Nanoseparation of Nanoparticle Mixtures with Similar Surface

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Thermodynamics, Transport, and Fluid Mechanics

Nanoseparation of Nanoparticle Mixtures with Similar Surface Structures through a Facile Two-step Approach Houyang Chen, and Eli Ruckenstein Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b05819 • Publication Date (Web): 28 Jan 2019 Downloaded from http://pubs.acs.org on February 8, 2019

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Industrial & Engineering Chemistry Research

Nanoseparation of Nanoparticle Mixtures with Similar Surface Structures through a Facile Two-step Approach

Houyang Chen*, Eli Ruckenstein* Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA

________________ * To whom correspondence should be addressed. Email: [email protected] (H.C.); [email protected] (E.R.) ACS Paragon Plus Environment

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract: Nanoparticles (NPs) with controlled surface modification have unique properties and broad applications, ranging from biomedicine to catalysis. However, surface modification processes usually generate a mixture of NPs with a range of different surface structures. Herein, based upon coarse-grained molecular simulations, we propose a facile two-step approach for recognition of targeted nanoparticles (TNPs) by a second type of nanostructure, followed by selective precipitation driven by an external force, to extract TNPs from NP mixture with similar surface structures. As an example, we consider mixtures of partially functionalized nanosheets representing graphene flakes of uniform size and shape but varying surface modification. Our results show that Janus particles can effectively recognize and selectively adsorb on targeted graphene NPs (TGNPs) to allow their separation from NP mixture. In our molecular simulations, high purity TGNPs (up 99.9%) could be extracted from a mixture containing only ~10% TGNPs after three to four rounds of separation.

Keywords: Separation; Janus particle; graphene flake; nanoparticle; surface modification

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1. Introduction Nanoparticles (NPs) have found numerous applications based upon their unique size-, shape-, and surface chemistry-dependent properties. However, available NP synthesis methods generally do not generate identical structures, but produce NPs with a distribution of sizes, shapes, and surface structures. Surface modification to control interactions of NPs with one another and their surroundings plays a significant role in their properties and applications1,2,3,4,5,6,7. However, surface modification processes usually produce a range of surface structures. That is, the pattern of attachment of surface-modifying molecules is not necessarily uniform. The different orientation and arrangement of functional groups on the NP surface generates different properties8,9 and affects the NPs’ applications10. Hence, purification of decorated NPs with specific patterns of surface functionalization can be important and meaningful from both scientific and technological perspectives. In the past, separation of NPs has mainly focused on NPs with different sizes and/or shapes. Numerous methods, such as chromatography11, centrifugation12, electrophoresis13, precipitation14, filtration15, extraction16, and ball milling and acid etching17, were developed to separate various types of NPs by size and shape. One can find more details in published reviews18,19. Separations based on highly specific biochemical reactions such as DNA hybridization or antibody-antigen interactions are also well known, but these methods generally accomplish targeting via a binary binding event between complementary components rather than discriminating between different patterns of functionalization with the same molecules. To best of our knowledge, no studies have investigated the separation of NPs with the same size, shape, and overall surface chemistry, but different surface structures, i.e. different patterns of functionalization with the same molecules. In this paper, we propose a facile two-step approach 3 ACS Paragon Plus Environment


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to separate nanoparticles with similar surface properties. The new technique includes recognition and separation processes based on van der Waals and electrostatic interactions, without requiring specific chemical interactions. In the recognition step of the process, the targeted nanoparticles (TNPs) are recognized by agents such as Janus particles (JPs) with size and surface functionalization complementary to the targeted region of surface modification, while in the separation step, the TNPs with these agents attached to them are precipitated by application of an external force. Here, we use an electric field for this second step, but one can imagine using magnetic fields or centrifugal forces instead. As an example, we conducted coarse-grained molecular simulations using Janus particles, which have been widely employed for targeted binding of cells20,21, virus particles22 and other (bio)particles23, and in self-assembly24,25, as agents to extract targeted partially functionalized graphene nanoparticles (TGNPs) from a mixture of partially functionalized graphene NPs with similar surface structures. The two types of graphene NPs in the mixture have the same size and shape and the same fraction of functional groups on their surface, but different patterns of functionalization, i.e. different distributions of the functional groups on their surface. We examine the roles of JPs in the recognition of TGNPs, and identify the temperature-dependent, electric-field-dependent, and initial-fraction-dependent purity and yield of TGNPs that can be achieved by this separation strategy. From this, we broadly outline the conditions required to efficiently separate the TGNPs from the NP mixture. We believe that the conceptually simple framework proposed in this work, and demonstrated through simulation of an idealized model system, can be extended to the separation of NP mixtures with different surface structures and different sizes as well as different shapes. Our Brownian dynamics (BD) simulation results show


