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Francisco H. Sánchez G3M, Physics Department and La Plata Institute of Physics, FCE,UNLP, CONICET, Argentina Physics Building, 1905 Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, and Ferrogels for Drug Delivery http://www.fisica.unlp.edu.ar/Members/sanchez/escola-de-magnetismo-vitoria-es- brasil-03-11-13-al-08-11-13
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Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

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Page 1: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Francisco H. Sánchez

G3M, Physics Department and La Plata Institute of Physics, FCE,UNLP,

CONICET, Argentina

Physics Building, 1905

Magnetic Nanomaterials.

Some Biomedical Applications: Magnetofection, Magnetic

Hyperthermia, and Ferrogels for Drug Delivery

http://www.fisica.unlp.edu.ar/Members/sanchez/escola-de-magnetismo-vitoria-es-

brasil-03-11-13-al-08-11-13

Page 2: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Why magnetic nanomaterials for biomedicine?

?

Page 3: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Introduction to Magnetic Materials B.D. Cullity,

(Massachusetts, Addison-Wesley, 1972).

Introduction to the Theory of Ferromagnetism, Amikam

Aharoni, Oxford Science Publications, 1998.

Modern Magnetic Materials, Robert C. O’Handley, John

Wiley & Sons, 1999

Introduction to Magnetism and Magnetic Materials,

David Jiles, Chapman & Hall 1996.

Nanomedicine: design and applications of magnetic

nanomaterials, nanosensors and nanosystems

Vijay K. Varadan, Linfeng Chen, Jining Xie, 2008

John Wiley & Sons, Ltd

Selected articles

Bibliography

http://www.fisica.unlp.edu.ar/Members/sanchez/curso-de-posgrado-

nanomateriales-magneticos-intema/bibliografia

Page 4: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

http://www.fisica.unlp.edu.ar/

Actividad Académica

Docentes

Profesores

Sánchez, Francisco Homero

Two links:

Escola de Magnetismo - Vitoria, ES,

Brasil

Curso de Posgrado "Nanomateriales

Magnéticos"

Page 5: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Index

Class 1

Brief revision: contributions to energy in magnetic nanoparticles

Stoner – Wohlfarth model

Two levels model

Paramagnetism

Superparamagnetism

Interacting superparamagnets

Demagnetizing factor NDef in samples with disperse magnetic NPs

Page 6: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Class 2a

Understanding SAR and searching for high performance nanomaterials

zinc-doped magnetite nanoparticles and ferrofluids for hyperthermia

applications

Citric Acid Coated Magnetite Nanoparticles for Magnetic Hyperthermia

In vitro experiments

Class 2b

In Vitro Magnetofection: Magnetic Force Influence

Ferrogels PVA/Fe oxide

Page 7: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

magnetite

magnetsmall domainsingle

Magnetic Nanocomposites. Examples:•Ferrofluids•Virus/NPs complexes•Ferrogels: magnetic hydrogels

Page 8: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

8

A brief introduction to nanomaterials magnetic state:

Exchange interactionMagnetic anisotropyMagnetostatic energy: dipolar interactionZeeman interaction: response to an applied field

Page 9: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Magnetic Anisotropy – phenomenological description

eK : anisotropy energyper volume unity

42

3

2

2

2

1123

222

i

i

iji

ij

iji

i

iK mKmmmKmmKmKe

EK : anisotropy energy dVeE KK

mi : magnetizationdirector cosines

...,,

3,2,1M

Mm

zyx

2m

3m

1m

x

y

z

Page 10: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Material K1

(105 J/m3)K1

(105 J/m3)Easy axis

Co 4.1 1.0 hexagonal

SmCo5 1100 - hexagonal

4

2

2

1 sinsin KKeK

Magnetocrystalline Anisotropy in Hexagonal Crystals

Magnetocrystalline Anisotropy in Cubic Crystals

2

3

2

2

2

12

22

1 mmmKmmKe ji

ij

K

Material K1

(105 J/m3)K2

(105 J/m3)Eje fácil

Ni -0.045 -0.023 (111)

