Classification of Zinc Sulfide Quantum Dots by Size - American

Article pubs.acs.org/JPCC

Classification of Zinc Sulfide Quantum Dots by Size: Insights into the Particle Surface−Solvent Interaction of Colloids Doris Segets,*,† Christian Lutz,† Kyoko Yamamoto,‡ So Komada,‡ Sebastian Süß,† Yasushige Mori,*,‡ and Wolfgang Peukert† †

Institute of Particle Technology, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstr. 4, 91058 Erlangen, Germany Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Tatara Miyakodani Kyotanabe, Kyoto 610-0321, Japan

‡

S Supporting Information *

ABSTRACT: We present a detailed study on the classification of ZnS quantum dots (QDs) by size selective precipitation (SSP). SSP allows the postsynthetic narrowing of a given feed distribution and is usually realized by titration of a poor solvent into a suspension of dispersed particles. Thereby preferred flocculation of larger structures is induced. Our results confirm that SSP is a highly robust process, following a law of mass action. That means a certain solvent composition always leads to the same ratio between coarse and fines particles with respect to a specific particle size xi. This ratio is independent of the particle size distribution (PSD) of the feed, the washing history of the particles, and the solid concentration of the particles. Regarding the illustration of our findings, we established a combined approach that takes Hansen solubility parameters (HSP) of solvent mixtures as well as changing van der Waals interactions into account. Relating both to each other, a size-dependent region of enhanced solubility is clearly identified. Our concept allows a differentiation between volume-related effects like van der Waals interactions and surface-related effects like the interaction of a ligand with a solvent mixture. A comprehensive interpretation of classification results obtained with different good solvents and poor solvents enables to deduce a general strategy for the demanding determination of HSP for small colloids. Our work makes an important contribution to the design of an appropriate colloidal postprocessing which is applicable to larger quantities.

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INTRODUCTION Quantum confined semiconductor nanoparticles (NPs), also known as quantum dots (QDs), are used for various applications such as photocatalysis,1 diagnostics,2 electronics,3 or light-emitting devices.4 Among their great potential within all those emerging fields they are highly interesting materials due to their pronounced structure−property relationships that are usually monitored within a size range of a few nanometers. Hence, the dispersity of a sample which is often only described by the mean particle size and the width of the particle size distribution (PSD) becomes one of the most important factors to tailor electro-optical product properties.5−7 In the case of wet chemical synthesis, QD samples with narrow size distributions are already achieved. For instance, by means of hot injection methods nucleation and growth of the particles are clearly separated from each other whereas gradients are reduced by confined spaces.8−10 In addition, QD synthesis usually leads to particle surfaces that are strongly passivated by chemi- or physisorbed molecules to inhibit (or at least to suppress) secondary particle formation processes like aggregation or ripening.11−13 However, even when sophisticated synthetic techniques are used, the obtained sample will always exhibit a certain dispersity7 which is expected to be even more dominant when larger quantities are produced. Therefore, not © XXXX American Chemical Society

only new synthesis concepts but also postprocessing approaches for classification have to be developed and sufficiently understood.14 Ideally, it should be possible to tailor the cut sizewhich is defined as the position where an assynthesized sample is split into a smaller (fines) and a larger sized fraction (coarse)throughout the whole particle size range of a feed distribution. In this work the classification on a nanometer scale of zinc sulfide (ZnS) QDs via size selective precipitation (SSP) using controlled solvent mixtures will be addressed. The technique was reported already 20 years ago by the groups of Murray and Weller but is still highly relevant due to its potential to be scaled up into industrial relevant dimensions.15,16 In principle, particles are classified according to their size by the gradual addition of a poor solvent to a well-dispersed colloidal suspension using the effect that larger particles flocculate first. This preferred flocculation is usually explained by stronger van der Waals forces that increase with the particle diameter.17,18 Though the method is widely applied in the lab, SSP is still far from being understood in terms of a predictive model. At this Received: August 29, 2014 Revised: January 29, 2015

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DOI: 10.1021/jp508746s J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