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that this technique works well to separate the TGNPs from a NP mixture and indicate that high purity (up to 99.9%) TGNPs could be extracted after one or more rounds of separation.

2. Modeling Similar to the production of multiple products by addition reactions in organic chemistry, functionalization of nanoparticles may generate multiple products with similar surface structures, and these nanoparticles with similar surface structures may possess different properties, which would significantly affect their further applications. For simplicity, we consider a mixture of only two types of NPs. Each NP is constructed as a single layer of a simple cubic cell (SCC) with a size of 4 × 4  0  , where  0 is the diameter of a bead. Each NP includes 4 coarse-grained 2

functionalized beads and 12 coarse-grained unfunctionalized beads. For the non-targeted graphene NPs (non-TGNPs), the functionalized beads are located in the corners of the 4 × 4 array, and, for the TGNPs, the functionalized beads are located at the center 4 positions of the 4 × 4 array (Figure S1a and S1b). We model the JPs as a simple cubic structure with a size of 2 × 2× 2  0  (Figure S1c and S1d). Each JP includes a van der Waals layer (VDW layer) of 4 3

uncharged beads that interact with their surroundings through van der Waals interactions and an electrostatic layer (ESI layer) in which each bead has a reduced charge, q*  q / (4 0  0 0 )1 2 , of -1, where 0 is the vacuum permittivity and  0 is the energy of a bead (well depth of LennardJones interaction potential between beads). Cations are employed to balance the charge in the simulation (Figure S1e). We employ Brownian dynamics (BD) simulations26,27 ,28,29 with an implicit solvent model to investigate the separation behavior. The van der Waals (VDW) interactions between beads 5 ACS Paragon Plus Environment


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follow the Lennard-Jones (LJ) 6-12 potential while the electrostatic interactions between point charges obey the coulomb potential. The VDW interaction between a functionalized bead in a graphene NP and a bead in the VDW layer of a JP is an attractive LJ potential with a cutoff radius rc  2.5 0 while the VDW interaction between the other bead pair includes only the repulsive portion of the LJ potential, with a cutoff radius rc  21 6  0 . Simulations were performed using the LAMMPS package28. Further details of simulation parameters and methodology are provided in the Supporting Information. As described above, and as is typical in coarse-grained molecular dynamics (Brownian dynamics) studies, all simulation parameters were unitless. Table S1 in the Supporting Information summarizes the definitions of the unitless parameters and makes explicit their relationship to real physical variables. As an example of this relationship, we can consider a situation in which the unit of length,  0 , is 25 nm, the unit of energy,  0 , is 8×10-21 J, and the unit of mass, m0, is 5×10-21 kg, which are one set of physically reasonable values. Then, a simulation conducted at unitless parameter values of T *  T /( 0 / k b ) = 0.5, q * = -1, and

E *f  E f (4 0  0 0 )1 2  0 /  0 = 0.1 would correspond to a physical temperature of T = 290 K, charge per bead of -1.5×10-19 C (roughly one elementary charge), and an electric field of 215,000 V/m, which are all realistic and physically achievable conditions. Note that the dielectric strength (electric field for dielectric breakdown) of virtually all solvents exceeds 1 MV/m. One can similarly transform other physical conditions into the unitless variables employed for simulations and vice versa. Of course, our simulations do not span all possible sets of physical conditions, but focus on the range of parameters where the separation process is effective. For a physical situation where one knows the particle size and strength of interactions between particles, one 6 ACS Paragon Plus Environment

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would have to tune the charge of the electrostatic portion of the Janus particles, the temperature, and the electric field to achieve parameter values where the separation process can be effective. In our modeling, we assume that the graphene nanoparticle mixture, the JPs, and the ions are initially randomly distributed in solution. After a particular simulation time, the system achieves an equilibrium state in which the JPs are preferentially adsorbed on the TGNPs. Then, an electric field is applied. In the presence of the electric field, the TGNPs that have JPs adsorbed on them are transported to the wall (which can be viewed as the positive electrode). To evaluate the separation performance of the separation strategy, we computed two quantities: (1) the fraction fe of the nanoparticles collected on the wall after the electric field is introduced, i.e. number of TGNPs collected on the wall as a fraction of total NPs collected on the wall; and (2) yield of TGNPs collected after the electric field is introduced, i.e. number of TGNPs collected on the wall divided by the total number of TGNPs in the system.

