Alessandro CunsoloINFM Operative Group in Grenoble and CRS-Soft, c/o Institut Laue-Langevin, Grenoble, France

On the new opportunities opened by the development of next generation IXS

spectrometers

-The construction of IXS spectrometers with .1 meV resolution would allow to partially bridge the dynamic gap existing with low Q spectroscopies……

No man’s land

In principle the access to lower Q = 4 sin(/2) can be achieved, but……

Potassium

-40.0 -20.0 0.0 20.0 40.00.0

1.0

2.0

Q = 3.0 nm-1

Q = 6.0 nm-1

Q = 1.7 nm-1

Frequency (ps-1)

0.0

0.3

S(Q

,)

(ar

b. u

nits

)

0.0

0.2

0.4

0.0

4.0

8.0

Q = 10.0 nm-1

The “bottle-neck” is the instrumental

resolution

1) relaxation processes in the dynamics of disordered systems

Various interesting subjects can be investigated inside such “dynamic gap”

•The propagation of a density fluctuation The propagation of a density fluctuation perturbs the local equilibrium of the fluid.perturbs the local equilibrium of the fluid.

•Such equilibrium is then restored through Such equilibrium is then restored through energy rearrangements affecting the energy rearrangements affecting the density density wavewave towards some towards some internal degree of internal degree of freedomfreedom (relaxation processes). (relaxation processes).

•The propagation of the density wave The propagation of the density wave depends on how its depends on how its periodperiod (T) (T) compares compares with the with the relaxation time-scalerelaxation time-scale ( ())..

Q=Q*~1/d*

Visco-elastic crossover

s(Q)

q

cSQviscous regime

c∞Qelastic regime

s(Q*)=1/

The dispersion curve

0.1 1 10

1E-4

1E-3

0.01 T1 = 453 K

T2 = 333 K

T3 = 278 K

s/cs (

nm

-1 )

Q ( nm-1 )

Resolution limited range

Dispersion curve of water: first evidence of a viscoelastic behavior

-10 -5 0 5 100

1

2

Inte

nsit

y (a

rbit

. uni

ts)

(meV)

T = 278 K

Q = 2 nm-1

ħs-ħs

EKEE

AEQS

SS

M

22222

),(

A typical DHO best fit lineshapeA typical DHO best fit lineshape

An improved resolution would

allow to studyviscoelastic effects also in the

overcooled phase

s,1~1/

q1

s,2~1/

q2

s,3~1/

q1

1/increases with increasing T

The viscoelastic behavior of the lineshapePossible effects of an improved instrumental resolution

-3 0 3

0.0

0.2

0.4

0.6

0.8

1.0

E = 0.1 meV

No

rmal

ized

res

olu

tion

fun

ctio

n

Energy (meV)

Convolution for an hypothetical .1 meV (lorentzian) resolution function

(meV)

Raw spectraHypothetical higher resolution spectra

Non convoluted (model)

line-shapes

(meV)

Q=2 nm-1

S(Q

,)/

S(Q

) (m

eV-1)

Elastic regime

Visco-elastic regime

Viscous regime

Evidence of an additional low frequency mode in water

0.0

0.5

1.0

Q=16.0 nm-1

0.0

0.5

Q=13.1 nm-1

0.0

0.5

Q=9.8 nm-1

0.0

0.5Q=7.8 nm

-1

0 10 20 30 40 500.0

0.5

CL

,T(Q

, E)

( ar

b. u

nits

)

Energy ( meV )

Q=5.8 nm-1

CT(Q,

CL(Q,)

0 10 20 30 400

5

10

15

20

25

30

35

L

,T

( m

eV )

Q ( nm-1 )

s from IXS spectra

T from IXS spectra

IXS results versus MD simulations

Crossover from viscoelasticity to transversedynamics: the experimental observation of the

gradual L-T mode-splitting would require a much better resolution ……

M. Sampoli et al. Phys. Rev. Lett. 79, 1678 (1997)

CL

(Q

,E)=

(E

/q)2 S

(Q

,E)

Experimental evidence of a modes bifurcationin the dynamic of mixtures

He

Ne

He77-Ne23 at T=60 K, cmix~1000 m/s

dynamic decoupling of the two componentsBafile et al., PRL 88 085502, (2002)

at higher Q’s, the heavy (“slow “) component cannot support the propagation of the fast

acoustic mode, which thereforepropagates only through the light component.

In the hydrodynamic limit the two components of a mixture “cooperate” in the sound propagation

→ only one acoustic mode.

Dynamics of materials under confined geometries

Models of critical dynamics debated, with nearly no existing experimental verification

Schoen and Porcheron, EPJ 2003

Simulation resultsfor a confined simple fluid

Collective modes in water confined in NafionSazcchetti et al. Submutted to PRL

The origin of this mode seems a bit controversial

Normal modes of confined water droplet? Transverse mode in confined water?

Life ScienceExamples

Collective dynamics in lipid membranes Collective modes affect

significantly the physical properties of phospholipids membranes

Correlated molecular motions of lipid acyl chains and the density fluctuations in the plane of bilayer are important for the transport of small molecules through the bilayer

Gel-fluid phase transitionM.C. Rheinstadter et al., PRL 93, 2004

ConclusionsConclusions

a) the study of relaxation processesa) the study of relaxation processes

b) the observation of a transverse dynamic in the THz response of fluidsb) the observation of a transverse dynamic in the THz response of fluids

e) the study of nearly-critical systemse) the study of nearly-critical systems

d) the dynamical characterization of liquids under geometrical confinementd) the dynamical characterization of liquids under geometrical confinement

c) the evidence of a mode splitting in the dynamics of liquid c) the evidence of a mode splitting in the dynamics of liquid mixturemixture

f) the study of the dynamics of biological systemsf) the study of the dynamics of biological systems

1) The development of an IXS spectrometer with .1 meV would 1) The development of an IXS spectrometer with .1 meV would reduce the gap between low and high frequency spectroscopiesreduce the gap between low and high frequency spectroscopies

2) Various scientific topics would benefit from such 2) Various scientific topics would benefit from such upgrade. Some mentioned examples:upgrade. Some mentioned examples: