Evolutionary pattern design for copolymer directed self-assembly

Qin, Jian; Khaira, Gurdaman; Su, Yongrui; Garner, Grant P.; Miskin, Marc Z.; Jaeger, Heinrich M.; Pablo, Juan J. de

doi:10.1039/c3sm51971f

Cited by 60 publications

(63 citation statements)

References 23 publications

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“…37 In prior work we found CMA-ES to deliver excellent performance in optimization problems ranging from the packing of granular materials 24,25 to directed self-assembly of copolymers. 38,39 The evolutionary algorithm worked in concert with molecular dynamics simulations of 'virtual experiments,' providing input parameters to these simulations and updating the parameters according to the simulated outcome in relation to the optimization target (for details see Ref.…”

Section: Simulation and Optimizationmentioning

confidence: 99%

Optimizing packing fraction in granular media composed of overlapping spheres

Roth

Jaeger

2016

Soft Matter

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What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution. Arbitrary particle shape is represented by a set of overlapping spheres of varying diameter, enabling us to approximate smooth surfaces with a resolution proportional to the number of spheres included. We discover a family of planar triangular particles, whose packing fraction of φ ∼ 0.73 outpaces almost all reported experimental results for random packings of frictionless particles. We investigate how φ depends on the arrangement of spheres comprising an individual particle and on the smoothness of the surface. We validate the simulations with experiments using 3D-printed copies of the simplest member of the family, a planar particle consisting of three overlapping spheres with identical radius. Direct experimental comparison with 3D-printed aspherical ellipsoids demonstrates that the triangular particles pack exceedingly well not only in the limit of large system size but also when confined to small containers.The relationship between particle shape and packing density for random particle arrangements continues to be a topic of considerable interest. 1-3 Going beyond spherical particles, there has been much recent progress for polyhedral or polygonal shapes, 4-9 ellipsoids, cuboids, or 'superballs,' 10-15 cylinders, cones, and frustums of different aspect ratios, [16][17][18] as well as various types of particles constructed by joining disks or spheres. 11,[19][20][21][22][23][24][25] Furthermore, in the last few years, increasing attention has been paid to particles that are highly non-convex or are sufficiently flexible to assume non-convex shapes during the packing process. 14,[26][27][28][29][30][31][32][33][34] In almost all cases, these studies proceeded from a given particle type to find the packing density. What has remained a major challenge is a general and systematic approach to the inverse problem: taking desired packing properties as a starting point to identify the appropriate particle shape.To make progress, it is necessary to address three main obstacles. Firstly, shape is an infinitely variable parameter, rendering an exhaustive investigation of all possible particle shapes infeasible and instead requiring a smart approach to quickly narrow the search. The second obstacle relates to the fundamental nature of amorphous, jammed aggregates. Because a jammed system exists far from equilibrium, the packing density φ can be affected not only by particle geometry but also by boundary and processing conditions. These effects become particularly pronounced when extrapolating from finite size experiments and simulations to the properties of an infinite system. Finally, different shapes may generate similar packing fractions when assembled into an aggregate under particular processing conditions, so that for a given level of approximation to the desired target density ...

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Section: Simulation and Optimizationmentioning

confidence: 99%

Optimizing packing fraction in granular media composed of overlapping spheres

Roth

Jaeger

2016

Soft Matter

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“…More recently, design approaches using inverse methods have been implemented. [8][9][10][11]18 In these cases, the forward simulation consists of a numerical engine to solve various trial morphologies by implementing, e.g., a self-consistent field theory, 69 a mean field model based on the Cahn-Hilliard equation, 10 or a theoretically informed coarse-grain model for block copolymers. 70 As before, the forward simulation is coupled to an inverse process that optimizes the parameter set in order to achieve a solution that closely approximates the targeted design.…”

Section: Directed Self-assembly Of Block Copolymer Thin Filmsmentioning

confidence: 99%

“…[4][5][6][7] Applied to polymers, such methods have paved the way towards optimizing directed self-assembly. [8][9][10][11] Similar methods have been employed to identify the crystal structures of patchy, colloidal particles. 12 For far-from-equilibrium systems like jammed, metastable aggregates of particles, 13 simulation-based optimization has been used to design bulk properties such as stiffness or packing density by tuning complicated microscale features like particle shape.…”

Section: Introductionmentioning

confidence: 99%

Perspective: Evolutionary design of granular media and block copolymer patterns

Jaeger

Pablo

2016

APL Materials

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The creation of new materials “by design” is a process that starts from desired materials properties and proceeds to identify requirements for the constituent components. Such process is challenging because it inverts the typical modeling approach, which starts from given micro-level components to predict macro-level properties. We describe how to tackle this inverse problem using concepts from evolutionary computation. These concepts have widespread applicability and open up new opportunities for design as well as discovery. Here we apply them to design tasks involving two very different classes of soft materials, shape-optimized granular media and nanopatterned block copolymer thin films.

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“…For the other numerical approach to simulate the block copolymer, we can refer the dynamic mean field theory [9], based on the selfconsistent field theory. In soft materials science, these numerical methods have been used to study the phenomenological structure of the copolymer [23,24].…”

Section: Introductionmentioning

confidence: 99%

An Unconditionally Gradient Stable Numerical Method for the Ohta-Kawasaki Model

Kim¹,

Shin²

2017

Bulletin of the Korean Mathematical Society

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Abstract. We present a finite difference method for solving the OhtaKawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the OhtaKawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.

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Evolutionary pattern design for copolymer directed self-assembly

Cited by 60 publications

References 23 publications

Optimizing packing fraction in granular media composed of overlapping spheres

Optimizing packing fraction in granular media composed of overlapping spheres

Perspective: Evolutionary design of granular media and block copolymer patterns

An Unconditionally Gradient Stable Numerical Method for the Ohta-Kawasaki Model

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