**Enhancing Photoluminescence Quenching in Donor–Acceptor PCE11:PPCBMB Films through the Optimization of Film Microstructure**

**Otto Todor-Boer 1,2,3, Ioan Petrovai 1,2, Raluca Tarcan 1,2, Adriana Vulpoi <sup>1</sup> , Leontin David <sup>2</sup> , Simion Astilean 1,2 and Ioan Botiz 1,\***


Received: 6 November 2019; Accepted: 5 December 2019; Published: 10 December 2019

**Abstract:** We show that a precise control of deposition speed during the fabrication of polyfullerenes and donor polymer films by convective self-assembly leads to an optimized film microstructure comprised of interconnected crystalline polymer domains comparable to molecular dimensions intercalated with similar polyfullerene domains. Moreover, in blended films, we have found a correlation between deposition speed, the resulting microstructure, and photoluminescence quenching. The latter appeared more intense for lower deposition speeds due to a more favorable structuring at the nanoscale of the two donor and acceptor systems in the resulting blend films.

**Keywords:** conjugated polymers; polyfullerenes; processing by convective self-assembly; thin films and microstructure; photoluminescence quenching

#### **1. Introduction**

Nowadays, alternative renewable energy sources are becoming essential in our society, and organic photovoltaics (OPVs) could become in the near future a viable technological solution for continuously increasing societal energy needs. OPVs are based on semiconducting conjugated materials, and at the moment, they can convert solar energy into electricity with a power conversion efficiency of about 16.5% [1]. Researchers have shown in this last decade that in order to make efficient OPVs, one has to manipulate a series of internal fundamental phenomena that occur in the active layer such as exciton diffusion and separation [2,3], charge transport and carrier migration [4,5], or exciton and charge recombination [6] directly by controlling the microstructure of the active layer from nano- to micro- and up to the macroscale [4,6–10]. Thus, a fine control over the microstructure in the active layer is expected to tune the resulting optoelectronic properties, including the emission properties. For instance, because photoluminescence (PL) quenching is a measure of excitons separation at the donor–acceptor interfaces [11], it is important to maximize PL quenching between the donor and the acceptor materials when fabricating OPVs.

In the literature, researchers have described many efficient techniques that can be used to control more or less molecular conformations and microstructure in the active layer [12–20] and thus, to efficiently tune the emission/quenching properties [21,22]. These techniques also include convective self-assembly (CSA), which is a blade coating type technique [23] that can permit the specific control

of the backbone/chain conformation by favoring more planarized polymer structures [24]. CSA is a specific methodology that is used to deposit colloidal solutions onto solid substrates. With CSA, by precisely controlling the deposition temperature and the specific tilt angle of the deposition 'blade' of the used coater, the forces acting at the triple air–substrate–solution interface can be manipulated while the solution is cast onto a carrier moving with controlled speed. As a consequence, CSA can allow us to control solvent evaporation rate and thus can be adapted to fabricate uniform, structured films using both oligomeric and macromolecular species. and polyfullerenes and thus, under specific CSA casting conditions, to control the size of resulting alternating donor–acceptor domains. Indeed, the deposition of PCE11:PPCBMB blended films using the CSA technique led to a film microstructure that could be differentiated from that obtained in spin-cast analogue films (Figure 1). On the surface of the film prepared by CSA, brighter crystalline regions are alternating with wide darker regions (Figure 1c–e). We attribute these crystalline structures to the electron donor PCE11, which is a polymer system that is known for its high crystallinity and preferential face-on orientation of domains [25]. Note that generally, crystalline phases can be identified when using both AFM topographic (height mode) and viscoelastic (phase mode) images simultaneously [29–31].

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Here, we employ CSA technique at various deposition speeds to produce donor–acceptor thin films of poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,30 -di(2-octyldodecyl)2,20 ;50 ,20 ; 5 0 ,20 -quaterthiophen-5,50 -diyl)] (PCE11; Figure 1a) and poly{[bispyrrolidino (phenyl-C61-butyric acid methyl ester)]-alt-[2,5-bis(octyloxy)benzene]} (PPCBMB; Figure 1b) that exhibit much higher PL quenching than their PCE11:PPCBMB analogues made by the spin-casting technique. As revealed by atomic force microscopy (AFM), this higher PL quenching is related to the changes in film microstructure induced upon film deposition using CSA. Our results are of importance in the OPVs field, as PCE11 and fullerenes are promising materials for organic solar cell fabrication [25–27]. Topography involves giving information about the surface profile/roughness while the phase is able to judge the structure of different material phases such as material softness/stiffness. As PCE11 is crystalline, i.e., stiffer material, it appears brighter in AFM phase images. Darker, most probably amorphous regions correspond to the electron acceptor PPCBMB. Moreover, these narrow crystalline domains displaying several tens of nanometers in lateral size are both randomly oriented and wellinterconnected, forming complex crystalline networks (an example of such a network is delimited by dotted lines in Figure 1c) surrounded by PPCBMB regions. Instead, when analyzing the spin-cast film, we have noticed the presence of crystalline structures of various sizes ranging from very small (~0.05 ± 0.02 µm2) to much bigger structures (~0.55 ± 0.2 µm2). No matter their size, these structures were separated from each other and surrounded by much narrower PPCBMB regions (Figure 1f–h).

Therefore, they appeared rather disconnected, as indicated by the dotted lines in Figure 1f.

**Figure 1.** (**a**,**b**) Chemical structure of poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,30 -di(2 octyldodecyl)2,20 ;50 ,20 ; 50 ,20 -quaterthiophen-5,50 -diyl)] (PCE11) (**a**) and poly{[bispyrrolidino (phenyl-C61-butyric acid methyl ester)]-alt-[2,5-bis(octyloxy)benzene]} (PPCBMB) (**b**) systems. Topography (**c**) and phase (**d**) atomic force microscopy (AFM) images of a PCE11:PPCBMB thin film prepared using convective self-assembly (CSA) at a casting speed of 10 µm/s. (**e**) Zoom-in of the image shown in (**d**). Topography (**f**) and phase (**g**) AFM images of a PCE11:PPCBMB as spin cast film. (**h**) Zoom-in of the image shown in (**g**). Dotted lines are for eye guiding only and are indicating various PCE11 structures.

#### **2. Materials and Methods**

PCE11 of a weight-average molecular weight M<sup>w</sup> = 112.707 kg/mol, number-average molecular weight M<sup>n</sup> = 55.674 kg/mol, and polydispersity index PDI = 2.02 was purchased from Ossila Ltd. (Sheffield, UK) PPCBMB of a weight-average molecular weight M<sup>w</sup> ≈ 73.8 kg/mol, number-average molecular weight M<sup>n</sup> ≈ 24.6 kg/mol and poly dispersity index PDI = 3 was obtained from sterically controlled azomethine ylide cycloaddition polymerization of the phenyl-C61-butyric acid methyl ester (PCBM) as described elsewhere [28].

Thin films of PCE11 and PPCBMB were made by spin casting at 2000 rpm from 6 g/L chlorobenzene solution (with the resulting film thickness of about 80 ± 8 nm) as well as by CSA at deposition speeds of 1000 µm/s, 500 µm/s, 100 µm/s, 50 µm/s, 25 µm/s, and 10 µm/s respectively (with the resulting film thickness varying between 30 ± 5 nm and 140 ± 15 nm, respectively). A 50/50 weight percentage ratio was used to obtain solutions of PCE11:PPCBMB blend. Films of PCE11:PPCBMB were also made employing the above described procedure. For all films, regular UV–ozone cleaned microscopy cover glass was used as substrate.

The CSA coater was comprised of a motorized translation stage using a linear actuator from Zaber Technologies and moving with speeds ranging between ~4.7 µm/s and 8 mm/s. A temperature controller was placed on top of the translation stage, and the temperature of the substrate was regulated between 17 ◦C and 24 ◦C using a water-controlled system (Accel 250 LC from Thermo Scientific). A cover glass that acted as a blade was fixed in the near vicinity of the substrate at the desired angle; the polymer solution was placed on the substrate, underneath and near the edge of the blade. This configuration allowed us to precisely control both the deposition speed and the temperature of the substrate.

For the acquisition of AFM images, an Alpha 300A microscope from Witec was used in tapping mode. PL spectra were collected using an FP-6500 Spectrofluorometer from Jasco (excitation wavelength range of 220–750 nm). All PL spectra were recorded using an excitation wavelength of 640 nm.

#### **3. Results and Discussion**

Most of the work performed on OPVs has focused on film microstructures resulted by blending conjugated donor polymers with various fullerenes. Obtained microstructures most often were characterized by the existence of randomly alternating donor and acceptor domains, each greatly varying in size. Aiming to gain control over molecular packing at the nanoscale, we have decided in this work to replace fullerenes with polyfullerenes and to blend them with a crystalline PCE11 polymer system. This way, we expected to stimulate the phase separation process between polymer and polyfullerenes and thus, under specific CSA casting conditions, to control the size of resulting alternating donor–acceptor domains.

Indeed, the deposition of PCE11:PPCBMB blended films using the CSA technique led to a film microstructure that could be differentiated from that obtained in spin-cast analogue films (Figure 1). On the surface of the film prepared by CSA, brighter crystalline regions are alternating with wide darker regions (Figure 1c–e). We attribute these crystalline structures to the electron donor PCE11, which is a polymer system that is known for its high crystallinity and preferential face-on orientation of domains [25]. Note that generally, crystalline phases can be identified when using both AFM topographic (height mode) and viscoelastic (phase mode) images simultaneously [29–31]. Topography involves giving information about the surface profile/roughness while the phase is able to judge the structure of different material phases such as material softness/stiffness. As PCE11 is crystalline, i.e., stiffer material, it appears brighter in AFM phase images. Darker, most probably amorphous regions correspond to the electron acceptor PPCBMB. Moreover, these narrow crystalline domains displaying several tens of nanometers in lateral size are both randomly oriented and well-interconnected, forming complex crystalline networks (an example of such a network is delimited by dotted lines in Figure 1c) surrounded by PPCBMB regions. Instead, when analyzing the spin-cast film, we have noticed the presence of crystalline structures of various sizes ranging from very small (~0.05 <sup>±</sup> 0.02 <sup>µ</sup>m<sup>2</sup> ) to much

bigger structures (~0.55 <sup>±</sup> 0.2 <sup>µ</sup>m<sup>2</sup> ). No matter their size, these structures were separated from each other and surrounded by much narrower PPCBMB regions (Figure 1f–h). Therefore, they appeared rather disconnected, as indicated by the dotted lines in Figure 1f. in (**d**). Topography (**f**) and phase (**g**) AFM images of a PCE11:PPCBMB as spin cast film. (**h**) Zoom-in of the image shown in (**g**). Dotted lines are for eye guiding only and are indicating various PCE11 structures.

using convective self-assembly (CSA) at a casting speed of 10 µm/s. (**e**) Zoom-in of the image shown

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**Figure 1.** (**a**–**b**) Chemical structure of poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,3′-di(2 octyldodecyl)2,2′;5′,2′; 5′,2′-quaterthiophen-5,5′-diyl)] (PCE11) (**a**) and poly{[bispyrrolidino (phenyl-C61-butyric acid methyl ester)]-alt-[2,5-bis(octyloxy)benzene]} (PPCBMB) (**b**) systems. Topography

Furthermore, the ratio between the area of crystalline PCE11 (~57% of the total surface) and the area of amorphous PPCBMB (~43% of the total surface) regions was about 1.32 for the film produced using CSA. In comparison, for the spin-cast film, this ratio was about 4 (with 80% of the surface covered by crystalline regions and 20% of the surface covered by amorphous regions). Although AFM measurements do not exclude the existence in both films of regions with intercalated PCE11 and PPCBMB molecules, it appears that the microstructure optimized using CSA was roughly comprised of interconnected, crystalline electron donating domains displaying a width comparable to molecular dimensions that were intercalated with similar electron-accepting domains. The above described microstructure could be much altered by increasing the CSA casting speed to, for example, 1000 µm/s. In these conditions, micrometer large crystalline regions of pure PCE11 were formed, and they were separated from intermixed regions containing small structures of both PCE11 and PPCBMB systems (Figure 2). Furthermore, the ratio between the area of crystalline PCE11 (~57% of the total surface) and the area of amorphous PPCBMB (~43% of the total surface) regions was about 1.32 for the film produced using CSA. In comparison, for the spin-cast film, this ratio was about 4 (with 80% of the surface covered by crystalline regions and 20% of the surface covered by amorphous regions). Although AFM measurements do not exclude the existence in both films of regions with intercalated PCE11 and PPCBMB molecules, it appears that the microstructure optimized using CSA was roughly comprised of interconnected, crystalline electron donating domains displaying a width comparable to molecular dimensions that were intercalated with similar electron-accepting domains. The above described microstructure could be much altered by increasing the CSA casting speed to, for example, 1000 µm/s. In these conditions, micrometer large crystalline regions of pure PCE11 were formed, and they were separated from intermixed regions containing small structures of both PCE11 and PPCBMB systems (Figure 2).

**Figure 2.** Topography (**a**) and phase (**b**) AFM images of a PCE11:PPCBMB thin film prepared by CSA at a deposition speed of 1000 µm/s. (**c**) Zoom-in of an intermixed region shown in (**b**). **Figure 2.** Topography (**a**) and phase (**b**) AFM images of a PCE11:PPCBMB thin film prepared by CSA at a deposition speed of 1000 µm/s. (**c**) Zoom-in of an intermixed region shown in (**b**).

Since PL quenching is a measure of exciton separation at the donor–acceptor interfaces, we have further compared the emission properties of the two films presented in Figure 1. We have found that there was a 65% PL quenching in the film produced using CSA compared to only a 25% PL quenching measured for the spin-cast film (Figure 3a). There are two reasons that could explain these rather low PL quenching values measured for PCE11:PPCBMB films. One reason is related to the lower unoccupied molecular orbital (LUMO) of PCE11 (−3.69 eV [25]) and of PPCBMB (−3.34 eV [28]) systems that are not necessarily favoring charge transfer (nonetheless, charge transfer conditions could still be fulfilled, because LUMO levels could be slightly modified when blending the two systems [32]). The other reason is related to the fact that long chains of polyfullerenes are more difficult to intercalate in between PCE11 polymer chains to form PCE11:PPCBMB co-crystalline domains, which could favor excitons generation/separation due to close molecular packing [32]. Since PL quenching is a measure of exciton separation at the donor–acceptor interfaces, we have further compared the emission properties of the two films presented in Figure 1. We have found that there was a 65% PL quenching in the film produced using CSA compared to only a 25% PL quenching measured for the spin-cast film (Figure 3a). There are two reasons that could explain these rather low PL quenching values measured for PCE11:PPCBMB films. One reason is related to the lower unoccupied molecular orbital (LUMO) of PCE11 (−3.69 eV [25]) and of PPCBMB (−3.34 eV [28]) systems that are not necessarily favoring charge transfer (nonetheless, charge transfer conditions could still be fulfilled, because LUMO levels could be slightly modified when blending the two systems [32]). The other reason is related to the fact that long chains of polyfullerenes are more difficult to intercalate in between PCE11 polymer chains to form PCE11:PPCBMB co-crystalline domains, which could favor excitons generation/separation due to close molecular packing [32].

