter

Many biomolecular systems such as cell membranes and actin filaments are organized as complex and dynamic mesoscopic structures. However, underlying this fascinating degree of organization are molecular-scale features such as protein structural elements and/or local chemistry (e.g., protonation equilibria and nucleotide hydrolysis) that can greatly affect the mesoscopic behavior. Multiscale simulation can help to reveal these molecular features along with their coupling to the mesoscale behavior. Such results for the membrane remodeling by proteins and ATP hydrolysis in actin filaments will be presented in this talk. The lessons learned from these multiscale simulations can also help to guide in the development of novel soft materials and to predict their mesoscopic behavior via systematic coarse-graining of the molecular-scale interactions.

In molecular self-assembly process, molecules spontaneously and reversibly form ordered aggregates through a number of attractive and repulsive forces. It has been shown that some dipeptide systems have the ability to self-assemble into various structures. We found that valine-alanine (Val-Ala) dipeptide molecules produce various self-assembled micro-/nano-structures, including square- and rectangular-plates, wires, and rods, depending on the solvents used, whereas alanine-valine (Ala-Val) dipeptides did not self-assemble into any distinct ordered structure under the same experimental conditions. Experimental as well as modeling studies towards the understanding of peptide self-assembly are still in their infancy. Thus, the fabrication of new peptide structures with desired properties mainly depends on our ability to understand/control peptide-peptide interactions in various solvents. In this work, we investigated the self-assembly of Val-Ala and Ala-Val dipeptides by using molecular modeling in aqueous environment. Molecular modeling studies revealed the decisive role of dipeptide/dipeptide and dipeptide/solvent H-bonding interactions on the final structures formed. Simulations also revealed that each one of the 2- and 4-mers of Val-Ala dipeptides have equally distributed intra- and inter-molecular H-bonds; however, this is not the case for Ala-Val peptides. This structural difference may be the reason for the formation of long-range ordered structures, which observed experimentally for Val-Ala dipeptides contrary to Ala-Val dipeptides. Supported by TUBA GEBIP awards to Demirel G. and Oren EE.

We develop a computational model by coupling implicit solvent coarse-grained dry martini model with a lattice-Boltzmann fluid in order to design and characterize nanostructured soft materials. The long range hydrodynamic effects are included in the system through the implementation of the Lattice-Boltzmann fluid. This removes the necessity of using explicit solvent molecules. The particle dynamics is resolved via the Molecular Dynamics simulation method. Our objective is to generate a stable vesicle composed of single (DPPC) and multiple (DPPC and DOPC) phospholipid species through the use of implicit solvent coarse grained model with long range hydrodynamics in order to investigate physiological processes occurring on the mesoscopic spatio-temporal scales. By using a four to one mapping scale of Martini model, the DPPC molecule is represented by four head beads and eight tail beads. The twelve beads are further divided into four types, each with different interaction energies and length scales. Analogous models are developed for the other phospholipids. The vesicle is initially equilibrated using the Dry Martini force field without Lattice-Boltzmann fluid. In order to couple Dry Martini model with Lattice-Boltzmann fluid, 36 nodes are built on the surface of the hydrophilic head beads of the phospholipid molecules. These nodes and the surrounding head beads are treated as a rigid particle so that hydrodynamic forces can be transferred from fluid to lipid molecules. We investigate the dynamical, structural and morphological properties of the resulting hybrid aggregates. The results of our investigations can be used for the design and prediction of novel hybrid soft and bio-materials at the mesoscale for various applications in medicine, sensing and energy.

Spiders spin their silk from an aqueous solution to a solid fiber in ambient conditions. However, to date the assembly mechanism in the spider gland has not been satisfactorily explained. By means of molecular dynamics simulations, we investigated structural transitions during the assembly of N. Clavipes MaSP1 dragline silk. These shear induced transitions in the core sequence ((AAAAAAGGAGQGGYGGLGSQGAGRGGLGGQGAG)_n; n=2-6) are important for the formation of aligned β-sheet nanostructures in the fiber. We found that a critical shear stress of 300 - 800 MPa induces an α-β-transition in the core poly-alanine region of the MaSP1 structure that is maintained after relaxation in aqueous media. While the transition stress is independent of the number of MaSP1 repeats, the β-crystal is stable only in larger configurations. The minimum size for a stable structure was shown to be six poly-alanine regions for a single chain and four poly-alanine regions for simulations performed on assemblages of multiple chains. This marks the smallest molecule size that gives rise to a ‘silk-like&’ structure. In addition, the presence of water was found to stimulate the formation of additional β-sheet secondary structure components not present after the shear induced transition.
Using a probability analysis of the secondary structure allowed us to identify specific amino acids that transition from α-helix to β-sheet. In addition to portions of the poly-alanine section these amino acids include glycine, leucine and glutamine. The stability of the β-sheet structure appears to arise from a close proximity in space of helices in the initial spidroin state. Our results are in agreement with the forces exerted by spiders in the silking process and the experimentally determined global secondary structure of spidroin and pulled MaSp1 silk. This is the first time that the shear stress has been quantified in connection with a secondary structure transition. Our study emphasizes the role of shear in the assembly process of silk and can guide the design of microfluidic devices that attempt to mimic the natural spinning process.

