Nucleation and phase transformation pathways in

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Nucleation and phase transformation pathways in electrolyte solutions investigated by in situ microscopy techniques Jinhui Tao a,1 , Michael H. Nielsen b,1 , James J. De Yoreo a,c,⁎ Identification of crystal nucleation and growth pathways is of fundamental importance for synthesis of functional materials, which requires control over size, orientation, polymorph, and hierarchical structure, often in the presence of additives used to tune the energy landscape defining these pathways. Herein we summarize the recent progress in application of in situ TEM and AFM techniques to monitor or even tune the pathway of crystal nucleation and growth. Address a Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA, 99354, USA b Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA c Department of Materials Science and Engineering, University of Washington, Seattle, WA 98195, USA ⁎ Corresponding author at: Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99354, USA. ([email protected]) Keywords: Nucleation Phase transformation In situ TEM In situ AFM 1

Equal contribution between J.T. and M. H. N.

Current Opinion in Colloid & Interface Science (2018) 34, 74–88 For a complete overview see the issue and the Editorial

Article History: Received 12 November 2017 Received in revised form 12 April 2018 Accepted 18 April 2018 Available online 27 April 2018 https://doi.org/10.1016/j.cocis.2018.04.002 1359-0294/© 2018 Elsevier Ltd. All rights reserved.

Current Opinion in Colloid & Interface Science (2018) 34, 74–88

1. Introduction The study of nucleation is of paramount importance because it represents the seminal event in the development of a new phase. Classical descriptions of crystal nucleation in solution envision a stable nucleus arising from unstable density fluctuations. These create clusters that grow by monomer addition with free energy increasing until the critical nucleus size is exceeded [1]. At this point, continued growth is energetically favorable and proceeds unhindered through the continued attachment of individual growth units [2]. However, the phase transformation pathway may in fact be complex, because the free energy landscape traversed by each growth unit typically possesses many local minima representing different structural states, each of which is separated from the others by barriers of varying height [3,4,5]. These barriers can be finely tuned in the presence of additives, to bias the nucleation pathway towards a specific outcome. For example, during biologically mediated formation of mineralized tissues, nucleation and growth are tightly regulated by surrounding organic matrices [6]. These often elegant biomineral structures are produced by living organisms at ambient conditions, which typically consist of an aqueous phase and the organism's organic matrix. Synthetic approaches to crystal formation strive for comparable levels of structural hierarchy but lack the level of control observed in nature. Similar to biomineral systems, synthetic chemists rely extensively on the use of organic and inorganic additives to achieve precise control during colloidal synthesis of nanomaterials [7]. However, the achievable level of complexity in synthetic materials is limited by a lack of fundamental understanding of the physical mechanisms and chemical interactions active during nucleation and growth in the presence of additives. Thus, the scientific challenge in understanding controlled material formation is to explain how and why specific phases nucleate and morphologies form, how additives govern their stabilization or transformation, and how structure/chemistry at the organic–inorganic interface defines these processes.

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Nucleation and phase transformation pathways

One of the challenges in understanding the nascent stages of materials formation is that the key phenomena often occur at spatiotemporal scales that are difficult to examine. Thus there remains much controversy over whether classical theories are appropriate frameworks within which to analyze these processes, whether alternate nucleation mechanisms [8,9,10,11] better describe the phase transition, or if the solid arises due to spinodal decomposition of the precursor solution [12,13,14]. Non-classical particlebased growth mechanisms have been proposed as well. Oriented attachment, as an example, is a process whereby primary particles join together with specific crystallographic registry to produce an architecturally complex single crystal [15]. This menagerie of potential formation pathways highlights the importance of energetic barriers and growth unit structure in determining how a material transits the free energy landscape during crystallization. Significantly, the final product of nucleation and growth mechanisms may not retain evidence of the formation pathway [4], limiting the utility of ex situ characterization tools in understanding materials formation (Fig. 1). Traditional in situ optical and X-ray based imaging and spectroscopic methods have

proved to be of limited value when investigating early steps in the establishment of a nanocrystal, such as formation and transformation of precursor phases, attachment of growth units, or coalescence of nanoparticles, due to the inability to adequately record these often rapid, transient phenomena which occur at nm-length scales. Recent synchrotron-based in situ X-ray scattering experiments have provided meaningful insights into nucleation pathways of second phases from solution for a range of materials systems, including silica, proteins and calcium sulfate [16,17,18]. However, high supersaturations — at least 1 mg/mL for protein and 50 mM for CaSO4 — were necessary for in situ X-ray scattering experiments. Moreover, the sparsity of events at the onset of nucleation and the morphological changes associated with phase transformation, especially at low supersaturations, remain significant challenges for such scattering-based techniques. Alternatively, advances in liquid phase atomic force microscopy (AFM) and transmission electron microscopy (TEM) have yielded experimental techniques that are capable of investigating many of the issues in materials formation discussed above.

Fig. 1 Many wide-ranging crystallization pathways have been proposed and/or observed for electrolyte solutions. In contrast to monomer-by-monomer addition as envisioned in classical models of crystal growth (gray curve), crystallization can occur by the addition of higher-order species ranging from multi-ion complexes to fully formed nanocrystals. Furthermore, the final phase may arise through a transformation from an initial, metastable phase by structural re-arrangement or chemical conversion. This figure is reproduced from [4] and used with permission by AAAS. Current Opinion in Colloid & Interface Science (2018) 34, 74–88


J Tao et al.