Moreover, PL quenching was dependent on the CSA deposition speed (and less dependent on the temperature at which the substrate was kept during casting), i.e., on the type of the resulting microstructure (Figure 3b). Thus, we attribute this improvement of PL quenching from 25% to 65% to the optimization of the film microstructure through the realization of alternating donor and acceptor domains comparable to molecular dimensions and displaying a much larger interface area that favors stronger polymer–polyfullerene quencher interactions. Similar results were obtained for several other blends when replacing PCE11 with other conjugated polymer donor systems such as poly[2,5-bis(3-alkylthiophen-2-yl)thieno(3,2-b)thiophene] (PBTTT), poly(3-(20 -ethyl)hexyl-thiophene) (P3EHT), poly (3-hexylthiophene) (P3HT), or poly(3-hexyl)selenophene (P3HS) (Figure 3c), indicating an extended applicability of the CSA technique in the processing of PPCBMB-based blends.

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**Figure 3.** (**a**) Photoluminescence (PL) spectra of PCE11 and PCE11:PPCBMB films deposited by spin casting and CSA. (**b**) Amount of PL quenching in PCE11:PPCBMB films deposited by spin casting and CSA at 17 °C and 21 °C using various casting speeds. (**c**) Amount of PL quenching measured in various PPCBMB based blends that were deposited by spin casting and CSA at low casting speeds. **Figure 3.** (**a**) Photoluminescence (PL) spectra of PCE11 and PCE11:PPCBMB films deposited by spin casting and CSA. (**b**) Amount of PL quenching in PCE11:PPCBMB films deposited by spin casting and CSA at 17 ◦C and 21 ◦C using various casting speeds. (**c**) Amount of PL quenching measured in various PPCBMB based blends that were deposited by spin casting and CSA at low casting speeds.

Moreover, PL quenching was dependent on the CSA deposition speed (and less dependent on the temperature at which the substrate was kept during casting), i.e., on the type of the resulting microstructure (Figure 3b). Thus, we attribute this improvement of PL quenching from 25% to 65% to the optimization of the film microstructure through the realization of alternating donor and acceptor domains comparable to molecular dimensions and displaying a much larger interface area that favors stronger polymer–polyfullerene quencher interactions. Similar results were obtained for several other blends when replacing PCE11 with other conjugated polymer donor systems such as poly[2,5-bis(3-alkylthiophen-2-yl)thieno(3,2-b)thiophene] (PBTTT), poly(3-(2′-ethyl)hexylthiophene) (P3EHT), poly (3-hexylthiophene) (P3HT), or poly(3-hexyl)selenophene (P3HS) (Figure 3c), indicating an extended applicability of the CSA technique in the processing of PPCBMB-based In order to further point out the efficiency of the CSA technique to induce structural changes in conjugated polymer/polyfullerene films, we have further investigated neat films of both PCE11 and PPCBMB. The results showed again that we can differentiate the microstructure of a PCE11 film that was deposited using CSA (Figure 4a–c) with respect to a PCE11 film that was simply spin cast (Figure 4d–f). The PCE11 film deposited using CSA at low casting speed displayed uniform granular structures that were often interconnected into rather elongated superstructures (indicated in Figure 4c by the broken lines) with a width of several tens of nanometers. Instead, the spin-cast film exhibited a microstructure that was comprised of many aggregated structures (indicated by the broken shapes in Figure 4f) randomly distributed on the surface along with much smaller granular structures. *Nanomaterials* **2019**, *9*, x FOR PEER REVIEW 6 of 10

**Figure 4.** Topography (**a**) and phase (**b**) AFM images of a PCE11 thin film made by CSA at a low deposition speed of 10 µm/s. (**c**) Zoom-in of the image shown in (**b**). Topography (**d**) and phase (**e**) AFM images of a PCE11 as spin-cast film. (**f**) Zoom-in of the image shown in (**e**). Broken lines and shapes are for eye guiding only. **Figure 4.** Topography (**a**) and phase (**b**) AFM images of a PCE11 thin film made by CSA at a low deposition speed of 10 µm/s. (**c**) Zoom-in of the image shown in (**b**). Topography (**d**) and phase (**e**) AFM images of a PCE11 as spin-cast film. (**f**) Zoom-in of the image shown in (**e**). Broken lines and shapes are for eye guiding only.

by CSA at high and low deposition speeds respectively, we have noticed that the microstructure of PCE11 film deposited at high CSA speed was comprised of both bigger aggregates (indicated by dotted shapes) and smaller granular structures (Figure 6b). In this latter case, the obtained microstructure was similar to that observed for the as spin-cast PCE11 film (Figure 6a). In contrary, as already shown in Figure 4a–c, the higher magnification AFM image of PCE11 film prepared at low CSA speed emphasized even clearer the existence of a microstructure comprised of monomodal

**Figure 5.** Topography (**a**) and phase (**b**) AFM images of a PCE11 thin film prepared by CSA at a

deposition speed of 500 µm/s. (**c**) Zoom-in of the image shown in (**b**).

(interconnected) granular structures (Figure 6c).

The microstructure obtained at low casting CSA speeds could again be altered when increasing

shapes are for eye guiding only.

The microstructure obtained at low casting CSA speeds could again be altered when increasing casting speed to, for instance, 500 µm/s (Figure 5). When we have looked into more details and compared high magnification AFM images of the three PCE11 films deposited by spin casting and by CSA at high and low deposition speeds respectively, we have noticed that the microstructure of PCE11 film deposited at high CSA speed was comprised of both bigger aggregates (indicated by dotted shapes) and smaller granular structures (Figure 6b). In this latter case, the obtained microstructure was similar to that observed for the as spin-cast PCE11 film (Figure 6a). In contrary, as already shown in Figure 4a–c, the higher magnification AFM image of PCE11 film prepared at low CSA speed emphasized even clearer the existence of a microstructure comprised of monomodal (interconnected) granular structures (Figure 6c). The microstructure obtained at low casting CSA speeds could again be altered when increasing casting speed to, for instance, 500 µm/s (Figure 5). When we have looked into more details and compared high magnification AFM images of the three PCE11 films deposited by spin casting and by CSA at high and low deposition speeds respectively, we have noticed that the microstructure of PCE11 film deposited at high CSA speed was comprised of both bigger aggregates (indicated by dotted shapes) and smaller granular structures (Figure 6b). In this latter case, the obtained microstructure was similar to that observed for the as spin-cast PCE11 film (Figure 6a). In contrary, as already shown in Figure 4a–c, the higher magnification AFM image of PCE11 film prepared at low CSA speed emphasized even clearer the existence of a microstructure comprised of monomodal (interconnected) granular structures (Figure 6c).

**Figure 4.** Topography (**a**) and phase (**b**) AFM images of a PCE11 thin film made by CSA at a low deposition speed of 10 µm/s. (**c**) Zoom-in of the image shown in (**b**). Topography (**d**) and phase (**e**)

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**Figure 5.** Topography (**a**) and phase (**b**) AFM images of a PCE11 thin film prepared by CSA at a deposition speed of 500 µm/s. (**c**) Zoom-in of the image shown in (**b**). **Figure 5.** Topography (**a**) and phase (**b**) AFM images of a PCE11 thin film prepared by CSA at a *Nanomaterials*  deposition speed of 500 **2019**, *9*, x FOR PEER REVIEW µm/s. (**c**) Zoom-in of the image shown in (**b**). 7 of 10

**Figure 6.** Comparison of phase AFM images of PCE11 thin films prepared by spin casting (**a**) and by CSA at a deposition speed of 500 µm/s (**b**) and of 10 µm/s (**c**). Dotted shapes are for eye guiding only. **Figure 6.** Comparison of phase AFM images of PCE11 thin films prepared by spin casting (**a**) and by CSA at a deposition speed of 500 µm/s (**b**) and of 10 µm/s (**c**). Dotted shapes are for eye guiding only.

The analysis of the PL spectra recorded for thin films of PCE11 deposited both by spin-casting and CSA techniques have further emphasized the differences in the film microstructures (Figure 7). We could notice the appearance of a red shift of ~10 nm in the main emission peak for films deposited very slowly using CSA in comparison to films spin cast or deposited via CSA but using higher casting speeds. According to the literature, these results are indicating at least that films deposited at higher speeds are comprised of polymer chains adopting less planarized (displaying more torsional disorder, i.e., shorter conjugation length) conformations of the backbone with excitons possibly experiencing a more disordered energy landscape than those cast at lower speeds [24]. The analysis of the PL spectra recorded for thin films of PCE11 deposited both by spin-casting and CSA techniques have further emphasized the differences in the film microstructures (Figure 7). We could notice the appearance of a red shift of ~10 nm in the main emission peak for films deposited very slowly using CSA in comparison to films spin cast or deposited via CSA but using higher casting speeds. According to the literature, these results are indicating at least that films deposited at higher speeds are comprised of polymer chains adopting less planarized (displaying more torsional disorder, i.e., shorter conjugation length) conformations of the backbone with excitons possibly experiencing a more disordered energy landscape than those cast at lower speeds [24].

**Figure 7.** Normalized PL spectra recorded for PCE11 thin films deposited both by spin-casting and

A further comparison of the microstructure between two films of PPCBMB obtained using CSA at low casting speed (Figure 8a–c) and spin casting (Figure 8d–f) also displayed structural differences. The microstructure of film prepared using CSA was comprised of disk-like structures of an average diameter of several tens of nanometers. Meanwhile, the microstructure of the spin-cast film was comprised of randomly distributed linear or circular fiber-like structures, with the average fiber width in the range of 20 ± 4 nm. When using CSA at higher casting speeds, a mixed microstructure comprised of both aggregated fiber-like and disk-like structures was obtained (Figure 9). Thus, similarly to PCE11, the PPCBMB system also exhibited differences in microstructure that were directly correlated to the casting techniques and conditions used for the preparation of thin films. Therefore, the above results indicate that the CSA technique is able to induce important microstructural changes in PCE11 and PPCBMB containing films, and thus that it can be efficiently

CSA techniques. The inset represents a zoom-in of the presented PL spectra.

used to control, for instance, PL quenching.

used to control, for instance, PL quenching.

experiencing a more disordered energy landscape than those cast at lower speeds [24].

**Figure 6.** Comparison of phase AFM images of PCE11 thin films prepared by spin casting (**a**) and by CSA at a deposition speed of 500 µm/s (**b**) and of 10 µm/s (**c**). Dotted shapes are for eye guiding only.

The analysis of the PL spectra recorded for thin films of PCE11 deposited both by spin-casting and CSA techniques have further emphasized the differences in the film microstructures (Figure 7). We could notice the appearance of a red shift of ~10 nm in the main emission peak for films deposited very slowly using CSA in comparison to films spin cast or deposited via CSA but using higher casting speeds. According to the literature, these results are indicating at least that films deposited at higher

**Figure 7.** Normalized PL spectra recorded for PCE11 thin films deposited both by spin-casting and CSA techniques. The inset represents a zoom-in of the presented PL spectra. **Figure 7.** Normalized PL spectra recorded for PCE11 thin films deposited both by spin-casting and CSA techniques. The inset represents a zoom-in of the presented PL spectra.

A further comparison of the microstructure between two films of PPCBMB obtained using CSA at low casting speed (Figure 8a–c) and spin casting (Figure 8d–f) also displayed structural differences. The microstructure of film prepared using CSA was comprised of disk-like structures of an average diameter of several tens of nanometers. Meanwhile, the microstructure of the spin-cast film was comprised of randomly distributed linear or circular fiber-like structures, with the average fiber width in the range of 20 ± 4 nm. When using CSA at higher casting speeds, a mixed microstructure comprised of both aggregated fiber-like and disk-like structures was obtained (Figure 9). Thus, similarly to PCE11, the PPCBMB system also exhibited differences in microstructure that were directly correlated to the casting techniques and conditions used for the preparation of thin films. Therefore, the above results indicate that the CSA technique is able to induce important microstructural changes in PCE11 and PPCBMB containing films, and thus that it can be efficiently A further comparison of the microstructure between two films of PPCBMB obtained using CSA at low casting speed (Figure 8a–c) and spin casting (Figure 8d–f) also displayed structural differences. The microstructure of film prepared using CSA was comprised of disk-like structures of an average diameter of several tens of nanometers. Meanwhile, the microstructure of the spin-cast film was comprised of randomly distributed linear or circular fiber-like structures, with the average fiber width in the range of 20 ± 4 nm. When using CSA at higher casting speeds, a mixed microstructure comprised of both aggregated fiber-like and disk-like structures was obtained (Figure 9). Thus, similarly to PCE11, the PPCBMB system also exhibited differences in microstructure that were directly correlated to the casting techniques and conditions used for the preparation of thin films. Therefore, the above results indicate that the CSA technique is able to induce important microstructural changes in PCE11 and PPCBMB containing films, and thus that it can be efficiently used to control, for instance, PL quenching. *Nanomaterials* **2019**, *9*, x FOR PEER REVIEW 8 of 10

**Figure 8.** Topography (**a**) and phase (**b**) AFM images of a PPCBMB thin film made using CSA at a low deposition speed of 10 µm/s. (**c**) Zoom-in of the image shown in (**b**). Topography (d) and phase (**e**) AFM images of a PPCBMB as spin cast film. (**f**) Zoom-in of the image shown in (e). **Figure 8.** Topography (**a**) and phase (**b**) AFM images of a PPCBMB thin film made using CSA at a low deposition speed of 10 µm/s. (**c**) Zoom-in of the image shown in (**b**). Topography (**d**) and phase (**e**) AFM images of a PPCBMB as spin cast film. (**f**) Zoom-in of the image shown in (**e**).

**Figure 9.** Topography (**a**) and phase (**b**) AFM images of a PPCBMB thin film prepared by CSA at a

deposition speed of 1000 µm/s. (**c**) Zoom-in of the image shown in (**b**).

**Figure 8.** Topography (**a**) and phase (**b**) AFM images of a PPCBMB thin film made using CSA at a low

AFM images of a PPCBMB as spin cast film. (**f**) Zoom-in of the image shown in (e).

**Figure 9.** Topography (**a**) and phase (**b**) AFM images of a PPCBMB thin film prepared by CSA at a deposition speed of 1000 µm/s. (**c**) Zoom-in of the image shown in (**b**). **Figure 9.** Topography (**a**) and phase (**b**) AFM images of a PPCBMB thin film prepared by CSA at a deposition speed of 1000 µm/s. (**c**) Zoom-in of the image shown in (**b**).

#### **4. Conclusions**

As revealed by AFM and PL spectroscopy, the quality of microstructure corresponding to thin films of PCE11 and PPCBMB depended on the casting conditions and technique. Only using CSA at low casting speed led to an optimized film microstructure that was comprised of crystalline domains of PCE11 alternated with PPCBMB amorphous regions and that exhibited strong PL quenching. These results indicate both that the microstructure of PCE11:PPCBMB films is highly sensitive to the conditions under which such films are prepared and that by carefully controlling the conditions of film preparation, we could finely tune the resulting optoelectronic properties as it is needed, for example, in OPV applications.

**Author Contributions:** I.B. and O.T.-B. designed the concept of paper. O.T.-B. conducted the experimental investigation and wrote the original draft. I.P., R.T., and A.V. participated in investigation. I.B., A.V., L.D., and S.A. reviewed and edited the final manuscript. I.B. and L.D. supervised O.T.-B.

**Funding:** This research was funded by the Romanian National Authority for Scientific Research and Innovation, CNCS – UEFISCDI, project number PN-II-RU-TE-2014-4-0013 and by the Romanian Ministry of Research and Innovation, PROINSTITUTIO project under contract nr.19PFE/17.10.2018.

