ARTICLE pubs.acs.org/Langmuir
Hamaker Constants of Iron Oxide Nanoparticles Bertrand Faure, German Salazar-Alvarez, and Lennart Bergstr€om* Department of Materials and Environmental Chemistry, Stockholm University, Stockholm, Sweden
bS Supporting Information ABSTRACT: The Hamaker constants for iron oxide nanoparticles in various media have been calculated using Lifshitz theory. Expressions for the dielectric responses of three iron oxide phases (magnetite, maghemite, and hematite) were derived from recently published optical data. The nonretarded Hamaker constants for the iron oxide nanoparticles interacting across water, A1w1 = 33 39 zJ, correlate relatively well with previous reports, whereas the calculated values in nonpolar solvents (hexane and toluene), A131 = 9 29 zJ, are much lower than the previous estimates, particularly for magnetite. The magnitude of van der Waals interactions varies significantly between the studied phases (magnetite < maghemite < hematite), which highlights the importance of a thorough characterization of the particles. The contribution of magnetic dispersion interactions for particle sizes in the superparamagnetic regime was found to be negligible. Previous conjectures related to colloidal stability and self-assembly have been revisited on the basis of the new Lifshitz values of the Hamaker constants.
’ INTRODUCTION Iron oxide nanoparticles have attracted a large research interest because of their superparamagnetic properties and potential use in catalysis, as sensors and magnetic storage devices, and as biomedical probes for magnetic resonance imaging.14 Ferrofluids, i.e., concentrated colloidal dispersions of iron-based nanoparticles, have already found extensive use, e.g., as liquid seals in hard disk drives and as lubricants.5,6 Significant efforts in the development of robust synthesis and surface functionalization methods have provided monodisperse nanocrystals of various shapes with tunable magnetic and surface properties, of interest in targeted drug delivery or hyperthermia.711 It is important to note that most, if not all, of these applications rely on the ability to form colloidally stable dispersions of the iron oxide nanoparticles in a suitable solvent. The colloidal stability is controlled by the balance of attractive and repulsive interparticle forces, e.g., double layer, structural, steric, depletion, hydration, hydrophobic, and van der Waals forces. The van der Waals or dispersion force is an ubiquitous interaction,1215 in most cases attractive, which needs to be screened by a sufficiently long-range repulsion to generate a colloidally stable dispersion. The magnitude and range of the van der Waals (vdW) interaction is closely related to the value of the Hamaker constant, A, which depends on the dielectric properties of the involved materials and the intervening medium.16 For example, the vdW interaction free energy, VvdW, between two spheres of radius r at surface separation s, can be approximated by Vvdw
A r ¼ 12 s
r 2011 American Chemical Society
ð1Þ
providing that s , r. In the original treatment, also called the microscopic approach, the Hamaker constant was calculated from the polarizabilities and number densities of the atoms in the two interacting bodies. Lifshitz presented an alternative, more rigorous approach where each body is treated as a continuum with certain dielectric properties. This approach automatically incorporates many-body effects, which are neglected in the microscopic approach. In a stable system, the maximum attractive interparticle energy should be less than once or twice the thermal energy to readily break all particleparticle bonds. Since the magnitude and range of the attractive vdW interaction scale with the effective Hamaker constant, it is in essence the value of the Hamaker constant that determines the minimum thickness that a surfactant layer adsorbed onto the surfaces of the iron oxide crystals needs to have to yield a colloidally stable nanoparticle dispersion.1720 The vdW interactions not only affect the colloidal stability, but also control the morphology and ordering in nanoparticle superlattices, e.g., via dewetting, segregation of nanoparticles due to size-dependent interactions, and directionality of vdW interactions between anisotropic building blocks.2127 Considering the wealth of theoretical and experimental studies dedicated to iron oxide nanoparticles, the lack of firmly established Hamaker constants for these systems is striking.20,2831 Previous estimates of the Hamaker constants of iron oxides have relied on measurements of the interfacial tension or the critical Received: April 15, 2011 Revised: June 3, 2011 Published: June 06, 2011 8659
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coagulation concentration.3234 However, these approaches are semiquantitative at best,13,35,36 and there are no reliable methods to extrapolate these indirectly determined Hamaker constants to other solvents and configurations, e.g., as the use of combining rules may not be applicable.37 Taking advantage of the recent publication of the optical properties of iron oxides,38,39 we have calculated the magnitude of the Hamaker constants for three scientifically and technologically relevant iron oxide phases: magnetite (Fe3O4), maghemite (γ-Fe2O3), and hematite (R-Fe2O3) in various media. The importance of magnetic dispersion interactions has been addressed for nanosized superparamagnetic particles. In addition, the interactions with two commonly used ceramic substrates (SiO2 and Si3N4) and a metal (gold) have been evaluated. We have used the calculated Hamaker constants to discuss the stability of ferrofluids and to revisit estimates of the relative importance of vdW and Coulombic forces in selfassembling systems.
