Timescale of molecular motion

One further point needs to be mentioned when probing the feasibility of a particular experiment. Apart from its dependence on temperature and concentration (for instance of ions, solutes, impurities, isotopes), relaxation times - in particular the longitudinal relaxation time Tj - depend on the field strength. This can be understood from the concept that energy exchange is most efficient if the timescale of molecular motion is equal to the Larmor frequency. Often, molecular motion takes place over a wide range of frequencies, so that the func-... 

Fig. 7.1.3 [Blii2] NMR-timescale of molecular motion and filter transfer functions of pulse sequences which can be utilized for selecting magnetization according to the timescale of molecular motion. The concept of transfer functions provides an approximative description of the filters. A more detailed description needs to take into account magnetic-field dependences and spectral densities of motion. The transfer functions shown for the saturation recovery and the stimulated-echo filter apply in the fast motion regime.

Another recent and important development " has been that of combining SERS with FSRS, thus opening the prospect of Raman spectroscopic detection of single molecules on the ultrafast timescale of molecular motion. Proof-of-prindple studies have been reported on small organic molecules, but studies on metal-centred species will undoubtedly come. More generally, tandem or hybrid methods involving innovative combination of two or... 

For high solute concentrations in the absence of crystallization, Vogel-Tammann-Fulcher (VTF) equation predicts the changes in the timescales of molecular motion as ... 

In presence of molecular motion the NMR line shape will change. A particularly simple situation arises, if the motion is rapid on timescale defined by the inverse width of the spectrum in absence of motion 6 1. In this fast exchange limit, which in 2H NMR is reached for correlation times tc < 1CT7 s, the motion leads to a partially averaged quadrupole coupling and valuable information about the type of motion can directly be obtained from analysis of the resulting line shapes. The NMR frequency is then given by... 

These TR results demonstrate that the localized model of Ru(bpy) + is valid on the timescales of electronic motions and molecular vibrations. It is virtually certain that delocalization (via, for example, intramolecular electron transfer or dynamic Jahn-Teller effects) occurs on some longer timescale. 

Fig. 25. Schematic pulse sequence for the reduced four-dimensional experiment to probe the spatial heterogeneity of molecular motions.54" 5 As for the experiment in Fig. 24, part A of the sequence selects out only signal from any slow components in the system. This experiment differs from that in Fig. 24 only in that the central mixing time, rmb, provided to allow the motional timescale to change if it can, now allows H- H spin diffusion instead, so that the size of the region with slow molecular motions may be estimated. The two other mixing times rma and rmc are equal.

Although the timescale and the principle of mobility filters are readily outlined in this way, the validity of the representation is limited, because relaxation times depend on the spectral densities of molecular motion at more than one frequency, which is neglected in Fig. 7.1.3. In addition, the spectral densities relevant to NMR of condensed matter... 

Thus, (33) has a close resemblance to the conventional expression in (3). Equation (33) takes the distribution of atomic positions into account as well as the finite duration of the X-ray probe pulse. Clearly, if the temporal duration of the X-ray pulse is short compared to the molecular dynamics, the diffraction signal corresponds to diffraction from the instantaneous distribution of atomic positions, p(R, tp). at time tp. Structure determination of short-lived intermediates can be accomplished with long probe pulses, i.e., long on the timescale of atomic motion but short compared to the lifetime of the population. This limit corresponds to current experiments where fast kinetics is studied by X-ray pulses from synchrotrons. 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

The particular physical state that the polymer exhibits during a DMA test depends on the ratio of the timescale of the measurement (in this case the inverse of frequency) to the speed of molecular motion. In general, the modulus decreases either with a decreasing frequency or an increasing temperature. There is a strong relationship between time and temperature, as will be discussed later in this chapter. The modulus values cited above for each of the five regions are fully characteristic of each physical state (Tobolsky 1960 ... 

An ideal gas has by definition no intermolecular structure. Also, real gases at ordinary pressure conditions have little to do with intermolecular interactions. In the gaseous state, molecules are to a good approximation isolated entities traveling in space at high speed with sparse and near elastic collisions. At the other extreme, a perfect crystal has a periodic and symmetric intermolecular structure, as shown in Section 5.1. The structure is dictated by intermolecular forces, and molecules can only perform small oscillations around their equilibrium positions. As discussed in Chapter 13, in between these two extremes matter has many more ways of aggregation the present chapter deals with proper liquids, defined here as bodies whose molecules are in permanent but dynamic contact, with extensive freedom of conformational rearrangement and of rotational and translational diffusion. This relatively unrestricted molecular motion has a macroscopic counterpart in viscous flow, a typical property of liquids. Molecular diffusion in liquids occurs approximately on the timescale of nanoseconds (10 to 10 s), to be compared with the timescale of molecular or lattice vibrations, to 10 s. 

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