Inelastic neutron scattering applied to the investigation of collective excitations in topologically disordered matter

Abstract

Inelastic neutron scattering techniques are introduced here as one of the most important experimental techniques in the investigation of collective excitations in fluids (liquids and compressed gases) and amorphous solids. The correlation functions involved, the spectra of which are determined in inelastic neutron scattering experiments, the dispersion relations of the collective excitations and how they are obtained from the measured spectra and finally two of the most often used instrumental techniques are briefly discussed.

Experimental mapping of short-wavelength phonons in proteins

“…Because of amorphous protein samples that lack a preferred orientation, it is not easy to explicitly differentiate between longitudinal and transverse acoustic modes. 26 , 39 , 44 However, the calculated values of low-frequency phonon-like excitations can be attributed to the transverse acoustic mode, which is in good agreement with recently published molecular dynamics simulations 45 and experiments. 30 , 46 , 47 Furthermore, for , an apparent softening of the localized intra-protein vibrations with an increase in temperature is observed, as indicated by the decrease in the excitation energy in both samples, whereas the acoustic mode is nearly temperature independent.…”

“…The dispersion curves overlaid on top of 2-dimensional (2D) raw INS spectra for dGFP samples at T = 150 K and Q = 0.64 Å −1 confirm that the calculated excitation energies are larger than the instrumental resolution ( Figures 2 C and 2D). Furthermore, the bending of the energy dispersion curve occurs at the boundary of the acoustic branch (i.e., Q m ∼ 1.1 Å −1 ), suggesting the existence of a pseudo-Brillouin zone 26 with a finite group velocity up to the value of Q m , after which a plateau develops or starts to deviate from the usual Q dependence. The value of Å −1 corresponds to the topological disorder length scale in the sample or half of the distance to the nearest pseudo-reciprocal lattice point.…”

“… 24 Compared with IXS, coherent inelastic neutron scattering (INS) technique is exceptionally suitable for investigating low-frequency collective excitations 24 , 25 and has been applied successfully to study collective density fluctuations in amorphous materials, glasses, or liquids. 25 , 26 , 27 Moreover, INS has a significant advantage when studying biological samples because it has much better resolution at the biologically relevant energy and length scales but causes almost no radiation damage compared with IXS. However, a large amount of fully deuterated protein samples is required for high-resolution INS experiments because of the huge incoherent scattering cross-section of hydrogen atoms to neutrons, hindering mapping and analysis of such collective motions in past decades.…”

Collective Excitations in Protein as a Measure of Balance Between its Softness and Rigidity

“…Inelastic X-ray scattering (IXS) technique is a unique tool to study the collective density fluctuations in amorphous materials, glasses, or liquids. − High energy resolution of the order of milli-electronvolt (meV) achieved by IXS spectrometers allows a precise investigation of highly damped collective modes and the phonon dispersion in topologically disordered systems. − Previously, there are evidence from inelastic neutron scattering (INS) experiments of collective motions in proteins, which are similar to the boson peak in the glass-forming liquids due to the collective excitations or density fluctuations. − Furthermore, IXS, INS, Brillouin neutron spectroscopy (BNS), and molecular dynamic (MD) simulations have revealed the propagation of acoustic phonons in proteins and their hydration water in the longer wavelength limit corresponding to the length scale larger than ∼ 1 nm. − However, very few studies reported investigation of local excitations within the protein secondary structure on a scale shorter than 1.5 nm. ,,, A recent IXS experiment by Wang et al has studied the collective excitations in a globular protein lysozyme and concluded that the phonon energy softening and phonon population enhancement in hydrated protein (both native and denatured) is induced by the hydration shell . On the other hand, MD simulation results clearly suggested that the strong coupling between the dynamics of a globular protein, such as maltose binding protein and its hydration shell, exists rather than protein dynamics being slaved to the hydration water .…”

Criterion of superfluidity, elementary excitations, and heat capacity singularity in superfluid helium

“…full circles -the experimental data of Copley and Rowe [11], vertical bars -the experimental data of Glaeser et al [12], solid curve -the numerical calculation of the dispersion equation [13].…”