**Acknowledgments:** We thank R. Hiorns (CNRS) for supplying PPCBMB.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

**Claudia Simone Plüisch, Rouven Stuckert and Alexander Wittemann \***

Colloid Chemistry, Department of Chemistry, University of Konstanz, Universitaetsstrasse 10, D-78464 Konstanz, Germany; simone.plueisch@uni-konstanz.de (C.S.P.); rouven.stuckert@uni-konstanz.de (R.S.) **\*** Correspondence: alexander.wittemann@uni-konstanz.de; Tel.: +49-(0)7531-88-5458

**Abstract:** Differential centrifugal sedimentation (DCS) is based on physical separation of nanoparticles in a centrifugal field prior to their analysis. It is suitable for resolving particle populations, which only slightly differ in size or density. Agglomeration presents a common problem in many natural and engineered processes. Reliable data on the agglomeration state are also crucial for hazard and risk assessment of nanomaterials and for grouping and read-across of nanoforms. Agglomeration results in polydisperse mixtures of nanoparticle clusters with multimodal distributions in size, density, and shape. These key parameters affect the sedimentation coefficient, which is the actual physical quantity measured in DCS, although the method is better known for particle sizing. The conversion into a particle size distribution is, however, based on the assumption of spherical shapes. The latter disregards the influence of the actual shape on the sedimentation rate. Sizes obtained in this way refer to equivalent diameters of spheres that sediment at the same velocity. This problem can be circumvented by focusing on the sedimentation coefficient distribution of complex nanoparticle mixtures. Knowledge of the latter is essential to implement and optimize preparative centrifugal routines, enabling precise and efficient sorting of complex nanoparticle mixtures. The determination of sedimentation coefficient distributions by DCS is demonstrated based on supracolloidal assemblies, which are often referred to as "colloidal molecules". The DCS results are compared with sedimentation coefficients obtained from hydrodynamic bead-shell modeling. Furthermore, the practical implementation of the analytical findings into preparative centrifugal separations is explored.

**Keywords:** nanoparticles; colloidal clusters; colloidal molecules; sedimentation; separation; classification of nanoparticles; analytical centrifugation; differential centrifugal sedimentation; disk centrifuge; density gradient centrifugation

#### **1. Introduction**

Pursuant to the International Union of Pure and Applied Chemistry, colloidal particles are defined as objects that have "a dimension roughly between 1 nm and 1 µm" [1]. This includes the nanoscale, which is associated to the size range of approximately 1 nm to 100 nm, in line with ISO/TS 80004-2:2015 specifications [2]. Colloidal particles underlie Brownian motion. The latter prevails over sedimentation if the nanoparticles do not form agglomerates with dimensions beyond the colloidal domain. However, agglomeration and heteroaggregation of colloidal particles are major and common problems in many natural and engineered processes [3]. Surface energy will promote the agglomeration of small particles in the absence of kinetic stabilization. The latter is strongly influenced by external parameters, such as pH, salinity, or the presence of depletants [4]. Furthermore, heteroaggregation is observed when different types of colloidal particles attract each other [5]. This can be mediated by opposite surface charges, but heteroaggregation may also occur between charged and neutral particles [6]. Attachment of macromolecules to their surface may result in bridging flocculation of colloidal particles [4,7]. In cases like these, clusters of a limited number of constituent particles are formed at the onset of

**Citation:** Plüisch, C.S.; Stuckert, R.; Wittemann, A. Direct Measurement of Sedimentation Coefficient Distributions in Multimodal Nanoparticle Mixtures. *Nanomaterials* **2021**, *11*, 1027. https://doi.org/ 10.3390/nano11041027

Academic Editor: Federico Ferrarese Lupi

Received: 17 March 2021 Accepted: 13 April 2021 Published: 17 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

nanoparticle aggregation. At this early stage of aggregation, the suspension contains a multimodal mixture of assemblies with dimensions still within the colloidal regime. An accurate analytical tool to identify the onset of aggregation has thus to provide a high resolving power for mixtures of different colloidal species.

Common particle sizing techniques such as scattering techniques permit only the precise measurement of average particle sizes of monomodal colloids or bimodal mixtures that differ by at least an order of magnitude in particle size [8]. For example, static and dynamic light scattering are inherently sensitive to larger species present in a colloidal suspension. Light scattering is thus an excellent tool to monitor the onset of aggregation because the scattered light intensity is widely governed by the aggregates, while the precursor particles only contribute slightly [9]. Other techniques, such as electron microscopy, have their strength in mapping individual aggregates [10]. However, they provide poor statistics, demand specific preparation requirements, and have harsh experimental conditions. In particular, they do not permit in-situ studies.

Analytical centrifugal methods pave the way to direct studies of water-borne colloidal particles in aqueous suspension [11]. Moreover, centrifugal separation of colloidal particles provides the extraordinary resolving power required for an in-depth analysis of polydisperse nanoparticle mixtures. Two common sedimentation techniques have been established: analytical ultracentrifugation (AUC) and differential centrifugal sedimentation (DCS). AUC is a valuable tool for analyzing structural aspects of synthetic and biological nanoparticles. It is based on integral sedimentation of colloidal particles, which means that, during the analysis, the sum (the integral) of all particles smaller than a certain size is being measured [12]. Mathematical differentiation with respect to diameter will yield the (differential) particle size distribution.

Differential centrifugal sedimentation (DCS), which is also known as disk centrifuge photosedimentometry (DCP) [13] or as analytical disk centrifugation [14], enables direct measurements of differential size distributions [12]. The method combines centrifugal separation of different nanoparticle populations with continuous light extinction measurement at a fixed position. The centrifugal separation is carried out in a rotating disk (Figure 1a). The latter contains a density gradient, whose densities increase in radial direction. The gradient counteracts a higher apparent density in the sample than in layers underneath and prevents the sample from behaving as a fluid of higher density [15]. This is necessary to make the particles sediment as individual species at rates specified by their sedimentation coefficients. A detector beam is passing the density gradient at a fixed position in the vicinity of the heaviest end of the gradient. As a differential technique, only particles of a specific sedimentation coefficient reach the detector beam and are quantified by the reduction of the detector beam resulting from light scattered by particles. The sedimentation rate of a given particle population depends on its size, buoyant density, and, to a lesser extent, also on its shape [16]. It is for this reason that DCS has been widely used as a highly versatile method for particle sizing in colloid science (Figure 1c). Particle size distributions can be precisely measured down to a few nanometers [12]. This allows for sizing of synthetic and biological particles as diverse as polymer latexes [17], silica particles [13,18], gold nanospheres [18] and nanorods [19], carbon nanotubes, [20], amyloid fibrils [21], and influenza viruses [22], amongst many others.

DCS can be viewed as a complementary method to AUC, which, however, permits fast particle sizing, likewise at excellent resolution, but without the need for solving complicated equations [19]. Further refinement of the instrumentation by the manufacturer in recent years, such as optically, virtually fully transparent disks resistant to organic solvents paired with lower wavelengths of the detector beam, has made DCS a routine tool for measuring particle size distributions at high quality. In addition, substantial scientific progress was made, thereby paving the way for new directions. Armes and co-workers pioneered the analysis of various nanocomposite particles, including sterically stabilized nanoparticles [23] and raspberry-type heteroaggregates [14]. Moreover, the potential to explore colloids with surface-bound proteins was demonstrated [24,25]. Such hybrid

particles are characterized by size distributions, which are superimposed by density distributions [14]. Knowledge of the particle size obtained from complementary techniques enables the determination of effective particle densities by DCS [17]. The latter are defined as the difference between the actual particle density and the density of the dispersing medium. DCS measurements thus carried out in density gradients of different composition permit simultaneous determination of particle size and density [13,22]. In the same way, combination of centrifugal sedimentation and flotation triggered by the densities of different dispersing fluids can be used for independent measurements of particle size and density [17]. *Nanomaterials* **2021**, *11*, 1027 3 of 18

**Figure 1.** Differential centrifugal sedimentation (DCS) using a disk centrifuge: (**a**) A density gradient capped with dodecane is built within a rotating hollow, optically transparent disk. The sample is placed on top of the gradient via a central injection port. Different particle populations migrate as discrete zones at rates specified by their respective sedimentation coefficients. Attenuation of laser light is recorded continuously to quantify the scattering by particles arriving at a fixed detector position as a function of the sedimentation time. (**b**) Raw data of a DCS run demonstrating the high-resolving power of DCS: As an example, the analysis of a bimodal nanoparticle mixture differing by a few nanometers is shown. The latter contains spherical polystyrene latex particles with number-averaged diameters of 142 nm and 108 nm. It should be noted that the first particle population is identical to the elementary units of the clusters studied in this work, whereas the smaller particles were obtained by increasing the emulsifier concentration during particle synthesis. (**c**) For spherical particles, a particle size distribution is obtained after (i) conversion of the light extinction into particle concentrations using Mie theory, and (ii) recalculation of sedimentation times according to Equation (4). DCS can be viewed as a complementary method to AUC, which, however, permits **Figure 1.** Differential centrifugal sedimentation (DCS) using a disk centrifuge: (**a**) A density gradient capped with dodecane is built within a rotating hollow, optically transparent disk. The sample is placed on top of the gradient via a central injection port. Different particle populations migrate as discrete zones at rates specified by their respective sedimentation coefficients. Attenuation of laser light is recorded continuously to quantify the scattering by particles arriving at a fixed detector position as a function of the sedimentation time. (**b**) Raw data of a DCS run demonstrating the high-resolving power of DCS: As an example, the analysis of a bimodal nanoparticle mixture differing by a few nanometers is shown. The latter contains spherical polystyrene latex particles with numberaveraged diameters of 142 nm and 108 nm. It should be noted that the first particle population is identical to the elementary units of the clusters studied in this work, whereas the smaller particles were obtained by increasing the emulsifier concentration during particle synthesis. (**c**) For spherical particles, a particle size distribution is obtained after (i) conversion of the light extinction into particle concentrations using Mie theory, and (ii) recalculation of sedimentation times according to Equation (4).

fast particle sizing, likewise at excellent resolution, but without the need for solving complicated equations [19]. Further refinement of the instrumentation by the manufacturer in recent years, such as optically, virtually fully transparent disks resistant to organic sol-In this article, we will demonstrate that DCS is a straightforward method to directly measure distributions of sedimentation coefficients in multimodal mixtures of nanopar-

progress was made, thereby paving the way for new directions. Armes and co-workers pioneered the analysis of various nanocomposite particles, including sterically stabilized nanoparticles [23] and raspberry-type heteroaggregates [14]. Moreover, the potential to explore colloids with surface-bound proteins was demonstrated [24,25]. Such hybrid particles are characterized by size distributions, which are superimposed by density distributions [14]. Knowledge of the particle size obtained from complementary techniques enables the determination of effective particle densities by DCS [17]. The latter are defined

ticles. Colloidal clusters varying in their number of spherical constituent particles and, closely related to this, their geometries will serve as a model system. Such supraparticles are often referred to as "colloidal molecules" as their configurations resemble those of true molecules [26–28]. They have well-defined shapes, which are defined by packing criteria for uniform spheres, and can thus be regarded as prototypical for the organization of matter into nanocomposites [27]. The exemplary case study can thus be easily transferred to many other practical problems, including microscopic mechanisms underlying aggregation in aqueous nanoparticle dispersions. In this regard, DCS permits proper discrimination among species differing in their number of constituent particles and provides quick and precise access to sedimentation coefficients. The latter ones can be used to optimize centrifugal routines, enabling effective separation of nanoparticle mixtures.

#### **2. Materials and Methods**

#### *2.1. Chemicals*

Ultra-pure D(+)-sucrose (≥99.9%, Proteomics Grade DNAse-, RNAse-free, VWR International GmbH, Darmstadt, Germany) and deionized water (resistivity > 18 MΩ cm) obtained from a reverse osmosis water purification system (Millipore Direct 8, Merck Chemicals GmbH, Darmstadt, Germany) were used for making aqueous density gradients. *n*-Dodecane (≥99%) was purchased from Sigma-Aldrich Chemie GmbH, Steinheim, Germany and used as received. A commercial polystyrene latex standard with a particle diameter of 251 nm (HS0025-20, BS-Partikel GmbH, Mainz, Germany) was used for calibration during DCS experiments.

#### *2.2. Colloidal Clusters*

The particle clusters studied in this work were prepared by assembly of narrowly dispersed cross-linked polystyrene latex particles while confined at the surface of evaporating emulsion droplets [29]. The polystyrene particles bearing a nanometer-thin hydrophilic surface were synthesized by emulsion polymerization of styrene, divinyl benzene, and *N*-isopropylacrylamide in the presence of sodium dodecyl sulfate as the emulsifier and potassium persulfate as the initiator. A detailed description of the synthesis of the latex particles can be found in [16]. Their average diameter of 144 nm (as determined by transmission electron microscopy) and very low polydispersity index of 1.001 (given by the weight-average diameter divided by the number-average diameter) makes the spherical polymer particles perfectly suited to assembly into well-defined clusters with dimensions in the colloidal regime. The assembly into clusters was accomplished along the lines specified in [16]. The nature of the assembly hinges on trapping a limited number of particles at the surfaces of toluene droplets and packing them into clusters by strong capillary forces that occur during evaporation of the droplet phase [30]. The binding of the particles to the droplets is driven by minimization of surface energy and represents a variation of the Pickering effect with strongly swollen particles at the oil–water interface [31]. The random distribution of the polymer particles across the droplets results in a mixture of clusters differing in the number of constituents, ranging mainly from 2 to 12. In addition, the aqueous suspension of colloidal clusters also contains a fraction of single particles, resulting from droplets bearing just one particle at the surface.

#### *2.3. Differential Centrifugal Sedimentation*

Sedimentation coefficient distributions were recorded on an analytical disk centrifuge (DC24000 UHR, CPS Instruments, Inc., Prairieville, LA, USA) [12]. A density gradient was built in situ from 8.0% to 2.0% (m/m) aqueous sucrose solutions by filling the hollow disk rotating at 24,000 rpm. The gradient was covered with a thin layer of *n*-dodecane, thus minimizing evaporation of water and extending the lifetime of the gradient. The step gradient built from nine sucrose solutions (1.6 mL each) was allowed to equilibrate within 30 min, yielding a continuous gradient, which is virtually linear in volume [32].

Diluted sample suspensions (0.02% (m/m)) were sonicated to eliminate any temporary agglomerates and injected into the spinning disk (100 µL in total). The sedimentation time scale of the DCS runs is calibrated with polystyrene nanospheres as a size standard. It must be noted that this calibration is a necessary step in the software of the device before the sample measurement can be performed. However, this calibration had no influence on the actual sedimentation coefficient profiles studied in this work as the latter ones are derived from the raw data (light attenuation at *λ* = 405 nm vs. sedimentation time, cf. Figure 1b) and by using the single particles left in the cluster mixture as an internal reference to determine the constant *k* in Equation (1). By going through this procedure, the sedimentation time scale is finally defined by a component facing the same conditions as the species being investigated in the same DCS run.

