Review pubs.acs.org/cm
The Heat-Up Synthesis of Colloidal Nanocrystals Joel van Embden,* Anthony S. R. Chesman,* and Jacek J. Jasieniak* CSIRO Manufacturing Flagship, Bayview Avenue, Clayton, Victoria 3168, Australia ABSTRACT: The successful transition of any nanocrystal-based product from the research phase to the commercial arena hinges on the ability to produce the required nanomaterial on large scales. The synthesis of colloidal nanocrystals using a heat-up (non-injection) method is a reliable means to achieve high quality nanomaterials on large scales with little or no batch-to-batch variation. In this class of synthesis precursors are heated within a reaction medium to induce a chemical reaction that yields monomer for nucleation and growth. Use of the heat-up technique circumvents the pitfalls of mixing time and poor heat management inherent to classical “hot-injection” methods. In heat-up syntheses monomer is produced in a more continuous fashion during the heating stage, making it more difficult to separate the nucleation and growth stages of the reaction, a factor that is conventionally considered detrimental toward achieving homogeneous colloidal dispersions. However, through the judicious selection of precursors, stabilizers, and reaction heating rates, these stages can be managed to yield colloids of comparable quality to those achieved via classical hot-injection methods. In this review we provide the reader with a fundamental basis upon which to understand the reaction requirements for achieving such favorable growth conditions. Given that the most important consideration in these reactions is precursor (and stabilizer) selection, we also provide an exposition of the precursor chemistry appropriate to achieving high quality products when using heat-up techniques. These topics form the foundation for critically evaluating the field of heat-up nanocrystal synthesis to date, including the synthesis of binary, ternary, and quaternary metal chalcogenide and pnictogenide nanocrystals, as well as metallic, metal oxide, and f-block conaining nanocrystals.
1. INTRODUCTION Wet-chemical colloidal syntheses are unparalled in their ability to grow a wide range of particle types, while offering control over particle size and shape, and minimizing particle polydispersity. The foundation of the wet-chemical synthesis of colloids dates back over 150 years to the pioneering work of Faraday, in which he added a strong reducing agent (phosphorus) into an aqueous solution of gold chloride to yield a colored solution of nanosized gold colloid.1 This was the first example of a methodology that has evolved into a class of reactions in which colloid formation is induced by the rapid combination of two or more critical reagents (almost always at high temperatures). This methodology has come to be known as the “hot injection” method. Spawned from the pioneering work of Henglein2−5 and Brus6−9 on CdS colloids, the hot-injection method was first popularized by Murray and co-workers with their synthesis of CdE (E = S, Se, Te) nanocrystal (NC) quantum dots over 20 years ago.10 Since that time this technique has been used successfully to synthesize a multitude of NCs of varying compositions, sizes, and shapes.11−13 Furthermore, the reactions themselves have evolved toward the use of more environmentally benign precursors and solvents.14 Although many modern methods have emerged that also induce NC formation in fluids, including laser illumination15 and ultrasonic or microwave irradiation,16,17 the hot-injection method has persisted as the most useful for producing homogeneous NC Published 2015 by the American Chemical Society
distributions. This may be attributed to the general applicability of this synthetic approach, which makes it an ideal method to evaluate new and unexplored colloidal systems. As such, it has been the most common method for the synthesis of NCs in the literature to date. Over the past decade the nanocrystal field has broadened significantly. It now includes a vast research base that focuses on the implementation of these materials for various applications rather than solely on their generation. This transition, and the fact that most of these applications require large quantities of high quality (nano)materials, has culminated in an increasing need to develop methods that reliably produce these materials on large scales. As a consequence, the quantity of the product, not simply its quality, has filtered down to become a vital consideration at a research level. Unfortunately, syntheses that employ the well established hot-injection method cannot be readily scaled, as inherent within this method are a number of insurmountable drawbacks as follows. (i) Reagent mixing time: Hot-injection syntheses rely on the rapid and homogeneous mixing of reagents at high temperatures in order to achieve a controlled nucleation event. This method possesses the intrinsic limit of mixing time, which becomes slower and less predictable as the volume of the batch Received: August 6, 2014 Revised: February 17, 2015 Published: February 20, 2015 2246
DOI: 10.1021/cm5028964 Chem. Mater. 2015, 27, 2246−2285
Chemistry of Materials
Review
