magnetic nanomaterials. some biomedical applications ...ebm/ix/arquivos/mc4-1.pdf · magnetic...

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

http://www.fisica.unlp.edu.ar/Members/sanchez/escola-de-magnetismo-vitoria-es-brasil-03-11-13-al-08-11-13

























Why magnetic nanomaterials for biomedicine?

?

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

http://www.fisica.unlp.edu.ar/Members/sanchez/curso-de-posgrado-nanomateriales-magneticos-intema/bibliografia











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"

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

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

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

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

magnetite

magnetsmall domainsingle

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

8

A brief introduction to nanomaterials magnetic state:

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

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

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

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

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

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

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

-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

cossz MM

H

HK-HK

0Easy axis

S

KM

KH

0

2

KT 0

Field in the easy direction

H

-HK

HK

Hard axis

S

KM

KH

0

2

KT 0

1; hHH

MM

K

Sz

Field in the hard direction

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


KC HH 479.0

SR MM 5.0


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

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


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



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

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



Two levels model

KVE

Simplification: 2 levels

Field in easy direction

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

Two levels model

34 J/m101.89 = K

D18 nm

f=2.6e4 Hz

Behavior at Radiofrecuency

Two levels model

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

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

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

Demagnetizing factors

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

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)(,

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

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

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

39

“Interacting Superparamagnets”

Dipolar Interactions

F.H. Sánchez

et al.

2181055.1 Am

Tesla0

Tesla2.0

9/2/ 32

0max kTdV 380/0 kTH

18104.18 HCennmd magnetita

F.H. Sánchez

Fe

F.H. Sánchez

F.H. Sánchez

Vogel-Fulcher law

Other propositions

F.H. Sánchez

F.H. Sánchez

'

''

F.H. Sánchez

12S

13S16S

nm5.4%50

nm5.5%55

nm5.8%70

kTKV /lnln 0

F.H. Sánchez

-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

2 4 6 nm8F.H. Sánchez

-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

-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

Ferrogel swelling

dry hydrated

sh VV 3

sh dd 44.1sdhd

F.H. Sánchez

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

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

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

z

k

VLM

kT

HVMLM

kT

HLMTHM S

SSS

000),(

T

HMz S

F.H. Sánchez

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

aparent

true

F.H. Sánchez

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

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

*),( 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

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

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

F.H. Sánchez

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

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

65


F.H. Sánchez, unpublished

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


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

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

Sii MH adimensional

,,,, i

69F.H. Sánchez

.,6/,1;3 etcDV using

SSpp VMMV 3 “global” sample magnetization

Volume per particle

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

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

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

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

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

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

Cluster with almost no interior demagnetizing field

76F.H. Sánchez

H

33333

ECIC

s

D

ECIC

c

D

s

D

IC

c

DDef

NNNNN

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

78

3/ ICDDef NN

Leads to

3

EC

c

D

s

Dc

DD

NNNN

F.H. Sánchez

Relationship between DDef NandN

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

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:

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

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

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

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

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

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

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

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

89

DEC

S

ppN

M

TkN3

2

0

3

/

2/ SMT

ppN

DEC N3

F.H. Sánchez

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

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

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

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

Diet and magnetic materials …

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

magnetic nanomaterials. some biomedical applications ...ebm/ix/arquivos/mc4-1.pdf · magnetic...

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