XPCS and Science Opportunities at NSLS-II

Bob LehenyJohns Hopkins University

Coherent Beam

Dynamic light scattering with x-rays

Autocorrelation of intensity…

Gives dynamic structure factor:

I(Q,t’)

t’

g 2(Q

,t)

t

X-ray Photon Correlation Spectroscopy(Image from B. Stevenson, ANL)

Examples of XPCS topics to date:

10-3

100

103

106

109

1012

1015

10-7 10-5 10-3 10-1 101

RamanScattering

LaserPCS

BrillouinScattering

XPCS

Inelastic X-ray Scattering

InelasticNeutron

Scattering

Wavevector [Å-1]

Freq

uenc

y [H

z]

(currently)Soft matter:

Hard matter:

• Polymers

• Antiferromagnetic domain motion

• Charge density wave motion

• surface & interfacial fluctuations

• reptation

• phase separation and mesophase ordering

• Smectic liquid crystals

• Colloids

• gels

• glass transitions

• Order-disorder transitions in alloys

Prospects for NSLS-II

= accumulation time (≈ minimum delay time t)

= source brilliance

= cross section per volume

Signal-to-Noise in g2(Q,t):

(Falus et al., JSR 2006)

• Optimization of coherent flux x 10

• Intrinsic brilliance

Consequences:

• Minimum delay time shortens substantially:

Potential improvement at NSLS-II over APS (8-ID)

- vertical focusing

x 30

• Weaker scatterers become accessible.

= energy bandpass

- wider

10 ms

3002 ~ 100 ns

What occurs in 100 ns? E.g., a 6 nm sphere in water diffuses its diameter

Nanoscale dynamics in aqueous solution become accessible to XPCS

Suggests studies of: • nanoparticle motion/self-assembly in low-viscosity solutions

in bulk and on surfaces• biologically relevant systems

10-3

100

103

106

109

1012

1015

10-7 10-5 10-3 10-1 101

RamanScattering

LaserPCS

BrillouinScattering

XPCS

Inelastic X-ray Scattering

InelasticNeutron

Scattering

Wavevector [Å-1]

Freq

uenc

y [H

z]

Projected for NSLS-II

Overlap with Neutron Spin Echo in reach!

S(Q,t) from 10-11 s < t < 104 s

protein conformation

NSE of higher Q dispersion indicates:

Potentially interesting range of length scales could be accessible at NSLS-II

≈ 10-6 s at Q ≈ 0.03 - 0.1 nm-1

membrane elastic modulus

protein conformation

active fluctuations driven by protein dynamics

•

•

(Image from E. Marcotte, UT Austin)

Fluctuations in lipid membranes

Another membrane system: bicontinuous microemulsions

• Numerous such nanostructured soft materials have intrinsic dynamics in the window that NSLS-II will fill.

oil

waterLong-standing theoretical predictions for dynamical behavior.

Important in applications

Fluctuations at relevant wave vectors (~2/d): too slow for NSE, too short for DLSwell suited for XPCS at NSLS-II

e.g. unique nanostructured materials through polymerization

d ~ 10 nm

templates for chemical reactions

Others likely include lamellar phases (smectics), ringing gels, etc.

(G. Gompper et al., Juelich)

Protein & protein complex conformational fluctuations

• Potentially important for function.

• Deviations of diffusion from rigid-body behavior

• Fluctuations involving large-scale conformational changes can occur on microseconds to milliseconds.

e.g. enzymatic activity

- Demonstrated with NSE for domain-scale fluctuations ( ~ 10 ns)

• Potential strategies to access fluctuations with XPCS:

• Time dependence of diffuse scattering around bragg peaks of protein crystals (???)

Enzyme from E. coli

(H. Yang, UC Berkeley)

(Z. Bu et al., PNAS 2005)

~ 100 s

Other interesting opportunities with XPCS at NSLS-II

1) Expanding polymer research:

Surface fluctuations

Reptation

• Highly successful phenomenological model

• Motion accessible to XPCS (Lumma et al,. PRL, 2001)

• Broader dynamic range will illuminate:

- Rouse-to-reptation crossover

- Specific nature of relaxation (e.g., constraint release)

• Well suited for XPCS (Kim et al., PRL, 2003)

- probe nature of fluctuations at molecular scales: Rg, entanglement length

• Access to shorter times higher Q

1.30

1.20

1.10

1.00

g 2(Q

,t)

log(t)

2) Local dynamics in glassy materials

Approach to glass transition characterized by growing separation of time scales:

“” and “” relaxations

slow, terminal relaxation

fast, localized motion

ergodic fluid

High T

nonergodic solid

Low T

Eg., gelation and aging in nanocolloidal suspensions accessed experimentally

increasing age

inferred

NSLS-II will have dynamic range to track full relaxation spectrum.

APS, 8-ID

Analysis beyond g2(Q,t) required.

Systems far from equilibrium characterized by:

Spatial and/or temporal heterogeneity

Intermittent (non-Gaussian) dynamics

Eg., “degree of correlation”:

dilute colloidal gels

Duri & Cipelletti, EPL (2006)

Large, non-Gaussian fluctuations

temporal heterogeneity

Other ideas from DLS for characterizing intermittent dynamics :

• Higher order moments:

• Speckle-visibility spectroscopy

NSLS-II should make these (and other) analysis approaches feasible for XPCS.

, etc.

(Lemieux and Durian, Appl. Opt. 2001)

(Bandyopadhyay et al., RSI 2006)

Measure variance in speckle intensity as a function of exposure time.

(Note: )

Conclusion

NSLS-II will revolutionize XPCS.

But,

Realizing many of these advancements will require a corresponding improvement in detector technology…

K = detector efficiencyT = total experiment duration = accumulation time = angle subtended by Q of interest = scattering cross section per unit volumeW = sample thickness= 1/attenuation lengthB = source brillianceE/E = normalized energy spreadr = factor depending on source size, pixel size, and slit size