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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 Introduction & motivation: Ionic liquids and their surface structure. Experimental technique:surface XPCS. Spontaneous heterodyne - homodyne switching. Results: Propagating and overdamped regimes of thermal CW. Critical behavior of thermal CW excitations. Future directions: Can XPCS measure surface viscoelasticity ?

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Room Temperature Molten Salts Classical Salts: NaCl T m = 1074 K MgCl 2 T m = 1260 K YBr 3 T m = 1450 K RT = 101 cP T m = -71 o C Butylmethylimidazolium tetrafluoroborate Ionic liquids: Solvent free electrolytes. “Green” industry. 100s synthesized since ’97.

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The static surface structure of ILs X-ray reflectivity studies Surface induced ordering is required to fit the reflectivity. Sloutskin et al., JACS 127, 7796 (2005) 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). z(Å) (e/Å 3 )

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Dynamic light scattering 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. The surface dynamics of ILs T c (???) Surface dipole density

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X-ray photocorrelation spectroscopy (XPCS) z o I qxqx qzqz qxqx q k in k out < c A. Madsen et al., website of ESRF. qxqx Intensity autocorrelation G( ) at a given wave vector q x is related to the dynamics of surface excitations for the same wave vector. Propagating mode t = Specular reflection (sec) ≠ Diffuse scattering by CW ≠ Diffuse scattering by CW Overdamped mode t G ) Troïka (ESRF) (sec) G )

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Capillary wave excitations with shorter wavelengths have higher frequencies. Damping increases for shorter wave lengths. Viscous dissipation is due to velocity gradients: ∆v term in the Navier-Stokes equation. At high q x and low T, capillary waves are overdamped. Experimental G(q x,t) functions: qualitative description. =ck k (s) G(q x, ) overdamped T=40 o C q x =24 mm -1 Propagating T=134 o C

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Theoretical description For incompressible fluid: divv = 0 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: h Navier-Stokes: Dispersion relation for the capillary waves: temporal damping

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Transition from propagating to overdamped waves: hydrodynamical theory T c =35 o C @ k=24 mm -1 Solve y(T c )= 0.145 Experimental T c is higher than 40 o C !!! Dispersion relation Damping Propagating log(y) log( ), log( ) Use independently-measured (T), (T) and (T) “ - Byrne and Earnshaw (1979) “ (sec) G(q x, ) k=24 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: J. Jäckle and K. Kawasaki, J. Phys.: Condens. Matter 7, 4351 (1995) (kHz) S(k, propagatingoverdamped T c =45 o C @ k=24 mm -1 k S(k, ) propagating overdamped The calculated T c seems now to be correct. Can we use JK for full shape analysis of our XPCS data ? T=const k=const Fluctuation-Dissipation Analytical approximations are inapplicable in the critical damping regime !

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Heterodyne vs. homodyne (sec) G ) Beating against a reference beam J.C. Earnshaw (1987) Grating laser PMT spontaneous switching Homodyne Who ordered a reference beam for XPCS ?

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Small effective sample size yields non-zero scattered intensity even for a perfectly smooth surface. The effective sample size changes in time: meniscus, dust particles, etc. The scattering peaks move in time, sometimes interfering with the diffuse signal. Why is the switching time-dependent ? 1 Gutt et al., PRL 91, 076104 (2005) 2 Ghaderi, PhD thesis (2006) What is the origin of the spontaneous reference beam in surface XPCS ? Interference with the reflected beam, R(q z ) (q x ) (q y ) ??? Fresnel (near field) conditions mix the low q values 1. Instrumental q resolution 2. Partial coherence of the beam. Set the reference beam intensity as a free fitting parameter !

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Full shape analysis I r – reference beam -“static” diffuse scattering Unknown Jäckle & Kawasaki (1995) Detector resolution G(q x, ) (s) q x =24 mm -1 L ln(I s ) ln(q x ) q x -2 Full shape analysis with only I s and I r being free. The fitted I s values show the diffuse intensity scaling known from CWT (for small q z values). Let’s calculate the experimental S(q,w) spectra…

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A. Madsen et al., PRL 92, 096104 (2004) F{..} t Stokes k in q rip k out anti-Stokes k in k out q rip Let’s introduce surface viscoelasticity into the same formalism ! The spectra are fully described by the JK theory, assuming an unstructured interface. No need to introduce Freyland’s modified elastic term in the CW spectrum. No evidence for “ferroelectric” transition, at least for T<130 o C. Does it mean that the surface of an IL is not layered ? S(q, ) (kHz) T=343 K Use the fitted values of I s and I r to evaluate the experimental S(q,w) (kHz) S(q, ) 313 K 323 K 333 K 343 K 371 K 403 K XPCS Lucassen Jäckle 24 mm -1 T ( o C) (kHz), XPCS Theory ln(T-T c ) ln( ) |T-T c | -1/2 36 mm -1 24 mm -1 ln(T-T c ) q x =24 mm -1

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(i) “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 (i) ideal interface – lateral displacement of surface element h – surface normal displacement D. Langevin and M.A. Bouchiat, C.R. Acad. Sc. Paris 272, 1422 (1971) (kHz) d/d/ S(q, ) d =0 time = d (Hz) d/d/ Resonance with Marangoni waves The changes are too small to be detected by XPCS… T=100 o C q=17 mm -1

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(kHz) S(q, ) d Future directions Langmuir films on low-viscosity liquids ? d Damping (kHz) (kHz) LF on water: q x = 20 mm -1 T = 25 o C = 50 mN/m Spontaneous surface structures: surface freezing in alkanes, surface layering in liq. metals… Higher coherent flux and stable experimental conditions are needed to avoid spontaneous homo-hetero switching. If switching is unavoidable, try to measure the intensity of the reference beam ! Go to higher q-values… (Far future: check dynamics at sub-micron scales) S(q, )/S max (kHz) d =0 d >> d = res

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What have we learned about surface XPCS ? Quantitative analysis, accounting for both homo- and hetero-dyne terms, critical damping conditions (no Lorentizan app.), finite detector resolution perfectly fits the experiment. Homo-hetero switching costs extra fitting parameters. Surface viscoelasticity is only measurable at low viscosity. 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

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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).

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