A revised jump-diffusion and rotation-diffusion model

Abstract

Quasi-elastic neutron scattering (QENS) has many applications that are directly related to the development of high-performance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model (rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate (MSH) sample are fitted well for the Q range from 0.3 Å−1 to 1.9 Å−1 and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water (or bound water) C and the confining radius of mobile water a 0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient D t, the average translational residence time τ 0, the rotational diffusion coefficient D r, and the mean squared displacement (MSD) 〈 u 2 〉 . The rJRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.

Role of Exchange Cations and Layer Charge on the Dynamics of Confined Water

“…In QENS experiments, the measured neutron intensity, I ( Q , E ), is proportional to the dynamic structure factor, S ( Q , E ), which describes the microscopic dynamics of a scattering system and has been traditionally analyzed using different models. − ,,− We used a simplified form of the rJRM, , which has newly been shown a good model for fitting QENS spectral data from water confined in cement pastes. In the simplified rJRM (hereafter srJRM), S ( Q , E ) is described by elastic and inelastic scattering component, arising from vibrational, translational, and rotational motions of the hydrogen atoms or water molecules as follows S ( Q , E ) = A { C δ false( E false) + false( 1 − C false) false[ S T ( Q , E ) ⊗ S R ( Q , E ) false] } ⊗ R ( Q , E ) + BG where Q is the neutron scattering vector, E the neutron energy transfer, A the Debye–Waller factor (DWF), C the ratio of bound/immobile hydrogens originating an elastic signal, δ( E ) the Dirac delta function describing the immobile hydrogen atoms, ⊗ is the convolution operator, BG is the flat background, S T ( Q , E ) and S R ( Q , E ) are, respectively, the scattering function of translational and rotational water diffusion, and R ( Q , E ) represents the resolution function obtained from the measured vanadium spectra.…”

“…The srJRM model presented in eqs – is a simplified form of the rJRM , in two aspects. First, the elastic contribution to S T ( Q , E ) in the rJRM model is omitted, because the very small value arises from mobile water within pores or interlayer space sized larger than 10 Å .…”

“…The study of water within the interlayer space of swelling clay minerals by neutron spectroscopy − has gained significant attention in recent years because of its ability to unveil the mobility and reactivity of confined water, features that strongly influence many chemical and physical properties important for medical − and geotechnical applications. , The sodium (Na) forms of montmorillonite (Mt) and hectorite (Ht), 2:1 phyllosilicates (smectites) with aluminum (Mt) or magnesium (Ht) octahedral sheets bonded between two silicon tetrahedral sheets that exist as stacked unit layers separated by an interlayer space, are among the most commonly studied clay minerals because of widespread and long-standing use in many industrial sectors. , Na–Mt is dioctahedral, in which two of the three available octahedral sites are occupied by (predominantly) Al 3+ , whereas Na–Ht is trioctahedral in which all three octahedral sites are occupied by (mostly) Mg 2+ . The constituent layers have some degree of isomorphic substitution by cations of lower valence (e.g., octahedral Mg 2+ for Al 3+ or tetrahedral Al 3+ for Si 4+ in Mt; octahedral Li + for Mg 2+ in Ht), resulting in a net negative surface charge, largely compensated by hydrated, exchangeable interlayer cations.…”

“…where j l (l = 0, 1, 2, 3) is the l-order spherical Bessel function, D r the water rotational diffusion coefficient, and a OH the radius of gyration taken as 0.98 for the O−H distance in a The srJRM model presented in eqs 1−5 is a simplified form of the rJRM 6,7 in two aspects. First, the elastic contribution to S T (Q,E) in the rJRM model is omitted, because the very small value arises from mobile water within pores or interlayer space sized larger than 10 Å.…”

“…In QENS experiments, the measured neutron intensity, I(Q,E), is proportional to the dynamic structure factor, S(Q,E), which describes the microscopic dynamics of a scattering system and has been traditionally analyzed using different models. 6−8,25,28−32 We used a simplified form of the rJRM, 6,7 which has newly been shown a good model for fitting QENS spectral data from water confined in cement pastes. In the simplified rJRM (hereafter srJRM), S(Q,E) is described by elastic and inelastic scattering component, arising from vibrational, translational, and rotational motions of the hydrogen atoms or water molecules as follows…”