Modern nanoscience: Convergence of AI, robotics, and colloidal synthesis

Colloidal nanocrystals have broad reaching applications and potential in chemical, biology, and energy-related technologies, including optoelectronics,^1–4 (photo)catalysis,^5–9 gas sequestration,^10,11 bio-imaging,^12–17 drug delivery,^18–21 and many others.^22–27 The sophistication of the nanomaterials spans from low-cost, solution-processed coatings^28–30 to high-end specialty applications,^31–34 and subsequent reagent costs can go from common inexpensive bulk chemicals^35–37 to expensive rare metals.^38–41 Regardless of the application, the synthesis of colloidal nanocrystals is often highly sensitive to controllable and uncontrollable reactive conditions, and the large number of relevant intrinsic and extrinsic parameters creates an unfathomably large accessible synthesis universe—shown in Fig. 1(a). Often solution-processed nanomaterials are synthesized using a nucleation and growth process, but the exact synthetic route is typically more complex and less clear. Colloidal synthesis of nanocrystals is conducted using a variety of strategies, including hot-injection, heat-up, and ligand-assisted reprecipitation, and many synthetic pathways feature difficult to characterize deviations from classical nucleation theories.^42–51 In addition to the complex and exponentially increasing input parameter space, colloidal syntheses can produce intricate, heterogeneous solutions of structurally and compositionally diverse nanocrystals,^52–54 which are often difficult to comprehensively characterize with a single measurement technique, as shown in Fig. 1(b).

Due to these compounding challenges in reaction control, reproducibility, and analysis of colloidal nanocrystals, quantitative model-driven experiment selection methods are generally less common in colloidal nanoscience than other fields. In organic chemistry, for example, models integrated with data mining algorithms from the literature enable the prediction and routing of multi-stage synthesis routes (retrosynthesis) with relatively high precision.^55–57 This approach is far more challenging in colloidal nanoscience due to a lack of unifying features and reactor-sensitive nature of the nanomaterials variation. Therefore, research in colloidal nanoscience often falls into highly specialized areas of focus that are subsets of an emerging material group. Broad unifying properties are difficult to observe, and each synthetic route generally requires its own tailor-made multi-stage synthesis and processing strategy. Within each of those synthetic strategies, further issues arise in significant batch-to-batch and lab-to-lab variation under the same reported protocols due to process-sensitive nature of the formation mechanisms of colloidal nanocrystals.

More efficient and more precise experimentation techniques are the next critical development in the discovery, development, and manufacturing of emerging colloidal nanocrystals for energy, chemical, and biological applications.⁵⁸ In addition to known system complexities, nanocrystal properties are often determined through deviations in dynamic and uncontrollable environmental parameters and combination rates—Figs. 2(a) and 2(b).^59–62 Day-to-day and hour-to-hour changes to the laboratory environment and reagent decomposition and variability all introduce unexpected and difficult to control variance in highly sensitive experimental outcomes. Furthermore, colloidal nanocrystal syntheses often rely on rapid nucleation events, yet the systems used in conventional reaction studies are often insufficient in consistently controlling mass transfer on relevant time scales, leading to batch-to-batch and lab-to-lab variability.⁶³ Greater reproducibility and rapid in-house data generation will help to alleviate these significant challenges in navigating complex and process-sensitive colloidal synthesis systems.

As a result of this need, recent years have seen a rise in automated experimental platforms for the exploration of colloidal nanocrystal syntheses. Even with automated, high-throughput reaction conduction technologies, however, the vast expanse of experimental spaces in emerging colloidal nanocrystals is too large to cover through brute force experiment conduction or systematic combinatorial screening. In response, a new class of autonomous [i.e., guided by an artificial intelligence (AI) algorithm], closed-loop robotic experimentation strategies, built from the backbone of automated reaction systems, are quickly rising in prominence. Such self-driving laboratories operate by integrating the entirety of AI-guided modeling and experiment selection, conduction, and measurement into a single unified workflow, removing the need for user intervention and thereby accelerating the reaction exploration and discovery process. AI-guided parameter space exploration and optimization algorithms are used to guide these automated nanocrystal synthesizers through any set of complex, high-dimensional nanocrystal synthesis parameters. With intelligent experiment selection, autonomous robotic experimentation systems can navigate complex experimental spaces with both rapid data generation and efficient experiment selection under uncertainty. While many aspects of autonomous experimentation technologies are early in development, it is highly likely that they will play a significant role in shaping the future of colloidal nanoscience and nanoengineering.

One of the primary barriers in autonomous reaction exploration is the multidisciplinary nature of the field. To develop autonomous nanocrystal synthesis systems, researchers must simultaneously build an understanding in multiple research areas, including colloidal synthesis, process automation, optimization, chemistry, robotics, and data science, which significantly raises the barrier for entry. Furthermore, the variety of methods and components implemented in the colloidal nanocrystal synthesis studies and the depth in which each component has been explored by focused experts often make it difficult to identify a clear methodology to get started in building an autonomous experimentation platform. Fortunately, many aspects of automated experimental studies have recently been moving toward more accessible and open access resources,^56,64–68 which will soon open many more opportunities to a wider variety of scientists.

