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Relaxometry, magnetometry, and EPR evidence for three magnetic phases in the MR contrast agent MION-46L
Journal of Magnetism and Magnetic Materials 194 (1999) 217—223
Relaxometry, magnetometry, and EPR evidence for three magnetic phases in the MR contrast agent MION-46L Jeff W.M. Bulte * , Rodney A. Brooks, Bruce M. Moskowitz, L. Henry Bryant Jr. , Joseph A. Frank Laboratory of Diagnostic Radiology Research (Clinical Center), National Institutes of Health, Bethesda, MD 20892, USA Neuroimaging Branch (National Institute of Neurological Disorders and Stroke), National Institutes of Health, Bethesda, MD 20892, USA Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455, USA
Abstract Magnetization curves, EPR spectra, and T1 and T2 nuclear magnetic relaxation times versus Larmor frequency have been measured for the MRI contrast agent MION-46L. The resulting data can be successfully explained by adding paramagnetic and antiferromagnetic terms to the known superparamagnetic component. 1999 Elsevier Science B.V. All rights reserved. Keywords: Superparamagnetic iron oxide; Magnetic nanoparticles; Relaxometry; Antiferromagnetism; Electron—spin relaxation
1. Introduction Superparamagnetic (SPM) nanoparticles are currently under investigation as potential contrast agents for both standard and functional magnetic resonance imaging (MRI). These particles possess a large ferrimagnetic moment that, because of the small crystal size, is free to align with an applied magnetic field (i.e., there is no hysteresis) — hence the term ‘superparamagnetic’. The aligned magne-
* Corresponding author. Tel.: #1-301-402-4547; fax: #301594-2979; e-mail: [email protected]. Present address: Laboratory of Diagnostic Radiology Research, National Institutes Of Health B10, B1N256, 10 Center Dr MSC 1074, Bethesda, MD 20892-1074, USA.
tization then creates microscopic field gradients that dephase nearby protons and shorten T2, over and beyond the usual dipole—dipole relaxation mechanism that affects both T1 and T2. The longitudinal relaxation time T1 is defined as the time constant of the exponential recovery of proton spins to their equilibrium distribution along an applied field after a disturbance. The transverse relaxation time T2 is the time constant that describes the exponential loss of magnetization in a plane transverse to the direction of the applied field, following an RF pulse that rotates the aligned magnetization into the transverse plane. The first attempt to explain T2-shortening by magnetic nanoparticles was unsuccessful because it did not take into account the induced magnetization [1]. A subsequent theory [2,3] remedied this
0304-8853/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 5 5 5 - 1
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defect and produced good agreement with T1 data for AMI-25 iron oxide particles, but was unable to explain T1 data of MION-46 at low fields. A variation of this theory was then introduced with an added low-field term [4] which is still under dispute [5]. There have been no theoretical comparisons of T2 data because of the difficulty of measuring T2 at different field strengths. MION-46L [6] is a good candidate for study because of its monocrystallinity and low tendency to agglomerate. This dextran-coated magnetic nanoparticle has an iron oxide core of 4.6$1.2 nm in diameter, with a superparamagnetic maghemiteor magnetite-like inverse spinel crystal structure [6]. The overall diameter is 8—20 nm, so that the effective coating ‘thickness’ is 2—8 nm. We report herein on the measurements of magnetization and electron—spin relaxation, as well as measurements of the nuclear magnetic relaxation times T1 and T 2. These results are interpreted in terms of a possible model that includes a SPM magnetic moment k , 1.+ a paramagnetic (PM) component k , and a small .+ antiferromagnetic (AFM) component k that $+ may result from incomplete chemical conversion of the core.
2. Methods MION-46L preparation: MION-46L was obtained from the Center for Molecular Imaging Research, Massachusetts General Hospital and Harvard Medical School (Boston, MA) as a 0.9% NaCl solution containing 11.6 mg Fe/ml and 75 mM sodium citrate. Shortly before the measurements (see below), unbound citrate was removed by dialysis and the solution was buffered and adjusted to the desired concentration in phosphate-buffered saline (10 mM phosphate, 0.15 M NaCl, pH"7.4). Magnetometry: The magnetization M of a MION-46L liquid sample was measured at 300 K for magnetic fields H from !2 to #2 T using a superconducting quantum interference device (SQUID) susceptometer (Quantum Design, San Diego, CA). A sample holder correction (subtraction of diamagnetic susceptibility) was applied and moment calibration was performed using palladium and nickel standards.