3. Results and Discussion Figure 1 illustrates the separation of TGNPs from a mixture of functionalized graphene NPs with similar surface structures. Snapshots of (a) the initial configuration, (b) the configuration at equilibrium, before application of an electric field, and (c) the configuration after applying the electric field are presented in panels (a) through (c). The initial fraction of the TGNPs in the NP mixture in this case was 50%. In the initial configuration (Figure 1a), all NPs and JPs as well as ions are distributed randomly. When the system reaches equilibrium (Figure 1b), JPs are selectively adsorbed on TGNPs and, to a lesser extent, on non-TGNPs due to the interaction between JPs and the functionalized beads in the graphene NPs. This behavior can be visualized in the snapshot shown in Figure 1b, and can be quantified by the radial pair 7 ACS Paragon Plus Environment


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distribution functions g TJ (r ) and g NJ (r ) (Figure 1f and g). Here g TJ (r ) is the radial pair distribution function of functionalized graphene beads in TGNPs and beads in the VDW layers of JPs, and g NJ (r ) is the radial pair distribution function of functionalized graphene beads in non-TGNPs and beads in the VDW layers of JPs. The first peak of g TJ (r ) is located at r /  0 = 1.2 and has a peak value of 590, while the first peak of g NJ (r ) reaches a value of only 11, indicating that the JPs selectively interact with the TGNPs from the graphene NP mixture. This is consistent with the intuitive expectation that the domains of attractive interaction between the JPs and graphene NPs are well-matched for the TGNPs, and are not well-matched for the nonTGNPs. The depletion behavior of the number density of functionalized beads in TGNPs,  T , and of functionalized beads in non-TGNPs,  N , along the z axis, perpendicular to the walls of the domain (squares in Figure 1d and e), demonstrates that all components of the NP mixture are distributed throughout the solution domain during the recognition step. Then, upon applying a reduced electric field, E *f  E f (4 0  0 0 )1 2  0 /  0 , of 0.1, the NPs to which the JPs have adsorbed are driven to the wall (Figure 1c). A few non-TGNPs are also adsorbed on the wall, because the JPs also interact, to some extent, with the non-TGNPs. Most of the non-TGNPs and a smaller fraction of TGNPs remain dispersed in the solution (Figure 1c). The qualitative observations from the snapshots are confirmed by the number density profiles and radial pair distribution functions presented in panels (d) through (g) of Figure 1. This can be explained as follows: (1) some TGNPs do not adsorb any JPs during the recognition step, and (2) some agents (JPs) attached to the TGNPs are desorbed during the separation step, because the force applied to the JPs by the electric field is much larger than the force due to interaction between JPs and TGNPs. The peaks of number density profiles along the z axis confirm the segregation of TGNPs 8 ACS Paragon Plus Environment