’ THEORY The nonretarded Hamaker constants between two half-spaces of material 1 and material 2 interacting across medium 3 can be calculated from the Lifshitz theory, assuming small differences in dielectric and magnetic properties:15,40 A132 ¼
3kB T 2
¥
∑¥m ¼ 0 0 s∑¼ 1
ðΔ13 3 Δ23 Þs þ ðΔ13 3 Δ23 Þs s3
4π2 kB T m h
ð3Þ
where kB is Boltzmann’s constant, T the temperature, h is Planck’s constant, and m a positive integer. The prime in the first summation in eq 2 indicates that the static term (m = 0) should be given half weight. According to eq 2, the dielectric and magnetic parts of the nonretarded Hamaker constant can be evaluated independently. A132 ¼
3kB T 2 þ
¥
∑¥m ¼ 0 0 s∑¼ 1
3kB T 2
ðΔ13 3 Δ23 Þs s3 ¥
∑¥m ¼ 0 0 s∑¼ 1
εðiξm Þ ¼ 1 þ
CIR CUV þ 1 þ ðξm =ωIR Þ2 1 þ ðξm =ωUV Þ2
ð5Þ
Each material is represented by 4 spectral parameters, C being the absorption strength and ω the frequency. The spectral parameters of the UV relaxation can be determined by fitting the frequency-dependent refractive index in the visible and UV range to the Cauchy equation:41 n2 ðωÞ 1 ¼
½n2 ðωÞ 1ω2 þ CUV ω2UV
ð6Þ
The frequency of the infrared oscillator can be readily obtained from the position of the bands in the IR spectra of the materials. Finally, the IR oscillator strength CIR is calculated from the static dielectric constant ε0 using eq 7. CIR ¼ ε0 CUV 1
ð7Þ
Magnetic Response Function. Van der Waals forces also encompass magnetic dispersion interactions. Similarly to the dielectric case, the magnetic behavior of the materials needs to be known over an extended range of frequencies. The magnetic response function was modeled with a single harmonic oscillator, as shown in eq 8:
ð2Þ
where Δkl = [εk(iξm) εl(iξm)]/[εk(iξm) þ εl(iξm)] and Δkl = [μk(iξm) μl(iξm)]/[μk(iξm) þ μl(iξm)]. ε and μ are the dielectric and magnetic response functions, respectively, of the imaginary frequency iξm. The frequency ξm (in rad/s) is sampled with a temperature-dependent interval (Matsubara frequency) ξm ¼
range. The imaginary dielectric response function is built over an infinite range of frequencies as shown in eq 5:41,42
μðiξm Þ ¼ 1 þ
4πχ 1 þ ðξm =ω0 Þ2
ð8Þ
where χ is the static volume magnetic susceptibility (cgs units, emu.cm3.Oe1) and ω0 is the Neel frequency of the magnetic moment, typically around 10 GHz.46,63 The magnetic term is often omitted in the Lifshitz calculation because of the low frequency of magnetic relaxations. Indeed, the magnetic response function declines away from the resonance frequency, already from the first Matsubara frequency m = 1 which falls in the infrared region at 1013 Hz (eq 3). For identical materials interacting across a nonmagnetic medium, the magnetic contribution in eq 4 reduces to the static magnetic term 3kB T ¥ 1 1 2s magnetic ¼ 1þ ð9Þ A131 4 s ¼ 1 s3 2πχ
∑
’ RESULTS AND DISCUSSION s
ðΔ13 3 Δ23 Þ magnetic ¼ Adielectric þ A132 132 s3 ð4Þ
The use of Lifshitz theory requires in principle the frequency-dependent dielectric and magnetic properties of the involved materials to be known. Fortunately, it is sufficient to model the dielectric response over a limited frequency range, primarily the UVvis and IR-range, for accurate Lifshitz calculations.41,42 Dielectric Response Function. The dielectric behavior of the iron oxides was modeled using the Ninham-Parsegian approximation, which is a good compromise between accuracy and ease of computation.4245 For the sake of simplicity, the iron oxide phases were represented with two harmonic oscillators, one in the infrared (IR) and the other in the ultraviolet (UV) spectral