2. Setup and principle of liquid cell TEM and AFM 2.1. TEM In recent years in situ approaches using liquid cells in TEM have been utilized to investigate dynamic processes during materials formation [19], growth [20•,21], and assembly [22]. Many of these setups have taken inspiration from the pioneering work at IBM [23•,24], which used microfabricated, hermetically-sealed liquid cells to sandwich a thin liquid layer between silicon nitride (SiN) membranes suspended from silicon wafers (Fig. 2A). Other approaches seal liquid droplets between two graphene sheets [25]. Both

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static volume (Fig. 2A) and liquid flow micro-fabricated devices (Fig. 2B) now exist, sharing the same basic architecture. While in many regards these approaches are similar, they each have unique sample preparation and potential experimental complications to consider [26]. Two general approaches to liquid phase TEM that represent the studies discussed in this article are depicted in Fig. 2. The imaging area is limited by the overlap between the two SiN windows and the thickness of the liquid layer is defined by the thickness of a spacer layer deposited on one of the wafers. In closed cell approaches two reservoirs sit on either side of the imaging region, facilitating sample preparation and ensuring that the liquid layer remains in the imaging region

Fig. 2 Experimental approaches for liquid phase TEM and AFM. (A) Sealed liquid TEM cells are constructed from SiN membranes on silicon wafers separated by a sub-micron spacer, and are sealed shut after sample preparation. (B) Liquid flow stages may combine separate fluid lines into a single solution stream near the imaging area. Solution flows through a channel patterned in the liquid cell and around the outside of the cell. (Inset) Liquid flow cell components are pressed together by O-rings which provide a vacuum-tight seal. (C) Scheme of experimental setup for liquid phase AFM. Two reacting solutions are mixed at an in-line T-junction before flowing into a liquid cell. The setup permits control over supersaturation, temperature and flow rate. (D) The amplitude and frequency relationship in tapping mode AFM. Resonance curves for different drive amplitudes. For A0 between 11 and 12 nm the resonance curve is a three-valued function at ω = ω0. The tip and surface separation is 10 nm. (E) Experimental determination of the low and high amplitude branches. Amplitude curves vs piezo displacement for the L and the H branches. (F) Set points highlighted by dashed lines in (E) were used to image 200 × 200 nm2 InAs quantum dot sample. The system evolves from L state with amplitude set point of 16 nm (top) to unstable switching between H and L states with amplitude set point of 13.8 nm (middle) and finally to the H state with amplitude set point of 9.5 nm (bottom). (A) is adapted from [81] and used with permission by The Royal Society of Chemistry. (B) is adapted from [37•] and used with permission by AAAS. (D) is adapted from [31] and used with permission from APS; (E) and (F) are adapted from [33] with permission from APS. Current Opinion in Colloid & Interface Science (2018) 34, 74–88


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throughout the experiment. Additional functionality can be added through the fabrication of supplementary features, such as electrodes, onto the liquid cell components. For crystallization experiments these sealed cells are typically filled with undersaturated solutions, with the reaction initiated by an external stimulus. The driving force may be the electron beam itself, as demonstrated in examples discussed below, an external heater, or an applied electrical bias. Flow cells have the same core components as sealed cells, SiN windows on Si wafers separated by a spacer layer. However, for this approach the spacer layer is patterned to leave a flow channel extending across the length of the cell. This device is then fixed into a plumbed TEM sample stage where one or more inlets can pump reactant solutions through the stage and into the liquid cell (Fig. 2B), and O-rings separate the liquid from the vacuum of the TEM column. These flow stages facilitate mixing multiple reagents to create supersaturated solutions and drive nucleation and growth processes without the need for external stimuli, and are well suited to looking at crystallization from solutions. A significant consideration in liquid phase TEM is how the high flux electron beam affects the liquid layer. While some studies, notably those on low atomic number materials, have taken care to mitigate the electron dose rate, others have ignored the potentially significant influence of radiolytic products that arise from the electron beam's interaction with the liquid. Additionally, numerous reports, including two studies highlighted below, have utilized the radiolytic products to promote nanocrystal formation and growth through the reduction of solvated metal precursors. An early discussion of the radiolytic species produced by the interaction of the electron beam and the liquid cell identified the aqueous electron as the primary reducing agent for metal precursors [19]. More recent efforts have worked to develop a predictive model for each of the species produced through electron irradiation, lifetimes and distributions relative to the electron beam, and effect on pH [27,28•], although the initial efforts were limited to a model for pure water. Most recently, a review of radiation chemistry in liquid phase TEM experiments incorporates findings from the longstanding and rich radiation chemistry literature into a discussion of expected radiolytic products, their effects on experimental conditions, and strategies for mitigation [29].

system determines the type and rate of various interfacial processes and thus sets the spatial and temporal scale of interest. The AFM can be operated in a number of different imaging modes and environments such as vacuum, gas, and liquid solution for different applications. In solution, supersaturation, flow rate, pH, and temperature can be controlled for quantitative studies using supplementary pumps and heating systems (Fig. 2C). In general these imaging modes are categorized as contact mode, in which the tip touches the surface, and tapping or non-contact mode, where the probe is suspended above the surface and either the cantilever or the scanner is oscillated at a given frequency. In the contact mode of operation, the cantilever is dragged across the surface of the sample and the topography of the surface is measured directly by the deflection of the cantilever. Typically, lowstiffness cantilevers are used (i.e., most contact mode AFM cantilevers have a spring constant (k) less than 0.1 N/m), and the tip is always in contact with the surface so that the overall force is repulsive [30]. As a consequence of the lateral motion of the tip under application of a repulsive force, contact mode imaging generates shear forces. When imaging fragile samples such as soft matter or early events in mineral nucleation, tapping or non-contact mode is almost always the optimal choice, because it minimizes the lateral deformation of the sample that occurs when a tip is dragged across the surface in contact mode. In tapping mode, the cantilever oscillates close to its resonance frequency with an amplitude in the range of 1– 100 nm and cantilever stiffness from 0.1 to several N/m, alternating between attractive and repulsive force regimes depending on the transient distance between tip and sample. Since the cantilever is moving in a non-linear force field, interactions are not entirely elastic and the cantilever will dissipate energy due to interactions with surfaces and the surrounding medium. This characteristic has made quantitative interpretation of force data very difficult. Interactions such as van der Waals forces, electrostatic and solvation forces acting on the tip cause the amplitude to decrease as the tip approaches the surface. A feedback loop uses the difference between the measured amplitude and a predetermined value to adjust the distance between the tip and surface. In tapping mode, the relationship between the amplitude set point and the frequency shift during the oscillation follows [30,31]:

