Calculation of partition functions for the self-assembly of patchy particles.

Partition functions encode all the thermodynamics of a system, but for most systems of practical importance, they cannot be calculated exactly. In this work we present a new hierarchical method for calculating partition functions to arbitrary precision. We discuss the algorithmic details of our implementation, including elements of shape-matching and entropy calculation for on-lattice and off-lattice systems. We highlight computational trade-offs between speed and accuracy, showing how this varies with temperature, and demonstrate its utility in studying nanoscale self-assembly for a system of model patchy particles.

[1]  H. Eugene Stanley,et al.  Phase behaviour of metastable water , 1992, Nature.

[2]  Brian C. Barnes,et al.  Structure, thermodynamics, and solubility in tetromino fluids. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[3]  F. Rosei,et al.  Playing Tetris at the nanoscale , 2006 .

[4]  A. Troisi,et al.  An agent-based approach for modeling molecular self-organization. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

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

[6]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[7]  Nicos Christofides.  The optimum traversal of a graph , 1973 .

[8]  David J. Wales,et al.  Free energy surfaces from an extended harmonic superposition approach and kinetics for alanine dipeptide , 2008 .

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

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

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

[12]  Matthew Tirrell,et al.  Modular materials by self‐assembly , 2005 .

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

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

[15]  Berend Smit,et al.  Understanding Molecular Simulations: from Algorithms to Applications , 2002 .

[16]  P. Rothemund.  Folding DNA to create nanoscale shapes and patterns , 2006, Nature.

[17]  D. Rapaport,et al.  Self-assembly of polyhedral shells: a molecular dynamics study. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  M Karplus,et al.  Theoretical studies of protein folding and unfolding. , 1995, Current opinion in structural biology.

[19]  David Jackson McGinty,et al.  Vapor phase homogeneous nucleation and the thermodynamic properties of small clusters of argon atoms , 1971 .

[20]  David J Wales,et al.  Potential energy and free energy landscapes. , 2006, The journal of physical chemistry. B.

[21]  F. Stillinger,et al.  Packing Structures and Transitions in Liquids and Solids , 1984, Science.

[22]  Andreas Stein,et al.  Colloidal assembly: the road from particles to colloidal molecules and crystals. , 2011, Angewandte Chemie.

[23]  A. Agarwal,et al.  Controllable side-by-side and end-to-end assembly of Au nanorods by lyotropic chromonic materials. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[24]  Seeram Ramakrishna,et al.  Electrospun nanofibrous filtration membrane , 2006 .

[25]  G. Whitesides,et al.  Self-Assembly at All Scales , 2002, Science.

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

[27]  M. Brenner,et al.  The Free-Energy Landscape of Clusters of Attractive Hard Spheres , 2010, Science.

[28]  Michael P Brenner,et al.  Algorithm for a microfluidic assembly line. , 2011, Physical review letters.

[29]  Stephan Mertens,et al.  A physicist's approach to number partitioning , 2000, Theor. Comput. Sci..

[30]  F. Sciortino,et al.  Extended law of corresponding states in short-range square wells: a potential energy landscape study. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Michael L Klein,et al.  Self-assembly and properties of diblock copolymers by coarse-grain molecular dynamics , 2004, Nature materials.

[32]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[33]  Arindam Banerjee,et al.  Submitted for publication , 1981 .

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

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

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

[37]  P. Wolynes,et al.  Spin glasses and the statistical mechanics of protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Ieee Xplore,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence Information for Authors , 2022, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[39]  Wu Wang,et al.  High-Performance Nanowire Electronics and Photonics on Glass and Plastic Substrates , 2003 .

[40]  C. Brooks,et al.  Deciphering the kinetic mechanism of spontaneous self-assembly of icosahedral capsids. , 2007, Nano letters (Print).

[41]  Charles M. Lieber,et al.  Growth of nanowire superlattice structures for nanoscale photonics and electronics , 2002, Nature.

[42]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[43]  G. Fredrickson,et al.  Block copolymer thermodynamics: theory and experiment. , 1990, Annual review of physical chemistry.

[44]  David A. Kofke,et al.  Virial coefficients of polarizable water : Applications to thermodynamic properties and molecular clustering , 2007 .

[45]  Mark A Burns,et al.  Programmable fluidic production of microparticles with configurable anisotropy. , 2008, Journal of the American Chemical Society.

[46]  W. Krauth,et al.  Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions , 1996 .

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