#### *2.4. Nanoparticle Separation*

Preparative separation of the clusters into fractions with the same number of constituent particles was accomplished by rate-zonal density gradient centrifugation [33]. The fundamental procedure corresponds to a large extent the one reported earlier in ref. [16]. However, the focus of the current work was on aligning optimized DCS routines with preparative fractionation as tightly as possible. For this reason, several adjustments became necessary. Sucrose density gradients (36 mL), linear in volume ranging from 2% (m/m) to 8% (m/m), were prepared using a simple gradient maker, originally used for biological separations [34]. The latter is based on two chambers filled with the heaviest and lightest part of the gradient to be built. Gradual mixing of the two sucrose solutions is achieved by a rotating stir bar located in the lighter solution. Gravity results in an outward flow, which is assisted by a peristaltic pump (Masterflex L/S® Digital Miniflex® Pump, Cole-Parmer GmbH, Wertheim, Germany), enabling flowrate (0.1 mL s−<sup>1</sup> )-controlled gradient formation. The latter was built inside a centrifuge tube (Ultra-Clear Centrifuge Tubes, Beckman Instruments, Inc., Fullerton, CA, USA) from below using a drain tube. To facilitate the evaluation of the preparative separation, the centrifuge tubes were equipped with a scale, thus allowing precise allocation of zones of banded particle populations.

Next, 2 mL of cluster suspension (0.36% (m/m)) was carefully placed on top of the density gradient. Centrifugation was performed on an Optima XPN-90 Ultracentrifuge equipped with an SW 32 Ti swinging-bucket rotor (Beckman Coulter GmbH, Krefeld, Germany). Run conditions were 15 min at 24,000 rpm (relative centrifugal forces: RCFav. = 70,963, RCFmax. = 98,703) and 25 ◦C.

The clusters separated into discrete zones were extracted from the top of the gradient using a self-built fraction recovery system. The tip of a drain tube was directly positioned into the center of the zone of banded particles to be collected. A slight negative pressure was used for gentle extraction. The cluster fractions were dialyzed exhaustively to remove sucrose prior to sample analysis (dialysis membrane: Spectra/Por® 7, MWCO 50,000 kD).

#### *2.5. Further Methods*

Transmission electron microscopy (TEM) on a Libra 120 microscope (Carl Zeiss AG, Oberkochen, Germany) at an acceleration voltage of 120 kV was used to determine the average size (144 nm) and polydispersity (1.001) of the cluster constituents based on 1000 individual particle counts. The hydrodynamic diameter of the latter is 145 nm, as demonstrated by dynamic light scattering measurements at 25 ◦C on an ALV/CGS-3 Compact Goniometer System (ALV-Laser Vertriebsgesellschaft m-b.H, Langen Germany). The particle density was derived by measuring the densities of a concentration series using a DMA 5000 M density meter (Anton Paar GmbH, Graz, Austria). Extrapolation of the reciprocal values of the measured densities (= specific volumes) to a solid content of 100% (m/m) yielded a particle density of 1.057 g cm−<sup>3</sup> at 25 ◦C. It should be noted that the particle density measured by this method corresponds to the density of the bulk material [35]. However, several studies demonstrated that polystyrene latex particles have buoyant densities, which are identical within the limits of experimental errors to the

density specified for the bulk material [36,37]. Fractions of colloidal clusters isolated after centrifugal separation in a density gradient were investigated by field emission scanning electron microscopy (FESEM) using a CrossBeam 1540 XB microscope (Carl Zeiss AG, Oberkochen, Germany) operating at 3 kV.

#### **3. Results and Discussion**

#### *3.1. Analysis of Sedimentation Coefficient Distributions*

Figure 1a shows schematically the basic principle of DCS. A mixture of different nanoparticle populations is physically separated into discrete zones of particles that migrate at velocities *u* characteristic to their size, shape, and density. This is achieved within a disk rotating at a constant angular velocity *ω*. Throughout the experiment, two quantities are continuously recorded. One of these is the time *t* it takes distinct particles to travel up a fluid density gradient from a starting position *R*<sup>0</sup> until they pass a detector position *R*D. Arrival of the particles is monitored by the extinction of light at a wavelength of 405 nm. For non-absorbing materials such as polymer particles, the attenuation of a laser beam resulting from light scattered by particles arriving at specified sedimentation times is monitored.

The sedimentation coefficient *s* of a distinct particle population *i* is the quotient of the sedimentation velocity (*u* = d*R*/d*t*) and the product *ω*2*R*, where *R* is the actual radial position with respect to the axis of rotation. *s* is inversely related to the sedimentation time *t<sup>i</sup>* measured in a DCS experiment [19]:

$$s\_i = \frac{u}{\omega^2 R} = \frac{\ln\left(\frac{R\_D}{R\_0}\right)}{\omega^2 t\_i} = \frac{k}{t\_i} \,\tag{1}$$

Run-specific parameters such as *R*0, *RD*, and *ω* can be summarized to one instrumental measurement constant *k*. It is recommended to determine this constant by using a particle standard of known sedimentation coefficient. This has turned out to be beneficial if compared with making measurements by quantifying *R*0, *RD*, and *ω* individually [8].

Polymer particles with spherical shapes are particularly suitable as particle standards because their sedimentation is governed by Stokes' law [14]. A narrow size distribution will facilitate the calibration process as the local maximum of the distribution, which should correspond to the Stokes diameter of the non-agglomerated particles, can be readily determined. The current work studies mixtures of supracolloidal assemblies built from spherical constituent particles. Consequently, the latter have the same density as clusters based on them. Moreover, these particles are virtually uniform, which is reflected by their low polydispersity index of 1.001. These two conditions make the polymer nanospheres ideal reference particles to precisely determine the constant *k* in Equation (1). To achieve this, the sedimentation coefficient of the particles must be calculated first.

The sedimentation coefficient of a particle *i* is defined as the ratio of the effective particle mass *meff* and the friction coefficient *f*:

$$s\_i = \frac{m\_{eff}}{f} = \frac{m\_p - m\_f}{f},\tag{2}$$

where the effective mass results from the difference in the actual particle mass *m<sup>p</sup>* and the mass of the fluid *m<sup>f</sup>* that is displaced by the particle. For spherical particles, the friction coefficient is given by Stokes' law and reads as follows:

$$f\_{\rm s} = \mathfrak{Z}\pi\eta d\_{\rm hv} \tag{3}$$

where *η* is the viscosity of the fluid and *d<sup>h</sup>* denotes the hydrodynamic diameter of the particles. The effective mass can be expressed by the corresponding volumes of a sphere with diameter *d<sup>h</sup>* and the densities of the particle *ρ<sup>p</sup>* = 1.057 g cm−<sup>1</sup> and the density of the displaced fluid *ρ<sup>f</sup>* (here: 0.997 g cm−<sup>3</sup> ) [21]:

$$s\_i = \frac{\left(\rho\_p - \rho\_f\right)d\_h^2}{18\eta}.\tag{4}$$

The number-average diameter of the non-agglomerated particles was 142 nm, which was determined by DCS measurement against the commercial polystyrene standard latex. This value is close to the TEM diameter (144 nm) and the hydrodynamic diameter measured by DLS (145 nm).

Due to the small differences related to the low polydispersity of the particles (right peak in Figure 1c represents the size distribution), the values of any of three methods can be used as a measure for the hydrodynamic particle size. The obvious approach would be to use the DCS value of the non-agglomerated species as an internal reference to calculate the sedimentation coefficients of other species present in the mixture (see below).

Alternatively, one might prefer to calculate the masses in Equation (2) from the TEM radius characteristic for dry particles to account for the fact that the hydrodynamic effective surface layer hardly contributes to the particle mass [16]. The friction coefficient given in Equation (3) can be calculated from the hydrodynamic diameter as measured by DCS or DLS. In this study, the DLS value was used to allow for a direct comparison with sedimentation coefficients predicted earlier by hydrodynamic bead-shell modeling. In that study, model building was based on the DLS diameter of the cluster constituents [16].

An important point to note is that by using the non-agglomerated particles as an internal calibration standard, it is guaranteed that any particles present in the same DCS run, whether those to be studied or those acting as a reference, face the same conditions during their migration through the density gradient. This compensation captured in the constant *k* goes beyond the parameters specified in Equation (1). It also considers variations in the density and viscosity of the dispersion medium during sedimentation. This is particularly important when studying sedimentation in a density gradient. In other words, a compensation for fluid densities and viscosities that differ from the actual conditions during the experiment is achieved by using an internal reference. The sedimentation characteristics within the gradient can thus be easily transferred to the sedimentation in other dispersion media. In the following, calculation of the sedimentation coefficient of the reference particles is based on the sedimentation in pure water at 25 ◦C (*ρ<sup>f</sup>* = 0.997 g cm−<sup>3</sup> ; *η* = 0.891 g m−<sup>1</sup> s −1 ). The latter is done not only for the sake of simplicity, but also to allow for direct comparison to predicted values from hydrodynamic modeling that have been reported previously [16]. Consequently, a sedimentation coefficient of *sN*=1 = 770 Sv is calculated from Equation (4). The sedimentation time of the nanospheres assigned from the DCS analysis of cluster mixtures is *<sup>t</sup>N*=1 = 401 s, which yields a *<sup>k</sup>*-value of 3.0877 <sup>×</sup> <sup>10</sup>−<sup>8</sup> according to Equation (1). This value is then used to calculate the sedimentation coefficients of any non-spherical species present in the nanoparticle mixture from their respective sedimentation times.

#### *3.2. Particle Clusters as Model Systems for Nanoparticle Mixtures*

Thanks to the seminal work by Pine and co-workers [30], it is known that evaporating emulsion droplets are suitable physical templates to assist the assembly of colloidal particles into an ensemble of stable clusters varying in their number of constituents. A mixture of various species is obtained, resulting from a random distribution of the elementary particles on the droplets [31]. The gradual increase in cluster mass follows directly from the number of constituent particles *N*. A linear correlation does not apply to the increase in surface area and, related to this, friction at the cluster surface. The growth in surface area is largest when going from single particles to dimers, followed by increasingly smaller growth rates with rising *N*. The latter is a direct consequence of the packing into dense cluster configurations. It is obvious that the sedimentation coefficients of the clusters gradually increase with

rising *N* in accordance with Equation (2). Moreover, based on the above, the increments for the rising sedimentation coefficients are becoming increasingly smaller with rising *N*. This fact underscores the suitability of particle clusters as model systems to explore the limits of sorting nanoparticle mixtures by centrifugal sedimentation. model systems to explore the limits of sorting nanoparticle mixtures by centrifugal sedimentation. The following studies are based on a mixture of particle clusters built from 144 nmsized polymer nanospheres (Inset of Figure 2). Most of the clusters consist of up to 12

particles on the droplets [31]. The gradual increase in cluster mass follows directly from the number of constituent particles *N*. A linear correlation does not apply to the increase in surface area and, related to this, friction at the cluster surface. The growth in surface area is largest when going from single particles to dimers, followed by increasingly smaller growth rates with rising *N*. The latter is a direct consequence of the packing into dense cluster configurations. It is obvious that the sedimentation coefficients of the clusters gradually increase with rising *N* in accordance with Equation (2). Moreover, based on the above, the increments for the rising sedimentation coefficients are becoming increasingly smaller with rising *N*. This fact underscores the suitability of particle clusters as

*Nanomaterials* **2021**, *11*, 1027 8 of 18

The following studies are based on a mixture of particle clusters built from 144 nmsized polymer nanospheres (Inset of Figure 2). Most of the clusters consist of up to 12 constituent particles and thus have spatial dimensions within the colloidal domain. Hence, Brownian motion will prevail over sedimentation unless the assemblies are exposed to a centrifugal field [38]. The morphology of the colloidal clusters in this work and of related supraparticles was discussed in earlier works [16,28,30,31,39,40]. It should be noted that clusters of more than four constituents may occur in different configurations. For example, clusters of five and six particles have two different configurations. Figure 3 shows common configurations that are observed experimentally and predicted by computer simulations. The cluster mixture contains both isotropic and anisotropic species. Single particles, tetrahedral, octahedral, and icosahedral clusters have isotropic geometries, whereas all other species exhibit anisotropic shapes. The further studies will thus deliberately dispense on any evaluations based on assuming a spherical particle geometry. The basic methodology is thus broadly applicable to particles of arbitrary shapes that do not have to obey Stokes' law. constituent particles and thus have spatial dimensions within the colloidal domain. Hence, Brownian motion will prevail over sedimentation unless the assemblies are exposed to a centrifugal field [38]. The morphology of the colloidal clusters in this work and of related supraparticles was discussed in earlier works [16,28,30,31,39,40]. It should be noted that clusters of more than four constituents may occur in different configurations. For example, clusters of five and six particles have two different configurations. Figure 3 shows common configurations that are observed experimentally and predicted by computer simulations. The cluster mixture contains both isotropic and anisotropic species. Single particles, tetrahedral, octahedral, and icosahedral clusters have isotropic geometries, whereas all other species exhibit anisotropic shapes. The further studies will thus deliberately dispense on any evaluations based on assuming a spherical particle geometry. The basic methodology is thus broadly applicable to particles of arbitrary shapes that do not have to obey Stokes' law.

**Figure 2.** Sedimentation coefficient distribution of a mixture of colloidal clusters as measured by DCS. Cluster species of more than 12 constituent particles are resolved separately as narrow bands. DCS analysis thus enables a clear classification of nanoparticles according to their sedimentation characteristics. The inset shows an FESEM micrograph of the cluster mixture studied by DCS. The scale bar represents 400 nm. **Figure 2.** Sedimentation coefficient distribution of a mixture of colloidal clusters as measured by DCS. Cluster species of more than 12 constituent particles are resolved separately as narrow bands. DCS analysis thus enables a clear classification of nanoparticles according to their sedimentation characteristics. The inset shows an FESEM micrograph of the cluster mixture studied by DCS. The scale bar represents 400 nm.

.

#### *3.3. DCS Analysis of Sedimentation Coefficient Distributions*

*3.3. DCS Analysis of Sedimentation Coefficient Distributions*  DCS is now applied as an analytical tool to explore the distribution of sedimentation coefficients of the mixture of colloidal clusters. The separation of the particles within the disk centrifuge follows the basic principles of rate-zonal density gradient centrifugation DCS is now applied as an analytical tool to explore the distribution of sedimentation coefficients of the mixture of colloidal clusters. The separation of the particles within the disk centrifuge follows the basic principles of rate-zonal density gradient centrifugation [15]. The proper design of the density gradient is key for accurate results. The following criteria must be considered when preparing the density gradient:



according to Equation (1).

experimental conditions. In case of nanoparticle aggregates, it makes sense to use the elementary particles as an internal reference. The *k*-value calculated from the sedimentation time of the reference particles and their sedimentation coefficient can thus be transferred to any other particle population within the same DCS run. Sedimentation coefficients of the different particle populations are calculated from the respective sedimentation times

**Figure 3.** Sedimentation coefficients of the cluster species varying in the number of constituent spheres *N* and, consequently, their configurations. Analytical values *sDCS* obtained from DCS are compared with sedimentation coefficients S*PC* estimated from preparative separations by ratezonal density gradient centrifugation. In addition, sedimentation coefficients *SBS* predicted from hydrodynamic bead-shell modeling, as taken from [16], are given for clusters with *N* ≤ 6. Model building considers the exact geometries of the colloidal clusters. Notwithstanding the shortcomings in deriving sedimentation coefficients from preparative centrifugations, the quantities thus obtained differ by less than 8% from the analytical values and the theoretical predictions. **Figure 3.** Sedimentation coefficients of the cluster species varying in the number of constituent spheres *N* and, consequently, their configurations. Analytical values *sDCS* obtained from DCS are compared with sedimentation coefficients S*PC* estimated from preparative separations by rate-zonal density gradient centrifugation. In addition, sedimentation coefficients *SBS* predicted from hydrodynamic bead-shell modeling, as taken from [16], are given for clusters with *N* ≤ 6. Model building considers the exact geometries of the colloidal clusters. Notwithstanding the shortcomings in deriving sedimentation coefficients from preparative centrifugations, the quantities thus obtained differ by less than 8% from the analytical values and the theoretical predictions.

