Characterizing complex particle morphologies through shape matching: Descriptors, applications, and algorithms

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for characterizing the unique and highly complex structures often encountered in the emerging field of nano and microscale self-assembly, or other disciplines involving complex structures such as computational biology. Computer science algorithms known as ''shape matching'' methods pose a unique solution to this problem by providing robust metrics for quantifying the similarity between pairs of arbitrarily complex structures. This pairwise matching operation, either implicitly or explicitly, lies at the heart of most standard structural characterization schemes for particle systems. By substituting more robust ''shape descriptors'' into these schemes we extend their applicability to structures formed from more complex building blocks. Here, we describe several structural characterization schemes and shape descriptors that can be used to obtain various types of structural information about particle systems. We demonstrate the application of shape matching algorithms to a variety of example problems, for topics including local and global structure identification and classification, automated phase diagram mapping, and the construction of spatial and temporal correlation functions. The methods are applicable to a wide range of systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.

[1]  Sharon C Glotzer,et al.  Complex crystal structures formed by the self-assembly of ditethered nanospheres. , 2009, Nano letters.

[2]  K. F. Riley,et al.  Mathematical methods for the physical sciences , 1975 .

[3]  D. Grier,et al.  Methods of Digital Video Microscopy for Colloidal Studies , 1996 .

[4]  Sharon C Glotzer,et al.  Local ordering of polymer-tethered nanospheres and nanorods and the stabilization of the double gyroid phase. , 2008, The Journal of chemical physics.

[5]  Karthik Ramani,et al.  Three-dimensional shape searching: state-of-the-art review and future trends , 2005, Comput. Aided Des..

[6]  Dietmar Saupe,et al.  Tools for 3D-object retrieval: Karhunen-Loeve transform and spherical harmonics , 2001, 2001 IEEE Fourth Workshop on Multimedia Signal Processing (Cat. No.01TH8564).

[7]  Randall D. Kamien,et al.  Molecular chirality and chiral parameters , 1999 .

[8]  Fernando A Escobedo,et al.  Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study. , 2005, The journal of physical chemistry. B.

[9]  D. Frenkel,et al.  Onset of heterogeneous crystal nucleation in colloidal suspensions , 2004, Nature.

[10]  N. D. Mermin,et al.  Crystalline Order in Two Dimensions , 1968 .

[11]  Ralph Roskies,et al.  Fourier Descriptors for Plane Closed Curves , 1972, IEEE Transactions on Computers.

[12]  Helmuth Möhwald,et al.  Decoration of microspheres with gold nanodots--giving colloidal spheres valences. , 2005, Angewandte Chemie.

[13]  Sharon C. Glotzer,et al.  Self-assembly of anisotropic tethered nanoparticle shape amphiphiles , 2005 .

[14]  Arthi Jayaraman,et al.  Structure and assembly of dense solutions and melts of single tethered nanoparticles. , 2008, The Journal of chemical physics.

[15]  Richard J. Farris,et al.  Nanostructured Polyethylene-POSS Copolymers: Control of Crystallization and Aggregation , 2002 .

[16]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[17]  K Henrick,et al.  Electronic Reprint Biological Crystallography Secondary-structure Matching (ssm), a New Tool for Fast Protein Structure Alignment in Three Dimensions Biological Crystallography Secondary-structure Matching (ssm), a New Tool for Fast Protein Structure Alignment in Three Dimensions , 2022 .

[18]  E. Kumacheva,et al.  Properties and emerging applications of self-assembled structures made from inorganic nanoparticles. , 2010, Nature nanotechnology.

[19]  Zhiyong Tang,et al.  Simulations and analysis of self-assembly of CdTe nanoparticles into wires and sheets. , 2007, Nano letters.

[20]  Lora Mak,et al.  An extension of spherical harmonics to region-based rotationally invariant descriptors for molecular shape description and comparison. , 2008, Journal of molecular graphics & modelling.

[21]  Thomas A. Funkhouser,et al.  The Princeton Shape Benchmark , 2004, Proceedings Shape Modeling Applications, 2004..

[22]  David R. Nelson,et al.  Dislocation-mediated melting in two dimensions , 1979 .

[23]  W. L. Mcmillan,et al.  Simple Molecular Model for the Smectic A Phase of Liquid Crystals , 1971 .