and the consequent injection volume increases. (ii) Reaction cooling time: In most cases, following the injection step, the reaction temperature is required to drop in order to limit nucleation to a short burst-like event and to slow subsequent NC growth. The rate of cooling does not scale linearly with reaction volume, thus leading to a scale-dependent cooling time, which perturbs the reaction outcome. (iii) Practicality: Given that typical injection volumes are on the order of 25− 50% of the volume of the mother solution it becomes impractical and less viable to inject large volumes. (iv) Reproducibility: The time taken to inject a reagent often varies between users and from batch-to-batch. This leads to small differences in the initial reaction kinetics, which hinders reproducibility. Collectively, these factors cause significant variation in the reaction conditions between batches of different sizes, making the syntheses of high-quality NCs performed in smaller batches very difficult to reproduce on large scales. An alternative approach to the synthesis of NCs is via a heatup based technique (also known as the “non-injection” method). The formation of NCs using a heat-up approach circumvents all of the aforementioned drawbacks and provides an avenue to completely controllable and scalable syntheses. In reactions employing this methodology, all reagents are mixed into a reaction vessel and heated controllably to induce the nucleation and growth of NCs. Figure 1 shows a schematic of
these precursors experience an increased thermodynamic driving force to form monomer. The heating process eventually triggers the nucleation of nascent crystallites, with continued heating required to grow these nuclei into mature NCs. The underlying particle formation mechanism in the heat-up approach is in principle similar to that for hot-injection methods. However, an additional challenge posed during the design of heat-up reactions is that the chemistry of the ligands and precursors require a greater level of attention to ensure that (i) nucleation is rapid enough to generate large quantities of nanosized nuclei within a relatively short period of time and (ii) appropriate decoupling of the nucleation and growth stages occurs to reduce particle polydispersity. Control over this chemistry is a particularly vital consideration for multielement NCs to ensure the reactivity of each component is well matched during the heating step in order to achieve a product with the desired composition and phase purity. It is perhaps this added level of complexity that has hindered the popularization of this method. However, as the field of NC synthesis has matured and a deeper understanding of each individual system has emerged, heat-up methods have become far more commonplace in the current literature. This literature base not only encompasses works that have investigated the conversion of existing hot-injection synthetic methods into heat-up methods, but also includes novel heat-up approaches that have developed without an origin in hot-injection syntheses. In this review we present the reader with a comprehensive treatise on the current state of NC syntheses performed using heat-up protocols. Throughout the course of this review we aim to provide the reader with an understanding of heat-up syntheses from both theoretical and practical perspectives. This understanding is developed over four main sections: (i) Nanocrystal Formation Mechanisms describes the underlying principles and theory of colloid formation. In this section we introduce the concepts needed to interpret how various reaction parameters, such as supersaturation, temperature, and surface energy, influence the outcome of a typical NC synthesis. We then derive (and analyze) theoretical expressions for both the nucleation and growth rates, with specific reference to the conditions these rates must obey for a heat-up synthesis to be considered viable. (ii) Understanding Heat-Up Syntheses through Simulation explores the nucleation and growth of colloids under realtime conditions, in which the reaction parameters change dynamically as the system evolves with time. To demonstrate the applicability of the established model to heat-up methods, we simulate a series of reactions wherein either the heating rate or precursor reactivity is varied. This provides valuable insight into the need to choose precursors and reaction conditions that are suitable for growing homogeneous colloids under heat-up conditions. (iii) Precursor Toolbox summarizes the major classes of precursors that are appropriate for the synthesis of NCs. By inspecting their formation and decomposition mechanisms, a deeper appreciation of their current and potential use in heatup syntheses is developed. This section has been tailored specifically to be used as both a toolbox of available precursors for those wishing to explore the synthesis of nanostructures by heat-up techniques as well as a basis for future rational precursor design. (iv) Nanocrystals Synthesized by Heat-Up Routes presents a library of the various colloidal materials produced by heat-up
Figure 1. Typical heat-up syntheses require a large reservoir of precursor that is stable at room temperature. As the temperature is increased upon heating the reaction vessel, the precursors must react to form monomer that then nucleates to form small nuclei, which eventually grow into mature NCs.
