SPIONs self-assembly and magnetic sedimentation in quadrupole magnets: Gaining insight into the separation mechanisms

Abstract

Superparamagnetic iron oxide nanoparticles (SPIONs) are currently popular materials experiencing rapid development with potential application value, especially in biomedical and chemical engineering fields. Examples include wastewater management, bio-detection, biological imaging, targeted drug delivery and biosensing. While not exclusive, magnetically driven isolation methods are typically required to separate the desired entity from the media in specific applications and in their manufacture and/or quality control. However, due to the nano-size of SPIONs, their magnetic manipulation is affected by Brownian motion, adding considerable complexities. The two most common methods for SPION magnetic separation are high and low gradient magnetic separation (HGMS and LGMS, respectively). Nevertheless, the effect of specific magnetic energy fields on SPIONs, such as horizontal (perpendicular to gravity), high fields and gradients (higher than LGMS) on the horizontal magnetophoresis and vertical sedimentation of SPIONs has only recently been suggested as a way to separate very small particles (5 nm). In this work, we continue those studies on the magnetic separation of 5–30 nm SPIONs by applying fields and gradients perpendicular to gravity. The magnetic field was generated by permanent magnets arranged in quadrupolar configurations (QMS). Different conditions were studied, and multiple variables were evaluated, including the particle size, the initial SPIONs concentration, the temperature, the magnetic field gradient and the magnetic exposure time. Our experimental data show that particles are subjected to horizontal magnetic forces, to particle agglomeration due to dipole–dipole interactions, and to vertical sedimentation due to gravity. The particle size and the type of separator employed (i.e. different gradient and field distribution acting on the particle suspension) have significant effects on the phenomena involved in the separation, whereas the temperature and particle concentration affect the separation to a lesser extent. Finally, the separation process was observed to occur in less than 3 mins for our experimental conditions, which is encouraging considering the long operation time (up to days) necessary to separate particles of similar sizes in LGMS columns that also employ permanent magnets.

1. Introduction

Significant progress has been made with respect to the use of magnetic nanoparticles in the last two decades. This has occurred in parallel with the significant improvement in relatively low-cost permanent magnets. With the development of advanced synthetic technologies, a series of magnetic nanoparticles with controllable shape and stability have been successfully produced [1]. Their size ranges from nano- to micro-scale. As the particle size decreases to several nanometers, these entities present special physical properties, such as high specific surface area, biocompatibility, multifunctionality and superparamagnetism [1]. Among those diverse magnetic particles, superparamagnetic iron oxide nanoparticles (SPIONs) have excellent behavior with sizes smaller than 50 nm in diameter. They are synthesized from iron oxides forming crystals, usually in the form of magnetite (Fe₃O₄) or maghemite (Fe₂O₃) [2], and have the potential to be further surface-modified or conjugated with various ligands. SPIONs are sensitive to magnetic fields; they can be magnetized by an external magnetic field and be separated from the medium in which they are suspended by a magnetic field gradient. However, unlike ferromagnetic materials, when the applied magnetic field is removed, the SPIONs do not maintain their magnetization, a fact that prevents them forming stable aggregates [3]. With these unique properties, SPIONs have gained much attention by researches in a wide range of applications, predominately in the biomedical and environmental fields [4–5]. More precisely, they can be applied in wastewater management (removal of heavy metals and dyes) [6], targeted drug delivery (surface modified with a certain functional group, like a binding specific antibody as a drug carrier) [3,7], magnetic resonance imaging (MRI) contrast agents [8], and biosensing.

In separation applications, the desired captured entity (typically suspended in the liquid media) needs to be moved through the media to a specific location through magnetophoresis. This represents an essential and complex step, which takes advantage of the differences in the magnetic properties of the components (i.e. the particles and the surrounding fluid) under externally applied magnetic field gradients. This technology is more promising than other conventional techniques for separating solids from liquids due to its multiple benefits, such as high separation efficiency, cost-effectiveness and low energy consumption [9]. During the last two decades, the two most common magnetophoretic methods for SPION separation have been the high gradient magnetic separation (HGMS) and low gradient magnetic separation (LGMS). These two technologies differ in the magnitude of the applied magnetic field gradient [10]. In most cases, HGMS systems are packed columns filled with ferromagnetic fibers or wires, which are often magnetized with electromagnets, especially when high flow rates or volumes need to be processed. With the surrounding electromagnet, high magnetic field gradients (more than 1,000 Tm⁻¹) can be produced [10–11,13–14]. On the contrary, LGMS does not involve specialized packed columns, which allows the separation process to be carried out in smaller volumes, even in microtubes [12]. Permanent magnets are usually employed as the magnetic field source for LGMS. This technology, although simple, typically provides low magnetic field gradients, less than 100 Tm⁻¹ [10].