ultrapure water was added again dropwise to the solution. After heating to 100 °C, the solution was refluxed for 12 h. The synthesized particles were concentrated in a rotary evaporator and flocculated with ethanol. The precipitate was separated by centrifugation, washed again twice with methanol, and then dried under vacuum. Preparation of Different Batches. A large batch, ZnS-0 (x1,3 = 1.69 nm) was generated by mixing the results of four different syntheses (syntheses were performed at Doshisha University Kyotanabe whereas mixing was done at FAU Erlangen). Powders after washing and drying were mixed manually in a vial. Then, this vial containing the four batches was fixed to a horizontally mounted stirring device and stirred with 30 rpm for 5 days. To ensure homogeneity of the sample, twice a day, the flask was knocked onto the laboratory table and shaken by hand. Additionally, a second (ZnS-1, x1,3 = 2.00 nm, synthesized at FAU Erlangen) and a third (ZnS-2, x1,3 = 1.83 nm, synthesized at FAU Erlangen) sample of TG-capped ZnS QDs were used to investigate the effect of different batches with varying particle size distributions (PSDs). For the synthesis of ZnS-1, 79 mmol of ZnAc·2H2O was dissolved in 800 mL of DMF. After addition of 140 mmol of TG dissolved in 200 mL of DMF, the reaction vessel was purged with nitrogen. The pH value around 8 was maintained by addition of 40 mL of 0.2 M NaOH. A solution of 11.2 mmol of Na2S·9H2O in water was added dropwise to the stirred reaction mixture. The mixture was heated to 100 °C and refluxed for 20 h. The second sample of TG-capped ZnS QDs (ZnS-2) was synthesized in the same way, but the volume of the reactant solutions and the reactant concentrations were doubled. The particles of each batch were concentrated in a rotary evaporator, precipitated with ethanol, washed twice with methanol, and dried under vacuum. For the synthesis of ZnS-3 (x1,3 = 1.74 nm, synthesized at Doshisha University, Kyoto), 22 mmol of ZnAc·2H2O was put into a reaction vessel and purged with nitrogen. Then, 400 mL of DMF was added to dissolve the powder, and 35 mmol of TG, also dissolved in DMF, was added dropwise to the zinc acetate solution. A subsequent addition of 20 mL of 0.1 M NaOH maintained the pH around 8. A solution of 5.5 mmol of Na2S·9H2O in 80 mL of water was added dropwise to the stirred reaction mixture. The mixture was heated to 100 °C and refluxed for 2 h. Characterization. Fourier transform infrared spectroscopy was performed with a Digilab Excalibur IR spectrometer (Digilab, USA) and KBr pellets. Absorbance measurements of ZnS-0...ZnS-2 were performed with a Cary 100 Scan spectrophotometer (Varian, Germany) without dilution using quartz glass cuvettes with an optical path length of 0.2 mm. Absorbance measurements of ZnS-3 were performed with a UV−vis spectrophotometer (Shimadzu, UV-2400) using a quartz glass cuvette with 10 mm optical path length. Absorbance measurements were analyzed with respect to their volume PSDs by means of a previously published deconvolution algorithm.27,29,30 It requires additive contributions of different particle size fractions, an assumption that has been already made by Mićić et al.,31 Pesika et al.,32 and Viswanatha and Sarma.33 For the size-dependent band gap energy a tight binding model (TBM) of Sapra and Sarma was used,34 and the absorption behavior of bulk ZnS was taken from Nanda et al.28 Selection of Poor Solvent Conditions. Preliminary studies revealed that the hydrophilic ZnS particles used for

point it needs to be mentioned that we think there is a general lack of understanding colloidal interfaces. Even the exact surface chemistry of citrate stabilized gold nanoparticles is still an important point of research.19 Thus, our work sheds light on an old but still challenging problem: the interaction of colloidal particle surfaces throughout a surrounding solvent (mixture). For noble metals, Shah et al. reported density-tunable sizeselective dispersibility of dodecanethiol-coated gold and silver NPs in supercritical ethane or CO2,20,21 but also fractionation by addition of a poor solvent is described.22 For semiconductors, Mastronardi et al. applied the technique to subdivide a starting suspension of Si NPs into the impressive amount of 14 differently sized samples with strongly varying quantum yields ranging from 50% down to below 10%.23 Recently, Komada and Mori performed a study on manganesedoped ZnS quantum dots (ZnS:Mn) where they confirmed that larger particles have better emission properties than smallest QDs.24,25 This is in line with previous findings of Nag et al., who demonstrated the improved emission properties of manganese-doped CdS nanocrystals. They found that larger particles contain more manganese ions than smaller ones.26 All these positive reports motivated a subsequent work by Segets and Komada et al. to develop strategies for the quantitative evaluation of QD classification results by applying established concepts from the field of powder processing and particle technology which have a long tradition in rigorous process design and scale-up including industrial classification processes and a wide range of industrial separation processes.27 Thereby PSDs for coarse and fines were derived by the careful analysis of optical absorbance measurements and weighed by their relative mass fractions. This procedure allowed the calculation of cut sizes, separation efficiencies, and yields. These are needed in the next step for the development of a suitable process to classify QDs at larger scale either by increasing the volume or even better by a continuous process. For both aspects, however, a fundamental understanding of SSP and its main influencing factors is needed. From our previous work we have access to an excellent toolbox for the evaluation of classification results in the lower nanometer range that enables to address the aforementioned issue: to adjust the cut size within a given feed PSD with high yields and excellent separation efficiencies based on a mechanistic understanding of SSP. Finally, being not only determined by the particle core but also by the complex interplay between the ligand at the particle surface and the solvent (mixture), SSP gives access to surface properties of QDs. Our work goes clearly beyond the phenomenological report of SSP. It is seen as a further key step for the application of this concept toward larger quantities and a rational process design for small nanoparticles with respect to formulation issues.

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EXPERIMENTAL SECTION Synthesis of ZnS QDs. For synthesis of 3-mercapto-1,2propanediol (TG)-capped ZnS QDs a method of Nanda et al. was applied.28 All chemicals used were of analytical purity. To remove oxygen, all flasks where degassed with nitrogen prior to synthesis. First, 19.8 mmol of zinc acetate dihydrate (ZnAc· 2H2O) were dissolved in 400 mL of dimethylformamide (DMF). Then, 35 mmol of TG dissolved in DMF was added dropwise to the zinc acetate solution. A subsequent addition of 20 mL of 0.1 M NaOH maintained the pH around 8. Finally, 2.8 mmol of sodium sulfide nonahydrate dissolved in 80 mL of B


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permittivities see Table SI 2_2). The total volume of solvent was adjusted that the particle concentration at the end of the experiment was again 1 g L−1. That means Vtotal = Vgood solvent + Vpoor solvent = 15 mL. The volumes of Vgood solvent and Vpoor solvent were calculated as summarized in Supporting Information SI 4. After addition of the poor solvent, the centrifugation procedure was the same as described for the redispersion experiments. In addition to those standard titrations, the final particle concentration was varied from 0.3 to 5 g L−1 as well as classifications from different starting PSDs in terms of their mean sizes and their widths were conducted. Data Evaluation. All experiments were analyzed with respect to the relative masses of the coarse fraction g and the fine fraction f after drying at room temperature under vacuum conditions (g = mrecovered/min and f = msupernatant/min) as well as with respect to the classification result. Classification results were evaluated based on the PSDs of the feed qF(x), the coarse qg(x), and the fines qf(x) derived from optical absorbance measurements.27,29,30 Thereby we consider the following: (i) The cut size xt at the intersection between the mass weighted density distributions of the coarse and the fines to characterize the position of the cut. (ii) The separation efficiency