[24]  Bing-Yu Chen,et al.  A web-based three-dimensional protein retrieval system by matching visual similarity , 2005, Bioinform..

[25]  J. Cahn,et al.  Metallic Phase with Long-Range Orientational Order and No Translational Symmetry , 1984 .

[26]  Pieter Rein ten Wolde,et al.  Numerical calculation of the rate of crystal nucleation in a Lennard‐Jones system at moderate undercooling , 1996 .

[27]  David Chandler,et al.  Transition path sampling: throwing ropes over rough mountain passes, in the dark. , 2002, Annual review of physical chemistry.

[28]  Priya Varadan,et al.  Direct Visualization of Long-Range Heterogeneous Structure in Dense Colloidal Gels , 2003 .

[29]  G. Dunteman Principal Components Analysis , 1989 .

[30]  Sharon C. Glotzer,et al.  Characterizing Structure Through Shape Matching and Applications to Self Assembly , 2010, ArXiv.

[31]  Ming Ouhyoung,et al.  On Visual Similarity Based 3D Model Retrieval , 2003, Comput. Graph. Forum.

[32]  J. Heath,et al.  Nanocrystal superlattices. , 1998, Annual review of physical chemistry.

[33]  C. Dellago,et al.  Transition path sampling and the calculation of rate constants , 1998 .

[34]  Sharon C. Glotzer,et al.  Tethered Nano Building Blocks: Toward a Conceptual Framework for Nanoparticle Self-Assembly , 2003 .

[35]  Hajime Tanaka,et al.  Frustration on the way to crystallization in glass , 2006 .

[36]  H. C. Andersen,et al.  Molecular dynamics study of melting and freezing of small Lennard-Jones clusters , 1987 .

[37]  Dexin Zhang,et al.  Efficient iris recognition by characterizing key local variations , 2004, IEEE Transactions on Image Processing.

[38]  Junichi Higo,et al.  Size-Dependent Separation of Colloidal Particles In Two-Dimensional Convective Self-Assembly , 1995 .

[39]  Sharon C Glotzer,et al.  Switchable helical structures formed by the hierarchical self-assembly of laterally tethered nanorods. , 2009, Small.

[40]  Y. Matsushita,et al.  Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers. , 2007, Physical review letters.

[41]  Francesco Stellacci,et al.  Divalent Metal Nanoparticles , 2007, Science.

[42]  Michael P. Allen,et al.  SIMULATION OF STRUCTURE AND DYNAMICS NEAR THE ISOTROPIC-NEMATIC TRANSITION , 1997 .

[43]  Remco C. Veltkamp,et al.  Shape matching: similarity measures and algorithms , 2001, Proceedings International Conference on Shape Modeling and Applications.

[44]  Marco Ronchetti,et al.  Icosahedral Bond Orientational Order in Supercooled Liquids , 1981 .

[45]  S. Glotzer,et al.  Self-Assembly of Patchy Particles. , 2004, Nano letters.

[46]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[47]  Peter T. Cummings,et al.  Phase transitions in nanoconfined fluids: The evidence from simulation and theory , 2010 .

[48]  Zhiyong Tang,et al.  Self-Assembly of CdTe Nanocrystals into Free-Floating Sheets , 2006, Science.

[49]  P. Bladon,et al.  Self-assembly in living nematics , 1993 .

[50]  David R. Nelson,et al.  Theory of Two-Dimensional Melting , 1978 .

[51]  Jonathan P. K. Doye,et al.  Quantum partition functions from classical distributions: Application to rare-gas clusters , 2001 .

[52]  A. M. Lesk A toolkit for computational molecular biology. III. MICRYFON– a (fairly) general program for input of protein coordinate files , 1987 .

[53]  Takeshi Kawasaki,et al.  Correlation between dynamic heterogeneity and medium-range order in two-dimensional glass-forming liquids. , 2007, Physical review letters.

[54]  P. Steinhardt,et al.  Bond-orientational order in liquids and glasses , 1983 .

[55]  R. Larson,et al.  Local stress control of spatiotemporal ordering of colloidal crystals in complex flows. , 2008, Physical review letters.