It is also notable that colloidal nanocrystal syntheses present a unique challenge in autonomous experimentation. The batch-to-batch and lab-to-lab variabilities that necessitate in-house data generation methods also limit the viable experiment selection algorithms. Literature and physical model-driven experimental search methods have not been effectively integrated with automated nanocrystal syntheses, due to the challenges in direct replication of existing synthesis protocols. Instead, the autonomous experimentation platforms in the field of colloidal nanoscience are typically coupled with uninformed optimization algorithms. Uninformed methods operate without any prior knowledge of the material or molecule of interest and use incoming experimental data to iteratively reduce the algorithm uncertainty over the system, ultimately attaining either a global understanding or optimized condition set. This technique stands as the opposite of cheminformatic strategies, which have found notable applications in self-guided systems outside of the field of colloidal nanoscience. Modern cheminformatics implement literature data mining and physical models into a single experiment selection algorithm, which can be used to efficiently direct experimental protocols where literature replication is less of an issue. A wide range of autonomous robotic experimentation systems leveraging literature data mining and automated protocol extraction have been developed across organic chemistry,^55,69,70 including retrosynthetic planning for the production of active pharmaceutical ingredients,⁵⁶ among many others. Self-driven nanocrystal synthesis methods must overcome several challenges before attaining the same degree of performance as the aforementioned autonomous organic chemistry focused studies.

This review will cover the existing automated experimentation technologies, spanning robotics (batch to microfluidic reactors), and the algorithms used to guide these automated systems in the development of solution-processed nanocrystals. Specifically, this work will discuss the strategies a select group of self-driving laboratories used to successfully take on complex, multi-dimensional input–output spaces of a wide range of colloidal nanocrystals along with opportunities for the immediate future. Furthermore, it will detail the fundamental requirements and techniques for developing a fully autonomous, closed-loop experimentation platform in colloidal nanoscience. For detailed discussions on different materials informatics and machine learning techniques related to materials science and chemistry, the readers are referred to comprehensive review articles elsewhere.^71–76 

Over the past decade, a range of automated experimental systems have been applied toward colloidal nanoscience, with widely varying approaches. Within the scope of robotics, the most direct route has been the development of isolated robotic workstations using batch reactors. These systems operate within an enclosed, dense footprint infrastructure and feature a highly streamlined and modular experimental workflow. Alternatively, the field of flow chemistry has presented a new approach toward automated nanocrystal synthesis through the controlled injection of reactive precursors in channels with diameters ranging from 0.1 to 2 mm. Flow chemistry platforms forego the complex robotic control and movement and replace it with the pump-driven flow of small reactive volumes. Fluidic experimental platforms range from continuous flow processes, suitable toward a nanomanufacturing setting, to complex multi-stage control of a single, microliter-sized droplet. In this section, we will cover the approaches implemented in both robotic and flow chemistry technologies and then discuss the advantages and challenges of each technique.

Batch synthesis of nanoparticles can be dated back to the fourth century with the dichroic glass formed by Ag–Au alloy nanoparticles found in the Late Roman Lycurgus cup.⁷⁷ While initially produced almost certainly through serendipitous circumstances, curious minds throughout the following centuries have generated a monolithic library of knowledge and techniques for understanding, controlling, and applying these materials. Flask-based technologies can build directly from this extensive literature background, with respect to synthesis protocols and technologies, and expand this library further. Automated systems built from flask-based architecture are, therefore, at a significant advantage in their accessible system modifications and chemistries. In spite of this, the number of flask-based automated experimental platforms used in colloidal nanoscience is fairly low, especially when compared to the success these technologies have found in organic chemistry and pharmaceutical manufacturing.^78,79 However, the limited number of existing examples has demonstrated considerable potential in studies of colloidal nanomaterials, and further development of similar platforms could provide flexible and effective tools for the field of colloidal nanoscience.

The robotic workstation was first introduced into colloidal nanoscience in 2010 by Chan et al.⁸⁰ through the Workstation for Automated Nanocrystals Discovery and Analysis (WANDA), shown in Fig. 3(a). WANDA was designed by adapting an autosampler framework to high-temperature colloidal synthesis and combinatorial screening. This robotic nanocrystal synthesis platform was used to study the synthesis of a wide range of colloidal nanocrystals, including cadmium selenide (CdSe), cadmium telluride (CdTe), and lanthanide-doped sodium yttrium fluoride (NaYF₄) nanocrystals under varying compositions, temperatures, and reaction times through aliquot collection and batch x-ray diffraction (XRD) analysis. Reactions were conducted in a custom low thermal mass reactor element, which housed replaceable 40- ml glass vials. Precursors were automatically injected into the vials and heated using the heating element or rapidly cooled with nitrogen flow, and aliquots were collected continuously. A 0.2% coefficient of variation in CdSe nanocrystal size was achieved with this robotic system, a full order of magnitude improvement over equivalent manual processes reported in the work. The experiment throughput of WANDA was limited by the need to manually replace each of the seven reaction vessels and the 96-well plate after a set of experiments. However, beyond the improved precision and workflow efficiency, the integration of solids dispensing, parallel high-temperature reaction capability, and aliquot collection, produced a system that was revolutionary in its abilities. Iterations of this robotic chemical workstation are routinely being applied to complex nanocrystal syntheses such as those of cadmium sulfide (CdS)/CdSe/zinc sulfide (ZnS) core–shell–shell heterostructures, photon avalanching sodium ytterbium/thulium fluoride (NaY_1−xTm_xF₄) NPs, and many other studies.^81–92 Recent studies have applied similar techniques in custom adapting an autosampler and commercially available laboratory automation technologies toward colloidal nanocrystal syntheses such as the temperature-controlled, size focusing of CdSe quantum dots (QDs) by Salaheldin et al.⁹³ In this work, the reactor mixing rates were systematically evaluated and optimized, ultimately attaining a nanocrystal size distribution with a relative standard deviation down to 9%. One alternative method was applied by Salley et al.⁹⁴ in the shape-controlled synthesis of gold nanocrystals. In this work, a batch vessel carousal was used to direct samples underneath a stationary formulation injection and optical sampling device. Experiments were conducted in batches of 15, using 10 ml of reagents per vial. The batch experimentation approach was particularly effective with respect to throughput for this synthesis route, as reaction times were typically 90 min per experiment, and reactions could be performed in parallel. While this platform did not have access to the same advanced capabilities as many of the adapted commercial automated synthesis platforms, it provides a promising introduction toward tailor-made solutions to the field of colloidal nanoscience. Parallel, combinatorial experimental techniques have been applied toward nanomaterials, but they have not been effectively integrated into an autonomous experimentation system.^93,95