this work can easily be redispersed in water (relative permittivity εr,H2O = 80) and dimethyl sulfoxide (DMSO, εr,DMSO = 47);35 with more energy input dispersion in dimethylformamide (DMF, εr,DMF = 38) is possible, too. By the addition of methanol (MeOH), ethanol (EtOH), 2propanol (PrOH), acetone (AC), or acetonitrile (ACN) to an e.g. aqueous ZnS dispersion, the relative permittivity is reduced and the solvent becomes less suitable for the nanoparticles. The preferred flocculation of larger particles is induced, and SSP takes place. For making results of different solvent mixtures comparable, we decided to fix for a first instance the relative permittivities εr,mix of either (i) the solvent mixture used for dispersion of a particle powder (redispersion experiments) or (ii) the final solvent mixture obtained after titrating a defined amount of a poor solvent to the dispersed colloid (titration experiments). Details on the adjustment of dielectric properties based on literature data for solvent mixtures can be extracted from the Supporting Information SI 1.36,37 Data on all applied good solvent/poor solvent combinations are summarized in Supporting Information SI 2. All experiments were performed at room temperature. Details on reproducibility and experimental error of our data are exemplarily shown in Supporting Information SI 3. Classification. All experiments started from a dried ZnS powder that was isolated after synthesis and several times of washing. As mentioned, two different approaches for the classification process were applied within this work: (i) redispersion and (ii) titration experiments. An overview of both of them is given in Scheme 1.

gqg (x)

T (x ) =

qF(x)

(1)

(iii) The therefrom-derived separation sharpness κ to characterize the steepness of the cut with x25,t and x75,t being defined as the particle size for which T(x) is 0.25 or 0.75, respectively. x 25, t κ= x 75, t (2)

Scheme 1. Sketch of the Performed Experiments by (i) Redispersion of the Powder in a Premixed, Binary Solvent Mixture (Violet, Shown Left) and (ii) Titration by the Addition of a Poor Solvent (Red) to Fully Dispersed ZnS Nanoparticles in a Good Solvent (Blue, Shown Right)

(iv) The yields for the coarse ηg and the fines ηf to evaluate the efficiency of the process ηg =

∫x

xmax t

∫x

[gqg (x) dx]

xmax t

[qF(x) dx]

(3)

xt

ηf =

∫x [fqf (x) dx] min

x

∫x t [qF(x) dx] min

Standard Redispersion Experiments. The aim of redispersion experiments was to see if classification can be achieved from a powder state or if a well-dispersed colloid is mandatory. Regarding the experimental procedure, 0.015 g of ZnS powder was provided, and 15 mL of liquid (either we used pure solvents like DMF and DMSO or preprepared solvent mixtures with the same relative permittivities like εr,DMF = 38 and εr,DMSO = 47; for details see Table SI 2_1) was added to achieve a final solid concentration of 1 g L−1. For redispersion, samples were stirred between 5 and 25 min or sonicated between 10 min and 4 h. Noteworthy, during sonication the water of the sonication bath was exchanged in appropriate time intervals to prevent unintended heating of the sample. Finally, samples were centrifuged for 10 min at 11900g (10700 rpm) to separate the dispersed particles from the larger flocs. Standard Titration Experiments. For titration experiments, ZnS QDs were first completely redispersed in water or DMSO as a good solvent. Then, a poor solvent was slowly added under stirring by means of a 20 mL syringe (for details on relative

(4)

Noteworthy, T(x) intrinsically addresses the mass balance and does not depend on the quantity r based on which the PSD is derived. Hence, it makes no difference if it is derived e.g. based on a number (r = 0) or based on a volume (r = 3) distribution. As already mentioned in the section on characterization, volume PSDs are used throughout this work. The fulfilled mass balance as well as the negligible change of the powders during storage can be extracted from the Supporting Information SI 5. For further details of the evaluation procedure the reader is referred to Figure 5 of our previous work orin the case of larger particlesto textbooks from the field of particle technology/chemical engineering.27,38,39 However, at this point it needs to be mentioned that for a comprehensive discussion of any separation these parameters, namely, coarse and fine fraction, separation efficiency, cut size, separation sharpness, and yields need to be considered together. For instance, when xt corresponds to xmin or xmax, no classification took place at all (either all particles flocculated C


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The Journal of Physical Chemistry C or stayed completely dispersed). In this situation an analysis of κ is not meaningful. Accordingly, the first step should always be the analysis of T(x) under consideration of xmin and xmax. For more detailed information we also refer to Supporting Information SI 6 where the approach is discussed in more detail. Additionally, some other well-established measures for the width of a PSD do exist, like the span which is defined as (x90 − x10)/x50 or the ratio between the full width at half-maximum (fwhm) and mean particle size xmean. However, especially the latter does not sufficiently address nonsymmetric PSDs. Therefore, measures that consider the variance (σ2) or the standard deviation (σ) like the relative standard deviation (RSD = σ/xmean) are seen to be more precise. Because of its use in colloidal systems not only in the context of SSP,16,40 RSD data will be provided on all distributions shown in the following and discussed in the section on theoretical description of SSP. In this context some important points need to be mentioned. First, RSD depends on the quantity r. Second, the mean particle size does not cross out during the calculation of RSD. Thus, it matters if e.g. either the mode (xmode,r, defined as the maximum of the size distribution), the median (x50,r, defined as the size at which 50% of the total amount of particles is smaller), or the balanced mean/mean volume weighted particle size (x1,r, defined as the abscissa of the center of gravity by area of the density distribution) is used. Herein, volume distributions were applied and for xmean the mean volume weighted particle size x1,3 was used. The latter was chosen due to the fact that we needed to address the nonsymmetric shape of our PSDs that always showed a slight tailing to larger particle sizes.

