Quantitative Evaluation of Fullerene Separation by Liquid

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Cite This: J. Phys. Chem. C 2019, 123, 16747−16756

Quantitative Evaluation of Fullerene Separation by Liquid Chromatography Sebastian Süß,†,‡,⊥ Vanessa Michaud,†,‡,⊥ Konstantin Amsharov,§ Vladimir Akhmetov,§ Malte Kaspereit,∥ Cornelia Damm,†,‡ and Wolfgang Peukert*,†,‡

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†

Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany ‡ Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstraße 9a, 91058 Erlangen, Germany § Chair of Organic Chemistry II, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Nikolaus-Fiebiger-Straße 10, 91058 Erlangen, Germany ∥ Institute of Separation Science and Technology (TVT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Egerlandstraße 3, 91058 Erlangen, Germany S Supporting Information *

ABSTRACT: Although a huge number of facile synthesis methods for nanoparticles (NPs) do exist, the products usually exhibit a distribution in particle size and shape. Thus, a separation step needs to be applied to adjust the particle properties according to the needs of the later application. Chromatography is a potentially scalable separation method which is well-established for separating molecules and promising for classifying NPs by size. Herein, we lay the foundations of particle chromatography by studying the separation of a C60/C70 fullerene mixture as well-defined particle probes using a pyrene-functionalized silica stationary phase. C60 fullerenes are perfect model particles as they are spherical, roughly 1 nm in diameter, interacting via van der Waals interactions only. First, we extract the Henry coefficients for C60 and C70 fullerenes from the elution behavior of the fullerene mixture. Using a particle-wall as well as particle-particle model for the van der Waals interaction potential, we determine the Hamaker constant of the stationary phase material from the measured Henry coefficients. Moreover, we investigate the concentration-dependent diffusion and mass transport in the column by quantitative evaluation of the flow rate dependent elution behavior of the fullerenes. Our study shows the huge potential of chromatography for the separation of nanoparticles and demonstrates the strength of physical-chemical concepts for the quantitative analysis and the prediction of nanoparticle classification.

1. INTRODUCTION Particles and especially nanoparticles (NPs) are an important class of materials with application in various fields ranging from electronics to medicine.1,2 To adjust the final properties and to obtain high-quality products, a defined and narrow particle size distribution (PSD) is desired, since even a small change in PSD can have a large impact on their properties.3,4 Although most of the particle formation processes (i.e., top-down processes or bottom-up synthesis) are continuously improved to produce well-defined NPs, usually a classification step is mandatory in most cases. Whereas high precision synthetic protocols are employed at the small scale, the scale-up of these processes typically leads to broader size and morphology distributions and, thus, to less-defined particle properties. As most technically relevant classification techniques, e.g., deflector wheel classifiers5,6 and gas cyclone7,8 in the gas phase or centrifuges9 and hydrocyclones7 in the liquid phase are restricted to particle sizes above 1 μm, feasible techniques for © 2019 American Chemical Society

the separation of NPs in technical scale need to be developed. Noteworthy, a few techniques for the classification of NPs like electrophoresis,10 mobility analysis,11 and analytical ultracentrifugation (AUC)12−14 do exist; however, they are mainly restricted to the labscale with very small throughput. Attempts to scale-up bowl centrifuges are promising but still restricted to liter-scale.15 Segets et al.16 used the technique of size-selective precipitation (SSP)17,18 to classify particles smaller than 5 nm. This separation method is based on the size-dependent van der Waals attraction and can be potentially applied in preparative scale. Unfortunately, it is limited to a defined set of materials, i.e., semiconductor NPs with strongly adsorbed Received: April 8, 2019 Revised: May 29, 2019 Published: June 17, 2019 16747

DOI: 10.1021/acs.jpcc.9b03247 J. Phys. Chem. C 2019, 123, 16747−16756

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The Journal of Physical Chemistry C