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from the solution, and the strong peaks of  T and weak peaks of  N near the wall indicate the high purity of TGNPs captured on the wall (triangles in Figure 1d and e). Although  T (triangles in Figure 1d) is strongly peaked near the wall, it has a non-zero value throughout the domain, confirming that a small fraction of TGNPs remain in solution, and indicating that the yield of collected TGNPs is less than one. The difference in intensity between the peaks of g TJ (r ) at the recognition stage (squares in Figure 1f) and at the separation stage (triangles in Figure 1f) supports the explanation that some JPs that were attached to the TGNPs during the recognition step were pulled away during the separation step. Overall, comparing the snapshots and number density profiles as well as radial pair distribution functions of a mixture of NPs before and after separation shows that this two-step approach can efficiently separate targeted NPs from a mixture of NPs with identical size and shape and a similar pattern of surface functionalization. To further assess the approach and identify its separation performance, we investigated the dependence of purity and yield of TGNPs collected on the wall upon the reduced inverse temperature (1/T*) and the reduced electric field (Ef*) for a fixed value of the reduced charge (q* = -1). Figure 2 presents the fraction of the TGNPs collected on the wall for different parameter combinations. When the initial fraction of TGNPs in the bulk is fi = 0.50 (fi is the fraction of TGNPs in the NP mixture before separation) and the reduced temperature is high (i.e. the reduced inverse temperature 1/T* (=1.0) is low), the purity of the collected TGNPs, fe, which is the fraction of TGNPs collected on the wall at equilibrium, is ~0.50, which is close to fi, for all values of reduced electric field. This is because, when 1/T*=1.0, the interaction between JPs and the functional groups in the TGNPs is too weak to overcome the entropy reduction associated with binding of the JPs to the TGNPs. Thus, the Janus particles cannot recognize and adsorb on the TGNPs. As 1/T* increases from 1.0 to 3.33 (absolute temperature decreases by a factor of 3), 9 ACS Paragon Plus Environment


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fe first increases then decreases. With increasing 1/T* (decreasing reduced temperature), the interaction between the VDW layers of JPs and functionalized beads in TGNPs overcomes the entropy reduction and the JPs bind to the TGNPs. Over a range of 1/T* the interaction between JPs and functionalized beads in most non-TGNPs is still too weak to overcome the entropy reduction associated with adsorption of JPs onto the non-TGNPs. However, upon further increasing 1/T*, the interaction between JPs and the functionalized beads in non-TGNPs is able to overcome the entropy reduction, and more JPs are adsorbed onto non-TGNPs in the recognition step. These can later be collected on the wall in the separation step, reducing the purity of the collected TGNPs. For values of 1/T* at which the JPs efficiently adsorb on TGNPs but rarely adsorb on non-TGNPs the recognition step of the separation is effective. Under these conditions, the purity of TGNPs collected first increases then decreases with increasing reduced electric field. At low reduced electric field, the TGNPs with adsorbed JPs are not driven to the walls, whereas at high reduced electric field, the JPs may be pulled away from the TGNPs. Based upon the above considerations, we identify suitable ranges of 1/T* and reduced electric fields to efficiently separate the NP mixtures with similar surface functionalization. For fi = 50%, we obtain fe > 80% in a single round of separation when 1/T* is between 1.67 and 3.33 and the reduced electric field is between 0.05 and 0.20. The highest purity achieved starting from fi = 50% was fe = 95% (Figure 2a). We also investigated the separation performance for fi = 0.125 and fi = 0.875 (Figure 2b and c). These scenarios could reflect purification through multiple rounds of separation, beginning from a starting mixture with a relatively low concentration of the targeted NPs. Observed trends with respect to 1/T* and reduced electric field were similar to those observed 10 ACS Paragon Plus Environment

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for fi = 0.5. From the results, we can draw four key conclusions: (1) a broad range of 1/T* values can produce fe > 0.98 when fi =0.875; (2) multiple rounds of separation may be required to obtain high purity targeted nanoparticles from nanoparticle mixtures with similar surface functionalization; (3) the highest purity reached was 99.9% with a yield of ~84%; and (4) high purity targeted NPs could be extracted from very low-grade TGNPs (e.g. fi ~10% ) via multiple rounds of separation, with the number of rounds required and the overall yield depending upon the fi in the first round. To further evaluate the separation of TGNPs from binary nanoparticles, the yields of TGNPs were computed (Figure 3). For 1/T*  1.5, the yields are less than 0.4 because few TGNPs adsorb the JPs. For 1/T* > 1.5, upon increasing the reduced electric field, the yield first increases and then decreases. For example, with 1/T* = 2.5 for fi = 0.125, 0.5, and 0.875, the yield is less than 0.07 when the reduced electric field (Ef*) is 0.01. When the reduced electric field is increased to 0.05, the yields are in the range of 0.5-0.65 and with further increases of the reduced electric field to 0.10 and 0.15, the yields exceed 0.75. The yields decrease at even higher electric field. These trends in yield of collected particles reflect a balance between the reduced electric field and the strength of interaction between VDW layers of JPs and the functionalized beads in TGNPs. As the strength of interaction between the JPs and the TGNPs increases, relative to the entropic cost of adsorption, more TGNPs adsorb JPs and can therefore be separated. When the interactions become stronger, some non-TGNPs also adsorb JPs. This primarily effects the purity of collected TGNPs, but could also affect the yield if the supply of JPs and capacity of the walls for collection is finite. Nanoparticles with JPs attached are collected on the wall upon the application of the electric field. As discussed above, a minimum value of reduced electric field is required to drive collection of the particles, but if the reduced electric 11 ACS Paragon Plus Environment