EPR measurements: Electron PM resonance (EPR) measurements were carried out at room temperature on a Bruker ESP-300 spectrometer at the X-band with 100 kHz magnetic field modulation, using a modulation amplitude of 5 G and a microwave power of 10 mW. Relaxometry: The MION-46L samples were prepared in phosphate-buffered saline (0.01 M phosphate, 0.15 M NaCl) at pH 7.4 and adjusted to concentrations in the range 0.25—1.0 mM Fe. T1 and T2 were measured on a variable-field relaxometer (Southwest Research Institute, San Antonio, TX) at temperatures of 3, 10, 23 and 37°C. For T1, 31 saturation-recovery sequences were used and T2 was measured with a CPMG sequence of 500 echoes with interecho time 2 ms. The range of Larmor frequencies was 1—63 MHz (H" 0.025—1.5 T). In addition, using an IBM research field cycling relaxometer (University of MonsHainaut, Mons, Belgium), T1 was measured from 0.01 to 1.0 MHz. This apparatus uses neither a saturation-recovery nor inversion-recovery sequence. Instead, the sample is first allowed to ‘soak’ in a field H , whose magnitude is different from the 1 desired field of measurement, H . After the nuclear + spins reach equilibrium, the field is abruptly changed to H for a short relaxation interval, after + which magnetization is measured with a standard spin—echo sequence (at a third field corresponding to 7.5 MHz). This sequence is repeated 16 times with different relaxation intervals, and the T1 is calculated from the respective signal amplitudes. All data were converted to relaxation rates R1 and R2 (reciprocals of T1 and T2); the buffer contribution was then subtracted and the result divided by iron concentration to obtain relaxivity values (s\/mM Fe). 3. Results Magnetometry: The magnetization curve demonstrates a saturating component that is clearly SPM, presumably arising from the maghemite core, plus an additional high-field slope that appears to be PM (Fig. 1). The curves were therefore fitted initially with M"F Nk H/(3k¹)#F Nk ¸(x), .+ .+ 1.+ 1.+
(1)
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219
Fig. 1. Magnetization versus field for MION-46L solution at room temperature. The solid line represents a best fit of the data with the sum of the PM, AFM and SPM terms (Eqs. (1) and (2)). The dashed line shows a best fit with the PM and AFM terms omitted.
where N is the total number of Fe atoms, F the .+ number of PM particles divided by N (molar fraction), k the effective PM moment (assumed to .+ be 5.9 BM for Fe>), F the number of SPM 1.+ particles divided by N (molar fraction), k the 1.+ SPM moment, T the absolute temperature, k the Boltzmann’s constant, L the Langevin function: ¸(x)"coth(x)!1/x, and x"k H/(k¹). 1.+ Note that the concentrations of PM#SPM particles, as given by F and F , are normalized (i.e., .+ 1.+ divided by the total number of iron atoms). Eq. (1) yielded a good fit, but the amount of PM iron, F "2.6, was unrealistic (there cannot be .+ more PM Fe> ions than there are total Fe atoms). Thus these terms alone do not provide a satisfactory explanation of the data. In addition, the fitted value of k corresponded to only half of the total 1.+ Fe atoms per molecule, based on a contribution of 1.09 Bohr Magnetons (BM) per atom [7]. Since the T2 results (see below) also suggest the presence of a second, weaker SPM component — one that is AFM in origin — a second Langevin term was added to Eq. (1), as follows: F Nk ¸(x ), $+ $+ $+
(2)
where F is defined similar to F (molar frac $+ 1.+ tion) and x is defined similar to x. Since there $+ were now too many parameters for meaningful fitting, F was set to 0.25, based on the arbitrary .+ assumption that half the remaining iron is PM and half AFM. This same assumption is used in fitting the relaxometry data (see below). The resulting fit is shown in Fig. 1. The final fitted parameters are: k "9300 BM, F "1/19 800, k "930 BM 1.+ 1.+ $+ and F "1/4 450. $+ Electron paramagnetic resonance: The EPR spectrum is shown in Fig. 2. An electronic relaxation time of 1.18 ns was calculated from this result. Relaxometry: The T1 and T2 results are shown in Figs. 3 and 4. Also included are T1 data at low fields, courtesy of Drs. Alain Roch and Robert Muller. At present there is some dispute as to the theory of MION-46L relaxation. The present approach follows that of Koenig and Kellar [4] except that a PM term is added. This PM term is important because it reduces the relative magnitude of the low-field plateau [4], enabling a better fit to the low-field T1 data.
