Using coherent x-rays to study the dynamics of condensed

matter

Simon Mochrie, Yale University

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

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.

Coherence

Coherence (cont.)

Coherence (cont.)

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.

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

XPCS signal to noise is linear in brightness

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

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.

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 ().

Small-angle x-ray scattering with coherent x-rays

150 ms exposure -- 200 nm radius silica spheres -- volume fraction 0.5

Dynamic scattering from colloidal suspensions

Multispeckle XPCS: 64x128 pixels at 500 Hz.Movie slowed from real time by a factor of 30.

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.

“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

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.

SAXS from silica in water-lutidine

Pop quiz: Which is the liquid? Which is the glass?

Multispeckle XPCS:128x128 pixels at 5 Hz

Multispeckle XPCS: Intermediate scattering functions

“Logarithmic relaxation in glass-forming systems”, Götze and Sperl, Phys. Rev. E 66, 011405 (2002)

Run C

Multispeckle XPCS: Intermediate scattering functions

Run B

Experimental phase diagram for silica nanoparticles in water-lutidine

soaps

Amphiphilic complex fluidslecithin block copolymers

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”

Dynamics of polymer membranes

Simulation from IBM Almaden website (?Farid Abraham?)

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.

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.

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.

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.

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

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.

Conclusions

• XPCS will benefit tremendously from a new generation of coherent x-ray sources, because brightness determines the XPCS SNR.

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.)

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.)

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.

Thanks to:Xinhui Lu (Yale)Peter Falus (Yale/MIT/ILL)Michael Sprung (APS)Alec Sandy (APS)Suresh Narayanan (APS)

THE END