Nanocrystal synthesis in flow reactors, compared to batch reactors, is a relatively new field of research, with the first work reported in 2002 by Edel et al.⁹⁶ Since then, researchers have pushed the boundaries of flow chemistry with high efficiency reaction execution, in situ nanocrystal characterization, real-time data availability, and extensive system automation.^{97–133,185–187} Automation in flow chemistry is generally more accessible than batch reactors, as the reactants are driven by individual pumps, which may be operated by a central control software. The other mechanical components typically found in an automated flow chemistry platform (e.g., optical sampling equipment or actuated valves) do not require the same robotic complexity as an automated nanocrystal synthesizer equipped with batch reactors. Consequently, most automated experimental strategies designed for solution-phase nanocrystal synthesis are using flow reactors, such as those shown in Fig. 3(b).

Flow chemistry also offers remarkably low chemical consumption per experimental condition compared to batch reactors (0.1–1000 μl vs 10–100 ml). For example, an oscillatory flow reactor operates by creating a reactive formulation in a single 5–20 μl droplet and moving that droplet through various controlled reaction modules (e.g., temperature, gas phase compositions).¹³⁴ In situ spectral monitoring of colloidal nanocrystals is carried out on the reactive droplet over time, and the oscillatory motion of the droplet within a single channel enables near-indefinite data collection on the same reaction mixture containing the colloidal nanocrystals.^135,136 Single droplet systems allow for incredibly high efficiency data collection.^137–143 Alternatively, continuous flow systems operate more similarly to conventional manufacturing processes, where reagents are continuously fed into the flow reactor. Reagent consumption per tested experimental condition in these platforms is generally greater than 100 μl; however, these systems are suitable for colloidal syntheses with fast formation kinetics—that is, reactions that occur in less than a minute—as they allow for spatial translation of the measurable reaction time (time-to-distance transformation). By moving an in situ spectral monitoring probe along a flow reactor, while reactants are continuously fed to the reactor at a high velocity, measurements at reaction times on the order of tens of milliseconds may be taken consistently.^63,118,121

Flow chemistry is a diverse and constantly growing field of research. The flow reactors developed over the past twenty years offer a high degree of control over the composition of the reactive solution, with temperature ramp rates as high as 2 °C/ms and precursor mixing times less than 1 ms.^144,145 Recent developments in low-cost and modular polymer and stainless-steel tubing-based flow technologies have also facilitated adoption of flow synthesis techniques by a larger audience of scientists. These tube-based flow chemistry strategies enable more rapid and accessible prototyping and reconfiguration of the flow reactors for plug-and-play system design. The topic has been frequently discussed in prior reviews, including the complete capabilities in nanoscience,^146–151 outside nanoscience,^152–157 advances in tubular systems,^158,159 and tutorials on how to get started in flow chemistry.^67,160–162

While automated chemical workstations equipped with batch reactors can attain high precision in nanocrystal syntheses through consistent chemical dosing and low reagent consumption through combinatorial screening techniques, flow reactors are the superior technology with respect to the controlled precursor combination and heating rates coupled with low chemical consumption, and waste generation.^147,148 Furthermore, a well-designed flow reactor can conduct a larger number of colloidal nanocrystal synthesis experiments without user intervention or precursor refilling, due to the small reagent costs. However, the unique capabilities of flow reactors come with two significant limitations: (1) only solution-phase processing can be conducted in flow, and (2) heat and mass-transfer dynamics of flow reactors do not directly replicate existing literature developed predominantly using batch reactors. The limitation of solution-phase processing most drastically impacts flexibility in reagent preparation, nanocrystal purification, and measurement processes to the extent that a complete end-to-end automated colloidal nanocrystal synthesis using only fluidic modules are not universally feasible. It also limits the range of accessible chemistries, as with many colloidal synthesis chemistries not all formulations are fully soluble, which leads to flow reactor clogging.

The challenges with flow chemistry in replicating literature studies of colloidal nanocrystals synthesized using high-temperature synthetic routes in batch reactors come with the increased control of the system and expanded accessible parameter space. Regardless of platform or field of research, every scientific study must be conducted with some assumed simplifications to the experimental parameters. For flask-based colloidal nanocrystal synthesis, this simplification is normally applied to the physical constraints of precursor combination, temperature change, and off-gassing rates in a reactive flask. Quite often, this assumption is valid and effective in producing high performing nanocrystals, and thus, precursors and synthetic routes are developed and optimized for this reaction environment. However, to produce an equivalent reaction environment in a flow reactor for colloidal nanocrystal synthesis generally requires a high level of experience in microfluidics and additional platform development. For example, to replicate a temperature ramp for a flask system in flow, the exact temporal gradient must be rebuilt spatially along the full length of the flow reactor. In most cases, the exact properties of the gradient produced in a flask are not perfectly recorded, and even then, the localized temperature and concentration profiles existing within the flask are extremely difficult to replicate in flow. Consequently, direct replication of high-temperature batch synthesis protocols in flow and vice versa, often results in varying nanocrystal size, composition, morphology, and polydispersity. Thus, to build from the centuries of knowledge in chemistry built using batch reactors, flow chemists must take additional steps and impose complexity that would not be required of a flask-based synthesis system. Like a scalpel is to an ax, a system with greater control does not inherently equate to being a better system, and flask- and flow-based technologies will always have their own specific functions for every set of needs in colloidal nanoscience and beyond.