Fe 0.480 0.05 (100)

2m

3m

1m

x

y

z

Page 11: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

21 nmKe SK

interface

Surface Anisotropy

sup//0 mKS

sup0 mKS

Interface anisotropy

Exchange anisotropy*

Sx

SSK umH

umKe

2

anti

ferr

o

Exchange bias field

n

Su

ferr

o

*called also unidirectional

cos2

mH

e xK

H

M

xH

Page 12: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

ef

VBef SKKK

d

KKK s

Bef

d

KKK s

Bef

6

SSSSef

V Kd

Kr

K

r

r

V

SKK

S

63

3

4

4

3

2

sphericalNP

Bødker et. Al (1994)

surfaces/interfaces:

-Compositional and configurational discontinuity

- Large anisotropic effect

KS = 10-5-10-4 J/m2, anisotropy energyper surface area

unit

surface

bulk

Surface anisotropy in nanoparticles

Page 13: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

F. Luis, J.M. Torres, L.M. Gracía, J. Bartolomé, J. Stankiewicz, F. Petroff, F. Fettar, J. L.

Maurice and A. Vaurés. Phys. Rev B, 65 (2002) 094409

Co/Al2O3

Bulk

Surface anisotropy in nanoparticles

Page 14: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Single domain NPs

Uniaxial anisotropy

Stoner – Wohlfarth Model

K

no interactions among NPsIdentical NPs

H

H

K

K

H

K

cossin 0

2 HMsVKVEEE HK

Easy

axis

-

H

z =MV

anisotropy Zeeman

Page 15: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

-1 0 1 2 3 4-3

-2

-1

0

1

2

3

h = 0.25

h = 0.00

h = 1.00

h = 0

h = 1.25

E

cos2sin2 hKVE

KH

Hh

H

S

KM

KH

0

2

hcos

hKV2

0

hKV2

Field in the easy direction

Page 16: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

cossz MM

H

HK-HK

0Easy axis

S

KM

KH

0

2

KT 0

Field in the easy direction

Page 17: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

H

-HK

HK

Hard axis

S

KM

KH

0

2

KT 0

1; hHH

MM

K

Sz

Field in the hard direction

Page 18: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

E.C. Stoner y E.P. Wohlfarth, IEEE Transactions on Magnetics 27, 3475-3518 (1991)

MK

HK

-HK HK

-HK

H

HH

H

S

KM

KH

0

2

KT 0

Stoner – Wohlfarth Model

Page 19: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Stoner – Wohlfarth Model

Page 20: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

KC HH 479.0

SR MM 5.0

Stoner – Wohlfarth Model

Page 21: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

kT

E

ij

ij

ec

00

0

ijT

0cijT

Atempt Frequency

kT

E

ij

ij

ec

1

0

Jump Frequency

Relaxation Time-1 0 1 2 3 4-1

0

1 12

21

1

2

H = 0.25 HK

E

2)1( hKV

2)1( hKV

2)1( hKVEij

KT 0

Extending the Stoner – Wohlfarth Model

Page 22: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

SKC

M

KHH

0

2

M

HHK

HC

T=0

T0

Coercive Field Temperature Dependence

-2 -1 0 1 2 3 4 5

-1

0

1

h = 0,75

E

K

HMHHh S

K2

/ 0

hKV2

hKV2)1( 2hKV

21 hKVE

kT

hKV

e

21

021

moment inversion occurs when21 exp

Extending the Stoner – Wohlfarth Model

Page 23: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

0exp

2/ln1 kThKV

0exp /ln1

KV

kTh

0exp /ln1

KV

kTHTH KC

KC HH 479.00

0exp /ln148.0

KV

kTHTH KC

KH

//

HK

H

NPs Random Orientation

Coercive Field Temperature Dependence

Extending the Stoner – Wohlfarth Model

Page 24: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

2/1

12

BS

CT

T

M

KH

Magnetic Interactions in ferromagneticnanotubes of LaCaMnO and LaSrMnO,

J.Curiale et al., AFA 2006

Uso extendido de la expresión

Marina Tortarola, Thesis, IB, 2008

M

HHK

HC

T=0

T0

Page 25: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Ferrogel of maghemite NP (8 nm) in PVA hydrogel, Mendoza Zélis et al.

