The molecular-level mobility and structure of polymers and proteins occur on timescales of picoseconds – nanoseconds and length scales of angstroms – nanometers. We use neutron scattering to investigate these time and spatial scales. Neutron scattering is similar to X-ray scattering, except neutrons interact with the nucleus of the atoms, whereas electrons interact with the electron cloud of the atoms in X-ray scattering. While the interaction strength between X-rays and atoms depends on the size of the electron cloud, the interaction strength of a neutron with an atom varies randomly with atomic number. In addition, neutron scattering can capture not only the structure, but also dynamics on small length scales.
We use quasi-elastic neutron scattering [QENS] to measure polymer dynamics. The QENS instrument we use are the Cold Neutron Chopper Spectrometer (CNCS), Disk Chopper Spectrometer (DCS), Backscattering Spectrometer (BASIS), and High Flux Backscattering Spectrometer (HFBS) and they cover a wide dynamic range from 0.5ps to 2.5ns. These measurements are made at NIST Center for Neutron Research in Gaithersburg, MD and Spallation Neutron Source ORNL in Oak Ridge, TN.
The instruments measure scattered intensity as a function of energy and spatial scale. The energy the neutron exchanges with the atoms in the sample is in the frequency domain, therefore we inverse-Fourier transform the data to the time domain (see Figure below). Decay in S(q,t) as a function of time indicates mobility on the timescale of the measurement. We can fit this decay to a stretch exponential equation:
\begin{aligned}
KWW=EISF(\mathbf{Q})+(1-EISF(\mathbf{Q}))e^{-(\frac{t}{\tau(\mathbf{Q})})^\beta(\mathbf{Q})}
\end{aligned}
Physically relevant parameters such as the polymer relaxation time and fraction of mobile atoms in the system can be extracted from the equation. In addition, S(q,t) allows us to compare experimental data with MD simulation data providing a way to verify MD simulations.
Small-angle neutron scattering [SANS] is a technique we use to measure structure on length scales of angstroms nanometers. SANS relies on a contrast in neutron scattering-length densities between the structure to be detected and the surrounding medium. For example, we have used SANS to investigate the structure of nanoparticle-filled solid polymer electrolytes (PEO + LiClO4 + Al2O3). The scattering length density of the alumina nanoparticles is sufficiently different from the surrounding PEO/LiClO4 medium, and therefore nanoparticle aggregation can be observed. The figure below illustrates intensity as a function of the wave vector q, (q is inversely proportional to the spatial scale) for this system. The feature at large q is associated with the primary nanoparticle size, and the increase in intensity with decreasing q indicates nanoparticle aggregation.
Unlike QENS, TR-SANS allows the examination of processes that occur over a time-scale of hours or days rather than ns. Neutron scattering intensity (I) is proportional to the square of the scattering length density (ρ) difference between two phases, such as a solvent and a dissolved particle:
\begin{aligned}
I\sim nP(Q)V^2(\rho_{particle}-\rho_{solvent})^2
\end{aligned}
The scattering intensity also depends on the particle volume V, the number of particles n, and a particle shape function P(Q). Using isotopic labeling (such as by substituting deuterium for hydrogen), we can adjust the scattering length density of one or more species to create or eliminate contrast, so that we choose what species are “visible” to the neutron beam. We use this method to study the mechanism of block copolymer (BC) transport between detergent/BC micelles, a key step in synthesizing biomimetic membranes in which these polymers incorporate transmembrane proteins. By mixing micelles containing deuterated and unsubstituted polymer, we can obtain the extent of exchange from the change in the micelles’ scattering length density contrast over time.
