Effect of metal ion solubility on the oxidative assembly of metal sulfide quantum dots

Due to their size-dependent optical properties associated with the quantum confinement effect, II-VI and IV-VI semiconducting chalcogenide nanocrystals (quantum dots, QDs) are promising candidates for applications in solar cells,¹ photodetectors,^2,3 light-emitting diodes (LEDs),⁴ field effect transistors (FETs),⁵ and radiation detectors.⁶ In solution-phase prepared QDs, the inorganic core material is surrounded by organic ligands on the surface, which are used to control the nanoparticle size and stabilize the colloidal suspension. However, applications in solid-state devices typically require efficient communication between nanoparticles. Organic ligands are commonly electrically insulating and also serve as physical spacers between particles, limiting the interparticle transport. Considerable research has focused on replacing these organic linkers with short, inorganic linkers, including chalcogenide ions, chalcogenidometallate ions, and halides, to enhance communication between particles.^7–11 

The Brock group has adopted a different approach based on an oxidative assembly gelation method that links metal chalcogenide QDs into two- and three-dimensional architectures without intervening ligands.^12–14 This process includes three main steps, shown in Fig. 1(a): the irreversible ligand removal due to the oxidation of surface thiolate ligands (step 1), the solubilization of exposed surface cations to reveal surface chalcogenides (step 2), and the assembly of QDs by the formation of di- or polychalcogenide cross-linkages between QDs (step 3). This method has been exploited for a range of single component assemblies including MQ (M = Cd, Zn, Pb Q = S, Se, Te), core/shell (CdSe/ZnS), Bi₂Te₃, and Bi_2−XSb_XTe_Z.^15–31 

Applications from photocatalysis to photovoltaics benefit from having multiple dissimilar, yet complementary, QD components integrated to drive photogenerated electrons and holes to active sites or electrodes.^32,33 Accordingly, there is a strong impetus to create composite QD architectures where the component placement is directed to achieve the stated goal. As a means to achieve such control in multicomponent QD systems prepared by oxidative gelation, we seek to establish a tool box of parameters governing the kinetics of the assembly of single component QD architectures, so as to tailor the gelation between dissimilar particles to favor well-mixed, phase-segregated, or gradient QD systems [Fig. 1(b)].

Previously, we demonstrated that QD size, QD concentration, oxidant concentration, the chain length of the surface ligands, and the redox characteristics of the chalcogenides affect the rate of oxidative gelation.^21,34,46 Not surprisingly, smaller particles with higher surface areas gelled more rapidly than larger particles and the higher concentration of QDs or oxidant similarly results in faster kinetics. With respect to chemical parameters that can be tuned, the thermodynamics of oxidation (2Q²⁻ → $Q22−+2e$⁠) has been shown to direct the kinetics, with the most rapidly gelling system being the easiest to oxidize [Te²⁻ > Se²⁻ > S²⁻, step 3, Fig. 1(a)]. Likewise, since ligand removal is a key step [step 1, Fig. 1(a)], dictated by the oxidation of bound thiolate, the kinetics can be altered by changing the length of the alkyl chain on the thiolate to limit oxidant penetration to the surface. Surprisingly, the structure also plays a key role, with QDs exhibiting cubic close packing kinetically slow relative to those with hexagonal close packing.

In the present work, we seek to determine whether the metal cation solubility may also play a role, based on step 2 of the process [Fig. 1(a)]. To evaluate the effect of metal ions on the rate of aggregation, we selected ZnS and CdS because these phases have been reported to have two to six orders of magnitude solubility differences for the bulk material in water. Accordingly, ∼10 nm diameter wurtzite (w) and zinc blende (zb) QDs of CdS and ZnS are prepared by ion-exchange of hexagonal and cubic polymorphs of Cu_2−XS, respectively, and the surface ligands exchanged with mercaptoundecanoic acid (MUA). The equilibrium free ion concentration of Cd²⁺ and Zn²⁺ in colloidal (methanol) solutions of CdS and ZnS is determined and assessed in the context of induction time and aggregation rate, as probed by Time-Resolved Dynamic Light Scattering (TR-DLS) for oxidative assembly.