Many applications of fibrous materials, such as scaffolds for tissue engineering or applications in fuel cells, rely on the control of network properties such as void size distributions. Fibrous networks formed in magnetorheological fluids offer the possibility of tuning such fibrous structures. A deep understanding of the mechanisms that lead to network formation is a prerequisite for controlling network architecture, potentially giving rise to novel devices.
Here, we use super-paramagnetic polystyrene particles and optical video microscopy to investigate field-induced structure formation at the mesoscale and single particle level. First we address the chain formation at low packing fractions and use simple statistical considerations to fully predict the distribution of coordination numbers for individual particles. The validity of our approach is confirmed using computer simulations in which the starting configuration of the chain forming system is systematically varied from random to deterministic. We show that chain growth proceeds via a compound Poisson process, such that at all times the coordination number distribution fully characterises the chain length distribution and vice versa.
We then investigate the formation of fibrous networks at higher packing fractions. We use statistical geometry and statistical modelling to quantify and rationalise the observed structures. We also apply our approach of analysing self-assembly through coordination number statistics to these network forming systems.
Finally, we explore the possibilities of network formation in mixtures of super-paramagnetic and non-magnetic particles suspended in a ferrofluid. In the presence of a magnetic field, these magnetic holes and excesses act as dipoles pointing in opposite directions and assemble into structures distinct from those of the single component system.

In this talk I'll discuss the use of molecular simulation techniques to probe the interaction between nanoparticle and biomolecules. This is motivated by the increasing interest in the environmental and health impact of nano materials. Molecular simulations are able to provide a molecular level understanding of physical factors that dictate the strength and specificity of such interactions. I'll discuss the challenges associated with such simulations and the relevant developments made in our group, which touch upon both sampling methodologies and model potentials at different resolutions. Applications to nano-particle interactions with peptides and lipids will be presented as examples.

Nucleic acid based nanotechnology and gene theraphy approaches depend on the compaction, or packaging, of the nucleic acids DNA and RNA. Though there has been much experimental work on the interactions of DNA with proteins, the atomic details of DNA- nanoparticle binding remain to be comprehensively elucidated. Even less is known about the binding of double stranded RNA with cationic molecules. Here, we report the results of a comprehensive large scale all-atom simulation investigation of the binding ligand-functionalized gold nanoparticles (NPs) binding to the nucleic acids double stranded DNA and RNA as a function of NP charge and solution salt con- centration. Our simulations show that low charge NPs bind to DNA and cause little distortion of the DNA helix, however, nanoparticles with charges of +30 or higher cause DNA to bend and wrap in a way similar to nucleosome. Moreover, shape of the NP ligand corona plays an essential role in quality of DNA wrapping. The nanoparticles cause different behavior with short segments of RNA in that they are not able to induce bending for even the most highly charged nanoparticles in 0.1M NaCl. To compact RNA, a combination of highly charged nanoparticles with low salt concentration is required.

First, we discuss our collaborative studies of colloidal nanoparticles with bio-active ligands. In our modeling of protein corona, we examine how different types of ligands control the adsorption, configuration and activity of proteins on nanoparticle surfaces [1]. Next, we investigate how nanoparticles couple to and affect the functions of larger cellular and biological units [2]. In our collaborative modeling of nanomedicines, we discuss the stability of micelles, their ability to carry drugs, and their interaction with membranes and receptors [3]. Many different types of monomeric units are considered and compared in these nanomedicines.
[1] W. Lyn et al., submitted.
[2] S. Sen, in preparation.
[3] L. Vukovicacute; et al., JACS 133, 13481 (2011); Langmuir 29, 15747 (2013); H.-J. Hsu et al., Macromol., 47, 6911 (2014); C. R. James et al., JACS 136, 11316 (2014); A. Lote et al., Macro Lett. 3, 829 (2014) & submitted.