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Fig. 2. EPR spectrum of MION-46L at room temperature.
The initial fitting equations were R "F R #F R .+ .+ 1.+ 1.+ R "F R #F R . (3) .+ .+ 1.+ 1.+ This approach is based on ‘outer-sphere’ theory, in which relaxation is caused by diffusion of water protons near the SPM particles. (The alternate ‘inner-sphere’ theory, involving exchange of water of hydration, is not considered for the SPM term). The PM terms herein are the standard PM ‘innersphere’ relaxivities: R "C q [3j (u)#7j (u )], .+ G G G G R "C q [3j (u)#4j (0)#13j (u )]/2, (4) .+ G G G G G where C "(12/5)ck r\;10\, c is the proton G .+ gyromagnetic ratio, r the binding distance, q the G inner-sphere correlation time (combination of rotational time q , exchange, time q , and PM spin 0 #6 correlation time q ), j the inner-sphere spectral .+ G density function, j (u)"(1#uq), u the angular G G Larmor frequency of the proton, and u the angu lar Larmor frequency of the electron. The SPM terms in Eq. (3) are outer-sphere SPM relaxivities (s\/mM particles) as given in Ref. [4]: R "C q [+1!¸(x),+3j (u)#7j (u ), 1.+ B #3¸(x)+3j (u) #7j (u ),]
R "C q [+1!¸(x),+1.5j (u)#6.5j (u ) 1.+ B #2j (0),#3¸(x)+1.5j (u) #6.5j (u )#2j (0),], where C "(32p/405)ck d\N ;10\, d is the 1.+ distance of the closest approach for protons, N the Avogadro’s number, q the time to diffuse distance B d, j the outer-sphere spectral density function [8], and j the same as j except q P. 1.+ In the above equations, we have ignored any difference between transverse and longitudinal electron—spin relaxation times (PM or SPM). These equations, however, were not able to fit the increase in 1/T2 at high fields (Fig. 4). Since a similar increase — proportional to field — has been noted for small AFM particles (9), the following term was added to the R2 equation: R "Aq ¸(x ), (6) $+ B $+ where x is defined analogously to x . The $+ 1.+ Langevin function was used on the hypothesis that the true proportionality is with respect to magnetization, not simply field strength, and the diffusion time q was inserted on the assumption that the B relaxation mechanism is outer-sphere. Since this term is semi-empirical, the coefficient A is arbitrary and has no theoretical meaning. In the fitting, the following parameters were fixed: PM: k "5.9 BM, .+ F "0.25. .+ SPM: k "9300 BM, 1.+ F "5;10\ (1 SPM particle per 20 000 1.+ Fe atoms), q "1.18 ns (independent of field and tem1.+ perature). AFM: k "930 BM. $+ Also, q was calculated from the temperature, using B the tabulated viscosity of water. The only parameters available for fitting were two distances, r and d, and the PM spin correlation time q ; only the last was allowed to vary with .+ temperature. The resulting fits are shown in Fig. 3A and Fig. 4A, and a breakdown into the three components is shown in Fig. 3B and Fig. 4B. The final parameter values are r"0.14 nm, d"7.4 nm,
(5)
q "5.2!2.9 ps for ¹"3!37°C. .+
J.W.M. Bulte et al. / Journal of Magnetism and Magnetic Materials 194 (1999) 217—223
221
Fig. 3. (A) 1/T1 relaxivities of MION-46L at four temperatures (䉱"3°C, 䊏"10°C, 䢇"23°C, "37°C). Open symbols represent T1 data taken on a different relaxometer (see text). The solid lines show the simultaneous fits using Eq. (3). (B) 1/T1 relaxivity of MION-46L at 3°C, with dashed lines representing the seperate contributions of the PM and SPM terms.
