Transport processes in nano-structured materials Transport processes in nano-structured materials by non-linear time-resolved spectroscopy by non-linear time-resolved spectroscopy

R. Torre

LENS e Dip. di Fisica , Università di Firenze INFM CRS Soft, c/o Universita’ La Sapienza

Dip. di Fisica, Univ. di Firenze

Transport Processes

These transport phenomena are relevant both for

fundamental physics and for technological applications.

Among them, the design of innovative materials for sound

and heat control.

• Acoustic waves propagation in nano-structured matter

• Flow of liquids in micro/nano pores

• Heat diffusion in heterogeneous media

Nano-structured materials

Nano-porous glasses filled with liquids

Colloidal suspensions

Gel-forming Mixtures

Random Structures

Ordered Structures

2D Fononic Crystals

Nano-porous glasses

Porous silica produced by sol-gel techniques.

These materials can be “easily” filled by liquids.

The physic models for these phenomena are still an open question .

The sound propagation in this materials shows extraordinary phenomena, as the

existence of a second slow longitudinal acoustic wave.

The flow processes are strongly modified by the porous dimension and surfaces.

Spectroscopic Techniques and Facilities

at the European Lab. for Non-Linear Spectroscopy (LENS)

Transient Grating Spectroscopy

Ultrafast Optical Kerr Effect Spectroscopy

Continuous Tech.

Time-Resolved Tech.

Light Scattering, Raman-Brilluoin Spectroscopy

Microscope for single-particle fluorescence

Time-Domain Tera Hertz Spectroscopy

Transient Grating Spectroscopy

DOE:Phase Grating LA2

APD

DigitalOscilloscope

Sample

CW Probe

Pulsed Excitation

InterferenzialFilter

LA1

El

Eso

Phase Control Neutral Filter

Chopper

SD

Eec

Eec

Eso

=532 nm

=1064 nm, t=20 ps

El+ES

LC

Nd-Yag mode-locked Laser

CW single-mode Laser

100 101 102 103 104

Data Fit

HD

-TG

sig

nal

(arb

.un.)

Time (ns)

T = 20 °C, q = 1.00 m-1

Damped acoustic oscillations, Cs and s

Thermal diffusion, tViscous flow, v

tvS tttS

TGHD CeBeetqCAS // sin

Transient Grating Exp. on Vycor glass with WaterR. Cucini, A.Taschin, P.Bartolini e R.Torre

Vycor 7930 (Corning), porous diameter 4 nmFilled with bi-distilled water

Eur. Phys. J. ST, 141, 133–136 (2007) ; Philos. Mag., 87, 715-722 (2007)Phys. Rev. Lett., submitted

100 101 102 103 104

T = 90 °C T = 80 °C T = 70 °C T = 60 °C T = 50 °C T = 40 °C T = 30 °C T = 20 °C T = 10 °C T = 4 °C T = 0 °C T = -5 °C T = -10 °C

HD

-TG

sig

nal

(ar

b.u

n.)

Time (ns)

-10 0 10 20 30 40 50 60 70 80 90

3.96

3.98

4.00

4.02

4.04

4.06

4.08

4.10

4.12

4.14

Cs

(Km

/sec

)

Temperature (°C)

Biot prediction

data q=1.00 m-1

-10 0 10 20 30 40 50 60 70 80 90

30

40

50

60

2000

4000

6000

8000

10000

Aco

usti

c re

laxa

tion

tim

e (n

s)

Temperature (°C)

data q = 1 m-1

Biot prediction

Transport Processes vs Biot model M. A. Biot, J. Acoust. Soc. Am., 28, 168 (1956).M. A. Biot, J. Acoust. Soc. Am., 28, 179 (1956).

• Very Good agreement on Cs A relatively simple theory based on continuum model

predicts correctly the high frequency (1.3 GHz) sound velocities in nano-structured materials.

• Very Poor predictions on s The model fails completely the sound damping.