Gold nanoparticles (NPs) are versatile materials with surface properties that can be chemically modified to mimic typical biological macromolecules. Recently, NPs protected by a binary monolayer of purely hydrophobic and anionic, end-functionalized alkanethiol ligands were found to embed within lipid bilayers as a precursor to non-disruptive, non-endocytic cellular uptake (1). This behavior is highly promising for applications in drug delivery, bioimaging, or biosensing, but optimizing NP coatings for such applications requires an improved understanding of the NP-bilayer insertion mechanism. In this work, we use atomistic molecular dynamics simulations to further elucidate the mechanism by which amphiphilic NPs establish a transmembrane configuration previously predicted by implicit modeling methods (1). We show that NP-bilayer insertion is initiated by the stochastic protrusion of aliphatic lipid tails into solvent and into contact with hydrophobic material in the amphiphilic NP monolayer. Hydrophobic ligands are then shielded within the bilayer, providing a driving force for the insertion process. In contrast, charged ligands face additional barriers to cross the low dielectric constant bilayer core region and stabilize a transmembrane NP configuration. We quantify the free energy cost for translocating charged end groups across the bilayer and show that the process mimics transbilayer lipid flip-flop. Together, our simulations reveal a mechanism for NP-bilayer insertion that is consistent with prior experimental results. Based on this mechanism, we suggest design guidelines for novel NP coatings that maximize NP-bilayer insertion, enabling the creation of novel nano-bio hybrid structures for biomedical applications.
(1) R. C. Van Lehn et al, “Effect of particle diameter and surface composition on the spontaneous fusion of monolayer-protected gold nanoparticles with lipid bilayers,” Nano Letters 13 (2013).

The mechanisms of interactions between inorganic nanoparticles and biomolecules are ubiquitously and critically related to the applications as diverse as biomaterials, photonics, and catalysis. The binding of biomolecules to inorganic calcium phosphate (CaP) phases was demonstrated to mediate the nucleation and growth of hydroxyapatite (HAP, Ca₁₀(PO₄)₆(OH)₂) during bone formation.^{1, 2} It has been previously shown that HAP can induce conformational changes between solution and surface-bound ensembles of the peptide.³ However, as a critical intermediate phase for HAP crystallization, little is known about the interaction mechanisms between amorphous calcium phosphate (ACP) and biomolecules. Molecular simulation has proven to be invaluable in this aspect.⁴ In the present work, we focus on understanding how ACP may affect the conformational behavior of a synthetic CaP-binding peptide VTK (VTKHLNQISQSY), by applying advanced simulation methods and benchmarking to circular dichroism spectra (CD). Taking advantage of the recently implemented parallel-tempering metadynamics⁵, we are able to sample exhaustively the conformational transition of VTK between solution state and ACP-bound state. To examine how ACP nanoparticle surface may influence VTK conformation, detailed analysis of the solution and the surface-bound ensembles of the peptide was performed. The comparison of the respective 2-D free energy landscapes suggests that, for the surface-bound peptide, the α-helix is favored over other conformations, which is reminiscent of the conformational selection mechanism discovered in many biomolecular recognition systems⁶. Interestingly, ACP can affect the relative distribution of peptide conformations in solution by dynamic binding-unbinding process. These two possible scenarios combine to contribute to an increase of random coil ratio in the solution ensemble as a consequence of binding to ACP. These results are confirmed by CD. The present work demonstrates, for the first time, that ACP can induce conformational transitions between solution and bound states of the peptide, which may lead to altering the role of the peptide in mediating HAP crystallization. The dynamic conformational selection and redistribution involved in ACP-peptide binding reveal a new molecular recognition paradigm for inorganic-organic interactions, potentially impacting the strategies in drug design and biomolecular engineering.
References
1. Flade, K.; Lau, C.; Mertig, M.; Pompe, W. Chem. Mater. 2001, 13, 3596-3602.
2. Glimcher, M. J. In Medical Mineralogy and geochemistry, Sahai, N.; Schoonen, M. A. A., Eds. 2006; Vol. 64.
3. Capriotti, L. A.; Beebe, T. P., Jr.; Schneider, J. P. J. Am. Chem. Soc. 2007, 129, 5281-7.
4. Yang, Y.; Zhijun, X.; Qiang, C.; Nita, S. In Biomineralization Sourcebook, DiMasi, E.; Gower, L. B., Eds. 2014; 265-283.
5. Deighan, M.; Pfaendtner, J. Langmuir 2013, 29, 7999-8009.
6. Boehr, D. D.; Nussinov, R.; Wright, P. E. Nat. Chem. Biol. 2009, 5, 789-96.

