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Suitability of commercial colloids for magnetic hyperthermia Mathew Kallumadil a,b, , Masaru Tada c , Takashi Nakagawa c , Masanori Abe c , Paul Southern a,b , Quentin A. Pankhurst a,b a Davy-Faraday Research Laboratories, The Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, UK b London Centre for Nanotechnology, University College London,17-19 Gordon Street, London WC1 H 0AH, UK c Department of Physical Electronics S3-41, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan article info Available online 21 February 2009 Keywords: Magnetic hyperthermia Ferrofluid Iron oxide Commercial colloids Intrinsic loss power Specific absorption rate Specific loss power Maghemite Magnetite Ferrous Ferric Crystallite diameter Cancer abstract Commercial nanoparticles supplied by Chemicell, Micromod and Bayer-Schering were characterised with regard to their nanocrystalline diameter, hydrodynamic diameter, total iron content and relative ferrous iron content. Additionally, calorimetric measurements were taken using a 900 kHz AC magnetic field of amplitude 5.66 kA/m. It was found that those samples containing relatively high (418%) ferrous content generated a substantially smaller (12% on average) intrinsic loss power (ILP) than those samples with a lower ferrous content. Two nominally identical Chemicell samples that differed only in their production date showed significantly different ILPs, attributed to a variation in batch-to-batch crystallite sizes. The highest ILP values in the cohort, ca. 3.1 nHm 2 /kg, were achieved for particles with hydrodynamic diameters of ca. 70 nm and nanocrystalline diameters of ca. 12 nm. These compare favourably with most samples prepared in academic laboratories, although they are not as high as the ca. 23.4 nHm 2 /kg reported for naturally occurring bacterial magnetosomes. & 2009 Elsevier B.V. All rights reserved. Many research groups are exploring the potential of magnetic nanoparticles (MNPs) in biomedical applications [1]. Most such studies utilise bespoke MNPs that are synthesised in-house, which is desirable for ease of sample control and modification, but raises issues regarding formulation, reproducibility and quality assurance for any future efforts at technology transfer – particularly when the intention is to use the MNPs in human clinical trials. For the latter, commercially produced materials, particularly those certified and guaranteed to GMP standards, are much preferred by medical ethics committees. In addition, MNP manufacturing companies often possess the required resources and commercial drive that are needed to push through the medical approval processes, and deliver the new therapy as rapidly as possible to the patient. One such case where the goal is the use of MNPs in human therapies is magnetic field hyperthermia – a cancer therapy involving the targeted administration of MNPs into the body, accumulation of those MNPs at sites of cancer, and the local heating of those MNPs with an externally applied AC magnetic field. To date, almost all reports in the literature deal with the heating properties of bespoke MNPs. In this paper, we report on a survey of some commercially available MNPs as possible candi- dates for hyperthermia applications. We also compare the results obtained with previously published data on bespoke MNPs, using a new design rule parameter – the intrinsic loss power (ILP), – which in the case of superparamagnetic nanoparticles, and under certain assumed conditions, allows direct comparison of the particle-heating capabilities of materials recorded in response to different AC field strengths and frequencies. The heat rise rate of a magnetic fluid in an AC magnetic field can be described by the phenomenological Box–Lucas equation: T ðtÞ¼ Að1 e Bt Þ (1) where T is the temperature, t is time, A is the saturation temperature and B is a parameter related to the curvature of the heating curve. The product A B at t ¼ 0 is also known as the initial heat rise rate and is equivalent to the ratio DT/Dt used in the specific absorption rate (SAR) formula [2]: SAR ¼ DT Dt C m Fe (2) where C is the heat capacity of the fluid per unit mass of fluid, and m Fe is the iron mass in the fluid per unit mass of fluid. Although the SAR parameter – also known as specific loss power (SLP) – is quite often used in the literature to characterise the heating ability of MNPs, it has a significant limitation in that it ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.02.075 Corresponding author at: Davy-Faraday Research Laboratories, The Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, UK. Tel.: +44 20 7670 2922. E-mail address: [email protected] (M. Kallumadil). Journal of Magnetism and Magnetic Materials 321 (2009) 1509–1513

Suitability of commercial colloids for magnetic hyperthermia

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Suitability of commercial colloids for magnetic hyperthermia