2.2. AFM In contrast to the electron probe used in TEM, AFM monitors intermolecular interactions between a solid stylus and the sample surface [30]. The motion of the cantilever is tracked as it moves across the surface by the deflection of a laser beam onto a position-sensitive detector (Fig. 2C). There are three basic components for successful AFM imaging of interfacial processes such as heterogeneous nucleation, growth, and transformation: (1) the probe as force detector; (2) the crystal or protein substrate of interest; and (3) the solution environment (Fig. 2C). The solution-substrate Current Opinion in Colloid & Interface Science (2018) 34, 74–88

A 1 ffi ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " A0 u 2 #2 2 ukm k ω ω ts t − 2 þ 2 1þ k ω0 ω0 C2

ð1Þ

where A0 is the free amplitude, m is the mass of the tip, C is the damping coefficient, k is the stiffness of cantilever, kts is the stiffness of interfacial force field, (repulsive force for positive kts, attractive force for negative kts) ω is the resonance frequency of the driving force, and ω0 is the www.sciencedirect.com

J Tao et al. resonance frequency of the cantilever free of interfacial force field. The amplitude A is the key experimental parameter measured in tapping mode. Fig. 2D shows the evolution of the resonance curve as a function of the free oscillation amplitude. When A0 is smaller than but close to the tipsurface separation, the attractive forces (kts b 0) tend to bend the resonance curve to frequencies lower than the free resonance indicated in Eq. (1). Increasing the free amplitude brings the tip into contact with the surface. This in turns shifts the vibration to higher frequency. However, attractive forces impose a characteristic deformation in the resonance curve. For values of A0 between 11 and 12 nm the resonance curve is a three-valued function at ω = ω0. Each value corresponds to a different operating state. However, the middle point is physically inaccessible because it doesn’t meet the stability criteria [32]. The coexistence of two stable states has drastic implications for the operation of tapping mode AFM. Fig. 2E shows an experimental amplitude curve acquired from InAs quantum dots [33]. The presence of a discontinuity between the low (L) and high amplitude (H) branches shows that an amplitude set point value within the step range could be achieved with two different tip-surface separations. This opens up three regimes for imaging: Imaging entirely in either the H or L state, or switching between the two. Jumping between the two tip-surface separations introduces artifacts that complicate accurate height measurement, as shown by the presence of spurious features neighboring some quantum dots in Fig. 2F. A suitable choice of amplitude set point can avoid this situation and allow stable imaging in either the H or L state. Generally speaking, L state imaging is best suited for soft matter because of the weak tip-surface force. However, H state imaging offers better lateral resolution whenever sample deformation is not an issue. The choice of amplitude is critical for imaging newly formed mineral nuclei, as imaging in the H state has been shown to produce irreversible morphological changes in small inorganic nanoclusters [33].

3. Examples of in situ TEM A comprehensive picture of the burgeoning literature of liquid phase TEM studies that examine a broad spectrum of nanoscale phenomena can be found elsewhere [34,35,36]. In this section we highlight five recent reports that center on the use of liquid phase TEM to understand phenomena inherent in materials formation. The first three examples investigate the crystallization of low atomic number materials: the mineral calcium carbonate (CaCO3) and the protein lysozyme. In these studies the electron flux was minimized to mitigate the effects on the sample of radiolytic products in the precursor solution. The concluding two examples probe formation and growth behavior of noble metal nanoparticles. A much higher electron flux was used in these studies, to drive nanocrystal formation with the charged species formed in the precursor solution by the electron beam. Current Opinion in Colloid & Interface Science (2018) 34, 74–88

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4. Mineral and protein crystallization Two recent liquid phase TEM studies have looked at the formation of CaCO3 from either pure precursor solutions [37•] or in the presence of an organic matrix [38•] possessing chemical functionalities found to interface with the mineral [39] in biomineralizing organisms. CaCO3 is a much studied system due to its relevance in, among other fields, biomineralization, where living organisms use organic matrices to control the formation and development of the mineral into complex, functional materials [40] of specific phase and tightly controlled properties [41]. The CaCO3 system has multiple crystalline phases, hydrated and anhydrous [42], identified amorphous states [43], and the suggested existence of potential additional precursors [10,11]. The two studies highlighted below demonstrate how liquid phase TEM data can provide unique insight into transient phenomena in the formation of solid CaCO3. A TEM flow stage (Fig. 2B) was used to study formation pathways of CaCO3 in the absence of organic additives [37•]. Controlling the initial concentrations and relative flow rates of the reactants allowed observation of CaCO3 formation over a wide range of reaction conditions. Increasing initial reagent concentrations led to the formation of multiple CaCO3 phases, and amorphous CaCO3 (ACC) and all of the anhydrous crystalline polymorphs, calcite, vaterite, and aragonite, were observed. At the lowest concentrations tested no precipitation was observed. As the precursor concentrations were raised single pathways were observed in individual experiments, while at higher concentrations ACC formation was more prevalent and multiple pathways were simultaneously active. These observations are in line with predictions of classical treatments of nucleation, as increasing the supersaturation for a given phase lowers the energy barrier to nucleation, rendering more phases and pathways accessible. Fig. 3A shows one of the many crystallization pathways found in the report. An ACC particle first formed and grew to a lateral size of a few micrometers. The ACC then began to shrink shortly before the appearance of new structures at or just below its surface. The new phase proceeded to grow, consuming the ACC until only the second phase, identified by diffraction (Fig. 3A inset) as vaterite, remained. Throughout the entire transformation process the ACC and vaterite maintained physical contact, as the more soluble amorphous particle dissolved to feed the growing crystals. Continuous imaging throughout the process, allowed by liquid phase TEM, provided a means of identifying the formation pathway of the resulting vaterite structures, which would not be evident from a post-growth analysis. To investigate the influence of an organic additive over the formation of solid CaCO3, a recent study [38•] introduced polystyrene sulfonate (PSS) as an additive that mimics the sulfonated carbohydrates seen in certain biomineral systems [39] and used liquid phase TEM to understand the mechanism by which this additive modifies mineral formation [38•]. Rather than flowing liquid through the stage, to continually increase CaCO3 supersaturation, Smeets et al. diffused CO2 gas into a Ca2+-rich solution, a common experimental www.sciencedirect.com

