1
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Chaimovich M, Chaimovich A. Relative Resolution: An Analysis with the Kullback-Leibler Entropy. J Chem Theory Comput 2024; 20:2074-2087. [PMID: 38416535 DOI: 10.1021/acs.jctc.3c01052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/29/2024]
Abstract
A novel type of a multiscale approach, called Relative Resolution (RelRes), can correctly retrieve the behavior of various nonpolar liquids while speeding up molecular simulations by almost an order of magnitude. In this approach in a single system, molecules switch their resolution in terms of their relative separation, with near neighbors interacting via fine-grained potentials, yet far neighbors interacting via coarse-grained potentials; notably, these two potentials are analytically parametrized by a multipole approximation. Our current work focuses on analyzing RelRes by relating it with the Kullback-Leibler (KL) entropy, which is a useful metric for multiscale errors. In particular, we thoroughly examine the exact and approximate versions of this informatic measure for several alkane systems. By analyzing its dependency on the system size, we devise a formula for predicting the exact KL entropy of an "infinite" system via the computation of the approximate KL entropy of an "infinitesimal" system. Demonstrating that the KL entropy can holistically capture many multiscale errors, we settle bounds for the KL entropy that ensure a sufficient representation of the structural and thermal behavior by the RelRes algorithm. This, in turn, allows the scientific community to readily determine the ideal switching distance for an arbitrary RelRes system.
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Affiliation(s)
- Mark Chaimovich
- Russian School of Mathematics, North Bethesda, Maryland 20852, United States
| | - Aviel Chaimovich
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States
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2
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Petix CL, Fakhraei M, Kieslich CA, Howard MP. Surrogate Modeling of the Relative Entropy for Inverse Design Using Smolyak Sparse Grids. J Chem Theory Comput 2024; 20:1538-1546. [PMID: 37703086 DOI: 10.1021/acs.jctc.3c00651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
Relative entropy minimization, a statistical-mechanics approach for finding potential energy functions that produce target structural ensembles, has proven to be a powerful strategy for the inverse design of nanoparticle self-assembly. For a given target structure, the gradient of the relative entropy with respect to the adjustable parameters of the potential energy function is computed by performing a simulation, and then these parameters are updated using iterative gradient-based optimization. Small parameter updates per iteration and many iterations can be required for numerical stability, but this incurs considerable computational expense because a new simulation must be performed to reevaluate the gradient at each iteration. Here, we investigate the use of surrogate modeling to decouple the process of minimizing the relative entropy from the computationally demanding process of determining its gradient. We approximate the relative-entropy gradient using Chebyshev polynomial interpolation on Smolyak sparse grids. Our approach potentially increases the robustness and computational efficiency of using the relative entropy for inverse design, primarily for physically informed potential energy functions that have a small number of adjustable parameters.
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Affiliation(s)
- C Levi Petix
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Mohammadreza Fakhraei
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Chris A Kieslich
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Michael P Howard
- Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
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3
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Beneduce C, Sciortino F, Šulc P, Russo J. Engineering Azeotropy to Optimize the Self-Assembly of Colloidal Mixtures. ACS NANO 2023; 17:24841-24853. [PMID: 38048489 PMCID: PMC10753881 DOI: 10.1021/acsnano.3c05569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Revised: 11/08/2023] [Accepted: 11/09/2023] [Indexed: 12/06/2023]
Abstract
The goal of inverse self-assembly is to design interparticle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new component increasing the thermodynamic degrees of freedom and, hence, the complexity of the self-assembly pathway. In this work we explore the possibility to use azeotropy, i.e., a special thermodynamic condition where the system behaves effectively as a one-component system, as a way to control the self-assembly of an arbitrary number of components. Exploiting the mass-balance equations, we show how to select patchy particle systems that exhibit azeotropic points along the desired self-assembly pathway. As an example we map the phase diagram of a binary mixture that, by design, fully assembles into cubic (and only cubic) diamond crystal via an azeotropic point. The ability to explicitly include azeotropic points in artificial designs reveals effective pathways for the self-assembly of complex structures.