Nevertheless, while those magnetophoretic driven separation methods have been applied to separate magnetic nanoparticles, the mechanisms behind the processes are not fully understood [15]. In HGMS systems, under the inhomogeneous magnetic field gradient conditions, the magnetic separation process is challenging for it to be predicted and modeled precisely [16]. The other major disadvantage of the HGMS is that the magnetic wires or filters may cause the blockage of the column by particle aggregation or sedimentation (i.e “plugging”) [17]. Moreover, these columns are expensive due to the use of electromagnets, with the corresponding high energy consumption. On the other hand, LGMS cannot provide the magnetic field gradient necessary to recover small SPIONs from the media in a reasonable amount of time. Moreover, due to the nanometer size of the SPIONs, their magnetic manipulation is hindered by Brownian motion [15]. Thus, it is of great significance to develop a simple, low cost and effective method to separate or recover small SPIONs from a liquid.

In our previous study [18], we reported the magnetophoretic behavior of 5 nm SPIONs after applying horizontal (i.e. perpendicular to gravity), high magnetic fields (1.36–1.68 T) and gradients (286–1750 T/m) provided by two quadrupole magnet sorters (QMSs). We suggested that some of the particles were able to aggregate and sediment (as a result of gravity) and the process was accomplished in a short time (within 20 min). In order to gain insight into the separation mechanisms, the study of more variables and parameters is required. Here we investigate the effect of other variables in the magnetophoretic behavior of SPIONs suspended in chloroform of sizes ranging between 5 and 30 nm, using two QMSs with different field intensities and gradients [19].

2. Theory

When the particle suspended in the chloroform solution is placed inside the QMS, it is subjected to several forces, including the magnetic force F_mag and gravitational force F_grav. The magnetophoretic force experienced by a single magnetic particle is governed by the particle size, its magnetization and the magnetic field gradient:

$$F_{mag}=\frac{4}{3}\pi {\mu }_0{r}^3{M}_P\nabla H$$ (1)

where μ₀ is the magnetic permeability of vacuum, r is the particle radius,M_p is the saturation magnetization of the particle, and H is the magnitude of the magnetic field intensity. On the other hand, the gravitational force acting on the particles is expressed as:

$$F_{grav}=\frac{4}{3}\pi r^{3}g\mathrm{\Phi >\Delta }\rho$$ (2)

where g is the standard gravity (approximately 9.8 m/s²) and Δρ is the density difference between the particles and the fluid (i.e. chloroform).

In addition to these important forces, the magnetic particles are suspended in the solvent liquid by Brownian motion, which is typically expressed as thermal energy (kT). Thus, here we introduce a term Φ, which represents the ratio between gravitational energy and thermal energy: [27]

$$\mathrm{\Phi }=\frac{gravitationalenergy}{thermalenergy}=\frac{\frac{4}{3}\pi r^{3}g\mathrm{\Delta }\rho L}{kT}$$ (3)

where L is a characteristic length, k is the Boltzmann’s constant, and T is the temperature. Analogously, the ratio between the magnetic energy and the thermal energy (ε) is expressed as: [27]

$$\epsilon =\frac{magneticenergy}{thermalenergy}=\frac{{\mu }_0\frac{4}{3}\pi r^3{M}_{P}H}{kT}$$ (4)

However, the magnetic behavior of the SPIONs is also influenced by the magnetic dipole–dipole interactions [20]. The ratio between the dipole–dipole contact energy and thermal energy, Ψ, can be expressed as:²⁹

$$\mathrm{\Psi }=\frac{dipole-dipolecontactenergy}{thermalenergy}=\frac{{\mu }_0\pi r^3{M}_P^2}{9kT}$$ (5)

The magnetic dipole–dipole interaction that exists between the particles induces their aggregation. Nevertheless, some researchers demonstrated that the assembly behavior does not depend only on Ψ but also on the volume fraction ϕ₀ for diluted suspensions (for volume fractions in the order of 10⁻⁶–10⁻⁴) [21].

It is generally assumed that, before the magnetic field is applied, the particles suspended in the solvent are distributed randomly, while the average separation distance between particles (d_pp) can be described as: [21]

$$d_{pp}=2.7\frac{d}{6{\varphi }_0^{\hspace{0.17em}\hspace{0.17em}1/3}}$$ (6)

where d is the diameter of the particles, and ϕ₀ is the volume fraction of the suspension occupied by the particles. After applying a sufficiently high magnetic field, the SPIONs experience magnetic dipole–dipole interactions. For this case, the magnetic Bjerrum length λ_B can be introduced, which represents the distance at which the energy associated to attractive magnetic interaction between the SPIONs is equal to the thermal energy: [21]

$${\lambda }_B=d^{\ast }{\mathrm{\Psi }}^{1/3}$$ (7)

According to Faraudo et al. [21], the kinetics of the self-assembly process can be determined by d_pp and λ_B. More specifically, the SPION motion is dominated by the magnetic dipole–dipole interaction when λ_B≫d_pp, whereas for the opposite case, the particle motion is essentially diffusive and a colloid only experiences the magnetic interaction with another particle after randomly diffusing across the distance separating both colloidal entities.