Determination of the Spectral Parameters. Optical data for three different iron oxide phases, magnetite (Fe3O4), maghemite (γ-Fe2O3), and hematite (R-Fe2O3), have recently been determined by spectroscopic ellipsometry.38,39 The spectral parameters of the UV relaxation (absorption strength CUV and frequency ωUV) were determined by fitting the ellipsometry data to the Cauchy equation, as shown in Figure 1.38,39 An absorbance threshold of 0.35, 0.45, and 0.1 was chosen to define the spectral range for magnetite, maghemite, and hematite, respectively. It was possible to obtain a reasonable linear fit to the Cauchy equation (coefficient of determination R2 > 0.991), despite the relatively high absorbance of both magnetite and maghemite in the visible range. The spectral parameters for the Ninham-Parsegian spectral representation are given in Table 1. The position of the strongest absorption band between 800 and 400 cm1 was chosen as the 8660
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Table 2. Nonretarded Hamaker Constants for Iron Oxides Interacting Across Vacuum and Watera vacuum A102 material
water A102
A1w2
A101 A101b (SiO2) (Si3N4) A1w1
A1w1b
A1w2
(SiO2) (Si3N4)
43
-
40
66
33
2040d
5
2
maghemite 68 hematite 92
c
55 69
90 113
36 39
3445e 1345f
8 10
12 26
magnetite
232 232c
a All values are in zJ. b Estimated values reported in the literature. c Value reported in ref 54. d Values reported in refs 28,55. e Values reported in refs 32,54. f Values reported in refs 3234.
Figure 1. Cauchy plots of magnetite, maghemite, and hematite. The symbols represent the experimental data38,39 and the lines correspond to the fit to the Cauchy equation (eq 6).
Table 3. Nonretarded Hamaker Constants for Iron Oxides Interacting Across Hydrocarbonsa
Table 1. Dielectric Constants and Spectral Parameters of the Iron Oxide Phases ωUV
A132
ωIR
material ε0 CUV (1015 rad.s1) CIR (1014 rad.s1)
material
optical data
magnetite 20 2.4
4.0
16.6
1.1
Goossens et al.39
maghemite 20 3.6
4.4
15.4
1.2
Tepper et al.38
hematite
5.4
6.8
1.0
Goossens et al.39
12 4.2
hexane
frequency of the IR oscillator for the respective phase.47 The static dielectric constant of the iron oxide phases,48 as well as the spectral parameters of the substrates (SiO2 and Si3N4)42 and of the solvents (hexane41 and toluene49), were taken from the literature. Information on the static dielectric constant of maghemite was unavailable, and we have assumed that it was identical to the value for magnetite. A dielectric response function constructed from the direct integration of experimental spectral data was used for water.50 The dielectric response function of gold was represented by a Drude-Lorentz model.15,51 The spectral parameters for the solvents and substrates can be found in the Supporting Information. Calculation of the Hamaker Constants. All the calculations were performed at room temperature (298 K), adding the dielectric and the magnetic contributions. The magnetic contribution was determined using the reported experimental values of magnetic susceptibility for 9 nm spherical nanoparticles of magnetite52 and maghemite.27 More information on the calculation of magnetic term is given in the next section. The summation in eq 2 converges quickly, and the computation was stopped for mmax = 3000 and smax = 4. The Hamaker constants for the three iron oxide phases interacting across vacuum and water are displayed in Table 2. If we first consider the Hamaker constants for identical materials interacting in vacuum, the Lifshitz estimates show that the value of the Hamaker constant A101 depends significantly on the phase, with hematite having a Hamaker constant twice as large as that of magnetite. This difference is directly related to the dielectric response function in the UV, where the oscillator strength CUV and frequency ωUV vary as magnetite < maghemite < hematite (Table 1). The differences among the iron oxide phases highlight the importance of a thorough phase characterization of the particles before attempting to quantify vdW interactions. It is interesting to note that the microscopic approach, which uses the atomic density to estimate
A132
A132
A132
A131 (SiO2) (Si3N4) A131 (SiO2) (Si3N4)
A131b
22
2
6
9
1
5
30400 c
maghemite 26
1
9
18
5
22
30300 d
4
23
29
12
40
30300 e
magnetite hematite a
hydrocarbonsb
toluene
29 b
All values are in zJ. Estimated values reported in the literature. c Values reported in refs 20,28,29,55. d Values reported in refs 29,31. e Values reported in ref 29.
