Technical Note pubs.acs.org/ac
Magnetophoretic Mole-Ratio Method Hitoshi Watarai* and Jayue Chen Institute for NanoScience Design, Osaka University, Toyonaka, Osaka 560-8531, Japan S Supporting Information *
ABSTRACT: The principle of the mole-ratio method utilizing magnetophoretic velocimetry was demonstrated for the first time. The feasibility of the magnetophoretic mole-ratio method was studied for the determination of the stoichiometry of the complexes formed between a hydrophobic phosphate ligand adsorbed in mesoporous hydrophobic silica particles and paramagnetic metal ions of Co(II), Tb(III), and Dy(III) in aqueous solutions. The present method is a nonspectroscopic method and carried out by a simple magnetic device.
ince Yoe and Jones reported the first paper of the moleratio method in 1944,1 it has been widely used to determine the composition of metal complexes mainly utilizing spectrophotometric measurements.2 The spectrophotometric mole-ratio method usually made the plots of the absorbance of a complex against the mole-ratio of a ligand to a metal ion. Mathematical formulation for such plots defined the meaning of the slopes and intercepts of the two straight lines observed under the conditions of an excess amount of a ligand or a metal ion.3 For example, a complex formation reaction between a metal ion, Mq+, and a monoacidic ligand, HL,
S
Mq + + qHL = MLq + qH+
The magnetophoresis is the phenomena that a particle having a magnetic susceptibility different from that of medium is migrated under the magnetic field gradient. Since the magnetophoretic force is proportional to the volume of a particle, the force is more effective for a larger particle and negligibly small for a molecule and an ion. The magnetophoretic velocity, v, of a spherical particle, in the case that the particle is migrated on a vertical x-axis, can be formulated from the balance of the gravity force, the friction force, the buoyancy, and the magnetic force, 2(χp − χm )r 2 ⎛ dB ⎞ ρm ⎞ mg ⎛⎜ ⎟ − v= B⎜ ⎟ + 1 ⎝ dx ⎠ 6πηr ⎜ ρp ⎟⎠ 9ημ0 ⎝
(1)
can be treated by the spectrophotometric mole-ratio method as follows: (1) Setting the initial concentration of Mq+ to be constant, the concentration of HL is varied at a fixed pH, (2) the absorbance of the complex MLq is observed at the wavelength, at which the complex has a substantial absorbance, (3) the absorbances are plotted against the ratio of the analytical concentration of HL and Mq+, which is equal to the mole-ratio of noHL/noM. The plots will change in the manner approaching two straight lines, which give an intersect corresponding to the situation of noHL/noM = q. The spectroscopic mole-ratio method is highly convenient and widely used. However, when the complex has no convenient absorption bands for the measurement, a nonspectroscopic method has to be used. In the present study, we have demonstrated the mole-ratio method utilizing the magnetophoretic velocimetry, which is a new nonspectroscopic determination method of diamagnetic and paramagnetic components in a single particle by using the magnetic susceptibility of the particle measured from the magnetophoretic velocity.4 © XXXX American Chemical Society
(2)
where χp and χm refer to the volume magnetic susceptibilities of the particle and the medium, respectively, r is the radius of the particle, B is the magnetic flux density at the position of the particle, η is the viscosity of the medium, μ0 is the permeability of vacuum, m is the mass of a single particle, g is the acceleration of gravity, and ρp and ρm are the densities of the particle and the medium, respectively. From the measurement of the magnetophoretic velocity, the value of χp is obtained according to eq 2, provided that the value of r can be measured and other parameters are known.5−7 Furthermore, when the particle includes a paramagnetic element, the amount of it can be determined from the molar magnetic susceptibility of the element.5,7 The magnitude of the magnetophoretic velocity depends on the value of B(dB/dx) (T2/m), so a superconducting magnet is effective to generate a larger value for B(dB/dx); for example, 4.7 × 104 T2/m was attained in a Received: March 17, 2017 Accepted: August 24, 2017 Published: August 24, 2017 A