Moreover, the self-assembly behavior of SPIONs can also be described by Θ, combining both the dipole–dipole contact energy and the particle volume fraction as: [21]

$$\mathrm{\Theta }={\mathrm{\Psi }}^{\ast }{\varphi }_0$$ (8)

When Θ≫0.1, the motion of the particles is dominated by the magnetic interaction (fast self-assembly), whereas the case in which Θ≪0.1 represents the situation at which diffusion dominates the particle motion. This threshold value of 0.1 results from combining Equations (6) and (7) and has been reported previously in the literature [21].

Finally, it should be noted that the SPIONs behavior can also be influenced by electric dipole–dipole interactions. However, the particles used in this study, iron oxide nanoparticles coated with oleic acid, have shown an outstanding colloidal stability, achieving a 7 times better performance against agglomeration and precipitation in comparison to other SPIONs with no coating (bare iron oxide nanocrystals) [22–24]. Therefore, and due to the improved zeta potential of SPIONs coated with oleic acid, electric dipole–dipole interactions have been neglected in this study. The forces, energies, and parameters provided in this section will be calculated for all the experimental conditions tested in this work.

3. Experimental methods

3.1. Sample preparation

The SPIONs (organic iron oxide nanoparticles in chloroform, catalog numbers SOR-5–50, SOR-15–50 and SOR-30–50) employed in this work were obtained from Ocean Nanotech (San Diego, CA, USA). These iron oxide nanocrystals have uniform sizes of 5 nm, 15 nm and 30 nm, respectively. They are coated with oleic acid and suspended in chloroform with an initial concentration of 25 g⋅L^-1. In this study, these SPIONs were diluted in toluene (Sigma-Aldrich, 99.9% purity) to reach the concentrations of 20, 15, 10, and 2.5 g⋅L^-1. In order to study the aggregation behavior of SPIONs, cross-sectionally square glass tubes (1 mm i.d., 1.4 mm o.d., VitroCom, catalog number 8100–600) of 6 cm of length were used, with the bottom melted. The width of the inner tube is denoted as w, where w = 0 indicates the position at the wall, and w = 0.5 mm represents the center of the tube. The suspensions were injected into the glass tubes up to a height (h) of 3 cm, and the top end of the tubes was sealed with Parafilm® M.

3.2. Magnetic separation experiments

The behavior of SPIONs suspended in chloroform/toluene was studied by using different QMSs, the magnetic field strengths B₀ and gradients B₀/r₀ were described in previous reports [25–26]. Briefly, the quadrupole magnet arrangement produces a constant magnetic gradient in the radial direction: B₀/r₀ = 1750 T/m for the 1.91 mm bore, denoted as QMS_A, with B₀ = 1.68 T on the wall, and B₀/r₀ = 286 T/m for the 10.2 mm bore, denoted as QMS_B, with B₀ 1.36 T on the wall.

The glass tubes containing the SPION suspensions were inserted in the QMSs (Fig. 1 a)) and left inside for varying times, up to 1 hr. At time intervals of 1, 3, 5, 10, 30 and 60 mins, the tubes were taken out of the QMSs for imaging, which allowed us to characterize the separation behavior of the SPIONs. The process was conducted under two different temperature conditions, room temperature (RT) at 20 °C, and a lower temperature (FT) at –24 °C, which was achieved by placing the devices inside a freezer. As a reference case, we employed the 30 nm SPIONs, at a concentration of 25 g⋅L⁻¹, at room temperature, inserted in QMS_B for 1 h. The analysis of the other variables was performed individually by changing our reference case conditions when needed.

Fig. 1.

a) 3-D isometric view of the QMS system, illustrating the location of the channel containing the SPIONs; b) Experimental set-up scheme of the CCD camera and the light source.

The image recording procedure was performed using a system consisting of a CCD camera (Retiga EXi Fast 1394, Qimaging, Burnaby, British Columbia, Canada), an infinity lens (Isco-Optic, Göttingen), a liquid crystal filter (Kurios-WL1, Thorlabs, Newton), and a lamp (Dolan-Jenner Fiber-Lite, Model 180, Boxborough) providing the illumination, as shown in Fig. 1 b). The wavelength of the filter was set at 550 nm in order to provide the optimal visualization of results as well as the clearest images.

The images taken by the camera were analyzed using ImageJ (https://imagej.nih.gov/ij/). More specifically, the greyscale of the image pixels could be correlated to the SPION concentration distribution (Supplementary figures S1 a)-c)). The measurements were taken at least twice for every condition. This image processing analysis method of digital images provides quantitative measurements of the system, similar to the method used by Mykhaylyk et al. [28] The relationship between the greyscale values and the concentration of SPIONs was obtained by measuring SPION suspensions of known concentrations (see Supplementary Figure S1). For each experimental condition, the SPION concentration was calculated based on the observed greyscale value.

4. Results and discussion

In order to understand the SPION separation mechanisms under high fields and gradients, different conditions were studied. Table 1 reports the most relevant experiments performed in this work (Supplementary material contains all the experimental conditions tested). Moreover, Table 2 provides the value of the forces acting on the SPIONs, as well as the ratios between different energies and other parameters introduced in Section 2 for those experimental conditions. To organize both the studies and results, the following subsections present the effect of: the field and gradient distribution, particle size, operation time, temperature and SPION initial concentration.

