simon mochrie - yale university - october 2008...sponge phase peak positions versus sebs volume...
TRANSCRIPT
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State of the art XPCS and XPCS at the LCLS
Simon Mochrie - Yale University - October 2008
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Outline
• Amphiphiles and amphiphilic complex fluids, sponge phases, and block copolymers.
• Polymer sponge phases and phase behavior of triblock copolymer-homopolymer blends
• XPCS and the dynamics of membranes
• Sponge phase dynamics.
• XPCS at the LCLS
• Conclusions
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What is XPCS (DXS)?
• XPCS (DXS) is the x-ray analogue of DLS, i.e. 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 at 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 -- of the sample 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, we need a (partially) coherent x-ray beam.
•To create a partially coherent beam, we need to restrict the beam dimensions at the sample position to be comparable to the coherence length of the source
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X-ray scattering measurements at Beamline 8-ID at the Advanced Photon Source at Argonne National Laboratory
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SMD1M60 x-ray area detector
• 1024x1024 14x14 μm2 pixels
• 62 Hz full-frame rate
• 500 Hz 1/16-frame rate
• counts individual photons
• 50% quantum efficiency
• inexpensive
n.b. Suitable for studying non-ergodic systems
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Confocal microscopy image from Eric Week’s web page
CCD images of the SAXS for a 0.28-volume-fraction suspension of 70 nm-radius colloidal spheres in glycerol.
SAXS from concentrated colloidal suspensions using coherent x-rays
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SAXS from concentrated colloidal suspensions using coherent x-rays (continued)
Azimuthally-averaged SAXS vs. volume fractionFor 70 nm-radius PS spheres in glycerol
Divide through bylowest volume fractionto obtain liquid structure factor
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XPCS for concentrated suspensions
Dynamic x-ray speckle from a 0.3 volume fraction suspension of 0.2 micron-radius silica spheres, recorded at 500 fps and played back at 25 fps.
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XPCS for concentrated suspensions (cont.)
Autocorrelations, g2(Q,t) for 70nm-radius PS spheres in glycerol at volume fractions of 0.28 (left, single exponential) and 0.52 (right, double exponential, but a stretched exponential can also be used).
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De Gennes narrowing
Measured and theoretical D0/Ds(squares and red lines) and S(Q) (circles and blue lines) vs. QR for PS spheres in glycerol.
Conclusion: XPCS works!
Short-time diffusion coefficientdefined by τ = 1/DsQ2
I.e. 1/Ds= τ Q2
D0 = kBT/6πηR is the Stokes-Einsteindiffusion coeffient
Physically, de Gennes narrowing is the manifestation of the fact that low-free-energy configurations are long-lived
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Amphiphilic complex fluidsAmphiphilic molecules possess two (or more) moieties with very different affinities
e.g. soaps, lecithin, block copolymers
..and organize immiscible fluids
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C12E5-H20 phase diagram
R.Strey et al. J. Chem. Soc. Faraday Trans. 86, 2253 (1990)
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Block copolymer phase diagrams: theory and experiment
Claim: Polymer-based materials offer the prospect of first-principles understanding of complex-fluid structure, phase behavior, and dynamics
e.g. calculate the parameters appearing in the sponge phase Landau free energy.
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Theoretical amphiphilic phase diagram
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Sponge-to-Droplet Transition in TEM:Coexistence at φ=0.19
“Inside” and “outside” are distinct, but notice vesicles inside vesicles
Can’t tell “inside” from “outside”
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Sponge-to-Lamellar Transition in TEM
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CCD image of SAXS pattern from φ=0.20 styrene) triblock copolymer (SEBS) in poly(styrene-ethylene/butylene- polystyrene homopolymer (PS)
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SAXS from blends of poly(styrene-ethylene/butylene-styrene) triblock copolymer (SEBS) with polystyrene homopolymer (PS): Large wavevector scattering
•Mw(SEBS)=87K with Mw /Mn=1.06 and a central P(E/B) volume fraction of 0.7 with PS fractions of 0.15 at each end.
•Mw(PS)=4K, Mw /Mn=1.06
•For all volume fractions studied, there are periodic oscilation in the SAXS intensity at relatively large wavevectors.
•The locations of the oscillation minima relative to zero point unambiguously to a microstructure built from P(E/B) membranes suspended in PS.
•Weaker scattering intensity than colloidal suspensions.