DOI: 10.1021/acs.analchem.7b00999 Anal. Chem. XXXX, XXX, XXX−XXX
Technical Note
Analytical Chemistry superconducting magnet and applied for the detection of Mn(II) in a single droplet at attomole level.5 However, in the case in which a little higher amount of paramagnetic metal ion is involved in a particle, an inexpensive device constructed by using permanent magnets is possible to measure the migration velocity of the particle. In the present study, the principle of the magnetophoretic mole-ratio method was formulated and the principle was demonstrated for the determination of composition of the complexes formed between a hydrophobic ligand, bis(2-ethylhexyl)hydrogen phosphate (HDEHP or HL), and metal ions, Co(II), Dy(III), and Tb(III), in a mesoporous octadecylsilyl (ODS) silica particle. The acidic extractant of HDEHP has been widely used in hydrometallurgy of lanthanide(III) and nuclear fuel treatment, but the reported composition of the extracted complex has included 1:3 and 1:6 complexes in the metal/ligand mole ratio.8−14 Therefore, it will be worthwhile to apply the magentophoretic mole-ratio method to the lanthanide(III)-HDEHP systems and to determine the composition of the complexes. The reason why the silica ODS particle was used as an adsorbent is that it is hydrophobic and effectively adsorbs HDEHP and its complex; therefore, the change in the magnetophoretic velocity can be attributable to the change in the amount of metal ion. In addition, the size controlled particles, which are convenient for the velocity measurement, are commercially available.
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Figure 1. (A) Reaction scheme of the formation of MLq in an ODS particle which migrates by a magnetophoretic force; (B) conceptual illustration of the magnetophoretic mole-ratio plot for the formation of MLq under the constant amount of HL.
PRINCIPLE OF MAGNETOPHORETIC MOLE-RATIO METHOD Hydrophobic silica particles (the total number of N) having each volume of Vp are dispersed in a sample aqueous solution o with a known volume, which contains nM (mol) of a q+ o paramagnetic metal ion, M , and nHL (mol) of a hydrophobic ligand, HL. The ligand is completely adsorbed in the hydrophobic particles. It is assumed that the metal ion and the ligand can form a very stable metal complex, MLq, in the particles according to the reaction of eq 1 (Figure 1A). That is, the metal ion is completely extracted into the particle forming MLq, if noM is smaller than 1/q times of noHL. Therefore, the initial amounts of the metal ion and the ligand are represented by
of (I) and (II), regarding the situation in which noM is changed by keeping noHL constant. For (I), when the initial amount of metal ion, noM, is much less than 1/q times of the initial amount of the ligand, noM ≪ noHL/q, the metal ion completely forms the complex and some free ligand will remain in the particles, nM = 0 o n MLq = nM
o nM = n MLq + nM o nHL
o o nHL = nHL − qnM
= qn MLq + nHL
It is assumed here that the binding constant is extremely large so that the redissociation of the complex due to equilibration and therefore free metal and free ligand from that redissociation are negligible. From eqs 4 and 5, the magnetic susceptibility of the particle under the condition, χp(I), is obtained.
(3)
where nMLq is the total amount of MLq in the particles, nM is the total amount of free metal ion in the aqueous solution, and nHL is the total amount of the free ligand in the particles. In a single particle, the amounts of nMLq/N and nHL/N are present for the metal complex and the free ligand, respectively. In this situation, the volume magnetic susceptibility of a single particle, χp, can be represented by χp =
χML n MLqVMLq q
NVp
+
χHL nHLVHL NVp
+
χp (I) =
χODS VODS Vp
(5)
+
o o ⎛ no ⎞ χ VHLnHL nHL (χML VMLq − qχHL VHL)⎜ oM ⎟ + HL q NVp NVp ⎝ nHL ⎠
χODS VODS Vp
(4)
(6)
Equation 6 will show a straight line, when χp(I) is plotted
where χMLq , χ HL , and χODS are the volume magnetic susceptibilities of the complex, the ligand, and the ODS silica particle, respectively, VMLq and VHL are the molar volumes of the complex and the ligand, and VODS is the net volume of the ODS particle. Now, we will think about two extreme conditions
against
o nM o nHL
( ) as illustrated in Figure 1B.