Table 1.

Experimental conditions tested in this work.

Experiment #	Particle size (nm)	Temperature (K)	Concentration (g⋅L−1)	Separator	Operation time
1	30	293	25	QMSA	1 h
2	30	293	25	QMSB	1 h
3	15	293	25	QMSB	1 h
4	5	293	25	QMSB	1 h
5	30	293	25	QMSB	1 min
6	30	293	25	QMSB	3 min
7	30	293	25	QMSB	5 min
8	30	293	25	QMSB	10 min
9	30	293	25	QMSB	30 min
10	30	249	25	QMSB	1 h
11	30	293	20	QMSB	1 h
12	30	293	15	QMSB	1 h
13	30	293	10	QMSB	1 h
14	30	293	2.5	QMSB	1 h

Table 2.

Forces and ratios of energies acting on the system for the experiments reported on Table 1.

Experiment #	Fmag (fN)	Fgrav (fN)	Φ (−)	ε (−)	Ψ (−)	dpp (nm)	λB (nm)	Θ (−)
1	7.44	4.87 ×10−4	3.61	4.6 ×102	32.90	78.9	96.1	0.16
2	1.22	4.87 ×10−4	3.61	1.23 ×103	32.90	78.9	96.1	0.16
3	0.152	6.09 ×10−5	0.45	1.54 ×102	4.11	39.5	24	2.1 ×10−2
4	5.63 ×10−3	2.26 ×10−6	0.02	5.69	0.15	13.2	2.67	2.1 ×10−2
5	1.22	4.87 ×10−4	3.61	1.23 ×103	32.90	78.9	96.1	7.6 ×10−4
6	1.22	4.87 ×10−4	3.61	1.23 ×103	32.90	78.9	96.1	0.16
7	1.22	4.87 ×10−4	3.61	1.23 ×103	32.90	78.9	96.1	0.16
8	1.22	4.87 ×10−4	3.61	1.23 ×103	32.90	78.9	96.1	0.16
9	1.22	4.87 ×10−4	3.61	1.23 ×103	32.90	78.9	96.1	0.16
10	1.22	4.76 ×10−4	4.16	1.45 ×103	38.78	78.9	102	0.19
11	1.22	5.04 ×10−4	3.74	1.23 ×103	32.90	85	96.1	0.13
12	1.22	5.22 ×10−4	3.86	1.23 ×103	32.90	93.6	96.1	9.9 ×10−2
13	1.22	5.39 ×10−4	3.99	1.23 ×103	32.90	107	96.1	6.6 ×10−2
14	1.22	5.65 ×10−4	4.18	1.23 ×103	32.90	170	96.1	1.6 ×10−2

4.1. Influence of the magnetic field and gradient distribution

To study the effect of the magnetic field and gradient distribution on the SPION magnetic separation, two magnetic separators, QMS_A and QMS_B, were used. In this set of experiments (Experiments 1 and 2 in Tables 1 and 2), suspensions of the 30 nm SPIONs at an initial concentration of 25 g⋅L⁻¹ were placed in the glass tubes at room temperature, respectively. The final equilibrium state of SPIONs (achieved at t = 1 h) was determined.

Fig. 2 a) presents the magnetic field intensity generated inside one of the QMSs. The magnetic field in both QMS_A and QMS_B increases uniformly from the center to the wall, i.e. the magnetic field intensities are maximum at the wall and zero at the center. On the other hand, Figures 2 b1) and b2) illustrate the locations of the glass channels containing the SPIONs when inserted into QMS_A and QMS_B, respectively. As it can be seen from the figures, because of the different bore sizes of the QMSs, the glass channels are located at different positions inside the QMSs. For QMS_A, the glass channel is inserted in the center of the bore, where a small part of the cross-sectional area of the tube (the center) experiences magnetic fields of almost 0 T. However, in QMS_B, which has a greater diameter, the glass channel is located next to the wall, where the field is higher and consequently, all the particles experience magnetic fields greater than 1 T. In addition to not all of the SPIONs achieving the maximum magnetization in the smaller diameter QMS (i.e. QMS_A), the different location of the tube subjects the SPIONs to a different magnetic field distribution inside the particle suspension; thus, different migration patterns of the SPIONs can be expected. Such different migration phenomena were observed in both devices: the SPIONs in QMS_A move radially, from the center of the tube to the four corners of the channel, while in QMS_B, the SPIONs migrate towards the two corners that are adjacent to the bore wall. Fig. 2 c) shows the experimental images of the final particle location after being inserted for 1 h in both QMS_A and QMS_B. As can be observed, the SPIONs migrate to different points within the glass channels, which is consistent with the fact that the magnetic field increases in the direction of the two corners next to the wall of QMS_B but radially from the center of the tube in QMS_A.

Fig. 2.

