Academia.eduAcademia.edu

Outline

Title
Abstract
Introduction
Objective Functions
Quality Metric Objective Functions
Properties of the Objective Functions
Optimization Methods
Methods for Generating Potentials
Geometric Method
Baseline Method
Trend Optimization Methods
Results
References
All Topics
Mathematics

Fast Generation of Potentials for Self-Assembly of Particles

Profile image of Philip du ToitPhilip du Toit

2009, arXiv: Adaptation and Self-Organizing Systems

Abstract

We address the inverse problem of designing isotropic pairwise particle interaction potentials that lead to the formation of a desired lattice when a system of particles is cooled. The design problem is motivated by the desire to produce materials with pre-specified structure and properties. We present a heuristic computation-free geometric method, as well as a fast and robust trend optimization method that lead to the formation of high quality honeycomb lattices. The trend optimization method is particularly successful since it is well-suited to efficient optimization of the noisy and expensive objective functions encountered in the self-assembly design problem. We also present anisotropic potentials that robustly lead to the formation of the kagome lattice, a lattice that has not previously been obtained with isotropic potentials.

Related papers

Self-assembly of anisotropic soft particles in two dimensions
Carlos Mendoza

The European Physical Journal E, 2013

The self assembly of core-corona discs interacting via anisotropic potentials is investigated using Monte Carlo computer simulations. A minimal interaction potential that incorporates anisotropy in a simple way is introduced. It consists in a core-corona architecture in which the center of the core is shifted with respect to the center of the corona. Anisotropy can thus be tuned by progressively shifting the position of the core. Despite its simplicity, the system self organize in a rich variety of structures including stripes, triangular and rectangular lattices, and unusual plastic crystals. Our results indicate that the amount of anisotropy does not alter the lattice spacing and only influences the type of clustering (stripes, micells, etc.) of the individual particles. *

View PDFchevron_right
Self-organization as a new method for synthesizing smart and structured materials
Jerzy Maselko

Materials Science and Engineering: C, 1996

Self-organization in chemical systems may be a basis for entirely new 21st-century technologies. During self-organization, concentrations of chemical species spontaneously organize in space and time, forming a variety of complex structures. Examples of these structures are Turing patterns which result from interaction between chemical kinetics and diffusion. In this paper we report numerical studies of Turing structures that develop spontaneously from single perturbations. Many of these structures are built from layers of different chemical concentrations. Others form skeletal type patterns, or respond to environment. These structures may find applications in formation of highly structured or smart materials.

View PDFchevron_right
Reversible self-assembly of patchy particles into monodisperse icosahedral clusters
pauline Wong

The Journal of Chemical Physics, 2007

We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity ͑the patches must be narrow enough to energetically select the desired clusters͒ and kinetic accessibility ͑they must be sufficiently wide to avoid kinetic traps͒. Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ordered clusters can form through a number of different dynamic pathways, including direct nucleation and indirect pathways involving large disordered intermediates. The latter pathway is related to a reentrant liquid-togas transition that occurs for intermediate patch widths upon lowering the temperature. We also find that the assembly process is robust to inaccurate patch placement up to a certain threshold and that it is possible to replace the five discrete patches with a single ring patch with no significant loss in yield.

View PDFchevron_right
Layer-by-layer assembly of patchy particles as a route to nontrivial structures
Niladri Patra

Physical Review E

We propose a new strategy for robust high-quality self-assembly of non-trivial periodic structures out of patchy particles, and investigate it with Brownian Dynamics (BD) simulations. Its first element is the use of specific patch-patch and shell-shell interactions between the particles, that can be implemented through differential functionalization of patched and shell regions with specific DNA strands. The other key element of our approach is the use of layer-by-layer protocol that allows to avoid a formations of undesired random aggregates. As an example, we design and self-assemble "in silico" a version of a Double Diamond (DD) lattice in which four particle types are arranged into BCC crystal made of four FCC sublattices. The lattice can be further converted to Cubic Diamond (CD) by selective removal of the particles of certain types. Our results demonstrate that by combining the directionality, selectivity of interactions and the layer-by-layer protocol, a high quality robust self-assembly can be achieved.

