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Universal Parameter Optimization of Density Gradient Ultracentrifugation Using CdSe Nanoparticles as Tracing Agents Pengsong Li, Jinyang Huang, Liang Luo, Yun Kuang, and Xiaoming Sun Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b01092 • Publication Date (Web): 26 Jul 2016 Downloaded from http://pubs.acs.org on July 31, 2016
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Analytical Chemistry
Universal Parameter Optimization of Density Gradient Ultracentrifugation Using CdSe Nanoparticles as Tracing Agents Pengsong Li, Jinyang Huang, Liang Luo, Yun Kuang* and Xiaoming Sun* State Key Lab of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, China Email:
[email protected];
[email protected]. Fax: +86-10-64438991
ABSTRACT: Density gradient ultracentrifugation (DGUC) has recently emerged as an effective nanoseparation method to sort polydispersed colloidal NPs mainly according to their size differences to reach monodispersed fractions (NPs), but its separation modeling is still lack and the separation parameters’ optimization mainly based on experience of operators. In this paper, we gave mathematical descriptions on the DGUC separation, which suggested the best separation parameters for a given system. The separation parameters, including media density, centrifuge speed and time, which affected the separation efficiency, were discussed in details. Further mathematical optimization model was established to calculate and yield the “best” (optimized) linear gradient for a colloidal system with given size and density. The practical experiment results matched well with theoretical prediction, demonstrating the DGUC method an efficient, practical and predictable separation technique with universal utilization for colloid sorting.
Since different sized nanoparticles show different sizedependent properties1-8, a sample with relatively wide size distribution should be regarded as a “mixture” of many monodispersed fractions. Although significant efforts have been devoted to optimize the synthesis conditions, high quality monodisperse NPs with a strictly defined size and morphology is only available for very limited components.9-12 By-products would inevitably exist unless extremely strictly controlled synthetic conditions were applied. To get “purer” nanoparticle samples, or, in other words, to “focus” the size distribution to make strictly monodispersed samples, developing nanoseparation methods has emerged as alternative ways besides synthesis optimization.13-17 The density gradient ultracentrifugation (DGUC) method, as a general, nondestructive and scalable separation method adapted from biomacromolecular separation technology,18-20 has recently been demonstrated as an efficient way of sorting colloidal NPs according to their chemical, structural, size or morphology differences5,21-24. For instance, Hersam’s group first introduced the DGUC method to the sorting of nanostructures by isopycnic mode, they have separated carbon nanotubes according to diameter, bandgap or electronic type difference, and also graphene nanosheets with controlled thickness.25-30 Cölfen’s group have shown that DGUC could be applied to the separation of chiral compounds.31 Dai’s group have ever reported length separation of SWNTs by centrifugal rate separation to obtain ultra-short nanotubes with narrow length distribution and experimentally evidenced the band gap widening of finite length SWNTs.32 Ozin et al. have introduced rate-zonal gradient separation for obtaining monodisperse silicon nanocrystals in organic gradient.33 Hongyu Chen et al. have successfully separated gold nanoparticle clusters with different stoichiometry.23,34 Our group have introduced organic solvents35 and organic/inorganic phase interfaces36 to rate-zonal separation system for ultraconcentration and purification of various nanostructures37,38. Besides, we have devel-
oped a “lab in a tube” analytic method based on DGUC for various mechanism investigations.39,40 These early reports demonstrated wide applicability and high separation efficiency of DGUC. However, few reports discussed carefully and systematically the separation mechanism as well as separation parameters that influencing the separation results. Among the very few reports, only empirical formulas were given to describe the force balanced systems but lack versatility to force unbalanced rate-zonal systems.22 Furthermore, as far as we know, no reports have given mathematical descriptions of the DGUC separation process or could quantitatively predict the “best” separation parameters for a given system, which greatly hinders the universal utilization of density gradient ultracentrifugation method. In this paper, a strict mathematical description was set up for universal separation systems, all the parameters that influencing the separation efficiency were discussed in details, and further a mathematical optimization model was established to calculate the best separation parameters for a given prerequisite. CdSe nanoparticles41, whose photoluminescence highly depends on their size with high quantum yield, was used as labeling agent to tracing the separation efficiency and evidencing the accuracy of the model. The experimental and theoretically predicted best separation parameters coincide very well, demonstrating the accuracy of the model, and also evidencing the DGUC method describable and predictable, which would benefit future nanoseparation applications.