Influence of the magnetic field and gradient distribution on the SPION separation. a) Cross sectional field (B) heat map calculated midway down the length of the QMS_A magnet. b1)-b2) Location of the glass channels filled with SPIONs in QMS_A and QMS_B, respectively, showing the movement of the SPIONs inside the channels. c) Experimental figures of the final location of the 30 nm SPIONs (25 g⋅L⁻¹) at room temperature after 1 h. d1)-d2) Greyscale values near the wall (w = 0) and in the center of the tubes (w = 0.5 mm) inside QMS_A and QMS_B. For both figures, the grayscale at time 0 and the grayscale of the background (clear solvent not containing particles) are reported. These represent the maximum (blank) and minimum (initial concentration value) greyscale value that can be achieved within the glass channels. e1)-e2) Ratio between the SPION concentration at t = 1 h and t = 0 near the wall (w = 0) and in the middle of the tube (w = 0.5 mm) for both devices.

The analysis of those experimental images is shown in Fig. 2 d) and e). The greyscale along the h direction near the wall (w = 0) is presented in Figure 2 d1), whereas Figure 2 d2) presents the greyscale values in the center of the tubes (w = 0.5 mm). Whereas the greyscale values reported at the channel wall are similar for both separators (it is difficult to measure the particles on the wall of the channel due to the small thickness of this layer), the analysis of the particles remaining at the center of the tube after 1 h exposure suggests that more particles are separated (removed from the fluid) in QMS_B. In fact, Figures e1) and e2) provide the concentration ratio (dimensionless) of the particles at 1 h over the initial value in both the wall and in the center of the tube. It can be seen that almost 95% of the suspension volume becomes clear for QMS_B at 1 h; however, there exists still a significant number of particles in the solvent after 1 h in QMS_A. This result indicates that more SPIONs migrate towards the wall and/or form aggregates and settle down in QMS_B in comparison to QMS_A. This may be due to the fact that the SPIONs in QMS_B experience larger magnetic field intensities as well as higher magnetic particle–particle interactions than that of in QMS_A. Moreover, different initial concentrations (10–20 g⋅L⁻¹) of the 30 nm SPION suspensions were also tested and the separation results are reported in Supplementary Figures S2 and S3. These figures report similar results, that QMS_B is more efficient in separating the SPIONs from the solution.

As presented in Table 2, whereas the magnetic force acting on the particles is similar in both devices when assuming that the particles are saturated (in fact, the magnetic field gradient is higher in QMS_A than in QMS_B), the parameter ε is one order of magnitude higher in QMS_B. This is due to the fact that the average magnetic field experienced by the particles is higher in this device. Finally, in both devices the particles seem to be accumulated at the bottom of the channel, rather than onto the channel walls. Even though the gravity force experienced by single particles is four orders of magnitude lower than the magnetic force, particles could aggregate, and both migrate to the wall (magnetic field gradient direction) and settle down (gravity direction). In fact, Φ and Ψ are higher than 1 in both devices, which implies that the gravitational and dipole–dipole contact energies are both higher than the thermal energy.

4.2. Effect of particle size

The effect of the particle size was analyzed by using SPIONs with sizes of 5 nm, 15 nm and 30 nm. These experiments were performed in QMS_B at room temperature, as presented in Table 1 (Experiments 2–4 in Tables 1 and 2). After inserting the different SPION suspensions in QMS_B for 1 h, images of the tubes were taken and analyzed.

Fig. 3 a) presents the experimental images of the tubes showing the initial and final SPION suspension distribution for the three sizes under analysis. It can be observed from this set of images that the particle size has a significant effect on the separation of SPIONs. For the 5 nm SPIONs, the separation does not completely take place, as there exists a concentration (or grayscale) gradient over the entire length of the tube. In comparison, the separation is nearly completed for the 30 nm SPIONs; for this size, the particles are accumulated on the bottom of the tube leaving a clear solvent behind. An intermediate behavior is presented for the 15 nm. In this case, more than half of the length of the tube remains clear at 1 h, and at the bottom of the tube, a greyscale/concentration gradient is observed. The different behavior experienced by particles with different sizes is correlated to the concentration plots presented in Fig. 3 b). It can be seen that the value of C_1h/C₀ is almost 0 for the entire tube length (h) for the 30 nm particles. It should be noted that for this particle size, C_1h/C₀ should be greater than 1 at h≈0, however, concentration values above 25 g⋅L⁻¹ are outside our calibration curve and not reported accurately (see Supplementary Figure S1). When the particle size is decreased to 15 nm, the value of C_1h/C₀ drops to almost 0 along the first 1 cm of the tube length, and it remains at around 0 from h = 1 cm to h = 3 cm. Finally, for the 5 nm SPIONs, the value C_1h/C₀ does not reach 0 at any point along h. In fact, for this particle size, the concentration ratio is above 1 from h = 0 to h = 1.5 cm, and below 1 from h = 1.5 cm to h = 3 cm. This suggests that the lower half of the tube has concentration values higher than the initial C₀, and the upper part has concentration values below the initial C₀. For the three cases, the fact that the particles are deposited at the bottom of the tubes suggests that the magnetic sedimentation process takes place for the three sizes. Experiments using suspensions of SPIONs with sizes of 15 nm and 30 nm at different initial concentrations (20, 15, and 10 g⋅L⁻¹) were also carried out. The results (Supplementary Figure S4) suggest that the 30 nm SPIONs experience complete separation for different initial concentration values; however, the 15 nm particles are not fully separated and a gradient in concentration in the vertical direction is observed.