4. Discussion There may be different ways to explain the data presented above. The explanation given here entails three magnetic phases, each of which contributes a significant amount to the magnetometry and re-
laxometry data. The SPM phase, with moment k "9300 BM, clearly arises from the maghemite 1.+ core and accounts for the curvature in the magnetization curve, from which the magnetic moment was deduced. It is also consistent with the EPR results, from which the relaxation time of 1.18 ns
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Fig. 4. (A) 1/T2 relaxivities of MION-46L at four temperatures (䉱"3°C, 䊏"10°C, 䢇"23°C, "37°C). The solid lines show the simultaneous fits using Eqs. (3) and (6). (B) 1/T2 relaxivity of MION-46L at 3°C, with dashed lines representing the seperate contributions of the PM, AFM and SPM terms.
was deduced, and with the relaxometry results, which produced the value d"7.4 nm. These values are not unreasonable; in particular, the ‘distance of closest approach’ is consistent with the estimated hydrodynamic radius of 4—10 nm (6) (which is the particle diameter). However, it is clear from the
magnetometry data that the SPM phase can account for only about half the total iron. The PM phase helps to explain the high-field increase in magnetization, and also accounts for the magnitude of the low-field T1 plateau. The fraction of Fe atoms which are PM was arbitrarily estimated
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as 0.25; they presumably are uncoupled Fe> ions at the surface of the maghemite cores. However, the magnitude of the PM contribution to 1/T1 is larger than that for solutions of chelated and unchelated Fe [10], while the binding distance r"0.14 nm, deduced from the relaxometry data, is about half the internuclear Fe—H distance for hexa-aquo-Fe ions [11] of 0.29 nm. These two problematic findings could be related. Another problem is the picosecond range of the PM spin time constant, deduced from the relaxation data, which could possibly arise from a very short exchange time. The experimental basis for the AFM component comes from the high-field behavior of both magnetization M and 1/T2 relaxation. The former shows a slope that is too large to be explained by simple PM ions, and the latter shows a linear dependence that is characterisitic of AFM particles such as Imferon, Niferex, ferritin and hemosiderin [9,12]; it is believed to result from the weak SPM found in small AFM crystals, as per a theory of Ne´el [13]. Since ferric and ferrous oxyhydroxide (‘green and brown rusts’) are formed during the synthesis of the nanoparticles, this AFM phase could occur if subsequent conversion to maghemite or magnetite core was incomplete, leaving AFM inclusions. In summary, while there may be interpretational problems, the three-phase model appears to be successful in explaining in a consistent and quantitative manner the results of the different experimental studies.
Acknowledgements We are grateful to Drs. Alain Roch and Robert Muller (Department of Organic Chemistry and
223
NMR Laboratory, University of Mons-Hainaut, Belgium) for graciously providing us with the lowfield T1 data on MION-46L samples. This is publication C9801 of the Institute for Rock Magnetism (IRM). The IRM is supported by grants from the National Science Foundation (Division of Earth Sciences: Instrumentation and Facilities) and the W.M. Keck Foundation.
