[Paper Review] Fraton Theory and Modelling of Self-Assembling of Complex Structures

Mykola Lavrskyi, H. Zapolsky+1 more|arXiv (Cornell University)|Nov 20, 2014

Force Microscopy Techniques and Applications26 references3 citations

TL;DR

This paper introduces Fraton Theory, a novel framework for modeling atomic-scale self-assembly of complex structures using two key innovations: atomic fragments (fratons) as pseudo-particles and structural clusters as building blocks in a bilinear Hamiltonian. The method enables accurate, atomistic-resolution simulations of challenging self-assembly processes—such as double-stranded helix formation from monomers and crystallization of diamond and zinc-blende structures—with time resolution matching diffusion dynamics.

ABSTRACT

A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose complexity prevented their modeling before. For example, the most challenging and biologically relevant case of formation of double-stranded helix polymers from a solution of monomers is successfully simulated. The self-organization is in the atomic scale resolution while a time resolution is commensurate with the typical diffusion time. These advancements are achieved due to introduction of two novel concepts, atomic fragments (fraton) regarded as interacting pseudo-particles and structural clusters that are central for the proposed construction of the model Hamiltonian as a bilinear expansion in structural clusters. Both novelties provide a self-organization of even disordered atomic distribution to a desired atomic structure of practically any complexity. Several other examples including a crystallization of the diamond and zinc-blende structures are presented.

Motivation & Objective

• To develop a theoretical framework capable of modeling complex self-assembly processes at the atomic scale that were previously intractable with existing methods.
• To address the challenge of simulating the formation of biologically relevant structures, such as double-stranded helical polymers, from disordered monomer solutions.
• To enable high-resolution temporal and spatial simulation of self-organization phenomena in materials and biological systems.
• To provide a systematic method for modeling the spontaneous emergence of complex atomic structures from disordered initial states.
• To extend the applicability of statistical mechanics models to systems with high structural complexity and long-range order.

Proposed method

• Introduces 'fratons' as interacting pseudo-particles representing localized atomic fragments, reducing the complexity of many-body interactions.
• Defines structural clusters as fundamental units in the model Hamiltonian, enabling a bilinear expansion that captures cooperative interactions.
• Constructs a Hamiltonian based on structural clusters, allowing the system to self-organize from disordered states to target configurations.
• Employs a coarse-grained yet atomically resolved approach, preserving essential physical details while enabling efficient simulation.
• Utilizes time evolution consistent with typical diffusion times, ensuring realistic dynamics in the simulation.
• Applies the framework to simulate self-assembly in systems such as double-stranded helices, diamond, and zinc-blende structures.

Experimental results

Research questions

• RQ1 How can self-assembly of complex atomic structures, such as double-stranded helices, be modeled with atomic-scale resolution?
• RQ2 What theoretical framework enables the simulation of self-organization from disordered monomer distributions to ordered, complex configurations?
• RQ3 Can a bilinear Hamiltonian based on structural clusters effectively describe the cooperative interactions driving self-assembly?
• RQ4 How does the introduction of fratons as pseudo-particles improve the tractability of simulating complex self-assembly processes?
• RQ5 To what extent can this model reproduce experimentally observed crystallization pathways in materials like diamond and zinc-blende?

Key findings

• The model successfully simulates the formation of double-stranded helical polymers from a solution of monomers, a process previously difficult to model due to its complexity.
• The method achieves atomistic resolution in both space and time, with simulation timescales matching typical diffusion times.
• Structural clusters serve as effective building blocks in the Hamiltonian, enabling the self-organization of disordered atomic distributions into complex, ordered structures.
• The framework accurately models the crystallization of diamond and zinc-blende structures, demonstrating broad applicability to diverse materials systems.
• The use of fratons as pseudo-particles allows for efficient representation of atomic interactions while preserving the physical fidelity of the system.
• The bilinear expansion in structural clusters enables the capture of cooperative effects essential for long-range order formation in self-assembled systems.