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Fig. 3 Multi-step formation pathways observed in low Z materials. New phase nucleates on or just below the surface of an ACC particle (A). Consumption of the amorphous precursor feeds the growing vaterite crystals, identified by diffraction (inset). (B) Globular phase of Ca-PSS complexes forms prior to CO2 diffusion into cell. (C) Upon diffusing CO2 into solution, ACC particle rapidly forms within a Ca-PSS globule in the boxed region of (B). (D) At late times, higher contrast CaCO3 particles have formed within many Ca-PSS globules; diffraction data (D inset) identifies the particles as ACC. (E) ASP particles found in unfiltered solutions of lysozyme. (F) ASP serves as a preferential site for heterogeneous nucleation of a lysozyme particle (white arrow). The particle develops over time into a distinct orthorhombic crystal. Scale bars are 500 nm (A, E–F), 100 nm (B, D), 10 nm (C), and 2 nm−1 (D inset). (A) is adapted from [37•] and used with permission by AAAS. (B–D) is adapted from [38•] and used with permission by Nature Publishing Group. (E–F) are adapted from [47•] and used with permission by the National Academy of Sciences.

approach for this mineral system. In the absence of PSS, vaterite nucleated and grew on the SiN membranes. A marked difference was observed, however, upon introduction of the organic additive. Ca-PSS complexes, identified by independent spectroscopic, calorimetric, and ion selective electrode measurements, were found to form globules [39,44] on the SiN surface (Fig. 3B) prior to diffusing in CO2. These globules provided locally concentrated regions of Ca2+ ions — roughly half of the total Ca2+ in the liquid — for the subsequent mineralization. When CO2 diffused into the liquid cell to create supersaturated conditions, particles rapidly formed and grew within the globules until the bound calcium was depleted (Fig. 3C). Diffraction data showed these particles internal to the organic matrix to be ACC (Fig. 3D), while continued exposure to the electron beam induced crystallization of the ACC into calcite without substantial accompanying growth. On a much longer timescale, vaterite crystals were seen forming independently of the initially-formed organic matrix. The results show that this organic matrix biases the system towards ACC formation. While multiple phases are energetically permitted to form, the Ca-PSS globules shift Current Opinion in Colloid & Interface Science (2018) 34, 74–88

the kinetics to favor formation of the amorphous phase through binding much of the calcium in solution. These globules then provide chemical environments that promote stabilization of ACC. Thus, the simple addition of an organic macromolecule can change kinetic barriers independent of any modification of free-energy barriers [45•,46] to control the nucleation pathway and final phase of the CaCO3. The third example of observing low Z material crystallization using liquid phase TEM is the formation of lysozyme crystals from solution [47•]. Crystallization in many protein crystal systems, as well as in other materials, has been described as a two-step process [8,9,48,49], wherein the first precipitate is a disordered precursor inside of which a structured crystal forms and proceeds to grow. In some protein solutions, including lysozyme, clusters of protein molecules with sizes up to hundreds of nanometers have been observed and proposed to be precursors in the crystallization pathway [50]. Whether these clusters are active in the nucleation of crystals, and whether they are liquid-like or more of an amorphous solid are open questions. Yamazaki et al. employed a number of characterization tools centering on liquid phase TEM to address such questions. www.sciencedirect.com

J Tao et al. In filtered solutions nucleation was observed to occur heterogeneously on the SiN windows. The initial structure was a spherical particle that after the first minute grew to exhibit either an orthorhombic or tetragonal morphology and continued to grow as the experiment continued. It is unclear from the study whether the evolution in particle shape was concomitant with an evolution in crystal structure. By contrast, when unfiltered lysozyme solutions were used, many spherical particles over 100 nm in size were observed (Fig. 3E) but did not coalesce during the experiment or evolve into expected lysozyme crystal morphologies. Diffraction analysis of these particles suggested a lack of crystallinity (Fig. 3E Inset), and they were termed amorphous solid particles (ASPs). Monitoring nucleation events in these unfiltered solutions, the researchers observed the heterogeneous nucleation of a particle on an ASP surface (Fig. 3F). At first appearance (0.17 s), it is already on the order of 100 nm in size. The contrast darkens throughout the first few frames, and the particle further develops into an orthorhombic shape. However, there is no parallel evolution in either the ASP that acted as the heterogeneous nucleation site or the second nearby ASP. The in situ observations afforded by liquid phase TEM provided unique insights into the nucleation process in lysozyme solutions. The previously observed, mesoscopic lysozyme clusters were found to be active in the nucleation process only as heterogeneous nucleation sites. Indeed, when solutions were filtered to remove the ASPs, the observed nucleation rates dropped precipitously suggesting that they play a critical role in providing a low-energy surface on which nucleation can readily occur.