Trioctylphosphine oxide (TOPO, 90%), tetranitromethane (TNM), tetramethylammonium hydroxide (TMAH), benzyl ether (99%), cadmium acetate dihydrate [Cd(OAc)₂, 90%], 11-mercaptoundecanoic acid (MUA), oleylamine (90%), oleic acid, sulfur (S, 99.998%), and di-tert-butyl disulfide (97%) were purchased from Sigma-Aldrich; copper(i) chloride (CuCl, 97% reagent), copper(ii) chloride (CuCl₂, 97%), and octadecene (ODE, 90%) were purchased from Acros Chemicals; trioctylphosphine (TOP > 85%) and zinc chloride (ZnCl₂) were purchased from Strem Chemicals. TOPO was distilled before use, and all other chemicals were used as received.

Digenite Cu_2−XS nanoparticles were synthesized according to the previously reported procedure.³⁵ A mixture of 0.320 g (0.01 mol) S and 20 ml octadecene (ODE) was heated at 120 °C under vacuum for 1 h, and the temperature was increased to 200 °C under Ar. Then, 0.990 g (0.01 mol) CuCl, 5 ml oleylamine, and 4 ml oleic acid (degassed under vacuum at 120 °C for 1 h) were added to the S-ODE solution rapidly at 200 °C and kept for 10 min. The synthesized nanoparticles were purified using isopropanol (precipitation) and hexane (dispersion).

Roxbyite Cu_2−XS nanoparticles were synthesized according to the previously reported procedure.³⁵ A mixture of 0.341 g (0.0025 mol) CuCl₂, 47.2 ml oleylamine, and 11.6 ml octadecene was heated at 120 °C for 30 min. The temperature was increased to 200 °C under Ar for 1 h. At 180 °C, 8 ml di-tert-butyl-disulfide was added, and the solution was annealed for 40 min and subsequently cooled rapidly. The nanoparticles were purified using 1:1 isopropanol:acetone (precipitation) and hexane (dispersion).

ZnS nanoparticles were synthesized by the modification of a literature procedure.³⁵ A mixture of 0.250 g (1.8 mmol) ZnCl₂, 8 ml oleylamine, 2 ml octadecene, and 15 ml benzyl ether was heated to 120 °C under vacuum for 30 min. Then, the temperature was increased to 200 °C under Ar. After 1 h, the temperature was reduced to 50 °C and 0.03 g of Cu_2−XS QDs in 3 ml of TOP was then added. The temperature was increased to 110 °C, and after 90 min, the reaction was allowed to cool down. The nanoparticles were purified using isopropanol (precipitation) and hexane (dispersion).

CdS nanoparticles were synthesized by the modification of a literature procedure.³⁵ A mixture of 0.250 g (1.1 mmol) Cd(OAc)₂, 8 ml oleylamine, 2 ml octadecene, and 15 ml benzyl ether was heated to 110 °C under vacuum for 1 h. After 1 h, the temperature was reduced to 50 °C and 0.03 g of Cu_2−XS QDs in 3 ml of TOP was then added. The temperature was increased to 110 °C, and after 90 min, the reaction was allowed to cool down. QDs were purified using isopropanol (precipitation) and hexane (dispersion).

The ligand mixture was prepared using 11-MUA (molar ratio of metal:11-MUA = 1:4) in 10 ml of methanol, and the pH was adjusted to 10 using TMAH. The ligand mixture was added to the nanoparticle solution and sonicated for ∼2 h. QDs were purified using ethyl acetate (precipitation) and methanol (dispersion).

A Bruker D2 Phaser X-ray diffractometer with a Cu Kα anode source was used to characterize the synthesized QDs (30 kV, 10 mA). Samples were supported on a zero-background quartz holder. The International Center for Diffraction Data (ICDD) powder diffraction file (PDF) (released in 2000) was used to establish the phase observed in the PXRD patterns.

Shape and size analyses of the QDs were carried out using a JEOL 2010 transmission electron microscope (200 kV) coupled with an energy dispersive spectrometer (EDS, EDAX, Inc.). The dispersed nanoparticles were deposited on carbon-coated 200 mesh Ni or Cu grids. The average particle sizes were analyzed by NIST Elements D3.10 software.