References [1] P. Gillis, S.H. Koenig, Magn. Reson. Med. 5 (1987) 323. [2] A. Roch, R.N. Muller, Proc. SMRM 11th Annual Meeting, 1992, p. 1447. [3] A. Roch. Ph.D. Thesis, University of Mons-Hainaut, 1994. [4] S.H. Koenig, K.E. Kellar, Magn. Reson. Med. 34 (1995) 227. [5] A. Roch, P. Gillis, R.N. Muller, Proc. SMR, 3rd Annual Meeting, 1995, p. 1094. [6] T. Shen, R. Weissleder, M. Papisov et al., Magn. Reson. Med. 29 (1993) 599. [7] R. Chevallier, in: J. Thewlis (Ed.), Encyclopaedic dictionary of physics, Vol. 4, Pergamon, Oxford, 1961. [8] J.H. Freed, J. Chem. Phys. 68 (1978) 4034. [9] J.W.M. Bulte, J. Vymazal, R.A. Brooks, C. Pierpaoli, J.A. Frank, J. Magn. Reson. Imaging 3 (1993) 641. [10] J. Vymazal, J.W.M. Bulte, J.A. Frank, G. Di Chiro, R.A. Brooks, J. Magn. Reson. Imaging 3 (1993) 637. [11] J. Kowalewski, L. Nordenskio¨ld, N. Benetis, P.-O. Westlund, Prog. NMR Spectrosc. 17 (1985) 141. [12] J.W.M. Bulte, G.F. Miller, J. Vymazal, R.A. Brooks, J.A. Frank, Magn. Reson. Med. 37 (1997) 530. [13] L. Ne´el, Comptes Rendus Acad. Sci. 252 (1961) 4075. (Translated in ‘Selected works of Louis Ne´el’, N. Kurti (Ed.), Gordon and Breach, New York, 1988, pp. 107—110.
Relaxometry, magnetometry, and EPR evidence for three magnetic phases in the MR contrast agent MION-46L Jeff W.M. Bulte * , Rodney A. Brooks, Bruce M. Moskowitz, L. Henry Bryant Jr. , Joseph A. Frank Laboratory of Diagnostic Radiology Research (Clinical Center), National Institutes of Health, Bethesda, MD 20892, USA Neuroimaging Branch (National Institute of Neurological Disorders and Stroke), National Institutes of Health, Bethesda, MD 20892, USA Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455, USA
Abstract Magnetization curves, EPR spectra, and T1 and T2 nuclear magnetic relaxation times versus Larmor frequency have been measured for the MRI contrast agent MION-46L. The resulting data can be successfully explained by adding paramagnetic and antiferromagnetic terms to the known superparamagnetic component. 1999 Elsevier Science B.V. All rights reserved. Keywords: Superparamagnetic iron oxide; Magnetic nanoparticles; Relaxometry; Antiferromagnetism; Electron—spin relaxation
1. Introduction Superparamagnetic (SPM) nanoparticles are currently under investigation as potential contrast agents for both standard and functional magnetic resonance imaging (MRI). These particles possess a large ferrimagnetic moment that, because of the small crystal size, is free to align with an applied magnetic field (i.e., there is no hysteresis) — hence the term ‘superparamagnetic’. The aligned magne-
* Corresponding author. Tel.: #1-301-402-4547; fax: #301594-2979; e-mail: [email protected]. Present address: Laboratory of Diagnostic Radiology Research, National Institutes Of Health B10, B1N256, 10 Center Dr MSC 1074, Bethesda, MD 20892-1074, USA.
tization then creates microscopic field gradients that dephase nearby protons and shorten T2, over and beyond the usual dipole—dipole relaxation mechanism that affects both T1 and T2. The longitudinal relaxation time T1 is defined as the time constant of the exponential recovery of proton spins to their equilibrium distribution along an applied field after a disturbance. The transverse relaxation time T2 is the time constant that describes the exponential loss of magnetization in a plane transverse to the direction of the applied field, following an RF pulse that rotates the aligned magnetization into the transverse plane. The first attempt to explain T2-shortening by magnetic nanoparticles was unsuccessful because it did not take into account the induced magnetization [1]. A subsequent theory [2,3] remedied this
0304-8853/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 5 5 5 - 1
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defect and produced good agreement with T1 data for AMI-25 iron oxide particles, but was unable to explain T1 data of MION-46 at low fields. A variation of this theory was then introduced with an added low-field term [4] which is still under dispute [5]. There have been no theoretical comparisons of T2 data because of the difficulty of measuring T2 at different field strengths. MION-46L [6] is a good candidate for study because of its monocrystallinity and low tendency to agglomerate. This dextran-coated magnetic nanoparticle has an iron oxide core of 4.6$1.2 nm in diameter, with a superparamagnetic maghemiteor magnetite-like inverse spinel crystal structure [6]. The overall diameter is 8—20 nm, so that the effective coating ‘thickness’ is 2—8 nm. We report herein on the measurements of magnetization and electron—spin relaxation, as well as measurements of the nuclear magnetic relaxation times T1 and T 2. These results are interpreted in terms of a possible model that includes a SPM magnetic moment k , 1.+ a paramagnetic (PM) component k , and a small .+ antiferromagnetic (AFM) component k that $+ may result from incomplete chemical conversion of the core.
