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Using coherent x-rays to study the dynamics of condensed
matter
Simon Mochrie, Yale University
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Outline
• What is x-ray photon correlation spectroscopy (XPCS)?
• Why coherent x-ray beams and brightness?
• Example 1:Glass transitions in a colloidal suspension with tunable attractions.
• Example 2: Dynamics of polymer membranes.
• Example 3: Near-field heterodyne speckle.
• Prospects, Comments and Conclusions
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What is XPCS?• XPCS is a method to characterize the equilibrium dynamics of
condensed matter by determining the intensity autocorrelation function, g2(Q,t), of the scattered x-ray intensity (x-ray speckle pattern) versus delay time t and wavevector Q.
• g2(Q,t) is related to the normalized intermediate scattering function [f(Q,t )=S(Q,t)/S(Q,0)]], i.e. the density-density correlation function via g2(Q,t)=1+[f(Q,t)]2.
• This is a quantity of central interest for any condensed matter system
• The trick for XPCS is whether S(Q,t) shows interesting behavior within the accessible t and Q range.
• To carry out XPCS experiments requires a (partially) coherent x-ray beam.
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Coherence
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Coherence (cont.)
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Coherence (cont.)
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PCS is much more difficult with x-rays than with laser light
•There are many fewer photons in beams from even a third-generation synchrotron than from laser sources•The x-ray scattering cross-section is generally much smaller that the light scattering cross-section.•As a result, one crucial aspect of an XPCS experiments is generally the signal-to-noise (SNR).•Another crucial aspect is sample x-ray damage.
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Requirements for XPCS
• The source must be as brilliant as possible.• The beamline optics must preserve brilliance.• It is helpful to study strongly scattering samples, in a
fashion that minimizes possible x-ray sample damage.• The detector must collect as many x-rays as possible,
over as wide an angular range as possible, but with an angular resolution sufficiently fine to (nearly) resolve speckle, on a time scale commensurate with the sample’s interesting dynamics.
• Synchrotron and beamline stability is essential
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XPCS signal to noise is linear in brightness
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Beamline 8-ID-I at the Advanced Photon Source
Channel-Cut Ge(111)
Monochromator
Preliminary Beam Defining Slits
SampleTemperature
Control(-30-230 °C)
SampleX, Y, Theta
CollimatingSlits
Guard
Slits
Direct Detection
CCD
Polished Be Window
65 m67 m71 m
2x109 ph/s/(20 μ m X 20 μm)/0.04%
Two Theta
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Structural arrest, glasses and jamming
Peter Pusey
Andrea Liu and Sid Nagel, Nature“Jamming is not just cool any more”
Heinrich Jaeger
Trappe et al.
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Mode coupling theory (MCT) for spheres with short-ranged attractions
L Fabbian, W Götze F Sciortino, P Tartaglia, F Thierry, Phys. Rev. E 59, R1347 (1999).
Mode coupling theory phase diagram for sticky hard spheres plotted vs. reduced temperature () and volume fraction ().
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Small-angle x-ray scattering with coherent x-rays
150 ms exposure -- 200 nm radius silica spheres -- volume fraction 0.5
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Dynamic scattering from colloidal suspensions
Multispeckle XPCS: 64x128 pixels at 500 Hz.Movie slowed from real time by a factor of 30.
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Dynamic scattering from colloidal suspensions
Nominal volume fraction 0.28
Simple, single exponential relaxations.c.f. solutions to the diffusion equation
Intensity autocorrelation functions (g2), calculated pixel-by-pixel, and averaged over all pixels within rings at a given QR to within some resolution.
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“Adsorption phenomena at the surface of silica spheres in a binary liquid mixture”, D. Beysens and D. Esteve, Phys. Rev. Lett. 54 (1985) 2123.
“Stability of colloids and wetting phenomena”, V. Gurfein, D. Beysens and F. Perrot, Phys. Rev. A 40 (1989) 2543.
D. Pontoni, T. Narayanan, J-M. Petit, G. Grubel, and D. Beysens, PRL 90, 188301 (2003).
Silica spheres in water-lutidine
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SAXS from silica in water-lutidine
Model for S(Q) for sticky hard spheres from K. Dawson, G. Foffi, M. Fuchs, W. Götze, F. Sciortino, M. Sperl, P. Tartaglia, Th. Voigtmann, and E. Zaccarelli, Phys. Rev. E 63, 011401 (2000).
Only one parameter () varied in the fits. R fixed. Volume fraction determined from transmission.