Alternatively, the precise process control offered with modular flow reactors presents a unique opportunity for flow chemists in the coming years. Flow technologies open a window into unexplored regions of the chemical universe through expansion of the available parameter space, and they allow for the study of larger experimental systems through time- and resource-efficient experimentation. The next decade will likely see more nanocrystal synthesis chemistries developed with flow chemistry specifically in mind, and it will be an important and exciting topic to follow as they attempt to overtake the performance of nanocrystals developed in batch reactors.

To mitigate the disparities between the two laboratory automation strategies in colloidal nanoscience (batch and flow reactors) without losing access to the respective advantages, hybrid robo-fluidic systems have recently been developed. The integration of flow reactors and system handling with robotics has been explored successfully in several fields,^56,78 but it is a new concept in colloidal nanoscience. Recent work by Li et al.¹⁶³ applied a hybrid system to the search for chiral perovskite synthesis compositions—shown in Fig. 3(c). Circular dichroism (CD) measurements, unlike UV-Vis absorption or photoluminescence spectroscopy, are not readily available through the conventional in situ monitoring techniques applied in flow reactors. As a result, samples must be collected and analyzed offline. The study utilized a robotic arm and sample collection carousel to collect the products of a temperature and concentration screening experiments in flow and transfer it to a CD spectrometer. Without this hybrid system design, the platform would not be able to take advantage of the control and efficiency of a flow system, while simultaneously implementing CD spectroscopy. This work is one of the first efforts in colloidal nanoscience to bridge the gaps between flow chemistry and automated batch sample handling.

However, the study on chiral perovskite QDs does not fully capture the capabilities of hybrid robo-fluidic systems. One of the greatest challenges in microfluidic systems is the limited techniques in handling solids (precursors, by-products, and products). As a result, most precursor preparation protocols must be carried out before the use of the flow reactors. This limitation imposes several significant sources of experimental deviation including inconsistent environmental control, human error in precursor preparation and reporting, and unknown precursor aging times. By using an automated flask-based precursor preparation system before a microfluidic reaction module, end-to-end precursor preparation to synthesis to characterization can be achieved in an automated and highly controlled manner. This design concept would bring the colloidal nanoscience community closer to universally reproducible protocols and comprehensive AI-guided material exploration strategies.

After developing an automated and reliable colloidal nanocrystal synthesis platform, the next major step in autonomous experimentation is the automated collection and analysis of experimental data. Data collection in flow reactors generally relies on in situ monitoring techniques, such as small/wide-angle x-ray scattering (SAX/WAX),¹⁶⁴ dynamic light scattering (DLS),¹⁴⁷ photoluminescence spectroscopy (PL),^107,110 fluorescence lifetime (FL),¹⁶⁵ infrared spectroscopy (IR),¹⁴⁷ UV-Vis absorption spectroscopy (UVA),^63,106,117 x-ray absorption spectroscopy (XAS),¹⁰⁸ among others.^108,147 Generally, the most accessible nanocrystal characterization techniques are PL and UVA. Standard spectroscopy equipment may be connected to an optical flow cell module that can be readily integrated with a flow reactor, allowing for measurements to be made on reactive solutions passing along a specific portion of the reactor. A variety of custom designs and commercial products are available for nanocrystal characterization using PL and UVA techniques, such as the quantum yield and spectral monitoring device shown in Fig. 4(a).^165,166 With in situ nanocrystal characterization techniques, it is also important to ensure that spectra are accurately extracted from any multi-phase flow system.⁶³ 

Robotic systems do not have the inherent access to in situ nanocrystal monitoring technologies; however, in some examples, optical fibers have been integrated into a reactive flask via a dip probe to attain continuous spectral monitoring capabilities.⁶⁰ Colloidal nanocrystal studies using batch reactors process samples either in series or through batch submission of vials to automated nanocrystal characterization instruments. Continuous series sampling during colloidal nanocrystal synthesis, such as the one demonstrated by Li et al.¹⁶³ in the hybrid robotic-flow platform, allows for more rapid data collection, which enables more frequent updating of model information in a real-time optimization setting. In situ access to nanocrystal properties during the synthesis also reduces the impact of potential sample degradation after collection from the reactor vessel, but the technical barrier of building a custom system to continuously insert and remove samples leads many researchers to find the approach to be not worth the extra complexity. For example, both Salaheldin et al.⁹³ [Fig. 4(b)] and Chan et al.⁸⁰ integrated an aliquot vial collection rack that would be transferred to an automated measurement system for UVA and XRD monitoring of the nanocrystal solutions, respectively. While this platform was not used in a real-time optimization setting, it did result in accurate modeling of the experimental system. Outside of colloidal nanoscience, the automated robotic batch processing approach has been used effectively.^78,167,168

Regardless of the measurement technique implemented in colloidal nanoscience, it is important to consider the quality of the data being generated. Good practices in experimental design become critical when the selection of experiments is left exclusively to the judgment of algorithms. Particularly in low data availability studies of complex colloidal nanocrystals with high dimensional space, order-dependent sampling can cripple the efficiency of any optimization system. This issue can arise in flask-based platforms through improper control of the reaction environment and in flow platforms through incomplete washing of the flow reactor channels between conditions or batch-to-batch precursor variability, among other possibilities. Therefore, it is necessary to demonstrate reaction sampling independence with any autonomous platform. Among other more advanced methods, the sampling independence can be achieved by simply taking a set of control experiments and alternating them randomly with experiments from throughout the accessible nanocrystal synthesis space—shown in Fig. 4(c).¹⁶⁶ With this approach, the nature of each experiment must be clearly defined. For example, in a flow synthesis system where a single batch of precursors is used over the course of a few hours within an isolated black-box nanocrystal synthesis optimization setting, it is often acceptable to conduct the sampling independence study with those same precursors within the dependence test because that experimental environment will be representative of the real optimization environment. However, if the same flow synthesis system were to require on the order of hours per nanocrystal synthesis experiment, precursor degradation or consumption would be more likely, and it is necessary for a new batch to be prepared periodically within the dependence testing.