Fig. 3.

Effect of the particle size on the separation performance. a) Experimental figures of the SPIONs contained in the tubes at t = 0 and t = 1 h (5, 15 and 30 nm SPIONs at C₀ = 25 g⋅L⁻¹ in QMS_B at RT). b) Ratio between the SPION concentration at t = 1 h and t = 0 in the middle of the tube (w = 0.5 mm) for SPIONs of 5, 15 and 30 nm. c) Relationship between the gravitational and magnetic (for QMS_A and QMS_B) forces and the particle size. d) Ψ and ε values (for QMS_A and QMS_B) as a function of the SPION size.

The lower separation performance achieved with the smaller particles is explained in Fig. 3 c) and d), where the magnetic and gravitational forces as well as the parameters ψ and ε are reported for the size range under analysis. It can be seen from Fig. 3 c) that both the magnetic force and the gravitational force is several orders of magnitude lower for the 5 nm SPIONs than what is experienced by the 30 nm particles. This decrease is due to the volume effect; when the particle size is decreased 6 times, the volume decreases three orders of magnitude. On the other hand, Fig. 3 d) represents the values of Ψ and ε (for both QMS_A and QMS_B). As presented in Table 2, ε remains above 1 for all the sizes, suggesting that the magnetic energy is higher than the thermal for all the conditions. However, Ψ is only higher than 1 for the 15 nm and 30 nm SPIONs (around 4 and 33 for the 15 and 30 nm SPIONs, respectively). This implies that the magnetic dipole–dipole interactions experienced by 30 and 15 nm particles are slightly higher than the thermal energy, but not for the 5 nm particles, where Ψ remains around 0.15. Therefore, the low performance in the separation of 5 nm particles is attributed to the low Ψ value. On the other hand, the ratio between the gravitational energy and the thermal energy (Φ) is smaller than 1 for the particle sizes of 5 nm and 15 nm (see Table 2). Nevertheless, we observed a sedimentation process for the 5 and 15 nm particle sizes (there exists a concentration gradient along h as presented in Fig. 3 b)), suggesting that there might exist a particle agglomeration inside the channel for the 5 and 15 nm SPIONs promoting the sedimentation of the smaller particles. Therefore, the general criterion to describe magnetic dipole–dipole interactions, through ψ, might not be valid under our experimental conditions. In fact, in our previous publication [18], we suggested that the special 3D magnetic field and gradient distribution generated in our QMS should be also taken into account to describe the separation performance of the smaller particles.

4.3. Separation kinetics

The temporal evolution of the magnetophoretic separation and sedimentation of 30 nm SPIONs (at an initial concentration C₀ of 25 g⋅L⁻¹) was studied in QMS_B at room temperature (Experiments 2, 5–9). Fig. 4 a) shows different control images of the tubes taken at different times when no magnetic field is applied. The value of the concentration ratio at times 1 h and 24 h over the initial t₀ is also reported. It can be seen that the separation (only sedimentation due to gravity under this condition) does not take place even after 24 h; the particles remain well dispersed in the solvent due to the action of Brownian motion. Even though the parameter Φ is higher than 1 for the 30 nm particles (see Table 2), 24 h is not enough to observe particle sedimentation in the absence of a magnetic field/gradient. The lack of separation in the absence of magnetic fields proves the outstanding colloidal stability of the particles against precipitation and agglomeration. On the other hand, the temporal evolution of the process after applying a magnetic field/gradient generated by QMS_B for 1, 3, 5, 10, 30 and 60 mins is reported in Fig. 4 b). Here, we observed that the particles initially moved towards the left wall of the channel (in 1 min), which is in the direction of increasing values of the magnetic flux density B (direction of the magnetic field gradient vector). A magnetic dipole–dipole attraction between the particles could also be taking place at the wall, where the interparticle distance is much lower, which may result in the aggregation of SPIONs. As a result of this combination of forces and interactions, the particles also move downwards; as suggested above, gravity force will be expected to increase several orders of magnitude for the particle clusters. As time progresses (3–5 min), the solvent became lighter in areas far from the left wall and the channel bottom, in comparison to the initial condition, indicating the separation of SPIONs. After 1 h, approximately 93% of the total fluid volume became clear, while there was a thin layer of particles aligned at the left wall surface, as well as particle sediments at the bottom of the channel. It should be noted that as time progressed from 3 to 60 min, the particles deposited on the bottom increased, leaving a clear solvent above.

Fig. 4.

Effect of the operation time on the particle separation. a) Concentration ratio (and experimental figures) showing that the particles do not sediment in the absence of a magnetic field for t = 1 h and t = 24 h. b) Experimentally-obtained images of the 30 nm SPIONs (25 g⋅L⁻¹) at room temperature in QMS_B at various time intervals. c) Temporal evolution of the greyscale value (at w = 0.5 mm) along the channel length h. d) Concentration ratio reported at different operation times.