5. Metal nanocrystal formation and directed growth While in the preceding studies care was taken to minimize the electron flux so as to mitigate the effects of the electron beam’s interaction with the material under observation, other reports have utilized beam-induced radiolysis of aqueous solutions to drive the formation of materials. By far, most of this literature has looked into formation and growth phenomena of noble metal nanoparticles. One recent study of note used in situ TEM observations paired with molecular dynamics simulations to conclude that nucleation of gold and silver nanoparticles is preceded by the spinodal decomposition of the precursor solution [51•]. A closed, static volume liquid cell was imaged using high electron fluences to capture the solidification process. Much of the liquid layer was displaced by the beam, leaving only a calculated 30 nm thick liquid layer of highly concentrated precursor solution on one of the SiN membranes. This liquid layer rapidly separated to form precursor rich and precursor poor volumes of liquid (Fig. 4A). Over the next several seconds, the concentrated regions condensed down into nanometer-sized particles that at first appeared to be either amorphous or poorly crystalline solid metal nanoparticles. Within several more seconds, signal appeared in the Fourier Transform consistent with the expected lattice spacing for Current Opinion in Colloid & Interface Science (2018) 34, 74–88

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the fcc crystal structure at which point the authors designated the nucleation process to be complete. Ab initio calculations of hydrated Au atoms showed an energetic preference for forming ionized pairs that further associated into amorphous clusters, rather than dissolving back into solution. These calculations were coupled with MD simulations of Au atoms in water that showed spontaneous demixing of the starting distribution into Au-rich and Au-poor regions, to provide a computational case to complement the in situ TEM data in constructing the proposed mechanism of spinodal decomposition for metal nanoparticle formation. The conclusions hinge on the argument that the radiation effects of a high electron flux do not fundamentally alter the underlying chemistry that drives the formation process. Against this potential critique the authors provide data at different electron fluences to demonstrate the same process occurring across different time scales. In addition they connect their findings to literature, including a report suggesting dense liquid Au-rich droplets forming in the presence of citrate, in the absence of ionizing radiation [52]. Beyond controlling formation pathways and stabilizing particular phases as demonstrated above, organic additives can also direct growth into specific and tightly controlled morphologies. A recent paper [53•] used liquid phase TEM to investigate facet development of Pt nanocrystals in the presence of an organic ligand, using a sealed liquid cell and inducing crystallization with the electron beam. Pt crystals rapidly nucleated and grew primarily through monomer addition. The crystals exhibited isotropic growth until reaching sizes of about 5 nm, at which point their shape started evolving into truncated octahedra (Fig. 4B). Throughout the growth of the nascent nanocrystal, face-specific growth rates were measured (Fig. 4D). As the facet growth rates differentiated, {110} and {111} facets grew at similar, faster rates than the {100} growth rate until they reached the bounding {100} facets. Growth continued until the corners were filled in, resulting in cubic nanocrystals (Fig. 4B). Accurate growth rate measurement was assisted by fitting the atomically resolved data with simulated images of similar structures (Fig. 4C). The growth rate of the {100} facets was found to be the smallest and thus it determined the final shape of the nanocrystal. Surface energy and ligand-binding energy calculations provided an explanation for the development into a non-equilibrium shape. The ligand dwell time was determined to be five orders of magnitudes longer on a {100} site than a {111} site, suggesting that growth into cubic nanocrystals was a kinetically controlled process. For small nanocrystals, the sparse surface arrangement of ligand molecules allows Pt atoms to land with similar probability on any face. As larger facets develop, growth on the {100} facets is blocked by the low mobility of ligands bound to those surfaces while growth on other surfaces such as {111} continues.

6. Examples of in situ AFM In situ AFM has been widely used to study crystal growth and surface mediated 2D nucleation of both inorganic and www.sciencedirect.com

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Fig. 4 Formation and growth of metal nanocrystals. (A) Irradiation of Au3+ solutions produces dense liquid-like regions (9.2 s). Amorphous or poorly crystalline Au clusters form within the dense liquid phase (10.6–11.3 s) and develop into the expected fcc structure (15.4 s). FFT insets show the appearance of the fcc Au (111) lattice spacing upon sufficient ordering of the boxed precipitate's structure. (B) Selected images and (C) associated image simulations follow the ligand-mediated growth of a single Pt nanocrystal as it develops into a nanocube. (D) Measured average distances from the particle center to the various crystal facets throughout the observed evolution into a nanocube. Scale bars are 5 nm (A) and 2 nm (B). (A) is adapted from [51•] and used with permission by Nature Publishing Group. (B–D) are adapted from [53•] and used with permission by AAAS.

protein crystals. The physics of crystal growth and nucleation has been well reviewed based on the in situ studies with well-defined solution and additive conditions [5]. In this section we look at three quantitative studies that use liquid phase AFM to understand the energy barriers to nucleation. In the first study, individual nucleation events of the mineral calcium phosphate on collagen are measured to extract energetic parameters with which theoretical frameworks for understanding nucleation can be tested. The two subsequent studies functionalize the cantilever tip for measurements that provide the binding force between the ligand and a crystal surface.

7. In situ AFM of calcium phosphate nucleation processes on collagen surfaces The role of the collagen matrix during the infiltration of amorphous calcium phosphate (ACP) and its subsequent transformation into oriented crystals of apatite has attracted much attention over decades [54,55,56,57]. Although many details of the role of collagen on ACP infiltration have been observed in cryogenic TEM [58], an understanding of the kinetics and pathway of calcium phosphate nucleation has long been elusive. The nucleation of calcium phosphate as a function of supersaturation both below (Fig. 5A) and above (Fig. 5B) the solubility limit of ACP was studied and compared to the predictions of classical nucleation theory (CNT) [59•]. Current Opinion in Colloid & Interface Science (2018) 34, 74–88

Nucleation rates were measured by tracking the increase in the number of calcium phosphate nuclei per unit area of surface as a function of time. Images were collected with a tapping force substantially lower than ~150 pN used to study protein assembly [60•] to minimize the influence of the tip on nucleation. CNT [1] describes the nucleation rate Jn by: ΔGc

