Structure and Dynamics at the Nanoscale
Probed by XPCS
Alec Sandy
X-Ray Science Division
Argonne National Laboratory
Outline
§  Motivation
§  XPCS
§  XPCS at beamline 8-ID at the APS
§  Selected XPCS results from 8-ID at the APS
–  Complex glass dynamics
–  Bimodal suspension dynamics
§  Future Directions
–  Protein Dynamics
§  Conclusions
NSSRC Users' Meeting - Oct. 2011
Motivation
Copolymer §  Dynamics as a probe of the energy landscape or stability of complex so6 materials –  Hierarchical order in so6 ma9er results from narrowly-­‐separated, compe>ng length and energy scales –  Resul>ng behavior is intermediate between that of fluids and crystalline solids §  Physical nature of slow equilibrium and non-­‐
equilibrium dynamics of complex nano-­‐structured materials vis-­‐à-­‐vis stability Melt Copolymer phases –  Jamming … aging … glass dynamics –  Consumer and industrial products •  Foods, personal care products, … –  Energy •  Oil recovery, … NSSRC Users' Meeting - Oct. 2011
Pictures courtesy of N. Balsara, UC-­‐Berkeley XPCS
Malvern Technical Note MRK-­‐656-­‐01 §  Dynamic light sca9ering (DLS) or photon correla>on spectroscopy (PCS) but with x-­‐rays rather than laser light: 1.  Illuminate a disordered sample with a (par>ally) coherent x-­‐ray beam 2.  Collect the speckled sca9ered beam with a high resolu>on detector NSSRC Users' Meeting - Oct. 2011
XPCS
3.  Monitor speckle pa9ern as a func>on of >me so that changes in the speckle pa9ern can be observed Small Particles
Intensity
Intensity
Large Particles
Time
Time
4.  Calculate the >me auto-­‐correla>on of the fluctua>ng signal at a par>cular wave vector to yield informa>on about the nature and >me scale of sample fluctua>ons at that length scale g 2 ( Q, τ ) ≡
I ( Q, t ) I ( Q , t + τ )
I
2
NSSRC Users' Meeting - Oct. 2011
g 2 (Q,τ )
"
XPCS
§  Why XPCS as opposed to PCS?
–  Smaller length scales than PCS
•  Natural length scale of many technologically and scientifically relevant emerging
materials
–  Flexibility per sample or solvent
combinations such as opaque and
translucent samples
•  Light scattering in similar systems is
state-of-the-art
NSSRC Users' Meeting - Oct. 2011
XPCS at 8-ID
§  Most measurements in small-angle geometry with
direct detection area detectors
–  Polymers, colloids, filled polymers
§  Simple but effective pinhole SAXS set-up
–  Very good at small Q scattering with minimal parasitic
scattering—near USAXS pinhole SAXS
–  Set-up naturally complementary with time-resolved
SAXS—pink-beam capable
Mono or
Pink beam
8-ID-I
Small-angle
XPCS
65 m
8-ID-D
8-ID-E
Mono beam
GISAXS “G”
large Q XPCS
Undulator A
8-ID-A FOE
0m
“E”
51 m
30 m
> 4X109 ph/s/(20 x 20 um)2
NSSRC Users' Meeting - Oct. 2011
> 1013 ph/s/2%
Complex Glass Dynamics
§  Motivation
–  Understanding the glass transition remains a grand challenge in condensed
matter physics
•  What is the nature of dynamics in the glassy state?
•  Are there distinct glassy phases?
U
R
R
F. Sciortino, Nature Materials 1, 145 (2002)
NSSRC Users' Meeting - Oct. 2011
Increasing attractive potential
Complex Glass Dynamics
repulsive glass
liquid
attractive glass
F. Sciortino, Nature Materials 1, 145 (2002)
NSSRC Users' Meeting - Oct. 2011
Mode coupling theory phase diagram for sticky hard
spheres plotted vs. stickiness and volume fraction (φ)
From L Fabbian, W Götze F Sciortino, P Tartaglia, F
Thierry, Phys. Rev. E 59, R1347 (1999).