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SAXS from silica in water-lutidine
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Pop quiz: Which is the liquid? Which is the glass?
Multispeckle XPCS:128x128 pixels at 5 Hz
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Multispeckle XPCS: Intermediate scattering functions
“Logarithmic relaxation in glass-forming systems”, Götze and Sperl, Phys. Rev. E 66, 011405 (2002)
Run C
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Multispeckle XPCS: Intermediate scattering functions
Run B
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Experimental phase diagram for silica nanoparticles in water-lutidine
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soaps
Amphiphilic complex fluidslecithin block copolymers
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Amphiphilic complex fluids (cont.)Droplet-to-sponge transition in PSEBS: Coexistence at
=0.19
“Inside” and “outside” are distinct, but notice vesicles inside vesicles
Can’t tell “inside” from “outside”
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Dynamics of polymer membranes
Simulation from IBM Almaden website (?Farid Abraham?)
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Dynamics of polymer membranes (cont.)
Intensity autocorrelations (left) and ISFs (right) for a 0.03 SEBS volume fraction sample at 160 C at several wavevectors.
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Dynamics of polymer membranes (cont.)
For individual membranes Zilman and Granek [PRL 77 4788 (1996), Chemical Physics 284, 195 (2002)] [see also Frey and Nelson, J. de Phys. I 1, 1715 (1991)] predict that=0.025(kBT/)1/2(kBTQ3/)
f(Q,t) = exp[-( t)]
with = 2[1+kBT/4)]/3 i.e. slightly larger than 2/3.
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Heterodyne near-field speckle
Left: X-ray heterodyne near-field speckle from Gillette Foamy. Right: Corresponding ISF at an aging time of 1000, obtained by analysis of successive HNFS images.
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XPCS at future coherent sources
• Scale from 8-ID using comparing APS and projected brightness.
• Currently, 8-ID is not fully optimized and we may hope for an improvement in SNR by a factor of 20.
• This suggests a factor of 10,000 or more improvement in XPCS SNR at an optimized ERL beamline!
• Strategies to minimize x-ray damage will be essential, such as (a) using flow cells, (b) using high x-ray energy, to reduced x-ray absorption, (c) using large beam cross-sectional areas, (d) etc.
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Possible future XPCS experiments at new coherent sources
• Dynamics of block copolymer melts and solutions, including at sub-RG length scales. Timescales needed 0.1 ms to 10 s.
• Dynamics of lipid and other small-molecule-surfactant membranes, and membrane phases in water. Time scales needed 10 s to 10 ms.
• Short-length scale dynamics of anti-microbial peptide pores within stacks of biological membranes.
• Charge density wave dynamics.
G. Wong
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Possible future XPCS experiments at new coherent sources (cont.)
• Dynamics of molecular and polymer glasses on molecular length scales in uncharacterized regime from 1 s to 10 s or longer.
• Molecular length scales characterization of molecular motors e.g. kinesin on microtubule network, or immobilized bacterial flagellar motor. From optical tweezers experiments, we know a lot, but not the molecular details. Stepping rates are 1s to 1ms.
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Conclusions
• XPCS will benefit tremendously from a new generation of coherent x-ray sources, because brightness determines the XPCS SNR.
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Be aware, however, that the single most important way to improve XPCS today -- and absolutely required at sources with 5000-fold improved brightness -- is with improved x-ray detectors.
Overall, we are behind where we should be w.r.t. x-ray area detectors and behind European detector efforts (e.g. Medipix, Pilatus)
Conclusions (cont.)
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Desirable XPCS detector characteristics include:
• High speed (determines the fastest processes that can be studied.)
• High efficiency at high x-ray energy. (High x-ray energy minimizes sample damage.)
• Large number of pixels. (Can be increased with multiple detectors.)
• Small pixel size to (nearly) resolve speckles.
• On-pixel correlation, in order to circumvent issue of the tremendous data rate for a framing camera.
Conclusions (cont.)
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Conclusions (cont.) • For many soft matter experiments, it
will be essential to address the issue of sample damage right from the start.
• Fortunately, to make meaningful XPCS measurements, it is necessary to illuminate for only a few times the (slowest) correlation time.
• This indicates a sample flow/translation scheme that effectively moves a new sample into the beam on a time scale slow compared to the correlation time, and fast compared to the damage time.
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Thanks to:Xinhui Lu (Yale)Peter Falus (Yale/MIT/ILL)Michael Sprung (APS)Alec Sandy (APS)Suresh Narayanan (APS)
THE END