EXPERIMENTAL SECTION Materials: All chemical reagents purchased were A.R. grade and were used without further purification. Cadmium stearate, selenium dioxide and 1-octadecene were purchased from Sigma Aldrich, other chemical reagents were purchased from BEIJING Chemical Reagent Corporation.
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Synthesis of CdSe nanoparticles35: cadmium stearate (0.2 mmol), selenium dioxide (0.2 mmol) and 1-octadecene (12.6 mL) were added into a flask (50mL). The solution was stirred whilst heating to 240 °C with oil bath. When the color of the solution turned into green yellow, 2.0 mL oleic acid was added into the flask with a speed of 1 drop per 5 seconds, then the reaction solution was kept at 240 °C for 1 hour. After that, the solution was cooled to room temperature naturally and the obtained CdSe nanoparticles were washed using cyclohexane/ ethanol for 3 times before use. Equipment and Measurements: All density gradient ultracentrifugation (DGUC) experiments were performed on a Beckman Optima L100-XP ultracentrifuge machine using the SW60Ti rotor. Fluorescence characterization was performed on a Hitachi F-4500 spectrophotometer over the range 800 to 400 nm. Measurements on the fractions were typically performed in a 1 cm path length quartz cuvette. Density Gradient Preparation: Typically a layer step gradient was made using different concentration (by volume) of cyclohexane/carbon tetrachloride (CCl4) solutions. For example, a volume ratio of CCl4: cyclohexane=1:4 was used to make 20% solution. A step gradient was created directly in Beckman centrifuge tubes (polycarbonate, length 60 mm) by adding layers to the tube with decreasing density (i.e., lower CCl4 concentration). To make a 20%+30%+40%+50%+60% gradient, 0.85 mL of 60% cyclohexane solution of CCl4 was added to the centrifuge tube first, then 0.85 ml 50% cyclohexane solution of CCl4 was slowly layered above the 60% layer. The subsequent layers were made following the same procedure and resulted in a density gradient along the centrifuge tube. Fractionation after DGUC: The gradient media containing separated nanoparticles were manually sampled and fractionated layer by layer (each layer containing 200 µL sample) from top to the bottom of the centrifugal vessel, then each layer was characterized by fluorescence spectroscopy.
RESULTS AND DISCUSSION Centrifugal Sedimentation: In a typical DGUC separation, a thin layer of the poly-dispersed CdSe colloidal suspension is loaded on a density gradient. Particles with a given sedimentation rate, which is determined by size and shape for a given material, travel down in the centrifuge vessel to form separated zones, as shown in Scheme 1A. When the sedimentation is stopped by removing the centrifugal force, the particles are captured and sorted along the vessel.
Scheme 1 Illustration of the separation mechanism. (A) Schematic diagram of density gradient centrifugation tube, ρ: the density of medium. (B) A hydrodynamic colloidal nanoparticle model. (C) Stress analysis of the NPs in a centrifugal field.
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Density Gradient Ultracentrifugation Mechanism Liquid synthesized nanoparticles usually have a ligand protecting layer and thus can be understood as a core-shell structure, the outside layer is solvation shell. For ideal spherical nanoparticles with core density ρc, radius r, solvation shell thickness h. When the nanoparticles are dispersed in a particular solvent, the shell thickness h and density ρh can be regarded as constants. (Scheme 1B), the core-shell apparent density ρp could be estimated by:
ρ p = ρh + ( ρc − ρh ) r3 / ( r + h)
3
(1)
It can draw a conclusion from the above formula that the apparent density of colloidal particles would increase when the core size increases with respect to solution shell thickness. In our previous work, we have discussed the NP sedimentation behavior and established a dynamic sedimentation model. As shown in Scheme 1C, under collective influence of the centrifugal force Fc, buoyancy Fb and viscous resistance Ff, the movement of NPs follows the following equation (see Supporting Information for detailed modeling process):
d2 x 9η dx ρm − ρp 2 + + ω x =0 ρp d t 2 2ρp (r + h)2 dt
(2)
where x is the distance from the NP to the rotation center, η is the viscosity of the solution, ω is the angular velocity of the centrifuge, ρp is the density of the NP and ρm is the density of the solution. It should be noted that ρp was the apparent density which was calculated considering both the solid NP and its solvation layer h. According to the theory of hydromechanics, the influence of particle shape is mainly manifested in the viscous resistance when the NPs are forced to move downward the centrifuge tube, and we could introduce a factor f to correct the morphology influence for non-spherical systems.37 According to this centrifugal sedimentation mechanism42, for a given separation system with certain particle size distribution, parameters involving in the above differential equation will influence the final separation efficiency. Here, the centrifugal forces (ω2r), centrifugation time (t), density range (ρm) and gradient interface were the four main factors, which will be discussed in detail by controlling experiments in the succeeding paragraphs.