View PDFchevron_right
Self-Assembly: From Crystals to Cells
Christopher Wilmer

Soft Matter, 2009

View PDFchevron_right
Self-assembly scenarios of patchy colloidal particles in two dimensions
Emanuela Bianchi

Journal of Physics: Condensed Matter, 2010

The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is extremely difficult to predict the large variety of ordered equilibrium structures that these particles are able to undergo under the variation of external parameters, such as temperature or pressure. Here we show that, by a novel combination of two theoretical tools, it is indeed possible to predict the self-assembly scenario of patchy colloidal particles: on one hand, a reliable and efficient optimization tool based on ideas of evolutionary algorithms helps to identify the ordered equilibrium structures to be expected at T = 0; on the other hand, suitable simulation techniques allow to estimate via free energy calculations the phase diagram at finite temperature. With these powerful approaches we are able to identify the broad variety of emerging self-assembly scenarios for spherical colloids decorated by four patches and we investigate the stability of the crystal structures on modifying in a controlled way the regular tetrahedral arrangement of the patches.

View PDFchevron_right
Self-assembly of nanoclusters: An energy landscape perspective
David Wales

2011

Judicious design of building blocks is the key to nanofabrication via programmed self-assembly.

View PDFchevron_right
Lessons from simulation regarding the control of synthetic self-assembly
Jack Douglas

Journal of Materials Research, 2007

We investigated the role of particle potential symmetry on self-assembly by Monte Carlo simulation with a particular view toward synthetically creating structures of prescribed form and function. First, we established a general tendency for the rotational potential symmetries of the particles to be locally preserved upon self-assembly. Specifically, we found that a dipolar particle potential, having a continuous rotational symmetry about the dipolar axis, gives rise to chain formation, while particles with multipolar potentials (e.g., square quadrupole) having discrete rotational symmetries lead to the self-assembly of “random surface” polymers preserving the rotational symmetries of the particles within these sheet structures. Surprisingly, these changes in self-assembly geometry with the particle potential symmetry are also accompanied by significant changes in the thermodynamic character and in the kinetics of the self-assembly process. Linear chain growth involves a continuous c...

View PDFchevron_right
Three-dimensional self-assembly using dipolar interaction
Per Löthman

Science Advances

Interaction between dipolar forces, such as permanent magnets, generally leads to the formation of one-dimensional chains and rings. We investigated whether it was possible to let dipoles self-assemble into three-dimensional structures by encapsulating them in a shell with a specific shape. We found that the condition for self-assembly of a three-dimensional crystal is satisfied when the energies of dipoles in the parallel and antiparallel states are equal. Our experiments show that the most regular structures are formed using cylinders and cuboids and not by spheroids. This simple design rule will help the self-assembly community to realize three-dimensional crystals from objects in the micrometer range, which opens up the way toward previously unknown metamaterials.

View PDFchevron_right
Using Hierarchical Self-Assembly To Form Three-Dimensional Lattices of Spheres
Hongkai Wu

Journal of The American Chemical Society, 2002

This paper describes an approach to the fabrication of three-dimensional (3-D) structures of millimeter-scale spherical beads having a range of latticesstetragonal, cubic, and hexagonalsusing hierarchical self-assembly. The process has five steps: (i) metal-coated beads are packed in a rod-shaped cavity in an elastomeric polymer (poly(dimethylsiloxane), PDMS); (ii) the beads are embedded in a second polymer (PDMS or polyurethane, PU) using a procedure that leaves the parts of the beads in contact with the PDMS exposed; (iii) the exposed areas of the beads are coated with a solder having a low melting point; (iv) the polymer rodsswith embedded beads and exposed solder dropssare suspended in an approximately isodense medium (an aqueous solution of KBr) and allowed to self-assemble by capillary interactions between the drops of molten solder; and (v) the assembly is finished by several procedures, including removing the beads from the polymer matrix by dissolution, filling the voids left with another material, and dissolving the matrix. The confinement of the beads in regular structures in polymer rods makes it possible to generate self-assembled structures with a variety of 3-D lattices; the type of the lattice formed can be controlled by varying the size of the beads, and the size and shape of the cross-section of the rods.

