Transport processes in nano-structured materials
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
• Acoustic waves propagation in nano-structured matter
• Flow of liquids in micro/nano pores
• Heat diffusion in heterogeneous media
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.
Nano-structured materials
Random Structures
Nano-porous glasses filled with liquids
Colloidal suspensions
Gel-forming Mixtures
Ordered Structures
2D Fononic Crystals
Nano-porous glasses
Porous silica produced by sol-gel techniques.
These materials can be “easily” filled by liquids.
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.
The physic models for these phenomena are still an open question .
Spectroscopic Techniques and Facilities
at the European Lab. for Non-Linear Spectroscopy (LENS)
Continuous Tech.
Light Scattering, Raman-Brilluoin Spectroscopy
Microscope for single-particle fluorescence
Time-Resolved Tech.
Transient Grating Spectroscopy
Ultrafast Optical Kerr Effect Spectroscopy
Time-Domain Tera Hertz Spectroscopy
Transient Grating Spectroscopy
=532 nm
CW Probe
Chopper
=1064 nm, t=20 ps
SD
CW single-mode Laser
Nd-Yag mode-locked Laser
Pulsed Excitation
LC
Phase Control
Neutral Filter
Interferenzial
Filter
Eec
El
Eso
El+ES
Eso
DOE:
Phase Grating
Eec
LA1
Sample
LA2
Digital
Oscilloscope
APD
Transient Grating Exp. on Vycor glass with Water
R. Cucini, A.Taschin, P.Bartolini e R.Torre
Vycor 7930 (Corning), porous diameter 4 nm
Filled with bi-distilled water
-1
HD-TG
signal
(arb.un.)
HD-TG
signal
(arb.un.)
T = 20 °C, q = 1.00 m
S HDTG 
10
0
10
T = 90 °C
Data
T = 80 °C
Fit
T = 70 °C
T = 60 °C
Viscous flow, v
Thermal diffusion, t
T = 50 °C
T = 40 °C
T = 30 °C
T = 20 °C
T = 10 °C
Damped acoustic oscillations, Cs and s
T = 4 °C
T = 0 °C
 t /-5
 t °C
T=
A sin CS q t e t  S  Be t / v  Ce
T = -10 °C


2
1
10
10
3
Time (ns)
0
10
1
10
2
10
3
10
4
10
Eur. Phys. J. ST, 141, 133–136 (2007) ; Philos. Mag., 87, 715-722 (2007)
Time (ns)
Phys. Rev. Lett., submitted
4
10
M. A. Biot, J. Acoust. Soc. Am., 28, 168 (1956).
M. A. Biot, J. Acoust. Soc. Am., 28, 179 (1956).
Transport Processes vs Biot model
4.14
Acoustic Propagation
Biot prediction
-1
data q=1.00 m
4.12
Temperature Dependence
Cs (Km/sec)
4.10
4.08
4.06
10000
-1
data q = 1 m
Biot prediction
4.04
8000
4.00
3.98
3.96
-10
0
10
20
30
40
Acoustic relaxation time (ns)
4.02
50
Temperature (°C)
• Very Good agreement on Cs
• Very Poor predictions on s

6000
4000
2000
6060
70
80
90
50
40
A relatively simple theory based on continuum model
30
predicts
correctly the high frequency (1.3 GHz) sound
velocities
in
nano-structured
materials.
-10
0
10
20
30
40
50
60
70
80
90
Temperature (°C)

The model fails completely the sound damping.
Transport Processes vs Biot model
Viscous Flow of the water inside the nano-porous
Thermal Diffusion in the nano-structured material
Temperature Dependence
6
fitBiot model
v
5
t
v & t (s)
4
3
2
1
0
-10
0
10
20
30
40
50
60
70
80
90
Temperature (°C)
• Very Good agreement on v

The water flow can be correctly described as the
diffusive wave predicted by Biot Model.
• No predictions on t

?
Transport Processes vs Biot model
Wave-Vector Dependence
Sound Velocities
4.4
0.18
T = -10 °C
T = 40 °C
4.2
Damping of Sound
0.12
4.0
3.5
-1
S (ns )
CS (km/s)
0.15
3.8
0.09
T = 40 °C
T= -10 °C
3.0
Diffusion Rate of the Liquid
T =2.5
40 °C
T = -10 °C
0.06
3.6
2.0
-1
v (s )
0.03
0.5
1.0
1.5
2.0
0.00
-1
q (m )
0.0
1.5
0.5 1.0
2.5
1.0
1.5
q
0.5
2.0
2.5
3.0
1.2
0.0
0
1
2
3
4
• Cs does not depend on q