Drawing a bright line between molecular structure and physical behaviour remains a goal of considerable interest and importance in the study of soft materials. To this end we have created two strategies: A simple, analytic model, derived from fundamental principles (the Locally Correlated Lattice, or LCL, theory), and a coarse-grained simulation approach (the Limited Mobility, or LM, model). The latter method has allowed us to study dynamic heterogeneity and glassy arrest in the bulk and in thin films, for single and for layered multicomponent systems. The LCL theory has been applied to model equibrium properties of complex fluids, solutions and blends. In recent work using the LCL approach we have shown that two pure-component metrics are valuable in predicting complex mixture miscibility: the percent free volume and the cohesive energy density. We have calculated the percent free volume for over fifty polymer melts and find that its value correlates strongly with a number of experimentally-determined quantities, for example the polymer's glass transition. This trend becomes strikingly linear when the percent free volume is calculated at the polymer glass transition temperature. Indeed, we have used the correlation to propose a melt-to-glass 'phase diagram', revealing that both percent free volume and temperature play important roles in understanding this transition. In this talk I will discuss some of aforementioned trends, along with our most current, new results.

Self-consistent field theory (SCFT) is a leading modeling paradigm for predicting the thermodynamic equilibrium behavior of thin film block copolymers (BCPs) under a variety of directed self-assembly (DSA) boundary conditions [1]. BCP DSA is one of the most promising fabrication methods for nanoscale devices with sub-10 nm feature sizes. Accurately predicting the self-assembly behavior of these BCP thin films is important for designing DSA templates. Although there has been a great deal of qualitative agreement between the theory and observed experimental morphological behavior, exact quantitative matching of experimental control variables and simulation parameters has been approximate at best. This issue is in part due to most experimental characterization methods of BCPs being limited to surface characterization methods that only give basic geometric quantitative data with little detail on the nanoscopic local density details that are essential for quantitative comparison of SCFT data. Some successful quantitative comparison of SCFT results has occurred using 3D transmission electron tomography imaging of PS-PDMS thin films with accurate measures of distinct features through the sample [2], but the method still does not give accurate local density information. Better quantitative matching of SCFT results with experiments is necessary for the model to be used as a true DSA template design tool.
Recent progress in characterization techniques using resonant soft X-ray scattering has demonstrated the ability of determining the morphology of BCP thin films through inverse structure determination algorithms. These algorithms used simple trapezoid slabs to model the shape of the block copolymer domains [3]. These shape models both require a large number of parameters and constrain the allowable shapes. BCP SCFT only requires upwards of ten parameters to be optimized for line patterning templates (e.g. chi;, N, f, film thickness, stripe widths and spacings, etc.) allowing more complex and realistic shapes than the trapezoid slab model while decreasing the parameter space. Here we demonstrate that by incorporating a realistic physical model such as SCFT into the methodology, precise quantitative prediction of the morphologies formed is possible. These results can then be used to develop the optimal template conditions necessary for a given BCP DSA application. Experimental scattering data taken of PS-PMMA lamellae thin films patterned by DSA chemoepitaxy templates of different commensurations are used for quantitative comparison between experiment and theory. The results of the best fits to the experimental data are used to enhance the SCFT model and help the design of desired BCP morphologies by giving optimal experimental processing conditions.
References:
[1] Hannon, A.F. 2014, MIT http://dspace.mit.edu/handle/1721.1/89842
[2] Gotrik, K.W. et al. Advanced Functional Materials2014, 24 (48), 7689-7697
[3] Sunday, D.F. et al. ACS Nano2014, 8 (8), 8426-8437

We present theoretical and simulation results informing the development of polymer-based optically switchable materials. This is an extension and generalization of our prior study of composites of paraffin wax and polydimethylsiloxane (PDMS), which have been shown to switch reversibly between a transparent and an opaque state due to a thermal phase transition of the wax. Due to the variety of control mechanisms available (e.g. electrical, thermal, optical), many applications may be viable in various fields. For example, such materials may be used to construct light-trapping geometries with a small input aperture that moves to track the position of the sun. They may therefore be incorporated into PV systems or solar concentrators to enhance photon utilization by the cells. In general, the class of materials being studied have a particle-in-matrix structure that strongly scatters light at low temperature but becomes non-scattering at high temperature, when the ‘particle&’ component melts and swell the matrix. In the present work we take a general approach to this class of materials, providing theoretical results that guide the developments of composites optimized for particular applications, using results from models of light scattering, phase evolution and the kinetics of diffusion in the particle-in-matrix system. We discuss means of optimizing the material specifically in the areas of 1) increasing the scattering power of the opaque state and 2) improving the long term mechanical stability of the composite, and present preliminary experimental results.