View PDFchevron_right

References (51)

  1. G. M. Whitesides and B. Grzybowski, Self-Assembly at All Scales, Science, 295(5564), 2418-2421 (2002).
  2. M. M. Murr and D. E. Morse, Fractal intermediates in the self-assembly of silicatein filaments, Pro- ceedings of the National Academy of Sciences of the United States of America, 102(33), 11657-11662 (2005).
  3. W. Zheng, P. Buhlmann, and H. Jacobs, Sequential shape-and-solder-directed self-assembly of func- tional microsystems, Proceedings of the National Academy of Sciences of the United States of America, 101(35), 12814-12817 (2004).
  4. S. A. Stauth and B. A. Parviz, Self-assembled single-crystal silicon circuits on plastic, Proceedings of the National Academy of Sciences of the United States of America, 103(38), 13922-13927 (2006).
  5. R. Gross and M. Dorigo, Evolution of Solitary and Group Transport Behaviors for Autonomous Robots Capable of Self-Assembling, Adaptive Behavior, 16(5), 285-305 (2008).
  6. K. Jakab, A. Neagu, V. Mironov, R. R. Markwald, and G. Forgacs, Engineering biological structures of prescribed shape using self-assembling multicellular systems, Proceedings of the National Academy of Sciences of the United States of America, 101(9), 2864-2869 (2004).
  7. V. Manoharan, M. Elsesser, and D. Pine, Dense packing and symmetry in small clusters of microspheres, Science, 301(5632), 483-487 (2003).
  8. P. Maksymovych, D. C. Sorescu, K. D. Jordan, and J. Yates, John T., Collective Reactivity of Molecular Chains Self-Assembled on a Surface, Science, 322(5908), 1664-1667 (2008).
  9. M. Engel and H. Trebin, Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential, Physical Review Letters, 98(22), 225505 (2007).
  10. M. A. Glaser, G. M. Grason, R. D. Kamien, A. Kosmrlj, C. D. Santangelo, and P. Ziherl, Soft spheres make more mesophases, EPL (Europhysics Letters), 78(4), 46004 (5pp) (2007).
  11. V. V. Hoang and T. Odagaki, Molecular dynamics simulations of simple monatomic amorphous nanoparticles, Physical Review B (Condensed Matter and Materials Physics), 77(12), 125434 (2008).
  12. Y. H. Liu, L. Y. Chew, and M. Y. Yu, Self-assembly of complex structures in a two-dimensional system with competing interaction forces, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 78(6), 066405 (2008).
  13. A. Quandt and M. P. Teter, Formation of quasiperiodic patterns within a simple two-dimensional model system, Phys. Rev. B, 59(13), 8586-8592 (1999).
  14. O. Sigmund and S. Torquato, Composites with extremal thermal expansion coefficients, Applied Physics Letters, 69(21), 3203-3205 (1996).
  15. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Existence of a photonic gap in periodic dielectric structures, Phys. Rev. Lett., 65(25), 3152-3155 (1990).
  16. T. A. Mary, J. S. O. Evans, T. Vogt, and A. W. Sleight, Negative Thermal Expansion from 0.3 to 1050 Kelvin in ZrW 2 O 8 , Science, 272(5258), 90-92 (1996).
  17. B. Xu, F. Arias, S. Brittain, X. Zhao, B. Grzybowski, S. Torquato, and G. Whitesides, Making negative Poisson's ratio microstructures by soft lithography, Advanced Materials, 11(14), 1186-1189 (1999).
  18. S. Hyun and S. Torquato, Designing composite microstructures with targeted properties, Journal of Materials Research, 16(1), 280-285 (2001).
  19. G. Ferey and A. Cheetham, Porous materials -Prospects for giant pores, Science, 283(5405), 1125-1126 (1999).
  20. B. Chen, M. Eddaoudi, S. Hyde, M. O'Keeffe, and O. Yaghi, Interwoven metal-organic framework on a periodic minimal surface with extra-large pores, Science, 291(5506), 1021-1023 (2001).
  21. A. Greer, Condensed matter -Too hot to melt, Nature, 404(6774), 134-135 (2000).
  22. C. A. Murray and D. G. Grier, Video Microscopy of Monodisperse Colloidal Systems, Annual Review of Physical Chemistry, 47(1), 421-462 (1996).
  23. Rechtsman, M., F. Stillinger, and S. Torquato [2006], Designed interaction potentials via inverse meth- ods for self-assembly. Phys. Rev. E 73, 011406.
  24. S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, Journal of Computational Physics, 117(1), 1 -19 (1995). See also the website at http://lammps.sandia.gov.