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Figure 1. Isolated coarse fractions for redispersion experiments (ZnS0) with mixtures of H2O and MeOH (red), EtOH (blue), and PrOH (green) as well as pure solvents (yellow) like DMF (diamonds) and used as a negative blindDMSO (stars) obtained after dispersion by stirring (small symbols) and sonication (large symbols); black frames and squares indicate relative permittivities adjusted for redispersion close to pure DMF (εr,DMF = 38), unframed circles indicate relative permittivities for redispersion close to pure DMSO (εr,DMF = 47); the small nonzero coarse fractions in the case of the good solvent DMSO are due to particles that were deposited during drying of the centrifuge vial. Details on solvent mixtures and relative permittivities can be found in the Supporting Information SI 1 and 2.

Though a certain trend toward better dispersion with increasing relative permittivity from 38 to 47 within one type of poor solvent (e.g., methanol shown in red or propanol shown in green) is observed, the success of the dispersion does clearly not solely depend on the dielectric permittivity. For a fixed εr (e.g., 38 or 47, black dashed vertical lines are introduced as guide to the eye) nearly the whole spectrum between complete redispersion (g = 0) and complete flocculation/incomplete redispersion (g = 1) is realized. Additionally, only a slight improvement in the redispersed amount of particles is observed when stirring times are increased (Figure 1, small symbols) or when sonication is used instead of stirring (Figure 1, large symbols). However, a restriction of the evaluation to the coarse fractions only solely addresses the integral amount of redispersed powder. For a meaningful evaluation if a classification effect is observed or not, the separation efficiencies have to be derived based on the mass weighted PSDs of the feed and the coarse material. Exemplarily, Figure 2a shows for εr = 38 and mixtures of H2O/PrOH the mass weighted PSDs obtained from a ZnS-0 powder after redispersion by stirring for 25 min (blue lines) as well as after redispersion by sonication for 240 min (red lines). It becomes clear that when the powder is redispersed by stirring, no significant change in the shape and position of the PSDs derived for the feed, the coarse, and the fines is observed (for details on the adjusted stirring parameters see Supporting Information SI 7). All modal values (maxima of the distributions) are with relative deviations below 2% nearly identical with the corresponding value of the feed distribution situated at 1.68 nm (see blue vertical lines in Figure 2a that are introduced as guide to the eye). However, in the presence of sonication which provides a higher maximum energy input than stirring, a slight shift of the PSDs in comparison to the feed distribution is noticed (see red vertical lines in Figure 2a that are introduced as guide to the eye). This improved classification behavior is further confirmed by the evolution of the separation efficiencies shown in Figure 2b where in addition to the sample evaluated after 240 min of sonication (red dashed-dotted line),

RESULTS AND DISCUSSION

Influence of Redispersion Procedure. By redispersion experiments we first wanted to investigate if classification only takes place when the process starts from a well-dispersed colloid or if SSP is also observed when a powder sample is brought in contact with a prefabricated solvent mixture. Second, we wanted to study the influence of the dielectric permittivity of the surrounding medium on the redispersibility of the ZnS powder (ZnS-0). As reference points we used the relative permittivities of the pure good solvents DMF (εr,DMF = 38) and DMSO (εr,DMSO = 47). Those two permittivities were adjusted in different binary solvents by premixing the good solvent water (εr,H2O = 80) with appropriate amounts of the poor solvents MeOH, EtOH, and PrOH (for details see Supporting Information SI 1 and SI 2). Pure DMF and DMSO as well as solvent mixtures were added to the dry powder as sketched in Scheme 1 (left) and stirred for 5, 10, and 25 min as well as sonicated for at least 10 min up to 4 h. A complete dissolution of the solid was solely observed for pure DMSO. For all samples, primary particles were separated from the larger structures by centrifugation. Figure 1 shows the results obtained from redispersion experiments when the amount of the isolated coarse fraction g is used for evaluation. Noteworthy, g includes the mass of particles which could not be redispersed at all plus the mass of reflocculated primary particles after redispersion and subsequent flocculation by SSP g=

mnot redispersed + m flocculated mrecovered = m in m in

(5) D


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Figure 2. (a) Classification results in terms of the mass weighted coarse (dashed lines) and fines (dotted lines) fractions achieved by redispersion of ZnS-0 QDs (black solid line, the feed is constant for both experiments) by means of stirring (blue) and sonication (red) in a H2O/PrOH mixture at a relative permittivity εr = 38. The vertical lines characterize the modal values of the coarse and the fines, respectively. (b) Separation efficiency curves derived from the PSDs shown in (a) for redispersion by stirring (blue solid line) and sonication for 10 min (green dotted line), 60 min (gray dashed line), and 240 min (red dashed-dotted line). RSDs are given in the legend in parentheses.