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field becomes too large, it may drive desorption of JPs from TGNPs, decreasing the yield of collected particles. Using only cations to balance the charge of the JPs may not be physically realistic. Thus, we also take the effect of the presence of salts into account. Our results (Figures S2 and S3) showed that the fraction and yield of TGNPs remain the same as those without salt at moderate reduced salt mass concentrations, whereas they decrease at high reduced salt mass concentrations. The reduction of the separation efficiency at high reduced salt mass concentrations may be attributed to the charge screening effects. For practical application of the proposed separation strategy one must address at least three key issues. The first one is that the agents that interact with the targeted NPs should enable application of an external force. In our work, we choose Janus particles whose electrical charge allows them to respond to an applied electric field. In other circumstances, one might select an agent that responds to a magnetic field, or simply a high density agent that allows force to be applied through centrifugation. The second key issue is the recognition capability of the agents used for separation. NPs with similar surface functionalization, differing only in the arrangement of functional groups on their surface, will inherently have similar interactions with the agents employed for separation. Chemical interaction strategies that rely on specific bonding between molecules on the targeted nanoparticles and on the separation agents are unlikely to succeed in this case, because they are insensitive to the arrangement of functional groups. Thus, creating an agent that strongly recognizes the targeted NPs and weakly recognizes the non-targeted NPs is extremely challenging. The present strategy, which relies on patterns of physical interactions, can overcome this challenge. The results presented here provide guidance for the interaction energy (1/T*) ranges that could allow one to selectively adsorb separation agents mainly on 12 ACS Paragon Plus Environment

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targeted NPs and less on non-targeted NPs. The third key issue is the strength of the external force to be applied, which in turn will depend on the properties of the targeted NPs and the separation agent. Here, we employed an electric field due to the Janus particles having charges and NP mixtures having van der Waals interactions only. In this case, a suitable strength of electric field is required for effective separation. Both too weak and too strong fields provide poor separation performance. The results presented here provide guidance on the selection of an appropriate field strength, or appropriate force applied to the targeted NPs, which is sufficient to drive separation, but not high enough to drive desorption of the agents from the targeted NPs. We have considered a single value of reduced charge of the Janus particles (q* = -1 for each bead in the ESI layer of JPs), but for separation of uncharged particles, the value of reduced charge will only affect the magnitude of electric field required for separation, and not the interactions between the Janus particles and the particles being separated. We note that most prior nanoparticle separation approaches have focused on nanoparticle mixtures of differing sizes, shapes, or overall surface functionalization. Separation of NPs of identical size, shape, and average functional group coverage, but different patterns of functional group coverage, has rarely, if ever, been considered. Prior separation methods relied on differences in NP properties induced by differences in size, shape, or overall surface functionalization, and thus cannot be applied to the case considered here. However, because NP mixtures with varying size, shape, and overall surface functionalization also inherently have different patterns of surface functionalization, we expect that the method proposed here can be extended to those systems as well. Because recognition of targeted NPs from a mixture of NPs with different surface structures and with different shapes and/sizes is easier than separating



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them from NP mixtures with similar patterns of surface functionalization, we expect high separation performance for those cases.

4.Conclusions In conclusion, by employing Janus nanoparticles as separation media, we proposed a new separation strategy, which includes targeted nanoparticle recognition and selective precipitation steps, to extract nanoparticles with a specific pattern of surface functionalization in high purity and with high yield. In Brownian dynamics simulations of this approach simulating the separation of targeted graphene nanoparticles (TGNPs) from a mixture of targeted and nontargeted NPs, we obtained TGNPs with a particular surface structure in high purity (up to 99.9%) directly from a mixture containing 87.5% TGNPs. This purity could be obtained from low-purity 12.5% TGNPs via 3 to 4 rounds of separation. The number of rounds required depends upon the fraction of TGNPs in the mixture. The separation concept developed in this work provides a new strategy to extract very high-purity targeted NPs from low-grade materials when the non-targeted NPs and targeted NPs have the same size, the same shape, and similar surface functionalization. Further, this approach could sequentially separate each type of NPs in a mixture and could be extended to separate NP mixtures with different surface structures and with different sizes and/or shapes.