the magnitude of the Hamaker constant,48,53 would predict that Amaghemite < Amagnetite < Ahematite. The presence of an intervening medium reduces the magnitude of the Hamaker constant and thus the vdW interactions. Iron oxide nanoparticles with a well-defined size and shape are commonly synthesized in organic solvents,56,57 while there is a strong interest for aqueous dispersions of these nanocrystals, e.g., for biomedical applications.4,7 Previous estimates for the Hamaker constants of iron oxides interacting across water, 1345 zJ, are in fairly good agreement with the values obtained in the present study (Table 2). We provide in Table 3 the values of nonretarded Hamaker constants calculated using Lifshitz theory in two typical organic solvents, hexane and toluene. Our calculations suggest that the symmetric Hamaker constants A131 of magnetite and maghemite are significantly smaller than most of the previous estimates in hexane and in toluene.28,29,31,55It is also interesting to note that the Hamaker constants in hexane and toluene are significantly different for magnetite and maghemite, a behavior that cannot be expected from a simple comparison of dielectric constants or surface tensions but requires accurate information on the dielectric response functions. Combining rules are convenient but may be highly misleading when used to estimate the Hamaker constants in systems where the dielectric response of the material and medium differ significantly.37 As spectral data for most common solvents are available, accurate and reliable Lifshitz estimates of Hamaker constants for iron oxides can now be easily obtained using the spectral parameters given in Table 1. The Hamaker constant A132 is relevant for the estimation of the vdW interaction between iron oxide particles and a substrate, important, e.g., in all types of film formation processes on substrates and in evaporation-driven self-assembly of 8661
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nanoparticles. The Hamaker constants for all three iron oxide phases interacting with silica (SiO2) are always significantly smaller in magnitude compared to the Hamaker constants of iron oxide interacting with itself. We find that silicon nitride (Si3N4), a commonly used substrate material with widespread use, e.g., in electron microscopy grids, electronics, implants, and cutting tools, interacts with iron oxide in a complex manner. The Hamaker constant across toluene is 8 times larger for hematite compared to magnetite. Estimates of the Hamaker constant with Si3N4 across water and hexane show that the sign of the vdW forces changes from repulsive for magnetite to attractive for maghemite and hematite. This fundamental difference between the two superparamagnetic phases, magnetite and maghemite, can have significant implications on their assembly behavior.24 Magnetic Contribution to the Hamaker Constant for Iron Oxides. We have made an attempt to estimate the contribution of magnetic interactions to the Hamaker constant. Using the asymptotic value of the Langevin equation for weak magnetic fields, the static volume magnetic susceptibility (cgs units, emu. cm3.Oe1) can be calculated as χ¼
μ0 M 2 d3 72kB T
Figure 2. Magnitude of the magnetic dispersion interactions for magnetite and maghemite nanoparticles as a function of particle size.