[56]  Edwin L. Thomas,et al.  Anisotropic Micellar Nanoobjects from Reactive Liquid Crystalline Rod−Coil Diblock Copolymers , 2004 .

[57]  M. Freiser,et al.  Ordered States of a Nematic Liquid , 1970 .

[58]  J Roth,et al.  Solid-phase structures of the dzugutov pair potential. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[59]  D Frenkel,et al.  Numerical prediction of absolute crystallization rates in hard-sphere colloids. , 2004, The Journal of chemical physics.

[60]  A. M. Lesk,et al.  A toolkit for computational molecular biology. II. On the optimal superposition of two sets of coordinates , 1986 .

[61]  Marcin Novotni,et al.  3D zernike descriptors for content based shape retrieval , 2003, SM '03.

[62]  David J. Wales,et al.  Global minima of water clusters (H2O)n, n≤21, described by an empirical potential , 1998 .

[63]  S. Glotzer,et al.  Anisotropy of building blocks and their assembly into complex structures. , 2007, Nature materials.

[64]  Remco C. Veltkamp,et al.  State of the Art in Shape Matching , 2001, Principles of Visual Information Retrieval.

[65]  Szymon Rusinkiewicz,et al.  Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors , 2003, Symposium on Geometry Processing.

[66]  J Z Chen,et al.  Helical structures in proteins. , 2001, Biomacromolecules.

[67]  Remco C. Veltkamp,et al.  A Survey of Content Based 3D Shape Retrieval Methods , 2004, SMI.

[68]  Sharon C. Glotzer,et al.  Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra , 2009, Nature.

[69]  D J Durian,et al.  Approach to jamming in an air-fluidized granular bed. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  J. D. Bernal,et al.  A Geometrical Approach to the Structure Of Liquids , 1959, Nature.

[71]  Sharon C. Glotzer,et al.  Simulation Study of Dipole-Induced Self-Assembly of Nanocubes , 2007 .

[72]  Sharon C Glotzer,et al.  Molecular simulation study of self-assembly of tethered V-shaped nanoparticles. , 2008, The Journal of chemical physics.

[73]  George C Schatz,et al.  What controls the melting properties of DNA-linked gold nanoparticle assemblies? , 2000, Journal of the American Chemical Society.

[74]  Ravi Radhakrishnan,et al.  Effect of the fluid-wall interaction on freezing of confined fluids: Toward the development of a global phase diagram , 2000 .

[75]  D. Astruc,et al.  Gold Nanoparticles: Assembly, Supramolecular Chemistry, Quantum‐Size‐Related Properties, and Applications Toward Biology, Catalysis, and Nanotechnology. , 2004 .

[76]  R. Larson The Structure and Rheology of Complex Fluids , 1998 .

[77]  R. Sadourny Conservative Finite-Difference Approximations of the Primitive Equations on Quasi-Uniform Spherical Grids , 1972 .

[78]  Tom C. Lubensky,et al.  First-order phase transitions in superconductors and smectic-A liquid crystals , 1974 .

[79]  Linda S. Schadler,et al.  Anisotropic self-assembly of spherical polymer-grafted nanoparticles. , 2009, Nature materials.

[80]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[81]  Sharon C. Glotzer,et al.  Phase behavior of ditethered nanospheres , 2009, 0907.5015.

[82]  Jitendra Malik,et al.  Shape matching and object recognition using shape contexts , 2010, 2010 3rd International Conference on Computer Science and Information Technology.

[83]  Michael Engel,et al.  Self-assembly of monatomic complex crystals and quasicrystals with a double-well interaction potential. , 2007, Physical review letters.

[84]  Stephanie E. A. Gratton,et al.  Imparting size, shape, and composition control of materials for nanomedicine. , 2006, Chemical Society reviews.

[85]  Uzi Landman,et al.  Cluster-derived structures and conductance fluctuations in nanowires , 1997, Nature.

[86]  P. Flory,et al.  Phase equilibria in solutions of rod-like particles , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[87]  L. Onsager THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES , 1949 .

[88]  Peter Harrowell,et al.  How reproducible are dynamic heterogeneities in a supercooled liquid? , 2004, Physical review letters.

[89]  G. Torrie,et al.  Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling , 1977 .