  25. Theil, F. [2006], A proof of crystallization in two dimensions. Comm. Math. Phys 262, 209.
  26. Rechtsman, M., F. Stillinger, and S. Torquato [2005], Optimized interactions for targeted self-assembly: Application to a honeycomb lattice. Phys. Rev. Lett. 95, 228301.
  27. Grubits, K. A., and J. E. Marsden (2008), Lattice Quality Assessment Tools and their Applications. in preparation.
  28. Booker, A. J. (1996), Case studies in design and analysis of computer experiments. Proceedings of the Section on Physical and Engineering Sciences, American Statistical Association.
  29. Myers, R., and D. C. Montgomery (1995), Response Surface Methodology: Process and product opti- mization using designed experiments. John Wiley & Sons, New York.
  30. Galassi, Davies, T. G. J. A. B. R. (2009). GNU Scientific Library Reference Manual -Third Edition (Third). Network theory Ltd..
  31. Booker, A. J., J. E. Dennis Jr., P. D. Frank, D. B. Serafini, V. Torzon, and M. W. Trosset (1999), A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization 17, 1.
  32. Torczon, V. [1997], On the convergence of pattern search algorithms. SIAM J. Optimization 7, (1), 1.
  33. Audet, C., and J. E. Dennis Jr. (2003), Analysis of generalized pattern searches. SIAM Journal on Optimization 13, 889.
  34. C. Audet and J. J. E. Dennis, Mesh Adaptive Direct Search Algorithms for Constrained Optimization, SIAM Journal on Optimization, 17(1), 188-217 (2006).
  35. C. Audet, V. Bchard, and J. Chaouki, Spent potliner treatment process optimization using a MADS algorithm, Optimization and Engineering, 9(2), 143-160 (2008).
  36. A. L. Marsden, J. A. Feinstein, and C. A. Taylor, A computational framework for derivative-free optimization of cardiovascular geometries, Computer Methods in Applied Mechanics and Engineering, 197(21-24), 1890 -1905 (2008).
  37. A. L. Marsden, M. Wang, J. E. Dennis, and P. Moin, Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation, Journal of Fluid Mechanics, 572(-1), 13-36 (2007).
  38. E. S. Siah, M. Sasena, J. L. Volakis, P. Y. Papalambros, and R. W. Wiese, Fast parameter optimization of large-scale electromagnetic objects using DIRECT with Kriging metamodeling, Microwave Theory and Techniques, IEEE Transactions on, 52(1), 276-285 (2004).
  39. W. Raza and K. Kim, Evaluation of Surrogate Models in Optimization of Wire-Wrapped Fuel Assembly, Journal of Nuclear Science and Technology, 44(6), 819-822 (2007).
  40. Cressie, N. (1990), The origins of kriging. Mathematical Geology 22, 239.
  41. Simpson, T. W., J. J. Korte, T. M. Mauery, and F. Mistree [1998], Comparison of response surface and kriging models for multidisciplinary design optimization. AIAA Paper, 98-4755.
  42. Giunta, A. A., and L. T. Watson (1998), A comparison of approximation modeling techniques: poly- nomial versus interpolating models. AIAA Paper, 98-4758.
  43. Hastie, T., R. Tibshirani, and J. H. Friedman (2001), The Elements of Statistical Learning, Springer.
  44. Tikhonov, A. N. and Arsenin, V. Y. (1977). Solutions of Ill-posed Problems. New York: Halsted Press.
  45. Dyn, N., D. Levin, and S. Rippa (1986), Numerical procedures for surface fitting of scattered data by radial basis functions. SIAM J. Sci. Statist. Comp. 7, 639.
  46. Fasshauer, G. E. (2007). Meshfree Approximation Methods with MATLAB. Singapore: World Scientific Publishing .
  47. Gutmann, H.-M. (2001), A radial basis function method for global optimization. Journal of Global Optimization 19(3), 201.
  48. M. D. McKay, R. J. Beckman, and W. J. Conover, A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics, 21(2), 239-245 (1979).
  49. M. Mekata, Kagome: The Story of the Basketweave Lattice, Physics Today, 56(2), 12-13 (2003).
  50. Jagla, E. A. (1999), Minimum energy configurations of repelling particles in two dimensions. J. Chem.
  51. M. C. Rechtsman, F. H. Stillinger, and S. Torquato, Synthetic diamond and wurtzite structures self- assemble with isotropic pair interactions, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 75(3), 031403 (2007).

