Critical dynamics of capillary waves


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Critical dynamics of capillary waves in an ionic
liquid XPCS studies
Eli Sloutskin
Physics Department Bar-Ilan University
Israel Now at SEAS Harvard
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OUTLINE
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Room Temperature Molten Salts

• Ionic liquids
• Solvent free electrolytes.
• Green industry.
• 100s synthesized since 97.

Butylmethylimidazolium tetrafluoroborate
Tm -71 oC
hRT 101 cP
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The static surface structure of ILs
X-ray reflectivity studies
Molecular dynamics

• Oscillatory surface electron density profile
• Surface mixture of cations and anions

R.M. Lynden-Bell and M. Del Pópolo PCCP 8 949
(2006). B.L. Bhargava and S. Balasubramanian
JACS 128 10073 (2006). Sloutskin et al. J.
Chem. Phys. 125 174715 (2006).
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The surface dynamics of ILs
Dynamic light scattering
V. Halka R. Tsekov and W. Freyland PCCP 7
2038 (2005).

• Modified elastic term in CW spectrum.
• Possible ferroelectric order-disorder phase
  transition at T380 K.

• XPCS yields the S(qw) of T-excited surface
  capillary waves.
• No contribution from bulk modes.
• Higher k-vectors can be probed.
• To date no XPCS for any ionic liquid.

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X-ray photocorrelation spectroscopy (XPCS)
b a Diffuse scattering by CW
A. Madsen et al. website of ESRF.
Intensity autocorrelation G(t) at a given wave
vector qx is related to the dynamics of surface
excitations for the same wave vector.
qx
Propagating mode
t
t (sec)
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Experimental G(qxt) functions qualitative
description.
qx24 mm-1
Propagating T134 oC
G(qxt)
overdamped T40 oC
t(s)

• Capillary wave excitations with shorter
  wavelengths have higher frequencies.
• Damping increases for shorter wave lengths.
  Viscous dissipation is due to velocity gradients
  hv term in the Navier-Stokes equation.
• At high qx and low T capillary waves are
  overdamped.

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Theoretical description
Assume liquid density and viscosity remain
constant up to the dividing surface
Boundary conditions at the interface
Stress tensor
ideal interface
(i)
Young-Laplace
(ii)
Surface tension
Dispersion relation for the capillary waves
E.H. Lucassen-Reynders and J. Lucassen Adv.
Colloid Interface Sci. 2 347 (1969)
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Solve y(Tc) 0.145
Tc35o C _at_ k24 mm-1
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XPCS measures the actual population of ripplon
energy levels at a given T not the energy
levels allowed by hydrodynamics.
Linear response theory (Jäckle Kawasaki 1995)
Spectrum of surface ripplons
Fluctuation-Dissipation
kconst
Tconst
Tc45o C _at_ k24 mm-1
overdamped
The calculated Tc seems now to be correct. Can we
use JK for full shape analysis of our XPCS data
J. Jäckle and K. Kawasaki J. Phys. Condens.
Matter 7 4351 (1995)
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Heterodyne vs. homodyne
Homodyne
Beating against a reference beam
Who ordered a reference beam for XPCS
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What is the origin of the spontaneous reference
beam in surface XPCS

• Interference with the reflected beam
  R(qz)d(qx)d(qy)
• Fresnel (near field) conditions mix the low q
  values1.
• Instrumental Dq resolution2.
• Partial coherence of the beam.

Why is the switching time-dependent
Set the reference beam intensity as a free
fitting parameter !
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Full shape analysis
Ir reference beam
Unknown
Detector resolution
Jäckle Kawasaki (1995)
qx24 mm-1
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Use the fitted values of Is and Ir to evaluate
the experimental S(qw)
T343 K
A. Madsen et al. PRL 92 096104 (2004)
Lets introduce surface viscoelasticity into the
same formalism !
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Change the boundary conditions to introduce
elasticity of the surface layer
Boundary conditions at the interface
Dilational modulus
Stress tensor
(i)
elastic interface
x lateral displacement of surface element h
surface normal displacement
(ii)
Resonance with Marangoni waves
Surface tension
time hd
hd0
The changes are too small to be detected by XPCS
D. Langevin and M.A. Bouchiat C.R. Acad. Sc.
Paris 272 1422 (1971)
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Future directions
LF on water
qx 20 mm-1 T 25 oC g 50 mN/m
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Summary

• What have we learned about surface capillary
  waves
• Linear response theory (JK) provides the correct
  description of CW dynamics in an IL.
• Hydrodynamics alone (LLR) is insufficient.
• Critical scaling of CW frequencies at T Tc
  even though the hydrodynamic Tc is not the actual
  Tc .

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Thanks

• Organizers (NSLS-II).
• Audience.
• Prof. Moshe Deutsch (Bar-Ilan University
  Israel).
• Dr. Ben Ocko (Brookhaven USA).
• Dr. Anders Madsen (ESRF France).
• Dr. Patrick Huber and M. Wolff (Saarland
  University Germany).
• Dr. Michael Sprung (APS USA).
• Dr. Julian Baumert (BNL deceased).
• Chemada Ltd. (Israel).
• German-Israeli Science Foundation GIF (Israel).