It should be noted that the concept of sampling dependence is not critical for an autonomous platform. Many optimization algorithms can consider some degree of biased sampling variability, and in some cases, it may be more efficient to collect biased datasets. For example, in a batch reactor with automated aliquot collection over the increasing reaction time, it would not be efficient to completely restart the experiment for every desired reaction time to measure, but simultaneously, the measured aliquots will have a bias correlated with the previous measurements, which could offset the experimental model prediction. In designing an experimental nanocrystal synthesis system, it may not be the most effective strategy to generate the largest number of data points possible, and this pursuit must be balanced with good statistical practices.

In addition to sampling independence, the precision of a measurement is an important consideration, specifically, the precision relative to the magnitude of the reaction space topography and peak features. Shown in Fig. 5(a), a simulated reaction space can demonstrate the importance of sampling precision within increasing dimensionality. The smooth surface shown in Fig. 5(a) represents the ground truth of a simulated experimental space. The ground truth is a term in optimization studies used to describe the “true” surface response of the system. In physical systems, the ground truth can never be known exactly but can be estimated through effective modeling. In simulations of reaction optimization, a ground truth model can be used as a surrogate for a real-world system. This ground truth is a normal probability distribution with a mean of 0.5 and standard deviation of 0.4 normalized across two dimensions. The surface in N-dimensional space may be represented as

where Y is the surface response function and X_i is the input condition for dimension i. The proceeding two surfaces of the smooth ground truth in Fig. 5(a) represent the same simulated experimental space with 1% and 5% relative errors (σ_E), respectively, on each sampled experiment. The relative error is calculated as a random sample from a normal probability distribution centered at zero and with a standard deviation of σ_E. This error variable is meant to represent the entirety of system errors that result experimental deviations of any kind. The scatter points illustrate a sample optimization of this reaction space using an upper confidence bound decision policy with Gaussian process regressions (GPs) and random sampling local optima convergence disruption. The components of this algorithm are discussed in more detail in Sec. IV, below. Studying this basic optimization algorithm on an idealized ground truth surrogate system allows us to isolate the influence of sampling noise magnitude on optimization efficiency. Shown in Fig. 5(b), the median number of experiments, and corresponding interquartile range, required for all input conditions to reach, on average, within 5% of their optima is shown as a function of input space dimensionality. Pure random sampling quickly surpassed reasonable sampling rates for most systems, with a requirement of over 7000 experiments to tune a four-dimensional space. Alternatively, the highly idealized no-error surface was able to reach optimal conditions within 40 experiments for a 20-dimensional space. It should be noted that GPs are particularly suitable to the surrogate system, likely inflating the performance. Regardless, only a minor increase in the standard error to 1% results in an order of magnitude higher experiment requirements and increasing the error from 1% to 5% results in approximately three times the necessary experiments.

To better represent potential real-world complexities, several additional iterations of the same optimization were conducted using more complex ground truth models—shown in Fig. 5(c). These systems were designed to reflect several potential occurrences in real-world experimentation including, the existence of local optima, large unviable sampling regions, and low-resolution output data. The ground truth functions are represented by the three equations below:

The results of the simulations with these higher complexity systems, shown in Fig. 5(d), demonstrate that, while more complex surfaces can require larger datasets to optimize and model, the dominant factor in efficient autonomous operation is the experimental precision. Further variations upon these systems including larger sparse data regions and narrower feature topography could significantly increase data requirements, but regardless, experimental precision is a critical consideration.

Just as important as establishing precise experiment conduction, measurement, and data extraction methods, the user of an autonomous experimentation platform (i.e., a self-driving laboratory) must define a meaningful experimental space to conduct the exploration and property optimization. Many of the constraints of an input space will be set by the limitations of the automated system (minimum and maximum flow rates, dispensing volumes, operating temperatures, etc.), but there is also considerable value in selecting input space ranges based on intuitive properties of the reaction class of interest. If the range for a condition is too large, the algorithm will have difficulty identifying optima within a relatively narrow feature window; however, if the range is too small, optimal properties will exist outside of the studied space. This challenge is further compounded by the inclusion of non-linear feature effects and interrelated parameter constraints. While these properties may typically be integrated directly into the AI-guided experiment selection algorithm, the simplest approach is to develop a system of non-dimensionalized equations that define the parameters from zero to one.^166,169 For example, to define three continuous parameters (X₁, X₂, and X₃), for example, injection volumes, into non-dimensionalized forms (x₁, x₂, and x₃), the following correlations would be used:

where X_i,Min and X_i,Max correspond to the lower and upper bounds of the parameter, respectively. However, if for example, a fixed total volume was desired, a constraining equation could be added to this system. The introduction of this equation would reduce the dimensionality of the problem and result in the following system of equations:

where X_Total corresponds to the set constant combined value, that is, total volume. Notice that x₃ is no longer a tunable parameter as the dimensional form, X₃, is defined directly by the remaining variables. In this example where X_i corresponds to injection volumes, it would be suitable to set X₃ as the solvent.

Furthermore, non-dimensionalizing equations can be used to tune the system for more efficient parameter space exploration. The linear functions applied in the two previous examples do not necessarily capture the form of feature properties associated with each parameter, but in an unknown system, this linear assumption is a reasonable first guess. However, if the feature response for a specific variable is well established, then a non-dimensionalizing equation can be applied to reflect that. As an example, the ligand-assisted reprecipitation of CsPbBr₃ perovskite QDs in microfluidic reactors has been demonstrated to present tunable peak emission energies (E_PL) as a function of droplet flow velocity (u_D).⁶³ This relationship, however, is a logarithmic correlation where E_PL over some range of velocities is proportional to the natural log of u_D [E_PL ∝ log(u_D)].¹¹⁹ Therefore, the parameter u_D, and similar variables, can more effectively be represented in the non-dimensional space as

These methods are built around continuous input conditions, but similar methods can also be applied toward discrete numerical variables. Shown in Figs. 5(e) and 5(f), converting a continuous parameter into a discrete parameter by rounding to the nearest level results in an efficient reaction space exploration. The simplification of the reaction space results in a faster optimization, and as the number of levels is increased, the optimization time converges with that of a continuous system. This strategy indicates that discrete variables can likely be seamlessly integrated with numerical variables in modeling systems. The handling of categorical data, however, can become more complex. Some studies treat non-numerically related treatments as completely different systems,¹⁶⁶ but these conditions in some cases can potentially be integrated into a singular model. Framed off of the successful applications in organic chemistry,¹⁷⁰ colloidal nanomaterial studies may be able to implement molecular and structural characteristics of different reagents into optimization algorithms through quantitative encoding of qualitative characteristics.

With a robust experiment conduction and monitoring system and a well-defined experimental space, the final step in developing an autonomous experimental platform is the intelligent navigation through the accessible nanocrystal synthesis universe (i.e., experiment selection algorithm). Closed-loop experimentation offers notable advantages over automated platforms coupled with user-directed studies. Any system reliant on user intervention will have a slower sampling rate, limited experimental campaign durations, and greater issues with reagent degradation. It is, therefore, a significant boost to experimental efficiency to remove this operator influence and reliance. Parameter space exploration and single/multi-objective optimization algorithms are a large and diverse field of study,^75,171,172 as shown in Fig. 6, but only a select group of algorithms have been implemented into automated nanocrystal synthesis systems. There is likely a great opportunity for developing new algorithms or applying established techniques toward nanocrystal discovery, feature extraction, knowledge transfer, and more efficient formulation optimization, but many of the strategies already used have proven to be reasonably effective. The aim of an intelligent experiment selection algorithm is generally either to optimize for a single target parameter or to attain a comprehensive understanding of the experimental space, also known as global learning. Many algorithms are aimed specifically at one of these two objectives, but some can operate between them mostly interchangeably.

The first implementation of intelligent experiment selection algorithms in a nanocrystal synthesis setting used Stable Noisy Optimization by Branch and Fit (SNOBFIT) in 2007.^173,174 SNOBFIT has also recently been used for the selection of chiral perovskite precursor formulations in the hybrid robotic-microflow platform by Li et al. discussed previously.¹⁶³ SNOBFIT is a quadratics-based algorithm designed to account for many of the irregularities of real-world experimentation, including noisy data, undefined experimental results, and desired user-selected experiments as augmentation of the standard search. Although SNOBFIT was proven to be an effective optimization technique throughout science and engineering research, more recent studies suggest that SNOBFIT underperforms relative to more modern optimization strategies.^166,175,176 However, it should be noted that none of the cited studies report extensive tuning of the algorithm parameters, so the assertion that SNOBFIT is an outdated algorithm may be inaccurate.

Another commonly employed algorithm in nanocrystal synthesis optimization is the Nelder–Mead Simplex Method (NMS).¹⁷⁷ Simplex methods operate by extrapolating the predicted model surface from a group of points and sampling toward the optimal position. This algorithm is frequently used as a benchmark method for comparison with newer optimization techniques—discussed below. In a recent example, NMS was applied as a high-level controller in the scaled-out flow synthesis of cesium lead bromide (CsPbBr₃) QDs.¹⁷⁸ This work used the algorithm to account for induced disturbances in flow stability and produce uniform linewidth nanocrystals (<35 nm) across 16 channels simultaneously. NMS, while it is a direct search method, was originally designed as a computational solution to multi-dimensional, non-linear optimization problems. The algorithm will continue to have focused applications in colloidal nanoscience, such as the one previously demonstrated in process control, but it is unlikely to be among the most efficient general optimization strategies due to its reliance on smooth surface response.

Evolutionary algorithms (EAs) operate by modifying a population of candidate conditions over a series of iterations (or mutations in the case of genetic algorithms), as shown in Fig. 6(a). While EAs may be applied to any experimental method, these algorithms are inherently structured in a way that suits batch nanocrystal collection and measurement techniques. In the previously discussed work of Salley et al.,⁹⁴ a custom genetic algorithm was used with an automated experimentation platform using flask reactors to evaluate absorption spectra of gold nanocrystals toward targeted morphologies—sphere, rod, and octahedron. The long reaction timescale studied in the work (90 min), as previously mentioned, and batch configuration of the automated experimentation platform make EA strategies particularly effective as all available information was implemented at the time of selection for the next experiments. Consequently, the work showed morphological tunability over three reactive processes. Other autonomous experimentation efforts with EAs^166,175,176 have integrated EA into series sampling with established algorithms such as non-dominated sorting genetic algorithm II (NSGA-II)¹⁷⁹ and covariance matrix adaptation-evolution strategy (CMA-ES).¹⁸⁰ Despite being compared with optimization algorithms, discussed in further detail below, specifically tailored for series sampling instead of batch of colloidal nanocrystals, NSGA-II and CMA-ES performed among the top candidates. EAs, while not extensively explored in existing nanocrystal synthesis studies, could be an efficient optimization strategy in autonomous nanocrystal synthesis platforms using batch reactors.

Bayesian optimization (BO) techniques have been the most employed nanocrystal formulation optimization method over the last several years. BO workflow initiates by building a model (current belief) from experimentally obtained data, which outputs a product estimate for any set of input conditions along with an associated uncertainty. The model can be built with a large variety of modeling methods, but the two most common ones are GPs and neural networks. Using this prediction-uncertainty model, a second algorithm called a decision policy under uncertainty is used to select the next colloidal nanocrystal experimental condition to be tested. Variation among decision policies is determined by how the uncertainty and model prediction are handled. For example, a decision policy on one extreme would be structured to select nanocrystal synthesis conditions in the sample space regions of the highest uncertainty [i.e., a maximum variance (MV) policy]. MV policies have applications in global learning strategies and are often coupled with the other extreme in decisions policies, pure exploitation (EPLT). EPLT policies strictly select nanocrystal synthesis conditions where the predicted output is optimal without considering the uncertainty of the model. This method was recently explored in Abdel-Latif et al.¹⁶⁹ where 200 experiments were conducted using an ensemble neural network (ENN) model and a MV policy to explore the synthesis space of a multi-stage CsPbX₃ (X = Cl, Br, I) QD synthesis and anion exchange in flow with eight independent input parameters. These global learning experiments were then preceded by EPLT on the same model with the MV-selected dataset. This strategy resulted in a rapid tuning of ten peak emission energies within 5 meV of the target, while minimizing emission linewidth, each within five additional experiments to the initial global learning stage or 40 min of continuous operation.

Most other autonomous nanocrystal synthesis studies attempt to impose a balance between the exploitation and exploration of the nanocrystal synthesis model with their decision policies. For example, Epps et al.¹⁶⁶ applied ENN models with upper confidence bound (UCB) and expected improvement (EI) policies to the anion exchange reactions of CsPbX₃ (X = Cl, Br, I) QDs in flow, both of which outperformed all other tested algorithms, including the same model with EPLT, SNOBFIT, and CMA-ES, in a five-dimensional input space. Later studies using surrogate modeling and simulations of the same experimental space further validated both findings.¹⁷⁵ In an extension of the original work with the real-world autonomous platform, simulated experiments were conducted by developing a surrogate model to represent the automated experimentation platform in a digital environment.¹⁷⁵ Within a virtual QD synthesis simulator, the same black box strategies were evaluated with replication, and the EI and UCB policies again outperformed established algorithms—CMA-ES, SNOBFIT, NSGA-II. Additionally, the work found that the ENN models resulted in more consistent improvement in model uncertainty and prediction accuracy with each added experiment relative to the tested GPs. However, more detailed studies are necessary before a superior model can be determined. For a global learning approach, the alternation of EI-selected experiments with EPLT sampling resulted in a more robust method for establishing comprehensive nanocrystal synthesis space control than MV-EPLT techniques.

Bezinge et al.¹⁸¹ integrated GPs with a custom-derived decision policy for the tuning of various multinary lead halide perovskite QD emission properties in an automated flow reactor with up to three input precursors. This study applied the availability of analytical parameter derivation, something that cannot be accomplished with (ensemble) neural networks, to simplifying the optimization problem. Through correlation of Kriging parameters directly to the likelihood of the selected input conditions producing the target emission, the adaptive sampling algorithm bypasses much of the computational requirements for searching a full response surface [Fig. 6(b)]. This method then selects the maximum of the likelihood estimate to conduct the nanocrystal synthesis experiment with the highest probability of producing the target emission wavelength. With this approach coupled with an initial grid sampling, emission tunability could be quickly achieved within a total of 100 experiments, equivalent to 3 h of operation and 50 ml of precursors.

Another unique approach that may be appearing more frequently in the field of autonomous colloidal nanoscience is the use of reinforcement learning (RL). The operation of RL algorithms is distinct from the previously discussed methods in that it maintains a memory of its current state and the route used to arrive there. This strategy was first presented toward colloidal nanoscience by Zhou et al.,¹⁷⁶ where recurrent neural networks in series were used to optimize silver nanocrystal properties for absorption at 500 nm wavelength to achieve approximately 100-nm-diameter NPs on a three-dimensional reaction space [Fig. 6(c)]. Furthermore, this method is promising in that it outperformed CMA-ES in the same system by approximately 20% after 50 experiments. There is likely to be notable opportunities for future development of RL in autonomous nanocrystal discovery.

In real-world colloidal nanocrystal studies, there is rarely one measurable quality that dictates the entirety of the nanocrystal performance, and multiple objectives are often necessary to provide a holistic representation. However, in most systems, the optimum of one parameter is unlikely to occur under the same conditions as another, and there will always be a trade-off between maximizing objectives within a fully mapped synthesis space. The optimal outputs then no longer become a single target point and traverse into multi-dimensional surfaces. This multi-dimensional surface is called the Pareto front. Exploration of the Pareto front is another active area of research with a large variety in the methodologies used to maximum exploration efficiency, including Pareto search algorithms¹⁸² and chimera objective functions.¹⁸³ However, within colloidal nanoscience only a select few algorithms have been employed to date.

The most basic and versatile strategy for multi-objective handling is an objective function, illustrated in Fig. 7(a). Objective functions allow for the combination of all objective parameters into a single quality metric. The function itself can be as simple as a weighted average of the target parameters, and the function can be integrated into belief models or applied to the output of individual parameter belief models. This approach was implemented by Epps et al.¹⁶⁶ to simultaneously reach a target emission peak, while minimizing emission linewidth and maximizing PL quantum yield for lead halide perovskite QDs through anion exchange reactions in flow. One advantage of utilizing an objective function is that it may be implemented into any single-objective experiment selection algorithm with relatively high efficiency. The complexity arises when deciding exactly which objective function to apply. Despite its name, selection of objective function weights, even within a simple weighted mean objective function, is often a subjective choice. The relevance of each output parameter is difficult to assign relative to other high value targets, and this is further complicated by often unintuitive interactions between parameter weight decisions. For example, in Epps et al.¹⁷⁵ objective function weights exclusively focused on tuning for a target emission wavelength were less effective at reaching that wavelength than functions that included additional output parameters due to a regularization effect induced by those added variables. Bezinge et al.¹⁸¹ implemented an alternative approach to this decision process through applying GPs and a multi-stage, dimension reduction process, shown in Fig. 7(b). In colloidal QD studies, the peak emission wavelength is a primary factor to control, and subsequent parameters are often considered secondary. Where Epps et al. took this into account by imposing a high weight for peak emission in the objective function, Bezinge et al. exclusively searched for the full parameter space of conditions that produced the desired target emission wavelength. Then, within the mapped synthesis space, parameters such as emission linewidth and intensity were optimized secondarily.

In Mekki-Berrada et al.,¹⁸⁴ a more high-level approach is applied to the evaluation of multiple material properties simultaneously, where the absorption spectra itself are the target function. This study used neural networks to model the predicted UV-Vis absorption spectra output for the synthesis of silver nanocrystals in a flow reactor; then, it used GPs with an EI policy to evaluate the loss function between the target and predicted spectra space and selected the next experiment [Fig. 7(c)]. This study demonstrated notable success with a colloidal nanocrystal synthesis space of high dimensionality relative to the other systems discussed in this review. The prediction of actual absorption spectra could be applied in further studies to bypass some of the difficulty in handling multiple outputs. The size of the output space for the neural network model (427 nodes corresponding to the spectra points) could become an issue in terms of efficiency, but this complexity could be further supplemented by the relationship between these nodes being smooth and dependent. This approach is an underexplored concept, worth future study.

In summary, there is not a clear winner among the currently explored algorithms intelligently navigating through complex colloidal nanocrystal synthesis universes. This is due to two primary reasons: (1) the diversity in needs and complexity of each nanocrystal synthesis space will likely mean that there is not one “most effective” algorithm, and (2) it is difficult to assess the effectiveness of a method without mapping a nanocrystal synthesis space. Currently in the field of autonomous robotic experimentation, there are more algorithms available to explore than can reasonably be evaluated with existing automated experimentation systems—as shown in Table I. Advancement of the field would be benefited the most through further development of high-throughput reproducible experimental hardware with minimal noise. With these capabilities, it is then important to publish all available data sets for benchmark surrogate modeling and simulations-guided algorithm development. With improvements to available algorithms established, there will be a need for accessible and intuitive software packages for implementation of developed autonomous modeling and decision-making algorithms into comparative colloidal nanoscience studies.

As discussed in this review, the completion of a fully autonomous, closed-loop experimentation platform (Fig. 8) relies on the complete integration of multiple fields. The development of a meaningful colloidal synthesis space to explore requires an understanding of the underlying chemistry, and the automated collection of precise measurements requires a background in experimental design, robotics, and material characterization. Finally, applying synthesis space exploration and optimization algorithms necessitates an understanding of the modeling and decision-making under uncertainty. Consequently, there are not many complete implementations of these platforms currently in the literature, and the findings of these studies have not significantly surpassed the cutting edge of materials development and discovery. However, interest in the field is rapidly growing, and an increasing number of multidisciplinary research groups are beginning to take on autonomous synthesis studies in the field of colloidal nanoscience. Greater integration of focused researcher skillsets will be vital for the progression of autonomous nanocrystal synthesis systems, and in the future, it is likely that such systems will begin to produce leading findings in colloidal nanoscience as these systems mature.

There are several prominent opportunities to expedite advancement of autonomous nanoscience experimentation in the near future. First, greater inclusion of mechanistic models into modeling and decision-making algorithms could present an opportunity for greater efficiency. Knowledge transfer of datasets is a common approach in other areas of chemistry, but the variability of colloidal nanocrystal syntheses makes a one-to-one correlation difficult to achieve. Using mechanistic algorithms to pretrain or constrain black box optimization models could result in improved algorithm performance with limited data availability in colloidal nanoscience. Furthermore, simply improving the reaction conduction precision and accuracy through automation could better develop knowledge transfer efficiency. Should this level of reproducibility be achieved, the digitization of synthetic processes—a standardization method implemented in organic chemistry systems—could also be realized in colloidal nanoscience.⁵⁷ Second, there is currently a need for rapid data generation within high-dimensionality colloidal nanocrystal synthesis spaces. Most of the established studies have primarily focused on parameter spaces with less than six dimensions, and it is therefore unclear how the developed algorithms will navigate higher dimension nanoscience problems as the complexity of colloidal nanocrystals increases. Generation of a data-rich (on the order of thousands of experiments), high-dimension (greater than ten parameters), closed-loop robotic experimentation strategy would be an invaluable tool to algorithm developers focused on autonomous nanocrystal synthesis space exploration. Further exploration of larger experimental spaces will also enable fundamental studies of the reactive system that would otherwise be unattainable. Finally, there is a need to not only produce precise, but also accurate experimental technologies. Transfer of knowledge between syntheses is currently challenging due to the highly sensitive and difficult to control reaction spaces involved, but a platform consistent and controlled enough to monitor intra-reaction effects and properties would offer a fundamental shift in how nano-chemistry is explored.

The authors gratefully acknowledge the financial support provided by the National Science Foundation (Award No. 1940959), the UNC Research Opportunities Initiative (UNC-ROI) Grant, and North Carolina State University.

The authors have no conflicts to declare.

The data that support the findings of this study (Fig. 5) are available from the corresponding author upon reasonable request.