Materials which exhibit nanoscale self-assembly have been a significant focus for both fundamental and applied research over the past few decades. Recent advances in microscopy and imaging of surfaces at nanoscale resolution have produced a sizable set of high-quality images of surface self-assembly, in particular. Analysis of these images and, subsequently, determination of relations between self-assembled pattern structure and desired physicochemical properties has not advanced at an equally rapid pace. Researchers predominantly rely on qualitative techniques such as visual inspection in order to interpret imaging data and, ultimately, determining qualitative structure/property relationships. Robust quantitative analysis is required to make further advancements in both determining these relationships and, subsequently, applying optimization and control methods. The primary existing approach for quantitative surface self-assembly analysis involves the use of bond-orientational order theory (BOO), but this method is limited with respect to its generality and robustness in the presence of measurement uncertainty.
In this work, a fundamentally different approach is presented for the analysis of surface self-assembled imaging (Suderman et al, 2015, Phys. Rev. E). It utilizes a set of localized orthogonal functions called "shapelets", which were originally developed for analysis of images of galaxies (~10^20 m). Here they are used to analyze images of nanoscale surface self-assembly (~10^-9 m). The method is applied to simulation data of self-assembled surfaces resulting from heteroepitaxial pattern formation and shown to robustly and efficiently determine local pattern characteristics using an appropriate set of shapelets and steerable filter theory. Local pattern measurements are enabled including pattern type (stripe, square, hexagonal, etc), pattern strength (degree of order), local orientation, and the presence of defects which enables researchers to quantitatively determine structure/property relationships. Furthermore, the method is robust in the presence of measurement noise, pattern degeneracies (defects), and the presence of heterogeneity in the image, such as multiple patterns being present.

Many body implantable devices are made of synthetic polymer which upon insertion absorb water, causing the polymer to swell and forming a gel (mixture of solid and fluid). Since the swelling leads to an expansion of the polymer, a gel is considered as a compressible material. A high concentration of stress due to the swelling leads to the nucleation and growth of cavities within the gel, likely to cause the debonding of the material from a support it is attached to. In this research, we focus on the cavitation in a gel occupying a spherical domain, applying a uniform extensional stress at the boundary of the domain. We consider a total energy of the gel which accounts for the compressible elasticity of the polymer and the mixing between polymer and fluid, called Flory-Huggins energy. In addition to penalizing gel deformation, the energy presents competing effects of entropy that favours mixing, polymer-polymer and fluid-fluid interaction forces. We study material properties necessary to allow for a nucleation, characterization of radially symmetric deformations and stability analysis of the cavity.

Materials innovation for consumer packaged goods involves engineering to the edge, the lightest possible bottle weights, formula / package compatibility, adhesives formulation to meet multiple performance criteria from making to long term shelf life, fiber spinning for non-woven web, battery performance materials, tooth enamel health, skin health. We&’re developing methods to enable material composition - performance relationships to be modeled to streamline development efforts and progress toward effective virtual design. Several common capability gaps illustrate the challenges: solubility and partitioning, migration, solid/liquid phase equilibria, nano- to micro-structural features, polymer rheological and mechanical properties.

Phase-separated morphologies of binary polymer mixtures are used as photo-active material in thin-film organic solar cells. These 100 nm thin films are usually spin-coated from solution, where solvent evaporation drives liquid-liquid phase separation. The fact that the mean composition of the mixture is time dependent gives rise to a coupling between the kinetics of evaporation and demixing. From a generalized diffusion equation accounting for evaporation, we find that evaporation influences the early-stage emergence of the dominant spinodal length scale, as well as the kinetics of late-stage coarsening. Consequently, for both regimes a clear difference is observed when blends are thermally quenched in the unstable region. In the early stages of demixing the typical structural length scale of the emerging morphology decreases with one over the square root of time, whereas in the late stages the rate of coarsening does not obey the classical Lifshitz-Slyozov-Wagner power law. The length scale at the cross-over from early to late stage dynamics itself exhibits a one-sixth power-law behavior with the evaporation rate that is set by the spin speed of the spin-coating process.
This research forms part of the research programme of the Dutch Polymer Institute (DPI), project #734.

While advances in quantum chemistry have rendered the accurate prediction of band alignment relatively straightforward for soft materials, the ability to forecast multimolecule electronic properties of soft, noncrystalline molecular or polymeric systems possesses no simple computational form. Adapting the theory of classical resistor networks, we develop an index for quantifying charge transport in bulk organic semiconducting systems, without the requirement of crystallinity. The basic behavior of this index is illustrated through its application to simple lattices, clusters of common organic photovoltaic molecules, and single-chain aggregates of high-performance conjugated polymers. Using accurately parameterized atomistic simulations we directly simulate molecular and polymeric morphologies, establishing robust correlations between synthetically tunable molecular attributes and multimolecule charge transport characteristics in soft materials. Extensions to exciton transport are presented and the role of single-chain folding in the development of robust polymeric optoelectronic devices is highlighted. These developments provide a quantitative computational means for determining a priori the bulk charge transport properties of soft molecular and polymeric materials.