Extending the Stoner – Wohlfarth Model

Coercive Field Temperature Dependence

Page 26: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Two levels model

KVE

Simplification: 2 levels

Field in easy direction

Page 27: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

KVE1E2

kTEe

/

011

kTE

e/

022

1

11211 1 ppt

p

tfHt

H

pMM

H

S

0

1 12

dHtfM

M

H

MdM

HS

S 12

0

1

Two levels model

Page 28: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Two levels model

Page 29: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

34 J/m101.89 = K

D18 nm

f=2.6e4 Hz

Behavior at Radiofrecuency

Two levels model

Page 30: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Magnetostatic Energy (dipolar interactions)

M uniformGeneral Case

Hint NO uniform

2nd degree surface

(conics)

Hint uniform

M uniform

1

222

c

z

b

y

a

x

ellipsoid

MNHD

ˆ

Demagnetizing

fieldDemagnetizing

Tensor

Diagonal if

coordinate axis

coincide with

ellipsoid ones

Number if M

iM S

jM S

kM S

Unit Trace

1 zyx NNN

Page 31: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

2220

2zzyyxxM MNMNMN

VE

Non quadratic surfaces

Valid also for bodies with non

quadratic surfaces: cubes, prisms,

cilinders, octahedra, etc.

( Brown-Morrish theorem)

Cube,

octahedra,

tetrahedra

3/1 zyx NNN

Regular

prism,

cilinder

zyx NNN

Limit case, z

0;2

1 zyx NNN

Page 32: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

zyx NNNcba

22202220

22zzyxxNNzzyyxxM MNMMN

VMNMNMN

VE

xy

constMNNV

constMNNV

E SxzzxzM 22020 cos

22

constVKconstMNNV

E MESxzM 2220 sinsin

2

2222

zyxS MMMM

2sinVKE MEM 20

2SzxME MNNK

Shape anisotropy: ellipsoidal NPs

Page 33: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Demagnetizing factors

Page 34: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Demagnetizing Factors– references

Formulae, tables y graphs for demagnetizing factors, Chen et al. IEEE Trans. Magnetics

27, 3601-19 (1991)

Demagnetizing Field y Magnetic Measurements, J.A. Brug y W.P. Wolf, J.Appl.Phys. 57,

4685-701 (1985)

Demagnetizing factors calculations,

http://magnet.atp.tuwien.ac.at/dittrich/?http://magnet.atp.tuwien.ac.at/dittrich/content/tool

s/magnetostatics/streufeld.htm

Page 35: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

35

Paramagnetism

J

kTHx /0

Ion angular moment

Cr3+ (J=3/2)

Fe3+

(J=5/2)

Gd3+

(J=7/2)

A/mK/T

Agreement withexperimental

results

BgJ

J

x

Jx

J

J

J

JTMxBTMTHM SJS

2coth

2

1

2

12coth

2

12)(,

Page 36: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

36

0xT

C

kT

N

H

M

3

2

0

-1

-0.4 -0.2 0.0 0.2 0.4

-0.4

-0.2

0.0

0.2

0.4

J=>inf

J=3/2

J=1/2

M/MS

x=g

BJH/kT

Paramagnetism

Page 37: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

37

Superparamagnetism

exp

B NP

xxTMxLTMTHM SS

1coth)(,

For a NP moment distribution

dkT

HLfNTHM

0

0,

dedf2

02

2

/ln

2

1

TNdfNTM S

0

Page 38: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

38

-2000 -1000 0 1000 2000

-60

-40

-20

0

20

40

60

10 20 30 4061

62

63

64

65 Ms(T)=Ms(0) (1-T)

M(A

m2/k

g)