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Affiliation(s)
- Camilla Beneduce
- Dipartimento
di Fisica, Sapienza Università di
Roma, P.le Aldo Moro 5, 00185 Rome, Italy
| | - Francesco Sciortino
- Dipartimento
di Fisica, Sapienza Università di
Roma, P.le Aldo Moro 5, 00185 Rome, Italy
| | - Petr Šulc
- School
of Molecular Sciences and Center for Molecular Design and Biomimetics,
The Biodesign Institute, Arizona State University, 1001 South McAllister Avenue, Tempe, Arizona 85281, United States
- School
of Natural Sciences, Department of Bioscience, TU Munich, Am Coulombwall
4a, 85748, Garching, Germany
| | - John Russo
- Dipartimento
di Fisica, Sapienza Università di
Roma, P.le Aldo Moro 5, 00185 Rome, Italy
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4
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de Las Heras D, Zimmermann T, Sammüller F, Hermann S, Schmidt M. Perspective: How to overcome dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:271501. [PMID: 37023762 DOI: 10.1088/1361-648x/accb33] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2023] [Accepted: 04/06/2023] [Indexed: 06/19/2023]
Abstract
We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.
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Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Toni Zimmermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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5
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Shao L, Ma J, Prelesnik JL, Zhou Y, Nguyen M, Zhao M, Jenekhe SA, Kalinin SV, Ferguson AL, Pfaendtner J, Mundy CJ, De Yoreo JJ, Baneyx F, Chen CL. Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction. Chem Rev 2022; 122:17397-17478. [PMID: 36260695 DOI: 10.1021/acs.chemrev.2c00220] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.
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Affiliation(s)
- Li Shao
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Jinrong Ma
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States
| | - Jesse L Prelesnik
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Yicheng Zhou
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Mary Nguyen
- Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States.,Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Mingfei Zhao
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Samson A Jenekhe
- Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States.,Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Sergei V Kalinin
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Jim Pfaendtner
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Christopher J Mundy
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
| | - James J De Yoreo
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States
| | - François Baneyx
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States.,Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Chun-Long Chen
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
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6
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Padilla LA, León-Islas AA, Funkhouser J, Armas-Pérez JC, Ramírez-Hernández A. Dynamics and phase behavior of two-dimensional size-asymmetric binary mixtures of core-softened colloids. J Chem Phys 2021; 155:214901. [PMID: 34879672 DOI: 10.1063/5.0067449] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
The self-assembly of binary colloidal mixtures provides a bottom-up approach to create novel functional materials. To elucidate the effect of composition, temperature, and pressure on the self-assembly behavior of size-asymmetric mixtures, we performed extensive dynamics simulations of a simple model of polymer-grafted colloids. We have used a core-softened interaction potential and extended it to represent attractive interactions between unlike colloids and repulsions between like colloids. Our study focused on size-asymmetric mixtures where the ratio between the sizes of the colloidal cores was fixed at σBσA=0.5. We have performed extensive simulations in the isothermal-isobaric and canonical (NVT) ensembles to elucidate the phase behavior and dynamics of mixtures with different stoichiometric ratios. Our simulation results uncovered a rich phase behavior, including the formation of hierarchical structures with many potential applications. For compositions where small colloids are the majority, sublattice melting occurs for a wide range of densities. Under these conditions, large colloids form a well-defined lattice, whereas small colloids can diffuse through the system. As the temperature is decreased, the small colloids localize, akin to a metal-insulator transition, with the small colloids playing a role similar to electrons. Our results are summarized in terms of phase diagrams.