Bicontinuous phases such as the double or single gyroid structure now have a firm place in self-assembly and biological formation of nanostructured materials. In this talk, we discuss recent progress towards the self-assembly of more complicated network phases based on a triplet of intergrown network-like domains, and provide some indication of their potential for photonic materials.
First, we use self-consistent field theory to show that a tricontinuous structure with monoclinic symmetry, called 3ths(5), based on the intergrowth of three distorted ths nets, is an equilibrium phase of triblock star-copolymer melts when an extended molecular core is introduced. The introduction of the core enhances the role of chain stretching by enforcing larger structural length scales, thus destabilizing the hexagonal columnar phase in favor of morphologies with less packing frustration. This study further demonstrates that the introduction of molecular cores is a general concept for tuning the relative importance of entropic and enthalpic free energy contributions, hence providing a tool to stabilize an extended repertoire of nanostructured phases (see Reference: Fischer et al, Macromolecules 47, 7424-7430, 2014)
Second, we demonstrate that a related phase, based on the intergrowth of three so-called etc nets and recently detected in gemini surfactants (see Sorenson et al, Soft Matter 10, 8229-8235, 2014), is close to thermodynamic stability even in a simple AB diblock copolymer system (see Fischer et al, Soft Matter 11, 1226-1227, 2015). This emphasizes the likely broader role of these tricontinuous geometries in soft materials.
Finally, we briefly consider the photonic properties of a hypothetical multiply-intergrown grown gyroid-geometry, known as 4-srs and 8-srs structures. These structures, which conceivably could form in self-assembly processes related to the above (see Schroeder-Turk et al, Faraday Discussions, 161, 215-247, 2013), can currently be nanofabricated by direct laser writing technologies. Theory and experiments demonstrate that these highly-chiral materials (composed of 4 or 8 equal-handed chiral gyroid networks) have strong circular-polarisation properties which could make them useful as chiro-optical photonic material designs (Saba et al, Phys. Rev. Lett. 106, 103902, 2011; Saba et al, Phys. Rev. B 88, 245116, 2013)

In connective tissues and in many other soft materials the structural function is performed by a fiber network. These networks are composite, meaning that they are made from fibers of different properties or from fiber bundles of various sizes. In this work we study the elasticity of such structures with the broad goal of learning how to design fiber networks for desired effective properties. We show that the composite networks are in average softer than the equivalent ‘homogeneous&’ networks (made from fibers of same type) and the amount of softening scales linearly with the variance of the fiber properties distribution. We also investigate the effect of fiber properties distribution on the non-linear deformation of the network under large deformations. Other types of composite networks, such as those resulting upon the addition of rigid fibers to a homogeneous base network, are also discussed

Today, computational and theoretical materials science play important role in product development. Computer models help researchers to better understand structure-property relationships on atomistic, molecular, meso- and macroscales. One specific example showing the integration of modeling in product development is Directed Self-Assembly (DSA) -- a potentially promising method of writing lithographic patterns on a sub-40 nm length-scale. While the utility of DSA has been demonstrated in principle, there are many challenges that need to be solved before its wide adoption in the semiconductor industry. Computational modeling is crucial in addressing many of those challenges, e.g., optimizing polymer formulations, producing a better pattern, or predicting the defect density. We utilize mesoscale modeling, and more specifically Self-Consistent Field Theory (SCFT) to predict phase behavior of block copolymers in thin films (undirected self-assembly), as well as in cases of chemo- and graphoepitaxy (directed self-assembly). All in all, DSA modeling is becoming an integral part of formulation design and screening process, as will be shown in several examples.

Lamellar microdomains with perpendicular orientation are useful in block copolymer nanolithography. However, it is challenging to produce perpendicularly oriented microdomains in high interaction parameter block copolymers (BCPs) due to the difference in surface energies of the blocks, which promotes in-plane orientation. We show here both by self consistent field theory (SCFT) and experimentally that perpendicular orientation can be obtained using high aspect-ratio grating substrates in which the grating dimensions and substrate chemistry are optimized based on SCFT calculations. One block is preferentially attracted to the vertical sidewalls leading to perpendicular lamellae. The grating substrates were fabricated by laser interference lithography with period 300 nm - 1 µm and a lamella-forming polystyrene-block-polydimethylsiloxane BCP with molecular weight 43 kg/mol was used for demonstration. The SCFT simulation and an analytic model were used to map the energies of lamellae of different orientations as a function of the grating aspect ratio and the surface energies of the sidewalls and top and bottom surfaces. The optimized grating dimensions were tested experimentally by solvent vapor annealing in toluene/heptane vapor mixtures and by thermal annealing. Both processes produced perpendicular lamellae in agreement with the model, with the number of lamellae in the trench determined by the ratio between the trench width and the equilibrium period of the BCP. A slight taper of the trench sidewalls produced a defect (branched lamella) in each trench.