Mathew Kallumadil a,b,!, Masaru Tada c, Takashi Nakagawa c, Masanori Abe c,Paul Southern a,b, Quentin A. Pankhurst a,b

a Davy-Faraday Research Laboratories, The Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, UKb London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1 H 0AH, UKc Department of Physical Electronics S3-41, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan

a r t i c l e i n f o

Available online 21 February 2009

Keywords:Magnetic hyperthermiaFerrofluidIron oxideCommercial colloidsIntrinsic loss powerSpecific absorption rateSpecific loss powerMaghemiteMagnetiteFerrousFerricCrystallite diameterCancer

a b s t r a c t

Commercial nanoparticles supplied by Chemicell, Micromod and Bayer-Schering were characterisedwith regard to their nanocrystalline diameter, hydrodynamic diameter, total iron content and relativeferrous iron content. Additionally, calorimetric measurements were taken using a 900kHz AC magneticfield of amplitude 5.66 kA/m. It was found that those samples containing relatively high (418%) ferrouscontent generated a substantially smaller (12% on average) intrinsic loss power (ILP) than those sampleswith a lower ferrous content. Two nominally identical Chemicell samples that differed only in theirproduction date showed significantly different ILPs, attributed to a variation in batch-to-batchcrystallite sizes. The highest ILP values in the cohort, ca. 3.1 nHm2/kg, were achieved for particles withhydrodynamic diameters of ca. 70nm and nanocrystalline diameters of ca. 12nm. These comparefavourably with most samples prepared in academic laboratories, although they are not as high as theca. 23.4 nHm2/kg reported for naturally occurring bacterial magnetosomes.

& 2009 Elsevier B.V. All rights reserved.

Many research groups are exploring the potential of magneticnanoparticles (MNPs) in biomedical applications [1]. Most suchstudies utilise bespoke MNPs that are synthesised in-house,which is desirable for ease of sample control and modification,but raises issues regarding formulation, reproducibility andquality assurance for any future efforts at technology transfer –particularly when the intention is to use the MNPs in humanclinical trials. For the latter, commercially produced materials,particularly those certified and guaranteed to GMP standards, aremuch preferred by medical ethics committees. In addition, MNPmanufacturing companies often possess the required resourcesand commercial drive that are needed to push through themedical approval processes, and deliver the new therapy asrapidly as possible to the patient.

One such case where the goal is the use of MNPs in humantherapies is magnetic field hyperthermia – a cancer therapyinvolving the targeted administration of MNPs into the body,accumulation of those MNPs at sites of cancer, and the localheating of those MNPs with an externally applied AC magneticfield. To date, almost all reports in the literature deal with the

heating properties of bespoke MNPs. In this paper, we report on asurvey of some commercially available MNPs as possible candi-dates for hyperthermia applications. We also compare the resultsobtained with previously published data on bespoke MNPs, usinga new design rule parameter – the intrinsic loss power (ILP), –which in the case of superparamagnetic nanoparticles, and undercertain assumed conditions, allows direct comparison of theparticle-heating capabilities of materials recorded in response todifferent AC field strengths and frequencies.

The heat rise rate of a magnetic fluid in an AC magnetic fieldcan be described by the phenomenological Box–Lucas equation:

T!t" # A!1$ e$Bt" (1)

where T is the temperature, t is time, A is the saturationtemperature and B is a parameter related to the curvature of theheating curve. The product A%B at t # 0 is also known as theinitial heat rise rate and is equivalent to the ratio DT/Dt used inthe specific absorption rate (SAR) formula [2]:

SAR #DTDt

CmFe

(2)

where C is the heat capacity of the fluid per unit mass of fluid, andmFe is the iron mass in the fluid per unit mass of fluid.

Although the SAR parameter – also known as specific losspower (SLP) – is quite often used in the literature to characterisethe heating ability of MNPs, it has a significant limitation in that it

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Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jmmm

Journal of Magnetism and Magnetic Materials

0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.jmmm.2009.02.075

! Corresponding author at: Davy-Faraday Research Laboratories, The RoyalInstitution of Great Britain, 21 Albemarle Street, London W1S 4BS, UK.Tel.: +442076702922.

E-mail address: [email protected] (M. Kallumadil).

Journal of Magnetism and Magnetic Materials 321 (2009) 1509–1513

is an extrinsic (equipment-specific) parameter. The SAR parameterfor the same magnetic fluid will change when measured in ACmagnetic field systems with different frequencies and strengths,as can be deduced from the formula for volumetric powerdissipation [3]:

P # m0pw00!f "fH2 (3)

where m0 is the permeability of free space (4p%10$7NA$2), w00 isthe out-of-phase (imaginary) component of susceptibility, and His the applied field strength. Note that w00is intrinsically a functionof f. The SAR parameter is proportional to P divided by the densityof the magnetic material, hence SAR varies with both H, and f.

