Molecular motion/dynamics, solid-state

M. Dracinsky, P. Hodgkinson, A molecular dynamics study of the effects of fast molecular motions on solid-state NMR parameters, CrystEngComm 15 (2013) 8705-8712. 

Molecular motion in solids has been the object of many studies in the field of physical chemistry of polymers , but dynamic processes in molecular crystals of organic and inorganic compounds are less well investigated. In fact, the average chemist is not aware of the fact that processes like internal rotation or ring inversion proceed in solids quite often with barriers which are not very different from those found for these types of internal motion in the liquid state. Thus, for the equatorial axial ring inversion of fluorocyclohexane values of 42.4 and 43.9 kJ mol have been measured in the liquid and the solid, respectively. The familiar thermal ellipsoids of individual atoms obtained from X-ray studies are qualitative indicators of molecular motion in the crystal, but a more quantitative study of such processes is only possible after appropriate solid state NMR techniques are applied. 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

The analogy drawn between -stacked solids and duplex DNA has provided a useful starting point for experiments to probe and understand DNA-medi-ated CT. As with the -stacked solids, the DNA base pair array can provide an effective medium for long range CT. Mechanistically, however, the differences between DNA and these solid state materials may be even more important to consider. Duplex DNA, as a molecular -stacked structure, undergoes dynamical motion in solution. The time-dependent and sequence-dependent structures that arise serve to modulate and gate CT. Indeed in probing DNA CT as a function of sequence and sequence-dependent structure, we may better understand mechanistically how CT proceeds and how DNA CT may be utilized. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

It has recently been demonstrated that the analysis of MAS sidebands patterns can be used to study molecular dynamics in the solid state [85-88]. Indeed, the line narrowing effect of MAS can be partly offset, or completely eliminated, if the 2H quadrupole tensor is reoriented due to motion on a time scale comparable to (first-order quadrupolar broadening, such motion-induced effects should be less evident in the DQMAS spectrum, as has indeed been observed by Wimperis and colleagues in several deuterated solids [87, 88]. For example, the simulation of the SQ spectrum of tetrathionate dihydrate-cfi yielded the same reorientational rate constant as the previously described quadrupolar echo approach (Fig. 6). 

Solid state 2H NMR parameters are almost exclusively governed by the quadrupole interaction with the electric field gradient (EFG) tensor at the deuteron site.1 8 The EFG is entirely intramolecular in nature. Thus molecular order and mobility are monitored through the orientation of individual C-2H bond directions. Therefore, 2H NMR is a powerful technique for studying local molecular motions. It enables us to discriminate different types of motions and their correlation times over a wide frequency range. Dynamics of numerous polymers has been examined by solid state 2H NMR.1 3,7,9 Dynamic information on polypeptides by NMR is however limited,10 26 although the main-chain secondary structures of polypeptides in the solid have been extensively evaluated by 13C and 15N CP/MAS NMR.27,28... 

A force field for solid state modeling of fluoropolymers predicted a suitable helical conformation but required further improvement in describing intermole-cular effects. Though victory cannot yet be declared, the derived force fields improve substantially on those previously available. Preliminary molecular dynamics simulations with the interim force field indicate that modeling of PTFE chain behavior can now be done in an all-inclusive manner instead of the piecemeal focus on isolated motions and defects required previously. Further refinement of the force field with a backbone dihedral term capable of reproducing the complex torsional profile of perfluorocarbons has provided a parameterization that promises both qualitative and quantitative modeling of fluoropolymer behavior in the near future. 

After the formulation of defect thermodynamics, it is necessary to understand the nature of rate constants and transport coefficients in order to make practical use of irreversible thermodynamics in solid state kinetics. Even the individual jump of a vacancy is a complicated many-body problem involving, in principle, the lattice dynamics of the whole crystal and the coupling with the motion of all other atomic structure elements. Predictions can be made by simulations, but the relevant methods (e.g., molecular dynamics, MD, calculations) can still be applied only in very simple situations. What are the limits of linear transport theory and under what conditions do the (local) rate constants and transport coefficients cease to be functions of state When do they begin to depend not only on local thermodynamic parameters, but on driving forces (potential gradients) as well Various relaxation processes give the answer to these questions and are treated in depth later. 

The application of nuclear magnetic resonance (NMR) spectroscopy to polymer systems has contributed to significant advances in understanding of their structure and dynamical properties at the molecular level. From the analytical point of view, NMR spectroscopy is particularly suitable for a determination of the polymer structure by direct observation of the protons and carbons in different structural moieties. However, until the mid-1970s the application of this technique was limited to polymer solutions and to some elastomers in the solid state with a relatively high degree of the molecular mobility which allows the observation of the motionally narrowed absorption signals. 

Any motion occurring within any polymer system leads to a change of the dynamic mechanical behaviour, in particular its mechanical loss. This makes the dynamic mechanical measurements the most appropriate technique for studying solid-state transitions. However, in order to assign the molecular motions involved in the considered transition from only the dynamic mechanical results, it is necessary to perform systematic studies on a large series of compounds with gradual modification of their chemical structure. Such an approach has been used in some cases, but it requires lots of effort in synthesising the various compounds. 

In another paper in this issue [1], the molecular motions involved in secondary transitions of many amorphous polymers of quite different chemical structures have been analysed in detail by using a large set of experimental techniques (dynamic mechanical measurements, dielectric relaxation, H, 2H and 13C solid state NMR), as well as atomistic modelling. 

For the investigation of the molecular dynamics in polymers, deuteron solid-state nuclear magnetic resonance (2D-NMR) spectroscopy has been shown to be a powerful method [1]. In the field of viscoelastic polymers, segmental dynamics of poly(urethanes) has been studied intensively by 2D-NMR [78, 79]. In addition to ID NMR spectroscopy, 2D NMR exchange spectroscopy was used to extend the time scale of molecular dynamics up to the order of milliseconds or even seconds. In combination with line-shape simulation, this technique allows one to obtain correlation times and correlation-time distributions of the molecular mobility as well as detailed information about the geometry of the motional process [1]. 

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