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Affiliation(s)
- Luis A Padilla
- Department of Biomedical Engineering and Chemical Engineering, The University of Texas at San Antonio, San Antonio, Texas 78249, USA
| | - Andres A León-Islas
- Department of Biomedical Engineering and Chemical Engineering, The University of Texas at San Antonio, San Antonio, Texas 78249, USA
| | - Jesse Funkhouser
- Department of Biomedical Engineering and Chemical Engineering, The University of Texas at San Antonio, San Antonio, Texas 78249, USA
| | - Julio C Armas-Pérez
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, CP 37150 León, Guanajuato, Mexico
| | - Abelardo Ramírez-Hernández
- Department of Biomedical Engineering and Chemical Engineering, The University of Texas at San Antonio, San Antonio, Texas 78249, USA
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7
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Mahynski NA, Shen VK. Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids. SOFT MATTER 2021; 17:7853-7866. [PMID: 34382053 PMCID: PMC9793339 DOI: 10.1039/d1sm00875g] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
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.
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Affiliation(s)
- Nathan A Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA.
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8
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Lindquist BA. Inverse design of equilibrium cluster fluids applied to a physically informed model. J Chem Phys 2021; 154:174907. [PMID: 34241069 DOI: 10.1063/5.0048812] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. We then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.
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Affiliation(s)
- Beth A Lindquist
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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9
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Piñeros WD, Tlusty T. Inverse design of nonequilibrium steady states: A large-deviation approach. Phys Rev E 2021; 103:022101. [PMID: 33735990 DOI: 10.1103/physreve.103.022101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
The design of small scale nonequilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for nonequilibrium systems is lacking, making the design problem particularly difficult. Here we show we can exploit the large-deviation behavior of a Brownian particle and design a variety of geometrically complex steady-state density distributions and flux field flows. We achieve this design target from direct knowledge of the joint large-deviation functional for the empirical density and flow, and a "relaxation" algorithm on the desired target states via adjustable force field parameters. We validate the method by replicating analytical results, and demonstrate its capacity to yield complex prescribed targets, such as rose-curve or polygonal shapes on the plane. We consider this dynamical fluctuation approach a first step towards the design of more complex NESS where general frameworks are otherwise still lacking.
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Affiliation(s)
- William D Piñeros
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
| | - Tsvi Tlusty
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
- Department of Physics and Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea
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10
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Chaimovich M, Chaimovich A. Relative Resolution: A Computationally Efficient Implementation in LAMMPS. J Chem Theory Comput 2021; 17:1045-1059. [PMID: 33512166 DOI: 10.1021/acs.jctc.0c01003] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Recently, a novel type of multiscale simulation, called Relative Resolution (RelRes), was introduced. In a single system, molecules switch their resolution in terms of their relative separation, with near neighbors interacting via fine-grained potentials yet far neighbors interacting via coarse-grained potentials; notably, these two potentials are analytically parametrized by a multipole approximation. This multiscale approach is consequently able to correctly retrieve across state space the structural and thermal, as well as static and dynamic, behavior of various nonpolar mixtures. Our current work focuses on the practical implementation of RelRes in LAMMPS, specifically for the commonly used Lennard-Jones potential. By examining various correlations and properties of several alkane liquids, including complex solutions of alternate cooligomers and block copolymers, we confirm the validity of this automated LAMMPS algorithm. Most importantly, we demonstrate that this RelRes implementation gains almost an order of magnitude in computational efficiency, as compared with conventional simulations. We thus recommend this novel LAMMPS algorithm for anyone studying systems governed by Lennard-Jones interactions.
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Affiliation(s)
- Mark Chaimovich
- Russian School of Mathematics, North Bethesda, Maryland 20852, United States
| | - Aviel Chaimovich
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States
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11
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O'Leary J, Mao R, Pretti EJ, Paulson JA, Mittal J, Mesbah A. Deep learning for characterizing the self-assembly of three-dimensional colloidal systems. SOFT MATTER 2021; 17:989-999. [PMID: 33284930 DOI: 10.1039/d0sm01853h] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems' stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. We first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.
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Affiliation(s)
- Jared O'Leary
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720, USA.
