Seminário termodifusão em colódes magnéticos

8/13/2019 Seminrio termodifuso em coldes magnticos

1/31

Determination of the Soretcoefficient value as a function ofthe particle size in Ionic

Ferrofluids

Master student: Andr Luiz Sehnem

Professor: Antnio Martins Figueiredo eto


2/31

Ferrofluids Magnetic nanoparticles disperded in a li!uid carrier"

#$pical size in %& nm range" Flo' properties are similar 'ith the li!uid (for moderate

concentrations) *+ternal control of the fluid movement: magnetic field, light

irradiation"

P FF surface covering determines its sta-ilit$ conditions. theelectrostatic interaction in the case of ionic FF or the stericinteraction for surfacted FF"


3/31

Representation of the IFF

De-$e length

Surface charges

/ounterions fromsolution

Ionic (eletrostatic nature) interactions areresponsi-le for colloidal e!uili-rium


4/31

Thermodiffusion

#hermodiffusion is the movement of particles induced -$ atemperature gradient" #'o directions of movement are possi-le,depending on the surface and solvent properties"

#he drift of particles in the temperature gradient is a su-0ect ofmuch interest in the condensed matter ph$sics of comple+s$stems"


5/31

Thermodiffusion of IFF

#emperature gradientinduces the directional

diffusion of the FFnanoparticles"

#he FF grains move in thesame direction (positivel$

charged) or against(negativel$ charged) the

temperature gradient"

#hermodiffusion is characterized -$ the Soret coefficient S T.

It ta1es positive values 'hen particles move against thetemperature gradient and negative values other'ise"


6/31

#he diffusion of particles induced -$ the temperature gradientmust -e accounted regarding the continuit$ e!uation:

c t J M =

0

'here appears the flu+ of particles due to thermal andconcentration gradients

DM

is the ordinar$ diffusion coefficient.

D# is thermal diffusion coefficient"

J M = D M c DT T

J M = D M ( c+ S T T ) S T = D

T D M

D M = k b T

6 R


7/31

Temperature gradient induced by a Gaussian beam

w2= w02 (1+() 2)

z 0 =

w 02

=( z

z 0

)


8/31

Light a-sorption -$ the sample material generates a

inhomogeneous temperature distri-ution" It gives rise to thetemperature gradient in the sample"

Solving the heat e!uation 'ith the 2aussian -eam as the heatsource:

T (r , t ) t D T (r , t )=

qc p

Temperature gradient induced by a Gaussian beam

D is the thermal diffusivit$. is the FF densit$. c

p the specific heat.

q is the heat generated"

#he temperature profile of the sample is found:

T (r , t )= P 4 (

ln (1+ 2tt th

) 2 r 2

w2( 2t

2t + t th)) t th=

w2

4D


9/31

T implies a n :

#he thermal lens is characterized:

z 0 f (t )= b z 0

nT

d 2

dr 2(T (r , t ))= P b z 0

w02 nT

11+ 2

2t2t + t c

= C T 1+ 2

2t2t + t c

C T = P b z 0

w 02

nT =

P b

nT

is the phase amplitude of thethermal lens

n (r , t )= n0+ T (r , t ) dndT


10/31

If T(r,t) is 1no'n, the mass diffusion e!uation ma$ -e anal$zedon stationar$ T(r) condition" An e+pression for c(r,t) is found in

terms of the parameters:

. c (r , t ) t = D M (

2c (r , t )+ S T

2T (r , t )) 2 T (r , t )= q

c (r , t ) t = D M

2c (r , t )

S T D M q

c (r , t )= P S T

4 (ln (1 +

2t

t D) 2 r

2

w2 (

2t

2t + t D)) t D=

w2

4 D M


11/31

#he matter lens o'ing to Soret effect is characterized:

z 0 f S (t )= b z 0

nc

d 2

dr 2 (c(r , t ))= P b z 0 S T

w02

n c

1

1+ 22t

2t + t D = C S 1+ 2

2t2t + t D

n= n0+ dndc

C S = P b z 0 S T

w02

n c =

P b S T

n c

is the phase amplitudeof the matter lens


12/31

A generalized thermal lens model 'as developed to ta1e intoaccount the change in focal length due to all effects"

n (r , t )= n I I (r , t )+nT T (r , t )+

nc c (r , t )