For II, on the other hand, when the initial amount of metal ion is much larger than the 1/q times of the initial amount of the ligand, noM ≫ noHL/q, B
DOI: 10.1021/acs.analchem.7b00999 Anal. Chem. XXXX, XXX, XXX−XXX
Technical Note
Analytical Chemistry o − n MLq nM = nM o n MLq = nHL /q
nHL = 0
(7)
Then, the magnetic susceptibility of the particle under the condition is obtained, χp (II) =
o χ VODS nHL 1 (χML VMLq) + ODS q NVp q Vp
(8)
Equation 8 will have a constant value in the plot of χp(II) against
o nM o nHL
o nM o nHL
( ), since it does not have a term including ( )
Finally, the value of the intersect of the two lines of eqs 6 and 8 will give o nM 1 o = nHL q
(9)
This determines the composition of the metal complex of MLq as 1:q as shown in Figure 1B.
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Figure 2. (A) Schematic drawing of the magnetophoretic apparatus. (B) Close view of the magnetophoretic cell. (C) Balance of the working forces on a particle in a sample solution; Fg is the gravity force; Ff is the friction force; Fb is the buoyancy; Fm is the magnetic force.
EXPERIMENTAL SECTION Chemicals. The metal salts of TbCl3, DyCl3, and CoCl2 were used as purchased from Nacalai Tesque (Japan). Bis(2ethylhexyl)hydrogen phosphate (HDEHP, Tokyo Chemical Industry Co. Ltd.) was used as a ligand for the metal ions. The suporting material of the ligand was a mesoporous hydrophobic silica gel (Wako silica gel ODS-Q3). The average diameter of the silica gel particles was determined to be 42.3 ± 5.2 μm by using an optical microscope. Triton X-100 (MP Biomedicals. Inc.) was used as a surfactant to assist with the dispersion of the silica gel. Manganese(II) chloride (Wako, GR) solution and the polystyrene particle with 15 μm in diameter (Funakoshi, 0.125 wt %) were used for the measurement of the magnetic field gradient generated in a capillary cell by a pair of permanent magnets. The reagents used in the present study were all reagent grade. Water was purified by a Milli-Q system. The sample solution for the mole-ratio experiments was prepared by mixing 10 mg of the silica gel, 50 μL of 0.10 M HDEHP in ethanol, 0−50 μL of 0.10 M metal salt aqueous solution, and 30 μL of 5% Triton X-100 solution and filled up to 3 mL by water. The pH of the solutions was all within 6.6− 6.8. In this preparation, the highly hydrophobic ligand of HDEHP was thought to be adsorbed completely into the ODS particles, and the complex formation proceeded in the particles. For the measurement of the magnetic field gradient around the observation area in a capillary cell, the polystyrene particles (χp = −8.21 × 10−6) were dispersed into a 0.50 M MnCl2 aqueous solution (χm = 91.2 × 10−6). The use of MnCl2 solution was effective to change the diamagnetic water to a paramagnetic solution, which was required to increase the magnetophoretic velocity of a diamagnetic polystyrene particle.7 Measurement of Magnetophoretic Velocity. Figure 2 shows the schematic diagram of the instrument of the magnetophoretic mole-ratio method constructed in the present study. A glass rectangular capillary (inside 0.20 mm × 0.20 mm, outside 0.43 mm × 0.43 mm, 5 cm long, Vitro Tubes, VitroCom, USA) was vertically positioned and sandwiched by two small Nd−Fe−B permanent magnets (0.45 T, 1 cm × 1 cm square, and 0.12 cm thickness, Magfine, Japan) with a 0.5 mm gap, which was made by a Pt wire of 0.5 mm diameter as a
spacer. The magnets and a Pt spacer were sandwiched by two glass slides and fixed on an xz stage (Figure 2B). A sample solution was fed from the bottom of the capillary by lifting a sample vessel (about 1 mL in volume). When the solution surface touched the bottom end of the empty capillary, the solution was spontaneously aspirated by the capillary force. After the initial flow of solution was ceased, the particles near the magnets were migrated by the magnetophoretic force, though it was continuously affected by the sedimentation velocity of the particle. For the Tb(III) and Dy(III) systems, the rising velocity of a particle in the lower region under the magnets was observed, since the particles were finally almost trapped at the magnets. On the other hand, in the Co(II) system, the falling particles were observed in the upper region from the magnet, since enough particles were raised up though the gap of magnets by the initial flow. The migrating behavior of particles was observed by a CCD camera (WAT-221S, Watec, Japan) with a lens (5×, NA = 0.10), and the video images were captured through a USB video-capturing device (GV-USB2/HQ, I-O DATA, Japan) by a PC. From the video images, the position of the particle was measured as a function of time in the range of 0.5−1.2 mm from the center of the magnets by using ImageJ software, and the velocities were calculated on an Excel file. Magnetic field gradient inside the capillary was measured from the magnetophoretic velocity of the polystyrene particle (15 μm in diameter) in 0.50 M MnCl2 solution. The result of B(dB/dx) was found to be represented as a function of the distance from the magnet center, x (μm),7 B(dB /dx)/T2m−1 = −0.647x + 545