T (K)

M (

Am

2/k

g)

H (kA/m)

10K

40K

90K

140K

190K

240K

290K

Superparamagnetism

Page 39: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

39

“Interacting Superparamagnets”

Dipolar Interactions

F.H. Sánchez

Page 40: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

et al.

2181055.1 Am

Tesla0

Tesla2.0

9/2/ 32

0max kTdV 380/0 kTH

18104.18 HCennmd magnetita

F.H. Sánchez

Page 41: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Fe

F.H. Sánchez

Page 42: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

F.H. Sánchez

Page 43: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Vogel-Fulcher law

Other propositions

F.H. Sánchez

Page 44: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

F.H. Sánchez

Page 45: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

'

''

F.H. Sánchez

Page 46: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

12S

13S16S

nm5.4%50

nm5.5%55

nm5.8%70

kTKV /lnln 0

F.H. Sánchez

Page 47: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

-2 -1 0 1 2 3 4 5

0.0

0.5

1.0

KV+Eint

H = 0

E

kTEBe/

0

DFB proposition

2sinBK EE

BtotB EE intfor

F.H. Sánchez

Page 48: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

2 4 6 nm8F.H. Sánchez

Page 49: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

-2000 -1000 0 1000 2000

-60

-40

-20

0

20

40

60

10 20 30 4061

62

63

64

65 Ms(T)=Ms(0) (1-T)

M(A

m2/k

g)

T (K)

M (

Am

2/k

g)

H (kA/m)

10K

40K

90K

140K

190K

240K

290K

KTforHC 400

TMTM SS 10

F.H. Sánchez

Page 50: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

-1 0 1 2 3 4

0

1E

= 4h(KV+E

int)

E0 = 0

h = H / HK = 0.25

int8/ EKVk

TMTM SS 10

SM

F.H. Sánchez

Page 51: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Ferrogel swelling

dry hydrated

sh VV 3

sh dd 44.1sdhd

F.H. Sánchez

Page 52: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200Ferrogel

Water

Ferrogel

Hydrogel

M

Time (min)

Alcohol+Ibuprofen

F.H. Sánchez

Ferrogel swelling

Page 53: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

0 100 200 3000

10

20

Dry

Hydrated

M (

Am

2/k

g)

T (K)

Tb

d=25K

Tb

h=17K

ZFC-FC, H=8kA/m

kTEKV

hyd

hyd

e/

0int

kTEKV

dry

dry

e/

0int

hyd

B

dry

B

hyddryTTEE

intint

F.H. Sánchez

Page 54: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

0 5000 10000 150000.0

0.5

1.0

1.5

parallel

M(A

m2/k

g)

H(A/m)

perpendicular

H

H

parallel perpendicular

Shape effects

F.H. Sánchez

Page 55: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

z

k

VLM

kT

HVMLM

kT

HLMTHM S

SSS

000),(

T

HMz S

F.H. Sánchez

Page 56: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

ginteractinnon

B 41058.1

ginteractin

B 41058.1

ginteractinnon

B 3104

Analysis of an interacting superparamagnet with theoretical expressions valid for non interacting systems (Langevin)

F.H. Sánchez

Page 57: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

aparent

true

F.H. Sánchez

Analysis of an interacting superparamagnet with theoretical expressions valid for non interacting systems (Langevin)

Page 58: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Dipolar interactions