However, at low frequencies such as those currently usedin most heating systems (ca. 105–106Hz), and for the case ofpolydisperse MNPs in solution (with a crystallite polydispersityindex (PDI) of more than 0.1), Rosensweig [3] has predicted that,to a good approximation, w00 is frequency-independent. In suchcases, the SAR parameter can be regarded as a function of f and thesquare of magnetic field strength only. Fig. 1 is an experimentalvalidation of this principle, showing calorimetric values varyinglinearly with frequency in the range of 100–900kHz for Micro-mod’s ‘nanomag 100nm’ MNPs.

We therefore introduce the ‘intrinsic loss power’ as a newdesign rule parameter, defining it as

ILP #P

rH2f#

SAR

H2f(4)

The ILP is a step towards an intrinsic, system-independentparameter, designed to allowmore direct comparisons to be madebetween experiments performed in different laboratories andunder different AC field strength and frequency conditions. It isvalid under the conditions outlined above (frequencies of up toseveral MHz, samples with a crystallite PDI of more than 0.1) andalso provided the applied field strength H is well below thesaturation field of the MNPs, so that the hysteretic behaviouris essentially parabolic in nature. A further condition for usingthe ILP parameter to compare results between different systems isthat similar environmental thermodynamic losses are involved.This is admittedly a difficult condition to guarantee betweendifferent laboratories, but to a first approximation it may be notedthat most reports in the literature to date deal with calorimetricmeasurements undertaken with a thermally insulated system at

room temperature, as opposed to either a fully adiabatic system,or a thermally equilibrated system. In any case, despite thelimitation inherent in the definition of the ILP parameter, wepropose that it is at least a move towards a more intrinsicmagnetic heating parameter than is the SAR parameter thatcurrently has the most coinage.

Sixteen different iron-oxide-based magnetic fluid samplesfrom Chemicell GmbH, Micromod GmbH and Bayer-ScheringPharma were tested (Table 1), with different sizes and core–shellconfigurations. Note that two nominally identical particles fromChemicell (1 and 15) are included, which differed only by batchproduction date (9 months apart; sample 15 being the older).Furthermore, Micromod’s BNF series (3, 10, 12, 16) are at theresearch stage and are not commercially available yet.

The hydrodynamic diameters of the samples were measuredvia dynamic light scattering (DLS) using a Malvern ZetasizerNanoseries, and compared with the suppliers’ specifications (seeTable 1). The total iron content for each sample was evaluatedusing ICP-AES, and then used in the calorimetric measurementsto prepare dilutions of samples with identical Fe concentrations.The relative ferric and ferrous iron concentrations in the sampleswere assessed using the chemical preparation process describedby Iwasaki et al. [4], calibrated against a standard solution withknown Fe content, and involving UV–vis spectroscopy (on a JascoV-570 spectrometer). Under the assumption that the MNPs inthe samples were magnetically non-interacting and log-normallydistributed in size, their nanocrystalline grain sizes weredetermined by fitting their room temperature DC magnetisationcurves (measured on a Quantum Design MPMS magnetometer)using the Langevin function [5].

Calorimetric measurements were made using a ThamwayT162-5723B radio frequency amplifier with two matchingboxes with a frequency range of 100–500kHz and 500–900kHz,respectively. The resonant circuit further consisted of a 20-turnwater-cooled solenoid with 8 cm diameter. The maximum ACmagnetic field amplitude that could be generated was 5.66 kA/mat 900kHz. A round-bottom-shaped plastic sample holder wasused and surrounded by layers of insulation to protect the sampleagainst ambient heating from the coil. Temperature measure-ments were conducted with fibre-optic temperature probes(Astech TEM-4).

Comparison of the DLS measurement results of particlehydrodynamic diameter (given in Table 1) with the size informa-tion provided by the manufacturers indicates the value ofindependent size analysis. In general the supplied dimensionstend to be underestimated, – which may indicate some degree ofaging-related agglomeration of the samples between manufactureand delivery, – which is more pronounced for larger particles.The polydispersity indices (PDI) for the hydrodynamic diametersof the MNPs ranged from 0.05–0.25, which indicate low- to mid-range polydispersity. After long-term observation (47 days) of thetwo samples with the largest measured hydrodynamic size, somesedimentation was observed.

ICP-AES measurements yielded data on the total Fe content foreach sample-information that some but not all of the commercialsuppliers had provided. Where comparison was possible, gener-ally acceptable agreement (within73%), was found.