ð10Þ
where d is the particle diameter, M the saturation magnetization, and μ0 the vacuum permeability.29 Previous work has shown that the Langevin equation can model the magnetic susceptibility accurately for particles smaller than 15 nm.58 We have based our calculations on characteristic values of the saturation magnetization of bulk magnetite and maghemite (480 emu.cm3 and 380 emu.cm3, respectively).59 It should be noted that using the bulk magnetization values sets an upper limit for the magnetic susceptibility, as the saturation magnetization of nanosized magnetite and maghemite nanoparticles is often smaller.58,60,61 The saturation magnetization of hematite is 1 order of magnitude lower than for magnetite and maghemite (18 emu.cm3).62 We show in the supplementary section that the magnetic contribution to the Hamaker constant for hematite is negligible and will not be discussed further here. A good agreement between the Langevin equation and the reported experimental values of the magnetic susceptibility was found (see Supporting Information).27,52 The Neel frequency of the magnetic relaxation ω0 was set to 1010 Hz in eq 8, similar to previous work by Dormann et al.46,63 The calculations were performed assuming that the intervening media and the substrates can be characterized by a constant magnetic response function (μ = 1). With this approach, the magnetic interactions will only appear in the calculation of the Hamaker constants of iron oxide interacting with itself (Δkl = 0 if neither material k nor l is iron oxide). Figure 2 shows the size-dependent magnetic contribution to the Hamaker constant calculated for magnetite and maghemite by combining eq 9 and eq 10. We find that the magnetic contribution to the Hamaker constant for magnetite and maghemite is at most 3 zJ, which is less than 14% of the dielectric contribution to the value of the Hamaker constants for these materials interacting across vacuum, water, or hexane. The magnetic term only becomes significant when the dielectric responses of the material and the medium are similar, resulting in a small Hamaker constant, as exemplified by magnetite in toluene (A121 = 9 zJ, Table 3). Colloidal Stability and Self-Assembly of Iron Oxide Nanoparticles. The colloidal stability and self-assembly behavior of iron oxide nanoparticles in aqueous and organic media are
Figure 3. Critical range of stability as a function of the Hamaker constant for nanoparticles in the superparamagnetic regime (2r < 15 nm). The range of stability is expressed as the dimensionless ratio l of the surface-to-surface separation distance s over the particle radius r. The full line represents the boundary between a colloidally stable (VvdW < 2kBT) and an unstable dispersion (VvdW > 2kBT). The dashed lines show the span covered by the Lifshitz values (929 zJ). The span using the previous estimates for hydrocarbons (30400 zJ) is much larger.
directly related to the interparticle forces. We have compared the stability range for iron oxide nanoparticles in hydrocarbons, defined as the surface-to-surface separation distance below which the attractive vdW interaction energy becomes larger than 2 kBT, using previous estimates of Hamaker constants and the values calculated using Lifshitz theory. The vdW interaction energy was calculated using an expression for two identical spheres= ! A 2 2 l2 þ 4l þ þ ln VvdW ¼ ð11Þ 6 l2 þ 4l ðl þ 2Þ2 ðl þ 2Þ2 where l is the dimensionless separation distance defined as l = s/ r.15,29 The previous estimates of the Hamaker constants for iron oxides across hydrocarbons span from 30 to 300 zJ (Table 3), which in terms of the critical range of stability translates to 1553% of the particle radius, as shown in Figure 3. Indeed, the Lifshitz calculations performed in this study show that the magnitude of vdW interactions has been previously overestimated, particularly for magnetite. Colloidal suspensions in hydrocarbons (e.g., ferrofluids) are often stabilized with an adsorbed layer of oleic acid with a thickness of 12 nm.20,27 In contrast with previous studies which partially attribute the 8662
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Table 4. Nonretarded Hamaker Constants for Iron Oxides Interacting with Golda A132 (zJ) material
a
vacuum
water
hexane
toluene
magnetite
99
20
10
16
maghemite hematite
135 168
11 38
22 49
51 82
All values are in zJ.
agglomeration in ferrofluids to attractive vdW interactions,29,64 we find that these interactions are insignificant for oleic-acidcoated superparamagnetic iron oxide nanoparticles compared with the attractive magnetic dipolar interactions, which exceed the threshold of 2 kBT for particles larger than 10 nm and increase more quickly than vdW interactions with the particle size.59,65,66 The controlled destabilization of colloidal suspensions is a convenient method to form nanoparticle superlattices. The lattice structure is governed by the interplay between various nanoscale forces, among which vdW and Coulombic interactions are of particular relevance.26 The former promote close-packed structures with a high coordination number, while the latter define the valency of each particle.67,68 In a previous study, Shevchenko (2006) showed that maghemite and gold nanoparticles could self-assemble into a NaCl-type binary superlattice upon the controlled drying of toluene-based suspensions.31 The Hamaker constant used to evaluate the magnitude of vdW interactions (100 zJ) was obtained from combining rules, and this calculation resulted in vdW and Coulombic interactions of comparable magnitudes. However, a Lifshitz-based computation of the Hamaker constant for the same system yields a value of A123 = 51 zJ only (maghemite against gold across toluene, Table 4), which indicates that vdW interactions are probably significantly smaller in magnitude than the Coulombic interactions. Indeed, weaker vdW interactions in this system could explain why a NaCl-type lattice with a coordination number Z = 6 formed instead of one with a higher coordination number, e.g., a CsCl-type lattice with Z = 8. Estimates of the Hamaker constants for all three iron oxide phases interacting with gold (Table 4) suggest that the magnitude of vdW interactions varies significantly among the studied iron oxide phases and various common solvents. Thus, subtle changes in the phase composition can have a strong impact on the balance of nanoscale forces and the final structure of the self-assembled arrays.