Figure 3. (a) Evolution of the separation efficiency for H2O/EtOH mixtures with relative permittivities adjusted between εr = 47 (green dasheddotted line, RSDcoarse = 0.28, RSDfines = 0.11), εr = 40 (red dotted line, RSDcoarse = 0.15, RSDfines = 0.15), εr = 38 (blue dashed line, RSDcoarse = 0.15, RSDfines = 0.11), and εr = 33 (black solid line, RSDcoarse = 0.12, RSDfines = 0.23). (b) Cut sizes for mixtures of water with MeOH (black triangles), EtOH (blue squares), PrOH (red circles), AC (green diamonds), and ACN (gray hexagons) as well as for mixtures of DMSO with EtOH (brown stars); the minimum (xmin) and the maximum (xmax) particle size of the feed PSD (ZnS-0, RSD = 0.18) are included by black horizontal lines as guide to the eye.

powder. All particles for which a redispersion could be achieved, reorganize and take part during SSP. However, due to the fact that a complete redispersion of the whole powder is not possible by applying standard stirrers and sonication baths found in a chemistry lab, titration experiments will be discussed in the next section. Titration Results. For titration, an appropriate amount of powder was first completely redispersed in a good solvent (H2O, DMSO) prior to the addition of a poor solvent (see also Scheme 1). For all titration experiments the latter was added slowly under stirring to prevent concentration peaks. However, throughout all our experiments neither an influence of the mixing conditions during the addition of poor solvent nor an influence of stirring and/or sonication of the mixture had a measurable influence on the classification result (see Supporting Information SI 8). The solvent volumes were adjusted as described in the classification section on standard titration experiments. All studies were performed in mixtures of H2O as good solvent with MeOH, EtOH, PrOH, AC, and ACN as well as in mixtures of DMSO as good solvent with EtOH (for exact values see Supporting Information SI 1,2,4). The evolution of the separation efficiency, exemplarily shown in Figure 3a for the titration of EtOH to an aqueous colloid, shows a clear dependence of the classification on the relative permittivity of the final mixture. With decreasing εr the classification is shifted to smaller particle sizes. Starting with the same feed distribution (ZnS-0), the cut size being the

data on samples sonicated for 10 min (green dotted line) as well as sonicated for 60 min (gray dashed line) are shown. In the case of redispersion by stirring a horizontal evolution of the separation efficiency around T(x) = 0.5 (blue solid line in Figure 2b) is observed. Thus, the feed is evenly distributed to coarse and fines throughout all particle sizes. This confirms the conclusion already discussed in the context of the PSDs shown in Figure 2a that no classification takes place. In contrast, when redispersion is performed in the presence of ultrasound, a small classification effect is observed thatat a first glance increases with dispersion time. However, after 60 min of sonication (gray dashed line in Figure 2b) no change in T(x) is noticed anymore, even when the sonication duration is extended to 240 min (red dashed-dotted line in Figure 2b). We think that a further improvement of the classification effect could only be achieved when the maximum local energy input is further increased. In brief, from the redispersion experiments we conclude that in addition to the relative permittivity of the solvent mixture, the chemical structure of the applied solvent plays a role. Classification results obtained by redispersion of a dried powder are not convincing in terms of the separation efficiency. However, with increasing energy input (exposure time and especially maximum differential energy input) classification results can be improved. This is explained by the fact that with increasing energy input during redispersion more primary particles are deliberated by a breakup of the dried, flocculated E


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Figure 4. FTIR spectra of feed particles (ZnS-2, upper black line) and the received coarse fractions after the first (coarse 1, middle blue line) and the second (coarse 2, lower red line) classification step (standard titration, H2O/MeOH, εr = 46); important regions are highlighted with different colors and are discussed in the main text.

Figure 5. (a) Classification results obtained by standard titration with H2O/MeOH and εr = 46 (ZnS-2) in terms of the feed (black solid line, RSD = 0.11), the coarse (blue dashed line, coarse 1, RSD = 0.10), the fines (red dotted line, RSD = 0.09), and the therefrom derived separation efficiency (black dashed-dotted line). (b) Classification results for the same process conditions like in (a) of coarse 1 (blue solid line, RSD = 0.10) into coarse 2 (gray dashed line, RSD = 0.16) and fines (orange dotted line, RSD = 0.10) together with the corresponding separation efficiency evolution (blue dashed-dotted line).

ZnS-2 was dispersed in H2O and classified using MeOH as poor solvent at εr = 46. The feed as well as the coarse powder after drying (coarse 1) was analyzed by Fourier-transformed infrared spectroscopy (FTIR) using KBr pellets. Then, coarse 1 was redispersed in water and classified once more, again with MeOH as poor solvent and a final εr = 46. After drying, IR measurements of the coarse powder from this second classification step (coarse 2) were performed and compared to the IR spectra of the feed and coarse 1. The results are summarized in Figure 4. From the synthesis protocol it is known that 3-mercapto-1,2-propandiol (TG) is the main ligand but also zinc acetate could be present due to the fact that it is used during particle synthesis as zinc source. All three spectra show a broad band at around 3370 cm−1 which is ascribed to the OH stretch. The next pronounced bands around 2926 and 2867 cm−1 that are highlighted in the left-hand plot of Figure 4 (gray region) are most probably assigned to the asymmetric CH2 and symmetric CH3 stretch. The former is ascribed to TG and the latter to acetate. However, both are comparatively weak, have a pronounced background, and especially the band at 2867 cm−1 could also be caused by the symmetric CH2 stretch.41 At next, smaller wavenumbers below 2000 cm−1 are enlarged in the right-hand side of Figure 4. Broad resonances between 1750 and 1500 cm−1 highlighted in green are monitored that indicate the presence of acetate in the samples in different binding modes (CO).25,42 The small shoulder at 1460 cm−1 (highlighted in yellow) is explained by the CH bend, whereas the more pronounced band at 1415 cm−1 is ascribed to C−OH bending (highlighted in blue). Both can originate from TG as well as