The relative ferrous (Fe2+) to ferric (Fe3+) content of thesamples were measured using UV–vis spectrometry after chemi-cal analysis as follows. Two aliquots of each sample (withidentical total Fe concentrations) were prepared, one of whichhad all its Fe3+ reduced to Fe2+. This was achieved by dissolving a500mL aliquot of the magnetic fluid in an equal volume of a 1:1mixture of 35% hydrochloric acid and water. The resulting solution(which was a yellow colour) was diluted to 25mL with deionised(DI) water. Then two 5mL parts of the solution were re-suspended

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Fig. 1. SAR versus frequency for Micromod’s nanomag-D 100nm. All measure-ments were taken at H # 5.66 kA/m. The straight line is a linear fit of the data withintercept at the origin.

M. Kallumadil et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1509–15131510

with 10mL pH acetate buffer, 3mL of aa0-bipyridine and DI water,into different 25mL flasks. Additionally, 1mL of hydroxylamine isadded to one flask to reduce the Fe3+ to Fe2+. UV–vis absorptionspectra were then recorded at 522nm to quantify the difference inFe2+ content between the two flasks, to an accuracy of less thanabout 5%.

This process was also repeated for a standard iron solution(Wako Pure Chemical Industries Ltd.) and was found to accuratelyconfirm the total Fe concentrations of the samples as measured byICP-AES.

Langevin fitting of the measured magnetisation curves(not shown) provided information on both the mean crystallitesize and also on the degree of polydispersity of the samples.Polydispersity indices for crystallite diameters were calculated torange from s # 0.39 to 0.98. Notably, Micromod’s BNF series (3,10, 12, 16) and Resovist (11) have the highest spread of particledistribution, with s in the range 0.65–0.98.

Calorimetric measurements were taken for all samples at a Feconcentration of 5mg/mL. All recordings were taken at 900 kHzwith a field amplitude of 5.66 kA/m. The field was only employedup to a maximum solution temperature of 50 1C, after which pointevaporative effects could have caused contamination of theStyrofoam insulation. The rates of heat rise, DT/Dt, for all thesamples were extracted by fitting the Box–Lucas equation tothe data. These data were then compared to the hydrodynamicdiameters (Fig. 2) and percentage ferrous Fe content (Fig. 3) of thesamples.

The ILP plotted against hydrodynamic diameter (Fig. 2)indicates a tendency for optimum heat generation at around

70nm. Four samples with diameters between 100 and 175nmshowed little heating, viz. Micromod’s BNF series and thenanomag-D 130nm (3, 12, 16 and 14). High Fe2+ content may

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Table 1Tested commercial ferrofluids.

Referencenumber

Manufacturer Particletype

Coating Givenhydrodynamicdiameter (nm)

DLShydrodynamicdiameter (nm)(PDI)

MPMScrystallitediameter(nm) (PDI)

Given particleconcentration(mg/mL)

Given Feconcentration(mg/mL)

ICP-AESmeasured total Feconcentration(mg/mL)

Intrinsicloss powerILP (nHm2/kg)