Influence of Centrifugal Force CdSe NPs were first made following slightly altered recipe reported to make poly-dispersed sample. They were used in DGUC separation because such kind of quantum dots showed obvious size-dependent luminescent properties, and fluorescence images of the centrifugal tubes after DGUC separation would be clear to show different separation efficiency, as shown in Figure 1. In order to explore factors affecting separation efficiency, we adopted the control variable method. For the centrifugal force influence, we prepared three identical samples and centrifuged them with the same time period (1.5h) but under different rotational speeds, which were 40000rpm (∼215000g), 50000rpm (∼336000g) and 60000rpm (∼485000g), respectively. The fluorescence image of the tubes after separation in
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Figure 1A showed obvious difference, revealing that the NPs located at different zones when applied to different centrifugal forces. Low centrifugal force enriched the as separated NPs at the upper part of the tube while high centrifugal force caused the NPs sediment to the bottom.
ever, at 40000 rpm, the largest CdSe NPs could only reach the location of f19 and the concentration of NPs in f13~f19 were much lower as revealed by the relatively low fluorescence intensities in Figure 1B-I. At 60000rpm, the separation was even worse, fractions with the index number larger than 17 could not be well separated as the peaks close to each other, and the fluorescence peak of f19~f23 were especially wide, indicating accumulation of several kinds of large NPs at the bottom. In order to quantitatively evaluate the separation efficiency, we introduced average deviation from ideal linear distribution (represented by the symbol Q) to compare each separation result. Q is defined as:
Figure 1 (A) Digital camera images of ultracentrifuge vessels containing CdSe nanoparticles before and after separation using a 20%-60% cyclohexane/carbon-tetrachloride gradient at 40000 rpm (vessel I), 50000 rpm (vessel II) and 60000 rpm (vessel III) for 1.5 h at 20 °C. The left images were recorded under white light; the right images were recorded under UV irradiation at 365 nm. (B) Digital camera images and (C) fluorescence spectra of fractions obtained from vessel I, II and III respectively.
After separation, the gradient media containing separated NPs was manually fractionated layer by layer into 23 fractions from top to the bottom of the centrifugal vessel, each containing 200 µL sample, as shown in Figure 1B (Enlarged figures can be found in Supporting Information, Figure S1). Under UV light, the fractions obtained from different centrifugal forces showed obvious different fluorescence intensities. At low centrifugal force (40000 rpm), the as separated nanoparticles mainly enriched in fraction 1 to fraction 12 (f1~f12), while high centrifugal force (60000 rpm) made the separated NPs concentrated in f6~f23, both of which could not separate the NPs with the highest efficiency that small NPs located at the most upper fraction while big NPs sediment to the bottom fraction. However, an intermediate centrifugal force (50000 rpm) could fractionate NPs in f2~f22, demonstrating a better separation efficiency. Fluorescence spectroscopy was also utilized to characterize the as separated fractions, as shown in Figure 1C. Separated peaks of fluorescence spectra revealed the successful separation of different sized CdSe NPs. However, the peak locations and widths revealed different separation efficiency under different centrifugal forces. Under an appropriate centrifugal force (50000 rpm), the fluorescence peaks of the fractions were well separated from 530nm to 660nm, and the peak widths were relatively narrow compared with lower or higher centrifugal forces, demonstrating that the size distributions in each fraction are narrower under 50000 rpm condition. How-
∑
(3) Where i is the fraction number, m is the starting fraction, N is the total number of fractions that contain nanoparticles after separation, ri is the average diameter of nanoparticles in fraction i, which were calculated from the fluorescence spectra using the equations reported by Peng et. al. 43, ri(ideal) is the ideal average diameter in fraction i, and it is in linear relationship to the location. Thus, the smaller the Q value of a separation, the better the separation efficiency. After calculation, it is found that separation under 50000 rpm possessed a Q value of 0.14, while 40000 rpm and 60000 rpm resulted in higher Q values (0.17 and 2.12, respectively), demonstrating 50000 rpm be the proper rotational speed under such separation condition.