The self-assembly of block copolymers BCPs proves to be a valuable tool for fabricating intricate nano-patterns. The natural ability of BCPs to micro-phase separate results in harmonic morphologies that have geometries controlled by the chain characteristics. The untreated morphology of BCPs typically exhibit local order that fades away as the sample size increases. Hence, generating complex engineering patterns with multiple morphologies, meshed structures, or variable periodicities in a single BCP system requires extra processes of surface patterning and chemical treatment. Here, a bilayer system of BCPs is studied to understand the effect of the underlying topography on the behavior of the top layer&’s self-assembly.
A self-consistent field theoretic simulation SCFT is employed to investigate the role of several key parameters including the commensurability between layers&’ periodicities, the magnitude of topography height, and the chemical treatment of the substrate and the bottom layer of the BCP behavior. We test four periodic templates that have been used in the literature namely: step trenches, cosine shaped trenches, saw tooth trenches, and cosine flat tranches.
The findings hint to the fact that chemical treatment of the underlying layer is crucial to transfer the bottom pattern to the one forming on top. More specifically, stable topography is found to be created, and guided by the lower one in the presence of chemical functionality of the bottom layer. Similarly, prominent topography forces the upper layer to conform, however the effect is shadowed by the role of chemical treatment.
The SCFT findings are further confirmed experimentally on a PS-b-PDMS system self-assembled between HSQ lines created through E-beam lithography. This serves as a guideline for multilayer polymer templating to create multistacked 3D structures.

Our goal is to design polymer-based nano-sized drug delivery systems through the self-assembly of ABA triblock copolymers in aqueous medium. Individual molecular species of Pluronic polymers (PEG-PPO-PEG) and Tyrosine-derived PEG-b-oligo(DTO-SA)-b-PEG block copolymers are represented by two segments of hydrophilic beads and one segment of hydrophobic beads. PEG-b-oligo(DTO-SA)-b-PEG is modeled to possess alternate rigid and flexible components along its hydrophobic chain. We use a molecular dynamics-based mesoscopic simulation technique called Dissipative Particle Dynamics (DPD) to simultaneously resolve the aggregation dynamics, structure and morphology of the initial aggregation of polymer molecules in aqueous medium. We demonstrate the self-assembled aggregates to have core-corona structure with individual polymers bending into v-shape, which agrees with the experimental observations. We also determine the sizes of core and corona for the aggregates composed of PEG-oligo(DTO-SA)-PEG, Pluronic F68 and F127. In addition, we measure the critical aggregation concentration (CAC) and compare our results with corresponding results obtained using experimental approach. CAC measurements for Pluronic polymers F68, F88, F108, and F127 obtained using simulations are found to be in a good agreement with experimental measurements. For PEG-b-oligo(DTO-SA)-b-PEG block polymers, the CAC values determined and predicted from simulations are found to be one order of magnitude higher than those measured experimentally. Our results can be used to determine structural and dynamical properties of polymer-based drug delivery systems and build a virtual library of numerous ABA block polymers. These libraries can be utilized to optimize the design of drug delivery systems by simulating the interactions between ABA block copolymers and various drug molecules, and predict their drug encapsulation and release features.

Polyelectrolyte block copolymers, which combine the properties of polyelectrolytes (i.e., sensitive to changes in solvent ionic strength and pH) with those of surfactants, can self-assemble in an aqueous environment into a variety of responsive morphologies, including spherical micelles, cylindrical micelles, vesicles, lamellar mesophases, micellar networks and micellar aggregates. Such assemblies are promising candidates as carriers for drug and gene delivery, where the morphology and the size of the assemblies determine their transport properties and delivery capabilities. The morphology and size of formed aggregates are determined by the characteristically complex equilibrium of noncovalent forces (electrostatic, steric, hydrogen bonding, Van der Waals, and hydrophobic interactions). The strength of repulsive Coulomb interactions between the polyelectrolyte segments can be efficiently tuned by variations in ionic strength or/and pH in the aqueous solution. In order to explore the self-assembly process of polyelectrolyte block copolymers, we developed implicit solvent ionic strength (ISIS) model for use with the Dissipative Particle Dynamics (DPD) method to simulate the behavior of polyelectrolyte block copolymers with incorporated electrostatic interactions to achieve a good balance between reasonable physical description and computational feasibility. We applied this coarse-grained model to explore the influence of block length, block architecture, and solvent quality on the properties of the assemblies formed in aqueous solutions. Our DPD model enables us to obtain the main characteristics of the micelles formed from the self-assembly of polyelectrolyte diblock/triblock copolymers as a function of the block length and salt concentration. Based on a comprehensive set of data obtained we constructed a morphological diagram of polyelectrolyte block copolymers in aqueous solution. The coarse-grained modeling and simulation, which is demonstrated as a complimentary approach in addition to experimental and theoretical methods, can deliver insight into self-assembly processes of diblock/triblock copolymers and provide evaluation of the size of aggregates obtained along with their scaling relation representation. The simulation results suggest that this coarse-grained simulation scheme gives a route wherein one can effectively and efficiently capture the self-assembly behaviors of polyelectrolyte block copolymers, such as DNA, RNA and other natural and synthetic polycations and polyanions. This study can provide key knowledge for the rational design and preparation of polyelectrolyte block copolymers materials with desired morphological, mechanical, and rheological properties.

