Methods of studying molecular motion

Methods of studying molecular motion in polymers have three principal objectives. The first is to ascertain what are the states of the molecules, interchange between which constitutes the motion. The second is to observe the rates of this interchange movement. The third is to evaluate the relative energies of the states and of the barrier between them. So studies fall into two categories measurement of the distribution of populations between various conformational states, and the dynamics of interchange between these states. 

Some techniques for examining materials give evidence that motion has occurred, but do not observe that motion directly. A good example of this is X-ray diffraction. We saw in Chapter 9 that drawing of semi-crystalline polymers induces a phase change in the crystalline lamellae at the second yield point. This is proved by the X-ray scattering patterns. Obviously, if the molecules have taken up new positions in the crystal, some sort of motion must have occurred. However, the X-rays do not show how this is happening. So such post hoc methods are not considered further in this chapter. 

Before considering the methods available for studying molecular motion, it is appropriate to remind ourselves of the timescales which the various techniques can access. In Chapter 4, we showed that the frequency of molecular movement and the observation frequency are equal at the transition 

As so often in polymer science, techniques developed for the study of small molecules are appHed to polymer solutions and soHds. The methods available use photons, electrons, or neutrons as probes and usually require times of the order of 10 s or greater to collect the data. On this timescale, the molecules may very well have undergone considerable movement. So it is unlikely that normal 

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These methods for studying molecular motion in solids are well understood and have been well documented in the literature prior to the review period. Therefore, it is not the intention of this review to discuss the underlying principles of these experiments in detail. However, there have been experimental and theoretical advances in all of these areas and these are discussed in Sections 2-4. 

Obtaining information from powder pattern lineshapes (or sideband patterns) always involves matching the experimental lineshapes to those obtained from simulation, and the simulations necessarily involve some model for the molecular motion. This model dependency is an inevitable limitation on this general method for studying molecular motion. The vast majority of studies assume some kind of Markov model for the motion,4 that is, it is assumed that the nucleus/molecule jumps between A discrete sites and that the time taken to... 

Both longitudinal and transverse relaxation are stimulated by time-dependent perturbations acting on the nuclei, such as dipole-dipole coupling. Usually the time-dependence arises from molecular motion, and measurements of relaxation times are a powerful method of studying polymer motion in both solution and the solid state. Detailed discussions of such applications. 

One method of investigating molecular motion in polymer physics is the observation of the temperature dependence of the line width of broad-line NMR spectra. However, since UPEC is composed of polyethylene and urea molecules, the protons in urea molecules must be replaced by deuterons in order to observe the behavior of the polyethylene chain by proton magnetic resonance. For this purpose, deuterated urea molecules were used in the preparation of UPEC (d-UPEC). In the preparation of d-UPEC, deuterated methanol has been used as a solvent in order to prevent proton exchange. In order to compare the new data with the data of bulk polymers, solution-grown polyethylene and extended-chain crystals of polyethylene were also used in the NMR study. 

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. 

An alternative method of studying the molecular motions of a polymeric chain is to measure the complex permitivity of the sample, mounted as dielectric of a capacitor and subjected to a sinusoidal voltage, which produces polarization of the sample macromolecules. The storage and loss factor of the complex permitivity are related to the dipolar orientations and the corresponding motional processes. The application of the dielectric thermal analysis (DETA) is obviously limited to macromolecules possessing heteroatomic dipoles but, on the other hand, it allows a range of frequency measurement much wider than DMTA and its theoretical foundations are better established. 

Special techniques in surface science to study molecular motion in adsorbed layers are a problem that has found little attention in surface science, even though it is of utmost importance. Electron spin resonance is one such method. We discuss diffusion of NO2, rotational motion of ((CH3)3C)2NO and melting of self-assembled layers of spin-labeled fatty acids adsorbed on Al203(0001). 

The molecular dynamic methods can also be very useful in the study of the molecular motions in polymer chains with bulky side groups. 

In order to study molecular motions effectively in systems in which they occur in the kHz region or below, the obvious thing to do is to lower HQ and thereby the resonance frequency. This method is only useful over a limited range of Hq, typically down to a Larmor frequency of a few MHz, because the sensitivity is approx-... 

Spin—lattice relaxation is the time constant for the recovery of magnetiTation along the z-axis in a NMR experiment. Various methods are available for the measurement of spin lattice relaxation times. The interested reader is referred to the series of monographs echted by Levy on Carbon-13 NMR spectroscopy [44, 45] for more details. The energy transfer between nuclear moments and the lattice , the three-dimensional system containing the nuclei, provides the mechanism to study molecular motion, e.g. rotations and translations, with correlation times of the order of the nuclear Larmour frequencies, tens to hundreds of MHz. We will limit our chscussion here to the simple inversion-recovery Tj relaxation time measurement experiment, which, in addition to providing a convenient means for the quick estimation of Tj to establish the necessary interpulse delay in two-dimensional NMR experiments, also provides a useful entry point into the discussion of multi-dimensional NMR experiments. 

The transient ESR technique [82, 83], recently employed in dynamic studies [84], does not suffer from this deficiency. Apparently, the decay of the transient magnetization is determined either by the spin lattice or the spin-spin relaxation time, depending on the motional state of the spin probes [84]. It is this dependence which makes transient ESR such a valuable technique for studying molecular motions over an extremely broad dynamic range. At slow motions the method is limited by the occur-... 

We have seen, on the other hand, that there is a second type of internal motions particularly in very large and mobile molecules, which do not arise from the action of intra-molecular forces but which, on the contrary, are so disposed that during their execution, the potential of the molecule remains constant. These motions are caused by the thermal energy of the individual parts of the large molecule and can best be compared to the chaotic motion of the molecules in a perfect gas. It is natural, therefore, in studying this kind of internal molecular motion, to employ methods similar to those that have proved useful in the theoretical treatment of... 

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