almost empirically and the separation of fullerenes is mostly described in a qualitative way only. In few papers the chromatographic separation of C60/C70 fullerenes was studied in more detail: Thermodynamic parameters were extracted from the temperature dependence of the retention factors.40,42−45 Moreover, Guillaume et al. were able to predict the retention factors of C60 and C70 fullerenes for a C18 stationary phase and alcohol/water mixtures as mobile phases from a thermodynamic model.44 As expected, the retention time of fullerenes was found to become shorter if the solubility in the mobile phase increases.42,45 The group of Guillaume explained the influence of mobile phase composition on the fullerene retention time by a geometric model based on the surface tension which links the retention factors with the fullerene curvature. From evaluation of the flow rate depending retention behavior of C60 and C70 fullerenes on different stationary phase materials by Knox plots, it was concluded that the mass transfer of fullerenes from the mobile to the stationary phase dominates the column efficiency.45,49 Values for the different mass transfer processes (axial, pore and film diffusion), however, were not determined. In this study we apply quantitative evaluation methods from chromatography and particle technology to describe the fullerene separation. Therefore, we first investigate the elution behavior of a C60/C70-fullerene mixture to determine the Henry coefficients of both fullerenes. We estimate the Hamaker constant of the stationary phase material from the interaction potential determined from the Henry coefficients33 Then, we study the elution behavior by variation of the flow rate in order to evaluate the separation quantitatively with respect to diffusion and mass transport by extracting the axial and the pore diffusivities from the van Deemter curves. Finally, we use a theoretical approach to model the chromatograms, which describes the experimental retention behavior, quantitatively demonstrating the huge potential of interaction chromatography for the separation of small NPs in nonpolar media, i.e., carbon allotropes or quantum dots with hydrophobic surface modification. Thus, material properties of the stationary phase as well as information on the mass transport of the particulate systems become accessible using liquid interaction-based chromatography.

ligands at the particle surface, and it requires large amounts of solvent mixtures. In contrast, chromatographic techniques are well established in biotechnology and polymer science for the separation of macromolecules like proteins (particle size 1.5 (black dashed line in Figure 2c) for a

Table 2. Coefficients of van Deemter Equation and Transport Coefficients: Dm Calculated from AUC Measurements; Dax and Dp Calculated from the van Deemter Equation for C60 and C70 Fullerenes (Concentration 0.1 g L−1, Flow Rate 1 mL min−1) fullerene C60 C70

A/cm 0.00122 0.00045

C/s 0.0077 0.0057

Dm/cm2 s−1

Dax/cm2 s−1

DP/cm2 s−1

−6

−5

4.5 × 10−7 6.0 × 10−7

8.76 × 10 8.45 × 10−6 16752

10.4 × 10 4.2 × 10−5

DOI: 10.1021/acs.jpcc.9b03247 J. Phys. Chem. C 2019, 123, 16747−16756

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The Journal of Physical Chemistry C

Figure 4. Theoretically calculated chromatograms for C60 (blue dashed line) and C70 (green dashed dotted line) and comparison to measured chromatogram (black solid line) for a flow rates of (a) 0.6, (b) 0.8, (c) 1.0, and (d) 1.3 mL min−1.

diffusion coefficients DP are less concentration-dependent than the axial diffusion coefficients Dax. One possible explanation could be that the concentration within the pores is limited by the pores itself, as the inflow is limited by the pore size and the particles which may block the pores. In summary, we showed that quantitative methods can be applied to the separation of a particle-like fullerene mixture in order to quantify van der Waals interactions, to measure Hamaker constants of the stationary phase and to evaluate transport processes acting during chromatographic separation. The obtained results indicate that peak broadening for the two fullerenes in the investigated range of conditions is dominated by axial dispersion for low flow rates, and by mass transfer resistances for higher flow rates. In the next step, we calculated chromatograms in order to describe the experimental results by a theoretical model. 3.4. Theoretical Description of Chromatograms. We used an equation for a Gaussian distribution (15) to calculate the chromatograms and compare the equation with the measured data. Therefore, exemplarily, the chromatograms obtained for the flow rates of 0.6, 0.8, 1.0, and 1.3 mL min−1 and a total concentration of C60 and C70 of 1.0 g L−1 were used. For the C60/C70 concentration ratio the values given by the manufacturer (i.e., 77% C60 and 22% C70) were used. The calculated chromatograms of C60 and C70 are shown in Figure 4a−d. The theoretical calculated chromatograms of C60 (blue dashed line) and C70 (green dashed dotted line) in comparison to the measured data (black solid line) for exemplarily chosen flow rates of 0.6 mL min−1, 0.8 mL min−1, 1.0 mL min−1 and 1.3 mL min−1 fit well to the measured data. The calculated chromatogram for C60 slightly overestimates the measured one, while the calculated chromatogram for C70 underestimates the measured data. The reason could be that the real C70/C60 concentration ratio differs slightly from the supplier data. Nevertheless, the shape of the peaks can be depicted and calculated by applying the simplified method assuming a Gaussian peak.