Hypothesis: dipolar interactions give rise to an aparent higher temperature

3

2

0d

D

d

*TTTa

con *kTD

1

kT

HL

M

THM

S

0),(

*

),( 0

TTk

HL

M

THM

S

N

M

kT S

2

0*

F.H. Sánchez

Dipolar interactions

Page 59: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

*),( 00

TTk

HLN

kT

HLNTHM a

aa

TT

a/*1

1

NTTNNTT

NN aaaa /*1/*1

1

when

0* 0

0

3

0

3

0

3

T

SSD

aM

kT

dM

kTdkTdkT

T

T

*TT

*kTD 3

2

0d

D

F.H. Sánchez

Page 60: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Low field susceptibility

*3

2

0

TTk

N

N

M

kT S

2

0*

3

333*3312

0

2

0

2

0

2

2

0

2

2

0

2

0

S

S

SS M

TkN

N

M

kMN

kN

MN

TkN

N

kT

N

kT

331

2

0

SM

TkN

F.H. Sánchez

Page 61: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Allia et al. show that when a NP moments distribution exists former expression becomes:

3

32

0

SM

TkN

where

2

2

2

2

a

a

F.H. Sánchez

N

M SN

M

kT S

2

0*

*kTD

2

SM

T3

0/3 kN

slope

measurements

At different temperatures

HvsM

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F.H. Sánchez

Page 63: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

0 50 100 150 200 250 3000

2000

4000

6000

8000

10000

FT

GA

a

p(A

m2/k

g)

T (K)

Aparent moment variation with temperature

F.H. Sánchez

Page 64: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

3

32

0

SM

TkN

FG

NPs

mass

mass

3/ mkg

2

2

nmd

nmD

J

FT

p

D

B

26

1.8

1037.1

9500

21

nmd

nmD

J

GA

p

D

B

32

1.9

1038.2

12600

21

F.H. Sánchez

Page 65: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

65

Demagnetizing factor NDef in samples with disperse magnetic NPs

F.H. Sánchez, unpublished

Page 66: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

ii

i

ii

i

ii

i

iM VHMHBE

222

1 00

Case 1: continuous material

Interacción among materials dipoles

mi

Hi iij

dip

ji rHH

i

dVHM

2

0

MNH D

Magnetostatic energy or magnetic self energy

66F.H. Sánchez

Demagnetizing factor NDef in samples with disperse magnetic NPs

Page 67: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

D

i

j

ijd

D

ijij Ded

If NPs are in contact: 1(case of a continuos magnetic material)

Case 2: magnetic NPs disperse in non magnetic media

67

...2,3/22,3/2,1..

...5,2,2,1..

ij

ij

ebccei

esquareei

Is a normalized array describing the geometry of NPs arrangementije

F.H. Sánchez

d

d: distance between neighbors

“dilution “ factor

Page 68: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

iii

i

ii

i

iM HHE

00

2

1

2

68

Identical NPs: .,6/,1;3 etcDV

F.H. Sánchez

4/13

1333333

j ij

ij

j

jijijj

ij

ie

s

Dvuuv

eDH

ii v

jijijjij vuuvs

3

Dipolar field on NP i:

33DH i

i

j ij

ij

ie

s3

defining

Just depends on the geometry of the NPs array, on the relative orientations between moments and relative orientations between them and the segment joining them. may take different orientations.

i

ijs

Page 69: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Sii MH adimensional

,,,, i

69F.H. Sánchez

.,6/,1;3 etcDV using

SSpp VMMV 3 “global” sample magnetization

Volume per particle

Page 70: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

MH S

ii

Assumption for non saturated sample: same proportionality constant between H and M holds.

SDN MNMH DSD

Averaging i on sample

S

S

i

S

i MH

Saturated sample, i corresponds to the saturation (sij) configuraciónS

i

70

Aproximation done: MM S

iSi

F.H. Sánchez

Page 71: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Using magnetization of magnetic phase (NPs)pM

MM p

3

pDefp

S

ii MNMH

3

hence

3D

Def

NN

71F.H. Sánchez

Determined by shapeDetermined by shape and NP dilution

DDef NNif 1.016.3 D

Dd

DDef Nd

DN

3

or

Page 72: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

1. NPs homogeneously distributed. ND is the demagnetizing factor which corresponde to sample shape.

2. NPs are aggregated in clusters, and clusters do not interact among them. ND is the demagnetizing factor which corresponds to cluster average shape.