Well-dried nanoparticle samples were digested in concentrated nitric acid and characterized for metal content using an Agilent 7700x series inductively coupled plasma mass spectrometer. Based on these data, along with the average particle size (determined by TEM), the mass of the sample, and the bulk density of the phase, the quantity of QDs in the sample was determined. Samples for solubility and oxidative gelation studies were prepared by dispersing solid QDs in methanol to achieve a concentration of 3.86 × 10⁻⁷ mol dm⁻³ of QDs for the analysis.

To carry out solubility studies, a 3 ml aliquot of freshly prepared 3.86 × 10⁻⁷ mol dm⁻³ QD solution in methanol was kept for 72 h to equilibrate under ambient conditions. After that, free ions and particles were separated by centrifugation (4000 rpm for 20 min) using Amicon filters (NMWL 3 K Da).³⁶ Only ions (10⁻²² g) filter through the Amicon Ultra filter; species with molecular weights higher than 5 × 10⁻²¹ (NB: synthesized QDs of ZnS and CdS are around 10⁻¹⁸ g) will remain on the membrane. The filtered free ions (Zn²⁺, Cd²⁺) were analyzed using the ICP-MS analysis in 2% nitric acid. The analysis was repeated three times for each sample of the MUA-capped QDs (w-ZnS, zb-ZnS, w-CdS, zb-CdS), and the average free ion concentration and the standard deviation were reported.

The dynamic light scattering technique is used to analyze the size distribution by employing intensity or photon autocorrelation functions (ACFs). A monochromatic light source is passed through the sample, and the scattered light produces an image pattern (speckle pattern). Speckle patterns are taken over short time intervals (nanoseconds to microseconds), and the autocorrelator analyzes the intensity of speckle patterns over time. The ACF converts the intensity change into the hydrodynamic radius, $R¯h$⁠, of the particles using a few mathematical conversions. First the intensity (I) of the speckle pattern is converted into the second-order autocorrelation function g⁽²⁾(q; τ) at a wave vector q, where the delay time is τ [Eq. (1)],^21,37,38

The Siegert relation [Eq. (2)] is used to couple the second-order autocorrelation function g⁽²⁾(q; τ) with the normalized first-order electric field correlation function g⁽¹⁾(q; τ) (based on the approximation that the photodetector only detects the scattered light and photon counting is a random Gaussian process),

where B represents the baseline of the correlator function (∼1) and β is the coherence factor, which depends on the optical alignment, detector area, and scattering properties of macromolecules. For monodisperse samples, g⁽¹⁾(q: τ) decays exponentially [Eq. (3)], where Γ is the decay rate. For polydisperse distributions, relevant to the present system, a sum of the exponentials is needed to represent g⁽¹⁾(q: τ) [Eq. (4)], where G(Γ) is the distribution function of Γ,

Cumulants analysis of the autocorrelation function yields the mean decay rate $Γ¯$⁠, which is a function of the average translational diffusion coefficient $D¯$⁠, and the scattering vector q [Eq. (5)],

where q is obtained from the refractive index, n, the angle at which the detector is placed relative to the sample cell, θ, and the wavelength of the laser, λ [Eq. (6)],

DLS measures the hydrodynamic radius, R_h, which refers to the size of a hypothetical “hard sphere” that diffuses in the solution at the same speed as the particle being assessed. Because in practice the nanoparticle aggregates are macromolecular, nonspherical, and dynamic, the terminology “hydrodynamic radius” is used in the present case to refer to the size of the gel aggregate that forms from the assembly of discrete QDs. Using the Strokes-Einstein equation, the average translational diffusion coefficient is converted into the average hydrodynamic radius, $R¯h$⁠, using the viscosity of the medium, η, the Boltzmann constant, k = 1.380 × 10⁻²³ kg m² s⁻² K⁻¹, and the absolute temperature, T,

A He–Ne laser (633 nm) with a detector positioned at 173° was used to acquire TR-DLS measurements (Malvern Instruments, Westborough, MA). MUA-capped QDs (w-ZnS, zb-ZnS, w-CdS, zb-CdS) with a concentration of 3.86 × 10⁻⁷ mol dm⁻³ in methanol were treated with 10 µl of 3% TNM in acetone, mixed briefly, and equilibrated for 3–5 min at 25 °C. Z-average hydrodynamic radii (⁠$R¯h$⁠) were acquired as a function of time.

