Model-free description of polymer-coated gold nanoparticle dynamics in aqueous solutions obtained by Bayesian analysis of neutron spin echo data

We present a neutron spin echo study of the nanosecond dynamics of polyethylene glycol (PEG) functionalizednanosized gold particles dissolved in D2O at two temperatures and two different PEG molecular weights (400Dand 2000D). The analysis of the neutron spin echo data was performed by applying a Bayesian approach to thedescription of time correlation function decays in terms of exponential terms, recently proved to be theoreticallyrigorous. This approach, which addresses in a direct way the fundamental issue of model choice in any dynamicalanalysis, provides here a guide to the most statistically supported way to follow the decay of the intermediatescattering functions I (Q, t ) by basing on statistical grounds the choice of the number of terms required for thedescription of the nanosecond dynamics of the studied systems. Then, the presented analysis avoids from the startresorting to a preselected framework and can be considered as model free. By comparing the results of PEGcoatednanoparticles with those obtained in PEG2000 solutions, we were able to disentangle the translationaldiffusion of the nanoparticles from the internal dynamics of the polymer grafted to them, and to show that thepolymer corona relaxation follows a pure exponential decay in agreement with the behavior predicted by coarsegrained molecular dynamics simulations and theoretical models. This methodology has one further advantage:in the presence of a complex dynamical scenario, I (Q, t ) is often described in terms of the Kohlrausch-Williams-Watts function that can implicitly represent a distribution of relaxation times. By choosing to describe the I (Q, t )as a sum of exponential functions and with the support of the Bayesian approach, we can explicitly determinewhen a finer-structure analysis of the dynamical complexity of the system exists according to the available datawithout the risk of overparametrization. The approach presented here is an effective tool that can be used ingeneral to provide an unbiased interpretation of neutron spin echo data or whenever spectroscopy techniquesyield time relaxation data curves.