3. NPs are aggregated in clusters, and clusters interact among them. ND is the demagnetizing factor which corresponds both to sample shape and to cluster average shape.

72F.H. Sánchez

Cases of interest

Page 73: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Case of interest 3

pccp nnn NP nuber

73F.H. Sánchez

3. NPs are aggregated in clusters, and clusters interact among them. ND is the demagnetizing factor which corresponds both to sample shape and to cluster average shape.

CECC Dd

CDCD

Dd IC

D

6cn

7pcn

DIC

CD

D

333 DnD ICpcC

Page 74: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

s

D

pc

S

ECS

IC

sample

D Nn

N

c

D

S

IC

cluster

D NN

Leads to

333

ECIC

cluster

D

sample

D

IC

cluster

DDef

NNNN

74

This is the sought result, it gives the dependency of the effective demagnetizing factor in terms of cluster and sample ones, and the characteristic distances (dilution factors) of the problem.

F.H. Sánchez

Page 75: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Continuous NPs distribution

1;1 ECIC Continuous Material

muestra

75F.H. Sánchez

Particular cases

s

D

ECIC

c

D

s

D

IC

c

DDef N

NNNN

333

Page 76: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Cluster with almost no interior demagnetizing field

76F.H. Sánchez

H

33333

ECIC

s

D

ECIC

c

D

s

D

IC

c

DDef

NNNNN

Page 77: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Clusters of random shape with orientations randomly distributed.

3/1c

DN

If clusters are far away from each other

33

1

IC

DefN

If clusters are in contact

3

IC

s

DDef

NN

77F.H. Sánchez

If sample does not present demagnetizing effect

H

33333

131

3

1

EC

s

D

ICECIC

c

D

s

D

IC

c

DDef

NNNNN

33

11

3

1

ECIC

DefN

Page 78: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

78

3/ ICDDef NN

Leads to

3

EC

c

D

s

Dc

DD

NNNN

F.H. Sánchez

Relationship between DDef NandN

Page 79: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

79

Other considerations

pccp nnn

NPs Magnetization3D

Mp

p

cluster Magnetization3

IC

p

C

MM

333

ECIC

p

EC

CMM

M

CD

D

F.H. Sánchez

Sample Magnetization

Page 80: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

c

D

s

D

EC

c

DD NNNN 3

1

c

D

s

D

c

DD

S

pS

IC

c

DD

c

D

s

D

EC

NN

NN

M

M

NN

NN

3

3

Lead to

33

1

ECICppS

S

M

M

M

M

80F.H. Sánchez

SMpSMy are measured. The dilution factors product can be estimated:

Page 81: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

81

For an isotropic clusters orientation distribution

3

11

3

13

s

D

EC

D NN

3/1

3/1

3/1

3/1

3

3

s

D

D

S

pS

IC

D

s

DEC

N

N

M

M

N

N

Leads to

F.H. Sánchez

3/1c

DN

Page 82: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Analysis with Langevin model. Comparison with Allia’s proposition

dipap HHH

kT

HHLM

kT

HLMM

dipap

pSpSp

00

pDef

dip MNH

82

Assumptions dip

p HHM

kT

MNHL

VkT

MNHLMTHM

pDef

ap

p

pDef

ap

pSp

00,

F.H. Sánchez

Page 83: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

83

p

pDef

ap

pkTV

MNHM

3

2

0

When Langevin function argument is << 1

Def

p

ap

p

NkTV

HM

2

0

3

F.H. Sánchez

Measured susceptibility of magnetic phase.