the essential stages of NC formation in a typical heat-up synthesis and their relation to the temperature of the reaction vessel. At low temperatures the reaction solution is comprised largely of precursor. Here we define precursor to be the initial source of monomer, i.e., the compounds in solution that will eventually react to form the atomic units that comprise the final crystallites. These precursors may be the initial reagents used or secondary complexes that form upon reaction of these initial reagents with the ligands in solution. As the reaction is heated 2247
DOI: 10.1021/cm5028964 Chem. Mater. 2015, 27, 2246−2285
Chemistry of Materials
Review
that of heterogeneous nucleation as it requires the formation of a new phase. The magnitudes of these barriers are dependent upon (i) the relevant binding constants within the precursors employed; (ii) the level of supersaturation (S) where S = [M]/ [M∞]; (iii) the solution temperature; and (iv) the concentration of additional ligands (surfactants) in solution, which directly influences both the supersaturation through [M∞] and the surface energy, γ. Homogeneous nucleation is the formation of a new surface surrounding a bulk component. In the case of spherical nuclei, the surface contribution (ΔGS) enhances the free energy of the system according to ΔGS = 4πr2γ, where γ is the surface energy. Meanwhile, the bulk contribution (ΔGB) reduces the free energy through ΔGB = (4 πr3/3)ΔGV, where ΔGV is the Gibbs free energy per unit volume. The total (radius dependent) free energy of the system (ΔGT) is given by the sum of the surface and bulk terms.
protocols, including binary, ternary, and quaternary metal chalcogenide and metal pnictogenide NCs, as well as metallic, metal oxide, lanthanoid, and f-block containing NCs. By analyzing these reactions in terms of the precursors employed, reaction conditions, and NC quality, the underlying principles established in sections (i)−(iii) are demonstrated. Furthermore, each subsection contains reaction tables, which may be used to expedite the discovery of heat-up syntheses specific to that class of material. To limit the scope of this work, we have focused only on batch processes involving non-aqueous heat-up methods that are performed under ambient pressure. This has been done, in part, because these methods typically produce the most crystalline, discrete, and monodisperse products. Further motivation for this particular focus stems from the vast literature on hot-injection methods that utilize similar chemistry, which provides a clear benchmark for comparison. For heat-up routes based on solvothermal or microwave techniques or aqueous heat-up methods, we refer the reader to the excellent reviews that exist.18−20
ΔGT = ΔG B + ΔGS
(1)
Substituting in for the ΔGS and ΔGB terms and given that ΔGv = −(RT/VM) ln S, where R, T, and VM are the gas constant, temperature, and molar volume of the monomer, respectively, the total free energy as a function of the nuclei radius can be expressed as
2. NANOCRYSTAL FORMATION MECHANISMS This section has been tailored to elucidate the concepts and governing equations that are critical to understanding NC nucleation and growth. It provides the foundation for appreciating the complexities of NC evolution both from a general perspective and specifically in relation to heat-up techniques. First, we introduce the concepts of supersaturation, free energy, and critical NC size. Next, we formulate an equation that governs the temperature dependent precursor to monomer conversion rate, which is central to simulating NC growth via heat-up methods. We then derive an accurate expression for the nucleation rate within the framework of equilibrium theory and explore the effects of changing various reaction parameters, such as supersaturation, surface energy, and temperature, on the nucleation rate. Finally, we derive an expression for the NC growth rate. 2.1. Background: Free Energy and the Critical Nucleus. LaMer21 was the first to outline that in a typical precipitation reaction within a closed system nucleation becomes thermodynamically allowed when the concentration of free monomer, [M], is raised above a critical (nucleation) concentration, [MC]. At this point the solution is supersaturated. As monomer is rapidly consumed during the nucleation event, the concentration of free monomer eventually drops below [MC] and nucleation ceases. For newly formed nuclei with a radius a, [M] is still well above its equilibrium monomer concentration, [Ma] (concentration of monomer required to prevent the dissolution of particles with r ≥ a), upon the cessation of nucleation. As such, all particles with r > a will grow through the accretion of monomer. Although [M] is still well above [M ∞ ] (the concentration of monomer in equilibrium with a flat surface), as monomer is consumed throughout the reaction, [M] eventually drops below [Ma] and coarsening (Ostwald ripening) follows. In this case all particles with r < a dissolve in order to support the growth of larger particles. This stage is typically characterized by a broadening of the particle size distribution.22 The precipitation of monomer from solution may proceed via the formation of a new phase nucleating from dissolved monomer (homogeneous nucleation) or by monomer growing onto an existing surface (heterogeneous nucleation). The barrier to homogeneous nucleation is always much higher than
ΔGT = −
4πr 3RT ln S + 4πr 2γ 3VM
(2)
Figure 2 shows a plot of the surface (ΔGS, dotted line), bulk (ΔGB, dashed line), and total free energies (ΔGT, solid line) for
Figure 2. Surface (ΔGS), bulk (ΔGB), and total (ΔGT) free energy contributions as a function of particle size for an arbitrary system. The critical radius (smallest stable particle) is also shown, along with the barrier to its transition from a metastable to a stable nuclei (ΔGN). (inset) Stepwise barriers to the sequential addition of monomer units leading to the formation of a stable nuclei.