2. Methods MION-46L preparation: MION-46L was obtained from the Center for Molecular Imaging Research, Massachusetts General Hospital and Harvard Medical School (Boston, MA) as a 0.9% NaCl solution containing 11.6 mg Fe/ml and 75 mM sodium citrate. Shortly before the measurements (see below), unbound citrate was removed by dialysis and the solution was buffered and adjusted to the desired concentration in phosphate-buffered saline (10 mM phosphate, 0.15 M NaCl, pH"7.4). Magnetometry: The magnetization M of a MION-46L liquid sample was measured at 300 K for magnetic fields H from !2 to #2 T using a superconducting quantum interference device (SQUID) susceptometer (Quantum Design, San Diego, CA). A sample holder correction (subtraction of diamagnetic susceptibility) was applied and moment calibration was performed using palladium and nickel standards.
EPR measurements: Electron PM resonance (EPR) measurements were carried out at room temperature on a Bruker ESP-300 spectrometer at the X-band with 100 kHz magnetic field modulation, using a modulation amplitude of 5 G and a microwave power of 10 mW. Relaxometry: The MION-46L samples were prepared in phosphate-buffered saline (0.01 M phosphate, 0.15 M NaCl) at pH 7.4 and adjusted to concentrations in the range 0.25—1.0 mM Fe. T1 and T2 were measured on a variable-field relaxometer (Southwest Research Institute, San Antonio, TX) at temperatures of 3, 10, 23 and 37°C. For T1, 31 saturation-recovery sequences were used and T2 was measured with a CPMG sequence of 500 echoes with interecho time 2 ms. The range of Larmor frequencies was 1—63 MHz (H" 0.025—1.5 T). In addition, using an IBM research field cycling relaxometer (University of MonsHainaut, Mons, Belgium), T1 was measured from 0.01 to 1.0 MHz. This apparatus uses neither a saturation-recovery nor inversion-recovery sequence. Instead, the sample is first allowed to ‘soak’ in a field H , whose magnitude is different from the 1 desired field of measurement, H . After the nuclear + spins reach equilibrium, the field is abruptly changed to H for a short relaxation interval, after + which magnetization is measured with a standard spin—echo sequence (at a third field corresponding to 7.5 MHz). This sequence is repeated 16 times with different relaxation intervals, and the T1 is calculated from the respective signal amplitudes. All data were converted to relaxation rates R1 and R2 (reciprocals of T1 and T2); the buffer contribution was then subtracted and the result divided by iron concentration to obtain relaxivity values (s\/mM Fe). 3. Results Magnetometry: The magnetization curve demonstrates a saturating component that is clearly SPM, presumably arising from the maghemite core, plus an additional high-field slope that appears to be PM (Fig. 1). The curves were therefore fitted initially with M"F Nk H/(3k¹)#F Nk ¸(x), .+ .+ 1.+ 1.+
(1)
J.W.M. Bulte et al. / Journal of Magnetism and Magnetic Materials 194 (1999) 217—223
219
Fig. 1. Magnetization versus field for MION-46L solution at room temperature. The solid line represents a best fit of the data with the sum of the PM, AFM and SPM terms (Eqs. (1) and (2)). The dashed line shows a best fit with the PM and AFM terms omitted.