Together with the profile of light extinction measured during DCS, a distribution of the sedimentation coefficients of the nanoparticle mixture is obtained. This distribution is weighted by the attenuation of light caused by the particle arriving at the detector position and thus differs from the weight distribution *c*(*s*) obtained from AUC [43]. In principle, conversion of the two contributions is possible if the scattering cross-sections of the various particle populations are known. According to the authors' opinion, this issue should be treated in a purist way to allow for a broad application of the methodology. Compliance with the two criteria makes the particles settle individually at rates specified by their sedimentation coefficients. In the present case, clusters of a single set of constituent particles were explored at 25 ◦C. Hence, the various species within the cluster mixture have the same density, which is 1.057 g cm−<sup>3</sup> . Their separation during DCS analysis was performed in an aqueous sucrose gradient ranging from 2% (m/m) to 8% (m/m). The minimum density within the gradient equals 1.0052 g cm−<sup>3</sup> and is thus, in accordance with criterion 2, higher than the density of the highly diluted sample suspension (0.02% (m/m), *ρ* = 0.997 g cm−<sup>3</sup> ). This prevents streaming, i.e., a downstream of particle-laden fluid following the centrifugal field [15]. In addition, the maximum density within the gradient (1.0285 g cm−<sup>3</sup> ) was kept lower than the actual particle density. This ensures that the particles can travel though the complete gradient fluid and will thus reach the detector position at a characteristic sedimentation time. The gradient design suitable for polystyrene latex particles can be easily adapted for other types of nanoparticles, simply by following

the two criteria. The densities of aqueous sucrose solutions as functions of weight fraction and temperature can be found in the literature [41]. Figure S5 displays densities in the concentration range up to 10% (m/m) sucrose.

The particle clusters do not absorb visible light, but light is scattered by the clusters, as for any other colloidal objects. The colloidal clusters can be thus detected by attenuation of a laser beam. The latter had a wavelength of 405 nm, which provides high sensitivity because violet light is subject to the strongest scattering within the visible region. For this reason, even marginal quantities of particles or particle agglomerates can still be detected.

During the DCS run, the light attenuation of the detector beam is continuously recorded as the function of the sedimentation time. Routines in the device software allow for conversion of the raw data into a particle size distribution. These routines are based on the Mie theory to derive the particle concentration from the measured light extinction [42]. Moreover, the device software assigns a distinct particle diameter to any given sedimentation time. However, this correlation is only correct if the drag force acting on the particles during sedimentation follows Stokes' law. The latter applies only to spherical particles and is thus not appropriate for accurately exploring particles with complex shapes. The deviation between the friction coefficients of an anisotropic particle and a spherical particle of the same mass can be at least partially compensated by the introduction of a non-sphericity factor [12]. However, this can only work if all the particles exhibit the same aspect ratio, which is rarely the case for mixtures of anisotropic particles. Nanoparticle aggregates such as the colloidal clusters in this study have various geometries (Figure 3), so that the assignment of a single non-sphericity factor that works for all species is not possible.

It is exactly for this reason that the present evaluation explicitly avoids any assumptions of a spherical shape and is thus applicable to particles of arbitrary shapes. The only exception is made when calculating the sedimentation coefficient of the spherical particles used as an internal reference. In this specific case, making use of Equation (3) is justified. Basically, it is also possible to replace the spherical particles by any other type of particles given that their sedimentation coefficient is known. Precise knowledge of the sedimentation coefficient of at least one set of reference particles is required to determine the instrumental measurement constant *k* in Equation (1). These reference particles can be either measured independently of the sample particles, or, as in the present case, constitute a distinct particle population within the nanoparticle mixture. The latter procedure is advantageous as different particle populations are compared, which are subject to the same experimental conditions. In case of nanoparticle aggregates, it makes sense to use the elementary particles as an internal reference. The *k*-value calculated from the sedimentation time of the reference particles and their sedimentation coefficient can thus be transferred to any other particle population within the same DCS run. Sedimentation coefficients of the different particle populations are calculated from the respective sedimentation times according to Equation (1).

Together with the profile of light extinction measured during DCS, a distribution of the sedimentation coefficients of the nanoparticle mixture is obtained. This distribution is weighted by the attenuation of light caused by the particle arriving at the detector position and thus differs from the weight distribution *c*(*s*) obtained from AUC [43]. In principle, conversion of the two contributions is possible if the scattering cross-sections of the various particle populations are known. According to the authors' opinion, this issue should be treated in a purist way to allow for a broad application of the methodology.

Figure 2 shows the light extinction-weighted sedimentation coefficient distribution of a mixture of colloidal clusters. As described above, the distribution is solely based on the raw data of the DCS run and knowledge of the sedimentation coefficient of the single particles used as an internal reference. The high resolution of the DCS run is immediately obvious. Single particles and cluster species of 2 to 12 constituents are resolved as discrete bands, which allows for a facile assignment of sedimentation coefficients according to the peak maxima (Figure 3). Remarkably, species that deviate by less than 1% in their sedimentation

coefficients can still be resolved. A more detailed discussion of the resolution of DCS is found in ref. [12].

Zone widths in a DCS experiment are governed by several factors. Because DCS detects particles arrive at a fixed position over time, the actual zone width of a given particle population is captured as a time interval within which all particles of this population arrive at the detector position. A broad zone is thus reflected by a larger time interval. This becomes apparent when the light extinction is plotted against the sedimentation time (Figure S1). The peak-width at half-height is largest for the non-agglomerated particles (25.2 s) and decrease systematically for the clusters with rising numbers of constituent particles *N* (13.0 s for dimers; 9.2 s for trimers; 7.3 s for tetramers; 6.0 s for pentamers; 5.4 s for hexamers). The polydispersity of the cluster constituents (1.001) and, consequently, of the clusters is rather low and virtually negligible compared to the broadening due to Brownian motion. Band broadening due to diffusion is an important aspect. Translational diffusion coefficients decrease with the number of constituent spheres [16,38] and, consequently, facilitate band narrowing with rising numbers of constituent particles *N* (Figure S1). The density gradient influences the band width as well. A steep gradient profile results in lower sedimentation velocities in the leading edge of the zone, whereas the velocities are higher at the trailing edge. The density gradient thus keeps the zone of a distinct particle population together. The density gradient equally affects all particle populations because the detector position is fixed in DCS measurement. This constitutes a difference from preparative centrifugal separations, where different particle populations are harvested from different sections of the density gradient (Figure 4). *Nanomaterials* **2021**, *11*, 1027 12 of 18

**Figure 4.** Centrifugal separation of colloidal clusters according to their sedimentation coefficients in a sucrose density gradient ranging from 2% (m/m) to 8% (m/m). The fractionation was carried out in a swing-out rotor at 24,000 rpm. Cluster populations of up to 12 constituent particles were isolated as individual zones that could be harvested by using a self-built fraction recovery unit. FESEM micrographs of fractions of particle monomers (*N* = 1), dimers (*N* = 2), trimers (*N* = 3), tetramers (*N* = 4), pentamers (*N* = 5), and hexamers (*N* = 6) are grouped around the centrifuge tube hosting the gradient and the particle zones. The scale bars represent 200 nm. **Figure 4.** Centrifugal separation of colloidal clusters according to their sedimentation coefficients in a sucrose density gradient ranging from 2% (m/m) to 8% (m/m). The fractionation was carried out in a swing-out rotor at 24,000 rpm. Cluster populations of up to 12 constituent particles were isolated as individual zones that could be harvested by using a self-built fraction recovery unit. FESEM micrographs of fractions of particle monomers (*N* = 1), dimers (*N* = 2), trimers (*N* = 3), tetramers (*N* = 4), pentamers (*N* = 5), and hexamers (*N* = 6) are grouped around the centrifuge tube hosting the gradient and the particle zones. The scale bars represent 200 nm.

basis to optimize preparative centrifugal separations. To this end, separations according to the sedimentation coefficients were carried out in a swinging-bucket rotor. The buckets host clear centrifuge tubes with a capacity of 38.5 mL. Compared to a fixed-angle centrifuge rotor, swing-out rotors significantly reduce collisions of the particles with the wall of the tube and help to reduce wall effects on sedimentation (see below). More importantly, the fluid layers and the particle zones follow the centrifugal field throughout the whole run, including acceleration and deceleration intervals, which is the prerequisite for excellent selectivity during fractionation. The orientation of the layers with respect to the axis of rotation is a feature which DCS analysis and separations carried out in a swing-out rotor have in common. In this context, the spinning hollow disk in DCS can be considered

as an extension of the centrifuge tube in a swing-out rotor by 360 °C (Figure 1).

Nevertheless, there are two important differences that should be kept in mind. The first one is related to the geometry of the disk, which has some similarities to a zonal rotor used for preparative separations at larger scales [32]. A density gradient linear in volume will be also linear along the sedimentation path if placed in a centrifuge tube. However, if prepared within the rotating hollow disk, a concave profile of the density gradient is obtained across the sedimentation path. The second difference to be considered relates to the substantial difference between an analytical technique and a preparative method. DCS probes the different particle populations after having reached a fixed position. This means that all particles have migrated along the same path, but they have reached their destina-

*3.4. Application for Preparative Nanoparticle Separations* 

According to Equation [2], there is an inverse relationship between sedimentation time and sedimentation coefficient. This must be considered when comparing actual zone widths during the DCS run with the widths of the individual peaks in the sedimentation coefficient distribution (Figure 2). It follows that the non-agglomerated particles which form the broadest zone (peak-width at half-height: 25.2 s) during the DCS run are presented by the narrowest peak in the sedimentation coefficient distribution (peak-width at half-height: 48 Sv). In comparison, the tetramers form narrower zones (peak-width at half-height: 7.3 s) but are represented by a broader peak in the sedimentation coefficient profile (peak-width at half-height: 81 Sv).

Accurate assessment of the sedimentation coefficients obtained from the DCS strategy can be based on a comparison with values obtained from theoretical modeling. García de la Torre and co-workers have established model building and calculation routines, which can be applied to rigid particles of arbitrary shapes. Recently, we reported on sedimentation coefficients of colloidal clusters calculated along these lines [16]. The clusters studied are identical to those in the present studies but limited to a maximum of six constituent particles. Nonetheless, a direct comparison can be made (Figure 3). The sedimentation coefficients obtained by DCS are in excellent correlation to the values predicted for clusters with the same spatial dimensions and geometries. Deviations are negligible for single particles and even for dimers, which are the geometries with the highest aspect ratio. Although the deviations increase with the number of constituents, they are less than 6% for six-particle clusters with octahedral symmetry. This underscores the suitability of DCS to directly measure sedimentation coefficient distributions of complex nanoparticle mixtures.

#### *3.4. Application for Preparative Nanoparticle Separations*

The separation quality accomplished during the DCS analysis should now serve as a basis to optimize preparative centrifugal separations. To this end, separations according to the sedimentation coefficients were carried out in a swinging-bucket rotor. The buckets host clear centrifuge tubes with a capacity of 38.5 mL. Compared to a fixed-angle centrifuge rotor, swing-out rotors significantly reduce collisions of the particles with the wall of the tube and help to reduce wall effects on sedimentation (see below). More importantly, the fluid layers and the particle zones follow the centrifugal field throughout the whole run, including acceleration and deceleration intervals, which is the prerequisite for excellent selectivity during fractionation. The orientation of the layers with respect to the axis of rotation is a feature which DCS analysis and separations carried out in a swing-out rotor have in common. In this context, the spinning hollow disk in DCS can be considered as an extension of the centrifuge tube in a swing-out rotor by 360 ◦C (Figure 1).

Nevertheless, there are two important differences that should be kept in mind. The first one is related to the geometry of the disk, which has some similarities to a zonal rotor used for preparative separations at larger scales [32]. A density gradient linear in volume will be also linear along the sedimentation path if placed in a centrifuge tube. However, if prepared within the rotating hollow disk, a concave profile of the density gradient is obtained across the sedimentation path. The second difference to be considered relates to the substantial difference between an analytical technique and a preparative method. DCS probes the different particle populations after having reached a fixed position. This means that all particles have migrated along the same path, but they have reached their destination at different times according to their sedimentation coefficient. In preparative separations, the principle of operation is reversed. The centrifugal run and thus the sedimentation are terminated for all particle populations at the same time. At precisely this time, they have traveled different distances, which are determined by their sedimentation coefficients. Hence, the two methods offer the opportunity to complement each other if aligned at the same experimental problem.

Parallel to the above-mentioned DCS analysis, sucrose density gradients ranging also from 2% (m/m) to 8% (m/m) were prepared in centrifuge tubes. In line with the DCS analysis, the centrifugation was performed at 24,000 rpm. Centrifugation times were chosen based on the sedimentation coefficients measured by DCS. In doing so, the time required to maximize the sedimentation path of a 12-particle cluster was estimated. This ensured maximum separation of the cluster populations.

Figure 4 shows the separation achieved in the centrifugal run. A total of twelve discrete zones, each of them corresponding to a particle population settling at the same rate, are observed. Classification of the zones to specific clusters follows the number of constituent particles *N*. This is in full accord with the sequence of sedimentation coefficients obtained from DCS (Figure 3). Verification of zone allocation was achieved by FESEM after extraction of the cluster fractions (Figure 4).

The separation of the cluster mixture into discrete zones within the centrifuge tube paved the way for a quantitative evaluation. There are a number of reports in the literature on the calculation of sedimentation coefficients from separations of biomacromolecules performed in a centrifuge tube [15,44,45]. According to Equation (1), it is possible to calculate sedimentation coefficients from the radial locations of the various zones once the centrifugal run is terminated. To this end, a centrifugal separation of the cluster mixture was carried out in a graduated test tube. The *R<sup>D</sup>* values in Equation (1) are taken from the center of mass of the zones. The initial position *R*<sup>0</sup> is assumed as the interface between sample zone and density gradient (Figure S3). The effective time of centrifugation was determined along the lines given by Schumaker [15]. To this end, the course of the rpm values during the entire centrifugal run was recorded. Periods of acceleration and deceleration are considered by plotting the angular velocity-squared ω<sup>2</sup> with the course of the centrifugation time (Figure S2). Integration of *ω*<sup>2</sup> over the entire time span and division by the maximum value of *ω*<sup>2</sup> *max* gave an effective centrifugation time of 470.4 s at maximum angular velocity *ωmax* (here: 2513.4 s−<sup>1</sup> ).

The calculation according to Equation (1) will yield the actual sedimentation coefficients of the different nanoparticle populations within the density gradient. The latter can be considered as dispersion medium with a gradual change not only in density but also in viscosity. In DCS, the impact of the medium is considered by the measurement constant *k*. Hence, sedimentation coefficients determined by DCS reflect experimental conditions identical to those assumed for the particles used as a calibration standard. The data gathered in Figure 3 refer to the sedimentation in pure water at 25 ◦C. To allow for a comparison with the DCS values, it is necessary to correct the values determined from preparative separations by the mean viscosities and densities, which the particles experience during their sedimentation. This correction can be made by using the following expression [44]:

$$s\_{\rm PC} = s\_{\rm G} \cdot \frac{\rho\_p - \rho\_W}{\rho\_p - \rho\_G} \cdot \frac{\eta\_G}{\eta\_W} \,\tag{5}$$

where *sPC* and *s<sup>G</sup>* denote the sedimentation coefficients of a given particle population at 25 ◦C in pure water and in the gradient. *ρ<sup>W</sup>* = 0.997 g cm−<sup>3</sup> and *η<sup>w</sup>* = 0.891 g m s−<sup>1</sup> are the density and viscosity of water at 25 ◦C.