Complex Glass Dynamics
n  Summary of theoretical predictions for glass behavior:
n  A colloidal glass with hard-sphere (HS) repulsions (repulsive glass)
may be melted by switching on a short-ranged attractive interaction
n  Density fluctuations decay logarithmically versus time, in the liquid
where attractive and repulsive arrest mechanisms compete
n  Such a melted glass may be re-vitrified upon further increase in the
attraction and become an attractive glass.
NSSRC Users' Meeting - Oct. 2011
Complex Glassy Dynamics
§  How are weakly attractive potentials added to colloidal systems
–  Depletion-like interactions
R"
Slide courtesy of B. Leheny, JHU
NSSRC Users' Meeting - Oct. 2011
More excluded volume … less entropy
Less excluded volume … more entropy … effective attraction
Complex Glassy Dynamics
§  Experimental realization at 8-ID is concentrated 200 nm radius silica
spheres in a 2-component fluid: water and lutadine
–  Vary temperature and silica sphere concentration to move through glass
phase diagram
200 nm radius silica spheres
V. Gurfein, D. Beysens and F. Perrot, Phys. Rev. A 40, 2543 (1989)
NSSRC Users' Meeting - Oct. 2011
Complex Glassy Dynamics
§  SAXS (and transmission) measurements and single parameter fits to a
theoretically predicted model for S(Q) provide information on the phase diagram
§  Model for S(Q) for sticky hard spheres from K. Dawson et al., Phys. Rev. E 63,
011401 (2000)
§  One parameter, the product of the attractive potential and depth, was varied in the
fits. R determined in the repulsive glass and Φ determined from transmission
NSSRC Users' Meeting - Oct. 2011
Complex Glassy Dynamics
§  Dynamics probed via XPCS (5 fps)
ΔT = +0.06 K
Liquid or glass?
Liquid or glass?
Complex Glassy Dynamics
§  Answers:
ΔT = +0.06 K
Glassy liquid
Attractive glass
Complex Glassy Dynamics
§  Intermediate scattering functions determined via XPCS
Repulsive glass
Revitrification—Attractive glass
Melted phase—logarithmic
correlation decays
Melted phase—liquid-like
correlation decays
Logarithmic relaxation in glass-forming systems , W. Götze and M. Sperl, Phys. Rev. E 66,
011405 (2002)
NSSRC Users' Meeting - Oct. 2011
Complex Glassy Dynamics
§  Experimentally-determined phase diagram for water, lutadine, silica spheres
Attractive Glass
Log. decay
Liquid
Stretched Exp.
Repulsive Glass
§  Summary
–  XPCS used to probe complex glassy dynamics
•  Re-entrant glass transition
•  Fluid with unusual correlation decays
NSSRC Users' Meeting - Oct. 2011
X. Lu, S. G. J. Mochrie, S. Narayanan, A. R.
Sandy, and M. Sprung, Phys. Rev. Lett. 100,
045701 (2008).
X. Lu, S. G. J. Mochrie, S. Narayanan, A. R.
Sandy, and M. Sprung, Soft Matter 6, 6160
(2010).