Fig. 4 c) and d) present the temporal evolution of the greyscale value and the concentration ratio (at the channel center w = 0.5 mm) along the channel length h. These figures reveal a slow decay in concentration from h = 0.5 to h = 1.5 cm for t = 1, 3 and 5 mins, whereas after 10 mins, a steep rise of the greyscale value was observed. It can also be seen that there is an increase in greyscale (decrease in concentration) in the h direction for all the operation times tested. Within the experimentally observed time period, the slope of the curve rises with time (the gradient of concentration increases), indicating that more particles settled down while less and less particles remained suspended and/or aggregated at the wall. Such behavior can also be explained from Fig. 4 b), where the particle layer deposited at the bottom of the channel shrunk over time.

The control experiments conducted during 24 h in the absence of a magnetic field demonstrate that no detectable sedimentation process takes place, even though the parameter Φ is higher than 1. In contrast, within one minute, changes in grayscale are apparent, and a steady state condition is achieved within 1 h with a magnetic energy gradient present. As discussed previously, and as presented in Table 2, the distance between particles (d_pp) is slightly smaller than λ_B, suggestive of a SPION motion dominated by magnetic dipole–dipole interactions. We have calculated the time scale of the self-assembly process for the case where the kinetics is dominated by the magnetic interactions. This represents the time needed for the aggregation of two particles initially separated by a distance d_pp, and can be estimated by balancing the viscous drag with the magnetic force [21]. The result is approximately in the order of 10 μs, which suggests an extremely fast self-assembly process that is consistent with the fast sedimentation process that occurs in the QMS (3 min would be necessary to achieve an almost complete separation).

4.4. Effect of temperature

The effect of the temperature on the separation of SPIONs was investigated at two temperatures: room temperature (RT at 20 °C) and inside a freezer (FT at –24 °C) (Experiments 2 and 10 in Table 1). Fig. 5 presents the effect of the temperature on the separation of 30 nm SPIONs using QMS_B. Fig. 5 a) presents the change in the greyscale value measured along the length h in the middle of the tubes (w = 0.5 mm), and in Fig. 5 b) C_1h/C₀ is shown, which is the ratio between the final concentration (at 1 h) and the initial (C₀).

Fig. 5.

Effect of the temperature on the SPION separation. a) Greyscale values in the center of the tubes (w = 0.5 mm) inside QMS_B at room temperature (RT) and in the freezer (FT). The greyscale at time 0 and the greyscale of the background are also reported. b) Ratio between the SPION concentration at t = 1 h and t = 0 in the middle of the tube (w = 0.5 mm) for both temperatures.

It is observed that the separation is not strongly affected by the temperature. However, it appears that the process is facilitated at RT. For example, as presented in Fig. 5 a), the greyscale value for h greater than 0.25 cm at FT is smaller than the value reported at RT. This implies that there were less particles still suspended in the solvent in the middle of the tube at room temperature than that at FT. On the other hand, it can be seen in Fig. 5 b) that the ratio between the final and the initial concentration reaches 0 at lower values of h for RT in comparison to FT. Moreover, Supplementary Figure S5 presents more experiments performed with different SPION initial concentrations (20, 15 and 10 g⋅L⁻¹). It can be seen that, for most of the conditions, increasing the temperature has a slightly positive effect on the separation process, however, for the initial concentration of 10 g⋅L⁻¹, the difference between the two temperatures is subtle.

Φ > 3 (Equation (3)) for both conditions (see Table 2), implying that the SPIONs can overcome the thermal energy and sediment due to gravity. Moreover, the ratios between the magnetic energy and thermal energy, ε, and between the dipole–dipole contact energy and thermal energy, Ψ, are in the same order of magnitude for both conditions and much bigger than 1 (see Table 2). This indicates that for both temperatures, the SPION self-assembly, magnetic separation and sedimentation occur, overcoming the Brownian motion due to thermal energy.

4.5. Effect of initial SPION concentration

To study the effect of the initial SPION concentration, the 30 nm SPION stock suspension (25 g⋅L⁻¹) was diluted with toluene to reach final concentrations of 20, 15, 10 and 2.5 g⋅L^-1. These experiments were performed in QMS_B at room temperature, as presented in Table 1 (Experiments 2, 11–14).

Fig. 6 a) shows the concentration ratio of the particles at 1 h over the initial value in the center of the tube. It can be seen that the value of C_1h/C₀ decreases from 1.2 to almost 0 along the first 0.2 cm of the tube length and it remains at around 0 from h = 0.2 cm to h = 3 cm, for C₀ greater than 10 g⋅L^-1. However, for the initial concentration of 2.5 g⋅L⁻¹, the ratio reaches 2.2 at the bottom of the tube and rapidly reaches zero after that point. The figure also shows that the value h at which the concentration ratio reaches zero increases with C₀, which implies that the higher the concentration, the thicker the layer of particles is formed at the bottom of the channel (i.e. the volume of the packed particles at the bottom increases with the SPION initial concentration).

Fig. 6.