Acoustic Propagation Temperature Dependence

Viscous Flow of the water inside the nano-porous

Thermal Diffusion in the nano-structured material

Temperature Dependence

-10 0 10 20 30 40 50 60 70 80 90

0

1

2

3

4

5

6

v & t (

s)

Temperature (°C)

fit

v

t

Biot model

Transport Processes vs Biot model

• Very Good agreement on v The water flow can be correctly described as the

diffusive wave predicted by Biot Model.

• No predictions on t ?

Wave-Vector Dependence

0.5 1.0 1.5 2.0 2.5

3.6

3.8

4.0

4.2

4.4

CS (

km/s

)

q (m-1)

T = 40 °C T = -10 °C

Sound Velocities

Transport Processes vs Biot model

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.00

0.03

0.06

0.09

0.12

0.15

0.18

S (

ns-1

)

q1.2

T = -10 °C T = 40 °C

Damping of Sound

0 1 2 3 4 5 6 7

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

T = 40 °C T= -10 °C

v (s

-1)

q2 (m-2)

Diffusion Rate of the Liquid

• Cs does not depend on q Very weak acoustic dispersion effect

s=1/s qx , with x ≈ 1.2 Anomalous sound damping

v=1/v q2 Simple diffusion process

2D Fononic Crystals

preliminary test

Ordered micro-Structures in Polymeric Films by Holographic Patterning.

100 m

2 m

1 m

Image from Optical Microscope

I. Malfanti, A.Taschin, P.Bartolini and R.Torre,

F.Simoni and F.Vita, Univ. Polit. Marche.

Epi-fluorescence image from a dye filled sample

Intensity profile in a selected direction

40 50 60 70 80 90 100

-0.5

0

0.5

1

1.5 Transient Grating preliminary results

Longitudinal Acoustic Phonon propagating in the 2D Lattice

Time nsec

Final Remarks

Non-linear time-resolved spectroscopy enables accurate and

precise investigations of the transport phenomena, covering a

particularly wide dynamic range.

Physics of transport phenomena in micro/nano-structured media

is a fundamental topic of material science.

Transient grating studies of filled nano-porous glasses show that

the Biot elastic model is able to predict correctly several transport

processes in a nano-structured medium. Nevertheless, some clear

limitations of the model are present.

Structured Glasses and Fluids

Group@LENS

• Permanent staff

R. Eramo

P. Bartolini

R. Torre

• Postdocs

A. Taschin

M. Plazanet

• PhD students

R. Cucini

I. Malfanti

LENS is an European FacilityEuropean Researchers can use the labs submitting a proposal.

www.lens.unifi.it

R

>> R,

Onde acustiche vs mezzi eterogenei

Le onde propagano in un mezzo efficace

R

Le onde vengono diffuse

Effetti di multiple scatteringTeorie mezzo-effettivo

risonante

Teorie di omogenizzazioneMezzo-effettivo non risonanteModello di Biot

~ R,

Mezzi eterogenei solido-liquido

Topologia• Sfere di vetro/silice in liquidi• Colloidi

• Sfere consolidate con liquidi• Vetri porosi Percolativa

Mezzo effettivo

Modello di Biot

Non-Percolativa

Sistemi non percolativi, mezzo-efficace

1 sola onda longitudinale che propaga con velocità efficace

Onde acustiche in sistemi solido-liquido

),,,(1 2

1

ls

ls

fKK

c

, porosità, , tortuosità

Ks, Kl , moduli elastici

s, l, densità

Sistemi percolativi, modello Biot

2 onde longitudinali che propagano con velocità diverse

),,,,,,(

),,,,,,(

22

11

fslsm

fslsm

KKKfc

KKKfc

Km , modulo elastico del solido percolante senza liquido

Teoria di Biot sulla propagazione acustica nei mezzi porosi (1956) (1)

c

2

2

aρl

lc

(1) M.A.Biot, J.Acoust. Soc. Am., 28, 168, (1956)

La teoria di Biot prevede l’esistenza di due onde acustiche longitudinali di prima e

seconda specie, corrispondenti al moto del liquido e della matrice rispettivamente in fase ed in controfase.

