# Presentation: 336165

## Critical dynamics of capillary waves 

**in an ionic liquid: XPCS studies**

**Eli Sloutskin**

***Physics Department***
***Bar-Ilan University****** ***
***Israel***
***Now at SEAS, Harvard***

## OUTLINE

## Room Temperature Molten Salts

****RT** = 101 cP**

**T****m**** = -71 ****o****C**

**Butylmethylimidazolium**
**tetrafluoroborate**

_**Ionic liquids:**_
** ****Solvent free electrolytes.**
** ****“****Green” ****industry.**
** ****100s synthesized since ’97.**

## 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 P**ópolo, PCCP ****8****, 949 (**2006).*
*B.L. Bhargava and S. Balasubramanian, JACS ****128****, 10073 (2006).*
*Sloutskin et al., J. Chem. Phys. ****125****, 174715 (2006).*

## The surface dynamics of ILs

-  Modified elastic term in CW spectrum.
-  Possible ferroelectric order-disorder phase transition at T≈380 K.

*V. Halka, R. Tsekov, and W. Freyland, PCCP ****7****, 2038 (2005).*

-  XPCS yields the S(q,) 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.

## X-ray photocorrelation spectroscopy (XPCS)

- A. Madsen *et al.*, website of ESRF.

- qx

- Intensity autocorrelation G() at a given wave vector qx is related to the dynamics of surface excitations for the same wave vector.

- Propagating mode

- t

-  (sec)

-  ≠ Diffuse scattering by CW

## Experimental G(qx,t) functions: qualitative description.

-  Damping increases for shorter wave lengths. Viscous dissipation is due to velocity gradients:   ****∆*v *term in the Navier-Stokes equation.
-  At high qx and low T, capillary waves are overdamped.

- Experimental G(qx,t) functions: qualitative description.

- (s)

- G(qx,)

- overdamped
- T=40 oC

- qx=24 mm-1

- Propagating
- T=134 oC

## Theoretical description

- Assume: liquid density and viscosity remain constant up to the dividing surface

- E.H. Lucassen-Reynders and J. Lucassen, *Adv. Colloid Interface Sci.* **2**, 347 (1969)

- Boundary conditions at the interface:

- Stress tensor:

- Surface tension

- (ii)

- (i)

- ideal interface

- Young-Laplace:

- Dispersion relation for the capillary waves:

## Tc=35o C @ k=24 mm-1

*T**c*=35o C @ k=24 mm-1

**Solve y(T****c****)= 0.145**

## Tc=45o C @ k=24 mm-1

- _Linear response theory (J__äckle & Kawasaki, 1995__)_

- Spectrum of surface ripplons:

- J. Jäckle and K. Kawasaki, *J. Phys.: Condens. Matter* **7**, 4351 (1995)

- Tc=45o C @ k=24 mm-1

- overdamped

- The calculated Tc seems now to be correct.
- Can we use JK for full shape analysis of our XPCS data ?

- T=const

- k=const

- Fluctuation-Dissipation

## Heterodyne vs. homodyne

**Heterodyne**** ****vs.**** ****homodyne**

- Beating against a reference beam

- Homodyne

- Who ordered a reference beam for XPCS ?

## Why is the switching time-dependent ?

_**Why is the switching time-dependent ?**_

_**What is the origin of the spontaneous reference beam in surface XPCS ?**_

-   Interference with the reflected beam, R(qz)(qx)(qy) ???
-   Fresnel (near field) conditions mix the low q values1.
-   Instrumental q resolution2.
-   Partial coherence of the beam.

**Set the reference beam intensity as a free fitting parameter !**

## Full shape analysis

*I**r* – reference beam

- Unknown

- Jäckle & Kawasaki (1995)

- Detector resolution

- qx=24 mm-1

## Use the fitted values of Is and Ir to evaluate the experimental S(q,w)

*A. Madsen et al., PRL 92, 096104 (2004)*

- Let’s introduce surface viscoelasticity into the same formalism !

- T=343 K

**Use the fitted values of I****s**** and I****r**** to evaluate the experimental S(q,w)**

##  – lateral displacement of surface element

- “elastic” interface

- Dilational modulus

- Boundary conditions at the interface:

- Stress tensor:

- Surface tension

- (ii)

- Change the boundary conditions to introduce elasticity of the surface layer

******* *– lateral displacement of surface element
***h*** – surface normal displacement

- D. Langevin and M.A. Bouchiat, *C.R. Acad. Sc. Paris* 272, 1422 (1971)

- d=0

- time = ****d

- Resonance with Marangoni waves

- The changes are too small
- to be detected by XPCS...

## Future directions

_**Future directions**_

- LF on water:

- qx = 20 mm-1
- T = 25 oC
- = 50 mN/m

## 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 ****→**** ****T****c**** , even though the hydrodynamic T****c**** is not the actual T****c**** .**

_**Summary**_

## 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).**