The mean density and viscosity of the gradient, *ρ<sup>G</sup>* and *ηG*, were determined as follows: first, the sucrose concentrations at the zone centers were calculated based on the linear profile of the gradient (Figure S3). Densities and viscosities of aqueous sucrose solutions given in ref. [41] were plotted against the weight proportion of sucrose and subjected to a polynomial fitting (Figures S4 and S5). The fitting functions were integrated from the minimal concentration of sucrose in the gradient (2% (m/m)) to the concentration of sucrose at the zone center (Figure S3). Division by the difference in the two sucrose concentrations yields the mean density and viscosity during the sedimentation of a given particle population. In the concentration range considered, the densities and viscosities increase virtually on a linear scale (Figures S4 and S5). Hence, the derivation of the quantities *ρ<sup>G</sup>* and *η<sup>G</sup>* could be also simplified by averaging the respective quantities at the beginning and at the end of the sedimentation path.

Figure 5 shows a comparison of the sedimentation coefficients *sPC* calculated from the radial positions of the zone centers within the centrifuge tube with the quantities

determined by DCS. Notably, the sedimentation coefficients obtained by the two strategies deviate by less than 8%. This is remarkable, inasmuch as there are a number of uncertainties in the calculation of accurate sedimentation coefficients from the results of rate-zonal separations carried out in centrifuge tubes [46]. The following issues must be considered: radial positions of the zone centers within the centrifuge tube with the quantities determined by DCS. Notably, the sedimentation coefficients obtained by the two strategies deviate by less than 8%. This is remarkable, inasmuch as there are a number of uncertainties in the calculation of accurate sedimentation coefficients from the results of rate-zonal separations carried out in centrifuge tubes [46]. The following issues must be considered:

Figure 5 shows a comparison of the sedimentation coefficients *sPC* calculated from the

from the minimal concentration of sucrose in the gradient (2% (m/m)) to the concentration of sucrose at the zone center (Figure S3). Division by the difference in the two sucrose concentrations yields the mean density and viscosity during the sedimentation of a given particle population. In the concentration range considered, the densities and viscosities increase virtually on a linear scale (Figures S4 and S5). Hence, the derivation of the quantities *ρG* and *ηG* could be also simplified by averaging the respective quantities at the be-


*Nanomaterials* **2021**, *11*, 1027 14 of 18

3. uncertainties in the positions of the zones; 3. uncertainties in the positions of the zones;

ginning and at the end of the sedimentation path.


**Figure 5.** Cross-comparison of sedimentation coefficients shows excellent agreement between the quantities determined by DCS and those estimated from preparative centrifugal separation. The bisecting red line is added for ease of classification and to indicate deviations from full convergence. **Figure 5.** Cross-comparison of sedimentation coefficients shows excellent agreement between the quantities determined by DCS and those estimated from preparative centrifugal separation. The bisecting red line is added for ease of classification and to indicate deviations from full convergence.

This study has shown that deviations in comparison to other methods can be kept This study has shown that deviations in comparison to other methods can be kept low. It is briefly outlined how this was achieved despite the uncertainties listed above.

low. It is briefly outlined how this was achieved despite the uncertainties listed above. This study is centered on the determination of the sedimentation of solid nanoparticles. In contrast to most biological particles or synthetic micro- or nanogels, solid particles do not vary their density while migrating through a density gradient. Uncertainty in particle density is thus limited to experimental errors in the determination of particle densi-This study is centered on the determination of the sedimentation of solid nanoparticles. In contrast to most biological particles or synthetic micro- or nanogels, solid particles do not vary their density while migrating through a density gradient. Uncertainty in particle density is thus limited to experimental errors in the determination of particle densities. The latter can be precisely measured with an uncertainty of less than 0.005 g cm−<sup>3</sup> .

ties. The latter can be precisely measured with an uncertainty of less than 0.005 g cm–3. Considerable uncertainties in the density gradient profile shown in Figure S3 are to be expected in the top layer of the gradient underneath the sample zone. Diffusion of gradient material (here: sucrose) into the sample zone may cause strong deviations from the Considerable uncertainties in the density gradient profile shown in Figure S3 are to be expected in the top layer of the gradient underneath the sample zone. Diffusion of gradient material (here: sucrose) into the sample zone may cause strong deviations from the expected gradient profile [32,46]. However, it turned out that this phenomenon had little effect on the calculated values of the sedimentation coefficients. This was achieved by setting an effective sedimentation time, allowing the zones of migrating particles to reach positions far from the first layers of the gradient (Figure S3).

Uncertainties in radial positions relate to both the starting zone and the final positions of the zones of banded particles. Precise allocation of the beginning of the sedimentation path is challenging inasmuch as the profile of density gradient is not well known at the interface between the sample zone and the top layer of the gradient. It may thus be justified to define the starting position either by the interface itself or as the center of mass within

the sample zone. In the present case, the two positions differed by 2.1 mm. This value can be reduced by smaller sample volumes at the expense of the number of particles that can be separated in a single run. In this work, the nanoparticles were dispersed in pure water. For this reason, streaming is to be expected within the sample zone. This is why the diverse nanoparticle populations rapidly accumulate near the interface of sample and gradient during acceleration of the centrifuge. It is exactly for this reason that the radial position of the beginning of the gradient (*R* = 70.14 mm) was chosen as the beginning of the sedimentation path for all nanoparticle populations. This definition was corroborated by the agreement with the values from DCS and hydrodynamic modeling.

The sedimentation coefficients were calculated from the radial positions of the centers of mass of the zones, which are affected by the centrifugal field. As a result, the particle distributions deviate from Gaussian profiles. In the present case, uncertainty of the zone position had little effect because of the low bandwidths resulting from the narrow size distributions of the particle populations. Nonetheless, further refinement could be achieved by taking into account the interplay of sedimentation and diffusion along the lines given by Schumaker [15].

Variation in the temperature inside the rotor chamber may have a marked effect on the sedimentation of the particles. An uncertainty of 1 ◦C will cause an error of over 2.5% in the determination of sedimentation coefficients [46]. Variations in temperature affect both the density and viscosity of the gradient and can become a major problem when calculating sedimentation coefficients from centrifugal separations. In the DCS measurements shown above, this problem was circumvented by using an internal calibration standard of known sedimentation coefficient. It is also possible to use the same strategy in preparative centrifugal separations. Alternatively, values obtained from preparative separations can be corrected by DCS analysis of at least one component. In the present case, this was not done to identify deviations among the methods.

Collisions of nanoparticles with the walls of cylindrically shaped centrifuge tubes may occur. Particles that hit the wall may stick to it or accumulate near the wall and then settle down as an ensemble at modified sedimentation velocities [15,47]. Only those particles that escape from collision with the side wall, exhibit ideal sedimentation behavior. The latter fraction is larger if the centrifuge tube is placed in a swinging bucket following the direction of the centrifugal field. Further improvement can be achieved by using either radially shaped centrifuge tubes [15] or zonal rotors that avoid wall effects by allowing the sedimentation to proceed within a bowl-shaped chamber [32].

Notwithstanding these uncertainties, the present results have shown that close agreement with sedimentation coefficients, either experimentally measured by DCS or predicted by theoretical modeling, can be achieved. Consequently, the three rather different approaches in determining sedimentation coefficients complement each other very well. Sedimentation coefficient distributions, which are readily accessible by DCS, have proven a valuable tool to optimize the centrifugal separation of nanoparticle mixtures.

#### **4. Conclusions**

The agglomeration of nanoparticles yields a large variety of supraparticles, which differ in their aggregation numbers, their compositions, their spatial dimensions, and, finally, their shapes. Clusters of a limited number of nanoscale constituents underlie Brownian motion and have well-defined geometries if prepared by a template-based assembling strategy. This makes the latter ideal model systems for testing analytical tools that are suitable for exploring multimodal mixtures of complex nanoparticles. The latter is challenging and time-consuming with common analytical methods. This is because they provide either poor statistics, such as electron microscopy, or require separation into monomodal fractions prior to their use. The strength of DCS to investigate multimodal mixtures lies in the fact that DCS performs the analytics online, while the nanoparticle mixture is being separated into its individual components. The application of DCS was demonstrated by the analysis of mixtures of colloidal clusters. Nanoparticle clusters of

more than 12 constituent particles could be resolved as discrete bands. This, in turn, allowed for an immediate allocation of the observed bands to distinct species. Without any sophisticated mathematical deconvolution, DCS gave access to accurate sedimentation coefficient distributions, simply by using the elementary units of the assemblies as an internal reference. In this way, DCS facilitates an easy-to-use and efficient analysis of colloids with anisotropic shapes, which do not obey Stokes' law. This was verified by comparison with theoretical predictions of sedimentation coefficients for various species of the multimodal mixture by hydrodynamic bead-shell modeling, which considers the exact geometry of the species.

The sedimentation coefficient distributions determined by DCS can be used to optimize routines for preparative centrifugal separations. This study has shown the separation of a total of 11 different populations of colloidal molecules into defined zones within a sucrose density gradient. In addition, the estimation of sedimentation coefficients from the locations of the zones was demonstrated. In this context, the present work could extend an approach, originally established in biological separations, to synthetic nanoparticles.

The feasibility of DCS analysis and its practical application to optimize centrifugal separations suggests the broad applicability of DCS to other nanoparticle systems, including irregularly shaped colloids or mixtures of compositionally heterogeneous nanoparticles.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/ 10.3390/nano11041027/s1, Figure S1: DCS raw data: light extinction recorded as the function of the sedimentation time, Figure S2: Centrifugal run log to estimate the effective time of centrifugation, Figure S3: Profile of the sucrose density gradient built in the centrifuge tube, Figure S4: Viscosities of aqueous sucrose solutions as functions of temperature and concentration; Figure S5: Densities of aqueous sucrose solutions as functions of temperature and concentration.

**Author Contributions:** Conceptualization, C.S.P. and A.W.; sedimentation analysis, C.S.P.; hydrodynamic modeling, R.S.; data validation, C.S.P., R.S. and A.W.; investigation, C.S.P. and R.S.; writing original draft preparation, A.W.; writing—review and editing, C.S.P., R.S. and A.W.; visualization and figures, C.S.P.; supervision, A.W.; project administration, C.S.P.; funding acquisition, A.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the DEUTSCHE FORSCHUNGSGEMEINSCHAFT within SFB1214/B4.

**Data Availability Statement:** The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

**Acknowledgments:** Technical support from the Particle Analysis Centre (PAC) and the Nanostructure Laboratory (nano.lab) at the University of Konstanz is gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


### *Article* **Multimaterial 3D Printing for Arbitrary Distribution with Nanoscale Resolution**

**Fengqiang Zhang <sup>1</sup> , Changhai Li 2,\*, Zhenlong Wang 1,2,\*, Jia Zhang 1,2 and Yukui Wang <sup>1</sup>**


Received: 3 July 2019; Accepted: 30 July 2019; Published: 2 August 2019

**Abstract:** At the core of additive manufacturing (3D printing) is the ability to rapidly print with multiple materials for arbitrary distribution with high resolution, which can remove challenges and limits of traditional assembly and enable us to make increasingly complex objects, especially exciting meta-materials. Here we demonstrate a simple and effective strategy to achieve nano-resolution printing of multiple materials for arbitrary distribution via layer-by-layer deposition on a special deposition surface. The established physical model reveals that complex distribution on a section can be achieved by vertical deformation of simple lamination of multiple materials. The deformation is controlled by a special surface of the mold and a contour-by-contour (instead of point-by-point) printing mode is revealed in the actual process. A large-scale concentric ring array with a minimum feature size below 50 nm is printed within less than two hours, verifying the capacity of high-throughput, high-resolution and rapidity of printing. The proposed printing method opens the way towards the programming of internal compositions of object (such as functional microdevices with multiple materials).

**Keywords:** 3D printing; nano-resolution; arbitrary distribution; multimaterials; deposition surface; rapidity; large scale

#### **1. Introduction**

Three-dimensional printing is well-known as one of the disruptive technologies affecting the future, which may bring about the third industrial revolution. Due to its capacity of rapid prototyping for arbitrary shape, it is widely applied in aerospace [1], medical health [2,3], structural electronics [4], and mold [5]. The traditional 3D printing technologies including stereolithography [6,7], selective laser sintering [8,9], fused deposition modeling [10,11] have consistently been improved, however they are still subject to the low-throughput and low-resolution fundamentally resulting from point-by-point printing and large printing unit size, in which the optimum printing resolution of approximately 20–50 µm is available [12]. Therefore, as an extension of 3D printing, continuous liquid interface production is developed with higher efficiency [13–15], as well as femtosecond laser direct writing based on two-photon polymerization with higher resolution of up to 100 nm [16–21]. Nevertheless, a trade-off of efficiency and resolution is still difficult to realize.

In addition, without an effective and precise controlling strategy of position of multiple materials, the state-of-the-art 3D printing technology still faces enormous challenges to achieve real printing of multiple materials for arbitrary distribution [22–28]. The study of 3D printing has been stagnating at the primary stage of controlling object shape for a long time [6] and a serious breakthrough is needed for the senior stage of programming internal compositions [29], despite some achievements such as the printing with hybrid multimaterials [22], printing via multiple nozzles with different materials [23,30], simple and imprecise controlling of compositions by the assisted physical morphology [24–26],

magnetism [27], chemical reaction [28], etc. Three-dimensional printing of multiple materials with nano-resolution can create further applications in micro- and nano-scale multifuctional device [31,32] and high-level biological tissues [33]. Therefore, how to control multiple materials with high resolution and efficiency to construct objects has attracted more interest from the researchers. As mentioned by American scientist Hod Lipson, the core of real 3D printing was the capacity of achieving arbitrary distribution of multiple materials [29], which is what we have been doing.

In this study, we demonstrate the precise control of the position of multiple materials for arbitrary distribution by means of the morphological characteristics. The established physical model shows that a complex distribution on a section can be achieved by the vertical deformation of multimaterial lamination. The deformation is controlled by a special surface of the mold and a contour-by-contour printing mode is revealed in the actual process. A large-scale concentric ring array with a minimum feature size below 50 nm is printed within less than two hours, demonstrating the nano-resolution and rapidity of printing. Simultaneous improvement of resolution and efficiency considered as a pair of contradictions is realized. The proposed printing strategy makes a great extension of function and application of 3D printing technologies.

#### **2. Experimental Details**

#### *2.1. Fabrication of Concentric Ring Array*

A 2-inch patterned sapphire substrate (PSS, Zhejiang Bolant Semiconductor Technology Co., Ltd., Zhejiang, China.) with conical structure array (Figure S1) was used as the deposition substrate and cleaned by argon (Ar) plasma before deposition of materials. Then the alternative depositions of tungsten and aluminium (99.99% purity, Beijing Goodwill Metal, Co., Ltd., Beijing, China) on the PSS were implemented in the argon atmosphere of 0.45 Pa using a high vacuum multiple target magnetron sputtering coating machine (JCP-350M2, Beijing Technol Science Co., Ltd., Beijing, China). Deposition thickness of W and Al was set at 120 nm except the first layer with thickness of 240 nm, and the total number of deposition layers was twenty-three (See Table S1 for details). To achieve uniform thickness of deposition film, the substrate holder was simultaneously cooled with circular liquid nitrogen and rotated during deposition. Finally, the required lamination was obtained (Figure S2) and the concentric ring array on the section *z* = 1.83 µm of lamination was further revealed after removing the upside materials using ultra-precision lathing and polishing paste (Al2O3, 10–50 nm, Microspectrum Technology Co., Ltd., Shanghai, China.). The whole process took less than 2 h.