[90]  Scott Grandison,et al.  The Application of 3D Zernike Moments for the Description of "Model-Free" Molecular Structure, Functional Motion, and Structural Reliability , 2009, J. Comput. Biol..

[91]  Anand Rangarajan,et al.  A new point matching algorithm for non-rigid registration , 2003, Comput. Vis. Image Underst..

[92]  Bernard Chazelle,et al.  Shape distributions , 2002, TOGS.

[93]  Peter T. Cummings,et al.  Rate-dependent energy release mechanism of gold nanowires under elongation. , 2008, Journal of the American Chemical Society.

[94]  Yasuhiro Sakamoto,et al.  Magnetic field-induced assembly of oriented superlattices from maghemite nanocubes , 2007, Proceedings of the National Academy of Sciences.

[95]  Guojun Lu,et al.  Review of shape representation and description techniques , 2004, Pattern Recognit..

[96]  P. Harrowell,et al.  Stability and structure of a supercooled liquid mixture in two dimensions. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[97]  Francesco Stellacci,et al.  Spontaneous assembly of subnanometre-ordered domains in the ligand shell of monolayer-protected nanoparticles , 2004, Nature materials.

[98]  Andrew Schofield,et al.  Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization , 2001, Science.

[99]  Daisuke Kihara,et al.  Potential for Protein Surface Shape Analysis Using Spherical Harmonics and 3D Zernike Descriptors , 2009, Cell Biochemistry and Biophysics.

[100]  Pengfei Wu,et al.  Photonic Crystals Based on Periodic Arrays of Aligned Carbon Nanotubes , 2003 .

[101]  M. Solomon,et al.  Stacking fault structure in shear-induced colloidal crystallization. , 2006, The Journal of chemical physics.

[102]  Aaron S. Keys,et al.  Self-assembly of patchy particles into diamond structures through molecular mimicry. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[103]  Sharon C Glotzer,et al.  Phase diagrams of self-assembled mono-tethered nanospheres from molecular simulation and comparison to surfactants. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[104]  Daniele Fava,et al.  Self-assembly of metal-polymer analogues of amphiphilic triblock copolymers. , 2007, Nature materials.

[105]  Sharon C. Glotzer,et al.  Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material , 2007, 1012.4830.

[106]  Alexander Varshavsky,et al.  The ubiquitin system. , 1998, Annual review of biochemistry.

[107]  Marco Cosentino Lagomarsino,et al.  Isotropic-nematic transition of long, thin, hard spherocylinders confined in a quasi-two-dimensional planar geometry , 2003 .

[108]  Sharon C Glotzer,et al.  How do quasicrystals grow? , 2007, Physical review letters.

[109]  D. Frenkel,et al.  Enhancement of protein crystal nucleation by critical density fluctuations. , 1997, Science.

[110]  Hans-Peter Kriegel,et al.  3D Shape Histograms for Similarity Search and Classification in Spatial Databases , 1999, SSD.

[111]  Sharon C Glotzer,et al.  Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[112]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[113]  Forward flux sampling-type schemes for simulating rare events: efficiency analysis. , 2006, The Journal of chemical physics.

[114]  U. Gasser,et al.  Local order in a supercooled colloidal fluid observed by confocal microscopy , 2002 .

[115]  G. Fredrickson,et al.  Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers. , 2005, The Journal of chemical physics.

[116]  Mattias Ohlsson,et al.  Matching protein structures with fuzzy alignments , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[117]  Andersen,et al.  Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[118]  Vincent M. Rotello,et al.  Self-assembly of nanoparticles into structured spherical and network aggregates , 2000, Nature.

[119]  A Paul Alivisatos,et al.  Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles. , 2005, Nano letters.

[120]  A. Goede,et al.  Voronoi cell: New method for allocation of space among atoms: Elimination of avoidable errors in calculation of atomic volume and density , 1997 .

[121]  Sharon C. Glotzer,et al.  A comparison of new methods for generating energy-minimizing configurations of patchy particles , 2009 .

[122]  Kai Sun,et al.  Light-Controlled Self-Assembly of Semiconductor Nanoparticles into Twisted Ribbons , 2010, Science.

[123]  Alireza Khotanzad,et al.  Invariant Image Recognition by Zernike Moments , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[124]  Anil K. Jain,et al.  Three-dimensional model based face recognition , 2004, ICPR 2004.