intersection between the mass weighted PSDs of the coarse and the fines, respectively, can be used to compare different classification experiments. Figure 3b shows the cut size evolution for several good solvent/poor solvent combinations. It becomes clear that within a fixed solvent combination the cut size can be easily tuned throughout the whole feed distribution. For better orientation, the whole size range of ZnS-0 exceeding from xmin (∼1.26 nm) to xmax (∼2.75 nm) is indicated by dashed horizontal lines. Moreover, all classifications are highly efficient. This is concluded from the fact that all separation sharpnesses κ are situated above 0.7, all yields for the coarse range from 0.53 (PrOH and εr = 39) up to 0.90 (PrOH and εr = 28) and all yields for the fines are situated between 0.56 (PrOH and εr = 36) and 0.93 (EtOH and εr = 47) (see Supporting Information SI 9). In addition, Figure 3b further confirms the previous observation from the redispersion studies, namely that the dielectric permittivity of the adjusted solvent is not the only influencing factor on SSP. Again, at a fixed relative permittivity, e.g., εr = 43, the cut size varies by roughly 1 nm and thus nearly extends throughout the whole feed PSD. Hence, the chemical nature of the good but also of the poor solvent and their interaction with the particle surfacethe latter consists of the core material with the adsorbed ligand(s)has to be considered. This will be addressed in the next sections. Influence of Ligand Composition. The titration experiments revealed a strong dependence of the classification results on the applied solvents. For a better understanding of the prevailing interaction at the solid−liquid interface, the surface of the particles needs to be considered. A starting powder of F


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Figure 6. (a) Classification results of ZnS-0 (black, RSD = 0.18) and ZnS-1 (blue, RSD = 0.14) including the PSDs of the feed (solid lines) as well as the mass weighted PSDs of the coarse (dashed lines, RSDZnS‑0,coarse = 0.18, RSDZnS‑1,coarse = 0.21) and the fines (dotted lines, RSDZnS‑0,fines = 0.10, RSDZnS‑1,fines = 0.09) obtained by a standard titration experiment with H2O/EtOH and εr = 38. Cut sizes are indicated by vertical lines. (b) Evolution of separation efficiencies for ZnS-0 (black solid line) and ZnS-1 (blue dashed line) for the classification results shown in (a).

Figure 7. (a) Relative (black triangles) and absolute (blue squares) concentration of ZnS QDs (ZnS-0, RSD = 0.18) in the supernatant for different solid concentrations between 0.3 and 5.0 g L−1 classified with H2O/MeOH, εr = 46. (b) Underlying evolution of separation efficiencies for the experiments of (a) exemplarily shown for particle concentrations of 0.6 g L−1 (black solid line, RSDcoarse = 0.15, RSDfines = 0.11), 2.5 g L−1 (blue dashed line, RSDcoarse = 0.15, RSDfines = 0.12), and 5.0 g L−1 (red dotted line, RSDcoarse = 0.15, RSDfines = 0.11).

Influence of Feed PSD. Another important factor on SSP that needs to be analyzed is the influence of the feed PSD. In Figure 6 we summarize the classification results of two differently sized feeds: ZnS-0 (Figure 6a, black solid line) with x1,3 = 1.69 nm and ZnS-1 (Figure 6a, blue solid line) with x1,3 = 2.00 nm. Both feeds were exposed to a standard titration experiment using EtOH as poor solvent and adjusting a final relative permittivity εr = 38. The cut sizes were determined from the intersections of the mass weighted PSDs of the coarse (dashed lines) and the fines (dotted lines) and are illustrated by black and blue vertical lines at 1.78 and 1.86 nm. Because of their negligible deviation of less than 1 Å, it already becomes clear that the classification results must be nearly identical. This is further confirmed by comparing the separation efficiency curves which are illustrated in Figure 6b. Both, TZnS−0(x) (black solid line) and TZnS−1(x) (blue dashed line) show the same behavior except the drop of TZnS−1(x) for particle sizes 2. Such good solvent conditions will be indicated by a blue color in the following. Medium solubility: particles of the considered size are homogeneously distributed into fines and coarse: 0.33 ≤ T(x) < 0.66 or 2 ≥ KDiss(x) > 0.5. Those medium solvent conditions will be indicated by a black color in the following. Poor solubility: particles of the considered size are mostly found in the coarse fraction: T(x) ≥ 0.66 or Kdiss(x) ≤ 0.5. Such poor solvent conditions will be indicated by a red color in the following. The second issue was addressed by deriving the δi’s of the final solvent mixture. This was realized by weighing the HSP of the used good solvent and poor solvent, respectively, by their volume fraction (for details and related literature see Supporting Information SI 12). Noteworthy, the Hansen space in that case is much more difficult to access in comparison to the original experiment. Evaluable data points are restricted to the applied solvent mixtures. They allow a screening of the different coordinates only from one side in 3D Hansen space, namely along the isolines of the solvent mixtures. All available data points were evaluated as described above by the separation efficiency and colored blue (high dispersibility), black (medium dispersibility), or red (low dispersibility). The results are summarized for the three particle sizes in Figures SI 12_1−3. They already reveal two solubility regions around H2O and DMSO as well as a clearly enhanced blue solubility window for smaller particles. However, the results are not yet convincing in terms of a clear separation of the different regions. Also, a clear statement if HSP of TGcapped ZnS QDs depend on the particle size is not possible. The third issue arises due to the fact that ZnS QDs are no dissolved molecules but solid particles. This is an important but often neglected aspect. By changing the solvent during a titration experiment, not only the solid surface−solvent interaction of a specific particle size xi is affected but also the van der Waals attraction is influenced due to the fact that the Hamaker constant changes in parts up to 33% as discussed previously. To include this particle-related contribution, we propose to divide the δi of the solvent mixtures by the relative deviation in the Hamaker constant σA. The latter was expressed by the Hamaker constant of plain ZnS in the solvent mixture AZnS,solvent mixture referred to the Hamaker constant between plain ZnS in vacuum AZnS,vacuum