a given standard set of reaction conditions. For very small nuclei, where the surface to volume ratio is high, the surface term governs the free energy. However, as the nuclei become larger, the bulk free energy term dominates and, as such, ΔGT climbs to a maximum (as indicated by the red part of the curve) and then declines. The thermodynamic barrier at this maximum is given by ΔGN. Setting dΔGT/dr to zero, we evaluate this barrier as 2248
DOI: 10.1021/cm5028964 Chem. Mater. 2015, 27, 2246−2285
Chemistry of Materials ΔG N =
Review
16πγ 3VM 2 2 2
2
3R T (ln S)
the solution within the reaction vessel at a given time. During the heating stage of a heat-up NC synthesis the rate of precursor-to-monomer conversion increases exponentially. This provides a rapidly increasing reservoir of available monomer for nucleation and growth. Recalling that S = [M]/[M∞], eq 6 can be used to determine time and temperature dependent increases to the supersaturation. Figure 3 displays a schematic outlining all the processes involved during the transformation of precursor into mature
(3)
This thermodynamic barrier represents the energy required to form a stable nuclei for a given supersaturation, surface energy, and temperature. The corresponding radius at this maximum is known as the critical radius, rC, which is given by
rC =
2γVM RT ln S
(4)
Given that a system strives to lower its free energy, existing nuclei with r > rC will reduce their ΔGT through growth via accretion of monomer, while nuclei with r < rC will reduce their ΔGT by partially or completely dissolving. As such, the critical radius represents the size that divides stable from metastable nuclei. The inset of Figure 2 shows the stepwise changes to ΔGT that occur as a given nucleus grows from a single monomer to its critical size. In this image n denotes the number of atoms (monomer units) in the nucleus and provides a highly accurate view of the free energy changes that occur in the system as monomers form dimers, then trimers, and so forth. The sequence of monomer addition increases the total free energy of the nucleus until it reaches a critical size consisting of p monomer units (where p is the number of monomer units in a critical nuclei with a radius rC), at which time it transforms from being a metastable to a stable nucleus. Further examination of this process reveals that the barrier to the incorporation of a single monomer unit is largest for the smallest n and that it decreases to zero as n → p. This implies that at early times during nucleation the reaction solution will contain extremely high concentrations of monomer, few dimers, even fewer trimers, and so forth. The barrier to the formation of p is indicated again by ΔGN (in this case for the formation of nuclei containing 42 monomer units). 2.2. Precursor to Monomer Conversion. For NCs to nucleate and grow they require free monomer (M). However, at the beginning of the synthesis most of this monomer is either bound to ligands that either prohibit or lower their reactivity, or are part of a larger complex that requires decomposition before the monomer becomes chemically available. For the purposes of this section we define precursors (P) as ligand−monomer complexes, whose reactivity is dependent upon the binding constant of the ligand and the reaction temperature. Precursor disassociates from its ligands or reacts to form free monomer, with a formation rate, kf. The monomer formation reaction may be expressed as kf
P→M
Figure 3. Schematic outlining the mechanism of NC nucleation and growth. First, precursors (P) disassociate into monomers (M), followed by the formation of nuclei (N). The nascent nuclei grow as monomer diffuses to the particle−solution interface and then reacts, becoming incorporated into the crystal lattice.