Bimodal Suspension Dynamics
§  Mo>va>on –  Bimodal suspensions occur frequently in nature Explosive (and non-­‐explosive) ash from Spring 2010 Icelandic volcano erup>on Milk BBC News S. Gislason et al., PNAS 108, 7307 (2011) –  Model system for exploring structure and dynamics versus poly-­‐dispersity NSSRC Users' Meeting - Oct. 2011
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Bimodal Suspension Dynamics
§  Sample –  Mixtures of sulfate latex spheres suspended in glycerol: RB = 54.6 nm and RS = 11 nm –  Fixed total volume frac>on Φ = ΦB + ΦS = 0.4 –  Mixture composi>on, εB, defined by: φB
φB
εB =
=
φ B + φS φ
–  Bimodal suspensions examined: εB = 0.00, 0.04, 0.17, 0.28, 0.48, 0.68, 0.77, 1.00 !=
RLARGE
!5
RSMALL
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Bimodal Suspension Dynamics
§  SAXS results well-­‐described by addi>on of a spheroid term: εB=0.68
εB a 0.00
b 0.04
c 0.17
d 0.28
e 0.48
f 0.68
g 0.77
h 1.00
Sticky Hard Spheres Model
u
RB
r
u0
Δ
I (q) ∝ φB S BB (q) f B (q) + φS S SS (q) f S (q) + φM f M (q)
Sticky Hard Sphere Model
Hard Sphere Model
Spheroid (RM)
With increasing εB, large spheres are less sticky
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Bimodal Suspension Dynamics
§  Dilute mixtures of large spheres exhibit dynamics slower than large-­‐sphere suspensions –  Deple>on induced aggregates of large (and small spheres) diffuse slowly and dominate measurements NSSRC Users' Meeting - Oct. 2011
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Bimodal Suspension Dynamics
§  Summary M. Sikorski, A.R. Sandy, S. Narayanan, PRL 106, 188301 (2011).
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Future Directions
§  Extensions to biologically-­‐relevant materials like proteins –  Brighter sources –  Harder x-­‐rays –  More sensi>ve and faster detectors §  Extensions to sample variables other than temperature and composi>on –  Brighter sources –  Harder x-­‐rays –  More sensi>ve and faster detectors Figure courtesy of M. Spannuth
Figure courtesy of W. Burghardt
NSSRC Users' Meeting - Oct. 2011
Protein Dynamics
§  XPCS to probe the dynamics of eye-­‐lens-­‐protein mixtures (L. Lurio, J. DeBartolo, G. Thurston, Nuwan K.) –  Physiological mo>va>on •  Cold cataract is due to reversible liquid-­‐liquid phase separa>on in young, mammalian eye lenses •  S>ffening of eye-­‐lens—presbyopia (far-­‐sightedness)—possibly associated with liquid-­‐glass transi>on in protein mixture –  Dynamics measurements provide informa>on on rate of phase separa>on, elas>city –  X-­‐rays provide informa>on on local nanoscale diffusion and diffusion of clusters of proteins (cf. light sca9ering) NSSRC Users’ Meeting – Oct. 2011
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Protein Dynamics
§  XPCS to probe the dynamics of eye-­‐lens proteins (L. Lurio, J. DeBartolo, G. Thurston, Nuwan K.) –  Physics mo>va>on •  Dynamics of concentrated s>cky “spheres” –  Technical mo>va>on •  Extend XPCS to biological materials in aqueous solu>on –  Faster >me scales –  Higher x-­‐ray energies •  Detector usability and robustness –  Experienced and local user group •  Intermi9ent trials over the years as test of state-­‐of-­‐the-­‐art XPCS NSSRC Users' Meeting - Oct. 2011
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Conclusions
§  XPCS can now be used to measure complex dynamics in a range of
physically interesting systems
§  There is significant room for additional growth with:
–  Brighter sources
•  New and improved 3rd generation light sources
•  4th generation light sources
–  Additional users from outside traditional communities
•  Biophysics, geophysics, …
–  Faster, more efficient detectors
NSSRC Users' Meeting - Oct. 2011
Acknowledgements
§  8-ID Personnel
–  Jin Wang, Time-Resolved Research Group Leader at the APS
–  Suresh Narayanan
–  Post-doc Marcin Sikorski (now at LCLS)
§  Partner Users
–  Prof. Larry Lurio, Northern Illinois University
–  Prof. Simon Mochrie, Yale University
§  Graduate Students
–  Xinhui Lu, Yale (now at BNL)
NSSRC Users' Meeting - Oct. 2011