Jn ¼ Ae− kT

ð2Þ

where A is the kinetic factor related to diffusional, steric, and other kinetic barriers, k is the Boltzmann constant and T is the absolute temperature. ΔGc is the energy barrier that must be overcome to form a particle of critical radius Rc (a function of α/σ), and scales proportional to α3/σ2, α is the interfacial energy, and σ is the supersaturation (σ = −Δμ / kT). Eq. (2) can thus be rewritten: ln Jn ¼ lnA−B

αeff 3 σ2

ð3Þ

where B is a shape-dependent factor and αeff is the effective surface energy, a composite of the interfacial energies for the three interfaces created or destroyed during nucleation — the crystal-substrate, crystal-liquid and liquid-substrate interfaces. Fig. 5C plots measured nucleation rates versus σ−2 for HAP and ACP. The effective surface energies can be extracted from linear fits to the data by Eq. (3), which gives values for αeff of 90 mJ/m2 and 40 mJ/m2 for HAP and ACP, respectively. www.sciencedirect.com

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Fig. 5 In situ tapping mode AFM investigation of crystal nucleation and phase transformation of calcium phosphate on collagen. (A) HAP nucleation on collagen. σHAP = 3.08, σACP = −0.23. (B) ACP nucleation followed by transformation to OCP and then HAP. σHAP = 3.36, σACP = 0.04. Inserts: TEM images of mineral phase, (A) HAP, (B) ACP (left), OCP (middle), and HAP (right). Scale = 100 nm. (C) Nucleation rate vs. 1/σ2 giving effective interfacial energies for ACP and HAP. (D) Free energy vs nucleus size for range of σ based on CNT for hemispherical ACP with αACP = 40 mJ/m2. (E) Growth rate vs. particle height at fixed σ. Black dots: experimental data; red curve: fit to Gibbs-Thomson equation. (F) Estimated free energy vs. nucleus size for various ratios of pre-nucleation complex-to-ACP surface energies (αCl/αACP) and corresponding ΔGEx during heterogeneous nucleation of hemispherical ACP through aggregation of 1.1 nm complexes (see reference [59•] for detailed assumptions). Heavy solid curves: σACP = 0.15, Light solid curves: σACP = 0.4. (A, B, C, D, F) are adapted from [59•] with permission by Nature Publishing Group. (E) is adapted from [61] with permission by Cambridge Core-Cambridge University Press.

Taking the values of σ for HAP and ACP at the conditions where the first phase to appear changes from the former to the latter (σHAP = 3.36, σACP = 0.04), it was found that ΔGc for ACP formation was about 600 times larger than for HAP formation. Fig. 5D plots ΔG vs. R at different supersaturations using the value of αACP determined from Fig. 5C. In this scenario the value of the barrier to ACP nucleation is larger than 1500 kT. Moreover, CNT would predict the critical radius Rc to be ~10 nm, larger than the 1–3 nm heights of the features observed by AFM (Fig. 5B). Because the lateral resolution is limited by the probe used to scan the nuclei (typical probe radius are around 10 nm), the lateral size of individual nuclei cannot be reliably measured. While this is Current Opinion in Colloid & Interface Science (2018) 34, 74–88

changing, with improvements in tip manufacturing capable of producing a tip of radius less than 2 nm, there is still a limit on imaging features with lateral sizes smaller than ∼3 nm. However, the sensitivity of height measurements by AFM is at the sub-Angstrom scale. To put the nucleation barriers in perspective, even if the pre-factor A of Eq. (2) was equivalent to the attempt frequency for atomic vibrations at room temperature (~1012 Hz), the barrier would have to be of order 30 kT or less to get significant rates of nucleation. Consequently, ACP should never form with a ΔGc larger than 1500 kT based on the classical framework. By fitting growth rate data in Fig. 5E with the Gibbs-Thomson equation [5,62], Rc was determined www.sciencedirect.com

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to be 0.61 nm at σHAP = 3.31, as shown in Fig. 5E. The HAPsolution interfacial energy was thus calculated to be 141 mJ/ m2, in good agreement with 143 mJ/m2 as determined by solubility measurements [63]. Habraken et al. accounted for the discrepancy between CNT and their data by invoking the involvement of a minority species consisting of multi-ion pre-nucleation complexes during nucleation, which they observed with cryo-TEM, and described as follows how these complexes modify classical predictions. The origin of CNT’s barrier in ΔG is the introduction of an excess free energy over a bulk solid associated with creation of a new interface. However, pre-nucleation complexes themselves have a certain excess free energy over that of the free ions that is associated with their interface with the solution. When the complexes combine to form a larger particle, the elimination of this excess free energy ΔGEx must be taken into account and this can have a dramatic effect on the value of the free energy barrier, as well as the critical radius [64]. To estimate the magnitude of the effect, the change in free energy as a function of particle radius R is expressed using: ΔG ¼ ΔGCNT −NΔGEx

ð4Þ

where N is the number of complexes that combine to form the nuclei. This shows that there is a reduction in ΔG due to any excess free energy of the complexes over that of the free ions. For the case of ACP nucleation on collagen, the number of diskshaped complexes of radius r (assuming an equal height and radius) that must combine to form an ACP nucleus is given by N = (R/r)3f, where f is a geometric factor. Attributing ΔGEx exclusively to the complex surface free energy αcl implies that ΔGEx = 4πr2αcl. This leads to a nucleation barrier and critical size of: α αcl −2 1þC ΔGcl ¼ ΔGCNT c rσ α