(R2 = 0.752) (10)
in the range of 600−800 μm from the magnet center. C
DOI: 10.1021/acs.analchem.7b00999 Anal. Chem. XXXX, XXX, XXX−XXX
Technical Note
Analytical Chemistry
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RESULTS AND DISCUSSION Magnetophoretic Velocity. The velocity of a particle falling or rising in a liquid through the magnetic field gradient is represented by eq 2. The velocity observed in the absence of magnetic field gradient, v0, corresponds to the last term of eq 2 and can be approximated by the velocity without metal ion. Therefore, eq 2 can be simplified as ημ0 9 χp = (v − vo) 2 + χm 2 r B(dB /dx) (11) When χm is negligibly smaller than χp and the velocity is observed at the same distance from the magnet center having a constant value for B(dB/dx), the net velocity of (v − v0) divided by r2 should be proportional to χp v − vo r2
⎡ 2B(dB /dx) ⎤ ⎥ = a(χp − χm ) ≈ aχp = (χp − χm )⎢ ⎢⎣ 9ημ0 ⎥⎦ (12)
where a is an experimental value independent of the particle given by a = 2B(dB/dx)/9ημ0. In the present study, the velocity of a silica ODS particle, which contained a constant amount of HDEHP and a various amount of metal ion, was obtained at various distances from the magnet center. The size of the ODS particle was almost constant, but to improve the accuracy, the observed velocity was corrected for the size dividing by the pixel area of the particle, which should be proportional to r2. Equation 12 suggests that (v − v0)/(pixel area) is proportional to χp. The observed falling velocity of the ODS particles in the Co(II) system ranged from 60 to 300 μm s−1 and clearly increased with the decrease of the distance above the magnet center. Also, the velocity depended remarkably on the amount of Co(II) added to the sample solution. In the absence of Co(II), the particle fell down slowly passing through the gap of magnets with a constant velocity suggesting that the difference of (χp − χm) is very small and cannot be detected by the present magnetic field gradient. The constant velocity was considered to be v0. In the presence of Co(II) ion, the particle fell down with faster velocity attracted by the magnetic force, indicating that the particle became paramagnetic by extracting Co(II) ion into the ODS particle by forming a complex with HDEHP. In the systems of Tb(III) and Dy(III), the magnetophoretic velocimetry measurement was done in the lower region of the capillary cell, below the magnet center. When the metal ion was added to the solution, the rising velocity of the particle was observed with the velocity range of 30−600 μm s−1, suggesting again that the particle became paramagnetic by the complex formation in the particle. Magnetophoretic Mole-Ratio Plots. The corrected velocity of the particles was obtained by dividing the observed velocity by the unitless pixel area, and it was plotted against the distance from the center of the magnets (refer to the figures in the Supporting Information). The values of the corrected velocity difference of (v − v0)/(pixel area) at a given distance from the center of the magnets, 700 μm above for the Co(II) system and 600 μm below for the Tb(III) and Dy(III) systems, was obtained from the regression curves and normalized to the corrected velocity difference at the maximum metal concentration. The normalized velocities were plotted against the mole-ratio of (noM/noHL) as shown in Figure 3. In the Co(II) system, an intersect point was obtained at noM/noHL = 1/2, suggesting the formation of Co(DEHP)2, and in the Tb(III)
Figure 3. Magnetophoretic mole-ratio plots determining Co(DEHP)2, Tb(DEHP)3, and Dy(DEHP)3. The plotted values are the averaged normalized velocities, and the error bars show the range of the normalized velocities observed in each mole-ratio (Figures S-1, S-2, and S-3).
