Project Description:

This project aims to develop a framework for predicting the assembly behavior for entropically driven self-assembly of hard polyhedra. Briefly, we first develop a psuedoparticle (pP) ansatz that facilitates the quantification of emergent directional attractions between hard polyhedra upon crowding. We then employ pP to quantitatively map out regions of interactions between neighboring polyhedra and develop a set of eigenvalue solvers to determine configurations that maximizes interactions between polyhedra. These calculations are subsequently extended to enable the input of test crystal in order to compute the excess free energy of formation of polyhedra occupying lattice sites of differing crystal structures, thereby facilitating the determination of the most thermodynamically stable lattice.
 
Here, we included sample scripts for both lattice predictions as well as MD simulations of pP that verifies the presence of "shape" and "bonding orbitals" as predicted by theory. Lattice energy calculations are written in MATLAB and MD simulations employ the usage of the HOOMD-Blue simulation engine. Sample data outputs are provided for a diamond lattice (lattice energy) and singe/binary NP orbital formations (MD simulations).


Link to paper describing the theory/simulations: 

Vo, T., & Glotzer, S. C. (2021). Microscopic Theory of Entropic Bonding for Colloidal Crystal Prediction. ArXiv:2107.02081 [Cond-Mat]. http://arxiv.org/abs/2107.02081



Short description of files:

*All energy calculations codes are ".m" files that can be run in either matlab or octave environments*

*All simulation scripts are for use with HOOMD-Blue v 2.9*

File: AIChE_Annual_Meeting_11_16_2020.pptx: AIChE conference presentation of theory

Folder: PP_sims_signac - signac project folder with JSON files describing PP simulation parameters

Folder: entropic_bond_signac - signac project folder with JSON files describing entropic bond calculation parameters	

Folder: energy_calculator

	Subfolder: lattice_files
		all relevant lattices tested for shapes studied organized by shape name
		Order of columns: x y z quaternion (q1, q2, q3, q4)
	Subfolder: shape_files
		all vertices of shapes used in calculations (tetrahedron varies truncation so that is organized into its own subfolder)
		Order of columns: x y z
	Subfolder: polyhedron_functions
		basis functions for shape manipulations, add to path before running

	Files:
		calc_rscale.m: compute relative scaling distances between shapes
		gen_kernel_evaluator.m: compute shape kernel for use in calculations
		parameterize_shape.m: working function to generate shape grid for use in  gen_kenel_evaluator
		sample_diamond_energy.m: code that computes sample entropic bond energy
			change name of lattice_type and pts_shape where indicated in code to switch testing for different shapes/lattices
		cubic_wavefunction.txt: sample output of wavefunction for cubic diamond
		hexagonal_wavefunction.txt: sample output of wavefunction for hexagonal diamond
		trunc_tetra.txt: shape vertices input for calculations
		cubicdiamond.txt: cubic diamond lattice coordinate inputs for calculations
		hexagonaldiamond.txt: hexagonal diamond lattice coordinate inputs for calculations

Folder: PP_simulations

	Subfolder: simulation_codes
		sample_sims_unary.py: HOOMD-Blue script for single NP within sea of PP for orbital visualization
		sample_sims_binary.py: HOOMD-Blue script for two NP within sea of PP for orbital visualization

	Subfolder: sample_results
		Folders
		cube: sample result for single cube NP
		prism6: sample result for single hexagonal prism NP
		tetrahedron: sample result for single tetrahedron NP
		dodecahedron: sample result for single dodecahedron NP
		cube_binary: sample result for binary cube NP
		prism6_binary: sample result for binary hexagonal prism NP
		tetrahedron_binary: sample result for binary tetrahedron NP
		dodecahedron_binary: sample result for binary dodecahedron NP

	Files:
		Tetrahedronorbital_full.txt: theory orbital output for tetrahedron
			Order of columns: x, y, z, 1st orbital value, 2nd orbital value, 3rd orbital value, 4th orbital value
		Cubeorbital_full.txt: theory orbital output for cube
			Order of columns: x, y, z, 1st orbital value, 2nd orbital value, 3rd orbital value, 4th orbital value
		Dodecahedronorbital_full.txt: theory orbital output for dodecahedron
			Order of columns: x, y, z, 1st orbital value, 2nd orbital value, 3rd orbital value, 4th orbital value
		Prism6orbital_full.txt: theory orbital output for hexagonal prism
			Order of columns: x, y, z, 1st orbital value, 2nd orbital value, 3rd orbital value, 4th orbital value