Effect of the SPION initial concentration on the separation performance. a) Ratio between the SPION concentration at t = 1 h and t = 0 in the middle of the tube (w = 0.5 mm) for SPION concentrations of 25, 20, 15, 10 and 2.5 g⋅L^-1. b) d_pp and Θ values as a function of the SPION initial concentration.

Fig. 6 b) represents the values of d_pp and Θ. As listed in Table 2, d_pp is between 3 and 6 times larger than the particle diameter for these concentrations. d_ppdecreases when increasing the concentration, consistent with the larger volume fraction of SPIONs at higher concentrations. On the other hand, Θ is only larger than 0.1 for the 20 and 25 g⋅L⁻¹ suspensions. This implies that the magnetic dipole–dipole interaction dominates for these conditions (higher C₀ values); a fast self-assembly is induced due to the lower interparticle distances. On the other hand, Θ is smaller than 0.1 for C₀ less than 15 g⋅L⁻¹, which indicates that the motion of the SPIONs is dominated by diffusion. For these conditions, the SPION motion is diffusive and a colloid only experiences the magnetic interaction with another particle after randomly diffusing across the d_pp [21]. Nevertheless, we observed the separation through magnetic/gravity means for all the concentration range tested. We did not observe any differences between the concentration range under evaluation. This could mean that the general criteria to predict and describe the self-assembly and magnetic sedimentation process might not be appropriate for our high field, high gradient quadrupolar magnets or for the concentration conditions tested in this work.

5. Conclusion

The availability of superparamagnetic iron oxide nanoparticles (SPIONs) over the last couple of decades has facilitated both basic studies of their properties as well as applications in a variety of fields. However, while the synthesis and applications of SPIONs are topics that have been well studied and reported in the literature, their separation remains a challenge. Thus, it is important to develop an effective method to separate and recover SPIONs with sizes smaller than 50 nm. In this work, we investigated the magnetophoretic behavior of SPIONs of sizes ranging from 5 to 30 nm in our custom designed separators, where high magnetic fields and gradients perpendicular to gravity are produced by quadrupole magnet designs.

In summary, we demonstrated the fast and efficient separation of different SPIONs under different working conditions (magnetic field gradient, particle size, operation time, temperature and SPION initial concentration). First, the analysis of the magnetic field and gradient distribution revealed a different migration pattern of the SPIONs in our different separators, QMS_A and QMS_B. Despite QMS_A has a significantly high gradient (six times higher than QMS_B), QMS_B can promote a more efficient separation than QMS_A. It is believed that this bigger bore magnet separator allows all of the SPIONs to be subjected to saturating magnetic fields (above 1 T), as opposed to QMS_A, where the average field experienced by the particles is two times lower (around 0.45 T). However, in both devices, the particles tend to aggregate and migrate in the direction of both gravity and magnetic field gradient, due to the higher gravitational and dipole–dipole energies in comparison to the thermal energy.

With these magnetic designs, we also demonstrated that the magnetic sedimentation process takes place for the three particle sizes under study (5, 15 and 30 nm). However, the complete separation between the solid particles and the liquid solvent was only achieved for the larger particles, being incomplete for the 5 nm particles. Since the ratios between the dipole–dipole contact energy and the thermal energy, ψ, and between the gravitational energy and thermal energy, Φ, are only smaller than 1 for the 5 nm SPIONs, it is likely that for the larger particles, magnetic dipole–dipole interactions generate particle aggregates that further settle down in our systems. Nevertheless, although the separation was not complete for the 5 nm SPIONs, the partial sedimentation of this material (and the separation of the 15 nm particles) also suggests the possible formation of particle aggregates through dipole–dipole interactions because the value of Φ (gravitational over thermal energy) is smaller than 1 for particle sizes smaller than 30 nm (i.e. the 5 nm and 15 nm particles should not settle down). Therefore, the partial sedimentation of the 5 nm and 15 nm SPIONs with the assistance of magnetic fields must be due to the fact that clusters are formed in the systems, probably through a combination of magnetic forces and magnetic dipole–dipole interactions between the particles after they diffuse through the solvent.

Moreover, the magnetic separation and sedimentation process occurs extremely fast, within 3 mins, which is likely facilitated and sped up by the SPION self-assembly. In fact, this rapid separation is consistent with the time scale needed for the particle self-assembly (10 μs). Further-more, the effect of other variables, such as the temperature and the SPION initial concentration is not very important for the process. For the temperature values that we have tested, the SPIONs can overcome Brownian motion under the effect of thermal energy, and the particle self-assembly, magnetic separation and sedimentation process is achieved. Moreover, no differences in the separation mechanisms were observed among different initial SPION concentrations. Overall, the results reported in this study indicate that the classical criterion to predict SPION aggregation and magnetic sedimentation is not applicable for our experimental conditions.

To conclude, this study demonstrates a fast self-assembly and magnetic separation/sedimentation process of SPIONs of sizes smaller than 30 nm in quadrupole magnets, evidencing that this is a feasible, economical and fast alternative to the complex HGMS/electromagnet separation devices. Thus, this work sheds light on the separation mechanism of SPIONs in quadrupole magnets by self-assembly and magnetic sedimentation.