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12
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Abstract
Crystallization is fundamental to materials science and is central to a variety of applications, ranging from the fabrication of silicon wafers for microelectronics to the determination of protein structures. The basic picture is that a crystal nucleates from a homogeneous fluid by a spontaneous fluctuation that kicks the system over a single free-energy barrier. However, it is becoming apparent that nucleation is often more complicated than this simple picture and, instead, can proceed via multiple transformations of metastable structures along the pathway to the thermodynamic minimum. In this article, we observe, characterize, and model crystallization pathways using DNA-coated colloids. We use optical microscopy to investigate the crystallization of a binary colloidal mixture with single-particle resolution. We observe classical one-step pathways and nonclassical two-step pathways that proceed via a solid-solid transformation of a crystal intermediate. We also use enhanced sampling to compute the free-energy landscapes corresponding to our experiments and show that both one- and two-step pathways are driven by thermodynamics alone. Specifically, the two-step solid-solid transition is governed by a competition between two different crystal phases with free energies that depend on the crystal size. These results extend our understanding of available pathways to crystallization, by showing that size-dependent thermodynamic forces can produce pathways with multiple crystal phases that interconvert without free-energy barriers and could provide approaches to controlling the self-assembly of materials made from colloids.
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13
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Lin Z, Emamy H, Minevich B, Xiong Y, Xiang S, Kumar S, Ke Y, Gang O. Engineering Organization of DNA Nano-Chambers through Dimensionally Controlled and Multi-Sequence Encoded Differentiated Bonds. J Am Chem Soc 2020; 142:17531-17542. [PMID: 32902966 DOI: 10.1021/jacs.0c07263] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Engineering the assembly of nanoscale objects into complex and prescribed structures requires control over their binding properties. Such control might benefit from a well-defined bond directionality, the ability to designate their engagements through specific encodings, and the capability to coordinate local orientations. Although much progress has been achieved in our ability to design complex nano-objects, the challenges in creating such nano-objects with fully controlled binding modes and understanding their fundamental properties are still outstanding. Here, we report a facile strategy for creating a DNA nanochamber (DNC), a hollow cuboid nano-object, whose bonds can be fully prescribed and complexly encoded along its three orthogonal axes, giving rise to addressable and differentiated bonds. The DNC can host nanoscale cargoes, which allows for the integration with functional nano-objects and their organization in larger-scale systems. We explore the relationship between the design of differentiated bonds and a formation of one-(1D), two-(2D), and three-(3D) dimensional organized arrays. Through the realization of different binding modes, we demonstrate sequence encoded nanoscale heteropolymers, helical polymers, 2D lattices, and mesoscale 3D nanostructures with internal order, and show that this assembly strategy can be applied for the organization of nanoparticles. We combine experimental investigations with computational simulation to understand the mechanism of structural formation for different types of ordered arrays, and to correlate the bonds design with assembly processes.
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Affiliation(s)
- Zhiwei Lin
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Hamed Emamy
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Brian Minevich
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Yan Xiong
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Shuting Xiang
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Sanat Kumar
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Yonggang Ke
- Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Georgia 30322, United States
| | - Oleg Gang
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States.,Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States.,Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, United States
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14
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Role of Entropy in Colloidal Self-Assembly. ENTROPY 2020; 22:e22080877. [PMID: 33286648 PMCID: PMC7517482 DOI: 10.3390/e22080877] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/05/2020] [Revised: 08/03/2020] [Accepted: 08/05/2020] [Indexed: 12/13/2022]
Abstract
Entropy plays a key role in the self-assembly of colloidal particles. Specifically, in the case of hard particles, which do not interact or overlap with each other during the process of self-assembly, the free energy is minimized due to an increase in the entropy of the system. Understanding the contribution of entropy and engineering it is increasingly becoming central to modern colloidal self-assembly research, because the entropy serves as a guide to design a wide variety of self-assembled structures for many technological and biomedical applications. In this work, we highlight the importance of entropy in different theoretical and experimental self-assembly studies. We discuss the role of shape entropy and depletion interactions in colloidal self-assembly. We also highlight the effect of entropy in the formation of open and closed crystalline structures, as well as describe recent advances in engineering entropy to achieve targeted self-assembled structures.
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