Influence of Centrifugal Time Centrifugal time is another significant parameter that affecting the DGUC separation efficiency. We also prepared three identical DGUC samples and centrifuged them under the same centrifugal forces (50000rpm, ∼336000g) but with different time periods (1h, 1.5h, 2h), as shown in Figure 2.
Figure 2 (A) Digital camera images of ultracentrifuge vessels containing CdSe nanoparticles before and after separation using a 20%-60% cyclohexane/carbon-tetrachloride gradient at 50000rpm for 1h (vessel I), 1.5h (vessel II) and 2h (vessel III) respectively.
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The left images were recorded under white light; the right images were recorded under UV irradiation at 365 nm. (B) Digital camera images and (C) fluorescence spectra of fractions obtained from vessel I, II and III respectively.
It could be seen from the fluorescence images of the tubes after separation (Figure 2A) that size distributions of NPs after separation are also sensitive to the centrifugal time: for a 1.5h centrifugal period, the NPs were well separated and different sized NPs enriched the full tube; however, only 0.5h shorter or longer time resulted in enrichment of NPs on the upper and bottom parts, respectively. This trend could also be evidenced by the fluorescence images of the fractions (Figure 2B and Figure S2) after separation. Furthermore, fluorescence spectra intuitively and quantitatively revealed different separation efficiency, as shown in Figure 2C. 1.5h centrifugal time resulted in wider separated fluorescence peaks and narrow peak widths, with a Q value of 0.14. However, either shorter or longer time resulted in narrower peak range and wider peak widths of the fractions, as well as larger Q values (0.35 and 1.13, respectively), demonstrating that NPs contained in each fraction had a wider size distribution and the size difference between two neighboring fractions was not as obvious as 1.5h separation.
Influence of Density Range Besides centrifugal force and centrifugal time, density range also played an important role in DGUC separation, because the density difference between the NPs and media would affect the viscous resistance and thus influencing the separation efficiency, i.e., zonal length, as shown in Figure 3.
Figure 3 (A) Digital camera images of ultracentrifuge vessels containing CdSe nanoparticles using a 10%-50% (vessel I), 20%60% (vessel II) and 30%-70% (vessel III) cyclohexane/ carbontetrachloride gradient after separation at 50000 rpm for 1.5 h at 20 °C. The left images were recorded under white light; the right images were recorded under UV irradiation at 365 nm. (B) Digital camera images and (C) Fluorescence spectra of fractions obtained from left vessel respectively.
Under a 50000 rpm rotational speed and 1.5h centrifugal time, we varied the density range from 10%-50% (vessel I) to
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20%-60% (vessel II) and to 30%-70% (vessel III) with a 10% increasing step (Figure 3A). In the gradient with low concentration of carbon tetrachloride (10%-50%), NPs mainly sediment to the bottom of the tube, as evidenced by the fluorescence images of the tube (Figure 3A-I), which showed much higher fluorescence signal at the bottom than other two separation systems. Besides, fluorescence spectra of f23 showed much wider peak widths due to particle enrichment and particle size distribution widening, demonstrating that the sedimentation rate was too fast. Due to the enrichment of NPs, Q evaluation possessed a high value (0.244), suggesting large deviation from ideal separation. Similarly, when the concentration of carbon tetrachloride was too high (30%-70%), the sedimentation resistance was also too high to prevent NP from sedimentation, as evidenced by upper shifts and enrichment of NPs as well as a relatively large Q value (0.19). Only when DGUC separation is performed within an appropriate density range (20%-60%) we could get the best separation efficiency (Q = 0.14), that is, wide spatial distribution along the centrifuge tube and focused size distribution of each fraction.
Influence of Gradient Interface Gradient interface also affects the separation efficiency by increasing the interfacial sedimentation resistance. Figure 4 shows three systems with the same density range but containing different layers (4, 5, 6). The same amount of CdSe solution were laid on the three gradient after 1.5h standing for linearization, then DGUC was performed on these three samples under the same centrifugal parameters, as shown in Figure 4.