#### *2.2. Characterization*

The scanning electron microscope (SEM) images were collected from the field emission scanning electron microscope (Supra 55 Sapphire, Carl Zeiss, Oberkochen, Germany) at an acceleration voltage of 20 kV. The morphology of microstructures array was measured by the atomic force microscope (AFM, dimension fastscan, Bruker, Billerica, MA, USA). The transmission electron microscopy (TEM) specimen was prepared by using Helios NanoLab 600i FIB/SEM Dual-Beam system (FEI, Hillsboro, OR, USA). The TEM, high-resolution TEM (HRTEM), energy-dispersive X-ray (EDX) and high-angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) images were taken from in-situ multifunctional transmission electron microscopy (Talos F200X, FEI, Hillsboro, OR, USA) at an acceleration voltage of 200 kV.

#### **3. Results and Discussion**

#### *3.1. 3D Printing Strategy for an Arbitrary Distribution of Multiple Materials*

Figure 1 illustrates the 3D printing strategy for an arbitrary distribution of multiple materials. The principle diagram of achieving arbitrary distribution is shown in Figure 1a–d. The lamination *S* is composed of materials *W*(*i*) (*i* = 1 . . . *n*) in a certain order, in which an arbitrary curved surface

*z* = *f*(*x*, *y*) and datum *z* = *g* are given (Figure 1a). Deformation from the surface *z* = *f*(*x*, *y*) to the datum *z* = *g* is implemented (Figure 1b). For instance, these points I–VII on the surface *z* = *f*(*x*, *y*) move vertically *h*I–*h*VII to the datum, respectively. Correspondingly, the transformation from the lamination *S* to lamination *V* is forced as well as the bottom plane *z* = *k* to the surface *z* = *F*(*x*, *y*) by the same rule. The distribution of multiple materials is obtained by intercepting the section *z* = *g* in the lamination *V* (Figure 1c). In addition, the curved surface *z* = *f*(*x*, *y*) is endowed with corresponding materials and projected vertically onto a plane, resulting in the transverse distribution (Figure 1d). The comparison reveals that the distribution on the section *z* = *g* is absolutely the same with the transverse distribution of the curved surface *z* = *f*(*x*, *y*) within the lamination *S*. Therefore, an arbitrary and complex distribution on a plane can be programmed and achieved via the designing of corresponding curved surface *z* = *f*(*x*, *y*) and longitudinal deforming of lamination *S* of multiple materials. The core of the strategy lies in the realizing of transformation from simply longitudinal laminating of multiple materials to complex transverse distribution via longitudinal deformation. *Nanomaterials* **2019**, *9*, x FOR PEER REVIEW 3 of 10 implemented (Figure 1b). For instance, these points I–VII on the surface *z* = *f*(*x*, *y*) move vertically *h*I– *h*VII to the datum, respectively. Correspondingly, the transformation from the lamination *S* to lamination *V* is forced as well as the bottom plane *z* = *k* to the surface *z* = *F*(*x*, *y*) by the same rule. The distribution of multiple materials is obtained by intercepting the section *z* = *g* in the lamination *V* (Figure 1c). In addition, the curved surface *z* = *f*(*x*, *y*) is endowed with corresponding materials and projected vertically onto a plane, resulting in the transverse distribution (Figure 1d). The comparison reveals that the distribution on the section *z* = *g* is absolutely the same with the transverse distribution of the curved surface *z* = *f*(*x*, *y*) within the lamination *S*. Therefore, an arbitrary and complex distribution on a plane can be programmed and achieved via the designing of corresponding curved surface *z* = *f*(*x*, *y*) and longitudinal deforming of lamination *S* of multiple materials. The core of the strategy lies in the realizing of transformation from simply longitudinal laminating of multiple

**Figure 1.** Three-dimensional printing strategy for arbitrary distribution of multiple materials. (**a**–**d**) Principle diagram of achieving arbitrary distribution of multiple materials. Arbitrary curved surface *z* = *f*(*x*, *y*) and datum *z* = *g* are given within lamination *S* of multiple materials *W*(*i*) (**a**). The deformation (**b**) from the surface *z* = *f*(*x*, *y*) to the datum *z* = *g* is implemented. For instance, the points I–VII of surface *z* = *f*(*x*, *y*) move vertically *h*I–*h*VII to the datum, respectively. Correspondingly, the transformation from lamination *S* to lamination *V* is forced by the same rule. Then the section *z* = *g* (**c**) is intercepted from lamination *V*, on which the multimaterial distribution can be obtained. That the distribution on the section *z* = *g* is exactly the same with transverse distribution of surface *z* = *f*(*x*, *y*) (**d**) is observed. (**e**–**l**) Schematic diagram of 3D printing process for arbitrary distribution of multiple materials. The deposition surface of the mold is prepared and source materials *W*(*i*) (*i* = 1 … *n*) are designed for printing (**e**). Materials *W*(1)…*W*(*i*)…*W*(*n*) are successively deposited on the deposition surface of the mold to further print corresponding material on the section *z* = *g* (**f**–**k**). The section *z* = *g* can be obtained by machining deposition body (**l**). Based on the principle, the schematic diagram of 3D printing process for arbitrary distribution of **Figure 1.** Three-dimensional printing strategy for arbitrary distribution of multiple materials. (**a**–**d**) Principle diagram of achieving arbitrary distribution of multiple materials. Arbitrary curved surface *z* = *f*(*x*, *y*) and datum *z* = *g* are given within lamination *S* of multiple materials *W*(*i*) (**a**). The deformation (**b**) from the surface *z* = *f*(*x*, *y*) to the datum *z* = *g* is implemented. For instance, the points I–VII of surface *z* = *f*(*x*, *y*) move vertically *h*I–*h*VII to the datum, respectively. Correspondingly, the transformation from lamination *S* to lamination *V* is forced by the same rule. Then the section *z* = *g* (**c**) is intercepted from lamination *V*, on which the multimaterial distribution can be obtained. That the distribution on the section *z* = *g* is exactly the same with transverse distribution of surface *z* = *f*(*x*, *y*) (**d**) is observed. (**e**–**l**) Schematic diagram of 3D printing process for arbitrary distribution of multiple materials. The deposition surface of the mold is prepared and source materials *W*(*i*) (*i* = 1 . . . *n*) are designed for printing (**e**). Materials *W*(1) . . . *W*(*i*) . . . *W*(*n*) are successively deposited on the deposition surface of the mold to further print corresponding material on the section *z* = *g* (**f**–**k**). The section *z* = *g* can be obtained by machining deposition body (**l**).

multiple materials is revealed, in which the longitudinal deformation is controlled by the morphology (Figure 1e–l). According to the bottom surface *z* = *F*(*x*, *y*) of lamination *V* (Figure 1b), the deposition surface *z* = *F*(*x*, *y*) of the mold is prepared and source materials is given for 3D printing (Figure 1e). Then the deposition on the deposition surface is conducted in order of *W*(1)…*W*(*i*)…*W*(*n*) through Based on the principle, the schematic diagram of 3D printing process for arbitrary distribution of multiple materials is revealed, in which the longitudinal deformation is controlled by the morphology (Figure 1e–l). According to the bottom surface *z* = *F*(*x*, *y*) of lamination *V* (Figure 1b), the deposition

surface *z* = *F*(*x*, *y*) of the mold is prepared and source materials is given for 3D printing (Figure 1e). Then the deposition on the deposition surface is conducted in order of *W*(1) . . . *W*(*i*) . . . *W*(*n*) through atomic deposition technology such as magnetron sputtering (Figure 1f–k, top), resulting in controllable printing of corresponding material on the section *z* = *g* (Figure 1f–k, bottom) and the lamination *V* can be achieved (Figure 1k). Finally, the designed distribution of multiple materials is obtained by removing these materials upon the section *z* = *g* (Figure 1l). Notably, deposition on the deposition surface is obviously the process of printing multiple materials for the distribution on the section *z* = *g*, and the deposition rate determines the printing speed. Contour-by-contour printing of materials is conducted according to these section contours of deposition surface from top to bottom (Figure 1f–k, bottom), in which the dependence of printing direction is on the height of morphology. The contour-by-contour (rather than point-by-point) printing brings about the rapidity of 3D printing of multiple materials. *Nanomaterials* **2019**, *9*, x FOR PEER REVIEW 4 of 10 atomic deposition technology such as magnetron sputtering (Figure 1f–k, top), resulting in controllable printing of corresponding material on the section *z* = *g* (Figure 1f–k, bottom) and the lamination *V* can be achieved (Figure 1k). Finally, the designed distribution of multiple materials is obtained by removing these materials upon the section *z* = *g* (Figure 1l). Notably, deposition on the deposition surface is obviously the process of printing multiple materials for the distribution on the section *z* = *g*, and the deposition rate determines the printing speed. Contour-by-contour printing of materials is conducted according to these section contours of deposition surface from top to bottom (Figure 1f–k, bottom), in

Figure 2 illustrates the analysis of the printing resolution. The lamination *V* is achieved via multimaterial deposition on a conical structure with triangular contour, in which the slope of the mold and the thickness of deposition layer *W*(*i*) are α and *h*, respectively (Figure 2a). Then the width *w* of *W*(*i*) on the section *z* = *g* in the lamination *V* is investigated. There is an equation *w* = *h*/tan(α) resulting in the width *w* of *W*(*i*) decreasing with the decrease of the thickness *h* of *W*(*i*) or the increase of the slope α of the mold. The width *w*<sup>1</sup> and *w*<sup>2</sup> of *W*(*i*) on the section *z* = *g* are obtained by decreasing the thickness (*h*<sup>1</sup> < *h*) of deposition layer *W*(*i*) and increasing the slope (α<sup>2</sup> > α) of the mold, resulting in the inequalities *w*<sup>1</sup> < *w* and *w*<sup>2</sup> < *w*, respectively (Figure 2b,c). From Figure 2, the width *w* of *W*(*i*) on the section *z* = *g* can theoretically reach nanoscale and even atomic level, when the thickness *h* of *W*(*i*) is small enough or the slope α of the mold is lager enough. Notably, the thickness of the monolayer atoms can be easily fabricated by the atomic deposition. Therefore, nanoscale resolution printing is feasible and suitable for the substrate with a complex structure. At this time, a good trade-off between the resolution and throughput is realized. which the dependence of printing direction is on the height of morphology. The contour-by-contour (rather than point-by-point) printing brings about the rapidity of 3D printing of multiple materials. Figure 2 illustrates the analysis of the printing resolution. The lamination *V* is achieved via multimaterial deposition on a conical structure with triangular contour, in which the slope of the mold and the thickness of deposition layer *W*(*i*) are α and *h*, respectively (Figure 2a). Then the width *w* of *W*(*i*) on the section *z* = *g* in the lamination *V* is investigated. There is an equation *w* = *h*/tan(α) resulting in the width *w* of *W*(*i*) decreasing with the decrease of the thickness *h* of *W*(*i*) or the increase of the slope α of the mold. The width *w*1 and *w*2 of *W*(*i*) on the section *z* = *g* are obtained by decreasing the thickness (*h*1 < *h*) of deposition layer *W*(*i*) and increasing the slope (α2 > α) of the mold, resulting in the inequalities *w*1 < *w* and *w*2 < *w*, respectively (Figure 2b,c). From Figure 2, the width *w* of *W*(*i*) on the section *z* = *g* can theoretically reach nanoscale and even atomic level, when the thickness *h* of *W*(*i*) is small enough or the slope α of the mold is lager enough. Notably, the thickness of the monolayer atoms can be easily fabricated by the atomic deposition. Therefore, nanoscale resolution printing is feasible and suitable for the substrate with a complex structure. At this time, a good trade-off between the

**Figure 2.** Analysis of the printing resolution. (**a**) The width *w* of *W*(*i*) on the section *z* = *g* in the lamination *V* under the conditions of the slope α of the mold and the thickness *h* of deposition layer *W*(*i*). There is an equation *w* = *h*/tan(α) resulting in the width *w* of *W*(*i*) decreasing with the decrease of the thickness of *W*(*i*) or the increase of the slope of the mold. (**b**) The width *w*1 of *W*(*i*) on the section *z* = *g* by decreasing the thickness (*h*1 < *h*) of deposition layer *W*(*i*). There is an inequality *w*1 < *w*. (**c**) The width *w*2 of *W*(*i*) on the section *z* = *g* by increasing the slope (α2 > α) of the mold. There is an inequality *w*2 < *w*. **Figure 2.** Analysis of the printing resolution. (**a**) The width *w* of *W*(*i*) on the section *z* = *g* in the lamination *V* under the conditions of the slope α of the mold and the thickness *h* of deposition layer *W*(*i*). There is an equation *w* = *h*/tan(α) resulting in the width *w* of *W*(*i*) decreasing with the decrease of the thickness of *W*(*i*) or the increase of the slope of the mold. (**b**) The width *w*<sup>1</sup> of *W*(*i*) on the section *z* = *g* by decreasing the thickness (*h*<sup>1</sup> < *h*) of deposition layer *W*(*i*). There is an inequality *w*<sup>1</sup> < *w*. (**c**) The width *w*<sup>2</sup> of *W*(*i*) on the section *z* = *g* by increasing the slope (α<sup>2</sup> > α) of the mold. There is an inequality *w*<sup>2</sup> < *w*.

In the process of 3D printing, the deposition surface acts as a series of masks, and contour-bycontour printing of same-material on the section *z* = *g* is conducted to further achieve self-assembly of multiple materials. The distribution on the section *z* = *g* is actually a mapping of the deposition surface and mapped by laminating multiple materials on the deposition surface. Therefore, this is a new method of 3D printing for rapidly achieving an arbitrary nano-resolution distribution of multiple materials on a large scale, which is called Morphology-Guided Printing (MGP). In the process of 3D printing, the deposition surface acts as a series of masks, and contour-by-contour printing of same-material on the section *z* = *g* is conducted to further achieve self-assembly of multiple materials. The distribution on the section *z* = *g* is actually a mapping of the deposition surface and mapped by laminating multiple materials on the deposition surface. Therefore, this is a new method of 3D printing for rapidly achieving an arbitrary nano-resolution distribution of multiple materials on a large scale, which is called Morphology-Guided Printing (MGP).

#### *3.2. Concentric Ring Array Fabricated by MGP Method 3.2. Concentric Ring Array Fabricated by MGP Method*

resolution and throughput is realized.