1 Chemicell Fluidmag-D

Starch 50 42 (0.13) 9.8 (0.39) 100 50 27.8 1.31

2 Micromod Nanomag-D-spio

Carboxyl 100 91 (0.13) 11.8 (0.56) 50 5.4 5.9 3.12

3 Micromod BNF-01908

Carboxyl 60 108 (0.08) 7.7 (0.65) 20 11.4 8.9 0.35

4 Chemicell Fluidmag-D

Starch 100 109 (0.10) 10 (0.45) 50 37.5 29.8 2.01

5 Chemicell Fluidmag-D

Starch 200 160 (0.18) 9.6 (0.47) 50 37.5 33.7 1.41

6 Chemicell FluidmagNC-D

Starch 200 177 (0.18) 9.5 (0.18) 80 – 48.2 1.31

7 Chemicell FluidmagNY-D

Starch 200 212 (0.17) 9.6 (0.41) 80 – 37.0 1.53

8 Chemicell Fluidmag-CMX

Carboxymethyl-dextran

200 220 (0.21) 9.9 (0.45) 200 – 125.4 1.71

9 Micromod Nanomag-D-spio

Carboxyl 250 346 (0.21) 8.9 (0.43) 50 23.5 22.6 0.37

10 Micromod BNF-02008

Carboxyl 400 512 (0.14) 7.6 (0.88) 50 11.8 8.1 0.16

11 Bayer-Schering

Resovist Carboxydextran

60 61 (0.19) 10.5 (0.67) – 28 27.8 3.1

12 Micromod BNF-01708

Carboxyl 80 130 (0.08) 7.1 (0.98) 50 29.7 29.5 0.15

13 Micromod Nanomag-D-spio

Carboxyl 20 84 (0.15) 11.2 (0.59) 50 6 6.0 2.31

14 Micromod Nanomag-D-spio

Carboxyl 130 165 (0.05) 8.3 (0.48) 50 25.3 25.1 0.23

15 Chemicell Fluidmag-D

Starch 50 39 (0.08) 12.6 (0.5) 70 – 14.7 2.67

16 Micromod BNF-01808

Carboxyl 90 129 (0.12) 8.2 (0.65) 50 32.1 28.0 0.17

Note that in some cases not full information was provided. Bayer-Schering’s Resovist is the only medically approved ferrofluid. Two apparently identical samples fromChemicell (1 and 15) differ only by batch production date spanning 9 months. Micromod’s BNF-series are not commercially available and in research stage.

Fig. 2. ILP versus hydrodynamic diameter as measured by DLS. The heating abilitytends to peak at around 70nm. Particles 3, 10, 12 and 16 are Micromod’s BNF-seriesthat have comparatively high Fe2+ content. Particle 14 was synthesised using adifferent procedure than other particles. Chemicell’s quasi-identical particles (1and 15) differ strongly in ILP.

M. Kallumadil et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1509–1513 1511

explain the former and the latter was produced using a differentsynthesis method according to the manufacturer.

Fig. 3 shows ILP measurements as a function of ferrous ironcontent. It is noted that the BNF series contains relatively largeparts of ferrous compound (ca. 20%), which seems to be negativelyaffecting the heating performance. Again, the two sets ofChemicell fluidmag-D 50nm differ strongly in their heatingability, whilst containing similar amounts of Fe2+.

On the other hand, ILP as a function of nanocrystallite diameter(Fig. 4) as estimated from the Langevin curve fitting, suggests a

clear trend, which may explain the difference in heatingefficiencies between the identical Chemicell batches. Smaller-sized crystallites apparently reduce the ILP by an order ofmagnitude over a range of about 5nm. These findings correspondwell with the theoretical and experimental data reported byFortin et al. [5].

Our findings show that when using commercial nano-particles comprehensive independent characterisation is required.Although the Fe2+/Fe3+ ratio could be affecting the heating abilityof particles, our data do not indicate any unambiguous correla-tion. A more clear-cut relationship is apparent between the ILPand the hydrodynamic diameter of the samples, with a peak ataround 70nm. However, arguably the most convincing correlationappears between the ILP and the nanocrystallite size, with thebest heating characteristics being seen for crystallites of diameterca. 11–13nm.

In terms of magnetic heating capability, the three bestmagnetic fluids measured in this study were Micromod’snanomag-D 100nm, Bayer-Schering’s medically approved Reso-vist, and Chemicell’s ‘aged’ fluidmag-D 50nm. (The latter showedsignificantly more ILP than a nominally identical, but freshlyprepared, batch of the same sample. The difference is most likelyexplained by some aging of the fluid, as evidenced by a largercrystallite size being found for the older sample). All three had ILPparameter values of order 3nHm2/kg.

It is interesting to compare these data against the bestsynthetic and natural particles reported in the literature, assum-ing that we can do so via the intrinsic loss power parameter.The best synthetic iron oxide particles in the literature todate were those reported by Fortin et al. [5] and Hergt et al.[7]. The former had a reported SLP parameter of 1650W/gat H # 24.8 kA/m and f # 700kHz, while the latter had an SLPof 600W/g at 11.2 kA/m and 410kHz. The system-normalisedILP parameters for these samples are 3.8 and 11.7nHm2/kg,respectively. The Fortin sample corresponds well with the datashown in Fig. 4, whereas the Hergt sample seems to besignificantly superior.

