X-ray Photon Correlation Spectroscopy (XPCS) and Science Opportunities at NSLS-II

1. XPCS and Science Opportunities at NSLS-II Bob Leheny Johns Hopkins University

2. (Image from B. Stevenson, ANL) Dynamic light scattering with x-rays X-ray Photon Correlation Spectroscopy Coherent Beam Autocorrelation of intensity… I(Q,t’) t’ Gives dynamic structure factor: g2(Q,t) t

3. Inelastic X-ray Scattering Inelastic Neutron Scattering Raman Scattering Brillouin Scattering Laser PCS Frequency [Hz] XPCS (currently) Wavevector [Å-1] Examples of XPCS topics to date: Hard matter: • Order-disorder transitions in alloys • Charge density wave motion • Antiferromagnetic domain motion Soft matter: • Smectic liquid crystals • Polymers • Colloids • gels • surface & interfacial fluctuations • glass transitions • reptation • phase separation and mesophase ordering

4. 10 ms ~ 100 ns 2 300 Signal-to-Noise in g2(Q,t): Prospects for NSLS-II (Falus et al., JSR 2006) = accumulation time (≈ minimum delay time t) = source brilliance = cross section per volume = energy bandpass Potential improvement at NSLS-II over APS (8-ID) x 30 • Intrinsic brilliance x 10 • Optimization of coherent flux - vertical focusing - wider Consequences: • Weaker scatterers become accessible. • Minimum delay time shortens substantially:

5. Inelastic X-ray Scattering Inelastic Neutron Scattering Raman Scattering Brillouin Scattering Laser PCS Frequency [Hz] Projected for NSLS-II XPCS Wavevector [Å-1] What occurs in 100 ns? Overlap with Neutron Spin Echo in reach! S(Q,t) from 10-11 s < t < 104 s 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

6. Fluctuations in lipid membranes (Image from E. Marcotte, UT Austin) at Q ≈ 0.03 - 0.1 nm-1 t ≈ 10-6 s NSE of higher Q dispersion indicates: Potentially interesting range of length scales could be accessible at NSLS-II protein conformation membrane elastic modulus protein conformation • • active fluctuations driven by protein dynamics

7. d ~ 10 nm Another membrane system: bicontinuous microemulsions Long-standing theoretical predictions for dynamical behavior. water oil Important in applications e.g. unique nanostructured materials through polymerization templates for chemical reactions Fluctuations at relevant wave vectors (~2p/d): too slow for NSE, too short for DLS well suited for XPCS at NSLS-II (G. Gompper et al., Juelich) • Numerous such nanostructured soft materials have intrinsic dynamics in the window that NSLS-II will fill. Others likely include lamellar phases (smectics), ringing gels, etc.

8. Protein & protein complex conformational fluctuations • Fluctuations involving large-scale conformational changes can occur on microseconds to milliseconds. t ~ 100 ms • Potentially important for function. e.g. enzymatic activity Enzyme from E. coli (H. Yang, UC Berkeley) • Potential strategies to access fluctuations with XPCS: • Time dependence of diffuse scattering around bragg peaks of protein crystals (???) • Deviations of diffusion from rigid-body behavior - Demonstrated with NSE for domain-scale fluctuations (t ~ 10 ns) (Z. Bu et al., PNAS 2005)

9. • Access to shorter times higher Q Other interesting opportunities with XPCS at NSLS-II Reptation • Highly successful phenomenological model 1) Expanding polymer research: • Motion accessible to XPCS (Lumma et al,. PRL, 2001) • Broader dynamic range will illuminate: - Specific nature of relaxation (e.g., constraint release) - Rouse-to-reptation crossover Surface fluctuations • Well suited for XPCS (Kim et al., PRL, 2003) - probe nature of fluctuations at molecular scales: Rg, entanglement length

10. High T Low T increasing age ergodic fluid nonergodic solid 2) Local dynamics in glassy materials Approach to glass transition characterized by growing separation of time scales: “b” and “a” relaxations fast, localized motion slow, terminal relaxation accessed experimentally Eg., gelation and aging in nanocolloidal suspensions inferred APS, 8-ID NSLS-II will have dynamic range to track full relaxation spectrum.

11. Systems far from equilibrium characterized by: Intermittent (non-Gaussian) dynamics Analysis beyond g2(Q,t) required. Spatial and/or temporal heterogeneity Eg., “degree of correlation”: dilute colloidal gels Large, non-Gaussian fluctuations temporal heterogeneity Duri & Cipelletti, EPL (2006)

12. • Higher order moments: Other ideas from DLS for characterizing intermittent dynamics : (Lemieux and Durian, Appl. Opt. 2001) , etc. (Note: ) • Speckle-visibility spectroscopy (Bandyopadhyay et al., RSI 2006) Measure variance in speckle intensity as a function of exposure time. NSLS-II should make these (and other) analysis approaches feasible for XPCS.

13. Conclusion NSLS-II will revolutionize XPCS. But, Realizing many of these advancements will require a corresponding improvement in detector technology…

14. K = detector efficiency • T = total experiment duration • = accumulation time • = angle subtended by Q of interest • = scattering cross section per unit volume W = sample thickness • = 1/attenuation length B = source brilliance DE/E = normalized energy spread r = factor depending on source size, pixel size, and slit size