Related papers

Self-assembly of anisotropic particles
David Wales

Soft Matter, 2011

We discuss the main features of the potential energy landscape that are associated with efficient 'structure-seeking' systems for particles interacting via anisotropic, pairwise additive forces. The interparticle potentials employed here are intended for a coarse-grained description of mesoscopic building blocks, such as colloids or functionalised metal clusters. We show that the anisotropy of the building blocks and the orientation-dependent interaction strengths are the most important factors that govern self-assembly into particular target morphologies. By varying the model parameters, the selfassembling behaviour can be systematically tuned. Design principles are outlined for various structures, and we postulate a sufficient condition for building-blocks to self-assemble into helical strands.

View PDFchevron_right
Inverse design of charged colloidal particle interactions for self assembly into specified crystal structures
Marjolein Dijkstra

The Journal of Chemical Physics

We study the inverse problem of tuning interaction parameters between charged colloidal particles interacting with a hard-core repulsive Yukawa potential, so that they assemble into specified crystal structures. Here, we target the body-centered-cubic (bcc) structure which is only stable in a small region in the phase diagram of charged colloids and is, therefore, challenging to find. In order to achieve this goal, we use the statistical fluctuations in the bond orientational order parameters to tune the interaction parameters for the bcc structure, while initializing the system in the fluid phase, using the Statistical Physics-inspired Inverse Design algorithm. We also find that this optimization algorithm correctly senses the fluid-solid phase boundaries for charged colloids. Finally, we repeat the procedure employing the covariance matrix adaptation-evolution strategy, a cutting edge optimization technique, and compare the relative efficacy of the two methods.