Given the strong effect of the structure (hexagonal vs cubic) on the assembly kinetics and the differing thermodynamic lattice preferences for ZnS (cubic, zinc blende, zb) and CdS (hexagonal, wurtzite, w), we sought to produce QDs of CdS and ZnS by ion exchange methods that preserve the anion structure of the host material.^34,35 This method also has the advantage of preserving the QD size, which also strongly affects the kinetics.²¹ Accordingly, Cu_2−XS QDs were synthesized in cubic (digenite) and hexagonal (roxbyite) forms to serve as precursors to ZnS and CdS.

Digenite and roxbyite Cu_2−XS QDs were prepared according to literature methods.³⁵ As shown in Figs. 2(a) and 3(a), the obtained Cu_2−XS QDs were spherical in shape and ∼10–11 nm in size with a standard deviation of <15%. The hexagonal roxbyite samples are more uniformly spherical, whereas the cubic digenite samples exhibit a variety of shapes with clear faceting in addition to spheres. TEM/EDS indicated formulas of Cu_1.87S for digenite and Cu_1.62S for roxbyite. These formulas are consistent with those noted in prior reports. Finally, the experimental PXRD patterns show good agreement with the literature reported PXRD patterns obtained from the ICDD database [Figs. 2(a) and 3(a)].

A successful cation exchange was carried out with digenite and roxbyite Cu_2−XS to form cubic and hexagonal ZnS and CdS [Figs. 2(b), 2(c), 3(b), and 3(c), respectively]. The exchange process is facilitated by vacancies in the Cu_2−XS lattice due to mixed-valent (Cu⁺/Cu²⁺) and the presence of trioctylphosphine, which is purported to bind tightly to the Cu⁺, thereby driving the equilibrium forward. This transformation was followed using PXRD and TEM.

As shown in Figs. 2(b) and 2(c), the products of the cation exchange of digenite were comparable in size to each other and to the starting Cu_2−XS QDs, ∼10 nm in diameter, with PXRD patterns characteristic of zb-ZnS and zb-CdS. Similarly, the products of the exchange of ∼10 nm roxbyite exhibited PXRD patterns characteristic of w-ZnS and w-CdS and no change in size [Figs. 3(b) and 3(c)].

The solubility of bulk w- and zb-ZnS in aqueous media has been measured by various groups, whereas the values for CdS are scarce and do not specify the structure type (most likely wurtzite, as that is the thermodynamically more stable form). Intriguingly, the solubility has a strong dependence on the structure, manifest in differences of 2 orders of magnitude between hexagonal closest packing and cubic closest packing. Thus, Latimer and co-workers³⁹ obtained values of 1.6 × 10⁻²³ and 7.0 × 10⁻²⁶ for w-ZnS and zb-ZnS, respectively. Ringbom and co-workers⁴⁰ (2.5 × 10⁻²² w and 1.6 × 10⁻²⁴ zb) and Helgeson and co-workers⁴¹ (2.2 × 10⁻²⁴ w and 1.9 × 10⁻²⁶ zb) obtained comparable values to those obtained by Latimer. For CdS, Latimer and co-workers³⁹ reported a value of ∼1.0 × 10⁻²⁸. This corresponds to a difference in solubility of 4–6 orders of magnitude relative to w-ZnS and 2–3 orders of magnitude relative to zb-ZnS. Assuming a solubility product of the form K_sp = [M²⁺][S²⁻] = [M²⁺]², free ion concentrations of Zn²⁺ are expected to range from ∼5 × 10⁻¹³ to 7 × 10⁻¹²M vs ∼10⁻¹⁴ for Cd²⁺