’ CONCLUSIONS The nonretarded Hamaker constants of magnetite, maghemite, and hematite have been determined from Lifshitz theory for various solvents and substrates. The results show that the studied phases display Hamaker constants which differ significantly in magnitude and sometimes even in sign. The contribution of magnetic interactions to the Hamaker constants amounts to 3 zJ at most, and can be safely neglected. The Hamaker constants for the iron oxides interacting across a medium calculated with the Lifshitz theory are in good agreement with previously published values for water, whereas they are significantly smaller than the reported values in hydrocarbons. We have revisited the effect of the vdW interactions on colloidal stability and nanoparticle self-assembly using the new
and more accurate values for the Hamaker constants. Considering only vdW and steric interactions for the stability of ferrofluids in hydrocarbons, the Lifshitz Hamaker constants suggest that iron oxide nanoparticles stabilized by oleic acid could be inherently stable in the superparamagnetic size range. It also demonstrated that revisiting the Hamaker constants between maghemite and gold can have important implications on the estimates of the balance between repulsive Coulombic forces and attractive vdW forces in self-assembling nanoparticle systems. The significant differences in both the magnitude and the sign of the Hamaker constants for the different iron oxide phases interacting with other materials across various solvents suggest that there is a possibility to fine-tune the balance of the nanoscale forces involved in the self-assembly process. We find that the vdW interactions with SiO2 is weak, with Hamaker constants smaller than or equal to 8 zJ for both magnetite and maghemite interacting across water and various hydrocarbons. The vdW interactions with Si3N4 are more complex and change sign, being repulsive with magnetite and attractive with maghemite and hematite interacting across water and hexane. With the availability of spectral parameters for iron oxides, the calculation of nonretarded Hamaker constants can now be performed reliably for many configurations. It should provide a firm ground for an accurate assessment of colloidal interactions in ferrofluids and advance our understanding of self-assembly.
’ ASSOCIATED CONTENT
bS
Supporting Information. Supplementary Figure 1: Magnetic susceptibility of magnetite, maghemite and hematite as a function of the particle diameter. Supplementary Table 1: Spectral parameters for the substrates and solvents. This material is available free of charge via the Internet at http://pubs.acs.org/.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The Swedish Research Council (VR) is acknowledged for funding. G.S.A. acknowledges the partial financial support from the WWSC. ’ REFERENCES (1) Cornell, R. M.; Schwertmann, U. The Iron Oxides, Structure, Properties, Reactions, Occurences and Uses, 2nd ed.; Wiley-VCH: Weinheim, 2003; p 664. (2) Teja, A. S.; Koh, P.-Y. Prog. Cryst. Growth Charact. Mater. 2009, 55, 22–45. (3) Laurent, S.; Forge, D.; Port, M.; Roch, A.; Robic, C.; Elst, L. V.; Muller, R. N. Chem. Rev. 2008, 108, 2064–2110. (4) Pankhurst, Q. A.; Connolly, J.; Jones, S. K.; Dobson, J. J. Phys. D: Appl. Phys. 2003, 36, R167. (5) Rosensweig, R. Annu. Rev. Fluid Mech. 1987, 19, 437–461. (6) Raj, K.; Moskowitz, B.; Casciari, R. J. Magn. Magn. Mater. 1995, 149, 174–180. (7) Gupta, A. K.; Gupta, M. Biomaterials 2005, 26, 3995–4021. (8) Tartaj, P.; del Puerto Morales, M.; Veintemillas-Verdaguer, S.; Gonzalez-Carre~ no, T.; Serna, C. J. J. Phys. D: Appl. Phys. 2003, 36, R182. (9) Redl, F.; Cho, K.; Murray, C.; O’Brien, S. Nature 2003, 423, 968–971. 8663
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