Motional frequencies

Both Ti and T2 relaxations of water protons are mainly due to fluctuating dipole-dipole interactions between intra- and inter-molecular protons [62]. The fluctuating magnetic noise from all the magnetic moments in the sample (these moments are collectively tamed the lattice) includes a specific range of frequency components which depends on the rate of molecular motion. The molecular motion is usually represented by the correlation time, xc, i.e., the average lifetime staying in a certain state. A reciprocal of the correlation time corresponds to the relative frequency (or rate) of the molecular motion. The distribution of the motional frequencies is known as the spectral density function. 

In order to go further in the characterisation of the processes involved in the secondary transitions, Starkweather [2-4] applied the transition state theory. It leads to expressing the motional frequency as ... 

The persistence of the fluctuating local fields before being averaged out by molecular motion, and hence their effectiveness in causing relaxation, is described by a time-correlation function (TCF). Because the TCF embodies all the information about mechanisms and rates of motion, obtaining this function is the crucial point for a quantitative interpretation of relaxation data. As will be seen later, the spectral-density and time-correlation functions are Fourier-transform pairs, interrelating motional frequencies (spectral density, frequency domain) and motional rates (TCF, time domain). 

As will be shown later, the NMR relaxation parameters are frequency-dependent quantities. Therefore, we are interested in ways to measure these frequencies associated with the nature of the rotational motion. The Fourier transform of the TCF, which evolves in the time domain, yields a spectrum of motional frequencies in which the value of the function, J((o), at each frequency is known as the spectral density423... 

Not all of these parameters provide information in a direct manner nonetheless, the inferred information is important in characterizing motional frequencies and amplitudes in macromolecules. Fundamental to this characterization is the measurement of relaxation data over a range of temperature. As an example, we report in this section very preliminary results on the Ti and Tip behavior for the carbons in a 90% isotactic, 70% crystalline sample of poly(propylene), PP. 

An inhomogeneous broadening refers to the collective motion frequency of the adsorbate and is the consequence of an inhomogeneous distribution of individual molecules either due to heterogeneity of adsorption sites or to nonhomogeneous in-termolecular distances. Whilst for a perfect ordered layer a sharp, symmetric band is expected, random occupation, island formation, and repulsive or attractive interactions give rise to a variety of characteristic lineshapes [21]. 

Vibrational class Vibrational motion Frequencies cm Intensity... 

Anharmonic nuclear motion, frequency changes, mode mixing, etc. 

The transverse magnetization of the REDOR experiment decays as a function of the decoupling field [23, 24]. Dipolar decoupling may be strongly interfered with by molecular motion, if any, when the motional frequency is of the same order of magnitude as the decoupling field and, hence, the transverse relaxation times (Ta s) are significantly shortened. In... 

Therefore, the combination of powder pattern and relaxation studies is very powerful in that the powder pattern analysis has seen the sum of the motions, and relaxation data can be used to selectively characterize given motional frequencies. Other relaxation parameters such as Tip can be used to pursue different frequency regimes. Again, solid-state NMR has been shown to be a very powerful approach for characterizing dynamics. Here the... 

Here, the first term empirically describes the motional averaging of the distribution of local conformations, where 5i is half the linewidth due to the distribution, a describes steepness of the transition, and To is a characteristic transition temperature. The second term describes the interference between motion and DD [58], where A is the reduction factor of the second moment M2, T is the correlation time of motion and cdi is the strength of DD. This shows that the interference is effective when the motional frequency comes close to the frequency of DD (tmi 1). The third term So is the intrinsic linewidth. 

The variation of the cation-motion frequency with cation charge shows that the spectrum probes a force field in which Coulombic interactions are important. This leads to the conclusion that it also should vary significantly with the charge on the anionic site. 

Figure 6. Plot of X (defined in text) versus cation motion frequency for MPSSA (6.9) ionomer films.

In the experiments described here, two separate techniques have been used for interferometric characterization of the shocked material s motion frequency domain interferometry (FDI) [69, 80-81] and ultrafast 2-d spatial interferometric microscopy [82-83]. Frequency domain interferometry was used predominantly in our early experiments designed to measure free surface velocity rise times [70-71]. The present workhorse in the chemical reaction studies presented below is ultrafast interferometric microscopy [82], This method can be schematically represented as in Figure 6. A portion of the 800 nm compressed spectrally-modified pulse from the seeded, chirped pulse amplified Ti sapphire laser system (Spectra Physics) was used to perform interferometry. The remainder of this compressed pulse drives the optical parametric amplifier used to generate tunable fs infrared pulses (see below). 

The locking rf fields can have a range of amplitudes. Thus a range of motional frequencies can be investigated by simply changing the amplitude of HH or Hq. 

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