Figure 4 (A) Digital camera images of ultracentrifuge vessels containing CdSe nanoparticles using a 20%-60% cyclohexane/carbon-tetrachloride gradient, with 13.3% (vessel I), 10% (vessel II) and 8% (vessel III) increasing steps after separation at 50000rpm at 20 °C for 1.5h. The left images were recorded under white light; the right images were recorded under UV irradiation at 365 nm. (B) Digital camera images and (C) Fluorescence spectra of fractions obtained from left vessel respectively.
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Though the digital camera image exhibited similar separation results, fluorescence spectra combined with Q evaluation of the fractions showed obvious difference. 5 layer gradients (i.e. 5 interfaces) showed well separated peaks with a Q value of 0.14. However, when reduced the layer number to 4, fluorescence spectrum showed enrichment regions in f7-f11 and f19-f23, and in this situation the Q value increased to 0.274. Similarly, when increase the layer number to 6, the enrichment in f15~f17 and f19~f23 were more obvious and the Q value increased to 0.313. Coincidently, all these fractions meet well with the location of interfaces. This is because the interfaces could tune down the sedimentation rate of NPs, and meanwhile Rayleigh instability on the interfaces44,45 would cause accumulation of nanoparticles, thus resulting in enrichment and polydispersity in the fractions after separation. Since all the gradient were left standing for 1.5h for gradient linearization before the laying of CdSe nanoparticle solutions, the diffusion effect in 4 layer gradient was not as good as 5 layer one, thus the interfaces were more obvious in 4 layer gradient and accumulation of nanoparticles became more obvious. While for a 6 layer gradient, though the diffusion effect is better, the more not fully diffused interfaces would also acted on the accumulation of nanoparticles. Thus there should be a balance for layer number and diffusion time. When longer diffusion time was applied, the interface effect would not be a limitation for separation. Above analyses have shown that centrifugal parameters including centrifugal forces, centrifugation time, density range and gradient interface could influence the final DGUC separation efficiency. However, previous reports on density gradient centrifugation neither could give exact dynamic mathematical descriptions of the DGUC separation mechanism nor could predict the best separation parameters for a given system, especially for force unbalanced rate-zonal systems in organic media, thus it is hard for a novice operator who hasn’t so much experience to choose an appropriate separation condition. This would hinder the practical application of the DGUC method and waste time of operators. Thus, in the succeeding pages, we will focus on the DGUC mathematical optimization to make such method efficient, practical and predictable.
where ω is the stable angular speed of the centrifuge after accelerating process, T0, T1 and T2 are the durations of accelerating, separation and moderating processes. In our CdSe NPs separation system, we chose cyclohexane and carbon tetrachloride as the density gradient, whose viscosities are 0.977mPa·S and 0.978mPa·S respectively at 20 ºC. Since their viscosities are almost the same, we assume the viscosity of density gradient is constant (η=0.9775mPa·S). In order further to simplify the optimization model, we assumed that the ideal distribution of the fractions after DGUC separation was linear: X(r) = ar + b (5) where X is the position of the particle with diameter of r, a and b are linear constants. As illustrated above, the gradient interfaces would influence the sedimentation resistance a little, thus in order to get better separation and meanwhile simplify the calculation, we assumed that the ideal density gradient was linear: + (6) where x is the distance between rotation center and the gradient with a density of ρm, c and d are linear constants. Actually, we could obtained a near linear gradient after 1.5h standing of the gradient (Figure S6), thus above hypothesis could be realized. Therefore, based on above modeling, the location of a nanoparticle with a diameter of r is the function of separation time T0, T1, T2, separation speed ω (i.e. centrifugal force), gradient ρm and media viscosity η. The location of a NP with diameter of r could be described as X(T0, T1, T2, ω, d, c, a, b, η ). The position X of a particle at moment t could be calculated by the following differential equation when the initial states were given. There are two initial conditions when the separation starts: the nanoparticles’ initial position is x0 and initial velocities are 0. So we could get the following conditional equation:
Mathematical Optimization of DGUC Separation
Because the viscosity of the density gradient was constant in our system, the influence of the viscosity could be ignored. Then optimization could be carried out using above X value. The objective function of the least square optimization model was set up as:
First, we define the best separation as: spatial size distribution of the as separated NPs along the centrifugal tube is linear with smallest and biggest NPs located at the top and bottom of the centrifugal tube; each fraction shows the narrowest fluorescence peak. In order to make the simulation close to reality, we considered the centrifugal accelerating and decelerating process and the following function was used as angular speed.
ω t T0 ω(t) = ω ω T0 +T1 +T2 −t T2
（0
