State of the art XPCS and XPCS at the LCLS

Simon Mochrie - Yale University - October 2008

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

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

X-ray scattering measurements at Beamline 8-ID at the Advanced Photon Source at Argonne National Laboratory

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

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

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

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.

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).

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

Amphiphilic complex fluidsAmphiphilic molecules possess two (or more) moieties with very different affinities

e.g. soaps, lecithin, block copolymers

..and organize immiscible fluids

C12E5-H20 phase diagram

R.Strey et al. J. Chem. Soc. Faraday Trans. 86, 2253 (1990)

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.

Theoretical amphiphilic phase diagram

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”

Sponge-to-Lamellar Transition in TEM

CCD image of SAXS pattern from φ=0.20 styrene) triblock copolymer (SEBS) in poly(styrene-ethylene/butylene- polystyrene homopolymer (PS)

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.

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

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.

Dynamics of polymer membranes

Simulation from IBM Almaden

Dynamics of “dilute” polymer membranes via XPCS

Intensity autocorrelations for a 0.03 SEBS volume fraction sample at 160 C at several wavevectors.

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].

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!

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

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.

Sponge phase dynamics: ISFs at 160C and 140C…but the stretching exponent decreases with decreasing temperature!!

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.

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

Sponge phase dynamics: Aging-time dependence of g2s

Compressed exponential ISFs, but no (obvious) aging time dependence.

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.

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

Microemulsion dynamics

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

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.

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

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

THE END