Supporting Information Quantities, their units and corresponding reduced quantities; simulation details; the model employed; fraction and yield of TGNPs collected at moderate and high reduced salt mass concentrations. 14 ACS Paragon Plus Environment

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The Supporting Information is available free of charge on the internet at

ACKNOWLEDGMENTS We thank the Center for Computational Research at the University at Buffalo (SUNY) for providing computational resources to carry out this study.

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Page 19 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Representative snapshots from a simulation of the separation of targeted graphene nanoparticles (TGNPs) from a mixture with non-targeted graphene nanoparticles (non-TGNPs) via the proposed two-step approach at 1/T* = 2.5 and reduced electric field E *f = 0.1. (a) Initial configuration; (b) configuration after equilibration, but prior to application of E *f ; (c) configuration after E *f has been applied; (d) number density profiles  T of functionalized graphene beads in TGNPs along the z axis, perpendicular to the walls, parallel to the electric field gradient; (e) number density profiles  N of functionalized graphene beads in non-TGNPs along the z axis; (f) radial pair distribution functions g TJ (r ) of functionalized graphene beads in TGNPs and beads in VDW layers of JPs; (g) radial pair distribution functions g NJ (r ) of functionalized graphene beads in non-TGNPs and beads in VDW layers of JPs. In panels (a-c) ions are not shown. In panels (d-g) symbols used are circle ( ): initial configurations; square ( ): configurations at equilibrium without electric field; triangle (

): configurations after the

electric field was applied. The inset in panel (d) shows an expanded vertical scale.



0.030

0.0020

(d)

0.025

(e) 0.0015

0.020

N(z)

T(z)

0.0015

0.0010

0.015 0.0005

0.010

0.0010 0.0005

0.0000

0.005

-20.0 -10.0

0.0

10.0

20.0

0.0000

0.000 -20.0 -10.0 0.0 10.0 20.0

-20.0 -10.0 0.0 10.0 20.0

z/0

z/0

600

(f)

15

400

gNJ(r)

gTJ(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 23

200

10 5 0

0 0.0

(g)

2.0

r/0

4.0

0.0

2.0

r/0

4.0


Page 21 of 23

Figure 2. Fraction fe of TGNPs collected on the wall at equilibrium for values of the initial fraction fi of TGNPs in the bulk of (a) 0.50; (b) 0.125; and (c) 0.875. Symbols used are circle ( ): reduced electric field E *f = 0.01; square ( ): E *f = 0.05; triangle up ( down (

): E *f = 0.10; triangle

): E *f = 0.15; diamond ( ): E *f = 0.20; star ( ): E *f = 0.30; plus ( ): E *f = 0.50.

Short dashed lines are a guide for the eye.

0.8

(a)

fraction fe

fraction fe

1.0

0.8

0.6

0.4 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1/T*

fraction fe

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0

(b)

0.6 0.4 0.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1/T*

(c)

0.9

0.8 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1/T*



Figure 3. Yield of TGNPs collected on the wall at equilibrium when the initial fraction fi of TGNPs in the bulk are (a) 0.50; (b) 0.125; and (c) 0.875. Symbols used are circle ( ): reduced electric field E *f = 0.01; square ( ): E *f = 0.05; triangle up (

): E *f = 0.10; triangle down (

):

E *f = 0.15; diamond ( ): E *f = 0.20; star ( ): E *f = 0.30; plus ( ): E *f = 0.50. Short dashed lines are a guide for the eye.

1.0

1.0

(a)

0.8

yield

yield

0.8 0.6 0.4

(b)

0.6 0.4

0.2

0.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1/T*

1/T*

1.0 0.8

yield

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 23

(c)

0.6 0.4 0.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1/T*


Page 23 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For Table of Contents Only

(1)Janus Particles (2)External force


Nanoseparation of Nanoparticle Mixtures with Similar Surface

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