Page 56 - ILL Annual Report 2019

SOFT CONDENSED MATTER
Alessio De Francesco. Italian
Consiglio nazionale delle Ricerche (CNR, IT) c/o OGG, Grenoble.
’In recent years, my work has been devoted to the search for data analysis methods that are able to provide solid and statistically based support for the results of analyses thanks to a Bayesian approach.’
A Bayesian approach to the
study of time correlation
functions in a soft complex system
Spin-echo spectrometers IN11 and IN15
If we could repeat a measurement many times, the average of the results would provide a
robust estimate of our observations. However,
a measurement is usually a single-time event
from which some general law needs to be deduced. In this situation, the help of Bayesian inference [1], here implemented within a Markov Chain Monte Carlo (MCMC) numerical recipe integrated with a Reversible Jump algorithm
[2], becomes invaluable. Furthermore, the
use of a multi-exponential expansion of the Neutron Spin Echo (NSE) signal, in principle extendable to any time correlation function [3], enabled us to capture the ‘fine-structure’ of relaxation processes in polymer-coated, gold nano particles (PEG-AuNP) (figure 1, left) and to compare them with the dynamics of the free polymer chain solution. Disentanglement of the internal dynamics of polymer chains from other contributions, whenever achievable, would not be possible with a commonly used description of the time correlation function decay in terms of stretched exponentials.
Figure 1
Left panel) Sketch of a functionalised PEG AuNP.
Right panel) Representative series of NSE curves representing I(Q, t)/I(Q, 0) of the PEG2000 AuNPs dispersed in D2O at neutron wavelength λ = 10 Å and a temperature of T = 280 K (symbols). The Q values increase from top to bottom. The lines represent the best fits to the data.
AUTHORS
A. De Francesco (CNR IOM c/o ILL, Grenoble, France) L. Scaccia (Università di Macerata, Italy)
E. Guarini (Università di Firenze, Italy)
U. Bafile (CNR IFAC, Firenze, Italy)
P. Falus (ILL)
M. Maccarini (Université Grenoble Alpes, Grenoble, France) A. Cunsolo (NSLS-II, BNL, Upton, USA)
ARTICLE FROM
Phys. Rev. E (2019)—doi: 10.1103/PhysRevE.99.052504
REFERENCES
[1] T. Bayes and R. Price, Philos. Trans. R. Soc. 53 (1763) 370
[2] P.J. Green, Biometrika 82 (1995) 711
[3] F. Barocchi, U. Bafile and M. Sampoli, Phys. Rev. E 85 (2012)
022102 and F. Barocchi, E. Guarini and U. Bafile, Phys. Rev. E
90 (2014) 032106
[4] A. De Francesco, L. Scaccia, R.B. Lennox, E. Guarini, U. Bafile,
P. Falus and M. Maccarini, Phys. Rev. E 99 (2019) 052504
In recent decades, the steady improvement of instrument performance in research, in the field of spectroscopy in particular, has made an enormous amount of new data available on a variety of physical systems. While in the early years a merely phenomenological observation
of new spectral features was considered a result per
se warranting scientific attention, increased accuracy
in data acquisition has shifted the objective towards a more quantitative and physically insightful scrutiny of
the line shape. Rather than minimising uncertainties, the improved quality of measurements has often paradoxically encouraged bold speculations, ultimately challenging scientific rigour and accuracy. To overthrow this course
of events, new data analysis protocols capable of quantifying the reliability of a given model are needed, in order to avoid over-parameterisation, minimise subjectivity in the choice of model and, ultimately, warn researchers off hazardous speculations.
To advance along this difficult route we applied a Bayesian approach, previously used on (energy-resolved) Brillouin neutron and X-ray spectra, to model the time decay of the intermediate scattering functions (ISFs) measured by spin-echo spectroscopy (NSE) of aqueous solutions of polymer-functionalised gold nanoparticles (figure 1, right) [4].
ANNUAL REPORT 2019