provides global information on all interactions between these molecules. A further development of this approach is the concept of Hansen, who established the HSP.60,61 Hansen subdivided the overall energy of cohesion into three contributions: a polar contribution δp, a disperse contribution δd, and the ability to exchange electrons δh according to the concept of Lewis acids and bases.62,63 These three contributions are used to create a 3-dimensional coordinate system, the 3D-Hansen space, in which the solubility of a solute can be visualized. Following the convention, for unknown, new substances the 3D-Hansen space is screened by a predefined list of solvents.62,63 The solubility of the solute according to a subjective scale is evaluated, e.g. ranging from 1 to 6 or 1 to 10. From the center of the region of high solubility, HSP of the unknown component are deduced and tabulated. As alternates to this highly laborious procedure also group contribution methods exist. Thereby the molecule of interest with unknown HSP is subdivided into individual chemical motifs with known solubility parameters. The unknown HSP are then derived by the proper addition of the different contributions. With known HSP (or coordinates) of the solute and known HSP (or coordinates) of the solvent (mixture), the distance DHSP between solute and solvent is derived by DHSP = 4(δd,solvent − δd,target)2 + (δp,solvent − δp,target)2 + (δ h,solvent − δ h,target)2

(11)

The factor 4 in the first term was introduced based on the empiric finding that by stronger weighing of δd, solubility data are usually represented by a sphere including the good solvents.63 The closer the values of the solubility parameters of solute and solvent, i.e., the smaller DHSP and thus the solute− solvent distance in 3D Hansen space, the better the solubility of the solute in the solvent. Implications of Solubility Parameters. A consideration of eq 11 is only possible with known δi of the target substance. For this study, the “solute of interest” would be the particle surface of TG-capped ZnS QDs. Unfortunately, such a nonideal particulate interface is neither sufficiently understood nor easy to access. Regarding the SSP experiments of this work, HSP of all solvents are well-known and tabulated.63 But HSP values of the TG ligand that is seen to be mostly chemisorbed at the particle surface are questionable. Pure TG is totally miscible (in its pure form it is a liquid) with all pure poor solvents applied in this study. Thus, it is obviously not possible to simplify the surface of the solid particles by just taking the HSP of the ligand molecule into account. In conclusion, HSP of TG-capped ZnS QDs are not known at all. This is not only the case for QDs of this study but a general issue, especially due to the fact that HSP are usually applied for the derivation of the solvent−ligand interaction parameter χ. This parameter is an important factor during the calculation of size-dependent osmotic interactions which are finally balanced in frameworks like extended DLVO theory (xDLVO).64,65 Therein they are compared to other interactionslike the aforementioned electrostatics or van der Waals interactionsand conclusions on colloidal stability are made. That means with incorrect HSP the whole theoretical description of colloidal stabilityprovided it is applicable to such small nanoparticlesis not possible at all. In addition to those general difficulties of a proper HSP determination of particles instead of molecules, further J


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Figure 9. Dispersibility determined for 1.75 nm ZnS-QDs in dependence of HSP divided by the deviation in the Hamaker constant σA; good solubility T(1.75 nm) < 0.33 or Kdiss(1.75 nm) > 2: blue, medium solubility 0.33 ≤ T(1.75 nm) < 0.66 or 2 ≥ Kdiss(1.75 nm) > 0.5: black and poor solubility T(1.75 nm) ≥ 0.66 or Kdiss(1.75 nm) ≤ 0.5: red; water and DMSO are good solvents (large, dark blue diamonds), MeOH (circles), EtOH (squares), PrOH (upward triangles), AC (leftward triangles) and ACN (stars) were used as poor solvents; data points for mixtures of the good solvents DMSO/H2O are represented by small, dark blue diamonds; experiments were performed on different ZnS batches processed in Erlangen (ZnS-0...ZnS-2, closed symbols) as well as in Kyoto (ZnS-3, open symbols).

σA =

A ZnS,solvent mixture A ZnS,vacuum

the region dominated by electron exchange according to the concept of Lewis acids and bases) around H2O. As can be seen from the corresponding plots of smaller as well as larger particles at 1.5 and 2.0 nm (see Supporting Information SI 13), this window becomes smaller with increasing particle size and is enhanced for smaller particles. Comparing the results of Figure 9 and Figures SI 13_1−2, it becomes clear that there is no indication for a parallel shift of the blue data along a specific δi/σA axis. Only a homogeneously expanded solubility window in all three directions is observed with decreasing particle size. This isin line with our findings on differently sized feed distributionsa strong indication that (i) the surface−solvent interaction is independent of the particle size and (ii) the classification effect comes from the size-dependent van der Waals interactions. The latter increase with the particle diameter and therefore clearly reduce the blue solubility window. Its relative change for different particle sizes determines if SSP takes place and if the classification process will be efficient or not. In conclusion, our data do not yet allow the proper, unambiguous determination of HSP for ZnS QDs but are of major importance en route to the determination of particulate solubility parameters and a knowledge-based process design. The most important findings up to now are the separation of particle-related van der Waals effects from surface-related solubility effects. Therefrom it is already deduced that for the TG-capped ZnS QDs of this study the center of the blue solubility window seems to be independent of the particle size.

(12)

As mentioned, all the values used for the derivation of Hamaker constants are summarized in Supporting Information SI 11. Figure 9 illustrates the results of δi/σA derived for a particle size of x = 1.75 nm after evaluation of all titration experiments by the color code described previously. Note that every data point reflects again one experimental condition being evaluated in terms of the separation efficiency T(x = 1.75 nm). The corresponding graphs for smaller and larger particle sizes (1.5 and 2.0 nm) can be extracted from Supporting Information SI 13. Though it was not possible to analyze the whole 3D space of interest due to the fact that much more experiments than the presented 69 process conditions (evaluated for three different particle sizes leading to 207 data points in sum) would be required, a clearly distinguishable blue region of high dispersibility (blue data points with T(x = 1.75 nm) < 0.33 or Kdiss(1.75 nm) > 2) is identified. In addition to the classification experiments, we analyzed mixtures of the good solvents DMSO and H2O (represented by small dark blue data points that evolve between the larger dark blue diamonds of H2O and DMSO). Independent of the mixing ratio, we found a complete redispersion of the ZnS powder (ZnS-0). Thus, the good solvents span the solubility window and connect the region dominated by dipole interactions around DMSO and the region dominated by hydrogen bonds (or more precisely K


