Scattering fingerprints of two-state dynamics

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle’s mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on “scattering fingerprints” of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures – the intermediate scattering function and dynamic structure factor – and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and X-ray scattering scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport.

Kinetics and Thermodynamics of Fe-X (X= Al, Cr, Mn, Ti, B, and C) Melts under High Pressure

The kinetic properties such as diffusivity and viscosity of the metal melt are the foundations to reveal the structure evolutions and the glass formation abilities during solidification of the investigated alloy, thus, to control the microstructures, defects and properties of materials. In this work, ab initio molecular dynamics simulations were utilized to investigate the kinetic and thermodynamic properties and the structural relaxations of Fe-X (X = 10-15 wt% Al, Cr, Mn and Ti, or 1-2wt% B and C) melts under various temperature and external pressure, which are in line with the interested concentration range of multi-component Fe-based alloys. The kinetics and structural relaxations are characterized by mean squared displacement, velocity autocorrelation function and self-intermediate scattering function. The thermodynamics properties including entropy and heat capacity are calculated by combining the vibrational and electronic contributions based on vibrational and electronic density of states. The predicted kinetics and thermodynamics properties under high temperature and pressure agree well with the experimental and theoretical results while the connection among structural relaxations and diffusion are revealed based on the Stokes-Einstein relation and the Hall-Wolynes (HW) relation. This work provides an insight into the structure-property relationships of metal melts, which are essential in the development of advanced multi-component Fe-based alloys.

Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime

Stochastic wave function formalism is briefly introduced and applied to study the dynamics of open quantum systems; in particular, the diffusion of Xe atoms adsorbed on a Pt(111) surface. By starting from a Lindblad functional and within the microscopic Caldeira–Leggett model for linear dissipation, a stochastic differential equation (Ito^-type differential equation) is straightforwardly obtained. The so-called intermediate scattering function within the ballistic regime is obtained, which is observable in Helium spin echo experiments. An ideal two-dimensional gas has been observed in this regime, leading to this function behaving as a Gaussian function. The influence of surface–adsorbate interaction is also analyzed by using the potential of two interactions describing flat and corrugated surfaces. Very low surface coverages are considered and, therefore, the adsorbate–adsorbate interaction is safely neglected. Good agreement is observed when our numerical results are compared with the corresponding experimental results and previous standard Langevin simulations.

Data Analysis and Background Subtraction in Neutron Spin Echo Spectroscopy

With the constantly improving performance of neutron spin echo (NSE) spectrometers it becomes possible to perform measurements on increasingly complex samples and to study more and more delicate effects. To properly study such effects, proper background correction becomes increasingly important. In this paper, we will review different methods to subtract the buffer from NSE measurements and study the effect of small errors in the subtraction of the background. In the large dynamic range of modern neutron spin-echo spectrometers multiple effects become visible in a single measurement. Specifically, for vesicles both membrane undulations and translational diffusion have an effect on the intermediate scattering function in the NSE time window and here, we will investigate how taking this into account differently affects the results obtained from data analysis.

Self-generated persistent random forces drive phase separation in growing tumors

A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Cells dynamics in the core is glass-like whereas those in the periphery undergo diffusive or super-diffusive behavior. Quantification of heterogeneity using the mean square displacement or the self-intermediate scattering function, which involves averaging over the cell population, hides the complexity of the collective movement. Using the t-distributed stochastic neighbor embedding (t-SNE), a popular unsupervised machine learning dimensionality reduction technique, we show that the phase space structure of an evolving colony of cells, driven by cell division and apoptosis, partitions into nearly disjoint sets composed principally of core and periphery cells. The non-equilibrium phase separation is driven by the differences in the persistence of self-generated active forces induced by cell division. Extensive heterogeneity revealed by t-SNE paves way towards understanding the origins of intratumor heterogeneity using experimental imaging data.

Kinematical Theory of Scattering

The chapter introduces the kinematical theory of scattering, which is based on the Born approximation. It is shown that the neutron scattering response function can be written as the time Fourier transform of a correlation function, or intermediate scattering function. Several general properties of the correlation function are derived, and the response function is shown to satisfy the Principle of Detailed Balance. The distinction between static and dynamic correlations is explained, and their correspondence to elastic and inelastic scattering is established. The meaning of the static approximation is explained, and the link between the dynamical part of the response function and the absorptive part of the generalized susceptibility via the Fluctuation-Dissipation theorem is established. Some general sum rules are proved, and a spectral-weight function is defined. Response functions are obtained for some simple models.

Predictive relation for the α-relaxation time of a coarse-grained polymer melt under steady shear

We examine the influence of steady shear on structural relaxation in a simulated coarse-grained unentangled polymer melt over a wide range of temperature and shear rates. Shear is found to progressively suppress the α-relaxation process observed in the intermediate scattering function, leading ultimately to a purely inertially dominated β-relaxation at high shear rates, a trend similar to increasing temperature. On the basis of a scaling argument emphasizing dynamic heterogeneity in cooled liquids and its alteration under material deformation, we deduce and validate a parameter-free scaling relation for both the structural relaxation time τα from the intermediate scattering function and the “stretching exponent” β quantifying the extent of dynamic heterogeneity over the entire range of temperatures and shear rates that we can simulate.

Coincident Correlation between Vibrational Dynamics and Primary Relaxation of Polymers with Strong or Weak Johari-Goldstein Relaxation

The correlation between the vibrational dynamics, as sensed by the Debye-Waller factor, and the primary relaxation in the presence of secondary Johari-Goldstein (JG) relaxation, has been investigated through molecular dynamics simulations. Two melts of polymer chains with different bond length, resulting in rather different strength of the JG relaxation are studied. We focus on the bond-orientation correlation function, exhibiting higher JG sensitivity with respect to alternatives provided by torsional autocorrelation function and intermediate scattering function. We find that, even if changing the bond length alters both the strength and the relaxation time of the JG relaxation, it leaves unaffected the correlation between the vibrational dynamics and the primary relaxation. The finding is in harmony with previous studies reporting that numerical models not showing secondary relaxations exhibit striking agreement with experimental data of polymers also where the presence of JG relaxation is known.

Efficient data extraction from neutron time-of-flight spin-echo raw data

Neutron spin-echo spectrometers with a position-sensitive detector and operating with extended time-of-flight-tagged wavelength frames are able to collect a comprehensive set of data covering a large range of wavevector and Fourier time space with only a few instrumental settings in a quasi-continuous way. Extracting all the information contained in the raw data and mapping them to a suitable physical space in the most efficient way is a challenge. This article reports algorithms employed in dedicated software, DrSpine (data reduction for spin echo), that achieves this goal and yields reliable representations of the intermediate scattering function S(Q, t) independent of the selected `binning'.