Interpretation of Specular XPCS measurements of Smectic ...€¦ · Interpretation of Specular XPCS...
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Interpretation of Specular XPCS measurements ofSmectic Liquid Crystal Membranes
Irakli Sikharulidze*, Wim H. de JeuFOM-Institute for Atomic and Molecular Physics (AMOLF)
Amsterdam, The Netherlands
Anders Madsen ID10, ESRFIgor Dolbnya B16, DiamondBela Farago ILLAndera Fera AMOLFBoris Ostrovskii ICRAN, AMOLF
*) present address: Department of Biophysical Structural Chemistry (BFSC)Leiden Institute of ChemistryLeiden University, The Netherlands
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Contents
� Smectic Liquid Crystal Membranes� Low-dimensional systems� Preparation� Relaxations of fluctuations
� X-ray Photon Correlation Spectroscopy (XPCS)� Experimental description� Results and Discussions
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Smectic liquid crystal membranes
-- Orientationally ordered elongated molecules(here assumed to be perfectly oriented).
- Stacked liquid layers give 1D ordering (smectic-A).
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Properties of Smectic Membranes
� Very well oriented (mosaic < 1 up to 10 mdeg)� Centro-symmetric (No substrate)� From two to thousands of layers
(about 5 nm to 20 µm)� Cross-over from bulk behaviour (3D) in thick films
to surface-dominated behaviour� Model systems of low-dimensional ordering
W.H. de Jeu, B.I. Ostrovskii, A.N. Shalaginov, Rev. Mod. Phys. 75, 181 (2003)
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Smectic Liquid Crystal Molecules
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Preparation
Typical sizes up to 25 × 70 mm2
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Reflectivity
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High-resolution rocking curve (8CB)
Bragg position reflectivity
Incoming beam:pinhole 10 µm Ø
Detector slits: 30×30 µm2
FWHM = 0.7 mdeg
N=13
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Scattering setup
(x,y) plane || to the surface of the membranez ⊥ to the surface of the membrane
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Setup parameters (Troika I, ESRF)Third/fifth harmonic of set of three undulators.
Source size: 928 × 23 µm2 (sH × sV)Mono: Si(111) at 8 or 13.4 keV
λ at 1.55 or 0.96 Å, ∆λ/ λ ≈ 10�4
Pinhole: 10 µm Ø at R = 44 m
Coherence lengths:
ξt,H = λR/(2sH) ≈ 8 µm; ξt,V ≈ 300 µm.
ξ l = λ /(∆λ/ λ) ≈ 1.6 µm.
At the Bragg position θ ≈ 1.5o →path length difference: 2L sin θ = 1.6 µm→ Lmax ≈ 30 µm.
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Detection systemAvalanche photo diodesPerkin Elmer C30703.
Time resolution: ~ 0.7 ns (rise time).Low background (thin, insensitive to high-energy photons).
A.Q.R. Baron, Hyperfine Interactions 125, 29 (2000)
Correlators
FLEX01-8D Correlator.com, small convenient box,lag time 8 ns.
Direct storage: store arrival times all individual pulses, calculate correlation function later.
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Bunch structure of the storage ring at ESRF
Continuous filling mode with 992 bunches equally spaced at 2.8 ns.Rising edge of avalanche photodiode stored in memory of a 2 GHz computer board.
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Landau-de Gennes-Hołyst Free Energy
Bendlayers
K ~ 10�11 N
Compressionlayers
B ~ 107 N/m2
Fluctuations destroy layer ordering for large L
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Relaxation regimes1
2442
3
02
3
0,
24112−
⊥⊥⊥⊥
+−≈ q
LKq
qqfsγ
ηρ
ηρτ m
Lq c
γρη
0
3,
22=⊥
transition attransition at
q < qq < q⊥⊥,c
23
/2 ⊥+=
KqLs γητ
q > qq > q⊥⊥,c,c ,c
Complex mode(oscillations):
*fs ττ =
γητ2
3Ls = 2
3
⊥
=Kqsητ
A.N Shalaginov, D.E. Sullivan Phys. Rev. E 62 699 (2000)
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Dispersion curve
I. Sikharulidze, B. Farago, I. Dolbnya, A. Madsen, W. H. de Jeu,Phys. Rev.Lett. 91 (2003) 165504
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Off-specular Measurements (FPP)
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Neutron Spin Echo: Results (8CB)
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Homodyne-heterodyne detection
Off-specular: τ = 3.3 µs → homodyne detection.Specular: τ = 6.2 µs → heterodyne detection.
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Homodyne-heterodyne detection (2)
In presence of a reference signal:
E(t) = Eref +Es(t)
Substitution in leads to
Dynamic light scattering: Amplification of heterodyne signalby external grating.
Here in XPCS: Strong elastic Bragg peak acts as�internal� secondary source!
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Dynamic Light Scattering
S. Sharma, K. Neupane, A. Adorjan,A. R.Baldwin, and S. SpruntPhys. Rev.Lett. 94 (2005) 067801
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Dispersion curve
I. Sikharulidze, B. Farago, I. Dolbnya, A. Madsen, W. H. de Jeu,Phys. Rev.Lett. 91 (2003) 165504
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Thickness dependence (4O.8)
I. Sikharulidze, I.P. Dolbnya, A. Fera, A. Madsen, B.I. Ostrovskii,W.H. de Jeu,Phys. Rev. Lett. 88, 115503 (2002)
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Scattering angle dependence
Coherence volume decreaseswith increasing scattering anglegiving faster relaxations.
I. Sikharulidze, I.P. Dolbnya, A. Madsen, W.H. de Jeu,Opt. Commun. 247, 111 (2005)
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Perfect membrane puzzle
In perfectly ordered membranes contrast at the Bragg disappears
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Model
Oscillations
Exponential relaxation
Zero contrast
I. Sikharulidze and W.H. de Jeu, Phys. Rev. E (in press)
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Mosaic vs. Cross-over Wavevector
ο 4O.8
• FPP
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Chellenge: Coherence induced oscillations
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Chellenge: Coherence induced oscillations (2)
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Conclusions
� Mosaicity of the sample and coherence volume define a wave vector �window� of fluctuations detected in specularXPCS measurements.
� If the cross-over wave vector is close to the lower edge of the �window� exponential relaxation is observed and if it is close to higher edge - oscillatory relaxations.
� In case of the highly uniform samples with narrow mosaic �window� is empty, which results in the absence of contrast in XPCS
� A qz-dependence is observed which parallels the projected coherence length (footprint).
� Both heterodyne (at the specular ridge) and homodyne(off-specular) detection schemes have been realized.