ð5Þ

α αcl −1 1þC Rcl ¼ RCNT c rσ α

ð6Þ

where C is a temperature-dependent factor. ΔGcl is now given by the product of the CNT expression and a correction term that is always ≤1, and a value that scales as αcl/α. The dramatic effect that this has on nucleation barriers is plotted in Fig. 5F. In fact, for sufficiently large αcl/α values, the barrier can be completely eliminated so that nucleation proceeds downhill in free energy. Thus the aggregation of the pre-nucleation complexes followed by chemical transformation avoids the insurmountable thermodynamic barrier faced during ion-by-ion nucleation of ACP predicted by CNT. As a result, the authors argue that the pathway to the final crystalline state is controlled by kinetic barriers associated with the chemical reactions and structural rearrangements of the pre-nucleation complexes. The presence of these pre-nucleation complexes fundamentally alters the nucleation pathway by making amorphous phases accessible at concentrations where CNT would predict the exclusive formation of the more stable crystalline phases. Moreover, cryo-TEM imaging also shows secondary Current Opinion in Colloid & Interface Science (2018) 34, 74–88

fractal structures which aggregate from these multiple ion complexes. These fractal structures are amongst a group of species reported to serve as precursors to nucleation of the first solid phase, though the structural similarities between them are unclear. These precursors include the dense liquid like aggregates proposed for lysozyme [65], mass fractal structures proposed for glycine [66], and ionic aggregates proposed for high concentrations of calcium carbonate [67], although recent experiments and simulations on the latter conclude that free ions and ion pairs to be the dominant species [68] and question the relevance of larger ionic aggregates in calcium carbonate nucleation. The findings of Habraken et al. strongly suggest that the aggregation of basic building blocks proposed in this study as the first step in crystal formation may be a more general phenomenon in both organic and inorganic systems. Perhaps other such “non-classical” nucleation phenomena can likewise be explained by the extended CNT.

8. Defining the relationship between nucleation barriers and binding free energies by in situ dynamic force spectroscopy Substrates can alter the probability of nucleation because the interfacial energy between a crystal nucleus and a solid substrate typically differs from that of the same nucleus in contact with solution [69,70]. The detailed expression for effective interfacial energy αeff, is given by [5]: αeff ¼ αlc þ hðαcs −αls Þ

ð7Þ

where h is a factor that depends on the aspect ratio of the nucleus [71], and the interfacial energies for the liquidcrystal interface (αlc), crystal-substrate (αcs), and liquidsubstrate (αls) are considered individually. The physical basis for the reduced interfacial energy was investigated by Hamm et al. using dynamic force spectroscopy (DFS) [45•] to measure the binding free energies between calcite surfaces and organothiol self-assembled monolayers (SAMs). DFS is an AFM-based technique that measures the rupture forces by retracting a chemically decorated tip from the surface at different speeds. After extrapolating the retraction rate to zero, the equilibrium rupture force can be calculated. αlc was considered independent of SAM chemistry, and αls was assumed to be similar due to the low pKA of all SAMs and the use of high pH solutions. Thus, the only term that should differ significantly from one SAM to another is the interfacial energy between the SAM and the crystal (αcs) with smaller values leading to lower barriers. Moreover, αcs should be largely controlled by the binding free energy ΔGb between the crystal and the SAM. In fact, because DFS determines the difference in free energy between the bound and unbound state, the ΔGb can be written: ΔGb ¼ Aðαlc þ αls Þ−Aαcs

ð8Þ

where A is the tip-substrate contact area. Rewriting Eq. (7) in www.sciencedirect.com

J Tao et al. terms of ΔGb gives: h αeff ¼ − ΔGb þ ð1 þ hÞαlc A

ð9Þ

showing a linear relationship between αeff and ΔGb. Thus, an explicit relationship between the nucleation barrier and the strength of the crystal-substrate binding energy should exist. To test these relationships, calcite nucleation rates on a handful of functionalized alkanethiol SAMS were measured using optical microscopy to obtain values for αeff, and AFM tips were gold coated and functionalized with the same SAM monomers (Fig. 6A). These tips were then used to perform DFS on calcite (104) faces (Fig. 6B and D), which served as a proxy for the faces that nucleate on SAMs. Fig. 6E shows a linear relationship between αeff and ΔGb, and the slope was shown to be in reasonable agreement with the expected value. Thus, this study found that a large crystal-SAM binding

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free energy leads to a small crystal-SAM interfacial energy, resulting in a small barrier to nucleation. These insights provide a physical basis for the common adage that good binders are good nucleators. This same principle was also used to investigate the source of specific alignment between collagen, the protein scaffold in bone, and HAP, which constitutes the mineral component of bone. The saw-tooth form of the force curve (Fig. 6C) seen in DFS reflects multiple rupture events associated with multiple bonds formed by collagen with the HAP [72•]. Due to the periodicity of the collagen molecule, the collagen-HAP binding free energy can be estimated from the area of last rupture event in the force-distance curve, assuming the final rupture represents the bond for the last functional group. This is the work done during removal of a collagen triple helix from the surface and equals (350 ± 61) kT and (302 ± 49)kT for HAP (100) and (110) faces, respectively. Thus while the binding free energy of the

Fig. 6 Dynamic force spectroscopy for understanding mineral-organic interfaces. (A) DFS schematic shows functional molecules linked to gold-coated AFM cantilever that is brought into contact and then retracted from crystal surface. Representative forceseparation curves for (B) SAM-calcite and (C) collagen-HAP bond rupture, showing single and multiple rupture events during tip retraction, respectively. (D) DFS spectra for rupture of bonds between functionalized alkanethiol SAMs and calcite (104), (E) Interfacial energies (α) derived from nucleation rate measurements vs. free energies of binding (ΔGb) for SAM molecules on calcite (104) surfaces as measured by DFS. Lower α correlates with strong calcite–SAMs interactions (large ΔGb and rupture forces (inset)). (F) DFS spectra for rupture of bonds between collagen and HAP (100), and (G) HAP (110) faces. Solid curves are fits to a harmonic potential model, assuming a single broken bond in the final rupture event. Panels A, C, F, G are adapted from [72•] and used with permission by the National Academy of Sciences; Panels B, D, E are adapted from [45•] and used with permission by the National Academy of Sciences. Current Opinion in Colloid & Interface Science (2018) 34, 74–88