'here the lens -ehavior of the nonlinear effect is alsoconsidered:

Ref: Alves, S.; Bourdon, A.; Neto, A. M. F.; JOSA B, 20, 713 2003!

z 0

f N = b z 0 n

I [ d

2

dr 2 I ]=

8bz 0 P 0

w4

n

I =

C N

(1 +2

)2

C N =8bz 0 P 0

w04

n I


13/31

#he change in the transmitted po'er is measured in thecenter of the -eam at a distant position of the -eam 'aist:

P 0 (t ) P ( z , t )=(

w02 Z

2

w d 2 z 0

2 )(1 2 z 0 f

+( 1 + 2 )( z 0 f

)2

) I =2P

w 2

And the normalized transmittance is defined as the ratio of intensities:

T N = I ( z , t ) I ' ( z , t )=

1

1 2 z 0 f

+(1+ 2)( z 0 f

)2

1

f =

1

f N +

1

f T +

1

f S

T N = 1

1 2 ( C S

(1 + 2)( 2t

2t + t D)+

C T (1 + 2)

( 2t2t + t DT

)+ C N

(1 + 2)2)+( 1 + 2)(

C S (1+ 2)

( 2t2t + t D

)+ C T

(1+ 2)( 2t

2t + t DT )+

C N (1+ 2)2

)2


14/31

As the characteristic time of the three phenomena are different, 'ecan use the last e!uation to estimate the phases amplitudes:

#he nonlinear effect has tc of 3 fs;

#hermal effects has tc of 3 % ms .

Mass diffusion of FF Ps occurs 'ith tc3 % s.

Irradiating the samples 'ith pulses of dozens milliseconds andseconds duration, remains onl$ one varia-le in the e!uation: the

position "" So, moving the sample through the path of a focused2aussian -eam allo's to o-serve the three lens effect"


15/31

Z scan technique*+perimental apparatus:

%"tpulse

4 5& 6 7& ms,

2. tpulse

= 1 seg.

spacers

Samples:

Filling

2lassslides


16/31

Lens beha ior in !"scan technique

Divergent lens: 8 &

#hermal lens.

Anionic FFs #D.

egative nonlinear"

dndr

/onvergent lens: 9 &

/ationic FFs #D.

Positive nonlinear"

dndr


17/31

#imulations

:5& & 5&

&,;

%,&&

%,&5

%,&7&7

Duhr S and Craun D. 5&&= Ph$s" Gev" Lett"#$ %=>7&%

igolo D, Cram-illa 2 and Piazza G. 5&&H Ph$s"Gev" * 7% &


28/31

A change in particles surface gives another -ehavior:

*omparision +ith literature

Duhr S and Craun D. Proc" at" Acad" Sci",

5&&=,103 %;=H>

In this 'or1, the Soret coefficientscales 'ith the surface area: S

# 3d 5


29/31

#emperature variation lead to reserval of movement:

*omparision +ith literature

Crai-anti M, igolo D and Piazza G. 5&&>Ph$s" Gev" Lett" 100 %&>7&7


30/31

*onclusion and ne%t steps,

#he -iggest particle (%< nm) has the -igger (smaller in modulus) Soretcoefficient, 'hile the others are close to the same value"

#he z scan techni!ue allo's to separate the signals from each induced lensin the sample, and a good evaluation of S

#"

ariation in concentration might indicate the collective -ehavior"

More samples 'ill come to fill the gaps in the S# (D

part)"

Does Soret coefficient depends on the particle size

#his 'or1 ma$ contri-ute to a -etter understanding of the thermodiffusionphenomena"


31/31

#han1s

#han1 $ou for attention

Seminário termodifusão em colódes magnéticos

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