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law of mass action like it is usually observed for chemical reactions or adsorption/desorption phenomena. The dissociation constant Kdiss(xi) is easily expressed by the separation efficiency T(xi). On the basis of this key finding, we illustrated the classification results in a comprehensive way by considering a combined approach of van der Waals interactions and Hansen solubility parameters (HSP). Similar to the determination of HSP of an unknown component, we evaluated the dispersed amount of material for fixed particle sizes of 1.5, 1.75, and 2.0 nm. However, the contributions δi which span the 3D Hansen space of all analyzed solvent (mixtures) were referred to the relative change (with respect to vacuum conditions) in the Hamaker constants. This accounts for changing van der Waals interactions in media with different polarity and optical properties. Noteworthy, our results are deduced from a large data set with experiments being performed in two groups: one in Erlangen, Germany, and one in Kyoto, Japan. We evaluated 4 differently sized batches of ZnS particles, 2 good solvents (H2O and DMSO), and 7 poor solvents, leading to 69 data points for each particle size. Our theoretical considerations allow a clear statement how HSP can be derived for particulate surfaces. We believe that such a standardized methodology is mandatory for many redispersion studies of small nanoparticles with sizes below 20 nm and a highly important aspect during colloidal processing in general.

That means size effects are only introduced by van der Waals interactions. In addition, two solubility regions around DMSO and H2O are identified which are dominated by polar interactions and the ability to exchange electrons. Such mechanistic insights are important for a fundamental understanding of the complex phenomena taking place at real particle surfaces. On the basis of the experimental and theoretical findings of this work, we think that HSP of ZnS QDs are accessible. The boundary conditions would be a properly defined experimental procedure that is applied to identical particles in terms of their PSDsin an ideal case a larger batch would be produced. In this case, the pure solvents proposed by Hansen should be applied together with a correction for the van der Waals interactions. An identical redispersion procedure (first aspect) would ensure a breakup of always the same relative amount of floccs and the use of identical PSDs (second aspect) would ensuredue to the constant cut following a law of mass actionthat always the same amount of particles is distributed to the coarse or the fines, respectively. When those requirements are fulfilled, the conduction of redispersion experiments and a global evaluation according to the coarse fraction is possible. Noteworthy, the latter is a macroscopic parameter that can be determined by a significantly reduced experimental effort. However, such an approach can only be justified by the quantitative understanding of SSP derived in this work. After having defined the HSP of TG-capped ZnS (or any other material), the solvent−ligand interaction parameter χ in the Flory−Huggins model is accessible49,63,66 which allows to balance e.g. osmotic vs van der Waals interactions.

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ASSOCIATED CONTENT

S Supporting Information *

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(1) Determination of the relative permittivity of the solvent mixtures, (2) summary of solvent compositions, (3) data on reproducibility and experimental error, (4) calculation of solvent compositions for standard titration experiments, (5) storage stability of the dried powders and proof of mass balance, (6) evaluation of classification processes, (7) parameters for redispersion by stirring and ultrasound, (8) classification results after titration with and without subsequent sonication, (9) separation sharpnesses κ and yields η obtained by titration experiments, (10) collapse of the system at high solid concentrations, (11) calculation of Hamaker constants, (12) HSP solubility mapping of ZnS QDs, and (13) solubility mapping considering HSP and Hamaker constants of particle cores. This material is available free of charge via the Internet at http://pubs.acs.org.

CONCLUSION We presented a detailed study on the classification of ZnS quantum dots (QDs) by size selective precipitation (SSP). SSP is an efficient postprocessing strategy for QDs that is based on titration of a poor solvent into an already existing dispersion. Flocculation occurs in a way that larger particles precipitate first. In the first part of our work we performed redispersion studies of dried ZnS powders using prefabricated solvent mixtures. The results already gave strong hints that the relative permittivity of the applied solvent(s) is not the only influencing factor on SSP. The chemical structure of the applied good and poor solvents is of major importance. Additionally, it was observed that with increasing energy input classification results could be improved. This is explained by the fact that with increasing intensity of the redispersion procedure more particles are available in the state of a dispersed colloid. Thus, more material takes part during the size selective reorganization into primary particles and flocs. The separation efficiency is enhanced. However, in general classification results were not convincing due to the fact that a complete redispersion of the powders was never achieved. Therefore, titration experiments were performed for which the powders were first fully redispersed in a good solvent prior to the poor solvent being added. Those experiments clearly revealed the high potential of SSP during QD processing. The distribution of one particle size x into coarse and fines was found to be independent of the washing history of the particles, the particle size distribution (PSD) of the feed, and the solid concentration. The only restriction that needs to be applied to the latter is that a critical concentration that is, however, still clearly higher than 10 g L−1 is not exceeded. From all the data it is concluded that SSP is a highly robust process which follows a

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected]; Ph +49 9131 8529404 (D.S.). *E-mail [email protected]; Ph +81 774 65 6626 (Y.M.). Author Contributions

D.S., C.L., and K.Y. contributed equally to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the funding of the Deutsche Forschungsgemeinschaft (DFG) through the Cluster of Excellence “Engineering of Advanced Materials” as well as the Federal Ministry of Economic Affairs through the Arbeitsgemeinschaft industrieller Forschungsvereinigungen “Otto von Guericke” e.V. (AiF, IGF-Vorhaben Nr. 18037 and KF L


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Classification of Zinc Sulfide Quantum Dots by Size - American

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