where N is the total number of Fe atoms, F the .+ number of PM particles divided by N (molar fraction), k the effective PM moment (assumed to .+ be 5.9 BM for Fe>), F the number of SPM 1.+ particles divided by N (molar fraction), k the 1.+ SPM moment, T the absolute temperature, k the Boltzmann’s constant, L the Langevin function: ¸(x)"coth(x)!1/x, and x"k H/(k¹). 1.+ Note that the concentrations of PM#SPM particles, as given by F and F , are normalized (i.e., .+ 1.+ divided by the total number of iron atoms). Eq. (1) yielded a good fit, but the amount of PM iron, F "2.6, was unrealistic (there cannot be .+ more PM Fe> ions than there are total Fe atoms). Thus these terms alone do not provide a satisfactory explanation of the data. In addition, the fitted value of k corresponded to only half of the total 1.+ Fe atoms per molecule, based on a contribution of 1.09 Bohr Magnetons (BM) per atom [7]. Since the T2 results (see below) also suggest the presence of a second, weaker SPM component — one that is AFM in origin — a second Langevin term was added to Eq. (1), as follows: F Nk ¸(x ), $+ $+ $+
(2)
where F is defined similar to F (molar frac $+ 1.+ tion) and x is defined similar to x. Since there $+ were now too many parameters for meaningful fitting, F was set to 0.25, based on the arbitrary .+ assumption that half the remaining iron is PM and half AFM. This same assumption is used in fitting the relaxometry data (see below). The resulting fit is shown in Fig. 1. The final fitted parameters are: k "9300 BM, F "1/19 800, k "930 BM 1.+ 1.+ $+ and F "1/4 450. $+ Electron paramagnetic resonance: The EPR spectrum is shown in Fig. 2. An electronic relaxation time of 1.18 ns was calculated from this result. Relaxometry: The T1 and T2 results are shown in Figs. 3 and 4. Also included are T1 data at low fields, courtesy of Drs. Alain Roch and Robert Muller. At present there is some dispute as to the theory of MION-46L relaxation. The present approach follows that of Koenig and Kellar [4] except that a PM term is added. This PM term is important because it reduces the relative magnitude of the low-field plateau [4], enabling a better fit to the low-field T1 data.
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Fig. 2. EPR spectrum of MION-46L at room temperature.
The initial fitting equations were R "F R #F R .+ .+ 1.+ 1.+ R "F R #F R . (3) .+ .+ 1.+ 1.+ This approach is based on ‘outer-sphere’ theory, in which relaxation is caused by diffusion of water protons near the SPM particles. (The alternate ‘inner-sphere’ theory, involving exchange of water of hydration, is not considered for the SPM term). The PM terms herein are the standard PM ‘innersphere’ relaxivities: R "C q [3j (u)#7j (u )], .+ G G G G R "C q [3j (u)#4j (0)#13j (u )]/2, (4) .+ G G G G G where C "(12/5)ck r\;10\, c is the proton G .+ gyromagnetic ratio, r the binding distance, q the G inner-sphere correlation time (combination of rotational time q , exchange, time q , and PM spin 0 #6 correlation time q ), j the inner-sphere spectral .+ G density function, j (u)"(1#uq), u the angular G G Larmor frequency of the proton, and u the angu lar Larmor frequency of the electron. The SPM terms in Eq. (3) are outer-sphere SPM relaxivities (s\/mM particles) as given in Ref. [4]: R "C q [+1!¸(x),+3j (u)#7j (u ), 1.+ B #3¸(x)+3j (u) #7j (u ),]
R "C q [+1!¸(x),+1.5j (u)#6.5j (u ) 1.+ B #2j (0),#3¸(x)+1.5j (u) #6.5j (u )#2j (0),], where C "(32p/405)ck d\N ;10\, d is the 1.+ distance of the closest approach for protons, N the Avogadro’s number, q the time to diffuse distance B d, j the outer-sphere spectral density function [8], and j the same as j except q P. 1.+ In the above equations, we have ignored any difference between transverse and longitudinal electron—spin relaxation times (PM or SPM). These equations, however, were not able to fit the increase in 1/T2 at high fields (Fig. 4). Since a similar increase — proportional to field — has been noted for small AFM particles (9), the following term was added to the R2 equation: R "Aq ¸(x ), (6) $+ B $+ where x is defined analogously to x . The $+ 1.+ Langevin function was used on the hypothesis that the true proportionality is with respect to magnetization, not simply field strength, and the diffusion time q was inserted on the assumption that the B relaxation mechanism is outer-sphere. Since this term is semi-empirical, the coefficient A is arbitrary and has no theoretical meaning. In the fitting, the following parameters were fixed: PM: k "5.9 BM, .+ F "0.25. .+ SPM: k "9300 BM, 1.+ F "5;10\ (1 SPM particle per 20 000 1.+ Fe atoms), q "1.18 ns (independent of field and tem1.+ perature). AFM: k "930 BM. $+ Also, q was calculated from the temperature, using B the tabulated viscosity of water. The only parameters available for fitting were two distances, r and d, and the PM spin correlation time q ; only the last was allowed to vary with .+ temperature. The resulting fits are shown in Fig. 3A and Fig. 4A, and a breakdown into the three components is shown in Fig. 3B and Fig. 4B. The final parameter values are r"0.14 nm, d"7.4 nm,
(5)
q "5.2!2.9 ps for ¹"3!37°C. .+
J.W.M. Bulte et al. / Journal of Magnetism and Magnetic Materials 194 (1999) 217—223
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Fig. 3. (A) 1/T1 relaxivities of MION-46L at four temperatures (䉱"3°C, 䊏"10°C, 䢇"23°C, "37°C). Open symbols represent T1 data taken on a different relaxometer (see text). The solid lines show the simultaneous fits using Eq. (3). (B) 1/T1 relaxivity of MION-46L at 3°C, with dashed lines representing the seperate contributions of the PM and SPM terms.