Free ion concentrations of Zn²⁺ and Cd²⁺ were determined by ICP-MS after 72 h equilibrium of thiolate-capped ZnS and CdS QDs (zb and w; 3.86 × 10⁻⁷ mol dm⁻³ in methanol). The concentration and solvent were chosen to reflect the conditions utilized in the TR-DLS studies (vide supra). As shown in Table I, the free ion concentrations are considerably higher than the values obtained from the solubility studies of bulk materials, on the order of 10⁻⁵ mol dm⁻³. This can be explained using the Ostwald-Freundlich equation, which demonstrates that nanoparticles have a higher equilibrium free metal concentration than the bulk [Eq. (8)],

where S and S₀ are the solubility of the nanocrystal dispersion and the bulk solubility, respectively, γ is the surface energy, $V¯$ is the molar volume, R is the gas constant, T is the absolute temperature, and r is the radius of the nanocrystal. As the radius of the particle decreases, the solubility is expected to be higher and the surface energy is expected to increase. In ZnS and CdS nanoparticles, a large fraction of the Zn/Cd atoms are located on the surface and are undercoordinated, facilitating their solubility. It has also been observed that the presence of amorphous layers can increase the solubility of ZnS QDs;³⁶ in our case, we have surface thiolate ligands that may assist in the solubilization of Zn²⁺ and Cd²⁺. The values obtained here are comparable to prior reports. For example, Rui Ma and co-workers have investigated sulfidized ZnO QDs (5 nm), for which free ion concentrations of 3.8 × 10⁻⁵ mol dm⁻³ were obtained;³⁶ likewise, Mudunkotuwa and co-workers reported [Zn²⁺] = 5.9 × 10⁻⁵ mol dm⁻³ for 24 nm ZnO QDs.⁴² Additionally, we observe that the ZnS produces a higher free cation concentration than CdS, by a factor of 3–4, and the trend observed in the bulk for ZnS in which w is more soluble than zb is maintained on the nanoscale and also extends to CdS.

Particle aggregation is characterized in the context of two limiting regimes: diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA).^43–45 DLCA corresponds to an aggregation regime where the aggregation rate is solely limited by the diffusion of clusters, i.e., the sticking probability, α, is one and every collision results in attachment. In contrast, for RLCA, α is < 1 due to interparticle repulsive forces, and several to many collisions are required before the productive attachment is achieved. In the DLCA regime, the growth in the average radius of gyration, $R¯g$⁠, as a function of time has a power law behavior and follows Eq. (9), where τ is the reciprocal Smoluchowski rate [Eq. (10), a function of the solution viscosity, η, temperature, T, and primary particle concentration, N₀], z is the dynamic exponent, and D_f is the fractal dimension,

In RLCA, $R¯g$ grows exponentially with time according to Eq. (11):

The TR-DLS analyses yield the Z-average hydrodynamic radius, $R¯h$⁠, plotted as a function of time, $t$⁠. As $R¯h$ is ∝$R¯g whenqR¯h≠1,$ $R¯h$ is employed as a surrogate for $R¯g$ in the kinetic analysis. Systems adhering to the DLCA kinetics should demonstrate a linear relationship between ln $R¯h$ and ln t (ln-ln plots), whereas for RLCA kinetics, a linear relationship is expected in plots of ln $R¯h$ vs t (semilog plots).

TR-DLS analyses were carried out using 3 ml of a 3.86 × 10⁻⁷ mol dm⁻³ concentrated sample of zb-ZnS, zb-CdS, w-ZnS, and w-CdS QDs in methanol. The oxidant (TNM, 10 μl, 3% in acetone) was added with agitation; then, the system was left to equilibrate for 3–5 min at 25 °C before initiating the data acquisition. The change in $R¯h$ was measured with respect to time until the sample became too polydisperse for the autocorrelator [Figs. 4(a) and 4(b)]. From a qualitative perusal of data, it is clear that (1) the assembly of CdS QDs is far slower than that of ZnS QDs, regardless of the polymorph, with CdS demonstrating a pronounced induction period that is absent in ZnS, and (2) the QDs adopting the hexagonal (wurtzite, w) polymorph assemble more rapidly than those that are cubic (zinc blende, zb), as we had observed previously.