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SAXS from blends of poly(styrene-ethylene/butylene-styrene) triblock copolymer (SEBS) with polystyrene homopolymer (PS):SEBS volume-fraction dependence at small wavevectors
•SEBS volume fractions varying from 0.07 to 0.43.
•At intermediate volume fractions, SAXS consistent with a sponge phase.
•At higher volume fractions, SAXS consistent with sponge/lamellar coexistence
• At low volume fractions, the sponge peak position does not track with the copolymer volume fraction as would be expected in a symmetric sponge phase. We propose a droplet phase for SEBS volume fractions below about 0.2
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Sponge phase peak positions versus SEBS volume fraction
For SEBS volume fractionsgreater than about 0.22, thepeak position varies linearlywith volume fraction, consistent with a symmetricsponge.
Below 0.22, the variation ofthe peak position versusvolume fraction is different,indicating a peak transitionto a new phase.
Guided by theory we identifythis as an asymmetricsponge.
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Dynamics of polymer membranes
Simulation from IBM Almaden
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Dynamics of “dilute” polymer membranes via XPCS
Intensity autocorrelations for a 0.03 SEBS volume fraction sample at 160 C at several wavevectors.
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Dynamics of polymer membranes via XPCS (cont.)
Normalized ISF for a 0.03 SEBS volume fraction sample at 160 C at several wavevectors, plotted so that a single exponential IFS would appear as a straight line, and fitted to a stretched exponential form: f=exp[(Γt)β].
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Dynamics of dilute polymer membranes: Zilman and Granek and Frey and Nelson predictions
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
Γ=0.025(kBT/ κ)1/2(kBTQ3/η)f(Q,t) = exp[-(Γ t)]β
with β = 2[1+kBT/4πκ)]/3 i.e. slightly larger than 2/3!
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Dynamics of polymer membranes: Fitting results for φ=0.03
Stretching exponent for φ=0.03Relaxation rate: Γ vs. Undulationrate (kBTQ3/η) for φ=0.03
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Normalized ISF for a 0.20 SEBS volume fraction sample at 180 C at several wavevectors fitted to a stretched exponential form: f=exp(Γt)β.
In this case the stretching is more pronounced -- smaller stretching exponent.
Sponge phase dynamics: ISF at 180C and φ=0.20.
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Sponge phase dynamics: ISFs at 160C and 140C…but the stretching exponent decreases with decreasing temperature!!
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Sponge phase dynamics: ISFs at 120C
At 120C, the ISF exhibits an compressedexponential form.
Such a crossover is not predicted by any of the theories of the dynamics of the sponge phase.
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What do these results mean?
Usually (in the case of molecular or colloidal glasses), stretched-exponential behavior is associated with transient particle “caging”.
Compressed exponential ISF are unusual, but have recently found for systems undergoing “aging”.
Does 20% PSEBS in PS realize a near-glassy fluid-to-jammed transition?
Sponge phase dynamics: Stretching/compression exponent vs. T and Q
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Sponge phase dynamics: Aging-time dependence of g2s
Compressed exponential ISFs, but no (obvious) aging time dependence.
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Sponge phase dynamics: De Gennes narrowing
In the stretch exponential regime, there is a minimum in the relaxation rate vs. Q -- this is “de Gennes narrowing”.
This feature disappears when the ISF is a compressed exponential.
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Microemulsion phase behaviorMacromolecules, 39 (25), 8822 -8831, 2006, Megan L. Ruegg, Amish J. Patel, Suresh Narayanan, Alec R. Sandy, Simon G. J. Mochrie, Hiroshi Watanabe, and Nitash P. Balsara
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Microemulsion dynamics
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Possible future XPCS experiments at the LCLS
• Dynamics of block copolymer melts and solutions, including at sub-RG length scales. Timescales needed 10 ms to 100 s.
• Short length scale dynamics of lipid and other small-molecule-surfactant membranes, and membrane phases in water. Time scales needed less that 1 ns to longer than 10 ns. Crossover from molecular motion to collective motion.
• Short-length scale dynamics of anti-microbial peptide pores within stacks of biological membranes.
• High field charge density wave dynamics.
G. Wong
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Possible future XPCS experiments at the LCLS (cont.)
• Dynamics of molecular and polymer glasses on molecular length scales in regime from 10 ps to 100 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 times are 10 ms to 10 s.
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Possible future XPCS experiments at the LCLS (cont.)
D=kBT/6πηR
τ=R2/2D=6πηR3/kBT
For R=4 nm, τ = 1 ns
Protein dynamics
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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