4. Discussion There may be different ways to explain the data presented above. The explanation given here entails three magnetic phases, each of which contributes a significant amount to the magnetometry and re-
laxometry data. The SPM phase, with moment k "9300 BM, clearly arises from the maghemite 1.+ core and accounts for the curvature in the magnetization curve, from which the magnetic moment was deduced. It is also consistent with the EPR results, from which the relaxation time of 1.18 ns
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Fig. 4. (A) 1/T2 relaxivities of MION-46L at four temperatures (䉱"3°C, 䊏"10°C, 䢇"23°C, "37°C). The solid lines show the simultaneous fits using Eqs. (3) and (6). (B) 1/T2 relaxivity of MION-46L at 3°C, with dashed lines representing the seperate contributions of the PM, AFM and SPM terms.
was deduced, and with the relaxometry results, which produced the value d"7.4 nm. These values are not unreasonable; in particular, the ‘distance of closest approach’ is consistent with the estimated hydrodynamic radius of 4—10 nm (6) (which is the particle diameter). However, it is clear from the
magnetometry data that the SPM phase can account for only about half the total iron. The PM phase helps to explain the high-field increase in magnetization, and also accounts for the magnitude of the low-field T1 plateau. The fraction of Fe atoms which are PM was arbitrarily estimated
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as 0.25; they presumably are uncoupled Fe> ions at the surface of the maghemite cores. However, the magnitude of the PM contribution to 1/T1 is larger than that for solutions of chelated and unchelated Fe [10], while the binding distance r"0.14 nm, deduced from the relaxometry data, is about half the internuclear Fe—H distance for hexa-aquo-Fe ions [11] of 0.29 nm. These two problematic findings could be related. Another problem is the picosecond range of the PM spin time constant, deduced from the relaxation data, which could possibly arise from a very short exchange time. The experimental basis for the AFM component comes from the high-field behavior of both magnetization M and 1/T2 relaxation. The former shows a slope that is too large to be explained by simple PM ions, and the latter shows a linear dependence that is characterisitic of AFM particles such as Imferon, Niferex, ferritin and hemosiderin [9,12]; it is believed to result from the weak SPM found in small AFM crystals, as per a theory of Ne´el [13]. Since ferric and ferrous oxyhydroxide (‘green and brown rusts’) are formed during the synthesis of the nanoparticles, this AFM phase could occur if subsequent conversion to maghemite or magnetite core was incomplete, leaving AFM inclusions. In summary, while there may be interpretational problems, the three-phase model appears to be successful in explaining in a consistent and quantitative manner the results of the different experimental studies.
Acknowledgements We are grateful to Drs. Alain Roch and Robert Muller (Department of Organic Chemistry and
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NMR Laboratory, University of Mons-Hainaut, Belgium) for graciously providing us with the lowfield T1 data on MION-46L samples. This is publication C9801 of the Institute for Rock Magnetism (IRM). The IRM is supported by grants from the National Science Foundation (Division of Earth Sciences: Instrumentation and Facilities) and the W.M. Keck Foundation.
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