View PDFchevron_right
Design of a Kagome lattice from soft anisotropic particles
David Wales

Soft Matter, 2015

We present a simple model of triblock Janus particles based on discoidal building blocks, which can form energetically stabilized Kagome structures. We find 'magic number' global minima in small clusters whenever particle numbers are compatible with a perfect Kagome structure, without constraining the accessible three-dimensional configuration space. The preference for planar structures with two bonds per patch among all other possible minima on the landscape is enhanced when sedimentation forces are included. For the building blocks in question, structures containing three bonds per patch become progressively higher in energy compared to Kagome structures as sedimentation forces increase. Rearrangements between competing structures, as well as ring formation mechanisms are characterised and found to be highly cooperative. In the experimental setup, 9 colloidal triblock Janus particles preferentially form a Kagome lattice if each particle has four nearest neighbours, each hydrophobic patch interacting with

View PDFchevron_right
Theory and Simulation Studies of Self-Assembly of Helical Particles
Achille Giacometti

Self-Assembling Systems, 2016

Self-assembly-a governing principle by which materials form-is the autonomous organization of matter into ordered arrangements [1, 2]. It is typically associated with thermodynamic equilibrium, the organized structures being characterized by a minimum in the system's free energy, although this definition is too broad. Self-assembling processes are ubiquitous in nature, ranging, for example, from the opalescent inner surface of the abalone shell to the internal compartments of a living cell [3]. By these processes, nanoparticles or other discrete components spontaneously organize due to direct specific interactions and/or indirectly, through their environment. Self-assembly is one of the few practical strategies for making ensembles of nanostructures. It will therefore be an essential part of nanotechnology. Self-assembly is also common to many dynamic, multicomponent systems, from smart materials and self-healing structures to netted sensors and computer networks. In the world of biology, living cells self-assemble, and understanding life will therefore require understanding self-assembly. The cell also offers countless examples of functional self-assembly that stimulate the design of non-living systems [4, 5]. Self-assembly reflects information coded (as shape, surface properties, charge, polarizability, magnetic dipole, mass, etc.) in individual components; these characters determine the interaction among them. The design of building blocks that organize themselves into desired structure and functions is the key to applications of self-assembly [2]. Much of materials science and soft condensed-matter physics in the past century involved the study of self-assembly of fundamental building blocks (typically atoms, molecules, macromolecules, and colloidal particles) into bulk thermodynamic phases [6]. Today, the extent to which these building blocks can be engineered has undergone a quantum leap. Tailor-made, submicrometer particles will be the building blocks of a new generation of nanostructured materials with unique physical properties [7-11]. These new building blocks will be the "atoms" and "molecules" of tomorrow's materials, self-assembling into novel structures made possible solely by their unique design [2]. For example, patchy particles consisting of various Self-Assembling Systems: Theory and Simulation, First Edition. Edited by Li-Tang Yan.

View PDFchevron_right
Self-assembly of (sub-)micron particles into supermaterials
Leon Abelmann

Journal of Micromechanics and Microengineering, 2010

We review aspects of static self-assembly with regard to the synthesizing of new types of three-dimensional materials made of specifically designed particles in the 100 nm to 10 μm range. Mechanical interconnection technologies based on static friction used in the assembly of macroscopic systems (such as screws and nails) are unsuitable for self-assembly. An analogy of self-assembly with first-order phase transitions is used to argue that self-assembly is a process requiring interfaces separating assembled and disordered regions. Available types of interaction are reviewed with emphasis on scaling. We discuss at some length how interaction and dynamic properties scale with respect to the particle size. Chains of particles seem to be of particular importance as they might form three-dimensional structures similar to proteins. These structures are constrained by the sequence of the particles and by their interactions between themselves and with the solvent. Using chains might provide a viable route to complex, inhomogeneous, supermaterials and systems. Kinetic processes, specifically nucleation and the relationship between self-assembly and thermodynamic phase transitions form a major part of this paper. Finally we review some applications of self-assembly, notably in MEMS, and put forward some ideas for the assembly of new types of (smart) supermaterials with interesting optical, mechanical, electrical and magnetic properties and describe some of the technological challenges we face when attempting to realize these materials and systems thereof.

View PDFchevron_right

Related topics

  • Mathematics
  • Physics
    • 580 California St., Suite 400
    San Francisco, CA, 94104
    © 2025 Academia. All rights reserved