and Dy(III) systems, the intersect point at noM/noHL = 1/3 suggested the formation of Tb(DEHP)3 and Dy(DEHP)3. These results demonstrate clearly the feasibility of the principle of the magnetophoretic mole-ratio method derived in eqs 3−9. The composition of the metal complexes of HDEHP has been reported in some solvent extraction studies.8−14 It is noteworthy that the composition of the complexes of Tb(III) and Dy(III) were determined as 1:3 in the present ODS silica systems, since an alternative composition of 1:6, M(DEHP)3(HDEHP)3, has been reported in some solvent extraction systems due to the dimer formation of HDEHP in the organic phase under acidic conditions.8,10,11 In the present neutral aqueous solution, it is thought that the dimerization of HDEHP in ODS particles is not proceeded. The present method is so fundamental by using a simple and less expensive device that it will be widely applicable to various systems, especially for the systems including paramagnetic metal ions. Amount of Metal Ion in a ODS Particle. Magnetophoretic velocity of a particle observed in the present study has valuable information about the amount of the paramagnetic ion extracted in a single ODS particle. The observed volume D
DOI: 10.1021/acs.analchem.7b00999 Anal. Chem. XXXX, XXX, XXX−XXX
Technical Note
Analytical Chemistry
Table 1. Summary of the Composition of the Complexes, the Magnetic Susceptibility of a Single Particle, and the Maximum Amount of the Metal Ion in a Single Particle, When 5.0 μmol of HDEHP and 10 mg of the Silica ODS Particles Are Included in a Sample metal ion
pa
composition of complex
maximum observed velocity of particleb (μm s−1)
magnetic susceptibility of a particle,c χp
molar magnetic susceptibility of metal ion,d χM (m3 mol−1)
mole of metal ion in a particle, nMLq/N (pmole)
Co(II) Tb(III) Dy(III)
4.8 9.8 10.6
Co(DEHP)2 Tb(DEHP)3 Dy(DEHP)3
255 340 367
8.4 × 10−6 1.9 × 10−5 2.3 × 10−5
1.2 × 10−7 5.1 × 10−7 5.9 × 10−7
3.3 1.8 1.9
a
Paramagnetic moment in the units of Bohr magneton; see ref 15. bEstimated from the experimental data at 0.6 mm from the magnet center. cThe observed magnetic susceptibility of a single particle including the maximum amount of metal ion calculated by eq 13. dCalculated from the magnetic moment of the metal ion by eq 14. eCalculated from the value of the volume magnetic susceptibility and the molar magnetic susceptibility, assuming Vp = 4.77 × 10−14 m3 by eq 15.
magnetic susceptibility of the single particle, χp, under the excess amount of a metal ion can be simply related to the maximum amount of the metal complex, nMLq/N, from eq 8 by using the molar magnetic susceptibility of the metal ion, χM, χML n MLqVMLq q
χp =
NVp
+
χODS VODS Vp
≈
biological systems, though it is required that the binding constant is large enough and the confinement of the ligands to the particles must not affect the binding ratio with the metal ion. It should be applied not only for micrometer sized particles but also for nanometer sized particles as suggested recently.16 Magnetophoretic methods will be developed further as an alternative or a complementary method of analytical spectroscopic methods.