PEG-based hydrogels conjugated with biomolecules (e.g., bioactive peptides, enzymes, nucleotides) are being widely investigated for tissue engineering, regenerative medicine, and biosensor applications. The bioactivity of bioconjugated hydrogels depends on the structure and activity of the bioactive component of the system. Experimental methods alone are quite limited in their ability to provide molecular-level insights into how a given design could be optimized to enhance its performance. We are therefore developing molecular modeling methods to visualize, predict, and understand the molecular structure and behavior of these types of complex molecular systems using a three-level multiscale approach. (1) A coarse-grained (CG) model of the bioconjugated hydrogel is first generated at experimentally determined cross-linked density on a 3-D lattice using the bond-fluctuation Monte-Carlo method. (2) The lattice is then removed, CG parameters are generated based on all-atom models of hydrogel segments using the polymer consistent force field (PCFF), and the hydrogel system equilibrated off-lattice using the TIGER2 advanced sampling algorithm. (3) The equilibrated CG model is then reverse-mapped back into an all-atom model, which is then hydrated with explicit TIP3P water and re-equilibrated to represent the final all-atom bioconjugated hydrogel structure. Structure factor plots of S(q) vs. q are then calculated for comparison with experimentally determined structure factor plots determined by X-ray diffraction and/or neutron scattering for model validation. Once validated, the resulting predicted structures are available for bioactivity assessment and evaluation and to serve as a guide for design optimization for enhanced bioactivity.

Hydrogel materials have been receiving a great deal of attention over the last decades due to their applications in tissue scaffolding, cell culture platforms, in-vivo bio-sensing, and drug delivery. When exposed to external stimuli such as temperature, pH levels, light intensity, and electric/magnetic fields hydrogels undergo a reversible and sometimes discontinuous volume transition. The micromechanics and kinetics of gels near this critical transition point is not fully understood which hinders developments in some of the aforementioned areas. In our study, we utilize dissipative particle dynamics (DPD) to develop a mesoscale model for responsive polymer networks. We use this model to examine how the bulk modulus of a hydrogel changes as a function of the Flory-Huggins parameter. This allows us to probe the micromechanics of these networks near the critical volume transition point. Our simulations show that the bulk modulus is minimized for theta solvent conditions. Additionally, for good solvent we demonstrate that the bulk modulus scales with the polymer volume fraction as: K ~ (1/phi;_p)^-9/4. At large strains and large values of Flory-Huggins parameter the network exhibits phase separation leading to abnormal variation of the modulus.
Support from NSF CAREER Award (DMR-1255288) is gratefully acknowledged

A Bicontinuous Interfacially Jammed Emulsion-geL, or bijel, is a canonical example of the use of computational techniques to design a new soft material [1]. In the lattice Boltzmann simulations, the material is created by trapping the spinodal pattern of two fluid domains using a layer of interfacial colloidal particles. Jamming of the particles arrests the phase separation of the fluids and gives the composite sample a yield stress.
By translating simulation variables into the real world, it can be shown that the simulations can only explore the fate of such a material for about a microsecond. Evidently part of the design process is finding out what happens after that! Experiments first showed that this new soft material could really be made and that it exhibits long-term stability [2]. The key step (which may ultimately prove to be unnecessary [3]) is tuning the wettability of the particle surfaces.
Curiously, subsequent experiments showed that the bijel does not always fall apart when the interfacial tension is removed. This inspired a return to simulations: molecular dynamics were used to demonstrate that a plausible combination of short-range attractive and long-range repulsive inter-particle interactions would hold the structure together [4]. The resulting colloidal scaffold was term