Shaping of crystals at the nanoscale by anisotropic capillary waves

Interfacial fluctuations and anisotropic capillary waves involved in the shaping of nanoparticle supracrystals are directly mapped by liquid-phase transmission electron microscopy.

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Great as the differences between underwater corals and nanoparticle superlattices, they are both the crystalline assemblies from nanosized building blocks, and they share the same importance of crystal shapes on their properties—whether the color and colony of life residing upon them or the wavelength and modes of light-matter interactions. However, despite the rapid progress in nanotechnology over the last few decades, understandings remain limited on how the functional nanosized building blocks assemble into highly ordered structures against stochastic Brownian motions in a liquid medium. Filling this gap requires high spatiotemporal resolution imaging of dynamics in a liquid environment, which has been challenging. In this work, the emergent technique of liquid-phase transmission electron microscopy (TEM) was used to overcome this challenge and capture the emergence of a faceted crystal shape from individual nanosized building blocks. Anisotropic capillary waves were imaged directly at nanometer and sub-second resolution to back out the facet-defined surface energy of the crystal.

Figure 1. A supracrystal–suspension interface visualized in real-time by liquid-phase transmission electron microscopy (TEM). (Top) Schematic showing the configuration of liquid-phase TEM. (Bottom) Illustration of how liquid-phase TEM is combined with automatic tracking and structural characterization to extract the surface profile of a supracrystal. Scale bars: 200 nm.

We integrate low-dose liquid-phase TEM imaging, single nanoparticle tracking, and quantitative structural analysis to identify and monitor real-space surface profiles of a growing nanoparticle supracrystal (Fig. 1). Interestingly, the supracrystal shifts its surface orientation within our observation time window as it grows from continuous attachments of nanoparticles, presenting two temporal stages (Fig. 2a). By closely looking into the surface profiles, we were reminded of the long-standing capillary wave theory by their dynamic fluctuations. Capillary wave theory treats surfaces or interfaces as superimposed waves and the equilibrium profile is a tradeoff between the surface energy and thermal fluctuation. We first demonstrate the theory’s applicability to the nanoscale and to the surface of a crystal (instead of the more disordered liquid phase), suggesting the randomness of Brownian motions still plays a major role in defining the surface. We are then able to measure a series of otherwise inaccessible physical parameters, including surface roughness, correlation length, interfacial stiffness and mobility, for different supracrystal facets. Interestingly, the interfacial properties we quantify in the experiments are anisotropic and the supracrystal grows towards exhibiting flatter surfaces with lower surface energy, consistent with the Wulff construction rule proposed to explain the equilibrium shape of a crystal (Fig. 2b‒c).

Figure 2: Shaping of crystals at the nanoscale by anisotropic capillary waves. (a) Temporal evolution of the crystal surface orientation shows two stages. (b) Typical liquid-phase TEM images for stage 1 and stage 2 highlighting the surface orientation shift. Scale bars: 200 nm. (c) Schematic illustrating the decomposition of the surface profile into superimposed waves with different wave vectors. (d) Anisotropic interfacial stiffness measured for different facets based on capillary wave theory.

Our capability to measure facet-dependent interfacial energies and our demonstration on their role in shaping the supracrystals can advance crystal design at the nanoscale. For example, one can control the interfacial stiffness and crystal habit by utilizing the toolkits of both intrinsic parameters of nanoparticle shape and surface chemistry as well as extrinsic parameters such as temperature, pH and ionic strength. Our approach can elucidate the fundamental role of these parameters in guiding crystallization. Broadly, our method can be applied to study other nanoscale fluctuations as liquid-phase TEM becomes more compatible with biological samples (e.g., fusion of lipid vehicles) and with applying external field (e.g., dendrite formation at the electrolyte–solid interface).

This work was recently published in Nature Communications:

Imaging How Thermal Capillary Waves and Anisotropic Interfacial Stiffness Shape Nanoparticle Supracrystals

Zihao Ou, Lehan Yao, Hyosung An, Bonan Shen and Qian Chen

Nature Communications, 11, 4555 (2020):

Qian Chen

Assistant Professor, University of Illinois at Urbana-Champaign

Qian Chen has been an assistant professor in the Department of Materials Science and Engineering at the University of Illinois at Urbana-Champaign since 2015. She received her PhD degree from the same department in 2012. Her research focuses on electron microscopy-based imaging, understanding, and engineering of soft materials, such as nanoparticle and colloidal self-assembly, protein transformation, battery materials, and energy-efficient filtration. Her awards include the American Chemistry Society (ACS) Victor K. LaMer Award in 2015, the Air Force Office of Scientific Research Young Investigator Program (AFOSR YIP) Award in 2017, the National Science Foundation CAREER Award in 2018, an Alfred P. Sloan Research Fellowship in 2018, and the ACS Unilever Award (2018). She also was recognized on the Forbes 30 Under 30 Science List in 2016. Chen can be reached by email at

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