Def

ppSp

NVM

kT

2

0

31

Def

pS

p

p

NM

kTN

2

0

31

pp VN /1

Page 84: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

84

Def

pS

p

p

NM

TkN

2

0

31

p

pS

p

p M

TkN

3

312

0

According to Allia

It’s concluded that pDefN 3

F.H. Sánchez

Page 85: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

85

For a sample with a distribution of NP moment sizes, Allia shows

p

pS

p

p M

TkN

3

32

0

2

2

2

2

a

a

and are NP moments. The former are “aparent” values which are obteined when analizing without considering dipolar interactions. The latter are values “corrected” from

a THM ,

ppDef

pS

p

p

VNNM

TkN/1,

32

0

F.H. Sánchez

In the present case

p

pS

N

M

Page 86: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

86

D

pS

D

pS

NVM

kTN

VM

kT32

0

3326

0

3

33

As a function of sample “global” magnetization for a homogeneous sample, SM

ppppp VVN 3/1/1 D

S

ppN

M

TkN

2

0

3

F.H. Sánchez

Measured sample susceptibility

3/1)3 AlliaND

Page 87: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

87

Measuring M vs. H at several temperatures, and plotting / vs. T/MS2 ND and Npp can

be retrieved

2/ pSMT

ppN

DN

From straight line slope

Data from M vs H

pp

S

N

M

pp

D

N

MN

2

2

0

Max dipolar energy per NPpp

SD

N

MN

2

2

0

Page 88: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

88

If there are clusters, SM

F.H. Sánchez

3266

0

33

3

IC

D

SpECICECIC

N

M

T

V

k

Def

pSp

NM

T

V

k

2

0

3

pp

ppm

p

m

pcc

pICEC

pICpcECcm NVV

n

V

nn

VVnnV

1133

33

using

3233

0

33

3

IC

D

SECIC

pp

ECIC

N

M

TkN

DEC

S

ppN

M

TkN3

2

0

3

Page 89: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

89

DEC

S

ppN

M

TkN3

2

0

3

/

2/ SMT

ppN

DEC N3

F.H. Sánchez

Page 90: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

H

H

parallel perpendicular

Shape effects

F.H. Sánchez

0 5000 10000 150000.0

0.5

1.0

1.5

parallel

M(A

m2/k

g)

H(A/m)

perpendicular

//

Ferrogel PVA/maghemite 15.7% mass concentration

Page 91: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

91

Assuming a uniform distribution of NPs

//

//3

DefDef

DD

NN

NN

1.2

kgm /1013.1 33

//

kgm /1008.1 33

//

3

//

11

4

10

DefDef NN

0.80 =

0.06 = //

N

N

De la forma de la muestra

F.H. Sánchez

D

Dd

Page 92: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Estimation of from FG density and mass concentration of Fe oxide x, assuming a uniform

distribution of NPs

FG

oFe

m

mx

FG

FGFG

V

m

3

33

666

xxd

DD

xV

N

xV

mN

xV

m

FG

NP

FG

NPNP

FG

oFeFG

3/1

6

FGx

F.H. Sánchez

Page 93: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

3/1

6

FGx

5.2

/1.1

157.0

/18.5

3

3

cmg

x

cmg

using

FG

For FG 10_1

F.H. Sánchez

D

Dd

Page 94: Magnetic Nanomaterials. Some Biomedical Applications ...ebm/ix/arquivos/MC4-1.pdf · Magnetic Nanomaterials. Some Biomedical Applications: Magnetofection, Magnetic Hyperthermia, ...

Diet and magnetic materials …

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97

Dipolar Energy

ppSDef VMN 20

2

Energy per particle for a homogeneous saturated sample

non saturated sample

ppDef VMN 20

2

In terms of sample global magnetization

ppDpDpD VMNVMNVM

N 2032026

3

0

222

N

MND

2

2

0

Using ppVN /1

F.H. Sánchez