• s=1/s  qx , with x ≈ 1.2

Anomalous sound damping
• v=1/v  q2

Simple diffusion process
5
6
Very weak acoustic
q (m )dispersion effect
2
-2
7
2D Fononic Crystals
I. Malfanti, A.Taschin, P.Bartolini and R.Torre,
F.Simoni and F.Vita, Univ. Polit. Marche.
preliminary test
Ordered micro-Structures in Polymeric Films by Holographic Patterning.
Image from Optical Microscope
Transient Grating
preliminary results
1.5
1 m
Epi-fluorescence image
from a dye filled100
sample
m
1
Intensity profile in a
selected direction
2 m
0.5
0
Longitudinal Acoustic Phonon
propagating in the 2D Lattice
-0.5
40
50
60
70
Time nsec
80
90
100
Final Remarks
Physics of transport phenomena in micro/nano-structured media
is a fundamental topic of material science.
Non-linear time-resolved spectroscopy enables accurate and
precise investigations of the transport phenomena, covering a
particularly wide dynamic range.
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
• Postdocs
P. Bartolini
A. Taschin
R. Torre
M. Plazanet
LENS is an European Facility
European Researchers can use the labs
submitting a proposal.
www.lens.unifi.it
• PhD students
R. Cucini
I. Malfanti
Onde acustiche vs mezzi eterogenei
 ~ R,
Le onde vengono diffuse
R
 >> R,
Effetti di multiple scattering
Teorie mezzo-effettivo
risonante
Le onde propagano in un mezzo efficace
R
Teorie di omogenizzazione
Mezzo-effettivo non risonante
Modello di Biot
Mezzi eterogenei solido-liquido
Topologia
Non-Percolativa
• Sfere di vetro/silice in liquidi
• Colloidi
Mezzo effettivo
Percolativa
• Sfere consolidate con liquidi
• Vetri porosi
Modello di Biot
Onde acustiche in sistemi solido-liquido
Sistemi non percolativi, mezzo-efficace
1 sola onda longitudinale che propaga con velocità efficace
1  
c  
 
Kl 
 Ks

1
2
f (  s , l ,  ,  )
 , porosità, , tortuosità
Ks, Kl , moduli elastici
s, l, densità
Sistemi percolativi, modello Biot
2 onde longitudinali che propagano con velocità diverse
c1  f1 ( K m , K s , K l ,  s ,  f ,  ,  )
c2  f 2 ( K m , K s , K l ,  s ,  f ,  ,  )
Km , modulo elastico del solido percolante senza liquido
Teoria di Biot sulla propagazione acustica nei mezzi porosi (1956) (1)
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.
2 l
c 
ρl a 2
Frequenza caratteristica c: funzione
della viscosità l, della densità del liquido
l e del diametro medio dei pori a.
  c
L’onda di seconda specie non si propaga
  c
Propagazione dell’onda di seconda specie
Vycor+CCl4
c  75 GHz
Mp200nm+CCl4
c  30 MHz
(1) M.A.Biot,
  3 GHz
J.Acoust. Soc. Am., 28, 168, (1956)
Matrice
Porzione di liquido
agganciata
a
  c  δ  a
Parte del liquido
disaccoppiata
d
Il fluido è viscosamente
agganciato alla matrice solida
e si muove in fase con esso:
propagazione di una sola onda
acustica.
2l
l
d
  c  d  R
Solamente uno strato d 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.
1.0
Vycor + CCl4
-1
Vycor-CCl4, q = 0.997 m , T = 293 K
0.0
-0.5
1.0
-1
PM-CCl4, q = 0.997 m , T = 293 K
0.5
0.0
-0.5
-1.0
10
0
10
1
10
2
10
3
10
Time [s]
1.5
HD-TG signal [Arb.Un.]
PM200 + CCl4
HD-TG signal [Arb.Un.]
0.5
-1
PM-CCl4, q = 0.997 m , T = 293 K
1.0
0.5
0.0
-0.5
-1.0
data
fit
0.1
0.0
-0.1
residues
10
0
1
10
Time [ns]
10
2
4
4.04
Biot, f << fc
4.02
4.00
Vycor
3.98
-1
3.76
q = 2.09 m
3.74
q = 1.39 m
-1
q = 1.00 m
Biot, f >> fc
CS [Km/s]
-1
3.72
3.70
PM
3.68
2.4
effective medium Vyvor-CCl4
effective medium PM-CCl4
2.0
-1
CCl4, q = 1 m
1.6
1.2
0.8
240
260
280
300
Temperature [K]
320
340
140
Vycor + CCl4
-1
q = 2.09 m
-1
q = 1.39 m
-1
q = 1.00 m
S [ns]
120
100
80
60
40
20
6000
3000
Sq
1.5
Sq
2
Biot theory predictions
120
100
80
60
90
80
70
60
50
40
240
260
280
300
Temperature [K]
320
340
S [ns]
PM200 + CCl4
21
18
15
12
9
6
3
-1
q = 2.09 m ,
-1
-1
q = 1.39 m ,
q = 1.00 m
80
Sq
0.5
60
Biot theory predictions
40
16
12
8
4
16
Sq
1.5
15
14
13
12
11
260
270
280
290
300
310
Temperature [K]
320
330
340
4
Nm
3
(1   )  s
Km 
Onda veloce
percolativo
c
Non percolativo
Modello Biot vs mezzo-efficace
Sfere di silice
consolidate in acqua
Veloc. long.
solido percolante
Kl
Velocità long.
liquido percolante
l
Sfere di silice
in acqua
Onda lenta
0
Parametro di rigidità della matrice solida
Km 
4
Nm
3
Fluidi elettroreologici
Sospensioni colloidali di particelle polarizzabili
in solventi non-polarizzabili
Sfere di silice, con o senza coatings,
in liquidi molecolari
+
+
-
-
Ordine colonnare indotto
Sistema non-percolativo
percolativo
Aumento della shear viscosity
Fluidi elettroreologici rappresentano mezzi eterogenei con
caratteristiche strutturali e dinamiche controllabili
Come varia la propagazione acustica in funzione del campo elettrico ?
c
Non
percolativo
Percolativo
• Anistropia di percolazione
• Fase solida con ordine cristallino delle nanosfere
Onda veloce ?
mutiple scattering e localizzazione ?
Onda lenta ?
effetti di bandgap fononiche ?
R
R
Campo elettrico
Parametro di rigidità del sistema
 << R
Misure di equilibrio
in funzione della geometria e di E
Prop. planare
Misure di non-equilibrio
in funzione del tempo
( misure strutturali e dinamiche dopo rapida accensione di E)
omeotropica
E
tempo