analytical ultracentrifugation. The obtained single contributions and the calculated transport coefficients are depicted in Table 1 and 2 for the concentrations 1.0 and 0.1 g L−1, respectively. The calculated molecular diffusion coefficient Dm for factor B is only slightly larger for C60 than the value for C70, which is line with the theory due to the smaller hydrodynamic radius of C60 particles. The deviation of Dm of both concentrations results from the concentration dependency of the AUC measurement due to molecular interactions. The calculated axial diffusion coefficient Dax at a flow rate of 1 mL min−1 and a fullerene concentration of 1.0 g L−1 for C60 is 4 times larger than that for C70. This result is, however, surprising as it is expected that C60 and C70 show very similar Dax values due to very similar structure and sizes. In an approximation from Chung and Wen, Dax was calculated for both fullerenes to 2.4 × 10−4 cm2 s−1, which is in line with the measurement for 1 g L−1.42 However, by using a smaller concentration of 0.1 g L−1, the difference of the axial diffusion coefficient Dax for C60 to C70 decreases to a factor of 2.5 and the values are overall smaller. At this point, it must be noted that the concentration of C60 is roughly 4 times higher than the concentration of C70. Thus, the effect of concentration on Dax is stronger for C60 in comparison to C70. Therefore, it is clear that the values of Dax of C60 and C70 depend enormously on concentration. As a higher concentration impedes the free flow of particles, the contribution of accumulation effects and interaction forces increase. Hence, a better approximation of Dax for C60 to C70 might be possible by using lower concentrations than 0.1 g/L. However, the peak signal-tonoise ratio meets its limit at 0.1 g/L for a proper evaluation. Finally, eqs 13 and 14 were used to determine the pore diffusion coefficient DP from the factor C, while a smaller Dp was obtained for C60 compared to C70 for both high and low concentrations (Table 1 and 2). The larger pore diffusion coefficient of C70 compared to C60 can be explained by size exclusion effects since C60 can enter smaller pores; i.e., the C60 “feels” more confinement than C70. The obtained pore 16753

DOI: 10.1021/acs.jpcc.9b03247 J. Phys. Chem. C 2019, 123, 16747−16756

Article

The Journal of Physical Chemistry C Accordingly, we showed that the chromatographic separation of C60/C70 mixture can be described very well by theoretical calculations. In combination with the quantitative evaluation of chromatograms, our work demonstrates that HPLC is a promising method for the continuous, postsynthetic separation of nanoparticles.

Author Contributions

4. CONCLUSIONS We studied the chromatographic separation of a C60/C70 fullerene mixture as a model system for nanoparticles and applied evaluation methods known from separation engineering to describe the fullerene separation quantitatively. First, we determined Henry coefficients to determine the Hamaker constant of the stationary phase material. This allows the determination of the Henry coefficients and thus the adsorption behavior at low coverage. Afterward, we showed the high reproducibility by evaluating the elution behavior with variation of fullerene concentration. In order to quantitatively evaluate the separation with respect to diffusion and mass transport, we examined the elution of fullerene at different flow rates by using two different fullerene concentrations. Therefrom, the van Deemter curves and the single contributions to axial dispersion and mass transfer resistance were estimated. Moreover, it could be shown, that the axial dispersion and pore diffusion strongly depend on the fullerene concentration. These effects are not yet understood and will be studied in future also for other particle systems. This issue will be a key for the realization of technical processes for nanoparticle classification. Finally, the calculated chromatograms agree very well with the measurements showing the large potential of chromatography for particle separation. With the quantitative description of the separation and thus knowing the Henry coefficients, fullerenes can be used as probe systems to characterize stationary phase materials. Furthermore, as the Henry coefficient is connected with the interaction potential and thus the Hamaker constant, material parameters of the stationary phase materials become accessible. Additionally, this method can now be transferred to the interaction-based chromatography of particulate systems, e.g., carbon allotropes and quantum dots.

Notes

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This manuscript was written through contribution of all authors. All authors have given approval to the final version of the manuscript. Author Contributions ⊥

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the Deutsche Forschungsgemeinschaft (DFG) within the priority program SPP 2045 (PE427/ Project C8) and by the Collaborative Research Centre SFB953: “Synthetic Carbon Allotropes” (Project Number 182849149). Moreover, we acknowledge the Federal Ministry of Economic Affairs through the Arbeitsgemeinschaft industrieller Forschungsvereinigungen “Otto von Guericke” e.V. (AiF, Project No. 18037 N).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b03247.

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These authors contributed equally.

Section S1, peak areas and peak widths of fullerene separation; section S2, chromatograms of fullerene separation for He coefficient evaluation; section S3, chromatograms of fullerene separation with varying flow rate; and section S4, retention time, peak width, and resolution in dependence on flow rate for the fullerene concentration 0.1 gL−1 (PDF)

AUTHOR INFORMATION

Corresponding Author

*(W.P.) E-mail: [email protected]. Telephone: +49 9131 85 29401. ORCID

Konstantin Amsharov: 0000-0002-2854-8081 Wolfgang Peukert: 0000-0002-2847-107X 16754

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DOI: 10.1021/acs.jpcc.9b03247 J. Phys. Chem. C 2019, 123, 16747−16756