NCs. Upon heating, the precursor transforms into monomer at a rate dictated by kf. The monomer then aids in the formation of stable nuclei by reacting with metastable clusters at a rate dictated by k1,p. The newly formed nuclei then grow via the accretion of monomer. This occurs as monomer diffuses to the particle−solution interface (at a rate D) and is then incorporated onto the particle at a rate governed by the relative magnitudes of the growth, kg, and dissolution, kd, rate constants. 2.3. Nucleation Theory. The nucleation rate of particles from monomer may be derived in the framework of equilibrium theory. We note that prior to the first nucleation event there are no “stable” nuclei and only reactions between monomer and “metastable” nuclei lead to the formation of the first stable nuclei (with p + 1 monomer units). To derive the nucleation rate let us first take the reaction between monomer, M, and nuclei of n units, Mn: k1, n
M + M n HoooI M n + 1
(5)
⎧ −E ⎫ d[M] d[P] =− = A exp⎨ A ⎬[P] dt dt ⎩ RTV ⎭
(7)
k −1, n
For simplicity, we assume the monomer formation is a first order reaction. This is reasonable as it has been established experimentally that during CdSe NC synthesis, Cd and Se monomer formation follows first order kinetics.23,24 As such, we postulate that the formation rate constant scales with the activation energy and the reaction temperature. This allows us to derive the monomer formation rate as
The equilibrium constant for the above reaction is K1, n =
k1, n k −1, n
=
[M n + 1] [M][M n]
(8)
This equilibrium constant may be expressed as the product of the equilibrium constant for condensation of monomer at an infinitely large surface, K∞, and the Gibbs free energy barrier to the addition of a monomer unit to a nucleus with n units:
(6)
N ⎫ ⎧ ⎪ − (ΔG 1, n) ⎪ ⎬ K1, n = K∞ exp⎨ ⎪ ⎪ ⎩ kBTV ⎭
Here A is the prefactor, EA is the activation energy (related to the magnitude of the ligand binding coefficient) for precursor decomposition or disassociation, and TV is the temperature of 2249
(9) DOI: 10.1021/cm5028964 Chem. Mater. 2015, 27, 2246−2285
Chemistry of Materials
Review
where kB is the Boltzmann constant. The equilibrium constant for nucleation, Knuc, is the product of all the sequential reactions that lead to the formation of a nucleus of critical size, p:
been developed and used by others to approximate the nucleation rate of NCs for both heat-up26 and hot-injection conditions.27 2.4. Applied Nucleation in Heat-Up Systems. We now look at the effects of each of these parameters in turn on the nucleation rate of NCs. Figure 4A shows the dependence of the
p−1
K nuc =
∏ K1,n
(10)
n=1
Through the use of eq 9 and by defining K∞ in the classical way, i.e. the reciprocal of the monomer concentration in equilibrium with an infinitely flat surface (K∞ =1/[M∞]), we may express eq 10 as K nuc =
N ⎫ ⎧ ⎪ −ΔG1, p ⎪ 1 ⎨ ⎬ exp ⎪ ⎪ [M∞]p − 1 ⎩ kBTV ⎭
(11)
Within the framework of equilibrium theory, all nuclei with n ≤ p (i.e., smaller than the critical radius) have condensation reactions that are in equilibrium; however, for n > p, [Mn] = 0. As such, the sequential reactions occurring simultaneously at equilibrium occur only for n = 1, 2, 3, ..., p. In this case p monomer units condense to form a critical nuclei (Mp) with an equilibrium constant given by Knuc = [Mp]/[M]p. This allows us to form an expression for the concentration of nuclei at the critical size, p, for a given set of reaction conditions as [M p] =
N ⎫ ⎧ ⎪ −ΔG1, p ⎪ [M]p ⎬ ⎨ exp ⎪ ⎪ [M∞]p − 1 ⎩ kBTV ⎭
(12)
The primary nucleation event occurs with the generation of the first stable nuclei (i.e., one that will reduce its free energy through growth). This occurs upon reaction of a monomer unit with a critical nucleus. As such, the rate of nucleation may be expressed as R nuc = k1, p[M][M p]
Figure 4. Effect of change in (A) supersaturation and (B) surface energy on the nucleaion rate. Nucleation rate as a function of temperature for various (C) supersaturations and (D) surface energies. The nucleation rates were calculated using D = 10−11 m2 s−1, rm = 2 × 10−10 m, [M∞] = 0.001 mol m−3, and u = 0.45.
(13)
nucleation rate on the level of supersaturation for a typical reaction at 523 K with a moderate surface energy of 0.5 J m−2. It can be seen that for low supersaturations (S < 1000) the nucleation rate is extremely sensitive to changes in S. This is mainly caused by drastic changes to the critical (stable) NC size at low supersaturations, which drops from 13.3 nm for S = 2 to 1.3 nm for S = 1000 (and only a further 0.2 nm decrease to 1.1 nm for S = 5000). Other important considerations during the synthesis of NCs are the types and concentrations of ligands used. In addition to influencing the precursor to monomer conversion rate, which will be discussed later, these choices directly affect γ because different ligands bind with varying strengths to the NC surface, altering its surface energy and consequently its stability in solution. Figure 4B shows the nucleation rate as a function of surface energy for a reaction at 523 K and S = 100. Upon examination we can see that the nucleation rate decreases as the surface energy is increased. Importantly, the nucleation rate is much less sensitive to changes in surface energy for low values of γ; the nucleation rate drops only 2 orders of magnitude between γ = 0.1 J m−2 and γ = 0.25 J m−2, whereas it decreases by 23 orders of magnitude as the surface energy is further increased to γ = 0.5 J m−2. We note that for the current set of simulation conditions, a surface energy