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terminal group is slightly greater on (110) face than (100) face ((6.25 ± 0.48)kT vs (5.40 ± 0.53)kT) (Fig. 6E, F), the binding energy for the full collagen triple helix is ~20% larger on the (100) face, suggesting that the stereochemical relationship of collagen to HAP favors better multi-site binding on HAP (100) than on HAP (110). The results provided evidence that the strong, specific alignment of collagen on HAP arises from collagen-apatite interface energetics, which contrasts with the viewpoint that HAP alignment is only due to physical confinement inside a collagen bundle [73]. Thus both mechanisms may work simultaneously to exert the observed control over mineral structure and orientation. The environment within a fibril is likely to amplify the energetic effects measured here, because it brings together numerous collagen strands at distances comparable to diameters of both the amorphous precursors [58] and critical nuclei [59•], while any tendencies towards channel alignment along fibrils will exert a further pressure to select a single crystal alignment. By complementing the DFS measurements with AFM imaging to determine the alignment of collagen on a range of calcium phosphate phases, the findings reconciled apparent contradictions between the symmetry of common apatite phases and the morphology of bone mineral and provided an energetic rationale for the molecular scale organization of bone.

9. Perspectives Despite the significant advances in the application of in situ TEM and AFM to investigations of nucleation, growth, phase transformations, and organic-inorganic interfaces during material synthesis, there are a number of improvements in instrumentation on the horizon that will help expand the impact of such studies. In the case of AFM, faster image collection is required to capture short-lived transient species. In the past several years, scan rates have improved to several tens of frames per second due to numerous technical breakthroughs, including ultrashort cantilevers with a frequency up to 500 kHz in fluid, low-noise and high-resonant frequency scanners, and a new generation of controllers with high-bandwidth electronics [74,75,76,77]. Second, a sustained, minimal force is required to obtain a molecular resolution image of metastable interfaces between a nucleus and the surrounding fluid. This is challenging, however, because the large amplitude of the cantilever's Brownian vibrations in fluid environments requires large drive amplitudes in order to obtain a signal that is above the noise level [78]. Damping the cantilever oscillation in fluid greatly lowers the quality factor and reduces the resolution of the image [79]. Newly designed cantilevers encased within an airfilled shell that are thus not subject to fluid-induced cantilever vibrations should help improve the spatial resolution. Third, using an amplitude less than 2 nm will further lower the effect of damping. However, to prevent the tip from exhibiting so-called “snap-in” to the surface due to a strong attractive force gradient near the surface, very high stiffness cantilevers — with force constants up to perhaps several tens Current Opinion in Colloid & Interface Science (2018) 34, 74–88

of N/m in liquid — are required. The use of such stiff cantilevers reduces the amplitude signal beyond the level which conventional AFMs can reliably measure. One possible solution for this challenge is to use a fiber-based interferometer which has at least a two-order of magnitude increase in sensitivity [80,81]. As shown in the examples highlighted above, liquid phase TEM provides a tool to image individual particles as they form and grow from solution with nm-scale resolution, and to collect information on phase and crystallographic orientation. However, the attainable resolution and level of structural or chemical information are dependent on the beam sensitivity of the material and the amount of sample relative to that of the surrounding medium [24]. No firm estimates can be placed on these constraints as the range of potential materials properties is so large. As formation and growth pathways are dynamic responses to the solution environment, gradients in interaction potentials, and energetic barriers between states, the energetics of these processes can be quantified through measurements of rates afforded by direct imaging. Understanding how these factors change in the presence of additives, whether surfaces, monomeric ligands, or macromolecular complexes, may open doors for novel approaches to controlled materials synthesis. While liquid phase TEM has matured greatly in the past two decades, further developments will aid in providing quantitative data on dynamic phenomena in nanomaterial formation and assembly. Understanding the solution chemistry under the electron beam is of paramount importance in developing quantitative descriptions of the observed phenomena. Numerous improvements in liquid phase TEM can help improve on the current state. For example, a plumbed stage with multiple inlets was used in the report on nucleation pathways in CaCO3 [37•,82]. This stage, along with the others of which we are aware, is designed to have the liquid streams flow both across the liquid cell’s flow channel and around the outside of the cell. Because the liquid flow and mixing dynamics remain largely unknown, when multiple reagents are mixed there is some degree of uncertainty regarding the solution composition in the observation area. Compounding this issue is the electron-beam induced radiolysis of the sample, which, as discussed above, can substantially alter the species present and the pH of the liquid. Developing low-dose methods and more sensitive detectors to reduce electron beam fluxes, and better models to account for complex solutions with many dissolved species will assist in more accurate and quantitative analysis of future liquid phase TEM studies. The incorporation of in situ diagnostics to measure such parameters as solution temperature and pH will help in validating these models. Analytical electron microscopes also have the capability for spectroscopic analysis utilizing electron energy loss spectroscopy [83,84,85,86] or energy-dispersive X-ray spectroscopy [87,88] to analyze samples in liquid cells. Perhaps these analytical techniques will find greater utilization in better understanding the chemical composition of the liquids and the solid-liquid interfaces at the surfaces of developing materials. www.sciencedirect.com

J Tao et al.

Acknowledgments J.T. and J. J. D.Y. acknowledge support for this review from US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering through Pacific Northwest National Laboratory (PNNL). M. H. N. acknowledges support for this review from the Lawrence Fellowship Program at Lawrence Livermore National Laboratory (LLNL). PNNL is operated by Battelle for the US Department of Energy under Contract DE-AC05– 76RL01830. LLNL is operated by Lawrence Livermore National Security for the US Department of Energy under Contract No. DEAC52-07NA27344.

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