The strongly heating particles reported by Hergt et al. [5] hadan average crystal diameter of 15.3 nm and hydrodynamicdiameter of ca. 70nm – parameters in common with the bestheating commercial samples in the present study – but and ILPapproximately four times bigger. The reason for this is not clear,although it is notable that the Hergt particles had a relativelynarrow size distribution. In this context it is especially interestingto note another result published by Hergt et al. [6], viz. aninvestigation of the magnetic heating characteristics of magneto-somes produced by magnetotactic bacteria, which yielded ameasured SLP of 960W/g at H # 10kA/m and f # 410kHz. Thistranslates into an ILP of 23.4 nHm2/kg – almost eight times thatof the best sample heater in this study, and twice that of thebest synthetic result yet reported. Although it should be notedthat bacterial magnetosomes are not superparamagnetic, and thattherefore a different ILP field-frequency relation might apply, itmay also be pertinent that they have a naturally constrainedgrowth habit such that their size distribution is quite mono-disperse. In any case, it is instructive to note that these naturallyoccurring nanoparticles have remarkable properties.

In conclusion, this survey of the magnetic heating character-istics of a range of commercially available magnetic fluids hasshown that some are on a par with the upper echelon (if notprecisely the best) of samples prepared to date obtained inindependent laboratories.

The author would like to thank the Japan Society for PromotingScience (JSPS) and EPSRC for funding this project as well asChemicell and Micromod for providing nanoparticles solutions.

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Fig. 3. ILP versus percentage Fe2+. No clear trend between these parameters can bededucted, although Micromod’s BNF series (3, 10, 12 and 16) show high ferrouscontent and low ILP. Also note that there is negligible difference in ferrous ironcontent between the two quasi-identical particles from Chemicell (1 and 15). Puremagnetite contains 33.3% Fe2+.

Fig. 4. ILP versus crystallite diameter. The mean diameter of a lognormal particledistribution for each sample was calculated by fitting a Langevin function tosuperparamagnetic hysteresis curve measured in the MPMS at 300K. Within thegiven range of diameters, larger core particle sizes result in higher heatingproperties, particularly noticeable for Micromod’s BNF series (3, 10, 12 and 16) thathave relatively smaller crystalline diameters than the better heaters.

M. Kallumadil et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1509–15131512

Thanks also to Wisdom Beyhum for invaluable advice and supporton fitting hysteresis curves.

Appendix A

The polydispersity index (PDI) is defined as the parameter s in thelog-normal probability distribution P!d" # 1=

!!!!!!2p

psd exp&$ln2!d=d0"=

2s2', where d is the crystallite particle diameter, and d0 thecharacteristic diameter. The mean diameter D can be calculated usingD # d0exp(s2/2).

References

[1] Q.A. Pankhurst, et al., J. Phys. D: Appl. Phys. 36 (2003) R167.[2] M. Ma, et al., J. Magn. Magn. Mater. 268 (2004) 33.[3] R.E. Rosensweig, J. Magn. Magn. Mater. 252 (2002) 370.[4] I. Iwasaki, et al., Bull. Volc. Soc. Japan 5 (1960) 9, (2nd series, in Japanese).[5] J.-P. Fortin, et al., J. Am. Chem. Soc. 129 (2007) 2628.[6] R. Hergt, et al., J. Phys.: Condens. Matter 18 (2006) S2919.[7] R. Hergt, et al., J. Magn. Magn. Mater. 270 (2004) 345.

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M. Kallumadil et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1509–1513 1513

Corrigendum

Corrigendum to ‘‘Suitability of commercial colloids for magnetichyperthermia’’ [J. Magn. Magn. Mater. 321 (2009) 1509–1513]

Mathew Kallumadil a,b,!, Masaru Tada c, Takashi Nakagawa c, Masanori Abe c, Paul Southern a,b,Quentin A. Pankhurst a,b

a Davy-Faraday Research Laboratories, The Royal Institution of Great Britain, 21 Albemarle Street ,London W1S 4BS, UKb London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UKc Department of Physical Electronics S3-41, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan

The publication is focused around the heating parameter, intrinsic loss parameter (ILP), which is correlated with hydrodynamicparticle size, relative ferrous content and crystallite size. Unfortunately, only in Fig. 4, the scale is correct, i.e. matches the range between0–4nHm2/kg, given in Table 1. For Figs. 2 and 3, an old calculation range has been used and has range from 0–12nHm2/kg. Please find thecorrect Figs. 2 and 3 below.

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Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jmmm

Journal of Magnetism and Magnetic Materials

Fig. 2

0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.jmmm.2009.06.069

DOI of original article: 10.1016/j.jmmm.2009.02.075! Corresponding author at: Davy-Faraday Research Laboratories, The Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, UK. Tel.: +442076702922.E-mail address: [email protected] (M. Kallumadil).

Journal of Magnetism and Magnetic Materials 321 (2009) 3650–3651

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Fig. 3

Corrigendum / Journal of Magnetism and Magnetic Materials 321 (2009) 3650–3651 3651