For the oxidative assembly of zb-ZnS, $R¯h$ has already reached a value of ∼260 nm for the first data point after the 3–5 min equilibrium time and reached 1 µm within 150 min. Similarly, w-ZnS exhibits a comparable initial $R¯h$ of ∼200 nm but grows at a much faster rate, achieving a $R¯h$ value of 1 µm within 25 min. The data for zb- and w-ZnS were evaluated on semi-ln [RLCA, Figs. 4(c) and 4(d)] and ln-ln (Fig. S3) plots, with the former providing the better linear fit, indicative of the RLCA kinetics. Fitting the equation of the line (Figs. S1a and S2a) and using the slope, α/τ, as a proxy for the rate constant, the values of 0.510 and 3.92 s⁻¹ were obtained for the oxidative assembly of zb- and w-ZnS QDs, respectively (Table I).

The data for CdS are distinct from those of ZnS. For the zb-CdS QD assembly, the initial $R¯h$ is ∼70 nm, and there is no evidence of growth over the first 50 min of the experiment; it takes nearly 275 min to achieve 1 µm. w-CdS has a much smaller induction time (∼10 min) and an initial $R¯h$ of ∼110 nm and hits the 1 µm mark just shy of 75 min. In contrast to ZnS, the semi-ln and ln-ln plots of $R¯h$ vs $t$ for zb- and w-CdS are not linear over the time of data acquisition (Figs. 4(c) and 4(d); Fig. S3). This is not surprising given the significant induction period. As a means of comparison with ZnS, we sought to evaluate the CdS data over the same range of aggregate sizes as ZnS, i.e., from 260 to 1000 nm for zb and from 200 to 1000 nm for w. Over this region, the linear plots are obtained in both ln-ln (Fig. S4) and semi-ln treatments (Figs. S1b and S2b); the growth regime cannot be distinguished. Again, for purposes of enabling a direct comparison with ZnS, the slopes of the semi-ln plots were obtained as a proxy for the rate constants. The values of 1.71 and 3.24 s⁻¹ were obtained for the assembly of zb-CdS and w-CdS, respectively (Table I).

The trends in dynamic light scattering, as illustrated in Fig. 4, clearly show that, all other things equal, the time it takes to assemble large, micrometer-sized aggregates of MS QDs by oxidative assembly is greater by a factor of 2–3 for M = Cd relative to M = Zn. These data correlate with the QD solubilities of ZnS and CdS, as measured by the differences in the free ion concentrations of Cd²⁺ vs Zn²⁺; Zn²⁺ concentrations exceed those of Cd²⁺ by a factor of 3–4 (Table I). Clearly, the identity of the metal cation matters, but why?

According to the proposed mechanism, the first two steps (ligand oxidation/loss and surface cation solubilization) precede the oxidative assembly [Fig. 1(a)]. Indeed, the effect of steps 1 and 2 on the rate can be largely expected to delay the onset of aggregation, not affect the aggregation rate itself, by extending the time needed to reach a critical concentration of exposed (reactive) sites for the assembly. In this way, the observed “induction period” for CdS is the best indicator of the importance of cation solubilization in the overall rate of gelation.