χML n MLqVMLq q
NVp
■
M
=
χ n MLq NVp
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.7b00999. Observed magnetophoretic velocity of ODS particles as a function of the distance from the center of magnets in Co(II), Tb(III), and Dy(III) systems (PDF)
The molar magnetic susceptibility, χM, can be calculated by
χM =
NAμ0 μB 2 p2 3kT
ASSOCIATED CONTENT
S Supporting Information *
(13)
(14)
where NA is Avogadro’s number, μB is Bohr magneton, k is the Boltzmann constant, T is the absolute temperature, and p is the paramagnetic moment in the units of Bohr magneton as shown in Table 1. Finally, the maximum amount of metal ion in a single particle can be calculated by n MLq χp = M Vp N χ (15)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Hitoshi Watarai: 0000-0003-0325-0497
The calculated results of nMLq/N for the Co(II), Tb(III), and Dy(III) systems are listed in Table 1. Here, it can be noticed that the amounts of maximum metal ion extracted into a single ODS particle were about 3 pmol for Co(II) and about 2 pmol for Tb(III) and Dy(III) under the present condition of 6.0 pmol for the initial amount of HDEHP in the particle, corresponding to the composition of the metal complexes. Furthermore, the number of particles, N, in 10 mg ODS silica gel particles was calculated as 8.6 × 105. In addition, it was confirmed from the values of χp and χM in Table 1 that the contribution of χm to χp due to the excess free metal ions in solution was less than 3% even in the highest metal concentration for Dy(III) in the present study and thus negligibly small.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Prof. Satoshi Tsukahara, Osaka University, for his kind support in the experimental facility. This research was financially supported by KAKENHI (No. 21245022 and No. 26288066) of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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REFERENCES
(1) Yoe, J. H.; Jones, A. L. Ind. Eng. Chem., Anal. Ed. 1944, 16, 111− 115. (2) Meyer, A. S., Jr.; Ayres, G. H. J. Am. Chem. Soc. 1957, 79, 49−53. (3) Wear, J. O. Arkansas Academy Sci. Proc. 1968, 22, 97−101. (4) Watarai, H.; Namba, M. Anal. Sci. 2001, 17, 1233−1236. (5) Suwa, M.; Watarai, H. Anal. Chem. 2002, 74, 5027−5032. (6) Watarai, H.; Suwa, M.; Iiguni, Y. Anal. Bioanal. Chem. 2004, 378, 1693−1699. (7) Suwa, M.; Watarai, H. Anal. Chem. 2001, 73, 5214−5219. (8) Motomizu, S.; Freiser, H. Solvent Extr. Ion Exch. 1985, 3, 637−65. (9) Ohashi, A.; Hashimoto, T.; Imura, H.; Ohashi, K. Talanta 2007, 73, 893−898. (10) Grimes, T. S.; Tian, G.; Rao, L.; Nash, K. L. Inorg. Chem. 2012, 51, 6299−6307. (11) Sato, T. Hydrometallurgy 1989, 22, 121−140.
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CONCLUSION We have demonstrated a new application of the magnetophoresis for the mole-ratio method, which is a classical but fundamental experimental method still useful in many situations in modern analytical technology. The magnetophoretic mole-ratio method does not require any spectroscopic characteristics but only depends on the magnetic susceptibility of sample. The present method can be applied to almost all paramagnetic elements such as transition metals and lanthanide metals, which are met very often in nanotechnology and E
DOI: 10.1021/acs.analchem.7b00999 Anal. Chem. XXXX, XXX, XXX−XXX
Technical Note
Analytical Chemistry (12) Xie, F.; Zhang, T. A.; Dreisinger, D.; Doyle, F. Miner. Eng. 2014, 56, 10−28. (13) Grimes, T. S.; Tillotson, R. D.; Martin, L. R. Solvent Extr. Ion Exch. 2014, 32, 378−390. (14) Svantesson, I.; Persson, G.; Hagstroem, I.; Liljenzin, J. O. J. Inorg. Nucl. Chem. 1980, 42, 1037−1043. (15) Coey, J. M. D. Magnetism and Magnetic Materials; Cambridge University Press: New York, 2010. (16) Kawano, M.; Watarai, H. Analyst 2012, 137, 4123−4126.
F
DOI: 10.1021/acs.analchem.7b00999 Anal. Chem. XXXX, XXX, XXX−XXX
