Kinetics of formation of a macroscale binary Coulombic material

Editors' Suggestion
Letter

Kinetics of formation of a macroscale binary Coulombic material

Sarah Battat, Amit A. Nagarkar, Frans Spaepen, David A. Weitz, and George M. Whitesides

Phys. Rev. Materials 7, L040401 – Published 13 April 2023

Abstract

The electrostatic self-assembly of charged Brownian objects typically occurs in cases of short-range interactions. The objects form Coulombic materials that are close-packed and have long-range order. Here, we present a system in which two kinds of non-Brownian millimeter-sized beads tribocharge differently, experience long-range electrostatic interactions, and still form ordered two-dimensional structures. We provide a complete characterization of the kinetics of formation of these materials, as the total number of beads is held constant and the relative number of beads that tribocharge negatively or positively is modified. We agitate the beads by shaking the dish in which they are contained. We show that the beads commonly adopt a transient structure that we call a rosette. A rosette consists of a central bead surrounded by six close-packed neighbors of a different kind. The symmetry of the final structure depends on the relative number of negatively and positively charged beads, and it is not necessarily the same as that of the transient structure. Our results bear important implications in the de novo design of Coulombic materials given our ability to isolate transient structures, identify the moment of their appearance, and quantify the impact of agitation, tribocharging, and Coulombic energy minimization on their persistence.

Received 13 December 2022
Revised 8 February 2023
Accepted 17 March 2023

DOI:https://doi.org/10.1103/PhysRevMaterials.7.L040401

Physics Subject Headings (PhySH)

Crystallization Electrostatic interactions Granular packing Nonequilibrium & irreversible thermodynamics Nucleation Order parameters Self-assembly

2-dimensional systems Composite materials Granular flows Granular materials

Condensed Matter, Materials & Applied PhysicsPolymers & Soft MatterNonlinear Dynamics

Authors & Affiliations

Sarah Battat ¹, Amit A. Nagarkar², Frans Spaepen¹, David A. Weitz^1,3,4,*, and George M. Whitesides^2,†

¹John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
²Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
³Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
⁴Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, Massachusetts 02115, USA

^*weitz@seas.harvard.edu
^†gwhitesides@gmwgroup.harvard.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 7, Iss. 4 — April 2023

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1

Schematic of the formation of an electrostatically self-assembled material. (a) The dish contains 400 beads, which cover approximately $30 %$ of the surface area of the dish. (b) As the dish is shaken, the beads undergo inelastic collisions, and their velocities are correlated. Their effective density is nearly double the fractional surface area coverage of beads on the dish. (c) The beads form hexagonally coordinated transient structures that we call rosettes and, in certain instances, hexagonally layered structures. (d) Finally, the beads undergo further rearrangements to form an energy-minimized structure. Here, for the case of equal numbers of nylon and polytetrafluoroethylene (PTFE) beads, the final structure has square symmetry. All scale bars correspond to 10 mm (about $4.2$ bead diameters).
Reuse & Permissions
Figure 2

Snapshots of the formation of the material in time for the cases of $N_{nylon} / N_{PTFE} = {\frac{1}{4}, 1, 4}$ . Important structures are outlined in red and reproduced in expanded form in the insets. In each experiment, 400 beads are agitated with an orbital shaker. The color of the images is adjusted for improved contrast. All scale bars correspond to 10 mm (about $4.2$ bead diameters).
Reuse & Permissions
Figure 3

Number of beads with at least five nearest neighbors of the opposite kind and number of rosettes for the cases of (a) $N_{nylon} / N_{PTFE} = \frac{1}{4}$ , (b) $N_{nylon} / N_{PTFE} = 1$ , and (c) $N_{nylon} / N_{PTFE} = 4$ . A polytetrafluoroethylene (PTFE)- or nylon-centered rosette is a structure in which a PTFE or nylon bead is surrounded by six nylon or PTFE nearest neighbors, respectively. A surrounding bead must be located within $1.2$ bead diameters of the central bead to be counted as a nearest neighbor. In each experiment, 400 beads are agitated with an orbital shaker. Each bolded trendline represents a rolling average of the raw data, which in turn is depicted in the corresponding lightened hue.
Reuse & Permissions
Figure 4

Average of the modulus of the $k$ -atic local bond order parameter, where $k = {3, 4, 5, 6}$ , for (a) all nylon beads in relation to their polytetrafluoroethylene (PTFE) neighbors when $N_{nylon} / N_{PTFE} = \frac{1}{4}$ and all PTFE beads in relation to their nylon neighbors when (b) $N_{nylon} / N_{PTFE} = 1$ and (c) $N_{nylon} / N_{PTFE} = 4$ . Frames are only included in the analysis if at least 90% of the beads of each type are detected. Each bolded trendline represents a rolling average of the raw data, which in turn is depicted in the corresponding lightened hue. In each experiment, 400 beads are agitated with an orbital shaker. (insets) Common transient and final structures are illustrated schematically in the insets of (a)–(c).
Reuse & Permissions
Figure 5

The evolution in time of the Coulombic energy of the system when accounting for image charges on the surface of the gold-coated dish for the cases of (a) $N_{nylon} / N_{PTFE} = \frac{1}{4}$ , (b) $N_{nylon} / N_{PTFE} = 1$ , and (c) $N_{nylon} / N_{PTFE} = 4$ . The structures at each point in time are shown in the insets. The beads that are included in the calculation are marked by dots in white or yellow (nylon) and black, green, or red [polytetrafluoroethylene (PTFE)] depending on their positions in the dish. The energy is reported as a distribution because the calculation is repeated 200 times.
Reuse & Permissions
Figure 6

Mechanical shaking helps in the formation of a final ordered structure. (from left to right) By increasing the centripetal acceleration of an orbital shaker from $1.85 m / s^{2}$ to $7.4 m / s^{2}$ , a mixture of 200 nylon beads and 200 polytetrafluoroethylene (PTFE) beads adopts an increasingly ordered final structure after 10 minutes of shaking. The total Coulombic energy of the system, accounting for image charges, at each centripetal acceleration is reported. The beads that are included in the calculation are marked by dots in white or yellow (nylon) and black or red (PTFE) depending on their positions in the dish. All scale bars correspond to 10 mm (about $4.2$ bead diameters).
Reuse & Permissions

Physical Review Materials