As alluded to in the Introduction and reinforced in Sec. III, the observation of faster kinetics for w vs zb has been noted in a prior work on CdS.²⁹ However, it was not clear from the original study if the differences were structural or due to the different synthetic methods required to make the two polymorphs (low-temperature inverse-micelle synthesis of zb-CdS vs high-temperature arrested precipitation of w-CdS). Specifically, an unresolved question was whether the noted defects in, and poorer crystallinity of, zb-CdS were major contributors to the kinetic differences. The present study, in which both polymorphs are made by high-temperature routes, would seem to affirm the importance of the structure in dictating the overall assembly rate. However, it is important to note that the solubilities are also structure-dependent, with the faster-gelling wurtzite phases demonstrating enhanced free-cation concentrations under inert conditions (i.e., in the absence of the gelation-inducing oxidant). Solubility, like reactivity, is a function of surface energy, and thus, it is difficult to deconvolute these parameters. Indeed, the stability of the core structures (wurtzite or zinc blende) is purported to be a function of the inorganic surface termination, with cation-rich surfaces favoring wurtzite and anion-rich surfaces favoring zinc blende.^39,40 Thus, it is not the core-structure that dictates the surface, but vice versa. Recall also that the stability of the structure depends sensitively on the methods of synthesis. The cubic digenite polymorph of Cu_2−xS is prepared using oleic acid and therefore can be thought of as having a chalcogenide-terminated surface (anion-rich) bound by a neutral (Z-type) copper-oleate complex as an acceptor. In contrast, hexagonal roxbyite was prepared with oleylamine, which serves as a neutral donor (L-type) to the copper ions (cation-rich surface). Thus, the ligand exchange with MUA is likely to proceed by different mechanisms in these two cases and lead to different extents of surface passivation, both in the context of the surface ligand density and in the quality and nature of the interaction. This is further complicated by the presence of facets in the digenite system, an indication that lower-energy surfaces may be present in excess (roxbyite particles are largely spherical, implying an even distribution of surface planes), reducing the thermodynamic drive toward the assembly in the cubic system relative to the hexagonal one. Synthesis-directed surface terminations and their ability to direct the core-structure and the surface faceting appear general to a number of systems, and it is not surprising that they would impact the surface-driven oxidative assembly.^39,40

Returning to the relative kinetics of CdS vs ZnS, we note that while the differences in the overall assembly/gelation (as assessed by the time required to reach 1 μm in $R¯h$⁠) correlate with solubilities and structural effects, this is not the case for aggregation rates compared after the induction period. Using the slope of the ln $R¯h$ vs time plots over the region corresponding to $R¯h$ = ∼260–1000 nm as a measure of growth kinetics (Table I), zb-CdS grows much faster than zb-ZnS (by a factor of 3.4), contrary to our expectations, whereas over a similar size regime (⁠$R¯h$ = ∼200–1000 nm) w-CdS grows slower than w-ZnS (by a factor of 0.82). While it is intriguing to think that the difference in the assembly rate after induction reflects the relative stability of the two structure types for ZnS and CdS (noting that, in each case, the higher rate is for the less thermodynamically stable polymorph, w-ZnS and zb-CdS), we think that it is more likely to reflect the inadequacy of the RLCA model (which unambiguously describes the kinetics for both polymorphs of ZnS) to describe the kinetics of the CdS system (modeled equally well by RLCA and DLCA after induction).

In the context of developing a synthetic tool box for multicomponent quantum dot assemblies by oxidative assembly, a new variable has been identified (cation identity/solubility) and the strong structural dependence noted in our prior study has been confirmed (zinc blende vs wurtzite). The poor cation solubility, as in the case of Cd²⁺, correlates with a significant induction period before the assembly is initiated, unlike the more soluble Zn²⁺, where no induction period is evident. Likewise, the samples based on the hexagonal closest packing (i.e., wurtzite structure) exhibit a much faster rate of assembly than those based on the cubic closest packing (i.e., zinc blende structure). These data suggest that kinetic tuning will be necessary to ensure the desired mixing of dissimilar QDs in the oxidatively assembled composites, and this can be accomplished using the previously established parameters (chalcogenide oxidation potential, particle size, particle concentration, oxidant concentration, and ligand chain length) as well as the solubility of the metal cation and the structure.

See the supplementary material for the semi-ln and ln-ln plots of $R¯h$ vs t for zb-ZnS, zb-CdS, w-ZnS, and w-CdS, including the linear fits for RLCA and DLCA kinetic analyses and induction period calculations.

This work has been supported by the National Science Foundation under Grant No. CHE 1709776. Electron microscopy was acquired in the WSU Lumigen Instrument Center on a JEOL 2010 purchased under NSF, Grant No. DMR 0216084, and powder diffraction measurements were conducted in the WSU Lumigen PXRD Facility, supported by NSF, Award No. 1427926. Dynamic light scattering and ICP-MS were acquired at the Lumigen Instrument Center, Wayne State University.