Vycor+CCl4

L’onda di seconda specie non si propaga

Frequenza caratteristica c: funzione della viscosità l, della densità del liquido l e del diametro medio dei pori a.

c Propagazione dell’onda di seconda specie

c 75 GHz

Mp200nm+CCl4 c 30 MHz 3 GHz

l

l2

a

aδc Rc

Il fluido è viscosamente agganciato alla matrice solida e si muove in fase con esso: propagazione di una sola onda acustica.

Solamente uno strato di liquido è viscosamente agganciato alla matrice. Il resto del liquido si disaccoppia: propagazione di una seconda onda con velocità prossima a quella del liquido di bulk.

Matrice

Porzione di liquido agganciata

Parte del liquido disaccoppiata

100 101 102 103 104-1.0

-0.5

0.0

0.5

1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

1.5

100 101 102

-0.1

0.0

0.1

PM-CCl4, q = 0.997 m-1, T = 293 K

HD

-TG

sig

nal [

Arb

.Un.

]

Vycor-CCl4, q = 0.997 m-1, T = 293 K

PM-CCl4, q = 0.997 m-1, T = 293 K

HD

-TG

sig

nal [

Arb

.Un.

]

data fit

Time [s]

residues

Time [ns]

Vycor + CCl4

PM200 + CCl4

3.68

3.70

3.72

3.74

3.76

240 260 280 300 320 340

0.8

1.2

1.6

2.0

2.4

3.98

4.00

4.02

4.04

q = 2.09 m-1 Biot, f >> fc

q = 1.39 m-1

q = 1.00 m-1

CS [

Km

/s]

PM

Temperature [K]

effective medium Vyvor-CCl4

effective medium PM-CCl4

CCl4, q = 1 m-1

Biot, f << fc

Vycor

20

40

60

80

100

120

140

60

80

100

120

30006000

240 260 280 300 320 34040

50

60

70

80

90

q = 2.09 m-1

q = 1.39 m-1

q = 1.00 m-1

Biot theory predictions

Sq1.5

S [ns

] Sq2

Temperature [K]

Vycor + CCl4

369

12151821

260 270 280 290 300 310 320 330 340

11

12

13

14

15

16

48

1216

40

60

80

q = 2.09 m-1, q = 1.39 m-1, q = 1.00 m-1

Sq1.

5 S

[ns

]

Temperature [K]

Sq0.

5

Biot theory predictions

PM200 + CCl4

Modello Biot vs mezzo-efficace

s

mm NK

)1(34

Veloc. long. solido percolante

l

lK

Velocità long.

liquido percolante

Onda veloce

Onda lenta

c

mm NK3

4

Parametro di rigidità della matrice solida0

Non

per

cola

tivo

per

cola

tivo

Sfere di silicein acqua

Sfere di silice consolidate in acqua

Fluidi elettroreologici

+

-

+

-

Sospensioni colloidali di particelle polarizzabili in solventi non-polarizzabili

Sfere di silice, con o senza coatings, in liquidi molecolari

Fluidi elettroreologici rappresentano mezzi eterogenei con caratteristiche strutturali e dinamiche controllabili

Aumento della shear viscosity

Ordine colonnare indotto

Sistema non-percolativo

percolativo

c

Parametro di rigidità del sistema

Non percolativo

Percolativo

Campo elettrico

Come varia la propagazione acustica in funzione del campo elettrico ?

mutiple scattering e localizzazione ?

effetti di bandgap fononiche ?

• Anistropia di percolazione• Fase solida con ordine cristallino delle nanosfere

Onda veloce ?

Onda lenta ?

R << RR

Misure di equilibrio in funzione della geometria e di E

Prop. planareom

eotropica

Misure di non-equilibrio in funzione del tempo

( misure strutturali e dinamiche dopo rapida accensione di E)

E

tempo