Figure 3a-f schematically illustrates the MGP process of multiple materials on the printing section *z*=*g* on the PSS with conical structure array (Figure S1). Half of a single conical structure is used for observing and has a like-parabola contour. The pattern on the section *z* = *g* is printed circle by circle from center to edge via the deposition of multiple materials. Using the MGP method, a Figure 3a–f schematically illustrates the MGP process of multiple materials on the printing section *z*=*g* based on the PSS with conical structure array (Figure S1). Half of a single conical structure is used for observing and has a like-parabola contour. The pattern on the section *z* = *g* is printed circle by circle from center to edge via the deposition of multiple materials. Using the MGP method, a concentric ring array is fabricated via alternative deposition of tungsten and aluminium within less than two hours for investigation (Figure 3g–j and Table S1). Figure 3g,h presents top and side view SEM images of pre-processing multimaterial lamination with a thickness of 4.32 µm, respectively. Honeycomb contour and good uniformity of microstructures (Figure S2) of lamination are observed, and uniformity of thickness of deposition layer and alternative laminating of tungsten (white) and aluminium (black) are demonstrated by the internal structure of lamination (red dotted box in Figure 3h). This demonstrates good capacity of deposition of materials and provides strong support for high-solution printing of multiple materials on a certain section. However, some bubbles on the lamination are observed, which may be the result of atomic aggregation in the process of deposition and affect printing accuracy of materials. Figure 3i,j reveals top and side SEM images of post-processing lamination of materials, respectively. The section *z* = 1.83 µm is obtained via removing upper materials, and the uniform concentric ring array is further developed. However, the insert of Figure 3i shows tortuous boundary of rings, resulting from these bubbles. For the section *z* = 1.83 µm of single microstructure, sequential same-material rings are printed circle by circle from center to edge and at the center of the section is just aluminum (red dotted circle shown in Figure 3j). Generally, a large-scale distribution of multiple materials can be rapidly printed on the specified section. *Nanomaterials* **2019**, *9*, x FOR PEER REVIEW 5 of 10 than two hours for investigation (Figure 3g–j and Table S1). Figure 3g,h presents top and side view SEM images of pre-processing multimaterial lamination with a thickness of 4.32 μm, respectively. Honeycomb contour and good uniformity of microstructures (Figure S2) of lamination are observed, and uniformity of thickness of deposition layer and alternative laminating of tungsten (white) and aluminium (black) are demonstrated by the internal structure of lamination (red dotted box in Figure 3h). This demonstrates good capacity of deposition of materials and provides strong support for highsolution printing of multiple materials on a certain section. However, some bubbles on the lamination are observed, which may be the result of atomic aggregation in the process of deposition and affect printing accuracy of materials. Figure 3i,j reveals top and side SEM images of post-processing lamination of materials, respectively. The section *z* = 1.83 μm is obtained via removing upper materials, and the uniform concentric ring array is further developed. However, the insert of Figure 3i shows tortuous boundary of rings, resulting from these bubbles. For the section *z* = 1.83 μm of single microstructure, sequential same-material rings are printed circle by circle from center to edge and at the center of the section is just aluminum (red dotted circle shown in Figure 3j). Generally, a largescale distribution of multiple materials can be rapidly printed on the specified section.

**Figure 3.** Morphology-Guided Printing (MGP) of multiple materials on printing section *z* = *g* based on patterned sapphire substrate (PSS). (**a**–**f**) Schematic diagram of MGP process. PSS and source materials *W*(*i*) (*i* = 1…*n*) for printing are given (**a**). Materials *W*(1)…*W*(*i*)…*W*(*n*) are successively printed circle by circle on the section *z* = *g* (**b**–**e**). The section *z* = *g* is obtained by machining (**f**). (**g**–**j**) MGP of concentric circle array. Top (**g**) and side (**h**) view SEM images of pre-processing multimaterial lamination with a thickness of 4.32 μm are revealed on the PSS. Lamination is formed via alternative depositing of tungsten and aluminum. Honeycomb contour of lamination and good uniformity of microstructures of lamination is demonstrated in (**g**) and a single microstructure is revealed in the insert. W (white)-and-Al (black) alternating lamination (red dotted box) and bulges on the surface of lamination (red dotted circle) are observed in (**h**). Top (**i**) and side (**j**) view SEM images of postprocessing lamination are shown. The section *z* = 1.83 μm is obtained via removing materials. Uniform concentric circle array is shown, and a single concentric circle is revealed in the insert. At the center of the section is just aluminum. **Figure 3.** Morphology-Guided Printing (MGP) of multiple materials on printing section *z* = *g* based on patterned sapphire substrate (PSS). (**a**–**f**) Schematic diagram of MGP process. PSS and source materials *W*(*i*) (*i* = 1 . . . *n*) for printing are given (**a**). Materials *W*(1) . . . *W*(*i*) . . . *W*(*n*) are successively printed circle by circle on the section *z* = *g* (**b**–**e**). The section *z* = *g* is obtained by machining (**f**). (**g**–**j**) MGP of concentric circle array. Top (**g**) and side (**h**) view SEM images of pre-processing multimaterial lamination with a thickness of 4.32 µm are revealed on the PSS. Lamination is formed via alternative depositing of tungsten and aluminum. Honeycomb contour of lamination and good uniformity of microstructures of lamination is demonstrated in (**g**) and a single microstructure is revealed in the insert. W (white)-and-Al (black) alternating lamination (red dotted box) and bulges on the surface of lamination (red dotted circle) are observed in (**h**). Top (**i**) and side (**j**) view SEM images of post-processing lamination are shown. The section *z* = 1.83 µm is obtained via removing materials. Uniform concentric circle array is shown, and a single concentric circle is revealed in the insert. At the center of the section is just aluminum.

To further investigate the printing capacity of MGP method for arbitrary distribution of multiple materials, the section *z* = 1.83 µm with a thickness of less than 100 nm is intercepted by focused ion beam (FIB) and characterized by TEM (Figure 4a–f). Figure 4b shows HAADF-STEM image of single concentric rings unit (red dotted box of Figure 4a), which demonstrates W (white)-and-Al (black) alternative concentric rings. Figure 4c–e exhibits the EDX elemental mapping images of Al, W and their overlap, respectively, which further verify W-and-Al alternative concentric distribution. Figure 4f reveals Al/W component distribution curves along the purple line shown (shown in Figure 4b), in which the position of zero coordinate presents the center of the concentric ring. The transforming of like-rectangle to triangle wave is accompanied by the decreasing of the period in the radial direction. This indicates the widths of the concentric rings have a decreasing trend with increasing in radius, which is caused by the increasing slope of the conical structure (Figure S1). And the W content of less than 100% indicates the doping in W region. Notably, the doping may be caused by atomic diffusion or environmental pollution in the process of deposition. For quantifying the distribution size of materials, the TEM image of specimen is processed using MATLAB software to get ten concentric nanorings with clear and tortuous boundaries (Figure 4g). Then the mean radii and width of distribution of materials are calculated (Table 1), further verifying the decreasing trend of the ring widths. The emphasis is on that the smallest feature size of 41.8nm demonstrates the nanoscale resolution of MGP method. *Nanomaterials* **2019**, *9*, x FOR PEER REVIEW 6 of 10 To further investigate the printing capacity of MGP method for arbitrary distribution of multiple materials, the section *z* = 1.83 μm with a thickness of less than 100 nm is intercepted by focused ion beam (FIB) and characterized by TEM (Figure 4a–f). Figure 4b shows HAADF-STEM image of single concentric rings unit (red dotted box of Figure 4a), which demonstrates W (white)-and-Al (black) alternative concentric rings. Figure 4c–e exhibits the EDX elemental mapping images of Al, W and their overlap, respectively, which further verify W-and-Al alternative concentric distribution. Figure 4f reveals Al/W component distribution curves along the purple line shown (shown in Figure 4b), in which the position of zero coordinate presents the center of the concentric ring. The transforming of like-rectangle to triangle wave is accompanied by the decreasing of the period in the radial direction. This indicates the widths of the concentric rings have a decreasing trend with increasing in radius, which is caused by the increasing slope of the conical structure (Figure S1). And the W content of less than 100% indicates the doping in W region. Notably, the doping may be caused by atomic diffusion or environmental pollution in the process of deposition. For quantifying the distribution size of materials, the TEM image of specimen is processed using MATLAB software to get ten concentric nanorings with clear and tortuous boundaries (Figure 4g). Then the mean radii and width of distribution of materials are calculated (Table 1), further verifying the decreasing trend of the ring widths. The emphasis is on that the smallest feature size of 41.8nm demonstrates the nanoscale resolution of MGP method.

**Figure 4.** Elemental analysis of single concentric ring unit. (**a**) TEM image of specimen. The section *z* = 1.83 μm with W-and-Al alternating rings printed is intercepted by FIB and the thickness of specimen is less than 100 nm. (**b**) HAADF-STEM image of single concentric ring unit shown in red dotted box of (**a**). EDX elemental mapping images of Al (**c**), W (**d**), and their overlap (**e**) are shown. (**f**) Material distribution curves **Figure 4.** Elemental analysis of single concentric ring unit. (**a**) TEM image of specimen. The section *z* = 1.83 µm with W-and-Al alternating rings printed is intercepted by FIB and the thickness of specimen is less than 100 nm. (**b**) HAADF-STEM image of single concentric ring unit shown in red dotted box of (**a**). EDX elemental mapping images of Al (**c**), W (**d**), and their overlap (**e**) are shown. (**f**) Material distribution curves along the purple dotted line shown in (**b**). Scale bar: 500 nm in (**b**–**e**). (**g**) Post-processing material distribution including ten concentric rings using MATLAB software. Material distribution is extracted from TEM image of specimen (**a**) using image processing technology and clearer boundaries are shown. Al (white)-and-W (black) alternative concentric rings are labeled 1 to 10 in turn.


**Table 1.** Radius and width of distribution of multiple materials in Figure 4g.

<sup>a</sup> The concentric rings marked 1 to 10 are shown in Figure 4g. <sup>b</sup> Presenting the mean radius and error of outer circle of each ring calculated by MATLAB software. <sup>c</sup> Determined by the difference between outer and inner radius of each ring.

Then the crystal analysis on the section *z* = 1.83 µm is conducted (Figure 5). Figure 5a shows the TEM image of specimen, where the white and black regions represent the materials of Al and W, respectively. Then the corresponding HRTEM images of these regions marked with red boxes shown in Figure 5a and their selected area electron diffraction (SAED) patterns are exhibited in Figure 5b–i top and bottom, respectively. The evolution of crystal state is shown in Figure 5b–e, in which Figure 5b displays the good single crystal nature of Al in the pure Al region, the crystals of W begin to appear with the doping of W in the transition region (Figure 5c,d) and Figure 5e exhibits the amorphous nature of W in pure W region. Additionally, the red curves (shown in Figure 5c,d) are the boundaries between pure Al, transition and pure W regions. It is worth noting that the single crystals nature of Al is not destroyed by a small amount of doped W in transition region (Figure 5c,d). However, the poly-crystallization occurs in other regions such as transition (Figure 5f,h), pure Al (Figure 5g), and W (Figure 5i) regions, induced by the doping of other elements. This further results in refinement of crystals, low crystallinity and diversification of crystal orientation. Generally, a small amount of doping in the process of printing is further revealed by the crystal analysis, and the same-material printing region of small enough size is vulnerable to contamination. Meanwhile, the doping can be eliminated by some measures, such as using the targets of higher purity, prevention of mutual contamination of targets, improved cooling system for restraining atomic diffusion, and maintaining the adequate cleanliness of the sputtering chamber by cleaning up impurities and an improved vacuum system.

*Nanomaterials* **2019**, *9*, x FOR PEER REVIEW 8 of 10

**Figure 5.** Crystal analysis of specimen. (**a**) TEM image of specimen. (**b**–**i**) HRTEM images (top) and corresponding SAED patterns (bottom) of these regions marked with red boxes in (**a**). Scale bar: 10 nm in (**b**–**i**). In addition, using the same substrate (such as PSS), other distributions are available by **Figure 5.** Crystal analysis of specimen. (**a**) TEM image of specimen. (**b**–**i**) HRTEM images (top) and corresponding SAED patterns (bottom) of these regions marked with red boxes in (**a**). Scale bar: 10 nm in (**b**–**i**).

Figure S3 exhibits a printed distribution on the specified section via depositing gradient materials on the morphology of monolayer cells. By comparison, a high consistency between SEM image of the distribution and optical image of the morphology is observed. Therefore, the feasibility and high resolution of MGP method is further validated as well as the diversity of distribution of multiple

In summary, a new method of nano-resolution 3D printing for rapidly achieving arbitrary distribution of multiple materials on a large scale is proposed. The designed distribution of multiple materials on the specified section can be obtained by the corresponding deformation of lamination of multiple materials. In fact, the deformation of lamination can be realized via the corresponding morphology. Based on atomic deposition on PSS, a concentric ring array with nanoscale resolution on a large scale is printed verifying the rapidity and nanoscale resolution of MGP method. The improvement of atomic deposition including collimation and secondary deposition, and the decreasing of thickness of each layer, will contribute to higher and even atomic resolution of MGP. In addition, almost all materials can be used and are mutually compatible for MGP due to the abundant deposition methods including physical vapor deposition (PVD) and chemical vapor deposition (CVD). Versatile MGP

materials. **4. Summary** 

In addition, using the same substrate (such as PSS), other distributions are available by programming the material type, sequence and thickness of each deposition layer. For instance, the radial gradient circle can be printed by depositing gradient materials on the PSS (Figure 3a–f). Furthermore, when the substrate with a different morphology is used as the substrate, the corresponding distribution can be achieved via the design and depositing of multiple materials. Figure S3 exhibits a printed distribution on the specified section via depositing gradient materials on the morphology of monolayer cells. By comparison, a high consistency between SEM image of the distribution and optical image of the morphology is observed. Therefore, the feasibility and high resolution of MGP method is further validated as well as the diversity of distribution of multiple materials.

#### **4. Summary**

In summary, a new method of nano-resolution 3D printing for rapidly achieving arbitrary distribution of multiple materials on a large scale is proposed. The designed distribution of multiple materials on the specified section can be obtained by the corresponding deformation of lamination of multiple materials. In fact, the deformation of lamination can be realized via the corresponding morphology. Based on atomic deposition on PSS, a concentric ring array with nanoscale resolution on a large scale is printed verifying the rapidity and nanoscale resolution of MGP method. The improvement of atomic deposition including collimation and secondary deposition, and the decreasing of thickness of each layer, will contribute to higher and even atomic resolution of MGP. In addition, almost all materials can be used and are mutually compatible for MGP due to the abundant deposition methods including physical vapor deposition (PVD) and chemical vapor deposition (CVD). Versatile MGP method is also suitable for particle deposition to print macro-scale architecture. More importantly, these sections with the designed distribution can be isolated by micro–nano processing technology such as FIB and further laminated to form an arbitrary distribution of multiple materials in three-dimensional space. Therefore, MGP method makes a great extension of function and application of additive manufacturing and opens the way towards the programming internal components of objects such as transistors.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2079-4991/9/8/1108/s1, Figure S1: Patterned sapphire substrate (PSS), Table S1: Parameters of magnetron sputtering, Figure S2: AFM image of lamination of multimaterials. Good uniformity of microstructures of lamination is demonstrated. Figure S3: Comparison of the morphology of monolayer cells and the distribution of multiple materials.

**Author Contributions:** C.L. and Z.W. conceived the project. F.Z. carried out the experiments, measurements, and analysis, and finished the draft. J.Z. participated in the measurements and modified the manuscript. Y.W. put forward some amendments.

**Funding:** The research was funded by Harbin Boshi Automation Co., Ltd. and Weihai Boshi 3D Technology Co., Ltd. This research was supported by National Natural Science Foundation of China (Grant No. 51775145) and the Major Project of Applied Technology Research and Development Plan of Heilongjiang Province (Grant No. GA16A404).

**Acknowledgments:** We thank Yongze Guo for processing TEM image, Junjie Yang and Likuan Zhu for revision.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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