XPCS and Science Opportunities at NSLS-II Bob Leheny Johns 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: Raman Scattering Laser PCS Brillouin Scattering XPCS Inelastic X-ray Scattering Inelastic Neutron Scattering Wavevector [Å -1 ] Frequency [Hz] (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 g 2 (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 ~ 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 Raman Scattering Laser PCS Brillouin Scattering XPCS Inelastic X-ray Scattering Inelastic Neutron Scattering Wavevector [Å -1 ] Frequency [Hz] Projected for NSLS-II Overlap with Neutron Spin Echo in reach! S(Q,t) from s < t < 10 4 s

protein conformation NSE of higher Q dispersion indicates: Potentially interesting range of length scales could be accessible at NSLS-II  ≈ s at Q ≈ 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 water Long-standing theoretical predictions for dynamical behavior. Important in applications Fluctuations at relevant wave vectors (~2  /d): too slow for NSE, too short for DLS well 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: R g, entanglement length Access to shorter times higher Q

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 g 2 (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 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  E/E = normalized energy spread r = factor depending on source size, pixel size, and slit size